TSTP Solution File: SWW395+1 by CSE---1.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW395+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n023.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 18:09:16 EDT 2024
% Result : Theorem 188.07s 187.95s
% Output : CNFRefutation 188.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWW395+1 : TPTP v8.2.0. Released v5.2.0.
% 0.08/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Jun 19 05:58:24 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.52/0.60 start to proof:theBenchmark
% 187.59/187.78 %-------------------------------------------
% 187.59/187.78 % File :CSE---1.7
% 187.59/187.78 % Problem :theBenchmark
% 187.59/187.78 % Transform :cnf
% 187.59/187.78 % Format :tptp:raw
% 187.59/187.78 % Command :java -jar mcs_scs.jar %d %s
% 187.59/187.78
% 187.59/187.78 % Result :Theorem 168.870000s
% 187.59/187.78 % Output :CNFRefutation 168.870000s
% 187.59/187.78 %-------------------------------------------
% 187.59/187.79 %------------------------------------------------------------------------------
% 187.59/187.79 % File : SWW395+1 : TPTP v8.2.0. Released v5.2.0.
% 187.59/187.79 % Domain : Software Verification
% 187.59/187.79 % Problem : Hoare's Logic with Procedures 435820, 5000 axioms selected
% 187.59/187.79 % Version : Especial.
% 187.59/187.79 % English :
% 187.59/187.79
% 187.59/187.79 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 187.59/187.79 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 187.59/187.79 % Source : [Bla11]
% 187.59/187.79 % Names : hoare_435820.5000.p [Bla11]
% 187.59/187.79
% 187.59/187.79 % Status : ContradictoryAxioms
% 187.59/187.80 % Rating : 0.81 v8.2.0, 0.78 v7.4.0, 0.90 v7.3.0, 0.86 v7.1.0, 0.83 v6.4.0, 0.81 v6.3.0, 0.83 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.93 v5.4.0, 0.96 v5.3.0, 1.00 v5.2.0
% 187.59/187.80 % Syntax : Number of formulae : 5242 (1736 unt; 0 def)
% 187.59/187.80 % Number of atoms : 12580 (4573 equ)
% 187.59/187.80 % Maximal formula atoms : 13 ( 2 avg)
% 187.59/187.80 % Number of connectives : 8325 ( 987 ~; 149 |; 702 &)
% 187.59/187.80 % ( 887 <=>;5600 =>; 0 <=; 0 <~>)
% 187.59/187.80 % Maximal formula depth : 22 ( 6 avg)
% 187.59/187.80 % Maximal term depth : 19 ( 2 avg)
% 187.59/187.80 % Number of predicates : 143 ( 142 usr; 0 prp; 1-6 aty)
% 187.59/187.80 % Number of functors : 380 ( 380 usr; 53 con; 0-10 aty)
% 187.59/187.80 % Number of variables : 16800 (16656 !; 144 ?)
% 187.59/187.80 % SPC : FOF_CAX_RFO_SEQ
% 187.59/187.80
% 187.59/187.80 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 187.59/187.80 % 2011-03-01 13:11:03
% 187.59/187.80 %------------------------------------------------------------------------------
% 187.59/187.80 %----Relevant facts (4987)
% 187.59/187.80 fof(fact_ext,axiom,
% 187.59/187.80 ! [V_g_2,V_f_2] :
% 187.59/187.80 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 187.59/187.80 => V_f_2 = V_g_2 ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_empty,axiom,
% 187.59/187.80 ! [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))) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_trueI,axiom,
% 187.59/187.80 ! [V_ca_2,V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fTrue)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_falseE,axiom,
% 187.59/187.80 ! [V_Qa_2,V_ca_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(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 187.59/187.80 ! [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))) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_single__asm,axiom,
% 187.59/187.80 ! [V_t_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,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))),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)))) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_triple_Oinject,axiom,
% 187.59/187.80 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
% 187.59/187.80 ( 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)
% 187.59/187.80 <=> ( V_fun1_2 = V_fun1_H_2
% 187.59/187.80 & V_com_2 = V_com_H_2
% 187.59/187.80 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_cut,axiom,
% 187.59/187.80 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
% 187.59/187.80 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
% 187.59/187.80 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
% 187.59/187.80 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_hoare__derivs_Oinsert,axiom,
% 187.59/187.80 ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
% 187.59/187.80 ( 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))))
% 187.59/187.80 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
% 187.59/187.80 => 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)) ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_derivs__insertD,axiom,
% 187.59/187.80 ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
% 187.59/187.80 ( 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))
% 187.59/187.80 => ( 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))))
% 187.59/187.80 & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_disj,axiom,
% 187.59/187.80 ! [V_Q_H_2,V_P_H_2,V_Qa_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] :
% 187.59/187.80 ( 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_Pa_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 187.59/187.80 => ( 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))))
% 187.59/187.80 => 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_COMBS(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_fdisj)),V_Pa_2))),V_P_H_2)),V_ca_2),hAPP(hAPP(c_COMBS(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_fdisj)),V_Qa_2))),V_Q_H_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_bot__fun__def,axiom,
% 187.59/187.80 ! [V_x_2,T_c,T_b] :
% 187.59/187.80 ( class_Orderings_Obot(T_b)
% 187.59/187.80 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_triple_Orecs,axiom,
% 187.59/187.80 ! [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) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_triple_Osimps_I2_J,axiom,
% 187.59/187.80 ! [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) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_empty__not__insert,axiom,
% 187.59/187.80 ! [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) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_insert__not__empty,axiom,
% 187.59/187.80 ! [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)) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_doubleton__eq__iff,axiom,
% 187.59/187.80 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.59/187.80 ( 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))))
% 187.59/187.80 <=> ( ( V_a_2 = V_ca_2
% 187.59/187.80 & V_b_2 = V_d_2 )
% 187.59/187.80 | ( V_a_2 = V_d_2
% 187.59/187.80 & V_b_2 = V_ca_2 ) ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_singleton__inject,axiom,
% 187.59/187.80 ! [V_b_2,V_a_2,T_b] :
% 187.59/187.80 ( 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)))
% 187.59/187.80 => V_a_2 = V_b_2 ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_bot__apply,axiom,
% 187.59/187.80 ! [V_x_2,T_c,T_b] :
% 187.59/187.80 ( class_Orderings_Obot(T_b)
% 187.59/187.80 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_escape,axiom,
% 187.59/187.80 ! [V_Qa_2,V_ca_2,V_Ga_2,T_b,V_Pa_2] :
% 187.59/187.80 ( ! [B_Z,B_s] :
% 187.59/187.80 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 187.59/187.80 => 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)))) )
% 187.59/187.80 => 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_Pa_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_hoare__derivs_OSkip,axiom,
% 187.59/187.80 ! [V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSKIP),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 187.59/187.80 ! [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)))) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_conseq2,axiom,
% 187.59/187.80 ! [V_Qa_2,V_Q_H_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] :
% 187.59/187.80 ( 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_Pa_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 187.59/187.80 => ( ! [B_Z,B_s] :
% 187.59/187.80 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 187.59/187.80 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s)) )
% 187.59/187.80 => 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_Pa_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_insert__code,axiom,
% 187.59/187.80 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 187.59/187.80 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 187.59/187.80 <=> ( V_y_2 = V_x_2
% 187.59/187.80 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_insert__commute,axiom,
% 187.59/187.80 ! [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)) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_insert__absorb2,axiom,
% 187.59/187.80 ! [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) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_the__elem__eq,axiom,
% 187.59/187.80 ! [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 ).
% 187.59/187.80
% 187.59/187.80 fof(fact_hoare__SkipI,axiom,
% 187.59/187.80 ! [V_Ga_2,T_b,V_Qa_2,V_Pa_2] :
% 187.59/187.80 ( ! [B_Z,B_s] :
% 187.59/187.80 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 187.59/187.80 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s)) )
% 187.59/187.80 => 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_Pa_2),c_Com_Ocom_OSKIP),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_conseq1,axiom,
% 187.59/187.80 ! [V_Pa_2,V_Qa_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] :
% 187.59/187.80 ( 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))))
% 187.59/187.80 => ( ! [B_Z,B_s] :
% 187.59/187.80 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 187.59/187.80 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 187.59/187.80 => 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_Pa_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_Comp,axiom,
% 187.59/187.80 ! [V_R_2,V_d_2,V_Qa_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] :
% 187.59/187.80 ( 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_Pa_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 187.59/187.80 => ( 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))))
% 187.59/187.80 => 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_Pa_2),c_Com_Ocom_OSemi(V_ca_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_LoopF,axiom,
% 187.59/187.80 ! [V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),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_Pa_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_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_hoare__sound,axiom,
% 187.59/187.80 ! [V_ts_2,V_Ga_2,T_b] :
% 187.59/187.80 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
% 187.59/187.80 => c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_ts_2) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_conseq12,axiom,
% 187.59/187.80 ! [V_Qa_2,V_Pa_2,V_Q_H_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] :
% 187.59/187.80 ( 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))))
% 187.59/187.80 => ( ! [B_Z,B_s] :
% 187.59/187.80 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 187.59/187.80 => ! [B_s_H] :
% 187.59/187.80 ( ! [B_Z_H] :
% 187.59/187.80 ( hBOOL(hAPP(hAPP(V_P_H_2,B_Z_H),B_s))
% 187.59/187.80 => hBOOL(hAPP(hAPP(V_Q_H_2,B_Z_H),B_s_H)) )
% 187.59/187.80 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) )
% 187.59/187.80 => 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_Pa_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_hoare__derivs_Oequations_I8_J,axiom,
% 187.59/187.80 ! [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)))) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_Ass,axiom,
% 187.59/187.80 ! [V_a_2,V_X_2,V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),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_Pa_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_X_2)),V_a_2))),c_Com_Ocom_OAss(V_X_2,V_a_2)),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_the__elem__def,axiom,
% 187.59/187.80 ! [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))))) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_Collect__conv__if,axiom,
% 187.59/187.80 ! [T_b,V_a_2,V_Pa_2] :
% 187.59/187.80 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 187.59/187.80 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 187.59/187.80 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 187.59/187.80 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_Collect__conv__if2,axiom,
% 187.59/187.80 ! [T_b,V_a_2,V_Pa_2] :
% 187.59/187.80 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 187.59/187.80 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 187.59/187.80 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 187.59/187.80 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_Collect__def,axiom,
% 187.59/187.80 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ).
% 187.59/187.80
% 187.59/187.80 fof(fact_empty__Collect__eq,axiom,
% 187.59/187.80 ! [V_Pa_2,T_b] :
% 187.59/187.80 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
% 187.59/187.80 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_Collect__empty__eq,axiom,
% 187.59/187.80 ! [V_Pa_2,T_b] :
% 187.59/187.80 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.59/187.80 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_empty__def,axiom,
% 187.59/187.80 ! [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)) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_insert__Collect,axiom,
% 187.59/187.80 ! [V_Pa_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_Pa_2)) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_singleton__conv2,axiom,
% 187.59/187.80 ! [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))) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_singleton__conv,axiom,
% 187.59/187.80 ! [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))) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I13_J,axiom,
% 187.59/187.80 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I12_J,axiom,
% 187.59/187.80 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I25_J,axiom,
% 187.59/187.80 ! [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) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I24_J,axiom,
% 187.59/187.80 ! [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) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I9_J,axiom,
% 187.59/187.80 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I8_J,axiom,
% 187.59/187.80 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I47_J,axiom,
% 187.59/187.80 ! [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) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I46_J,axiom,
% 187.59/187.80 ! [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) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I17_J,axiom,
% 187.59/187.80 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I16_J,axiom,
% 187.59/187.80 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I29_J,axiom,
% 187.59/187.80 ! [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) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I28_J,axiom,
% 187.59/187.80 ! [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) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I5_J,axiom,
% 187.59/187.80 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 187.59/187.80 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 187.59/187.80 <=> ( V_fun_2 = V_fun_H_2
% 187.59/187.80 & V_com_2 = V_com_H_2 ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I1_J,axiom,
% 187.59/187.80 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] :
% 187.59/187.80 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2)
% 187.59/187.80 <=> ( V_vname_2 = V_vname_H_2
% 187.59/187.80 & V_fun_2 = V_fun_H_2 ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_com_Osimps_I3_J,axiom,
% 187.59/187.80 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 187.59/187.80 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 187.59/187.80 <=> ( V_com1_2 = V_com1_H_2
% 187.59/187.80 & V_com2_2 = V_com2_H_2 ) ) ).
% 187.59/187.80
% 187.59/187.80 fof(fact_the__sym__eq__trivial,axiom,
% 187.59/187.80 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 187.59/187.80
% 187.59/187.80 fof(fact_the__eq__trivial,axiom,
% 187.59/187.80 ! [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 ).
% 187.59/187.80
% 187.59/187.80 fof(fact_Loop__sound__lemma,axiom,
% 187.59/187.80 ! [V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
% 187.59/187.81 ( 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_Pa_2,V_b_2)),V_ca_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 187.59/187.81 => 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_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 187.59/187.81
% 187.59/187.81 fof(fact_Loop,axiom,
% 187.59/187.81 ! [V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
% 187.59/187.81 ( 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_Pa_2,V_b_2)),V_ca_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 187.59/187.81 => 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_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 187.59/187.81
% 187.59/187.81 fof(fact_insert__compr__raw,axiom,
% 187.59/187.81 ! [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))) ).
% 187.59/187.81
% 187.59/187.81 fof(fact_insert__compr,axiom,
% 187.59/187.81 ! [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))) ).
% 187.59/187.81
% 187.59/187.81 fof(fact_enum__the__def,axiom,
% 187.59/187.81 ! [V_Pa_2,T_b] : c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ).
% 187.59/187.81
% 187.59/187.81 fof(fact_com_Osimps_I64_J,axiom,
% 187.59/187.81 ! [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 ).
% 187.59/187.81
% 187.59/187.81 fof(fact_com_Osimps_I67_J,axiom,
% 187.59/187.81 ! [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) ).
% 187.59/187.81
% 187.59/187.81 fof(fact_com_Osimps_I65_J,axiom,
% 187.59/187.81 ! [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) ).
% 187.59/187.81
% 187.59/187.81 fof(fact_insert__def,axiom,
% 187.59/187.81 ! [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) ).
% 187.59/187.81
% 187.59/187.81 fof(fact_com_Osimps_I69_J,axiom,
% 187.59/187.81 ! [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) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_equalityCE,axiom,
% 187.63/187.81 ! [V_ca_2,T_b,V_B_2,V_A_2] :
% 187.63/187.81 ( V_A_2 = V_B_2
% 187.63/187.81 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.81 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) )
% 187.63/187.81 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.81 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_emptyE,axiom,
% 187.63/187.81 ! [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)))) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_insertE,axiom,
% 187.63/187.81 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 187.63/187.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 187.63/187.81 => ( V_a_2 != V_b_2
% 187.63/187.81 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_insertCI,axiom,
% 187.63/187.81 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 187.63/187.81 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 187.63/187.81 => V_a_2 = V_b_2 )
% 187.63/187.81 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_UnE,axiom,
% 187.63/187.81 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 187.63/187.81 ( 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)))
% 187.63/187.81 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.81 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_UnCI,axiom,
% 187.63/187.81 ! [V_A_2,V_B_2,V_ca_2,T_b] :
% 187.63/187.81 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 187.63/187.81 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
% 187.63/187.81 => 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))) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_CollectI,axiom,
% 187.63/187.81 ! [T_b,V_a_2,V_Pa_2] :
% 187.63/187.81 ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 187.63/187.81 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_Un__absorb,axiom,
% 187.63/187.81 ! [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 ).
% 187.63/187.81
% 187.63/187.81 fof(fact_mem__def,axiom,
% 187.63/187.81 ! [V_A_2,V_x_2,T_b] :
% 187.63/187.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.81 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_Un__commute,axiom,
% 187.63/187.81 ! [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) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_Un__left__absorb,axiom,
% 187.63/187.81 ! [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) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_Un__left__commute,axiom,
% 187.63/187.81 ! [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)) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_Un__iff,axiom,
% 187.63/187.81 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 187.63/187.81 ( 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)))
% 187.63/187.81 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.81 | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_Un__assoc,axiom,
% 187.63/187.81 ! [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)) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_bex__Un,axiom,
% 187.63/187.81 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 187.63/187.81 ( ? [B_x] :
% 187.63/187.81 ( 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)))
% 187.63/187.81 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.63/187.81 <=> ( ? [B_x] :
% 187.63/187.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.63/187.81 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.63/187.81 | ? [B_x] :
% 187.63/187.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 187.63/187.81 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_ball__Un,axiom,
% 187.63/187.81 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 187.63/187.81 ( ! [B_x] :
% 187.63/187.81 ( 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)))
% 187.63/187.81 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.63/187.81 <=> ( ! [B_x] :
% 187.63/187.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.63/187.81 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.63/187.81 & ! [B_x] :
% 187.63/187.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 187.63/187.81 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_UnI1,axiom,
% 187.63/187.81 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 187.63/187.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.81 => 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))) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_UnI2,axiom,
% 187.63/187.81 ! [V_A_2,V_B_2,V_ca_2,T_b] :
% 187.63/187.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 187.63/187.81 => 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))) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_eqset__imp__iff,axiom,
% 187.63/187.81 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 187.63/187.81 ( V_A_2 = V_B_2
% 187.63/187.81 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.81 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_eqelem__imp__iff,axiom,
% 187.63/187.81 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 187.63/187.81 ( V_x_2 = V_y_2
% 187.63/187.81 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.81 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_eq__mem__trans,axiom,
% 187.63/187.81 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 187.63/187.81 ( V_a_2 = V_b_2
% 187.63/187.81 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 187.63/187.81 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_Un__def,axiom,
% 187.63/187.81 ! [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))) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_Un__empty__left,axiom,
% 187.63/187.81 ! [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 ).
% 187.63/187.81
% 187.63/187.81 fof(fact_Un__empty__right,axiom,
% 187.63/187.81 ! [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 ).
% 187.63/187.81
% 187.63/187.81 fof(fact_Un__empty,axiom,
% 187.63/187.81 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.81 ( 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))
% 187.63/187.81 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.81 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_Un__insert__right,axiom,
% 187.63/187.81 ! [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)) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_Un__insert__left,axiom,
% 187.63/187.81 ! [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)) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_all__not__in__conv,axiom,
% 187.63/187.81 ! [V_A_2,T_b] :
% 187.63/187.81 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.63/187.81 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_ex__in__conv,axiom,
% 187.63/187.81 ! [V_A_2,T_b] :
% 187.63/187.81 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.63/187.81 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_empty__iff,axiom,
% 187.63/187.81 ! [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)))) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_equals0D,axiom,
% 187.63/187.81 ! [V_a_2,T_b,V_A_2] :
% 187.63/187.81 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.81 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_insertI1,axiom,
% 187.63/187.81 ! [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))) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_insert__iff,axiom,
% 187.63/187.81 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 187.63/187.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 187.63/187.81 <=> ( V_a_2 = V_b_2
% 187.63/187.81 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_insert__ident,axiom,
% 187.63/187.81 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 187.63/187.81 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.81 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 187.63/187.81 => ( 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)
% 187.63/187.81 <=> V_A_2 = V_B_2 ) ) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_insertI2,axiom,
% 187.63/187.81 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 187.63/187.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 187.63/187.81 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_insert__absorb,axiom,
% 187.63/187.81 ! [V_A_2,V_a_2,T_b] :
% 187.63/187.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.81 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_peek__and__def,axiom,
% 187.63/187.81 ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] :
% 187.63/187.81 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2))
% 187.63/187.81 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2))
% 187.63/187.81 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_Collect__disj__eq,axiom,
% 187.63/187.81 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 187.63/187.81
% 187.63/187.81 fof(fact_Collect__mem__eq,axiom,
% 187.63/187.81 ! [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 ).
% 187.63/187.81
% 187.63/187.81 fof(fact_mem__Collect__eq,axiom,
% 187.63/187.81 ! [V_Pa_2,V_a_2,T_b] :
% 187.63/187.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 187.63/187.82 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_CollectD,axiom,
% 187.63/187.82 ! [V_Pa_2,V_a_2,T_b] :
% 187.63/187.82 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 187.63/187.82 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_CollectE,axiom,
% 187.63/187.82 ! [V_Pa_2,V_a_2,T_b] :
% 187.63/187.82 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 187.63/187.82 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_insert__is__Un,axiom,
% 187.63/187.82 ! [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) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_singleton__iff,axiom,
% 187.63/187.82 ! [V_a_2,V_b_2,T_b] :
% 187.63/187.82 ( 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)))))
% 187.63/187.82 <=> V_b_2 = V_a_2 ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_singletonE,axiom,
% 187.63/187.82 ! [V_a_2,V_b_2,T_b] :
% 187.63/187.82 ( 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)))))
% 187.63/187.82 => V_b_2 = V_a_2 ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_hoare__derivs_OIf,axiom,
% 187.63/187.82 ! [V_d_2,V_Qa_2,V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
% 187.63/187.82 ( 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_Pa_2,V_b_2)),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 187.63/187.82 => ( 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_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 187.63/187.82 => 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_Pa_2),c_Com_Ocom_OCond(V_b_2,V_ca_2,V_d_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup1CI,axiom,
% 187.63/187.82 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 187.63/187.82 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 187.63/187.82 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 187.63/187.82 => 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)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup1E,axiom,
% 187.63/187.82 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 187.63/187.82 ( 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))
% 187.63/187.82 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 187.63/187.82 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup__fun__def,axiom,
% 187.63/187.82 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 187.63/187.82 ( class_Lattices_Olattice(T_b)
% 187.63/187.82 => 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)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup__Un__eq,axiom,
% 187.63/187.82 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 187.63/187.82 ( 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))
% 187.63/187.82 <=> 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))) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_bot__empty__eq,axiom,
% 187.63/187.82 ! [V_x_2,T_b] :
% 187.63/187.82 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 187.63/187.82 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup__apply,axiom,
% 187.63/187.82 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 187.63/187.82 ( class_Lattices_Olattice(T_b)
% 187.63/187.82 => 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)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup__bot__left,axiom,
% 187.63/187.82 ! [V_x,T_a] :
% 187.63/187.82 ( class_Lattices_Obounded__lattice__bot(T_a)
% 187.63/187.82 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup__bot__right,axiom,
% 187.63/187.82 ! [V_x,T_a] :
% 187.63/187.82 ( class_Lattices_Obounded__lattice__bot(T_a)
% 187.63/187.82 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup__eq__bot__iff,axiom,
% 187.63/187.82 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.82 ( class_Lattices_Obounded__lattice__bot(T_b)
% 187.63/187.82 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 187.63/187.82 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 187.63/187.82 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_K__record__comp,axiom,
% 187.63/187.82 ! [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 ).
% 187.63/187.82
% 187.63/187.82 fof(fact_o__def,axiom,
% 187.63/187.82 ! [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)) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_com_Osimps_I4_J,axiom,
% 187.63/187.82 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 187.63/187.82 ( 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)
% 187.63/187.82 <=> ( V_fun_2 = V_fun_H_2
% 187.63/187.82 & V_com1_2 = V_com1_H_2
% 187.63/187.82 & V_com2_2 = V_com2_H_2 ) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_com_Osimps_I53_J,axiom,
% 187.63/187.82 ! [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) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_com_Osimps_I52_J,axiom,
% 187.63/187.82 ! [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) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_com_Osimps_I26_J,axiom,
% 187.63/187.82 ! [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) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_com_Osimps_I27_J,axiom,
% 187.63/187.82 ! [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) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_com_Osimps_I14_J,axiom,
% 187.63/187.82 ! [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) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_com_Osimps_I15_J,axiom,
% 187.63/187.82 ! [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 ).
% 187.63/187.82
% 187.63/187.82 fof(fact_com_Osimps_I44_J,axiom,
% 187.63/187.82 ! [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) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_com_Osimps_I45_J,axiom,
% 187.63/187.82 ! [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) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_com_Osimps_I68_J,axiom,
% 187.63/187.82 ! [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) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_eq__mem,axiom,
% 187.63/187.82 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.82 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 187.63/187.82 <=> V_x_2 = V_y_2 ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup_Oidem,axiom,
% 187.63/187.82 ! [V_a,T_a] :
% 187.63/187.82 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.82 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup__idem,axiom,
% 187.63/187.82 ! [V_x,T_a] :
% 187.63/187.82 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.82 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup_Ocommute,axiom,
% 187.63/187.82 ! [V_b,V_a,T_a] :
% 187.63/187.82 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.82 => 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) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_inf__sup__aci_I5_J,axiom,
% 187.63/187.82 ! [V_y,V_x,T_a] :
% 187.63/187.82 ( class_Lattices_Olattice(T_a)
% 187.63/187.82 => 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) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup__commute,axiom,
% 187.63/187.82 ! [V_y,V_x,T_a] :
% 187.63/187.82 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.82 => 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) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup_Oleft__idem,axiom,
% 187.63/187.82 ! [V_b,V_a,T_a] :
% 187.63/187.82 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.82 => 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) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_inf__sup__aci_I8_J,axiom,
% 187.63/187.82 ! [V_y,V_x,T_a] :
% 187.63/187.82 ( class_Lattices_Olattice(T_a)
% 187.63/187.82 => 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) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup__left__idem,axiom,
% 187.63/187.82 ! [V_y,V_x,T_a] :
% 187.63/187.82 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.82 => 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) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup_Oleft__commute,axiom,
% 187.63/187.82 ! [V_c,V_a,V_b,T_a] :
% 187.63/187.82 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.82 => 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)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_inf__sup__aci_I7_J,axiom,
% 187.63/187.82 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.82 ( class_Lattices_Olattice(T_a)
% 187.63/187.82 => 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)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup__left__commute,axiom,
% 187.63/187.82 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.82 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.82 => 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)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup_Oassoc,axiom,
% 187.63/187.82 ! [V_c,V_b,V_a,T_a] :
% 187.63/187.82 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.82 => 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)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_inf__sup__aci_I6_J,axiom,
% 187.63/187.82 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.82 ( class_Lattices_Olattice(T_a)
% 187.63/187.82 => 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)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup__assoc,axiom,
% 187.63/187.82 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.82 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.82 => 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)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup1I1,axiom,
% 187.63/187.82 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 187.63/187.82 ( hBOOL(hAPP(V_A_2,V_x_2))
% 187.63/187.82 => 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)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_sup1I2,axiom,
% 187.63/187.82 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 187.63/187.82 ( hBOOL(hAPP(V_B_2,V_x_2))
% 187.63/187.82 => 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)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_o__assoc,axiom,
% 187.63/187.82 ! [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) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_o__apply,axiom,
% 187.63/187.82 ! [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)) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_o__eq__dest__lhs,axiom,
% 187.63/187.82 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 187.63/187.82 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_ca_2
% 187.63/187.82 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_o__eq__dest,axiom,
% 187.63/187.82 ! [V_v_2,V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 187.63/187.82 ( 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)
% 187.63/187.82 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_o__eq__elim,axiom,
% 187.63/187.82 ! [V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 187.63/187.82 ( 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)
% 187.63/187.82 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_pred__equals__eq,axiom,
% 187.63/187.82 ! [V_S_2,V_R_2,T_b] :
% 187.63/187.82 ( 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)
% 187.63/187.82 <=> V_R_2 = V_S_2 ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_the__inv__into__def,axiom,
% 187.63/187.82 ! [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))) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_override__on__def,axiom,
% 187.63/187.82 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 187.63/187.82 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.82 => 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) )
% 187.63/187.82 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.82 => 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) ) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_comp__cong,axiom,
% 187.63/187.82 ! [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] :
% 187.63/187.82 ( 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))
% 187.63/187.82 => 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) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_Sup__fin_Oidem,axiom,
% 187.63/187.82 ! [V_x,T_a] :
% 187.63/187.82 ( class_Lattices_Olattice(T_a)
% 187.63/187.82 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_override__on__emptyset,axiom,
% 187.63/187.82 ! [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 ).
% 187.63/187.82
% 187.63/187.82 fof(fact_image__constant,axiom,
% 187.63/187.82 ! [V_ca_2,T_c,V_A_2,V_x_2,T_b] :
% 187.63/187.82 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.82 => 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))) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_override__on__apply__notin,axiom,
% 187.63/187.82 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 187.63/187.82 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.82 => 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) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_override__on__apply__in,axiom,
% 187.63/187.82 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 187.63/187.82 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.82 => 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) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_vimage__insert,axiom,
% 187.63/187.82 ! [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)) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_vimage__singleton__eq,axiom,
% 187.63/187.82 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 187.63/187.82 ( 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))))))
% 187.63/187.82 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_insert__Diff,axiom,
% 187.63/187.82 ! [V_A_2,V_a_2,T_b] :
% 187.63/187.82 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.82 => 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 ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_image__eqI,axiom,
% 187.63/187.82 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 187.63/187.82 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 187.63/187.82 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 187.63/187.82 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_DiffI,axiom,
% 187.63/187.82 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 187.63/187.82 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.82 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 187.63/187.82 => 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))) ) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_DiffE,axiom,
% 187.63/187.82 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 187.63/187.82 ( 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)))
% 187.63/187.82 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.82 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_vimageI,axiom,
% 187.63/187.82 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 187.63/187.82 ( hAPP(V_f_2,V_a_2) = V_b_2
% 187.63/187.82 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 187.63/187.82 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_fun__diff__def,axiom,
% 187.63/187.82 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 187.63/187.82 ( class_Groups_Ominus(T_b)
% 187.63/187.82 => 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)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_minus__apply,axiom,
% 187.63/187.82 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 187.63/187.82 ( class_Groups_Ominus(T_b)
% 187.63/187.82 => 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)) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_vimage__Diff,axiom,
% 187.63/187.82 ! [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)) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_Diff__idemp,axiom,
% 187.63/187.82 ! [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) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_vimage__code,axiom,
% 187.63/187.82 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.82 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 187.63/187.82 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_image__image,axiom,
% 187.63/187.82 ! [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) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_image__ident,axiom,
% 187.63/187.82 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 187.63/187.82
% 187.63/187.82 fof(fact_vimage__ident,axiom,
% 187.63/187.82 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 187.63/187.82
% 187.63/187.82 fof(fact_image__iff,axiom,
% 187.63/187.82 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 187.63/187.82 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 187.63/187.82 <=> ? [B_x] :
% 187.63/187.82 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.63/187.82 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 187.63/187.82
% 187.63/187.82 fof(fact_imageI,axiom,
% 187.63/187.82 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 187.63/187.82 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => 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))) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_rev__image__eqI,axiom,
% 187.63/187.83 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_empty__is__image,axiom,
% 187.63/187.83 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( 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)
% 187.63/187.83 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_image__empty,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_image__is__empty,axiom,
% 187.63/187.83 ! [V_A_2,V_f_2,T_b,T_c] :
% 187.63/187.83 ( 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))
% 187.63/187.83 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_image__insert,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_image__Un,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_image__compose,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Diff__iff,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 187.63/187.83 ( 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)))
% 187.63/187.83 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.83 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_DiffD1,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 187.63/187.83 ( 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)))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_DiffD2,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 187.63/187.83 ( 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)))
% 187.63/187.83 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimage__eq,axiom,
% 187.63/187.83 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 187.63/187.83 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimageD,axiom,
% 187.63/187.83 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimageI2,axiom,
% 187.63/187.83 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_empty__Diff,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Diff__empty,axiom,
% 187.63/187.83 ! [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 ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Diff__cancel,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimage__empty,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__Diff__cancel,axiom,
% 187.63/187.83 ! [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) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__Diff__cancel2,axiom,
% 187.63/187.83 ! [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) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__Diff,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimage__Un,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimage__compose,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimage__Collect__eq,axiom,
% 187.63/187.83 ! [V_Pa_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_insert__image,axiom,
% 187.63/187.83 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => 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) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_insert__Diff1,axiom,
% 187.63/187.83 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 187.63/187.83 => 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) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_insert__Diff__if,axiom,
% 187.63/187.83 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 187.63/187.83 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 187.63/187.83 => 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) )
% 187.63/187.83 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 187.63/187.83 => 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)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Diff__insert,axiom,
% 187.63/187.83 ! [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)))) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Diff__insert2,axiom,
% 187.63/187.83 ! [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) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_insert__Diff__single,axiom,
% 187.63/187.83 ! [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) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_image__constant__conv,axiom,
% 187.63/187.83 ! [V_ca_2,T_c,T_b,V_A_2] :
% 187.63/187.83 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.83 => 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)) )
% 187.63/187.83 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.83 => 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))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_set__diff__eq,axiom,
% 187.63/187.83 ! [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)))) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimage__def,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Diff__insert__absorb,axiom,
% 187.63/187.83 ! [V_A_2,V_x_2,T_b] :
% 187.63/187.83 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => 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 ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__upd__image,axiom,
% 187.63/187.83 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 187.63/187.83 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => 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)))))) )
% 187.63/187.83 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => 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) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 187.63/187.83 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => ( 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)
% 187.63/187.83 => 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)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__on__insert,axiom,
% 187.63/187.83 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 187.63/187.83 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.83 & ~ 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))))))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_subset__insert__iff,axiom,
% 187.63/187.83 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 187.63/187.83 ( 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)))
% 187.63/187.83 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => 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)) )
% 187.63/187.83 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_diff__single__insert,axiom,
% 187.63/187.83 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 187.63/187.83 ( 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))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => 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))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_the__inv__into__comp,axiom,
% 187.63/187.83 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 187.63/187.83 ( 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))
% 187.63/187.83 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 187.63/187.83 => ( 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))))
% 187.63/187.83 => 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) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_imageE,axiom,
% 187.63/187.83 ! [V_A_2,V_f_2,T_c,V_b_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 187.63/187.83 => ~ ! [B_x] :
% 187.63/187.83 ( V_b_2 = hAPP(V_f_2,B_x)
% 187.63/187.83 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimage__const,axiom,
% 187.63/187.83 ! [T_c,V_A_2,V_ca_2,T_b] :
% 187.63/187.83 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.83 => 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)) )
% 187.63/187.83 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.83 => 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)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimageE,axiom,
% 187.63/187.83 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_if__image__distrib,axiom,
% 187.63/187.83 ! [V_S_2,V_g_2,V_f_2,V_Pa_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_Pa_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2))))) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__left__comm__idem__remove,axiom,
% 187.63/187.83 ! [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))))) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_order__refl,axiom,
% 187.63/187.83 ! [V_x,T_a] :
% 187.63/187.83 ( class_Orderings_Opreorder(T_a)
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_equalityI,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.63/187.83 => V_A_2 = V_B_2 ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_top1I,axiom,
% 187.63/187.83 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf1E,axiom,
% 187.63/187.83 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( 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))
% 187.63/187.83 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 187.63/187.83 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf1I,axiom,
% 187.63/187.83 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 187.63/187.83 ( hBOOL(hAPP(V_A_2,V_x_2))
% 187.63/187.83 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 187.63/187.83 => 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)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__upd__triv,axiom,
% 187.63/187.83 ! [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 ).
% 187.63/187.83
% 187.63/187.83 fof(fact_subsetD,axiom,
% 187.63/187.83 ! [V_ca_2,V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_UNIV__I,axiom,
% 187.63/187.83 ! [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)))) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_IntE,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 187.63/187.83 ( 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)))
% 187.63/187.83 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.83 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_IntI,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 187.63/187.83 => 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))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_empty__subsetI,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__on__empty,axiom,
% 187.63/187.83 ! [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))) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_image__Int,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__image__subset__iff,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.83 => ( 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)))
% 187.63/187.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__on__image__Int,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 187.63/187.83 => 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)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Inf__fin_Oidem,axiom,
% 187.63/187.83 ! [V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Olattice(T_a)
% 187.63/187.83 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__left__comm__idem__inf,axiom,
% 187.63/187.83 ! [T_b] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_b)
% 187.63/187.83 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 187.63/187.83 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 187.63/187.83 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 187.63/187.83 => 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) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_linorder__le__cases,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Orderings_Olinorder(T_a)
% 187.63/187.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__funE,axiom,
% 187.63/187.83 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 187.63/187.83 ( class_Orderings_Oord(T_c)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 187.63/187.83 => 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))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_equalityE,axiom,
% 187.63/187.83 ! [T_b,V_B_2,V_A_2] :
% 187.63/187.83 ( V_A_2 = V_B_2
% 187.63/187.83 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__mono,axiom,
% 187.63/187.83 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 187.63/187.83 => 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))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__greatest,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 187.63/187.83 => 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))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_xt1_I6_J,axiom,
% 187.63/187.83 ! [V_z,V_x,V_y,T_a] :
% 187.63/187.83 ( class_Orderings_Oorder(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_xt1_I5_J,axiom,
% 187.63/187.83 ! [V_x,V_y,T_a] :
% 187.63/187.83 ( class_Orderings_Oorder(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.63/187.83 => V_x = V_y ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_order__trans,axiom,
% 187.63/187.83 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.83 ( class_Orderings_Opreorder(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_order__antisym,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Orderings_Oorder(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.63/187.83 => V_x = V_y ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_xt1_I4_J,axiom,
% 187.63/187.83 ! [V_c,V_a,V_b,T_a] :
% 187.63/187.83 ( class_Orderings_Oorder(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 187.63/187.83 => ( V_b = V_c
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_ord__le__eq__trans,axiom,
% 187.63/187.83 ! [V_c,V_b,V_a,T_a] :
% 187.63/187.83 ( class_Orderings_Oord(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.63/187.83 => ( V_b = V_c
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_subset__trans,axiom,
% 187.63/187.83 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_xt1_I3_J,axiom,
% 187.63/187.83 ! [V_c,V_b,V_a,T_a] :
% 187.63/187.83 ( class_Orderings_Oorder(T_a)
% 187.63/187.83 => ( V_a = V_b
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_ord__eq__le__trans,axiom,
% 187.63/187.83 ! [V_c,V_b,V_a,T_a] :
% 187.63/187.83 ( class_Orderings_Oord(T_a)
% 187.63/187.83 => ( V_a = V_b
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_order__antisym__conv,axiom,
% 187.63/187.83 ! [V_x_2,V_y_2,T_b] :
% 187.63/187.83 ( class_Orderings_Oorder(T_b)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.63/187.83 <=> V_x_2 = V_y_2 ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__absorb1,axiom,
% 187.63/187.83 ! [V_A_2,V_B_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.63/187.83 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__absorb2,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__funD,axiom,
% 187.63/187.83 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 187.63/187.83 ( class_Orderings_Oord(T_c)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 187.63/187.83 => 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))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_order__eq__refl,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Orderings_Opreorder(T_a)
% 187.63/187.83 => ( V_x = V_y
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_equalityD2,axiom,
% 187.63/187.83 ! [T_b,V_B_2,V_A_2] :
% 187.63/187.83 ( V_A_2 = V_B_2
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_equalityD1,axiom,
% 187.63/187.83 ! [T_b,V_B_2,V_A_2] :
% 187.63/187.83 ( V_A_2 = V_B_2
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__assoc,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__left__commute,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__left__absorb,axiom,
% 187.63/187.83 ! [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) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_order__eq__iff,axiom,
% 187.63/187.83 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.83 ( class_Orderings_Oorder(T_b)
% 187.63/187.83 => ( V_x_2 = V_y_2
% 187.63/187.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.63/187.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_set__eq__subset,axiom,
% 187.63/187.83 ! [T_b,V_B_2,V_A_2] :
% 187.63/187.83 ( V_A_2 = V_B_2
% 187.63/187.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_linorder__linear,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Orderings_Olinorder(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.63/187.83 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__commute,axiom,
% 187.63/187.83 ! [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) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__fun__def,axiom,
% 187.63/187.83 ! [V_g_2,V_f_2,T_b,T_c] :
% 187.63/187.83 ( class_Orderings_Oord(T_c)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 187.63/187.83 <=> ! [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))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__lower2,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__lower1,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__absorb,axiom,
% 187.63/187.83 ! [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 ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__UNIV__right,axiom,
% 187.63/187.83 ! [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 ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__UNIV__left,axiom,
% 187.63/187.83 ! [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 ).
% 187.63/187.83
% 187.63/187.83 fof(fact_top__apply,axiom,
% 187.63/187.83 ! [V_x_2,T_c,T_b] :
% 187.63/187.83 ( class_Orderings_Otop(T_b)
% 187.63/187.83 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_subset__refl,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_top__greatest,axiom,
% 187.63/187.83 ! [V_x,T_a] :
% 187.63/187.83 ( class_Orderings_Otop(T_a)
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_subset__UNIV,axiom,
% 187.63/187.83 ! [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)))) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf1D2,axiom,
% 187.63/187.83 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( 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))
% 187.63/187.83 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf1D1,axiom,
% 187.63/187.83 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( 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))
% 187.63/187.83 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__upd__idem,axiom,
% 187.63/187.83 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 187.63/187.83 ( hAPP(V_f_2,V_x_2) = V_y_2
% 187.63/187.83 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__infE,axiom,
% 187.63/187.83 ! [V_b,V_a,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => ( 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)))
% 187.63/187.83 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 187.63/187.83 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__mono,axiom,
% 187.63/187.83 ! [V_d,V_b,V_c,V_a,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 187.63/187.83 => 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))) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__greatest,axiom,
% 187.63/187.83 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 187.63/187.83 => 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))) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__infI,axiom,
% 187.63/187.83 ! [V_b,V_a,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 187.63/187.83 => 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))) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__on__Int,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.83 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 187.63/187.83 => 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)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_subset__inj__on,axiom,
% 187.63/187.83 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_predicate1D,axiom,
% 187.63/187.83 ! [V_x_2,V_Qa_2,V_Pa_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
% 187.63/187.83 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.63/187.83 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__absorb2,axiom,
% 187.63/187.83 ! [V_x,V_y,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.63/187.83 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__absorb1,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.63/187.83 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__infI2,axiom,
% 187.63/187.83 ! [V_a,V_x,V_b,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 187.63/187.83 => 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)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__infI1,axiom,
% 187.63/187.83 ! [V_b,V_x,V_a,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 187.63/187.83 => 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)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_injD,axiom,
% 187.63/187.83 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.83 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 187.63/187.83 => V_x_2 = V_y_2 ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__eq,axiom,
% 187.63/187.83 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.83 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 187.63/187.83 <=> V_x_2 = V_y_2 ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__fun,axiom,
% 187.63/187.83 ! [T_d,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.83 => 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))) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_rev__predicate1D,axiom,
% 187.63/187.83 ! [V_Qa_2,T_b,V_x_2,V_Pa_2] :
% 187.63/187.83 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
% 187.63/187.83 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__upd__other,axiom,
% 187.63/187.83 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 187.63/187.83 ( V_z_2 != V_x_2
% 187.63/187.83 => 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) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__upd__twist,axiom,
% 187.63/187.83 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] :
% 187.63/187.83 ( V_a_2 != V_ca_2
% 187.63/187.83 => 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) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__upd__apply,axiom,
% 187.63/187.83 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 187.63/187.83 ( ( V_z_2 = V_x_2
% 187.63/187.83 => 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 )
% 187.63/187.83 & ( V_z_2 != V_x_2
% 187.63/187.83 => 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) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__upd__same,axiom,
% 187.63/187.83 ! [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 ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__upd__upd,axiom,
% 187.63/187.83 ! [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) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__apply,axiom,
% 187.63/187.83 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( class_Lattices_Olattice(T_b)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__upd__idem__iff,axiom,
% 187.63/187.83 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2
% 187.63/187.83 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__assoc,axiom,
% 187.63/187.83 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__sup__aci_I2_J,axiom,
% 187.63/187.83 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Olattice(T_a)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf_Oassoc,axiom,
% 187.63/187.83 ! [V_c,V_b,V_a,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__eq__top__iff,axiom,
% 187.63/187.83 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.83 ( class_Lattices_Obounded__lattice__top(T_b)
% 187.63/187.83 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 187.63/187.83 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 187.63/187.83 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__inf__iff,axiom,
% 187.63/187.83 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_b)
% 187.63/187.83 => ( 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)))
% 187.63/187.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.63/187.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__left__commute,axiom,
% 187.63/187.83 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__sup__aci_I3_J,axiom,
% 187.63/187.83 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Olattice(T_a)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf_Oleft__commute,axiom,
% 187.63/187.83 ! [V_c,V_a,V_b,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__left__idem,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => 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) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__sup__aci_I4_J,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Olattice(T_a)
% 187.63/187.83 => 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) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf_Oleft__idem,axiom,
% 187.63/187.83 ! [V_b,V_a,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => 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) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__iff__inf,axiom,
% 187.63/187.83 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_b)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.63/187.83 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__on__def,axiom,
% 187.63/187.83 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.83 <=> ! [B_x] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.63/187.83 => ! [B_xa] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 187.63/187.83 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 187.63/187.83 => B_x = B_xa ) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__commute,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => 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) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__sup__aci_I1_J,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Olattice(T_a)
% 187.63/187.83 => 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) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf_Ocommute,axiom,
% 187.63/187.83 ! [V_b,V_a,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => 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) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__fun__def,axiom,
% 187.63/187.83 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( class_Lattices_Olattice(T_b)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__le2,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__sup__ord_I2_J,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Olattice(T_a)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__le1,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__sup__ord_I1_J,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Olattice(T_a)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__idem,axiom,
% 187.63/187.83 ! [V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf_Oidem,axiom,
% 187.63/187.83 ! [V_a,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.83 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__top__right,axiom,
% 187.63/187.83 ! [V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Obounded__lattice__top(T_a)
% 187.63/187.83 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__top__left,axiom,
% 187.63/187.83 ! [V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Obounded__lattice__top(T_a)
% 187.63/187.83 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__image__eq__iff,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.83 => ( 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)
% 187.63/187.83 <=> V_A_2 = V_B_2 ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__comp,axiom,
% 187.63/187.83 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.83 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 187.63/187.83 => 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))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_distrib__inf__le,axiom,
% 187.63/187.83 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Olattice(T_a)
% 187.63/187.83 => 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)))) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_distrib__sup__le,axiom,
% 187.63/187.83 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Olattice(T_a)
% 187.63/187.83 => 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)))) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__on__id2,axiom,
% 187.63/187.83 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_image__Int__subset,axiom,
% 187.63/187.83 ! [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)))) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__Int__assoc__eq,axiom,
% 187.63/187.83 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( 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))
% 187.63/187.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimage__subsetI,axiom,
% 187.63/187.83 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.83 => ( 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)))
% 187.63/187.83 => 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)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_the__inv__f__f,axiom,
% 187.63/187.83 ! [V_x_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.83 => 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 ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__upd__def,axiom,
% 187.63/187.83 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 187.63/187.83 ( ( V_x_2 = V_a_2
% 187.63/187.83 => 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 )
% 187.63/187.83 & ( V_x_2 != V_a_2
% 187.63/187.83 => 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) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__left__comm__idem__insert,axiom,
% 187.63/187.83 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_range__ex1__eq,axiom,
% 187.63/187.83 ! [V_b_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.83 => ( 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)))))
% 187.63/187.83 <=> ? [B_x] :
% 187.63/187.83 ( V_b_2 = hAPP(V_f_2,B_x)
% 187.63/187.83 & ! [B_y] :
% 187.63/187.83 ( V_b_2 = hAPP(V_f_2,B_y)
% 187.63/187.83 => B_y = B_x ) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__image__mem__iff,axiom,
% 187.63/187.83 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.83 => ( 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)))
% 187.63/187.83 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__left__comm__idem__sup,axiom,
% 187.63/187.83 ! [T_b] :
% 187.63/187.83 ( class_Lattices_Osemilattice__sup(T_b)
% 187.63/187.83 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__on__image__set__diff,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 187.63/187.83 => 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)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_image__set__diff,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 187.63/187.83 ! [V_x_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 187.63/187.83 => 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) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__on__contraD,axiom,
% 187.63/187.83 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.83 => ( V_x_2 != V_y_2
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 187.63/187.83 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__on__iff,axiom,
% 187.63/187.83 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 187.63/187.83 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 187.63/187.83 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__onD,axiom,
% 187.63/187.83 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.83 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 187.63/187.83 => V_x_2 = V_y_2 ) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__vimage__image__eq,axiom,
% 187.63/187.83 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.83 => 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 ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__on__fun__updI,axiom,
% 187.63/187.83 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.83 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 187.63/187.83 => 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) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__on__imageI2,axiom,
% 187.63/187.83 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 187.63/187.83 ( 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)
% 187.63/187.83 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_image__vimage__eq,axiom,
% 187.63/187.83 ! [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)))) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__on__diff,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.83 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__bot__right,axiom,
% 187.63/187.83 ! [V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Obounded__lattice__bot(T_a)
% 187.63/187.83 => 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) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__bot__left,axiom,
% 187.63/187.83 ! [V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Obounded__lattice__bot(T_a)
% 187.63/187.83 => 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) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimage__subsetD,axiom,
% 187.63/187.83 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 187.63/187.83 ( 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))
% 187.63/187.83 => ( 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))
% 187.63/187.83 => 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))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__sup__absorb,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Olattice(T_a)
% 187.63/187.83 => 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 ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_sup__inf__absorb,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Olattice(T_a)
% 187.63/187.83 => 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 ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__sup__distrib1,axiom,
% 187.63/187.83 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Odistrib__lattice(T_a)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_sup__inf__distrib1,axiom,
% 187.63/187.83 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Odistrib__lattice(T_a)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__sup__distrib2,axiom,
% 187.63/187.83 ! [V_x,V_z,V_y,T_a] :
% 187.63/187.83 ( class_Lattices_Odistrib__lattice(T_a)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_sup__inf__distrib2,axiom,
% 187.63/187.83 ! [V_x,V_z,V_y,T_a] :
% 187.63/187.83 ( class_Lattices_Odistrib__lattice(T_a)
% 187.63/187.83 => 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)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 187.63/187.83 ! [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) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 187.63/187.83 ! [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) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inj__singleton,axiom,
% 187.63/187.83 ! [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))) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_IntD2,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 187.63/187.83 ( 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)))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_IntD1,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 187.63/187.83 ( 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)))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__iff,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 187.63/187.83 ( 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)))
% 187.63/187.83 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.83 & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_disjoint__iff__not__equal,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( 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))
% 187.63/187.83 <=> ! [B_x] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.63/187.83 => ! [B_xa] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 187.63/187.83 => B_x != B_xa ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__empty__right,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__empty__left,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_insert__inter__insert,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_set__mp,axiom,
% 187.63/187.83 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_set__rev__mp,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_in__mono,axiom,
% 187.63/187.83 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_iso__tuple__UNIV__I,axiom,
% 187.63/187.83 ! [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)))) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_bot__least,axiom,
% 187.63/187.83 ! [V_x,T_a] :
% 187.63/187.83 ( class_Orderings_Obot(T_a)
% 187.63/187.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__Int__crazy,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__Int__distrib2,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__Un__distrib2,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__Int__distrib,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__Un__distrib,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_subset__empty,axiom,
% 187.63/187.83 ! [V_A_2,T_b] :
% 187.63/187.83 ( 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))))
% 187.63/187.83 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__sup__ord_I3_J,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Olattice(T_a)
% 187.63/187.83 => 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))) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_sup__ge1,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.83 => 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))) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_inf__sup__ord_I4_J,axiom,
% 187.63/187.83 ! [V_x,V_y,T_a] :
% 187.63/187.83 ( class_Lattices_Olattice(T_a)
% 187.63/187.83 => 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))) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_sup__ge2,axiom,
% 187.63/187.83 ! [V_x,V_y,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.83 => 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))) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__iff__sup,axiom,
% 187.63/187.83 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.83 ( class_Lattices_Osemilattice__sup(T_b)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.63/187.83 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__sup__iff,axiom,
% 187.63/187.83 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 187.63/187.83 ( class_Lattices_Osemilattice__sup(T_b)
% 187.63/187.83 => ( 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))
% 187.63/187.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 187.63/187.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__supI1,axiom,
% 187.63/187.83 ! [V_b,V_a,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 187.63/187.83 => 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))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__supI2,axiom,
% 187.63/187.83 ! [V_a,V_b,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 187.63/187.83 => 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))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_sup__absorb2,axiom,
% 187.63/187.83 ! [V_y,V_x,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.63/187.83 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_sup__absorb1,axiom,
% 187.63/187.83 ! [V_x,V_y,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.63/187.83 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__supI,axiom,
% 187.63/187.83 ! [V_b,V_x,V_a,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 187.63/187.83 => 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)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_sup__least,axiom,
% 187.63/187.83 ! [V_z,V_x,V_y,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 187.63/187.83 => 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)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_sup__mono,axiom,
% 187.63/187.83 ! [V_d,V_b,V_c,V_a,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 187.63/187.83 => 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))) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_le__supE,axiom,
% 187.63/187.83 ! [V_x,V_b,V_a,T_a] :
% 187.63/187.83 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.83 => ( 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))
% 187.63/187.83 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 187.63/187.83 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_UNIV__not__empty,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Diff__Int2,axiom,
% 187.63/187.83 ! [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) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Diff__Int__distrib2,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Int__Diff,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Diff__Int__distrib,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_insert__mono,axiom,
% 187.63/187.83 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 187.63/187.83 => 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))) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_subset__insertI2,axiom,
% 187.63/187.83 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 => 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))) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_subset__insertI,axiom,
% 187.63/187.83 ! [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))) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_image__mono,axiom,
% 187.63/187.83 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 => 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))) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_subset__image__iff,axiom,
% 187.63/187.83 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 187.63/187.83 ( 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)))
% 187.63/187.83 <=> ? [B_AA] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 187.63/187.83 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__mono,axiom,
% 187.63/187.83 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 187.63/187.83 => 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))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__least,axiom,
% 187.63/187.83 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 187.63/187.83 => 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)) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__absorb2,axiom,
% 187.63/187.83 ! [V_A_2,V_B_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.63/187.83 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__absorb1,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_subset__Un__eq,axiom,
% 187.63/187.83 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__upper2,axiom,
% 187.63/187.83 ! [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))) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__upper1,axiom,
% 187.63/187.83 ! [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))) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__UNIV__right,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Un__UNIV__left,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_double__diff,axiom,
% 187.63/187.83 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 187.63/187.83 => 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 ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Diff__mono,axiom,
% 187.63/187.83 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 187.63/187.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 187.63/187.83 => 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))) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_Diff__subset,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimage__Int,axiom,
% 187.63/187.83 ! [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)) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_thin,axiom,
% 187.63/187.83 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
% 187.63/187.83 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
% 187.63/187.83 => ( 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))
% 187.63/187.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_weaken,axiom,
% 187.63/187.83 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] :
% 187.63/187.83 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2)
% 187.63/187.83 => ( 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))
% 187.63/187.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_asm,axiom,
% 187.63/187.83 ! [V_Ga_2,V_ts_2,T_b] :
% 187.63/187.83 ( 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))
% 187.63/187.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimage__mono,axiom,
% 187.63/187.83 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 187.63/187.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.83 => 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))) ) ).
% 187.63/187.83
% 187.63/187.83 fof(fact_vimage__UNIV,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inj__vimage__singleton,axiom,
% 187.63/187.84 ! [V_a_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.84 => 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))))) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inf__Int__eq,axiom,
% 187.63/187.84 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 <=> 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))) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Collect__conj__eq,axiom,
% 187.63/187.84 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_pred__subset__eq,axiom,
% 187.63/187.84 ! [V_S_2,V_R_2,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_the__inv__into__into,axiom,
% 187.63/187.84 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 => 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)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_UNIV__def,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_range__composition,axiom,
% 187.63/187.84 ! [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)))) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fun__upd__comp,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_sup__top__left,axiom,
% 187.63/187.84 ! [V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Obounded__lattice__top(T_a)
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_sup__top__right,axiom,
% 187.63/187.84 ! [V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Obounded__lattice__top(T_a)
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inj__on__Un,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.84 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 187.63/187.84 & 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)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 => ( 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)
% 187.63/187.84 <=> V_A_2 = V_B_2 ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inj__on__imageI,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 187.63/187.84 ( 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)
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_comp__inj__on,axiom,
% 187.63/187.84 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.84 => ( 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))
% 187.63/187.84 => 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) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_comp__inj__on__iff,axiom,
% 187.63/187.84 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.84 => ( 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))
% 187.63/187.84 <=> 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) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Int__insert__right,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 187.63/187.84 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.84 => 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)) )
% 187.63/187.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.84 => 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) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Int__insert__left,axiom,
% 187.63/187.84 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 187.63/187.84 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 187.63/187.84 => 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)) )
% 187.63/187.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 187.63/187.84 => 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) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Int__insert__right__if0,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 187.63/187.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Int__insert__left__if0,axiom,
% 187.63/187.84 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 187.63/187.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Int__insert__right__if1,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Int__insert__left__if1,axiom,
% 187.63/187.84 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Diff__disjoint,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Diff__triv,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_insert__subset,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 187.63/187.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_subset__insert,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 187.63/187.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.84 => ( 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)))
% 187.63/187.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_the__inv__into__f__eq,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.84 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.84 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_the__inv__into__f__f,axiom,
% 187.63/187.84 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.84 => 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 ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_range__eqI,axiom,
% 187.63/187.84 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 187.63/187.84 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 187.63/187.84 => 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))))) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_rangeI,axiom,
% 187.63/187.84 ! [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))))) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Un__Diff__Int,axiom,
% 187.63/187.84 ! [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 ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Diff__Un,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Diff__Int,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_subset__singletonD,axiom,
% 187.63/187.84 ! [V_x_2,V_A_2,T_b] :
% 187.63/187.84 ( 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)))))
% 187.63/187.84 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.84 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_the__inv__into__onto,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.84 => 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 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inj__on__the__inv__into,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Diff__UNIV,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_comp__surj,axiom,
% 187.63/187.84 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 187.63/187.84 ( 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))
% 187.63/187.84 => ( 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))
% 187.63/187.84 => 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)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_image__diff__subset,axiom,
% 187.63/187.84 ! [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)))) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Diff__partition,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 => 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 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Diff__subset__conv,axiom,
% 187.63/187.84 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 <=> 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))) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_image__vimage__subset,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_surj__image__vimage__eq,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_b,T_c] :
% 187.63/187.84 ( 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))
% 187.63/187.84 => 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 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Int__Collect,axiom,
% 187.63/187.84 ! [V_Pa_2,V_A_2,V_x_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))))
% 187.63/187.84 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.84 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Int__def,axiom,
% 187.63/187.84 ! [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))) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_f__the__inv__into__f,axiom,
% 187.63/187.84 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 187.63/187.84 => 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 ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inj__on__iff__surj,axiom,
% 187.63/187.84 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 187.63/187.84 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.84 => ( ? [B_f] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 187.63/187.84 & 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)) )
% 187.63/187.84 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_flat__lub__def,axiom,
% 187.63/187.84 ! [V_b_2,V_A_2,T_b] :
% 187.63/187.84 ( ( 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)))))
% 187.63/187.84 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 187.63/187.84 & ( ~ 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)))))
% 187.63/187.84 => 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)))))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 187.63/187.84 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.84 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 187.63/187.84 | ? [B_x,B_y] :
% 187.63/187.84 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 187.63/187.84 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 187.63/187.84 & 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) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_diff__eq__diff__less__eq,axiom,
% 187.63/187.84 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.63/187.84 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.63/187.84 => ( 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)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 187.63/187.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__fun_I1_J,axiom,
% 187.63/187.84 ! [V_g_2,V_f_2,T_b,T_c] :
% 187.63/187.84 ( ( class_Orderings_Oorder(T_c)
% 187.63/187.84 & class_Enum_Oenum(T_b) )
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 187.63/187.84 <=> 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))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_psubset__insert__iff,axiom,
% 187.63/187.84 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 187.63/187.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 187.63/187.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.84 => 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)) )
% 187.63/187.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Int__Collect__mono,axiom,
% 187.63/187.84 ! [V_Qa_2,V_Pa_2,V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 => ( ! [B_x] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.63/187.84 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 187.63/187.84 => hBOOL(hAPP(V_Qa_2,B_x)) ) )
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Qa_2)))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Diff1__fold__graph,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.84 => 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))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_vimage__if,axiom,
% 187.63/187.84 ! [V_B_2,T_c,V_d_2,V_A_2,V_ca_2,T_b] :
% 187.63/187.84 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 187.63/187.84 => 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)) )
% 187.63/187.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 187.63/187.84 => 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 ) ) )
% 187.63/187.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 187.63/187.84 => 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) )
% 187.63/187.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 187.63/187.84 => 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)) ) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_rangeE,axiom,
% 187.63/187.84 ! [V_f_2,T_c,V_b_2,T_b] :
% 187.63/187.84 ( 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)))))
% 187.63/187.84 => ~ ! [B_x] : V_b_2 != hAPP(V_f_2,B_x) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_dom__override__on,axiom,
% 187.63/187.84 ! [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))))) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inj__uminus,axiom,
% 187.63/187.84 ! [V_A_2,T_b] :
% 187.63/187.84 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.63/187.84 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_ComplI,axiom,
% 187.63/187.84 ! [V_A_2,V_ca_2,T_b] :
% 187.63/187.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.84 => 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))) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fun__Compl__def,axiom,
% 187.63/187.84 ! [V_x_2,V_A_2,T_c,T_b] :
% 187.63/187.84 ( class_Groups_Ouminus(T_b)
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_double__compl,axiom,
% 187.63/187.84 ! [V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Oboolean__algebra(T_a)
% 187.63/187.84 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_uminus__apply,axiom,
% 187.63/187.84 ! [V_x_2,V_A_2,T_c,T_b] :
% 187.63/187.84 ( class_Groups_Ouminus(T_b)
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_compl__eq__compl__iff,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.84 ( class_Lattices_Oboolean__algebra(T_b)
% 187.63/187.84 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 187.63/187.84 <=> V_x_2 = V_y_2 ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__less__irrefl,axiom,
% 187.63/187.84 ! [V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Opreorder(T_a)
% 187.63/187.84 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_double__complement,axiom,
% 187.63/187.84 ! [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 ).
% 187.63/187.84
% 187.63/187.84 fof(fact_linorder__neq__iff,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.84 ( class_Orderings_Olinorder(T_b)
% 187.63/187.84 => ( V_x_2 != V_y_2
% 187.63/187.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 187.63/187.84 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_not__less__iff__gr__or__eq,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.84 ( class_Orderings_Olinorder(T_b)
% 187.63/187.84 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 187.63/187.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 187.63/187.84 | V_x_2 = V_y_2 ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_linorder__less__linear,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Olinorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.84 | V_x = V_y
% 187.63/187.84 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__eq__Compl__iff,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( 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)
% 187.63/187.84 <=> V_A_2 = V_B_2 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_linorder__antisym__conv3,axiom,
% 187.63/187.84 ! [V_x_2,V_y_2,T_b] :
% 187.63/187.84 ( class_Orderings_Olinorder(T_b)
% 187.63/187.84 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 187.63/187.84 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 187.63/187.84 <=> V_x_2 = V_y_2 ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_linorder__neqE,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Olinorder(T_a)
% 187.63/187.84 => ( V_x != V_y
% 187.63/187.84 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_less__imp__neq,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Oorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.84 => V_x != V_y ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__less__not__sym,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Opreorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.84 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__less__imp__not__less,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Opreorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.84 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__less__imp__not__eq,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Oorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.84 => V_x != V_y ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__less__imp__not__eq2,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Oorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.84 => V_y != V_x ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__less__asym_H,axiom,
% 187.63/187.84 ! [V_b,V_a,T_a] :
% 187.63/187.84 ( class_Orderings_Opreorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.63/187.84 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_xt1_I9_J,axiom,
% 187.63/187.84 ! [V_a,V_b,T_a] :
% 187.63/187.84 ( class_Orderings_Oorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 187.63/187.84 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_ord__eq__less__trans,axiom,
% 187.63/187.84 ! [V_c,V_b,V_a,T_a] :
% 187.63/187.84 ( class_Orderings_Oord(T_a)
% 187.63/187.84 => ( V_a = V_b
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_xt1_I1_J,axiom,
% 187.63/187.84 ! [V_c,V_b,V_a,T_a] :
% 187.63/187.84 ( class_Orderings_Oorder(T_a)
% 187.63/187.84 => ( V_a = V_b
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_psubset__trans,axiom,
% 187.63/187.84 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_ord__less__eq__trans,axiom,
% 187.63/187.84 ! [V_c,V_b,V_a,T_a] :
% 187.63/187.84 ( class_Orderings_Oord(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.63/187.84 => ( V_b = V_c
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_xt1_I2_J,axiom,
% 187.63/187.84 ! [V_c,V_a,V_b,T_a] :
% 187.63/187.84 ( class_Orderings_Oorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 187.63/187.84 => ( V_b = V_c
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__less__trans,axiom,
% 187.63/187.84 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Opreorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_xt1_I10_J,axiom,
% 187.63/187.84 ! [V_z,V_x,V_y,T_a] :
% 187.63/187.84 ( class_Orderings_Oorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__less__asym,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Opreorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.84 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_linorder__cases,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Olinorder(T_a)
% 187.63/187.84 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.84 => ( V_x != V_y
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_neg__less__iff__less,axiom,
% 187.63/187.84 ! [V_a_2,V_b_2,T_b] :
% 187.63/187.84 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.63/187.84 => ( 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)))
% 187.63/187.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_neg__equal__iff__equal,axiom,
% 187.63/187.84 ! [V_b_2,V_a_2,T_b] :
% 187.63/187.84 ( class_Groups_Ogroup__add(T_b)
% 187.63/187.84 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 187.63/187.84 <=> V_a_2 = V_b_2 ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_minus__less__iff,axiom,
% 187.63/187.84 ! [V_b_2,V_a_2,T_b] :
% 187.63/187.84 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 187.63/187.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_minus__equation__iff,axiom,
% 187.63/187.84 ! [V_b_2,V_a_2,T_b] :
% 187.63/187.84 ( class_Groups_Ogroup__add(T_b)
% 187.63/187.84 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 187.63/187.84 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_less__minus__iff,axiom,
% 187.63/187.84 ! [V_b_2,V_a_2,T_b] :
% 187.63/187.84 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 187.63/187.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_equation__minus__iff,axiom,
% 187.63/187.84 ! [V_b_2,V_a_2,T_b] :
% 187.63/187.84 ( class_Groups_Ogroup__add(T_b)
% 187.63/187.84 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 187.63/187.84 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_minus__minus,axiom,
% 187.63/187.84 ! [V_a,T_a] :
% 187.63/187.84 ( class_Groups_Ogroup__add(T_a)
% 187.63/187.84 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_le__imp__neg__le,axiom,
% 187.63/187.84 ! [V_b,V_a,T_a] :
% 187.63/187.84 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.63/187.84 => 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))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_neg__le__iff__le,axiom,
% 187.63/187.84 ! [V_a_2,V_b_2,T_b] :
% 187.63/187.84 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.63/187.84 => ( 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)))
% 187.63/187.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_minus__le__iff,axiom,
% 187.63/187.84 ! [V_b_2,V_a_2,T_b] :
% 187.63/187.84 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.63/187.84 => ( 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))
% 187.63/187.84 <=> 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)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_le__minus__iff,axiom,
% 187.63/187.84 ! [V_b_2,V_a_2,T_b] :
% 187.63/187.84 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.63/187.84 => ( 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)))
% 187.63/187.84 <=> 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))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_minus__diff__eq,axiom,
% 187.63/187.84 ! [V_b,V_a,T_a] :
% 187.63/187.84 ( class_Groups_Oab__group__add(T_a)
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_all__code,axiom,
% 187.63/187.84 ! [V_Pa_2,T_b] :
% 187.63/187.84 ( class_Enum_Oenum(T_b)
% 187.63/187.84 => ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 187.63/187.84 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_enum__all,axiom,
% 187.63/187.84 ! [V_Pa_2,T_b] :
% 187.63/187.84 ( class_Enum_Oenum(T_b)
% 187.63/187.84 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2))
% 187.63/187.84 <=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_diff__eq__diff__less,axiom,
% 187.63/187.84 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.63/187.84 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.63/187.84 => ( 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)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 187.63/187.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_compl__le__compl__iff,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.84 ( class_Lattices_Oboolean__algebra(T_b)
% 187.63/187.84 => ( 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)))
% 187.63/187.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_compl__mono,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Oboolean__algebra(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.63/187.84 => 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))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__iff,axiom,
% 187.63/187.84 ! [V_A_2,V_ca_2,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_ComplD,axiom,
% 187.63/187.84 ! [V_A_2,V_ca_2,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_ComplE,axiom,
% 187.63/187.84 ! [V_A_2,V_ca_2,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_less__fun__def,axiom,
% 187.63/187.84 ! [V_g_2,V_f_2,T_b,T_c] :
% 187.63/187.84 ( class_Orderings_Oord(T_c)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 187.63/187.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 187.63/187.84 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__subset__Compl__iff,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__anti__mono,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 => 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))) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_linorder__not__less,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.84 ( class_Orderings_Olinorder(T_b)
% 187.63/187.84 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 187.63/187.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_linorder__not__le,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.84 ( class_Orderings_Olinorder(T_b)
% 187.63/187.84 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.63/187.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_linorder__le__less__linear,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Olinorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.63/187.84 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__less__le,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.84 ( class_Orderings_Oorder(T_b)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 187.63/187.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.63/187.84 & V_x_2 != V_y_2 ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_less__le__not__le,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.84 ( class_Orderings_Opreorder(T_b)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 187.63/187.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.63/187.84 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__le__less,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.84 ( class_Orderings_Oorder(T_b)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.63/187.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 187.63/187.84 | V_x_2 = V_y_2 ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_leI,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Olinorder(T_a)
% 187.63/187.84 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_not__leE,axiom,
% 187.63/187.84 ! [V_x,V_y,T_a] :
% 187.63/187.84 ( class_Orderings_Olinorder(T_a)
% 187.63/187.84 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_linorder__antisym__conv1,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.84 ( class_Orderings_Olinorder(T_b)
% 187.63/187.84 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.63/187.84 <=> V_x_2 = V_y_2 ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__neq__le__trans,axiom,
% 187.63/187.84 ! [V_b,V_a,T_a] :
% 187.63/187.84 ( class_Orderings_Oorder(T_a)
% 187.63/187.84 => ( V_a != V_b
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_xt1_I12_J,axiom,
% 187.63/187.84 ! [V_b,V_a,T_a] :
% 187.63/187.84 ( class_Orderings_Oorder(T_a)
% 187.63/187.84 => ( V_a != V_b
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_leD,axiom,
% 187.63/187.84 ! [V_x,V_y,T_a] :
% 187.63/187.84 ( class_Orderings_Olinorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.63/187.84 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__less__imp__le,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Opreorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_linorder__antisym__conv2,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,T_b] :
% 187.63/187.84 ( class_Orderings_Olinorder(T_b)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.63/187.84 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 187.63/187.84 <=> V_x_2 = V_y_2 ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__le__imp__less__or__eq,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Oorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.84 | V_x = V_y ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__le__neq__trans,axiom,
% 187.63/187.84 ! [V_b,V_a,T_a] :
% 187.63/187.84 ( class_Orderings_Oorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.63/187.84 => ( V_a != V_b
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_xt1_I11_J,axiom,
% 187.63/187.84 ! [V_a,V_b,T_a] :
% 187.63/187.84 ( class_Orderings_Oorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 187.63/187.84 => ( V_a != V_b
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__less__le__trans,axiom,
% 187.63/187.84 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Opreorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_xt1_I7_J,axiom,
% 187.63/187.84 ! [V_z,V_x,V_y,T_a] :
% 187.63/187.84 ( class_Orderings_Oorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__le__less__trans,axiom,
% 187.63/187.84 ! [V_z,V_y,V_x,T_a] :
% 187.63/187.84 ( class_Orderings_Opreorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_xt1_I8_J,axiom,
% 187.63/187.84 ! [V_z,V_x,V_y,T_a] :
% 187.63/187.84 ( class_Orderings_Oorder(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_psubsetD,axiom,
% 187.63/187.84 ! [V_ca_2,V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_not__psubset__empty,axiom,
% 187.63/187.84 ! [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)))) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_less__supI2,axiom,
% 187.63/187.84 ! [V_a,V_b,V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 187.63/187.84 => 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))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_less__supI1,axiom,
% 187.63/187.84 ! [V_b,V_a,V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Osemilattice__sup(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 187.63/187.84 => 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))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_less__infI1,axiom,
% 187.63/187.84 ! [V_b,V_x,V_a,T_a] :
% 187.63/187.84 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 187.63/187.84 => 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)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_less__infI2,axiom,
% 187.63/187.84 ! [V_a,V_x,V_b,T_a] :
% 187.63/187.84 ( class_Lattices_Osemilattice__inf(T_a)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 187.63/187.84 => 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)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_psubset__eq,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 & V_A_2 != V_B_2 ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_subset__iff__psubset__eq,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 | V_A_2 = V_B_2 ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_psubset__imp__subset,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_psubset__subset__trans,axiom,
% 187.63/187.84 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_subset__psubset__trans,axiom,
% 187.63/187.84 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_vimage__Compl,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fold__graph_OemptyI,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_empty__fold__graphE,axiom,
% 187.63/187.84 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 => V_x_2 = V_z_2 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Collect__neg__eq,axiom,
% 187.63/187.84 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inf__compl__bot,axiom,
% 187.63/187.84 ! [V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Oboolean__algebra(T_a)
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_compl__inf__bot,axiom,
% 187.63/187.84 ! [V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Oboolean__algebra(T_a)
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_compl__bot__eq,axiom,
% 187.63/187.84 ! [T_a] :
% 187.63/187.84 ( class_Lattices_Oboolean__algebra(T_a)
% 187.63/187.84 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_compl__top__eq,axiom,
% 187.63/187.84 ! [T_a] :
% 187.63/187.84 ( class_Lattices_Oboolean__algebra(T_a)
% 187.63/187.84 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_diff__eq,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Oboolean__algebra(T_a)
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_compl__inf,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Oboolean__algebra(T_a)
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_compl__sup,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Oboolean__algebra(T_a)
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_sup__compl__top,axiom,
% 187.63/187.84 ! [V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Oboolean__algebra(T_a)
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_compl__sup__top,axiom,
% 187.63/187.84 ! [V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Oboolean__algebra(T_a)
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_subset__Compl__self__eq,axiom,
% 187.63/187.84 ! [V_A_2,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__UNIV__eq,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__empty__eq,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__disjoint2,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__disjoint,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__partition,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__partition2,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__Int,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__Un,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 187.63/187.84 ! [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) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__Diff__eq,axiom,
% 187.63/187.84 ! [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) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Diff__eq,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Diff__Compl,axiom,
% 187.63/187.84 ! [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) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inj__on__strict__subset,axiom,
% 187.63/187.84 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 => 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))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Compl__eq,axiom,
% 187.63/187.84 ! [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))) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_Collect__imp__eq,axiom,
% 187.63/187.84 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fold__graph_OinsertI,axiom,
% 187.63/187.84 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 187.63/187.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.84 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 187.63/187.84 => 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))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_dom__if,axiom,
% 187.63/187.84 ! [V_g_2,V_f_2,V_Pa_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_Pa_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_Pa_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_Pa_2)))) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_disjoint__eq__subset__Compl,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 <=> 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))) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_surj__Compl__image__subset,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_b,T_c] :
% 187.63/187.84 ( 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))
% 187.63/187.84 => 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)))) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_diff__eq__diff__eq,axiom,
% 187.63/187.84 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.63/187.84 ( class_Groups_Oab__group__add(T_b)
% 187.63/187.84 => ( 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)
% 187.63/187.84 => ( V_a_2 = V_b_2
% 187.63/187.84 <=> V_ca_2 = V_d_2 ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_compl__unique,axiom,
% 187.63/187.84 ! [V_y,V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Oboolean__algebra(T_a)
% 187.63/187.84 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 187.63/187.84 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 187.63/187.84 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inj__image__Compl__subset,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.84 => 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)))) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fold1Set_Ointros,axiom,
% 187.63/187.84 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 187.63/187.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.84 => 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)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_order__fun_I2_J,axiom,
% 187.63/187.84 ! [V_g_2,V_f_2,T_b,T_c] :
% 187.63/187.84 ( ( class_Orderings_Oorder(T_c)
% 187.63/187.84 & class_Enum_Oenum(T_b) )
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 187.63/187.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 187.63/187.84 & 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)))) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fold__graph__permute__diff,axiom,
% 187.63/187.84 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 187.63/187.84 ( class_Groups_Oab__semigroup__mult(T_b)
% 187.63/187.84 => ( 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))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 187.63/187.84 => 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)) ) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_restrict__fun__upd,axiom,
% 187.63/187.84 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 187.63/187.84 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 187.63/187.84 => 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) )
% 187.63/187.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 187.63/187.84 => 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) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fun__upd__restrict__conv,axiom,
% 187.63/187.84 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inv__into__comp,axiom,
% 187.63/187.84 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 187.63/187.84 => ( 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))))
% 187.63/187.84 => 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) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_mk__less__def,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 187.63/187.84 ( c_Partial__Function_Omk__less(T_b,V_R_2,V_x_2,V_y_2)
% 187.63/187.84 <=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 187.63/187.84 & ~ hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_dom__fun__upd,axiom,
% 187.63/187.84 ! [V_x_2,V_f_2,T_c,T_b,V_y_2] :
% 187.63/187.84 ( ( V_y_2 = c_Option_Ooption_ONone(T_b)
% 187.63/187.84 => 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)))) )
% 187.63/187.84 & ( V_y_2 != c_Option_Ooption_ONone(T_b)
% 187.63/187.84 => 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)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_vimage__subset__eq,axiom,
% 187.63/187.84 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => ( 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))
% 187.63/187.84 <=> 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))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_psubset__imp__ex__mem,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.84 => ? [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))) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_empty__upd__none,axiom,
% 187.63/187.84 ! [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) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inv__inv__eq,axiom,
% 187.63/187.84 ! [V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => 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 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__imp__bij__inv,axiom,
% 187.63/187.84 ! [V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => 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))) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__betw__inv__into,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 187.63/187.84 ! [V_c,V_b,V_a,T_a] :
% 187.63/187.84 ( class_Groups_Oab__semigroup__mult(T_a)
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_restrict__map__empty,axiom,
% 187.63/187.84 ! [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) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_restrict__out,axiom,
% 187.63/187.84 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 187.63/187.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.84 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inv__into__inv__into__eq,axiom,
% 187.63/187.84 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.84 => 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) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_mult__left__idem,axiom,
% 187.63/187.84 ! [V_b,V_a,T_a] :
% 187.63/187.84 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_mult__idem,axiom,
% 187.63/187.84 ! [V_x,T_a] :
% 187.63/187.84 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 187.63/187.84 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_times_Oidem,axiom,
% 187.63/187.84 ! [V_a,T_a] :
% 187.63/187.84 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 187.63/187.84 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_enum__ex,axiom,
% 187.63/187.84 ! [V_Pa_2,T_b] :
% 187.63/187.84 ( class_Enum_Oenum(T_b)
% 187.63/187.84 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2))
% 187.63/187.84 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_exists__code,axiom,
% 187.63/187.84 ! [V_Pa_2,T_b] :
% 187.63/187.84 ( class_Enum_Oenum(T_b)
% 187.63/187.84 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 187.63/187.84 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_restrict__map__def,axiom,
% 187.63/187.84 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 187.63/187.84 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.84 => 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) )
% 187.63/187.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.84 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_restrict__map__to__empty,axiom,
% 187.63/187.84 ! [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) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_o__inv__distrib,axiom,
% 187.63/187.84 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => ( 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)))
% 187.63/187.84 => 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)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__betw__empty2,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__betw__empty1,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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)
% 187.63/187.84 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__betw__comp__iff,axiom,
% 187.63/187.84 ! [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] :
% 187.63/187.84 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 187.63/187.84 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 187.63/187.84 <=> 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) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__betw__trans,axiom,
% 187.63/187.84 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 187.63/187.84 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
% 187.63/187.84 => 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) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__betw__imp__inj__on,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 187.63/187.84 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_restrict__in,axiom,
% 187.63/187.84 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_restrict__map__insert,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__betw__the__inv__into,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_restrict__restrict,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fun__left__comm__idem,axiom,
% 187.63/187.84 ! [T_b] :
% 187.63/187.84 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 187.63/187.84 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__vimage__eq__inv__image,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_restrict__complement__singleton__eq,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__image__Collect__eq,axiom,
% 187.63/187.84 ! [V_Pa_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_Pa_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__betw__subset,axiom,
% 187.63/187.84 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.63/187.84 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2
% 187.63/187.84 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__betw__imp__surj,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__is__surj,axiom,
% 187.63/187.84 ! [V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__comp,axiom,
% 187.63/187.84 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => ( 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)))
% 187.63/187.84 => 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))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fun__upd__None__restrict,axiom,
% 187.63/187.84 ! [V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 187.63/187.84 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 187.63/187.84 => 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))))) )
% 187.63/187.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 187.63/187.84 => 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) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inj__on__imp__bij__betw,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__betw__def,axiom,
% 187.63/187.84 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 187.63/187.84 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.84 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__is__inj,axiom,
% 187.63/187.84 ! [V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fold1Set__nonempty,axiom,
% 187.63/187.84 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 187.63/187.84 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_empty__fold1SetE,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_domIff,axiom,
% 187.63/187.84 ! [V_m_2,T_c,V_a_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2)))
% 187.63/187.84 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inv__into__injective,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
% 187.63/187.84 ( 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)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 187.63/187.84 => V_x_2 = V_y_2 ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inv__into__into,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_f__inv__into__f,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
% 187.63/187.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 187.63/187.84 => 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 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inv__into__f__eq,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.84 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 187.63/187.84 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inv__into__f__f,axiom,
% 187.63/187.84 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.84 => 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 ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_image__inv__into__cancel,axiom,
% 187.63/187.84 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 187.63/187.84 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
% 187.63/187.84 => 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 ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_image__surj__f__inv__f,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_b,T_c] :
% 187.63/187.84 ( 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))
% 187.63/187.84 => 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 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_surj__f__inv__f,axiom,
% 187.63/187.84 ! [V_y_2,V_f_2,T_b,T_c] :
% 187.63/187.84 ( 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))
% 187.63/187.84 => 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 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_surj__iff__all,axiom,
% 187.63/187.84 ! [V_f_2,T_b,T_c] :
% 187.63/187.84 ( 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))
% 187.63/187.84 <=> ! [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 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inv__f__f,axiom,
% 187.63/187.84 ! [V_x_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.84 => 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 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inv__f__eq,axiom,
% 187.63/187.84 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.84 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 187.63/187.84 => 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 ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_dom__empty,axiom,
% 187.63/187.84 ! [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)) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_dom__eq__empty__conv,axiom,
% 187.63/187.84 ! [V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.84 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_dom__def,axiom,
% 187.63/187.84 ! [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)))) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_dom__restrict,axiom,
% 187.63/187.84 ! [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) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__betw__combine,axiom,
% 187.63/187.84 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 187.63/187.84 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
% 187.63/187.84 => ( 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))
% 187.63/187.84 => 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)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__betw__Disj__Un,axiom,
% 187.63/187.84 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 => ( 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))
% 187.63/187.84 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 187.63/187.84 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
% 187.63/187.84 => 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)) ) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__betw__comp__iff2,axiom,
% 187.63/187.84 ! [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] :
% 187.63/187.84 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 187.63/187.84 => ( 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))
% 187.63/187.84 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
% 187.63/187.84 <=> 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) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__def,axiom,
% 187.63/187.84 ! [V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.84 & 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)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bijI,axiom,
% 187.63/187.84 ! [V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.84 => ( 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))
% 187.63/187.84 => 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))) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_bij__image__Compl__eq,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_dom__minus,axiom,
% 187.63/187.84 ! [V_A_2,T_c,T_b,V_x_2,V_f_2] :
% 187.63/187.84 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_b)
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fold__graph__insert__swap,axiom,
% 187.63/187.84 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 187.63/187.84 ( class_Groups_Oab__semigroup__mult(T_b)
% 187.63/187.84 => ( 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))
% 187.63/187.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 187.63/187.84 => 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))) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inj__on__inv__into,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 187.63/187.84 ( 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)))
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inv__into__image__cancel,axiom,
% 187.63/187.84 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
% 187.63/187.84 => 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 ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_surj__imp__inj__inv,axiom,
% 187.63/187.84 ! [V_f_2,T_b,T_c] :
% 187.63/187.84 ( 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))
% 187.63/187.84 => 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))) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inv__image__comp,axiom,
% 187.63/187.84 ! [V_X_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.84 => 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 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_image__inv__f__f,axiom,
% 187.63/187.84 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.84 => 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 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inj__imp__surj__inv,axiom,
% 187.63/187.84 ! [V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_o__inv__o__cancel,axiom,
% 187.63/187.84 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.84 => 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 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fun__upd__restrict,axiom,
% 187.63/187.84 ! [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) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fold1Set__sing,axiom,
% 187.63/187.84 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 <=> V_a_2 = V_b_2 ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_minus__mult__right,axiom,
% 187.63/187.84 ! [V_b,V_a,T_a] :
% 187.63/187.84 ( class_Rings_Oring(T_a)
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_minus__mult__left,axiom,
% 187.63/187.84 ! [V_b,V_a,T_a] :
% 187.63/187.84 ( class_Rings_Oring(T_a)
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_minus__mult__commute,axiom,
% 187.63/187.84 ! [V_b,V_a,T_a] :
% 187.63/187.84 ( class_Rings_Oring(T_a)
% 187.63/187.84 => 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)) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_minus__mult__minus,axiom,
% 187.63/187.84 ! [V_b,V_a,T_a] :
% 187.63/187.84 ( class_Rings_Oring(T_a)
% 187.63/187.84 => 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) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_square__eq__iff,axiom,
% 187.63/187.84 ! [V_b_2,V_a_2,T_b] :
% 187.63/187.84 ( class_Rings_Oidom(T_b)
% 187.63/187.84 => ( 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)
% 187.63/187.84 <=> ( V_a_2 = V_b_2
% 187.63/187.84 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_inj__transfer,axiom,
% 187.63/187.84 ! [V_x_2,V_Pa_2,V_f_2,T_c,T_b] :
% 187.63/187.84 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.84 => ( ! [B_y] :
% 187.63/187.84 ( 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)))))
% 187.63/187.84 => hBOOL(hAPP(V_Pa_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_y))) )
% 187.63/187.84 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_insert__fold1SetE,axiom,
% 187.63/187.84 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 => ~ ! [B_a,B_A] :
% 187.63/187.84 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 187.63/187.84 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 187.63/187.84 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 187.63/187.84
% 187.63/187.84 fof(fact_fold1Set_Oequations,axiom,
% 187.63/187.84 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 187.63/187.84 ( 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))
% 187.63/187.84 <=> ? [B_a,B_A] :
% 187.63/187.84 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 187.63/187.85 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 187.63/187.85 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_dom__eq__singleton__conv,axiom,
% 187.63/187.85 ! [V_x_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( 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)))
% 187.63/187.85 <=> ? [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)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__upd__eqD1,axiom,
% 187.63/187.85 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] :
% 187.63/187.85 ( 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))
% 187.63/187.85 => V_x_2 = V_y_2 ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__upd__triv,axiom,
% 187.63/187.85 ! [T_c,V_x_2,T_b,V_k_2,V_t_2] :
% 187.63/187.85 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 187.63/187.85 => 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 ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__upd__Some__unfold,axiom,
% 187.63/187.85 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_b,T_c] :
% 187.63/187.85 ( 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)
% 187.63/187.85 <=> ( ( V_x_2 = V_a_2
% 187.63/187.85 & V_b_2 = V_y_2 )
% 187.63/187.85 | ( V_x_2 != V_a_2
% 187.63/187.85 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_domI,axiom,
% 187.63/187.85 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 187.63/187.85 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_image__map__upd,axiom,
% 187.63/187.85 ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 187.63/187.85 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.85 => 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) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_insert__dom,axiom,
% 187.63/187.85 ! [T_c,V_y_2,T_b,V_x_2,V_f_2] :
% 187.63/187.85 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 187.63/187.85 => 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) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_dom__const,axiom,
% 187.63/187.85 ! [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)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__upd__nonempty,axiom,
% 187.63/187.85 ! [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)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_enum__all__option__def,axiom,
% 187.63/187.85 ! [V_Pa_2,T_b] :
% 187.63/187.85 ( class_Enum_Oenum(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_b)),V_Pa_2))
% 187.63/187.85 <=> ( hBOOL(hAPP(V_Pa_2,c_Option_Ooption_ONone(T_b)))
% 187.63/187.85 & 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_Pa_2),c_Option_Ooption_OSome(T_b)))) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_enum__ex__option__def,axiom,
% 187.63/187.85 ! [V_Pa_2,T_b] :
% 187.63/187.85 ( class_Enum_Oenum(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_b)),V_Pa_2))
% 187.63/187.85 <=> ( hBOOL(hAPP(V_Pa_2,c_Option_Ooption_ONone(T_b)))
% 187.63/187.85 | 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_Pa_2),c_Option_Ooption_OSome(T_b)))) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_linorder__neqE__linordered__idom,axiom,
% 187.63/187.85 ! [V_y,V_x,T_a] :
% 187.63/187.85 ( class_Rings_Olinordered__idom(T_a)
% 187.63/187.85 => ( V_x != V_y
% 187.63/187.85 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_restrict__upd__same,axiom,
% 187.63/187.85 ! [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))))) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_UNIV__option__conv,axiom,
% 187.63/187.85 ! [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)))) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_ran__map__upd,axiom,
% 187.63/187.85 ! [V_b_2,T_c,T_b,V_a_2,V_m_2] :
% 187.63/187.85 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b)
% 187.63/187.85 => 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)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_option_Osimps_I2_J,axiom,
% 187.63/187.85 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_option_Osimps_I3_J,axiom,
% 187.63/187.85 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_not__Some__eq,axiom,
% 187.63/187.85 ! [T_b,V_x_2] :
% 187.63/187.85 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y)
% 187.63/187.85 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_not__None__eq,axiom,
% 187.63/187.85 ! [T_b,V_x_2] :
% 187.63/187.85 ( V_x_2 != c_Option_Ooption_ONone(T_b)
% 187.63/187.85 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Cantor__Bernstein,axiom,
% 187.63/187.85 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.63/187.85 => ( 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))
% 187.63/187.85 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 187.63/187.85 => ( 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))
% 187.63/187.85 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_ran__empty,axiom,
% 187.63/187.85 ! [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)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__add__upd__left,axiom,
% 187.63/187.85 ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] :
% 187.63/187.85 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2)))
% 187.63/187.85 => 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)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__add__assoc,axiom,
% 187.63/187.85 ! [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) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__add__None,axiom,
% 187.63/187.85 ! [V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 187.63/187.85 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b)
% 187.63/187.85 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 187.63/187.85 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__add__find__right,axiom,
% 187.63/187.85 ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] :
% 187.63/187.85 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2)
% 187.63/187.85 => 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) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_inj__on__map__add__dom,axiom,
% 187.63/187.85 ! [V_m_H_2,V_m_2,T_c,T_b] :
% 187.63/187.85 ( 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))
% 187.63/187.85 <=> 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)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_empty__map__add,axiom,
% 187.63/187.85 ! [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 ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__add__empty,axiom,
% 187.63/187.85 ! [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 ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 187.63/187.85 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 187.63/187.85 => 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) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 187.63/187.85 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 187.63/187.85 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 187.63/187.85 => 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) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 187.63/187.85 ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] :
% 187.63/187.85 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2)))
% 187.63/187.85 => 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) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__add__Some__iff,axiom,
% 187.63/187.85 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 187.63/187.85 ( 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)
% 187.63/187.85 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 187.63/187.85 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 187.63/187.85 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__add__SomeD,axiom,
% 187.63/187.85 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 187.63/187.85 ( 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)
% 187.63/187.85 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 187.63/187.85 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 187.63/187.85 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_dom__map__add,axiom,
% 187.63/187.85 ! [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)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__add__upd,axiom,
% 187.63/187.85 ! [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)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__add__comm,axiom,
% 187.63/187.85 ! [V_m2_2,V_m1_2,T_c,T_b] :
% 187.63/187.85 ( 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))
% 187.63/187.85 => 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) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_inj__Some,axiom,
% 187.63/187.85 ! [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) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_option_Oinject,axiom,
% 187.63/187.85 ! [V_a_H_2,V_a_2,T_b] :
% 187.63/187.85 ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2)
% 187.63/187.85 <=> V_a_2 = V_a_H_2 ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_ranI,axiom,
% 187.63/187.85 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 187.63/187.85 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 187.63/187.85 ! [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))) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_ran__restrictD,axiom,
% 187.63/187.85 ! [V_A_2,V_m_2,T_c,V_y_2,T_b] :
% 187.63/187.85 ( 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))))
% 187.63/187.85 => ? [B_x] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.63/187.85 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__add__def,axiom,
% 187.63/187.85 ! [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)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 187.63/187.85 ! [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)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_set__empty__eq,axiom,
% 187.63/187.85 ! [V_xo_2,T_b] :
% 187.63/187.85 ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 <=> V_xo_2 = c_Option_Ooption_ONone(T_b) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_elem__set,axiom,
% 187.63/187.85 ! [V_xo_2,V_x_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2)))
% 187.63/187.85 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__range__updI,axiom,
% 187.63/187.85 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( 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)))))
% 187.63/187.85 => 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))))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_option_Orecs_I2_J,axiom,
% 187.63/187.85 ! [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) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_option_Osimps_I5_J,axiom,
% 187.63/187.85 ! [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) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite_OemptyI,axiom,
% 187.63/187.85 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite_OinsertI,axiom,
% 187.63/187.85 ! [V_a_2,V_A_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__imageI,axiom,
% 187.63/187.85 ! [V_h_2,T_c,V_F_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__Int,axiom,
% 187.63/187.85 ! [V_Ga_2,V_F_2,T_b] :
% 187.63/187.85 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 187.63/187.85 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) )
% 187.63/187.85 => 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))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__Diff,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => 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))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__Collect__conjI,axiom,
% 187.63/187.85 ! [V_Qa_2,V_Pa_2,T_b] :
% 187.63/187.85 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 187.63/187.85 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) )
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Qa_2)))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__Collect__subsets,axiom,
% 187.63/187.85 ! [V_A_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => 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)))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_nat__seg__image__imp__finite,axiom,
% 187.63/187.85 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 187.63/187.85 ( 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)))
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__fun__UNIVD2,axiom,
% 187.63/187.85 ! [T_c,T_b] :
% 187.63/187.85 ( 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))))
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__Plus__UNIV__iff,axiom,
% 187.63/187.85 ! [T_c,T_b] :
% 187.63/187.85 ( 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))))
% 187.63/187.85 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 187.63/187.85 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__Prod__UNIV,axiom,
% 187.63/187.85 ! [T_c,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 187.63/187.85 => 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)))) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite,axiom,
% 187.63/187.85 ! [V_A_2,T_b] :
% 187.63/187.85 ( class_Finite__Set_Ofinite(T_b)
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__code,axiom,
% 187.63/187.85 ! [V_A_2,T_b] :
% 187.63/187.85 ( class_Finite__Set_Ofinite(T_b)
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite_Oequations_I1_J,axiom,
% 187.63/187.85 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__insert,axiom,
% 187.63/187.85 ! [V_A_2,V_a_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 187.63/187.85 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__subset,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_rev__finite__subset,axiom,
% 187.63/187.85 ! [V_A_2,V_B_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__UNIV,axiom,
% 187.63/187.85 ! [T_b] :
% 187.63/187.85 ( class_Finite__Set_Ofinite(T_b)
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__UnI,axiom,
% 187.63/187.85 ! [V_Ga_2,V_F_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
% 187.63/187.85 => 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))) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__Un,axiom,
% 187.63/187.85 ! [V_Ga_2,V_F_2,T_b] :
% 187.63/187.85 ( 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)))
% 187.63/187.85 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 187.63/187.85 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__Diff2,axiom,
% 187.63/187.85 ! [V_A_2,V_B_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => ( 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)))
% 187.63/187.85 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_bij__betw__finite,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_fold__graph__imp__finite,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__option__UNIV,axiom,
% 187.63/187.85 ! [T_b] :
% 187.63/187.85 ( 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))))
% 187.63/187.85 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__Collect__disjI,axiom,
% 187.63/187.85 ! [V_Qa_2,V_Pa_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Qa_2))))
% 187.63/187.85 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 187.63/187.85 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__surj,axiom,
% 187.63/187.85 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( 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)))
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__Diff__insert,axiom,
% 187.63/187.85 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 187.63/187.85 ( 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))))
% 187.63/187.85 <=> 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))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__imageD,axiom,
% 187.63/187.85 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 187.63/187.85 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__compl,axiom,
% 187.63/187.85 ! [V_A_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 187.63/187.85 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__Collect__not,axiom,
% 187.63/187.85 ! [V_Pa_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))))
% 187.63/187.85 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__range__imageI,axiom,
% 187.63/187.85 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 187.63/187.85 ( 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)))))
% 187.63/187.85 => 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))))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__surj__inj,axiom,
% 187.63/187.85 ! [V_f_2,V_A_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( 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)))
% 187.63/187.85 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_endo__inj__surj,axiom,
% 187.63/187.85 ! [V_f_2,V_A_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( 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))
% 187.63/187.85 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 187.63/187.85 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__UNIV__inj__surj,axiom,
% 187.63/187.85 ! [V_f_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 187.63/187.85 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.63/187.85 => 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)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__UNIV__surj__inj,axiom,
% 187.63/187.85 ! [V_f_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 187.63/187.85 => ( 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))
% 187.63/187.85 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__vimageD,axiom,
% 187.63/187.85 ! [V_F_2,V_h_2,T_c,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 187.63/187.85 => ( 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))
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__vimageI,axiom,
% 187.63/187.85 ! [V_h_2,T_c,V_F_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 187.63/187.85 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__vimage__iff,axiom,
% 187.63/187.85 ! [V_F_2,V_h_2,T_c,T_b] :
% 187.63/187.85 ( 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)))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 187.63/187.85 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_option_Osimps_I4_J,axiom,
% 187.63/187.85 ! [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 ).
% 187.63/187.85
% 187.63/187.85 fof(fact_option_Orecs_I1_J,axiom,
% 187.63/187.85 ! [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 ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding_Oremove,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.85 => 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)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__one_Oremove,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.85 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.63/187.85 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 187.63/187.85 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.63/187.85 => 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)))))) ) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__image__simple_Oremove,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 187.63/187.85 => 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)))))) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__image_Oreindex,axiom,
% 187.63/187.85 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 187.63/187.85 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 187.63/187.85 => 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) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding_Ounion,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => ( 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))
% 187.63/187.85 => 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)) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding_Oinsert__remove,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => 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)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__one_Ounion__inter,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => ( 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))
% 187.63/187.85 => 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)) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__one_Ounion__disjoint,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( 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))
% 187.63/187.85 => 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)) ) ) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__Collect__le__nat,axiom,
% 187.63/187.85 ! [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)))) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__Collect__less__nat,axiom,
% 187.63/187.85 ! [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)))) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_termination__basic__simps_I5_J,axiom,
% 187.63/187.85 ! [V_y,V_x] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 187.63/187.85 ! [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] :
% 187.63/187.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 187.63/187.85 => 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) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding_Ocommute__comp,axiom,
% 187.63/187.85 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => 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)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding_Ocommute__left__comp,axiom,
% 187.63/187.85 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => 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)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__image__simple_Oempty,axiom,
% 187.63/187.85 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 187.63/187.85 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__image_Odistrib,axiom,
% 187.63/187.85 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 187.63/187.85 => 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)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding_Ocommute__comp_H,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => 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)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 187.63/187.85 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => 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)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => 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)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 187.63/187.85 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => 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)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__one_Osingleton,axiom,
% 187.63/187.85 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 187.63/187.85 => 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 ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__image__simple_Oinsert,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 187.63/187.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 187.63/187.85 => 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)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 187.63/187.85 => 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)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding_Oinsert,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.85 => 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)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding_Ounion__inter,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => 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)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__one_Oinsert,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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)) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 187.63/187.85 => 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)))))) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__one_Oinsert__remove,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.63/187.85 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 187.63/187.85 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.63/187.85 => 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)))))) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 187.63/187.85 => ( 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))
% 187.63/187.85 => 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)) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__M__bounded__by__nat,axiom,
% 187.63/187.85 ! [V_i_2,V_Pa_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_Pa_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__pointwise,axiom,
% 187.63/187.85 ! [V_Qa_2,V_Pa_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_c,V_U_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_U_2))
% 187.63/187.85 => ( ! [B_p] :
% 187.63/187.85 ( 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))))
% 187.63/187.85 => 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_Pa_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)))) )
% 187.63/187.85 => ( 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))
% 187.63/187.85 => 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_Pa_2)),V_c0_2)),V_Qa_2)),V_U_2)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Inf__fin_Oremove,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.85 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.63/187.85 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 187.63/187.85 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.63/187.85 => 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)))))) ) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Sup__fin_Oremove,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.85 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.63/187.85 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 187.63/187.85 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.63/187.85 => 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)))))) ) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__idem_Ounion__idem,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => 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)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.63/187.85 => 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) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__idem_Oinsert__idem,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => 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)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__one_Oclosed,axiom,
% 187.63/187.85 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( ! [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))))))
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_infinite__UNIV__nat,axiom,
% 187.63/187.85 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 187.63/187.85 ! [V_N_2] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 187.63/187.85 <=> ? [B_m] :
% 187.63/187.85 ! [B_x] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Inf__le__Sup,axiom,
% 187.63/187.85 ! [V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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))) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Inf__fin_Osingleton,axiom,
% 187.63/187.85 ! [V_x_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => 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 ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Sup__fin_Osingleton,axiom,
% 187.63/187.85 ! [V_x_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => 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 ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 187.63/187.85 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => 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) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__idem_Oidem__comp,axiom,
% 187.63/187.85 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => 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) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__nat__set__iff__bounded,axiom,
% 187.63/187.85 ! [V_N_2] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 187.63/187.85 <=> ? [B_m] :
% 187.63/187.85 ! [B_x] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Sup__fin_Oin__idem,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.85 => 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) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_sup__Inf__absorb,axiom,
% 187.63/187.85 ! [V_a_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.85 => 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 ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Inf__fin_Oin__idem,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.85 => 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) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_inf__Sup__absorb,axiom,
% 187.63/187.85 ! [V_a_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.63/187.85 => 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 ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Sup__fin_Osubset__idem,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.63/187.85 => 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) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Inf__fin_Osubset__idem,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.63/187.85 => 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) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Sup__fin_Ounion__idem,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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)) ) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Inf__fin_Ounion__idem,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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)) ) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Sup__fin_Oinsert,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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)) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Inf__fin_Oinsert,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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)) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.63/187.85 => 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 )
% 187.63/187.85 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.63/187.85 => 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)))))) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.63/187.85 => 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 )
% 187.63/187.85 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.63/187.85 => 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)))))) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Sup__fin_Ounion__inter,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => ( 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))
% 187.63/187.85 => 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)) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( 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))
% 187.63/187.85 => 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)) ) ) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( 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))
% 187.63/187.85 => 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)) ) ) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Inf__fin_Ounion__inter,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => ( 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))
% 187.63/187.85 => 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)) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.63/187.85 => 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) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Inf__fin_Oclosed,axiom,
% 187.63/187.85 ! [V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( ! [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))))))
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Sup__fin_Oclosed,axiom,
% 187.63/187.85 ! [V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( ! [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))))))
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 187.63/187.85 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 187.63/187.85 ( 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)))
% 187.63/187.85 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 187.63/187.85 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 187.63/187.85 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 187.63/187.85 ( 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)))
% 187.63/187.85 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 187.63/187.85 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 187.63/187.85 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 187.63/187.85 ( 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)))
% 187.63/187.85 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 187.63/187.85 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 187.63/187.85 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 187.63/187.85 ( 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)))
% 187.63/187.85 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 187.63/187.85 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_ord_OgreaterThan__iff,axiom,
% 187.63/187.85 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 187.63/187.85 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_ord_OlessThan__iff,axiom,
% 187.63/187.85 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 187.63/187.85 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_ord_OatMost__iff,axiom,
% 187.63/187.85 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 187.63/187.85 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_ord_OatLeast__iff,axiom,
% 187.63/187.85 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 187.63/187.85 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_less__or__eq__imp__le,axiom,
% 187.63/187.85 ! [V_n,V_m] :
% 187.63/187.85 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.63/187.85 | V_m = V_n )
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_le__neq__implies__less,axiom,
% 187.63/187.85 ! [V_n,V_m] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 187.63/187.85 => ( V_m != V_n
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_less__imp__le__nat,axiom,
% 187.63/187.85 ! [V_n,V_m] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_le__eq__less__or__eq,axiom,
% 187.63/187.85 ! [V_n_2,V_m_2] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.63/187.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 187.63/187.85 | V_m_2 = V_n_2 ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_nat__less__le,axiom,
% 187.63/187.85 ! [V_n_2,V_m_2] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 187.63/187.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.63/187.85 & V_m_2 != V_n_2 ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_diff__less__mono,axiom,
% 187.63/187.85 ! [V_c,V_b,V_a] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 187.63/187.85 => 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))) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_diff__mult__distrib2,axiom,
% 187.63/187.85 ! [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)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_diff__mult__distrib,axiom,
% 187.63/187.85 ! [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)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_diff__commute,axiom,
% 187.63/187.85 ! [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) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_diff__less__mono2,axiom,
% 187.63/187.85 ! [V_l,V_n,V_m] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 187.63/187.85 => 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))) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_less__imp__diff__less,axiom,
% 187.63/187.85 ! [V_n,V_k,V_j] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 187.63/187.85 => 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)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_nat__less__cases,axiom,
% 187.63/187.85 ! [V_Pa_2,V_n_2,V_m_2] :
% 187.63/187.85 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 187.63/187.85 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 187.63/187.85 => ( ( V_m_2 = V_n_2
% 187.63/187.85 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 187.63/187.85 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 187.63/187.85 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 187.63/187.85 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_less__not__refl3,axiom,
% 187.63/187.85 ! [V_t,V_s] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 187.63/187.85 => V_s != V_t ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_less__not__refl2,axiom,
% 187.63/187.85 ! [V_m,V_n] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 187.63/187.85 => V_m != V_n ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_less__irrefl__nat,axiom,
% 187.63/187.85 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_linorder__neqE__nat,axiom,
% 187.63/187.85 ! [V_y,V_x] :
% 187.63/187.85 ( V_x != V_y
% 187.63/187.85 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_nat__neq__iff,axiom,
% 187.63/187.85 ! [V_n_2,V_m_2] :
% 187.63/187.85 ( V_m_2 != V_n_2
% 187.63/187.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 187.63/187.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_less__not__refl,axiom,
% 187.63/187.85 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_le__square,axiom,
% 187.63/187.85 ! [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))) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_le__cube,axiom,
% 187.63/187.85 ! [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)))) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_mult__le__mono1,axiom,
% 187.63/187.85 ! [V_k,V_j,V_i] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.63/187.85 => 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))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_mult__le__mono2,axiom,
% 187.63/187.85 ! [V_k,V_j,V_i] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.63/187.85 => 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))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_mult__le__mono,axiom,
% 187.63/187.85 ! [V_l,V_k,V_j,V_i] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 187.63/187.85 => 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))) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_le__antisym,axiom,
% 187.63/187.85 ! [V_n,V_m] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.63/187.85 => V_m = V_n ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_le__trans,axiom,
% 187.63/187.85 ! [V_k,V_j,V_i] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_eq__imp__le,axiom,
% 187.63/187.85 ! [V_n,V_m] :
% 187.63/187.85 ( V_m = V_n
% 187.63/187.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_nat__le__linear,axiom,
% 187.63/187.85 ! [V_n,V_m] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 187.63/187.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_le__refl,axiom,
% 187.63/187.85 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_diff__le__self,axiom,
% 187.63/187.85 ! [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)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_diff__le__mono2,axiom,
% 187.63/187.85 ! [V_l,V_n,V_m] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 187.63/187.85 => 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))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_diff__le__mono,axiom,
% 187.63/187.85 ! [V_l,V_n,V_m] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 187.63/187.85 => 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))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_diff__diff__cancel,axiom,
% 187.63/187.85 ! [V_n,V_i] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 187.63/187.85 => 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 ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_eq__diff__iff,axiom,
% 187.63/187.85 ! [V_n_2,V_m_2,V_k_2] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 187.63/187.85 => ( 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)
% 187.63/187.85 <=> V_m_2 = V_n_2 ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Nat_Odiff__diff__eq,axiom,
% 187.63/187.85 ! [V_n,V_m,V_k] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 187.63/187.85 => 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) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_le__diff__iff,axiom,
% 187.63/187.85 ! [V_n_2,V_m_2,V_k_2] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 187.63/187.85 => ( 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)))
% 187.63/187.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_less__diff__iff,axiom,
% 187.63/187.85 ! [V_n_2,V_m_2,V_k_2] :
% 187.63/187.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 187.63/187.85 => ( 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)))
% 187.63/187.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_inf__Sup2__distrib,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Odistrib__lattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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))))))) ) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_inf__Sup1__distrib,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Odistrib__lattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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))))) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_sup__Inf2__distrib,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Odistrib__lattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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))))))) ) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_sup__Inf1__distrib,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.63/187.85 ( class_Lattices_Odistrib__lattice(T_b)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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))))) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_,axiom,
% 187.63/187.85 ! [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) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Inf__fin_Ohom__commute,axiom,
% 187.63/187.85 ! [V_N_2,V_h_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( ! [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))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 187.63/187.85 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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)) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_Sup__fin_Ohom__commute,axiom,
% 187.63/187.85 ! [V_N_2,V_h_2,T_b] :
% 187.63/187.85 ( class_Lattices_Olattice(T_b)
% 187.63/187.85 => ( ! [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))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 187.63/187.85 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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)) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__empty__induct,axiom,
% 187.63/187.85 ! [V_Pa_2,V_A_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(V_Pa_2,V_A_2))
% 187.63/187.85 => ( ! [B_a,B_A] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 187.63/187.85 => ( hBOOL(hAPP(V_Pa_2,B_A))
% 187.63/187.85 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
% 187.63/187.85 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_nat__mult__commute,axiom,
% 187.63/187.85 ! [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) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_nat__mult__assoc,axiom,
% 187.63/187.85 ! [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)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__image__set,axiom,
% 187.63/187.85 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 187.63/187.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_Pa_2))))) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__Collect__bounded__ex,axiom,
% 187.63/187.85 ! [V_Qa_2,T_c,V_Pa_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2)))))
% 187.63/187.85 <=> ! [B_y] :
% 187.63/187.85 ( hBOOL(hAPP(V_Pa_2,B_y))
% 187.63/187.85 => 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)))) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_ran__def,axiom,
% 187.63/187.85 ! [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)))) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.63/187.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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)) ) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_map__comp__def,axiom,
% 187.63/187.85 ! [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)) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 187.63/187.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.63/187.85 => 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) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__subset__induct,axiom,
% 187.63/187.85 ! [V_Pa_2,V_A_2,V_F_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 187.63/187.85 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 187.63/187.85 => ( ! [B_a,B_F] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 187.63/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 187.63/187.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 187.63/187.85 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 187.63/187.85 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 187.63/187.85 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 187.63/187.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 187.63/187.85 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 187.63/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.63/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.63/187.85 => 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)) ) ) ) ).
% 187.63/187.85
% 187.63/187.85 fof(fact_finite__conv__nat__seg__image,axiom,
% 187.63/187.85 ! [V_A_2,T_b] :
% 187.63/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 <=> ? [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))) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_image__eq__fold__image,axiom,
% 187.79/187.85 ! [V_f_2,T_c,V_A_2,T_b] :
% 187.79/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => 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) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_fold1__Un,axiom,
% 187.79/187.85 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.85 ( class_Groups_Oab__semigroup__mult(T_b)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.85 => ( 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))
% 187.79/187.85 => 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)) ) ) ) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_folding__one__idem_Oidem,axiom,
% 187.79/187.85 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 187.79/187.85 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 187.79/187.85 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_fold__image__empty,axiom,
% 187.79/187.85 ! [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 ).
% 187.79/187.85
% 187.79/187.85 fof(fact_fold1__singleton,axiom,
% 187.79/187.85 ! [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 ).
% 187.79/187.85
% 187.79/187.85 fof(fact_fold1__singleton__def,axiom,
% 187.79/187.85 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 187.79/187.85 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 187.79/187.85 => 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 ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_map__comp__simps_I1_J,axiom,
% 187.79/187.85 ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] :
% 187.79/187.85 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 187.79/187.85 => 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) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_map__comp__Some__iff,axiom,
% 187.79/187.85 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 187.79/187.85 ( 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)
% 187.79/187.85 <=> ? [B_k_H] :
% 187.79/187.85 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 187.79/187.85 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_map__comp__simps_I2_J,axiom,
% 187.79/187.85 ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] :
% 187.79/187.85 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2)
% 187.79/187.85 => 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) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 187.79/187.85 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 187.79/187.85 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 187.79/187.85 => 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) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_folding__image_Oeq__fold,axiom,
% 187.79/187.85 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 187.79/187.85 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 187.79/187.85 => 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) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_folding__one_Oeq__fold,axiom,
% 187.79/187.85 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 187.79/187.85 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_map__comp__empty_I1_J,axiom,
% 187.79/187.85 ! [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) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_map__comp__empty_I2_J,axiom,
% 187.79/187.85 ! [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) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_fold1__def,axiom,
% 187.79/187.85 ! [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)) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_Sup__fin_OF__eq,axiom,
% 187.79/187.85 ! [V_A_2,T_b] :
% 187.79/187.85 ( class_Lattices_Olattice(T_b)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => 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) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_Inf__fin_OF__eq,axiom,
% 187.79/187.85 ! [V_A_2,T_b] :
% 187.79/187.85 ( class_Lattices_Olattice(T_b)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => 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) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_folding__one__idem_Oin__idem,axiom,
% 187.79/187.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 187.79/187.85 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.85 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_fold__image__insert,axiom,
% 187.79/187.85 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 187.79/187.85 ( class_Groups_Oab__semigroup__mult(T_c)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.85 => 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)) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_fold1__belowI,axiom,
% 187.79/187.85 ! [V_a_2,V_A_2,T_b] :
% 187.79/187.85 ( class_Lattices_Osemilattice__inf(T_b)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.85 => 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)) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_below__fold1__iff,axiom,
% 187.79/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.85 ( class_Lattices_Osemilattice__inf(T_b)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.85 => ( 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)))
% 187.79/187.85 <=> ! [B_x] :
% 187.79/187.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_fold1__insert__idem,axiom,
% 187.79/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.85 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 187.79/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => 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)) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_fold1__Un2,axiom,
% 187.79/187.85 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.85 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.85 => 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)) ) ) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_map__comp__None__iff,axiom,
% 187.79/187.85 ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 187.79/187.85 ( 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)
% 187.79/187.85 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c)
% 187.79/187.85 | ? [B_k_H] :
% 187.79/187.85 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 187.79/187.85 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_fold__image__reindex,axiom,
% 187.79/187.85 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 187.79/187.85 ( class_Groups_Oab__semigroup__mult(T_d)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 187.79/187.85 => 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) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_fold1__insert,axiom,
% 187.79/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.85 ( class_Groups_Oab__semigroup__mult(T_b)
% 187.79/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.85 => 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)) ) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_semilattice__big_OF__eq,axiom,
% 187.79/187.85 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 187.79/187.85 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_comm__monoid__big_OF__eq,axiom,
% 187.79/187.85 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 187.79/187.85 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 187.79/187.85 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 187.79/187.85 => 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) )
% 187.79/187.85 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 187.79/187.85 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_fold1__in,axiom,
% 187.79/187.85 ! [V_A_2,T_b] :
% 187.79/187.85 ( class_Groups_Oab__semigroup__mult(T_b)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.85 => ( ! [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))))))
% 187.79/187.85 => 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)) ) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_hom__fold1__commute,axiom,
% 187.79/187.85 ! [V_N_2,V_h_2,T_b] :
% 187.79/187.85 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 187.79/187.85 => ( ! [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))
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 187.79/187.85 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.85 => 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)) ) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_fold__Un__disjoint,axiom,
% 187.79/187.85 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.85 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.85 => ( 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))
% 187.79/187.85 => 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)) ) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_Option_Omap__def,axiom,
% 187.79/187.85 ! [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)) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_card__Diff1__less,axiom,
% 187.79/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.85 => 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))) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_card__Diff2__less,axiom,
% 187.79/187.85 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 187.79/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 187.79/187.85 => 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))) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_one__reorient,axiom,
% 187.79/187.85 ! [V_x_2,T_b] :
% 187.79/187.85 ( class_Groups_Oone(T_b)
% 187.79/187.85 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 187.79/187.85 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_mult_Ocomm__neutral,axiom,
% 187.79/187.85 ! [V_a,T_a] :
% 187.79/187.85 ( class_Groups_Ocomm__monoid__mult(T_a)
% 187.79/187.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_mult__1__right,axiom,
% 187.79/187.85 ! [V_a,T_a] :
% 187.79/187.85 ( class_Groups_Omonoid__mult(T_a)
% 187.79/187.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_mult__1,axiom,
% 187.79/187.85 ! [V_a,T_a] :
% 187.79/187.85 ( class_Groups_Ocomm__monoid__mult(T_a)
% 187.79/187.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_mult__1__left,axiom,
% 187.79/187.85 ! [V_a,T_a] :
% 187.79/187.85 ( class_Groups_Omonoid__mult(T_a)
% 187.79/187.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_bij__betw__same__card,axiom,
% 187.79/187.85 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.85 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 187.79/187.85 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_nat__mult__1,axiom,
% 187.79/187.85 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 187.79/187.85
% 187.79/187.85 fof(fact_nat__1__eq__mult__iff,axiom,
% 187.79/187.85 ! [V_n_2,V_m_2] :
% 187.79/187.85 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 187.79/187.85 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 187.79/187.85 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_nat__mult__1__right,axiom,
% 187.79/187.85 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 187.79/187.85
% 187.79/187.85 fof(fact_nat__mult__eq__1__iff,axiom,
% 187.79/187.85 ! [V_n_2,V_m_2] :
% 187.79/187.85 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 187.79/187.85 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 187.79/187.85 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_option__map__comp,axiom,
% 187.79/187.85 ! [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) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_Option_Omap_Ocompositionality,axiom,
% 187.79/187.85 ! [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) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_Option_Omap_Ocomp,axiom,
% 187.79/187.85 ! [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)) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_option__map__None,axiom,
% 187.79/187.85 ! [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) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_option__map__is__None,axiom,
% 187.79/187.85 ! [V_opt_2,V_f_2,T_b,T_c] :
% 187.79/187.85 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b)
% 187.79/187.85 <=> V_opt_2 = c_Option_Ooption_ONone(T_c) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_option__map__Some,axiom,
% 187.79/187.85 ! [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)) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_option__map__eq__Some,axiom,
% 187.79/187.85 ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] :
% 187.79/187.85 ( 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)
% 187.79/187.85 <=> ? [B_z] :
% 187.79/187.85 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z)
% 187.79/187.85 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 187.79/187.85 ! [V_A_2,T_b] :
% 187.79/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 187.79/187.85 => ( 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)))
% 187.79/187.85 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_option__map__o__empty,axiom,
% 187.79/187.85 ! [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) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_card__image,axiom,
% 187.79/187.85 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.79/187.85 => 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) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_BIJ,axiom,
% 187.79/187.85 ! [V_B_2,T_c,V_A_2,T_b] :
% 187.79/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 187.79/187.85 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
% 187.79/187.85 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_less__1__mult,axiom,
% 187.79/187.85 ! [V_n,V_m,T_a] :
% 187.79/187.85 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 187.79/187.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 187.79/187.85 => 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))) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_dom__option__map,axiom,
% 187.79/187.85 ! [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) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_square__eq__1__iff,axiom,
% 187.79/187.85 ! [V_x_2,T_b] :
% 187.79/187.85 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 187.79/187.85 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 187.79/187.85 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 187.79/187.85 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_card__Diff__insert,axiom,
% 187.79/187.85 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 187.79/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 187.79/187.85 => 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)) ) ) ) ).
% 187.79/187.85
% 187.79/187.85 fof(fact_card__Diff__singleton__if,axiom,
% 187.79/187.85 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.85 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.86 => 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)) )
% 187.79/187.86 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.86 => 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) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__Diff__singleton,axiom,
% 187.79/187.86 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.86 => 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)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__insert__le,axiom,
% 187.79/187.86 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => 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)))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__mono,axiom,
% 187.79/187.86 ! [V_A_2,V_B_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.86 => 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__seteq,axiom,
% 187.79/187.86 ! [V_A_2,V_B_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.86 => ( 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)))
% 187.79/187.86 => V_A_2 = V_B_2 ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__image__le,axiom,
% 187.79/187.86 ! [V_f_2,T_c,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_eq__card__imp__inj__on,axiom,
% 187.79/187.86 ! [V_f_2,T_c,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => ( 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)
% 187.79/187.86 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_inj__on__iff__eq__card,axiom,
% 187.79/187.86 ! [V_f_2,T_c,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.79/187.86 <=> 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) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_pigeonhole,axiom,
% 187.79/187.86 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.86 ( 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)))
% 187.79/187.86 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_option__map__o__map__upd,axiom,
% 187.79/187.86 ! [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))) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_psubset__card__mono,axiom,
% 187.79/187.86 ! [V_A_2,V_B_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.86 => 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_fold__image__distrib,axiom,
% 187.79/187.86 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 187.79/187.86 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => 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)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__bij__eq,axiom,
% 187.79/187.86 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.79/187.86 => ( 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))
% 187.79/187.86 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 187.79/187.86 => ( 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))
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 187.79/187.86 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__Diff__subset,axiom,
% 187.79/187.86 ! [V_A_2,V_B_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.79/187.86 => 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)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__Diff__subset__Int,axiom,
% 187.79/187.86 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.86 ( 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)))
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__card__le__card__Diff,axiom,
% 187.79/187.86 ! [V_A_2,V_B_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.86 => 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)))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__psubset,axiom,
% 187.79/187.86 ! [V_A_2,V_B_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.86 => ( 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)))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 187.79/187.86 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 187.79/187.86 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 187.79/187.86 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 187.79/187.86 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__Diff1__le,axiom,
% 187.79/187.86 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__inj__on__le,axiom,
% 187.79/187.86 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.79/187.86 => ( 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))
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_inj__on__iff__card__le,axiom,
% 187.79/187.86 ! [V_B_2,T_c,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 187.79/187.86 => ( ? [B_f] :
% 187.79/187.86 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 187.79/187.86 & 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)) )
% 187.79/187.86 <=> 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_fold__image__Un__Int,axiom,
% 187.79/187.86 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.86 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 187.79/187.86 ! [V_x,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__ring__1(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_fold__image__Un__one,axiom,
% 187.79/187.86 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 187.79/187.86 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 187.79/187.86 => ( ! [B_x] :
% 187.79/187.86 ( 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)))
% 187.79/187.86 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 187.79/187.86 => 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)) ) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card_Oremove,axiom,
% 187.79/187.86 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.86 => 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)))))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__Suc__Diff1,axiom,
% 187.79/187.86 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.86 => 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) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 187.79/187.86 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 187.79/187.86 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 187.79/187.86 => ( ! [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))
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 187.79/187.86 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.86 => 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)) ) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 187.79/187.86 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 187.79/187.86 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 187.79/187.86 => ( ! [B_x] :
% 187.79/187.86 ( 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)))
% 187.79/187.86 => hAPP(V_g_2,B_x) = V_z_2 )
% 187.79/187.86 => 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)) ) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__mono,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_lessI,axiom,
% 187.79/187.86 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_inj__on__add__nat,axiom,
% 187.79/187.86 ! [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) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__UNIV__unit,axiom,
% 187.79/187.86 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) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__Suc__right,axiom,
% 187.79/187.86 ! [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)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__Suc,axiom,
% 187.79/187.86 ! [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)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_crossproduct__eq,axiom,
% 187.79/187.86 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 187.79/187.86 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 187.79/187.86 => ( 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))
% 187.79/187.86 <=> ( V_w_2 = V_x_2
% 187.79/187.86 | V_y_2 = V_z_2 ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 187.79/187.86 ! [V_b,V_m,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_crossproduct__noteq,axiom,
% 187.79/187.86 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 187.79/187.86 => ( ( V_a_2 != V_b_2
% 187.79/187.86 & V_ca_2 != V_d_2 )
% 187.79/187.86 <=> 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)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 187.79/187.86 ! [V_z,V_y,V_x,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 187.79/187.86 ! [V_d,V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 187.79/187.86 ! [V_d,V_c,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 187.79/187.86 ! [V_d,V_c,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 187.79/187.86 ! [V_c,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oab__semigroup__add(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__left__cancel,axiom,
% 187.79/187.86 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Groups_Ocancel__semigroup__add(T_b)
% 187.79/187.86 => ( 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)
% 187.79/187.86 <=> V_b_2 = V_ca_2 ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__right__cancel,axiom,
% 187.79/187.86 ! [V_ca_2,V_a_2,V_b_2,T_b] :
% 187.79/187.86 ( class_Groups_Ocancel__semigroup__add(T_b)
% 187.79/187.86 => ( 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)
% 187.79/187.86 <=> V_b_2 = V_ca_2 ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__left__imp__eq,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Ocancel__semigroup__add(T_a)
% 187.79/187.86 => ( 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)
% 187.79/187.86 => V_b = V_c ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__imp__eq,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 187.79/187.86 => ( 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)
% 187.79/187.86 => V_b = V_c ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__right__imp__eq,axiom,
% 187.79/187.86 ! [V_c,V_a,V_b,T_a] :
% 187.79/187.86 ( class_Groups_Ocancel__semigroup__add(T_a)
% 187.79/187.86 => ( 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)
% 187.79/187.86 => V_b = V_c ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_inj__Suc,axiom,
% 187.79/187.86 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_n__not__Suc__n,axiom,
% 187.79/187.86 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__n__not__n,axiom,
% 187.79/187.86 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__add__commute,axiom,
% 187.79/187.86 ! [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) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__Suc__right,axiom,
% 187.79/187.86 ! [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)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__add__left__commute,axiom,
% 187.79/187.86 ! [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)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__Suc,axiom,
% 187.79/187.86 ! [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)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__Suc__shift,axiom,
% 187.79/187.86 ! [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)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat_Oinject,axiom,
% 187.79/187.86 ! [V_nat_H_2,V_nat_2] :
% 187.79/187.86 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 187.79/187.86 <=> V_nat_2 = V_nat_H_2 ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__add__assoc,axiom,
% 187.79/187.86 ! [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)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__add__left__cancel,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2,V_k_2] :
% 187.79/187.86 ( 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)
% 187.79/187.86 <=> V_m_2 = V_n_2 ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__add__right__cancel,axiom,
% 187.79/187.86 ! [V_n_2,V_k_2,V_m_2] :
% 187.79/187.86 ( 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)
% 187.79/187.86 <=> V_m_2 = V_n_2 ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__inject,axiom,
% 187.79/187.86 ! [V_y,V_x] :
% 187.79/187.86 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 187.79/187.86 => V_x = V_y ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__iff__Suc__add,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.86 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__add__Suc2,axiom,
% 187.79/187.86 ! [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)))) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__add__Suc1,axiom,
% 187.79/187.86 ! [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)))) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__Suc__diff__eq2,axiom,
% 187.79/187.86 ! [V_m,V_j,V_k] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__Suc__diff__eq1,axiom,
% 187.79/187.86 ! [V_m,V_j,V_k] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__le__imp__le__left,axiom,
% 187.79/187.86 ! [V_b,V_a,V_c,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__le__imp__le__right,axiom,
% 187.79/187.86 ! [V_b,V_c,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__mono,axiom,
% 187.79/187.86 ! [V_d,V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__left__mono,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.86 => 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__right__mono,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.86 => 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__le__cancel__left,axiom,
% 187.79/187.86 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 187.79/187.86 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__le__cancel__right,axiom,
% 187.79/187.86 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__less__imp__less__left,axiom,
% 187.79/187.86 ! [V_b,V_a,V_c,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__less__imp__less__right,axiom,
% 187.79/187.86 ! [V_b,V_c,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__strict__mono,axiom,
% 187.79/187.86 ! [V_d,V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__strict__left__mono,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.86 => 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__strict__right__mono,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.86 => 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__less__cancel__left,axiom,
% 187.79/187.86 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 187.79/187.86 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__less__cancel__right,axiom,
% 187.79/187.86 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__class_Odistrib,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_combine__common__factor,axiom,
% 187.79/187.86 ! [V_c,V_b,V_e,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Osemiring(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__diff__cancel,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Ogroup__add(T_a)
% 187.79/187.86 => 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 ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__add__cancel,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Ogroup__add(T_a)
% 187.79/187.86 => 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 ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_minus__add__cancel,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Ogroup__add(T_a)
% 187.79/187.86 => 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 ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__minus__cancel,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Ogroup__add(T_a)
% 187.79/187.86 => 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 ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_minus__add,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Ogroup__add(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_minus__add__distrib,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oab__group__add(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_not__less__eq,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2] :
% 187.79/187.86 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__Suc__eq,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 187.79/187.86 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.86 | V_m_2 = V_n_2 ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__less__eq,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2] :
% 187.79/187.86 ( 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)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_not__less__less__Suc__eq,axiom,
% 187.79/187.86 ! [V_m_2,V_n_2] :
% 187.79/187.86 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 187.79/187.86 <=> V_n_2 = V_m_2 ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__antisym,axiom,
% 187.79/187.86 ! [V_m,V_n] :
% 187.79/187.86 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 187.79/187.86 => V_m = V_n ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__SucI,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__lessI,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.86 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__trans__Suc,axiom,
% 187.79/187.86 ! [V_k,V_j,V_i] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__SucE,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 187.79/187.86 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.86 => V_m = V_n ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__lessD,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__less__SucD,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__n__not__le__n,axiom,
% 187.79/187.86 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_not__less__eq__eq,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2] :
% 187.79/187.86 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__Suc__eq,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 187.79/187.86 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.86 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__le__mono,axiom,
% 187.79/187.86 ! [V_m_2,V_n_2] :
% 187.79/187.86 ( 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)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__SucI,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__SucE,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 187.79/187.86 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 187.79/187.86 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__leD,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_not__add__less1,axiom,
% 187.79/187.86 ! [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)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_not__add__less2,axiom,
% 187.79/187.86 ! [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)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__add__left__cancel__less,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2,V_k_2] :
% 187.79/187.86 ( 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)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_trans__less__add1,axiom,
% 187.79/187.86 ! [V_m,V_j,V_i] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_trans__less__add2,axiom,
% 187.79/187.86 ! [V_m,V_j,V_i] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__less__mono1,axiom,
% 187.79/187.86 ! [V_k,V_j,V_i] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__less__mono,axiom,
% 187.79/187.86 ! [V_l,V_k,V_j,V_i] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 187.79/187.86 => 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__add__eq__less,axiom,
% 187.79/187.86 ! [V_n,V_m,V_l,V_k] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 187.79/187.86 => ( 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)
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__lessD1,axiom,
% 187.79/187.86 ! [V_k,V_j,V_i] :
% 187.79/187.86 ( 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))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_termination__basic__simps_I1_J,axiom,
% 187.79/187.86 ! [V_z,V_y,V_x] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_termination__basic__simps_I2_J,axiom,
% 187.79/187.86 ! [V_y,V_z,V_x] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__diff__diff,axiom,
% 187.79/187.86 ! [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) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__Suc__Suc,axiom,
% 187.79/187.86 ! [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) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__Suc__1,axiom,
% 187.79/187.86 ! [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 ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__mult__cancel1,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2,V_k_2] :
% 187.79/187.86 ( 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)
% 187.79/187.86 <=> V_m_2 = V_n_2 ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__add2,axiom,
% 187.79/187.86 ! [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))) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__add1,axiom,
% 187.79/187.86 ! [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))) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__iff__add,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.86 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__add__left__cancel__le,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2,V_k_2] :
% 187.79/187.86 ( 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)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_trans__le__add1,axiom,
% 187.79/187.86 ! [V_m,V_j,V_i] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_trans__le__add2,axiom,
% 187.79/187.86 ! [V_m,V_j,V_i] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__le__mono1,axiom,
% 187.79/187.86 ! [V_k,V_j,V_i] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__le__mono,axiom,
% 187.79/187.86 ! [V_l,V_k,V_j,V_i] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 187.79/187.86 => 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__leD2,axiom,
% 187.79/187.86 ! [V_n,V_k,V_m] :
% 187.79/187.86 ( 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))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__leD1,axiom,
% 187.79/187.86 ! [V_n,V_k,V_m] :
% 187.79/187.86 ( 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))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__leE,axiom,
% 187.79/187.86 ! [V_n,V_k,V_m] :
% 187.79/187.86 ( 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))
% 187.79/187.86 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 187.79/187.86 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_termination__basic__simps_I3_J,axiom,
% 187.79/187.86 ! [V_z,V_y,V_x] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_termination__basic__simps_I4_J,axiom,
% 187.79/187.86 ! [V_y,V_z,V_x] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__cancel2,axiom,
% 187.79/187.86 ! [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) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__cancel,axiom,
% 187.79/187.86 ! [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) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__diff__left,axiom,
% 187.79/187.86 ! [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)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__add__inverse,axiom,
% 187.79/187.86 ! [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 ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__add__inverse2,axiom,
% 187.79/187.86 ! [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 ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__mult__distrib,axiom,
% 187.79/187.86 ! [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)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__mult__distrib2,axiom,
% 187.79/187.86 ! [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)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 187.79/187.86 ! [V_m,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 187.79/187.86 ! [V_a,V_m,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 187.79/187.86 ! [V_m,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 187.79/187.86 ! [V_y,V_x,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__ring__1(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__less__le__mono,axiom,
% 187.79/187.86 ! [V_d,V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__le__less__mono,axiom,
% 187.79/187.86 ! [V_d,V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__add__one,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.86 => 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)))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_eq__add__iff1,axiom,
% 187.79/187.86 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Rings_Oring(T_b)
% 187.79/187.86 => ( 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)
% 187.79/187.86 <=> 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 ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_eq__add__iff2,axiom,
% 187.79/187.86 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Rings_Oring(T_b)
% 187.79/187.86 => ( 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)
% 187.79/187.86 <=> 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) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__minus__eq__add,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Ogroup__add(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_ab__diff__minus,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oab__group__add(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__def,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Ogroup__add(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__le__lessD,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__less__Suc__eq,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 187.79/187.86 <=> V_n_2 = V_m_2 ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__leI,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__imp__less__Suc,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__le__eq,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__Suc__eq__le,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__eq__Suc__le,axiom,
% 187.79/187.86 ! [V_m_2,V_n_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__less__Suc,axiom,
% 187.79/187.86 ! [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))) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__mult__less__cancel1,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2,V_k_2] :
% 187.79/187.86 ( 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)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__diff__le,axiom,
% 187.79/187.86 ! [V_m,V_n] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__mult__le__cancel1,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2,V_k_2] :
% 187.79/187.86 ( 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)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__diff__conv,axiom,
% 187.79/187.86 ! [V_k_2,V_j_2,V_i_2] :
% 187.79/187.86 ( 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)))
% 187.79/187.86 <=> 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__diff__inverse,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.86 => 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 ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__add__assoc2,axiom,
% 187.79/187.86 ! [V_i,V_j,V_k] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__diff__assoc2,axiom,
% 187.79/187.86 ! [V_i,V_j,V_k] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__add__assoc,axiom,
% 187.79/187.86 ! [V_i,V_j,V_k] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__imp__diff__is__add,axiom,
% 187.79/187.86 ! [V_k_2,V_j_2,V_i_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 187.79/187.86 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 187.79/187.86 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__add__diff__inverse2,axiom,
% 187.79/187.86 ! [V_m,V_n] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.79/187.86 => 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 ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__diff__conv2,axiom,
% 187.79/187.86 ! [V_i_2,V_j_2,V_k_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> 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)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__diff__assoc,axiom,
% 187.79/187.86 ! [V_i,V_j,V_k] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__add__diff__inverse,axiom,
% 187.79/187.86 ! [V_m,V_n] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.79/187.86 => 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 ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__add__diff,axiom,
% 187.79/187.86 ! [V_m,V_n,V_k] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__diff__conv,axiom,
% 187.79/187.86 ! [V_i_2,V_k_2,V_j_2] :
% 187.79/187.86 ( 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))
% 187.79/187.86 <=> 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__diff__right,axiom,
% 187.79/187.86 ! [V_i,V_j,V_k] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__eq__Suc__le__raw,axiom,
% 187.79/187.86 ! [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)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__add__iff2,axiom,
% 187.79/187.86 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Rings_Oordered__ring(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__add__iff1,axiom,
% 187.79/187.86 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Rings_Oordered__ring(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> 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)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__add__iff1,axiom,
% 187.79/187.86 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Rings_Oordered__ring(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> 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)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__add__iff2,axiom,
% 187.79/187.86 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Rings_Oordered__ring(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 187.79/187.86 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 187.79/187.86 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 187.79/187.86 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 187.79/187.86 ! [V_rx,V_ly,V_lx,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 187.79/187.86 ! [V_rx,V_ly,V_lx,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 187.79/187.86 ! [V_ry,V_rx,V_lx,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 187.79/187.86 ! [V_ry,V_rx,V_lx,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__insert__disjoint,axiom,
% 187.79/187.86 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.86 => 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)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__insert__if,axiom,
% 187.79/187.86 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.86 => 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) )
% 187.79/187.86 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.86 => 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)) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card_Oinsert,axiom,
% 187.79/187.86 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.86 => 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)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__Un__Int,axiom,
% 187.79/187.86 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.86 => 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card_Ounion__inter,axiom,
% 187.79/187.86 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.86 => 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)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__insert,axiom,
% 187.79/187.86 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => 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)))))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card_Oinsert__remove,axiom,
% 187.79/187.86 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => 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)))))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_card__Un__disjoint,axiom,
% 187.79/187.86 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.86 => ( 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))
% 187.79/187.86 => 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)) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__less__add__iff2,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__less__add__iff1,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> 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)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__eq__add__iff2,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 187.79/187.86 => ( 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)
% 187.79/187.86 <=> 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) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__diff__add__eq2,axiom,
% 187.79/187.86 ! [V_n,V_m,V_u,V_j,V_i] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.79/187.86 => 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)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__le__add__iff2,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__eq__add__iff1,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 187.79/187.86 => ( 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)
% 187.79/187.86 <=> 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 ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__diff__add__eq1,axiom,
% 187.79/187.86 ! [V_n,V_m,V_u,V_i,V_j] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__le__add__iff1,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> 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)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_left__add__mult__distrib,axiom,
% 187.79/187.86 ! [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) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 187.79/187.86 ! [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) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__eq__plus1,axiom,
% 187.79/187.86 ! [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)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__eq__plus1__left,axiom,
% 187.79/187.86 ! [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) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_finite__fun__UNIVD1,axiom,
% 187.79/187.86 ! [T_c,T_b] :
% 187.79/187.86 ( 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))))
% 187.79/187.86 => ( 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))
% 187.79/187.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__Max__commute,axiom,
% 187.79/187.86 ! [V_k_2,V_N_2,T_b] :
% 187.79/187.86 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 187.79/187.86 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.86 => 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))))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__Min__commute,axiom,
% 187.79/187.86 ! [V_k_2,V_N_2,T_b] :
% 187.79/187.86 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 187.79/187.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 187.79/187.86 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.86 => 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))))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__zeroE,axiom,
% 187.79/187.86 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le0,axiom,
% 187.79/187.86 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_zero__less__Suc,axiom,
% 187.79/187.86 ! [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))) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_zero__reorient,axiom,
% 187.79/187.86 ! [V_x_2,T_b] :
% 187.79/187.86 ( class_Groups_Ozero(T_b)
% 187.79/187.86 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 187.79/187.86 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_bot__nat__def,axiom,
% 187.79/187.86 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__0__iff,axiom,
% 187.79/187.86 ! [V_a_2,V_b_2,T_b] :
% 187.79/187.86 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 187.79/187.86 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 187.79/187.86 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__0__left,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Groups_Omonoid__add(T_a)
% 187.79/187.86 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__0,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.79/187.86 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_double__zero__sym,axiom,
% 187.79/187.86 ! [V_a_2,T_b] :
% 187.79/187.86 ( class_Groups_Olinordered__ab__group__add(T_b)
% 187.79/187.86 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 187.79/187.86 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__0__right,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Groups_Omonoid__add(T_a)
% 187.79/187.86 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add_Ocomm__neutral,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.79/187.86 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_divisors__zero,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ono__zero__divisors(T_a)
% 187.79/187.86 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.86 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.86 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_no__zero__divisors,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Ono__zero__divisors(T_a)
% 187.79/187.86 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.86 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__eq__0__iff,axiom,
% 187.79/187.86 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Rings_Oring__no__zero__divisors(T_b)
% 187.79/187.86 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.86 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.86 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__zero__right,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Rings_Omult__zero(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__zero__left,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Rings_Omult__zero(T_a)
% 187.79/187.86 => 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) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_right__minus__eq,axiom,
% 187.79/187.86 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Groups_Ogroup__add(T_b)
% 187.79/187.86 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.86 <=> V_a_2 = V_b_2 ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_eq__iff__diff__eq__0,axiom,
% 187.79/187.86 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Groups_Oab__group__add(T_b)
% 187.79/187.86 => ( V_a_2 = V_b_2
% 187.79/187.86 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__self,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Groups_Ogroup__add(T_a)
% 187.79/187.86 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__0__right,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Groups_Ogroup__add(T_a)
% 187.79/187.86 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_one__neq__zero,axiom,
% 187.79/187.86 ! [T_a] :
% 187.79/187.86 ( class_Rings_Ozero__neq__one(T_a)
% 187.79/187.86 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_zero__neq__one,axiom,
% 187.79/187.86 ! [T_a] :
% 187.79/187.86 ( class_Rings_Ozero__neq__one(T_a)
% 187.79/187.86 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_neg__equal__zero,axiom,
% 187.79/187.86 ! [V_a_2,T_b] :
% 187.79/187.86 ( class_Groups_Olinordered__ab__group__add(T_b)
% 187.79/187.86 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 187.79/187.86 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_neg__equal__0__iff__equal,axiom,
% 187.79/187.86 ! [V_a_2,T_b] :
% 187.79/187.86 ( class_Groups_Ogroup__add(T_b)
% 187.79/187.86 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.86 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_equal__neg__zero,axiom,
% 187.79/187.86 ! [V_a_2,T_b] :
% 187.79/187.86 ( class_Groups_Olinordered__ab__group__add(T_b)
% 187.79/187.86 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 187.79/187.86 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_neg__0__equal__iff__equal,axiom,
% 187.79/187.86 ! [V_a_2,T_b] :
% 187.79/187.86 ( class_Groups_Ogroup__add(T_b)
% 187.79/187.86 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 187.79/187.86 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_minus__zero,axiom,
% 187.79/187.86 ! [T_a] :
% 187.79/187.86 ( class_Groups_Ogroup__add(T_a)
% 187.79/187.86 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Zero__not__Suc,axiom,
% 187.79/187.86 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat_Osimps_I2_J,axiom,
% 187.79/187.86 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__not__Zero,axiom,
% 187.79/187.86 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat_Osimps_I3_J,axiom,
% 187.79/187.86 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Zero__neq__Suc,axiom,
% 187.79/187.86 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Suc__neq__Zero,axiom,
% 187.79/187.86 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_not__less0,axiom,
% 187.79/187.86 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_neq0__conv,axiom,
% 187.79/187.86 ! [V_n_2] :
% 187.79/187.86 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__nat__zero__code,axiom,
% 187.79/187.86 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_gr__implies__not0,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.86 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_gr0I,axiom,
% 187.79/187.86 ! [V_n] :
% 187.79/187.86 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_plus__nat_Oadd__0,axiom,
% 187.79/187.86 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 187.79/187.86
% 187.79/187.86 fof(fact_Nat_Oadd__0__right,axiom,
% 187.79/187.86 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__is__0,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2] :
% 187.79/187.86 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.86 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.86 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__eq__self__zero,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 187.79/187.86 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 187.79/187.86 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_le__0__eq,axiom,
% 187.79/187.86 ! [V_n_2] :
% 187.79/187.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 187.79/187.86 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diffs0__imp__equal,axiom,
% 187.79/187.86 ! [V_n,V_m] :
% 187.79/187.86 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.86 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.86 => V_m = V_n ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__self__eq__0,axiom,
% 187.79/187.86 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_minus__nat_Odiff__0,axiom,
% 187.79/187.86 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 187.79/187.86
% 187.79/187.86 fof(fact_diff__0__eq__0,axiom,
% 187.79/187.86 ! [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) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__cancel2,axiom,
% 187.79/187.86 ! [V_n_2,V_k_2,V_m_2] :
% 187.79/187.86 ( 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)
% 187.79/187.86 <=> ( V_m_2 = V_n_2
% 187.79/187.86 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__cancel1,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2,V_k_2] :
% 187.79/187.86 ( 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)
% 187.79/187.86 <=> ( V_m_2 = V_n_2
% 187.79/187.86 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__is__0,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2] :
% 187.79/187.86 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.86 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.86 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__0__right,axiom,
% 187.79/187.86 ! [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) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__0,axiom,
% 187.79/187.86 ! [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) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 187.79/187.86 ! [V_n_2,V_m_2,V_k_2] :
% 187.79/187.86 ( 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)
% 187.79/187.86 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.86 | V_m_2 = V_n_2 ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_sum__squares__eq__zero__iff,axiom,
% 187.79/187.86 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.86 ( class_Rings_Olinordered__ring__strict(T_b)
% 187.79/187.86 => ( 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)
% 187.79/187.86 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.86 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_sum__squares__le__zero__iff,axiom,
% 187.79/187.86 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.86 ( class_Rings_Olinordered__ring__strict(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.86 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_sum__squares__ge__zero,axiom,
% 187.79/187.86 ! [V_y,V_x,T_a] :
% 187.79/187.86 ( class_Rings_Olinordered__ring(T_a)
% 187.79/187.86 => 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)))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_not__sum__squares__lt__zero,axiom,
% 187.79/187.86 ! [V_y,V_x,T_a] :
% 187.79/187.86 ( class_Rings_Olinordered__ring(T_a)
% 187.79/187.86 => ~ 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_sum__squares__gt__zero__iff,axiom,
% 187.79/187.86 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.86 ( class_Rings_Olinordered__ring__strict(T_b)
% 187.79/187.86 => ( 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))))
% 187.79/187.86 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.86 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 187.79/187.86 ! [V_a_2,T_b] :
% 187.79/187.86 ( class_Groups_Olinordered__ab__group__add(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 187.79/187.86 ! [V_a_2,T_b] :
% 187.79/187.86 ( class_Groups_Olinordered__ab__group__add(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__nonneg__nonneg,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__nonneg__eq__0__iff,axiom,
% 187.79/187.86 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.86 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 187.79/187.86 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.86 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.86 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__increasing,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__increasing2,axiom,
% 187.79/187.86 ! [V_a,V_b,V_c,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__nonpos__nonpos,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_split__mult__neg__le,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Oordered__cancel__semiring(T_a)
% 187.79/187.86 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 187.79/187.86 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 187.79/187.86 => 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_split__mult__pos__le,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Oordered__ring(T_a)
% 187.79/187.86 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 187.79/187.86 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 187.79/187.86 => 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))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__mono,axiom,
% 187.79/187.86 ! [V_d,V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Oordered__semiring(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.86 => 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))) ) ) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__mono_H,axiom,
% 187.79/187.86 ! [V_d,V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Oordered__semiring(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.86 => 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))) ) ) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__left__mono__neg,axiom,
% 187.79/187.86 ! [V_c,V_a,V_b,T_a] :
% 187.79/187.86 ( class_Rings_Oordered__ring(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__right__mono__neg,axiom,
% 187.79/187.86 ! [V_c,V_a,V_b,T_a] :
% 187.79/187.86 ( class_Rings_Oordered__ring(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_comm__mult__left__mono,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Oordered__comm__semiring(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__left__mono,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Oordered__semiring(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__right__mono,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Oordered__semiring(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__nonpos__nonpos,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Oordered__ring(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__nonpos__nonneg,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Oordered__cancel__semiring(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__nonneg__nonpos2,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Oordered__cancel__semiring(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__nonneg__nonpos,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Oordered__cancel__semiring(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__nonneg__nonneg,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Oordered__cancel__semiring(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_mult__le__0__iff,axiom,
% 187.79/187.86 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Rings_Olinordered__ring__strict(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 187.79/187.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 187.79/187.86 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_zero__le__mult__iff,axiom,
% 187.79/187.86 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.86 ( class_Rings_Olinordered__ring__strict(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 187.79/187.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 187.79/187.86 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_zero__le__square,axiom,
% 187.79/187.86 ! [V_a,T_a] :
% 187.79/187.86 ( class_Rings_Olinordered__ring(T_a)
% 187.79/187.86 => 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))) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_pos__add__strict,axiom,
% 187.79/187.86 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.86 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 187.79/187.86 ! [V_a_2,T_b] :
% 187.79/187.86 ( class_Groups_Olinordered__ab__group__add(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 187.79/187.86 ! [V_a_2,T_b] :
% 187.79/187.86 ( class_Groups_Olinordered__ab__group__add(T_b)
% 187.79/187.86 => ( 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)))
% 187.79/187.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__pos__pos,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_add__neg__neg,axiom,
% 187.79/187.86 ! [V_b,V_a,T_a] :
% 187.79/187.86 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.86 => 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))) ) ) ) ).
% 187.79/187.86
% 187.79/187.86 fof(fact_not__square__less__zero,axiom,
% 187.79/187.87 ! [V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__ring(T_a)
% 187.79/187.87 => ~ 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))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__less__cancel__right__disj,axiom,
% 187.79/187.87 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 187.79/187.87 ( class_Rings_Olinordered__ring__strict(T_b)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 187.79/187.87 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__less__cancel__left__disj,axiom,
% 187.79/187.87 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 187.79/187.87 ( class_Rings_Olinordered__ring__strict(T_b)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 187.79/187.87 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__less__cancel__left__pos,axiom,
% 187.79/187.87 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 187.79/187.87 ( class_Rings_Olinordered__ring__strict(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__pos__pos,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__pos__neg,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__pos__neg2,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_zero__less__mult__pos,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_zero__less__mult__pos2,axiom,
% 187.79/187.87 ! [V_a,V_b,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__less__cancel__left__neg,axiom,
% 187.79/187.87 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 187.79/187.87 ( class_Rings_Olinordered__ring__strict(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__neg__pos,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__neg__neg,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__strict__right__mono,axiom,
% 187.79/187.87 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__strict__left__mono,axiom,
% 187.79/187.87 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_comm__mult__strict__left__mono,axiom,
% 187.79/187.87 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__strict__right__mono__neg,axiom,
% 187.79/187.87 ! [V_c,V_a,V_b,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__strict__left__mono__neg,axiom,
% 187.79/187.87 ! [V_c,V_a,V_b,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_le__iff__diff__le__0,axiom,
% 187.79/187.87 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.87 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 187.79/187.87 <=> 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))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_less__iff__diff__less__0,axiom,
% 187.79/187.87 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.87 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 187.79/187.87 <=> 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))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_add__scale__eq__noteq,axiom,
% 187.79/187.87 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 187.79/187.87 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 187.79/187.87 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.87 => ( ( V_a = V_b
% 187.79/187.87 & V_c != V_d )
% 187.79/187.87 => 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)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_zero__le__one,axiom,
% 187.79/187.87 ! [T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.87 => 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))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_not__one__le__zero,axiom,
% 187.79/187.87 ! [T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.87 => ~ 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))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_zero__less__one,axiom,
% 187.79/187.87 ! [T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_not__one__less__zero,axiom,
% 187.79/187.87 ! [T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.87 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_neg__0__le__iff__le,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_le__minus__self__iff,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Groups_Olinordered__ab__group__add(T_b)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_neg__le__0__iff__le,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_minus__le__self__iff,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Groups_Olinordered__ab__group__add(T_b)
% 187.79/187.87 => ( 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))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_less__minus__self__iff,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_neg__less__nonneg,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Groups_Olinordered__ab__group__add(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_neg__less__0__iff__less,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_neg__0__less__iff__less,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_minus__Min__eq__Max,axiom,
% 187.79/187.87 ! [V_S_2,T_b] :
% 187.79/187.87 ( class_Groups_Olinordered__ab__group__add(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.87 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => 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)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_minus__Max__eq__Min,axiom,
% 187.79/187.87 ! [V_S_2,T_b] :
% 187.79/187.87 ( class_Groups_Olinordered__ab__group__add(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.87 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => 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)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_minus__unique,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Groups_Ogroup__add(T_a)
% 187.79/187.87 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.87 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_ab__left__minus,axiom,
% 187.79/187.87 ! [V_a,T_a] :
% 187.79/187.87 ( class_Groups_Oab__group__add(T_a)
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_left__minus,axiom,
% 187.79/187.87 ! [V_a,T_a] :
% 187.79/187.87 ( class_Groups_Ogroup__add(T_a)
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 187.79/187.87 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.87 ( class_Groups_Ogroup__add(T_b)
% 187.79/187.87 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 187.79/187.87 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_right__minus,axiom,
% 187.79/187.87 ! [V_a,T_a] :
% 187.79/187.87 ( class_Groups_Ogroup__add(T_a)
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_diff__0,axiom,
% 187.79/187.87 ! [V_a,T_a] :
% 187.79/187.87 ( class_Groups_Ogroup__add(T_a)
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_less__Suc__eq__0__disj,axiom,
% 187.79/187.87 ! [V_n_2,V_m_2] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 187.79/187.87 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.87 | ? [B_j] :
% 187.79/187.87 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 187.79/187.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_less__Suc0,axiom,
% 187.79/187.87 ! [V_n_2] :
% 187.79/187.87 ( 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))))
% 187.79/187.87 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_gr0__conv__Suc,axiom,
% 187.79/187.87 ! [V_n_2] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 187.79/187.87 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_one__is__add,axiom,
% 187.79/187.87 ! [V_n_2,V_m_2] :
% 187.79/187.87 ( 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)
% 187.79/187.87 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 187.79/187.87 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.79/187.87 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.87 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_add__is__1,axiom,
% 187.79/187.87 ! [V_n_2,V_m_2] :
% 187.79/187.87 ( 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))
% 187.79/187.87 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 187.79/187.87 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.79/187.87 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.87 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_add__gr__0,axiom,
% 187.79/187.87 ! [V_n_2,V_m_2] :
% 187.79/187.87 ( 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)))
% 187.79/187.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 187.79/187.87 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_card_Oempty,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_card__infinite,axiom,
% 187.79/187.87 ! [V_A_2,T_b] :
% 187.79/187.87 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__eq__1__iff,axiom,
% 187.79/187.87 ! [V_n_2,V_m_2] :
% 187.79/187.87 ( 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))
% 187.79/187.87 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 187.79/187.87 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_zero__less__diff,axiom,
% 187.79/187.87 ! [V_m_2,V_n_2] :
% 187.79/187.87 ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_diff__less,axiom,
% 187.79/187.87 ! [V_m,V_n] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 187.79/187.87 => 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)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_nat__0__less__mult__iff,axiom,
% 187.79/187.87 ! [V_n_2,V_m_2] :
% 187.79/187.87 ( 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)))
% 187.79/187.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 187.79/187.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__less__cancel1,axiom,
% 187.79/187.87 ! [V_n_2,V_m_2,V_k_2] :
% 187.79/187.87 ( 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)))
% 187.79/187.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 187.79/187.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__less__cancel2,axiom,
% 187.79/187.87 ! [V_n_2,V_k_2,V_m_2] :
% 187.79/187.87 ( 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)))
% 187.79/187.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 187.79/187.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__less__mono1,axiom,
% 187.79/187.87 ! [V_k,V_j,V_i] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 187.79/187.87 => 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))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__less__mono2,axiom,
% 187.79/187.87 ! [V_k,V_j,V_i] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 187.79/187.87 => 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))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_nat__mult__eq__cancel1,axiom,
% 187.79/187.87 ! [V_n_2,V_m_2,V_k_2] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 187.79/187.87 => ( 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)
% 187.79/187.87 <=> V_m_2 = V_n_2 ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_nat__mult__less__cancel1,axiom,
% 187.79/187.87 ! [V_n_2,V_m_2,V_k_2] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_diff__add__0,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_diff__is__0__eq_H,axiom,
% 187.79/187.87 ! [V_n,V_m] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 187.79/187.87 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_diff__is__0__eq,axiom,
% 187.79/187.87 ! [V_n_2,V_m_2] :
% 187.79/187.87 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_One__nat__def,axiom,
% 187.79/187.87 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max_Osingleton,axiom,
% 187.79/187.87 ! [V_x_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => 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 ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min_Osingleton,axiom,
% 187.79/187.87 ! [V_x_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => 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 ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__eq__self__implies__10,axiom,
% 187.79/187.87 ! [V_n,V_m] :
% 187.79/187.87 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 187.79/187.87 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 187.79/187.87 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Suc__pred_H,axiom,
% 187.79/187.87 ! [V_n] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.87 => 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))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_add__eq__if,axiom,
% 187.79/187.87 ! [V_n,V_m] :
% 187.79/187.87 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.87 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 187.79/187.87 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.87 => 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)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_add__pos__nonneg,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_add__nonneg__pos,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_add__strict__increasing,axiom,
% 187.79/187.87 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_add__strict__increasing2,axiom,
% 187.79/187.87 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_add__neg__nonpos,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_add__nonpos__neg,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__le__cancel__left__pos,axiom,
% 187.79/187.87 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 187.79/187.87 ( class_Rings_Olinordered__ring__strict(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__le__cancel__left__neg,axiom,
% 187.79/187.87 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 187.79/187.87 ( class_Rings_Olinordered__ring__strict(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__strict__mono,axiom,
% 187.79/187.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.87 => 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))) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__strict__mono_H,axiom,
% 187.79/187.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.87 => 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))) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__less__le__imp__less,axiom,
% 187.79/187.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.87 => 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))) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__le__less__imp__less,axiom,
% 187.79/187.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.87 => 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))) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__right__less__imp__less,axiom,
% 187.79/187.87 ! [V_b,V_c,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring(T_a)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__less__imp__less__right,axiom,
% 187.79/187.87 ! [V_b,V_c,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__left__less__imp__less,axiom,
% 187.79/187.87 ! [V_b,V_a,V_c,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring(T_a)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__less__imp__less__left,axiom,
% 187.79/187.87 ! [V_b,V_a,V_c,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__right__le__imp__le,axiom,
% 187.79/187.87 ! [V_b,V_c,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__left__le__imp__le,axiom,
% 187.79/187.87 ! [V_b,V_a,V_c,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__eq__if,axiom,
% 187.79/187.87 ! [V_n,V_m] :
% 187.79/187.87 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.79/187.87 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.87 => 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)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__left__le__one__le,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 187.79/187.87 => 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)) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__right__le__one__le,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 187.79/187.87 => 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)) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_zero__less__two,axiom,
% 187.79/187.87 ! [T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.87 => 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)))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_card__eq__0__iff,axiom,
% 187.79/187.87 ! [V_A_2,T_b] :
% 187.79/187.87 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.87 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_card__ge__0__finite,axiom,
% 187.79/187.87 ! [V_A_2,T_b] :
% 187.79/187.87 ( 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)))
% 187.79/187.87 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Suc__pred,axiom,
% 187.79/187.87 ! [V_n] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.87 => 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 ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_diff__Suc__less,axiom,
% 187.79/187.87 ! [V_i,V_n] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_one__less__mult,axiom,
% 187.79/187.87 ! [V_m,V_n] :
% 187.79/187.87 ( 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))
% 187.79/187.87 => ( 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))
% 187.79/187.87 => 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))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_n__less__n__mult__m,axiom,
% 187.79/187.87 ! [V_m,V_n] :
% 187.79/187.87 ( 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))
% 187.79/187.87 => ( 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))
% 187.79/187.87 => 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))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_n__less__m__mult__n,axiom,
% 187.79/187.87 ! [V_m,V_n] :
% 187.79/187.87 ( 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))
% 187.79/187.87 => ( 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))
% 187.79/187.87 => 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))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_nat__diff__split__asm,axiom,
% 187.79/187.87 ! [V_b_2,V_a_2,V_Pa_2] :
% 187.79/187.87 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 187.79/187.87 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 187.79/187.87 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 187.79/187.87 | ? [B_d] :
% 187.79/187.87 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 187.79/187.87 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_nat__diff__split,axiom,
% 187.79/187.87 ! [V_b_2,V_a_2,V_Pa_2] :
% 187.79/187.87 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 187.79/187.87 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 187.79/187.87 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 187.79/187.87 & ! [B_d] :
% 187.79/187.87 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 187.79/187.87 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_one__le__mult__iff,axiom,
% 187.79/187.87 ! [V_n_2,V_m_2] :
% 187.79/187.87 ( 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)))
% 187.79/187.87 <=> ( 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))
% 187.79/187.87 & 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)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__le__cancel2,axiom,
% 187.79/187.87 ! [V_n_2,V_k_2,V_m_2] :
% 187.79/187.87 ( 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)))
% 187.79/187.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_mult__le__cancel1,axiom,
% 187.79/187.87 ! [V_n_2,V_m_2,V_k_2] :
% 187.79/187.87 ( 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)))
% 187.79/187.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_nat__mult__le__cancel1,axiom,
% 187.79/187.87 ! [V_n_2,V_m_2,V_k_2] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min__le,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.87 => 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)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max__ge,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max__in,axiom,
% 187.79/187.87 ! [V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min__in,axiom,
% 187.79/187.87 ! [V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_card__less__Suc2,axiom,
% 187.79/187.87 ! [V_i_2,V_M_2] :
% 187.79/187.87 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 187.79/187.87 => 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))))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_card__less,axiom,
% 187.79/187.87 ! [V_i_2,V_M_2] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_card__less__Suc,axiom,
% 187.79/187.87 ! [V_i_2,V_M_2] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 187.79/187.87 => 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))))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_convex__bound__le,axiom,
% 187.79/187.87 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__1(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 187.79/187.87 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 187.79/187.87 => 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)) ) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_card__gt__0__iff,axiom,
% 187.79/187.87 ! [V_A_2,T_b] :
% 187.79/187.87 ( 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)))
% 187.79/187.87 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_finite__UNIV__card__ge__0,axiom,
% 187.79/187.87 ! [T_b] :
% 187.79/187.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 187.79/187.87 => 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))))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Suc__diff__1,axiom,
% 187.79/187.87 ! [V_n] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.87 => 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 ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min__antimono,axiom,
% 187.79/187.87 ! [V_N_2,V_M_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 187.79/187.87 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 187.79/187.87 => 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))) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max__mono,axiom,
% 187.79/187.87 ! [V_N_2,V_M_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 187.79/187.87 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 187.79/187.87 => 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))) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_card__def,axiom,
% 187.79/187.87 ! [V_A_2,T_b] :
% 187.79/187.87 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => 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) )
% 187.79/187.87 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_card_Oeq__fold__g,axiom,
% 187.79/187.87 ! [V_A_2,T_b] :
% 187.79/187.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_convex__bound__lt,axiom,
% 187.79/187.87 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 187.79/187.87 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 187.79/187.87 => 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)) ) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_triple_Osize_I1_J,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_even__less__0__iff,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_triple_Osize_I2_J,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_card_Ounion__inter__neutral,axiom,
% 187.79/187.87 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.87 => ( ( ? [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)))
% 187.79/187.87 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.79/187.87 => 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)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_card__Suc__eq,axiom,
% 187.79/187.87 ! [V_k_2,V_A_2,T_b] :
% 187.79/187.87 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 187.79/187.87 <=> ? [B_b,B_B] :
% 187.79/187.87 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 187.79/187.87 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 187.79/187.87 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 187.79/187.87 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.87 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_option_Osize_I2_J,axiom,
% 187.79/187.87 ! [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))) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_com_Osize_I4_J,axiom,
% 187.79/187.87 ! [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))) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_option_Osize_I1_J,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_com_Osize_I2_J,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_com_Osize_I1_J,axiom,
% 187.79/187.87 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_com_Osize_I6_J,axiom,
% 187.79/187.87 ! [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))) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_double__eq__0__iff,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Groups_Olinordered__ab__group__add(T_b)
% 187.79/187.87 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.87 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_com_Osize_I5_J,axiom,
% 187.79/187.87 ! [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))) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_nat_Osize_I2_J,axiom,
% 187.79/187.87 ! [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))) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_nat_Osize_I4_J,axiom,
% 187.79/187.87 ! [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))) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_option_Osize_I4_J,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_option_Osize_I3_J,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Ints__odd__less__0,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_card__Plus__conv__if,axiom,
% 187.79/187.87 ! [V_B_2,T_c,V_A_2,T_b] :
% 187.79/187.87 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 187.79/187.87 => 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)) )
% 187.79/187.87 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 187.79/187.87 => 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) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_nat__size,axiom,
% 187.79/187.87 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Ints__0,axiom,
% 187.79/187.87 ! [T_b] :
% 187.79/187.87 ( class_Rings_Oring__1(T_b)
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Ints__add,axiom,
% 187.79/187.87 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.87 ( class_Rings_Oring__1(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Ints__mult,axiom,
% 187.79/187.87 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.87 ( class_Rings_Oring__1(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_nat_Osize_I3_J,axiom,
% 187.79/187.87 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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Ints__diff,axiom,
% 187.79/187.87 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.87 ( class_Rings_Oring__1(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Ints__1,axiom,
% 187.79/187.87 ! [T_b] :
% 187.79/187.87 ( class_Rings_Oring__1(T_b)
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Ints__minus,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Rings_Oring__1(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 187.79/187.87 => 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))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_nat_Osize_I1_J,axiom,
% 187.79/187.87 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Ints__double__eq__0__iff,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Int_Oring__char__0(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 187.79/187.87 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.87 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_finite__Plus__iff,axiom,
% 187.79/187.87 ! [V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.87 ( 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)))
% 187.79/187.87 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_finite__Plus,axiom,
% 187.79/187.87 ! [V_B_2,T_c,V_A_2,T_b] :
% 187.79/187.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 187.79/187.87 => 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))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_finite__PlusD_I1_J,axiom,
% 187.79/187.87 ! [V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.87 ( 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)))
% 187.79/187.87 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_finite__PlusD_I2_J,axiom,
% 187.79/187.87 ! [V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.87 ( 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)))
% 187.79/187.87 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_card__Plus,axiom,
% 187.79/187.87 ! [V_B_2,T_c,V_A_2,T_b] :
% 187.79/187.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 187.79/187.87 => 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)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Ints__odd__nonzero,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Int_Oring__char__0(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 187.79/187.87 => 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) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_UNIV__Plus__UNIV,axiom,
% 187.79/187.87 ! [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)) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Plus__eq__empty__conv,axiom,
% 187.79/187.87 ! [V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.87 ( 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))
% 187.79/187.87 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_com_Osize_I12_J,axiom,
% 187.79/187.87 ! [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))) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_com_Osize_I13_J,axiom,
% 187.79/187.87 ! [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))) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_com_Osize_I14_J,axiom,
% 187.79/187.87 ! [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))) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_ex__least__nat__less,axiom,
% 187.79/187.87 ! [V_n_2,V_Pa_2] :
% 187.79/187.87 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 187.79/187.87 => ( hBOOL(hAPP(V_Pa_2,V_n_2))
% 187.79/187.87 => ? [B_k] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 187.79/187.87 & ! [B_i] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 187.79/187.87 => ~ hBOOL(hAPP(V_Pa_2,B_i)) )
% 187.79/187.87 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_com_Osize_I10_J,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_com_Osize_I9_J,axiom,
% 187.79/187.87 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_sgn__neg,axiom,
% 187.79/187.87 ! [V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.87 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_sgn__1__neg,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.87 => ( 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))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_sgn__if,axiom,
% 187.79/187.87 ! [V_x,T_a] :
% 187.79/187.87 ( class_Groups_Osgn__if(T_a)
% 187.79/187.87 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.87 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 187.79/187.87 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.87 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.79/187.87 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 187.79/187.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.79/187.87 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min_Oremove,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.87 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.87 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 187.79/187.87 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.87 => 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)))))) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max_Oremove,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.87 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.87 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 187.79/187.87 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.87 => 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)))))) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_diff__Suc,axiom,
% 187.79/187.87 ! [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)) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_max__Suc2,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_max__Suc1,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_minus__min__eq__max,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Groups_Olinordered__ab__group__add(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_minus__max__eq__min,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Groups_Olinordered__ab__group__add(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup_Oidem,axiom,
% 187.79/187.87 ! [V_a,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf_Oidem,axiom,
% 187.79/187.87 ! [V_a,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup_Ocommute,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup__commute,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf_Ocommute,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf__commute,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup__inf__absorb,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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 ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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 ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup__left__idem,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf__left__idem,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 187.79/187.87 ! [V_c,V_a,V_b,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup__left__commute,axiom,
% 187.79/187.87 ! [V_z,V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 187.79/187.87 ! [V_c,V_a,V_b,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf__left__commute,axiom,
% 187.79/187.87 ! [V_z,V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 187.79/187.87 ! [V_z,V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 187.79/187.87 ! [V_z,V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup_Oassoc,axiom,
% 187.79/187.87 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup__assoc,axiom,
% 187.79/187.87 ! [V_z,V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf_Oassoc,axiom,
% 187.79/187.87 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf__assoc,axiom,
% 187.79/187.87 ! [V_z,V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 187.79/187.87 ! [V_x,V_z,V_y,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 187.79/187.87 ! [V_x,V_z,V_y,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max_Oidem,axiom,
% 187.79/187.87 ! [V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min_Oidem,axiom,
% 187.79/187.87 ! [V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_sgn__sgn,axiom,
% 187.79/187.87 ! [V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Odistrib__inf__le,axiom,
% 187.79/187.87 ! [V_z,V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Odistrib__sup__le,axiom,
% 187.79/187.87 ! [V_z,V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_le__maxI1,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_le__maxI2,axiom,
% 187.79/187.87 ! [V_x,V_y,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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))) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ole__iff__sup,axiom,
% 187.79/187.87 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.79/187.87 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ole__sup__iff,axiom,
% 187.79/187.87 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( 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))
% 187.79/187.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 187.79/187.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ole__supI1,axiom,
% 187.79/187.87 ! [V_b,V_a,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 187.79/187.87 => 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))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ole__supI2,axiom,
% 187.79/187.87 ! [V_a,V_b,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 187.79/187.87 => 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))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup__absorb2,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.79/187.87 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup__absorb1,axiom,
% 187.79/187.87 ! [V_x,V_y,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.79/187.87 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ole__supI,axiom,
% 187.79/187.87 ! [V_b,V_x,V_a,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 187.79/187.87 => 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)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup__least,axiom,
% 187.79/187.87 ! [V_z,V_x,V_y,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 187.79/187.87 => 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)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Osup__mono,axiom,
% 187.79/187.87 ! [V_d,V_b,V_c,V_a,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ole__supE,axiom,
% 187.79/187.87 ! [V_x,V_b,V_a,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( 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))
% 187.79/187.87 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 187.79/187.87 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_le__max__iff__disj,axiom,
% 187.79/187.87 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 187.79/187.87 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf__le1,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf__le2,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ole__iff__inf,axiom,
% 187.79/187.87 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.79/187.87 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ole__inf__iff,axiom,
% 187.79/187.87 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.79/187.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ole__infI1,axiom,
% 187.79/187.87 ! [V_b,V_x,V_a,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 187.79/187.87 => 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)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ole__infI2,axiom,
% 187.79/187.87 ! [V_a,V_x,V_b,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 187.79/187.87 => 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)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf__absorb1,axiom,
% 187.79/187.87 ! [V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.79/187.87 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf__absorb2,axiom,
% 187.79/187.87 ! [V_x,V_y,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.79/187.87 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ole__infI,axiom,
% 187.79/187.87 ! [V_b,V_a,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf__greatest,axiom,
% 187.79/187.87 ! [V_z,V_y,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oinf__mono,axiom,
% 187.79/187.87 ! [V_d,V_b,V_c,V_a,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 187.79/187.87 => 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))) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ole__infE,axiom,
% 187.79/187.87 ! [V_b,V_a,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 187.79/187.87 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__le__iff__disj,axiom,
% 187.79/187.87 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( 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))
% 187.79/187.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 187.79/187.87 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oless__supI1,axiom,
% 187.79/187.87 ! [V_b,V_a,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 187.79/187.87 => 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))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oless__supI2,axiom,
% 187.79/187.87 ! [V_a,V_b,V_x,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 187.79/187.87 => 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))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_less__max__iff__disj,axiom,
% 187.79/187.87 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 187.79/187.87 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_max__less__iff__conj,axiom,
% 187.79/187.87 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( 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))
% 187.79/187.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 187.79/187.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oless__infI1,axiom,
% 187.79/187.87 ! [V_b,V_x,V_a,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 187.79/187.87 => 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)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Oless__infI2,axiom,
% 187.79/187.87 ! [V_a,V_x,V_b,T_a] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 187.79/187.87 => 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)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__less__iff__conj,axiom,
% 187.79/187.87 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 187.79/187.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__less__iff__disj,axiom,
% 187.79/187.87 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( 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))
% 187.79/187.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 187.79/187.87 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_max__add__distrib__left,axiom,
% 187.79/187.87 ! [V_z,V_y,V_x,T_a] :
% 187.79/187.87 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__add__distrib__left,axiom,
% 187.79/187.87 ! [V_z,V_y,V_x,T_a] :
% 187.79/187.87 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_max__diff__distrib__left,axiom,
% 187.79/187.87 ! [V_z,V_y,V_x,T_a] :
% 187.79/187.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__diff__distrib__left,axiom,
% 187.79/187.87 ! [V_z,V_y,V_x,T_a] :
% 187.79/187.87 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_sup__max,axiom,
% 187.79/187.87 ! [T_b] :
% 187.79/187.87 ( ( class_Lattices_Osemilattice__sup(T_b)
% 187.79/187.87 & class_Orderings_Olinorder(T_b) )
% 187.79/187.87 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_max__0L,axiom,
% 187.79/187.87 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 187.79/187.87
% 187.79/187.87 fof(fact_max__0R,axiom,
% 187.79/187.87 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 187.79/187.87
% 187.79/187.87 fof(fact_inf__min,axiom,
% 187.79/187.87 ! [T_b] :
% 187.79/187.87 ( ( class_Lattices_Osemilattice__inf(T_b)
% 187.79/187.87 & class_Orderings_Olinorder(T_b) )
% 187.79/187.87 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__0L,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__0R,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_max__Suc__Suc,axiom,
% 187.79/187.87 ! [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)) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__Suc__Suc,axiom,
% 187.79/187.87 ! [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)) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__diff,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 187.79/187.87 ! [T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 187.79/187.87 ! [T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__Suc2,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__Suc1,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_sgn0,axiom,
% 187.79/187.87 ! [T_a] :
% 187.79/187.87 ( class_Groups_Osgn__if(T_a)
% 187.79/187.87 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_sgn__0__0,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.87 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.87 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_sgn__times,axiom,
% 187.79/187.87 ! [V_b,V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.87 => 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)) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_nat__minus__add__max,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_nat__case__0,axiom,
% 187.79/187.87 ! [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 ).
% 187.79/187.87
% 187.79/187.87 fof(fact_nat__case__Suc,axiom,
% 187.79/187.87 ! [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) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max_Oin__idem,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.87 => 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) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min_Oin__idem,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.87 => 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) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_sgn__less,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_sgn__greater,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max_OF__eq,axiom,
% 187.79/187.87 ! [V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => 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) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min_OF__eq,axiom,
% 187.79/187.87 ! [V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => 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) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Ofold1__belowI,axiom,
% 187.79/187.87 ! [V_a_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.87 => 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)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> ! [B_x] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_fold1__below__iff,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( 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))
% 187.79/187.87 <=> ? [B_x] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_strict__below__fold1__iff,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( 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)))
% 187.79/187.87 <=> ! [B_x] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_fold1__strict__below__iff,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( 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))
% 187.79/187.87 <=> ? [B_x] :
% 187.79/187.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max__insert,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => 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)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min__insert,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => 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)) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max_Osubset__idem,axiom,
% 187.79/187.87 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.79/187.87 => 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) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min_Osubset__idem,axiom,
% 187.79/187.87 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.79/187.87 => 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) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max__Un,axiom,
% 187.79/187.87 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.87 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => 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)) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min__Un,axiom,
% 187.79/187.87 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.87 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => 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)) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_sgn__pos,axiom,
% 187.79/187.87 ! [V_a,T_a] :
% 187.79/187.87 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.87 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_sgn__1__pos,axiom,
% 187.79/187.87 ! [V_a_2,T_b] :
% 187.79/187.87 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.87 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 187.79/187.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max_Oinsert,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => 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)) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min_Oinsert,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => 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)) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_fold1__antimono,axiom,
% 187.79/187.87 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.87 => 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))) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max_Oinsert__remove,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.87 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 187.79/187.87 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.87 => 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)))))) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max_Ounion__disjoint,axiom,
% 187.79/187.87 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.87 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( 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))
% 187.79/187.87 => 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)) ) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Max_Ounion__inter,axiom,
% 187.79/187.87 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.87 => ( 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))
% 187.79/187.87 => 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)) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min_Oinsert__remove,axiom,
% 187.79/187.87 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.87 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 187.79/187.87 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.87 => 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)))))) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min_Ounion__disjoint,axiom,
% 187.79/187.87 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.87 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.87 => ( 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))
% 187.79/187.87 => 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)) ) ) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_Min_Ounion__inter,axiom,
% 187.79/187.87 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.87 => ( 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))
% 187.79/187.87 => 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)) ) ) ) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_dual__min,axiom,
% 187.79/187.87 ! [T_b] :
% 187.79/187.87 ( class_Orderings_Olinorder(T_b)
% 187.79/187.87 => 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) ) ).
% 187.79/187.87
% 187.79/187.87 fof(fact_dual__max,axiom,
% 187.79/187.88 ! [T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => 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) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_max__ord__max,axiom,
% 187.79/187.88 ! [T_b] :
% 187.79/187.88 ( class_Orderings_Oord(T_b)
% 187.79/187.88 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__ord__min,axiom,
% 187.79/187.88 ! [T_b] :
% 187.79/187.88 ( class_Orderings_Oord(T_b)
% 187.79/187.88 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 187.79/187.88 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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))))) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 187.79/187.88 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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))))) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_inf__nat__def,axiom,
% 187.79/187.88 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_sup__nat__def,axiom,
% 187.79/187.88 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OInf__le__Sup,axiom,
% 187.79/187.88 ! [V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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))) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 187.79/187.88 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.88 => 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) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 187.79/187.88 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.88 => 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) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 187.79/187.88 ! [V_x_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => 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 ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 187.79/187.88 ! [V_x_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => 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 ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 187.79/187.88 ! [V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => 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) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 187.79/187.88 ! [V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => 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) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 187.79/187.88 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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)) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 187.79/187.88 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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)) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 187.79/187.88 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.79/187.88 => 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) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 187.79/187.88 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.79/187.88 => 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) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 187.79/187.88 ! [V_a_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.88 => 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 ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 187.79/187.88 ! [V_a_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.88 => 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 ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 187.79/187.88 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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)) ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 187.79/187.88 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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)) ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 187.79/187.88 ! [V_n_2,V_m_2] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 187.79/187.88 <=> 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 187.79/187.88 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 187.79/187.88 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 187.79/187.88 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.88 => 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 )
% 187.79/187.88 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.88 => 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)))))) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 187.79/187.88 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.88 => 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 )
% 187.79/187.88 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.88 => 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)))))) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 187.79/187.88 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => ( 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))
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 187.79/187.88 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => ( 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))
% 187.79/187.88 => 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)) ) ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 187.79/187.88 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => ( 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))
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 187.79/187.88 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => ( 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))
% 187.79/187.88 => 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)) ) ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 187.79/187.88 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.88 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.88 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 187.79/187.88 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.88 => 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)))))) ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 187.79/187.88 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.88 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.88 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 187.79/187.88 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 187.79/187.88 => 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)))))) ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 187.79/187.88 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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))))))) ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 187.79/187.88 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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))))))) ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 187.79/187.88 ! [V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => ( ! [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))))))
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 187.79/187.88 ! [V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => ( ! [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))))))
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_Max_Oclosed,axiom,
% 187.79/187.88 ! [V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => ( ! [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))))))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_Min_Oclosed,axiom,
% 187.79/187.88 ! [V_A_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => ( ! [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))))))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 187.79/187.88 ! [V_N_2,V_h_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( ! [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))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 187.79/187.88 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 187.79/187.88 ! [V_N_2,V_h_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( ! [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))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 187.79/187.88 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_Max_Ohom__commute,axiom,
% 187.79/187.88 ! [V_N_2,V_h_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( ! [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))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 187.79/187.88 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_Min_Ohom__commute,axiom,
% 187.79/187.88 ! [V_N_2,V_h_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( ! [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))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 187.79/187.88 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_pigeonhole__infinite,axiom,
% 187.79/187.88 ! [V_f_2,T_c,V_A_2,T_b] :
% 187.79/187.88 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 187.79/187.88 => ? [B_x] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.88 & ~ 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)))))) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_finite__range__map__of__map__add,axiom,
% 187.79/187.88 ! [V_l_2,V_f_2,T_c,T_b] :
% 187.79/187.88 ( 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)))))
% 187.79/187.88 => 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))))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_inj__on__diff__nat,axiom,
% 187.79/187.88 ! [V_k_2,V_N_2] :
% 187.79/187.88 ( ! [B_x] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 187.79/187.88 => 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) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__diff1,axiom,
% 187.79/187.88 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Oab__group__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.88 => 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)) )
% 187.79/187.88 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.88 => 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) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__commute,axiom,
% 187.79/187.88 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => 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) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__0,axiom,
% 187.79/187.88 ! [V_A_2,T_c,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => 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) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__addf,axiom,
% 187.79/187.88 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__product,axiom,
% 187.79/187.88 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.88 ( class_Rings_Osemiring__0(T_b)
% 187.79/187.88 => 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) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__left__distrib,axiom,
% 187.79/187.88 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.88 ( class_Rings_Osemiring__0(T_b)
% 187.79/187.88 => 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) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__right__distrib,axiom,
% 187.79/187.88 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 187.79/187.88 ( class_Rings_Osemiring__0(T_b)
% 187.79/187.88 => 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) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__subtractf,axiom,
% 187.79/187.88 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 187.79/187.88 ( class_Groups_Oab__group__add(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__negf,axiom,
% 187.79/187.88 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.88 ( class_Groups_Oab__group__add(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__empty,axiom,
% 187.79/187.88 ! [V_f_2,T_c,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => 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) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum_Oempty,axiom,
% 187.79/187.88 ! [V_g_2,T_c,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => 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) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__infinite,axiom,
% 187.79/187.88 ! [V_f_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => 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) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum_Oinfinite,axiom,
% 187.79/187.88 ! [V_g_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => 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) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__eq__0__iff,axiom,
% 187.79/187.88 ! [V_f_2,V_F_2,T_b] :
% 187.79/187.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 187.79/187.88 => ( 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)
% 187.79/187.88 <=> ! [B_x] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 187.79/187.88 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum_Odistrib,axiom,
% 187.79/187.88 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => 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)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_finite__dom__map__of,axiom,
% 187.79/187.88 ! [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)))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_card__eq__setsum,axiom,
% 187.79/187.88 ! [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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__eq__Suc0__iff,axiom,
% 187.79/187.88 ! [V_f_2,V_A_2,T_b] :
% 187.79/187.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( 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))
% 187.79/187.88 <=> ? [B_x] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.88 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 187.79/187.88 & ! [B_xa] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 187.79/187.88 => ( B_x != B_xa
% 187.79/187.88 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__reindex,axiom,
% 187.79/187.88 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_d)
% 187.79/187.88 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 187.79/187.88 => 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) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__eq__1__iff,axiom,
% 187.79/187.88 ! [V_f_2,V_A_2,T_b] :
% 187.79/187.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( 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)
% 187.79/187.88 <=> ? [B_x] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.88 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 187.79/187.88 & ! [B_xa] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 187.79/187.88 => ( B_x != B_xa
% 187.79/187.88 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__delta_H,axiom,
% 187.79/187.88 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.88 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 187.79/187.88 => 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) )
% 187.79/187.88 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 187.79/187.88 => 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) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__delta,axiom,
% 187.79/187.88 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.88 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 187.79/187.88 => 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) )
% 187.79/187.88 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 187.79/187.88 => 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) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__setsum__restrict,axiom,
% 187.79/187.88 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_d)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 187.79/187.88 => 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) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum_Oinsert,axiom,
% 187.79/187.88 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.88 => 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)) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__insert,axiom,
% 187.79/187.88 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 187.79/187.88 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 187.79/187.88 => 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)) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__Un__Int,axiom,
% 187.79/187.88 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => 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)) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__diff,axiom,
% 187.79/187.88 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Oab__group__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.79/187.88 => 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)) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum_Oreindex,axiom,
% 187.79/187.88 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 187.79/187.88 => 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) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum_OF__eq,axiom,
% 187.79/187.88 ! [V_g_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => 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) )
% 187.79/187.88 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => 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) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum_Oeq__fold,axiom,
% 187.79/187.88 ! [V_g_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => 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) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__diff__nat,axiom,
% 187.79/187.88 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 187.79/187.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.79/187.88 => 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)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__restrict__set_H,axiom,
% 187.79/187.88 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => 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) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__restrict__set,axiom,
% 187.79/187.88 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => 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) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__image__gen,axiom,
% 187.79/187.88 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.88 => 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)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_finite__range__map__of,axiom,
% 187.79/187.88 ! [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))))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum_Oinsert__remove,axiom,
% 187.79/187.88 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => 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)))))) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__Un__disjoint,axiom,
% 187.79/187.88 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => ( 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))
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__Un,axiom,
% 187.79/187.88 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Oab__group__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => 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))) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__diff1__nat,axiom,
% 187.79/187.88 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 187.79/187.88 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.88 => 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)) )
% 187.79/187.88 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.88 => 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) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__Un__nat,axiom,
% 187.79/187.88 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 187.79/187.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => 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))) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__cases,axiom,
% 187.79/187.88 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_Pa_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))))) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum_Oremove,axiom,
% 187.79/187.88 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.88 => 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)))))) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__diff1_H,axiom,
% 187.79/187.88 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.88 => 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)))))) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__diff1__ring,axiom,
% 187.79/187.88 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Rings_Oring(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.88 => 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)) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__mono2,axiom,
% 187.79/187.88 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.88 => ( ! [B_b] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 187.79/187.88 => 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))) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_arith__series__nat,axiom,
% 187.79/187.88 ! [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)))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 187.79/187.88 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => ( ! [B_x] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__Un__zero,axiom,
% 187.79/187.88 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 187.79/187.88 => ( ! [B_x] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__mono3,axiom,
% 187.79/187.88 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 187.79/187.88 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.88 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.88 => ( ! [B_x] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 187.79/187.88 => 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))) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__reindex__nonzero,axiom,
% 187.79/187.88 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_d)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.88 => ( ! [B_x] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 187.79/187.88 => ! [B_y] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 187.79/187.88 => ( B_x != B_y
% 187.79/187.88 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 187.79/187.88 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 187.79/187.88 => 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) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_finite__lessThan,axiom,
% 187.79/187.88 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_lessThan__eq__iff,axiom,
% 187.79/187.88 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 187.79/187.88 <=> V_x_2 = V_y_2 ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_lessThan__0,axiom,
% 187.79/187.88 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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_lessThan__Suc,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_card__lessThan,axiom,
% 187.79/187.88 ! [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 ).
% 187.79/187.88
% 187.79/187.88 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 187.79/187.88 ! [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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__lessThan__Suc,axiom,
% 187.79/187.88 ! [V_n_2,V_f_2,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_lessThan__iff,axiom,
% 187.79/187.88 ! [V_k_2,V_i_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oord(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_lessThan__subset__iff,axiom,
% 187.79/187.88 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( 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)))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_lessThan__strict__subset__iff,axiom,
% 187.79/187.88 ! [V_n_2,V_m_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( 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)))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_single__Diff__lessThan,axiom,
% 187.79/187.88 ! [V_k_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__multicount,axiom,
% 187.79/187.88 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 187.79/187.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 187.79/187.88 => ( ! [B_x] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 187.79/187.88 => 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 )
% 187.79/187.88 => 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)) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_arith__series__general,axiom,
% 187.79/187.88 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Rings_Ocomm__semiring__1(T_b)
% 187.79/187.88 => 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)))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__multicount__gen,axiom,
% 187.79/187.88 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 187.79/187.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 187.79/187.88 => ( ! [B_x] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 187.79/187.88 => 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) )
% 187.79/187.88 => 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) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__nonneg__0,axiom,
% 187.79/187.88 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Oordered__ab__group__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 187.79/187.88 => ( ! [B_i] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 187.79/187.88 => ( 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)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 187.79/187.88 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__nonneg__leq__bound,axiom,
% 187.79/187.88 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 187.79/187.88 ( class_Groups_Oordered__ab__group__add(T_c)
% 187.79/187.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 187.79/187.88 => ( ! [B_i] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 187.79/187.88 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_sum__diff__distrib,axiom,
% 187.79/187.88 ! [V_n_2,V_Pa_2,V_Qa_2] :
% 187.79/187.88 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Qa_2,B_x)),hAPP(V_Pa_2,B_x)))
% 187.79/187.88 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Pa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Qa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_Pa_2)),V_Qa_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_negative__zless,axiom,
% 187.79/187.88 ! [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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__eq__iff,axiom,
% 187.79/187.88 ! [V_n_2,V_m_2,T_b] :
% 187.79/187.88 ( class_Nat_Osemiring__char__0(T_b)
% 187.79/187.88 => ( 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)
% 187.79/187.88 <=> V_m_2 = V_n_2 ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_negative__eq__positive,axiom,
% 187.79/187.88 ! [V_m_2,V_n_2] :
% 187.79/187.88 ( 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)
% 187.79/187.88 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.88 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_int__eq__0__conv,axiom,
% 187.79/187.88 ! [V_n_2] :
% 187.79/187.88 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.88 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_int__0,axiom,
% 187.79/187.88 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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_int__le__0__conv,axiom,
% 187.79/187.88 ! [V_n_2] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_int__zle__neg,axiom,
% 187.79/187.88 ! [V_m_2,V_n_2] :
% 187.79/187.88 ( 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))))
% 187.79/187.88 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.88 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_not__zle__0__negative,axiom,
% 187.79/187.88 ! [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))))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_negative__zless__0,axiom,
% 187.79/187.88 ! [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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zless__iff__Suc__zadd,axiom,
% 187.79/187.88 ! [V_z_2,V_w_2] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 187.79/187.88 <=> ? [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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_int__Suc,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zless__int,axiom,
% 187.79/187.88 ! [V_n_2,V_m_2] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zadd__int,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zadd__int__left,axiom,
% 187.79/187.88 ! [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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zle__int,axiom,
% 187.79/187.88 ! [V_n_2,V_m_2] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_int__mult,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zmult__int,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_int__1,axiom,
% 187.79/187.88 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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_inj__int,axiom,
% 187.79/187.88 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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_int__setsum,axiom,
% 187.79/187.88 ! [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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_int__Suc0__eq__1,axiom,
% 187.79/187.88 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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zero__less__int__conv,axiom,
% 187.79/187.88 ! [V_n_2] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zmult__zless__mono2__lemma,axiom,
% 187.79/187.88 ! [V_k,V_j,V_i] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 187.79/187.88 => 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))) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zero__le__imp__of__nat,axiom,
% 187.79/187.88 ! [V_m,T_a] :
% 187.79/187.88 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.88 => 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__0__le__iff,axiom,
% 187.79/187.88 ! [V_n,T_a] :
% 187.79/187.88 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.88 => 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zdiff__int,axiom,
% 187.79/187.88 ! [V_m,V_n] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__less__0__iff,axiom,
% 187.79/187.88 ! [V_m,T_a] :
% 187.79/187.88 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.88 => ~ 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__0,axiom,
% 187.79/187.88 ! [T_a] :
% 187.79/187.88 ( class_Rings_Osemiring__1(T_a)
% 187.79/187.88 => 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) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__less__imp__less,axiom,
% 187.79/187.88 ! [V_n,V_m,T_a] :
% 187.79/187.88 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.88 => ( 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)))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_less__imp__of__nat__less,axiom,
% 187.79/187.88 ! [V_n,V_m,T_a] :
% 187.79/187.88 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.88 => 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))) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__less__iff,axiom,
% 187.79/187.88 ! [V_n_2,V_m_2,T_b] :
% 187.79/187.88 ( class_Rings_Olinordered__semidom(T_b)
% 187.79/187.88 => ( 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)))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__le__iff,axiom,
% 187.79/187.88 ! [V_n_2,V_m_2,T_b] :
% 187.79/187.88 ( class_Rings_Olinordered__semidom(T_b)
% 187.79/187.88 => ( 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)))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__add,axiom,
% 187.79/187.88 ! [V_n,V_m,T_a] :
% 187.79/187.88 ( class_Rings_Osemiring__1(T_a)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__mult,axiom,
% 187.79/187.88 ! [V_n,V_m,T_a] :
% 187.79/187.88 ( class_Rings_Osemiring__1(T_a)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__1,axiom,
% 187.79/187.88 ! [T_a] :
% 187.79/187.88 ( class_Rings_Osemiring__1(T_a)
% 187.79/187.88 => 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) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_Ints__of__nat,axiom,
% 187.79/187.88 ! [V_n_2,T_b] :
% 187.79/187.88 ( class_Rings_Oring__1(T_b)
% 187.79/187.88 => 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__setsum,axiom,
% 187.79/187.88 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.88 ( class_Rings_Osemiring__1(T_b)
% 187.79/187.88 => 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) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_inj__of__nat,axiom,
% 187.79/187.88 ! [T_b] :
% 187.79/187.88 ( class_Nat_Osemiring__char__0(T_b)
% 187.79/187.88 => 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__Suc,axiom,
% 187.79/187.88 ! [V_m,T_a] :
% 187.79/187.88 ( class_Rings_Osemiring__1(T_a)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__diff,axiom,
% 187.79/187.88 ! [V_m,V_n,T_a] :
% 187.79/187.88 ( class_Rings_Oring__1(T_a)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.79/187.88 => 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)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__constant,axiom,
% 187.79/187.88 ! [V_A_2,V_y_2,T_c,T_b] :
% 187.79/187.88 ( class_Rings_Osemiring__1(T_b)
% 187.79/187.88 => 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) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__0__less__iff,axiom,
% 187.79/187.88 ! [V_n_2,T_b] :
% 187.79/187.88 ( class_Rings_Olinordered__semidom(T_b)
% 187.79/187.88 => ( 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)))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 187.79/187.88 ! [V_n_2,T_b] :
% 187.79/187.88 ( class_Rings_Osemiring__1(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zdiff__int__split,axiom,
% 187.79/187.88 ! [V_y_2,V_x_2,V_Pa_2] :
% 187.79/187.88 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
% 187.79/187.88 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 187.79/187.88 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) )
% 187.79/187.88 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 187.79/187.88 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__bounded,axiom,
% 187.79/187.88 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 187.79/187.88 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 187.79/187.88 & class_Rings_Osemiring__1(T_c) )
% 187.79/187.88 => ( ! [B_i] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 187.79/187.88 => 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))) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 187.79/187.88 ! [V_x_2,V_y_2,V_ca_2] :
% 187.79/187.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 187.79/187.88 => 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)) )
% 187.79/187.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 187.79/187.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 187.79/187.88 => 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))) )
% 187.79/187.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_greaterThan__0,axiom,
% 187.79/187.88 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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__natinterval__difff,axiom,
% 187.79/187.88 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 187.79/187.88 ( class_Groups_Oab__group__add(T_b)
% 187.79/187.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.88 => 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)))) )
% 187.79/187.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.88 => 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) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_finite__atLeastLessThan,axiom,
% 187.79/187.88 ! [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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_finite__atLeastAtMost,axiom,
% 187.79/187.88 ! [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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_negative__zle,axiom,
% 187.79/187.88 ! [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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zle__iff__zadd,axiom,
% 187.79/187.88 ! [V_z_2,V_w_2] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 187.79/187.88 <=> ? [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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_not__int__zless__negative,axiom,
% 187.79/187.88 ! [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)))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_int__int__eq,axiom,
% 187.79/187.88 ! [V_n_2,V_m_2] :
% 187.79/187.88 ( 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)
% 187.79/187.88 <=> V_m_2 = V_n_2 ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_negative__zle__0,axiom,
% 187.79/187.88 ! [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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zero__zle__int,axiom,
% 187.79/187.88 ! [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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_int__less__0__conv,axiom,
% 187.79/187.88 ! [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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_le__imp__0__less,axiom,
% 187.79/187.88 ! [V_z] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.79/187.88 => 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_odd__nonzero,axiom,
% 187.79/187.88 ! [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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_odd__less__0,axiom,
% 187.79/187.88 ! [V_z_2] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zadd__zminus__inverse2,axiom,
% 187.79/187.88 ! [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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zadd__0__right,axiom,
% 187.79/187.88 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zadd__0,axiom,
% 187.79/187.88 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zmult__zless__mono2,axiom,
% 187.79/187.88 ! [V_k,V_j,V_i] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 187.79/187.88 => 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))) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zminus__0,axiom,
% 187.79/187.88 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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_less__bin__lemma,axiom,
% 187.79/187.88 ! [V_l_2,V_k_2] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 187.79/187.88 <=> 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_pos__zmult__eq__1__iff,axiom,
% 187.79/187.88 ! [V_n_2,V_m_2] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 187.79/187.88 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 187.79/187.88 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 187.79/187.88 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_int__0__less__1,axiom,
% 187.79/187.88 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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_int__0__neq__1,axiom,
% 187.79/187.88 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_int__one__le__iff__zero__less,axiom,
% 187.79/187.88 ! [V_z_2] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zle__diff1__eq,axiom,
% 187.79/187.88 ! [V_z_2,V_w_2] :
% 187.79/187.88 ( 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))))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zmult__1,axiom,
% 187.79/187.88 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zmult__1__right,axiom,
% 187.79/187.88 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zless__le,axiom,
% 187.79/187.88 ! [V_w_2,V_z_2] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 187.79/187.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 187.79/187.88 & V_z_2 != V_w_2 ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zle__antisym,axiom,
% 187.79/187.88 ! [V_w,V_z] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 187.79/187.88 => V_z = V_w ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zle__trans,axiom,
% 187.79/187.88 ! [V_k,V_j,V_i] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zle__linear,axiom,
% 187.79/187.88 ! [V_w,V_z] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 187.79/187.88 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zle__refl,axiom,
% 187.79/187.88 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zminus__zminus,axiom,
% 187.79/187.88 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zless__linear,axiom,
% 187.79/187.88 ! [V_y,V_x] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 187.79/187.88 | V_x = V_y
% 187.79/187.88 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zmult__zminus,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zmult__commute,axiom,
% 187.79/187.88 ! [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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zmult__assoc,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zdiff__zmult__distrib,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zdiff__zmult__distrib2,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_diff__int__def__symmetric,axiom,
% 187.79/187.88 ! [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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_diff__int__def,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zadd__zless__mono,axiom,
% 187.79/187.88 ! [V_z,V_z_H,V_w,V_w_H] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 187.79/187.88 => 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))) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zadd__left__mono,axiom,
% 187.79/187.88 ! [V_k,V_j,V_i] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 187.79/187.88 => 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zadd__commute,axiom,
% 187.79/187.88 ! [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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zadd__left__commute,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zadd__assoc,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zminus__zadd__distrib,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zadd__strict__right__mono,axiom,
% 187.79/187.88 ! [V_k,V_j,V_i] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 187.79/187.88 => 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zadd__zmult__distrib2,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zadd__zmult__distrib,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zless__add1__eq,axiom,
% 187.79/187.88 ! [V_z_2,V_w_2] :
% 187.79/187.88 ( 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))))
% 187.79/187.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 187.79/187.88 | V_w_2 = V_z_2 ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zle__add1__eq__le,axiom,
% 187.79/187.88 ! [V_z_2,V_w_2] :
% 187.79/187.88 ( 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))))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_add1__zle__eq,axiom,
% 187.79/187.88 ! [V_z_2,V_w_2] :
% 187.79/187.88 ( 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))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zless__imp__add1__zle,axiom,
% 187.79/187.88 ! [V_z,V_w] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_greaterThan__eq__iff,axiom,
% 187.79/187.88 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 187.79/187.88 <=> V_x_2 = V_y_2 ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 187.79/187.88 ! [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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zsgn__def,axiom,
% 187.79/187.88 ! [V_i] :
% 187.79/187.88 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.88 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 187.79/187.88 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 187.79/187.88 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 187.79/187.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 187.79/187.88 => 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)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_ivl__disj__un_I21_J,axiom,
% 187.79/187.88 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 187.79/187.88 => 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) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_ivl__disj__int_I15_J,axiom,
% 187.79/187.88 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_ivl__disj__int_I7_J,axiom,
% 187.79/187.88 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastLessThan__eq__iff,axiom,
% 187.79/187.88 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 187.79/187.88 => ( 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)
% 187.79/187.88 <=> ( V_a_2 = V_ca_2
% 187.79/187.88 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 187.79/187.88 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( 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)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 187.79/187.88 => V_a_2 = V_ca_2 ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 187.79/187.88 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( 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)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 187.79/187.88 => V_b_2 = V_d_2 ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastLessThan__add__Un,axiom,
% 187.79/187.88 ! [V_k_2,V_j_2,V_i_2] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 187.79/187.88 => 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastLessThan0,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeast0LessThan,axiom,
% 187.79/187.88 ! [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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_ivl__disj__un_I6_J,axiom,
% 187.79/187.88 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 187.79/187.88 => 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) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_subset__card__intvl__is__intvl,axiom,
% 187.79/187.88 ! [V_k_2,V_A_2] :
% 187.79/187.88 ( 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)))))
% 187.79/187.88 => 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_card__atLeastLessThan,axiom,
% 187.79/187.88 ! [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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastatMost__empty__iff2,axiom,
% 187.79/187.88 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => ( 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)
% 187.79/187.88 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastatMost__empty__iff,axiom,
% 187.79/187.88 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => ( 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))
% 187.79/187.88 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastatMost__empty,axiom,
% 187.79/187.88 ! [V_a_2,V_b_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 187.79/187.88 => 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)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastatMost__subset__iff,axiom,
% 187.79/187.88 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => ( 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)))
% 187.79/187.88 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 187.79/187.88 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 187.79/187.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_image__Suc__atLeastLessThan,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastLessThan__empty,axiom,
% 187.79/187.88 ! [V_a_2,V_b_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 187.79/187.88 => 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)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastAtMost__singleton,axiom,
% 187.79/187.88 ! [V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 187.79/187.88 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => ( 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)))
% 187.79/187.88 <=> ( V_a_2 = V_b_2
% 187.79/187.88 & V_b_2 = V_ca_2 ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastAtMost__singleton_H,axiom,
% 187.79/187.88 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => ( V_a_2 = V_b_2
% 187.79/187.88 => 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))) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 187.79/187.88 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => ( 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)
% 187.79/187.88 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastLessThan__empty__iff,axiom,
% 187.79/187.88 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => ( 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))
% 187.79/187.88 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastLessThan__subset__iff,axiom,
% 187.79/187.88 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( 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)))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 187.79/187.88 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 187.79/187.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 187.79/187.88 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_ivl__disj__un_I17_J,axiom,
% 187.79/187.88 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 187.79/187.88 => 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) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 187.79/187.88 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_image__uminus__atLeastAtMost,axiom,
% 187.79/187.88 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.88 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_ivl__diff,axiom,
% 187.79/187.88 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 187.79/187.88 => 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) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_ivl__disj__int_I11_J,axiom,
% 187.79/187.88 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_image__Suc__atLeastAtMost,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 187.79/187.88 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 187.79/187.88 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_image__add__atLeastLessThan,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_image__add__atLeastAtMost,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__add__nat__ivl,axiom,
% 187.79/187.88 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 187.79/187.88 => 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)) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__diff__nat__ivl,axiom,
% 187.79/187.88 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 187.79/187.88 ( class_Groups_Oab__group__add(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 187.79/187.88 => 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)) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_greaterThan__iff,axiom,
% 187.79/187.88 ! [V_k_2,V_i_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oord(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 187.79/187.88 ! [V_i_2,V_inc_2,T_b] :
% 187.79/187.88 ( class_Rings_Osemiring__1(T_b)
% 187.79/187.88 => 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 ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 187.79/187.88 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 187.79/187.88 ( class_Rings_Osemiring__1(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_greaterThan__subset__iff,axiom,
% 187.79/187.88 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( 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)))
% 187.79/187.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_card__atLeastAtMost,axiom,
% 187.79/187.88 ! [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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastAtMostSuc__conv,axiom,
% 187.79/187.88 ! [V_n_2,V_m_2] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastLessThan__singleton,axiom,
% 187.79/187.88 ! [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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 187.79/187.88 ! [V_k_2,V_f_2] :
% 187.79/187.88 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_Int__atLeastAtMost,axiom,
% 187.79/187.88 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastatMost__psubset__iff,axiom,
% 187.79/187.88 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => ( 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)))
% 187.79/187.88 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 187.79/187.88 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 187.79/187.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 187.79/187.88 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2))
% 187.79/187.88 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 187.79/187.88 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_Int__atLeastLessThan,axiom,
% 187.79/187.88 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_ivl__disj__int_I4_J,axiom,
% 187.79/187.88 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_ivl__disj__un_I8_J,axiom,
% 187.79/187.88 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.88 ( class_Orderings_Olinorder(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 187.79/187.88 => 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) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_ivl__disj__int_I2_J,axiom,
% 187.79/187.88 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.88 ( class_Orderings_Oorder(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 187.79/187.88 ! [V_k_2,V_f_2,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.88 => 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)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__head__upt__Suc,axiom,
% 187.79/187.88 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.88 => 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))) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__head__Suc,axiom,
% 187.79/187.88 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.88 => 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))) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastLessThanSuc,axiom,
% 187.79/187.88 ! [V_n_2,V_m_2] :
% 187.79/187.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.88 => 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)) )
% 187.79/187.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.88 => 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)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__op__ivl__Suc,axiom,
% 187.79/187.88 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 187.79/187.88 => 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) )
% 187.79/187.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 187.79/187.88 => 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)) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_image__uminus__lessThan,axiom,
% 187.79/187.88 ! [V_x_2,T_b] :
% 187.79/187.88 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_image__uminus__greaterThan,axiom,
% 187.79/187.88 ! [V_x_2,T_b] :
% 187.79/187.88 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.79/187.88 => 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)) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_greaterThan__Suc,axiom,
% 187.79/187.88 ! [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)))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__cl__ivl__Suc,axiom,
% 187.79/187.88 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 187.79/187.88 => 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) )
% 187.79/187.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 187.79/187.88 => 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))) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_setsum__ub__add__nat,axiom,
% 187.79/187.88 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 187.79/187.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.88 => ( 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))))
% 187.79/187.88 => 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)))) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_gauss__sum,axiom,
% 187.79/187.88 ! [V_n_2,T_b] :
% 187.79/187.88 ( class_Rings_Ocomm__semiring__1(T_b)
% 187.79/187.88 => 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_self__quotient__aux2,axiom,
% 187.79/187.88 ! [V_q,V_r,V_a] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.88 => ( 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))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_self__quotient__aux1,axiom,
% 187.79/187.88 ! [V_q,V_r,V_a] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.88 => ( 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))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 187.79/187.88 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 187.79/187.88 ( 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)
% 187.79/187.88 => ( 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)))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_unique__quotient__lemma__neg,axiom,
% 187.79/187.88 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_zdiv__mono2__lemma,axiom,
% 187.79/187.88 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 187.79/187.88 ( 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)
% 187.79/187.88 => ( 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)))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 187.79/187.88 ! [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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 187.79/187.88 ! [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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_simp__from__to,axiom,
% 187.79/187.88 ! [V_i_2,V_j_2] :
% 187.79/187.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 187.79/187.88 => 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)) )
% 187.79/187.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 187.79/187.88 => 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)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_image__add__int__atLeastLessThan,axiom,
% 187.79/187.88 ! [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) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_q__pos__lemma,axiom,
% 187.79/187.88 ! [V_r_H,V_q_H,V_b_H] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_q__neg__lemma,axiom,
% 187.79/187.88 ! [V_r_H,V_q_H,V_b_H] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_unique__quotient__lemma,axiom,
% 187.79/187.88 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 187.79/187.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 187.79/187.88 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_Pa_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_all__nat__less,axiom,
% 187.79/187.88 ! [V_Pa_2,V_n_2] :
% 187.79/187.88 ( ! [B_m] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 187.79/187.88 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 187.79/187.88 <=> ! [B_x] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_ex__nat__less,axiom,
% 187.79/187.88 ! [V_Pa_2,V_n_2] :
% 187.79/187.88 ( ? [B_m] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 187.79/187.88 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 187.79/187.88 <=> ? [B_x] :
% 187.79/187.88 ( 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)))
% 187.79/187.88 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 187.79/187.88 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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_finite__atLeastAtMost__int,axiom,
% 187.79/187.88 ! [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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_finite__atLeastLessThan__int,axiom,
% 187.79/187.88 ! [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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_infinite__UNIV__int,axiom,
% 187.79/187.88 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 187.79/187.88 ! [V_B_2,V_A_2] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.88 <=> 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 187.79/187.88 ! [V_B_2,V_A_2] :
% 187.79/187.88 ( V_A_2 = V_B_2
% 187.79/187.88 <=> 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) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 187.79/187.88 ! [V_y_2,V_x_2] :
% 187.79/187.88 ( 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)
% 187.79/187.88 <=> V_x_2 = V_y_2 ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 187.79/187.88 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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 187.79/187.88 ! [V_A_2,V_x_2] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 187.79/187.88 <=> 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 187.79/187.88 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))) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 187.79/187.88 ! [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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 187.79/187.88 ! [V_A_2] :
% 187.79/187.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 187.79/187.88 <=> 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 187.79/187.88 ! [V_B_2,V_A_2] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.88 <=> 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))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 187.79/187.88 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)) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 187.79/187.88 ! [V_y,V_x] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.79/187.88 => 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))) ) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 187.79/187.88 ! [V_Pa_2] :
% 187.79/187.88 ( ! [B_x] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 187.79/187.88 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.79/187.88 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 187.79/187.88 ! [V_Pa_2] :
% 187.79/187.88 ( ? [B_x] :
% 187.79/187.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 187.79/187.88 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.79/187.88 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 187.79/187.88
% 187.79/187.88 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 187.79/187.88 ! [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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 187.79/187.89 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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 187.79/187.89 ! [V_y,V_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.79/187.89 => 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))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 187.79/187.89 ! [V_y_2,V_x_2] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 187.79/187.89 ! [V_y_2,V_x_2] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ex__nat__less__eq,axiom,
% 187.79/187.89 ! [V_Pa_2,V_n_2] :
% 187.79/187.89 ( ? [B_m] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 187.79/187.89 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 187.79/187.89 <=> ? [B_x] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_all__nat__less__eq,axiom,
% 187.79/187.89 ! [V_Pa_2,V_n_2] :
% 187.79/187.89 ( ! [B_m] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 187.79/187.89 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 187.79/187.89 <=> ! [B_x] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_bset_I6_J,axiom,
% 187.79/187.89 ! [V_t_2,V_B_2,V_D_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.79/187.89 => ! [B_x] :
% 187.79/187.89 ( ! [B_xa] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => ! [B_xb] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 187.79/187.89 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 187.79/187.89 => 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)) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_aset_I8_J,axiom,
% 187.79/187.89 ! [V_t_2,V_A_2,V_D_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.79/187.89 => ! [B_x] :
% 187.79/187.89 ( ! [B_xa] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => ! [B_xb] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 187.79/187.89 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 187.79/187.89 => 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))) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_bset_I8_J,axiom,
% 187.79/187.89 ! [V_B_2,V_t_2,V_D_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.79/187.89 => ( 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))
% 187.79/187.89 => ! [B_x] :
% 187.79/187.89 ( ! [B_xa] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => ! [B_xb] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 187.79/187.89 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 187.79/187.89 => 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))) ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_aset_I6_J,axiom,
% 187.79/187.89 ! [V_A_2,V_t_2,V_D_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.79/187.89 => ( 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))
% 187.79/187.89 => ! [B_x] :
% 187.79/187.89 ( ! [B_xa] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => ! [B_xb] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 187.79/187.89 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 187.79/187.89 => 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)) ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_periodic__finite__ex,axiom,
% 187.79/187.89 ! [V_Pa_2,V_d_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 187.79/187.89 => ( ! [B_x,B_k] :
% 187.79/187.89 ( hBOOL(hAPP(V_Pa_2,B_x))
% 187.79/187.89 <=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
% 187.79/187.89 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 187.79/187.89 <=> ? [B_x] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_aset_I4_J,axiom,
% 187.79/187.89 ! [V_A_2,V_t_2,V_D_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 187.79/187.89 => ! [B_x] :
% 187.79/187.89 ( ! [B_xa] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => ! [B_xb] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 187.79/187.89 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.79/187.89 => ( B_x != V_t_2
% 187.79/187.89 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_bset_I4_J,axiom,
% 187.79/187.89 ! [V_B_2,V_t_2,V_D_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 187.79/187.89 => ! [B_x] :
% 187.79/187.89 ( ! [B_xa] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => ! [B_xb] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 187.79/187.89 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.79/187.89 => ( B_x != V_t_2
% 187.79/187.89 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_bset_I7_J,axiom,
% 187.79/187.89 ! [V_B_2,V_t_2,V_D_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 187.79/187.89 => ! [B_x] :
% 187.79/187.89 ( ! [B_xa] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => ! [B_xb] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 187.79/187.89 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 187.79/187.89 => 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))) ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_aset_I5_J,axiom,
% 187.79/187.89 ! [V_A_2,V_t_2,V_D_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 187.79/187.89 => ! [B_x] :
% 187.79/187.89 ( ! [B_xa] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => ! [B_xb] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 187.79/187.89 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 187.79/187.89 => 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)) ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_aset_I3_J,axiom,
% 187.79/187.89 ! [V_A_2,V_t_2,V_D_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.79/187.89 => ( 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))
% 187.79/187.89 => ( ! [B_x] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => ! [B_xa] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 187.79/187.89 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 187.79/187.89 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_bset_I3_J,axiom,
% 187.79/187.89 ! [V_B_2,V_t_2,V_D_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.79/187.89 => ( 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))
% 187.79/187.89 => ( ! [B_x] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => ! [B_xa] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 187.79/187.89 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 187.79/187.89 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_aset_I7_J,axiom,
% 187.79/187.89 ! [V_t_2,V_A_2,V_D_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.79/187.89 => ! [B_x] :
% 187.79/187.89 ( ! [B_xa] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => ! [B_xb] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 187.79/187.89 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 187.79/187.89 => 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))) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_bset_I5_J,axiom,
% 187.79/187.89 ! [V_t_2,V_B_2,V_D_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.79/187.89 => ! [B_x] :
% 187.79/187.89 ( ! [B_xa] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => ! [B_xb] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 187.79/187.89 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 187.79/187.89 => 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)) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atLeast__Suc,axiom,
% 187.79/187.89 ! [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)))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_small_H_Osimps,axiom,
% 187.79/187.89 ! [V_f_2,V_i_2,V_d_2] :
% 187.79/187.89 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 187.79/187.89 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 187.79/187.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atLeast__eq__iff,axiom,
% 187.79/187.89 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 187.79/187.89 <=> V_x_2 = V_y_2 ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atLeast__iff,axiom,
% 187.79/187.89 ! [V_k_2,V_i_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oord(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atLeast__subset__iff,axiom,
% 187.79/187.89 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atLeast__0,axiom,
% 187.79/187.89 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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Compl__lessThan,axiom,
% 187.79/187.89 ! [V_k_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Compl__atLeast,axiom,
% 187.79/187.89 ! [V_k_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atLeast__Suc__greaterThan,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I14_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 187.79/187.89 => 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) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__int_I8_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Int__atLeastAtMostL2,axiom,
% 187.79/187.89 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Int__atLeastAtMostR2,axiom,
% 187.79/187.89 ! [V_d_2,V_ca_2,V_a_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I1_J,axiom,
% 187.79/187.89 ! [V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I13_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 187.79/187.89 => 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) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_tsub__def,axiom,
% 187.79/187.89 ! [V_x,V_y] :
% 187.79/187.89 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 187.79/187.89 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 187.79/187.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 187.79/187.89 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I18_J,axiom,
% 187.79/187.89 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 187.79/187.89 => 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) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I3_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 187.79/187.89 => 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) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I5_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 187.79/187.89 => 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) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 187.79/187.89 ! [V_u_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 187.79/187.89 => 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_finite__greaterThanAtMost,axiom,
% 187.79/187.89 ! [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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_finite__greaterThanLessThan,axiom,
% 187.79/187.89 ! [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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_finite__greaterThanAtMost__int,axiom,
% 187.79/187.89 ! [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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_finite__greaterThanLessThan__int,axiom,
% 187.79/187.89 ! [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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__int,axiom,
% 187.79/187.89 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 187.79/187.89
% 187.79/187.89 fof(fact_card__greaterThanAtMost__int,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__int_I10_J,axiom,
% 187.79/187.89 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I16_J,axiom,
% 187.79/187.89 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 187.79/187.89 => 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) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 187.79/187.89 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__0,axiom,
% 187.79/187.89 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 187.79/187.89 ! [V_y,V_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ex__nat,axiom,
% 187.79/187.89 ! [V_Pa_2] :
% 187.79/187.89 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 187.79/187.89 <=> ? [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 187.79/187.89 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_all__nat,axiom,
% 187.79/187.89 ! [V_Pa_2] :
% 187.79/187.89 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 187.79/187.89 <=> ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 187.79/187.89 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 187.79/187.89 ! [V_y_2,V_x_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 187.79/187.89 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 187.79/187.89 <=> V_x_2 = V_y_2 ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_eq__nat__nat__iff,axiom,
% 187.79/187.89 ! [V_z_H_2,V_z_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 187.79/187.89 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 187.79/187.89 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 187.79/187.89 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 187.79/187.89 ! [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 ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 187.79/187.89 ! [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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_card__greaterThanLessThan__int,axiom,
% 187.79/187.89 ! [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)))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I4_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 187.79/187.89 => 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) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I19_J,axiom,
% 187.79/187.89 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 187.79/187.89 => 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) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_greaterThanAtMost__empty,axiom,
% 187.79/187.89 ! [V_k_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 187.79/187.89 ! [V_l_2,V_k_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => ( 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)
% 187.79/187.89 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 187.79/187.89 ! [V_l_2,V_k_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => ( 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))
% 187.79/187.89 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I20_J,axiom,
% 187.79/187.89 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 187.79/187.89 => 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) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 187.79/187.89 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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_greaterThanLessThan__empty,axiom,
% 187.79/187.89 ! [V_k_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__int_I14_J,axiom,
% 187.79/187.89 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__le__0,axiom,
% 187.79/187.89 ! [V_z] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.89 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__0__iff,axiom,
% 187.79/187.89 ! [V_i_2] :
% 187.79/187.89 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__mono__iff,axiom,
% 187.79/187.89 ! [V_w_2,V_z_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_zless__nat__conj,axiom,
% 187.79/187.89 ! [V_z_2,V_w_2] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 187.79/187.89 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 187.79/187.89 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 187.79/187.89 ! [V_y_2,V_x_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__1,axiom,
% 187.79/187.89 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__0__le,axiom,
% 187.79/187.89 ! [V_z] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.79/187.89 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_int__eq__iff,axiom,
% 187.79/187.89 ! [V_z_2,V_m_2] :
% 187.79/187.89 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 187.79/187.89 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 187.79/187.89 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_int__nat__eq,axiom,
% 187.79/187.89 ! [V_z] :
% 187.79/187.89 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.79/187.89 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 187.79/187.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.79/187.89 => 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) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_zless__nat__eq__int__zless,axiom,
% 187.79/187.89 ! [V_z_2,V_m_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 187.79/187.89 <=> 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__zminus__int,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_card__greaterThanAtMost,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 187.79/187.89 ! [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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 187.79/187.89 ! [V_A_2,V_f_2,T_b] :
% 187.79/187.89 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.89 & class_Groups_Ocomm__monoid__mult(T_b) )
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_card__atLeastLessThan__int,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_zero__less__nat__eq,axiom,
% 187.79/187.89 ! [V_z_2] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 187.79/187.89 ! [V_y_2,V_x_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__less__eq__zless,axiom,
% 187.79/187.89 ! [V_z_2,V_w_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__eq__iff2,axiom,
% 187.79/187.89 ! [V_w_2,V_m_2] :
% 187.79/187.89 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 187.79/187.89 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 187.79/187.89 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 187.79/187.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 187.79/187.89 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__eq__iff,axiom,
% 187.79/187.89 ! [V_m_2,V_w_2] :
% 187.79/187.89 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 187.79/187.89 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 187.79/187.89 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 187.79/187.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 187.79/187.89 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__le__eq__zle,axiom,
% 187.79/187.89 ! [V_z_2,V_w_2] :
% 187.79/187.89 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 187.79/187.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_split__nat,axiom,
% 187.79/187.89 ! [V_i_2,V_Pa_2] :
% 187.79/187.89 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2)))
% 187.79/187.89 <=> ( ! [B_n] :
% 187.79/187.89 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 187.79/187.89 => hBOOL(hAPP(V_Pa_2,B_n)) )
% 187.79/187.89 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.89 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 187.79/187.89 ! [V_y,V_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__add__distrib,axiom,
% 187.79/187.89 ! [V_z_H,V_z] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 187.79/187.89 ! [V_y,V_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__mult__distrib,axiom,
% 187.79/187.89 ! [V_z_H,V_z] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 187.79/187.89 ! [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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__diff__distrib,axiom,
% 187.79/187.89 ! [V_z,V_z_H] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I22_J,axiom,
% 187.79/187.89 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 187.79/187.89 => 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) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__int_I16_J,axiom,
% 187.79/187.89 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Int__greaterThanAtMost,axiom,
% 187.79/187.89 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_image__uminus__atLeastLessThan,axiom,
% 187.79/187.89 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 187.79/187.89 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__int_I12_J,axiom,
% 187.79/187.89 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__int_I13_J,axiom,
% 187.79/187.89 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__int_I9_J,axiom,
% 187.79/187.89 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Int__greaterThanLessThan,axiom,
% 187.79/187.89 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I11_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 187.79/187.89 => 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) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_card__greaterThanLessThan,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__int_I5_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__int_I6_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_one__less__nat__eq,axiom,
% 187.79/187.89 ! [V_z_2] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__less__iff,axiom,
% 187.79/187.89 ! [V_m_2,V_w_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 187.79/187.89 <=> 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))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 187.79/187.89 ! [V_z] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 187.79/187.89 ! [V_y,V_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.79/187.89 => 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))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__mult__distrib__neg,axiom,
% 187.79/187.89 ! [V_z_H,V_z] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.89 => 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 187.79/187.89 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_Pa_2),c_Int_Onat)))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_tsub__eq,axiom,
% 187.79/187.89 ! [V_x,V_y] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 187.79/187.89 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_card__atLeastAtMost__int,axiom,
% 187.79/187.89 ! [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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I15_J,axiom,
% 187.79/187.89 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 187.79/187.89 => 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) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_setsum__head,axiom,
% 187.79/187.89 ! [V_Pa_2,V_n_2,V_m_2,T_b] :
% 187.79/187.89 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.89 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I12_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 187.79/187.89 => 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) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__aux__def,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__morphism__nat__int,axiom,
% 187.79/187.89 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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 187.79/187.89 ! [V_n_2,V_m_2] :
% 187.79/187.89 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 187.79/187.89 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 187.79/187.89 => 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))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__of__nat,axiom,
% 187.79/187.89 ! [V_k,T_a] :
% 187.79/187.89 ( class_Rings_Oring__1(T_a)
% 187.79/187.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.89 => 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)))) )
% 187.79/187.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.89 => 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)) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2] :
% 187.79/187.89 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.89 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.79/187.89 => 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))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 187.79/187.89 ! [V_y_2,V_x_2] :
% 187.79/187.89 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 187.79/187.89 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2] :
% 187.79/187.89 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.89 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2] :
% 187.79/187.89 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.89 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__eq__iff,axiom,
% 187.79/187.89 ! [V_z_2,V_w_2,T_b] :
% 187.79/187.89 ( class_Int_Oring__char__0(T_b)
% 187.79/187.89 => ( 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)
% 187.79/187.89 <=> V_w_2 = V_z_2 ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 187.79/187.89 ! [V_x_2,V_A_2] :
% 187.79/187.89 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 187.79/187.89 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__int__eq,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2] :
% 187.79/187.89 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.89 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.79/187.89 => ( V_A_2 = V_B_2
% 187.79/187.89 <=> 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) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 187.79/187.89 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 187.79/187.89 ! [V_y,V_x] :
% 187.79/187.89 ( c_Nat__Transfer_Ois__nat(V_x)
% 187.79/187.89 => ( c_Nat__Transfer_Ois__nat(V_y)
% 187.79/187.89 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 187.79/187.89 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 187.79/187.89 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 187.79/187.89 ! [V_y,V_x] :
% 187.79/187.89 ( c_Nat__Transfer_Ois__nat(V_x)
% 187.79/187.89 => ( c_Nat__Transfer_Ois__nat(V_y)
% 187.79/187.89 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 187.79/187.89 ! [V_y,V_x] :
% 187.79/187.89 ( c_Nat__Transfer_Ois__nat(V_x)
% 187.79/187.89 => ( c_Nat__Transfer_Ois__nat(V_y)
% 187.79/187.89 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 187.79/187.89 ! [V_A_2,V_x_2] :
% 187.79/187.89 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 187.79/187.89 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 187.79/187.89 <=> 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))) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__eq__0__iff,axiom,
% 187.79/187.89 ! [V_z_2,T_b] :
% 187.79/187.89 ( class_Int_Oring__char__0(T_b)
% 187.79/187.89 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.89 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__0__eq__iff,axiom,
% 187.79/187.89 ! [V_z_2,T_b] :
% 187.79/187.89 ( class_Int_Oring__char__0(T_b)
% 187.79/187.89 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 187.79/187.89 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__0,axiom,
% 187.79/187.89 ! [T_a] :
% 187.79/187.89 ( class_Rings_Oring__1(T_a)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 187.79/187.89 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__le__iff,axiom,
% 187.79/187.89 ! [V_z_2,V_w_2,T_b] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__less__iff,axiom,
% 187.79/187.89 ! [V_z_2,V_w_2,T_b] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__add,axiom,
% 187.79/187.89 ! [V_z,V_w,T_a] :
% 187.79/187.89 ( class_Rings_Oring__1(T_a)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__mult,axiom,
% 187.79/187.89 ! [V_z,V_w,T_a] :
% 187.79/187.89 ( class_Rings_Oring__1(T_a)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__1,axiom,
% 187.79/187.89 ! [T_a] :
% 187.79/187.89 ( class_Rings_Oring__1(T_a)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__diff,axiom,
% 187.79/187.89 ! [V_z,V_w,T_a] :
% 187.79/187.89 ( class_Rings_Oring__1(T_a)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__of__nat__eq,axiom,
% 187.79/187.89 ! [V_n,T_a] :
% 187.79/187.89 ( class_Rings_Oring__1(T_a)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__minus,axiom,
% 187.79/187.89 ! [V_z,T_a] :
% 187.79/187.89 ( class_Rings_Oring__1(T_a)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Ints__of__int,axiom,
% 187.79/187.89 ! [V_z_2,T_b] :
% 187.79/187.89 ( class_Rings_Oring__1(T_b)
% 187.79/187.89 => 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__set__def,axiom,
% 187.79/187.89 ! [V_S_2] :
% 187.79/187.89 ( c_Nat__Transfer_Onat__set(V_S_2)
% 187.79/187.89 <=> ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 187.79/187.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_is__nat__def,axiom,
% 187.79/187.89 ! [V_x_2] :
% 187.79/187.89 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__setsum,axiom,
% 187.79/187.89 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.89 ( class_Rings_Oring__1(T_b)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 187.79/187.89 ! [V_y_2,V_x_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 187.79/187.89 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2] :
% 187.79/187.89 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.89 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.79/187.89 => 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))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 187.79/187.89 ! [V_A_2] :
% 187.79/187.89 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.89 => 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 ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 187.79/187.89 ! [V_x_2,V_A_2] :
% 187.79/187.89 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 187.79/187.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__le__0__iff,axiom,
% 187.79/187.89 ! [V_z_2,T_b] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__0__le__iff,axiom,
% 187.79/187.89 ! [V_z_2,T_b] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__less__0__iff,axiom,
% 187.79/187.89 ! [V_z_2,T_b] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__0__less__iff,axiom,
% 187.79/187.89 ! [V_z_2,T_b] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__nat__nat,axiom,
% 187.79/187.89 ! [V_z,T_a] :
% 187.79/187.89 ( class_Rings_Oring__1(T_a)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.79/187.89 => 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) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 187.79/187.89 ! [V_f_2,V_A_2,T_b] :
% 187.79/187.89 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.89 & class_Groups_Ocomm__monoid__mult(T_b) )
% 187.79/187.89 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 187.79/187.89 ! [V_A_2] :
% 187.79/187.89 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 187.79/187.89 <=> 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))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 187.79/187.89 ! [V_A_2] :
% 187.79/187.89 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 187.79/187.89 ! [V_Pa_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2] :
% 187.79/187.89 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.89 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.89 <=> 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))) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2] :
% 187.79/187.89 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.89 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.89 <=> 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))) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 187.79/187.89 ! [V_f_2,V_A_2,T_b] :
% 187.79/187.89 ( ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.89 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 187.79/187.89 ! [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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_decr__mult__lemma,axiom,
% 187.79/187.89 ! [V_k_2,V_Pa_2,V_d_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 187.79/187.89 => ( ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(V_Pa_2,B_x))
% 187.79/187.89 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 187.79/187.89 => ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(V_Pa_2,B_x))
% 187.79/187.89 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_negD,axiom,
% 187.79/187.89 ! [V_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.89 => ? [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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_incr__mult__lemma,axiom,
% 187.79/187.89 ! [V_k_2,V_Pa_2,V_d_2] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 187.79/187.89 => ( ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(V_Pa_2,B_x))
% 187.79/187.89 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 187.79/187.89 => ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(V_Pa_2,B_x))
% 187.79/187.89 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_finite__atMost,axiom,
% 187.79/187.89 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atMost__eq__iff,axiom,
% 187.79/187.89 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 187.79/187.89 <=> V_x_2 = V_y_2 ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atLeast0AtMost,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_lessThan__Suc__atMost,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_card__atMost,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atMost__Suc,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atMost__iff,axiom,
% 187.79/187.89 ! [V_k_2,V_i_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oord(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atMost__subset__iff,axiom,
% 187.79/187.89 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Compl__atMost,axiom,
% 187.79/187.89 ! [V_k_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Compl__greaterThan,axiom,
% 187.79/187.89 ! [V_k_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_setsum__atMost__Suc,axiom,
% 187.79/187.89 ! [V_n_2,V_f_2,T_b] :
% 187.79/187.89 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.89 => 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atMost__0,axiom,
% 187.79/187.89 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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Int__atLeastAtMostR1,axiom,
% 187.79/187.89 ! [V_d_2,V_ca_2,V_b_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Int__atLeastAtMostL1,axiom,
% 187.79/187.89 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I9_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 187.79/187.89 => 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) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__int_I3_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__int_I1_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_image__uminus__atMost,axiom,
% 187.79/187.89 ! [V_x_2,T_b] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_image__uminus__atLeast,axiom,
% 187.79/187.89 ! [V_x_2,T_b] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I2_J,axiom,
% 187.79/187.89 ! [V_u_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I10_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 187.79/187.89 => 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) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_atMost__Int__atLeast,axiom,
% 187.79/187.89 ! [V_n_2,T_b] :
% 187.79/187.89 ( class_Orderings_Oorder(T_b)
% 187.79/187.89 => 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ivl__disj__un_I7_J,axiom,
% 187.79/187.89 ! [V_u_2,V_l_2,T_b] :
% 187.79/187.89 ( class_Orderings_Olinorder(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 187.79/187.89 => 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) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_zero__less__imp__eq__int,axiom,
% 187.79/187.89 ! [V_k] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 187.79/187.89 => ? [B_n] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 187.79/187.89 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_setsum__mono__zero__left,axiom,
% 187.79/187.89 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 187.79/187.89 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 187.79/187.89 => ( ! [B_x] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 187.79/187.89 => 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) ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_setsum__mono__zero__right,axiom,
% 187.79/187.89 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 187.79/187.89 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 187.79/187.89 => ( ! [B_x] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 187.79/187.89 => 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) ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_setsum__strict__mono,axiom,
% 187.79/187.89 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 187.79/187.89 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.89 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 187.79/187.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.89 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => ( ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 187.79/187.89 => 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))) ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_decr__lemma,axiom,
% 187.79/187.89 ! [V_z,V_x,V_d] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_setsum__abs,axiom,
% 187.79/187.89 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 187.79/187.89 => 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_setsum__abs__ge__zero,axiom,
% 187.79/187.89 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 187.79/187.89 => 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__one,axiom,
% 187.79/187.89 ! [T_a] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.89 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__eq__0,axiom,
% 187.79/187.89 ! [V_a_2,T_b] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 187.79/187.89 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.89 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__zero,axiom,
% 187.79/187.89 ! [T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__mult__self,axiom,
% 187.79/187.89 ! [V_a,T_a] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__mult,axiom,
% 187.79/187.89 ! [V_b,V_a,T_a] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__add__abs,axiom,
% 187.79/187.89 ! [V_b,V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__minus__cancel,axiom,
% 187.79/187.89 ! [V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__idempotent,axiom,
% 187.79/187.89 ! [V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__int__eq,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__of__nat,axiom,
% 187.79/187.89 ! [V_n,T_a] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__minus__commute,axiom,
% 187.79/187.89 ! [V_b,V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__ge__self,axiom,
% 187.79/187.89 ! [V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__le__D1,axiom,
% 187.79/187.89 ! [V_b,V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 187.79/187.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__setsum__abs,axiom,
% 187.79/187.89 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__of__nonneg,axiom,
% 187.79/187.89 ! [V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.89 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__le__zero__iff,axiom,
% 187.79/187.89 ! [V_a_2,T_b] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__ge__zero,axiom,
% 187.79/187.89 ! [V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__of__pos,axiom,
% 187.79/187.89 ! [V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.89 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_zero__less__abs__iff,axiom,
% 187.79/187.89 ! [V_a_2,T_b] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__not__less__zero,axiom,
% 187.79/187.89 ! [V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => ~ 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__triangle__ineq,axiom,
% 187.79/187.89 ! [V_b,V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => 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)))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__mult__less,axiom,
% 187.79/187.89 ! [V_d,V_b,V_c,V_a,T_a] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 187.79/187.89 => 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))) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__triangle__ineq2__sym,axiom,
% 187.79/187.89 ! [V_b,V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => 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)))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__triangle__ineq2,axiom,
% 187.79/187.89 ! [V_b,V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => 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)))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__triangle__ineq3,axiom,
% 187.79/187.89 ! [V_b,V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => 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)))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__le__D2,axiom,
% 187.79/187.89 ! [V_b,V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 187.79/187.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__leI,axiom,
% 187.79/187.89 ! [V_b,V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 187.79/187.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__le__iff,axiom,
% 187.79/187.89 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 187.79/187.89 => ( 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))
% 187.79/187.89 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 187.79/187.89 & 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)) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__ge__minus__self,axiom,
% 187.79/187.89 ! [V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__less__iff,axiom,
% 187.79/187.89 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 187.79/187.89 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 187.79/187.89 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__zmult__eq__1,axiom,
% 187.79/187.89 ! [V_n,V_m] :
% 187.79/187.89 ( 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)
% 187.79/187.89 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_mult__sgn__abs,axiom,
% 187.79/187.89 ! [V_x,T_a] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.89 => 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 ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__sgn,axiom,
% 187.79/187.89 ! [V_k,T_a] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__mult__pos,axiom,
% 187.79/187.89 ! [V_y,V_x,T_a] :
% 187.79/187.89 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__eq__mult,axiom,
% 187.79/187.89 ! [V_b,V_a,T_a] :
% 187.79/187.89 ( class_Rings_Oordered__ring__abs(T_a)
% 187.79/187.89 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 187.79/187.89 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__diff__triangle__ineq,axiom,
% 187.79/187.89 ! [V_d,V_c,V_b,V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => 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))))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__triangle__ineq4,axiom,
% 187.79/187.89 ! [V_b,V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => 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)))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__of__nonpos,axiom,
% 187.79/187.89 ! [V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.89 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__minus__le__zero,axiom,
% 187.79/187.89 ! [V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__if,axiom,
% 187.79/187.89 ! [V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oabs__if(T_a)
% 187.79/187.89 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.89 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 187.79/187.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.89 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_abs__of__neg,axiom,
% 187.79/187.89 ! [V_a,T_a] :
% 187.79/187.89 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.89 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_zabs__less__one__iff,axiom,
% 187.79/187.89 ! [V_z_2] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_zabs__def,axiom,
% 187.79/187.89 ! [V_i] :
% 187.79/187.89 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.89 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 187.79/187.89 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.89 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat__abs__mult__distrib,axiom,
% 187.79/187.89 ! [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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_incr__lemma,axiom,
% 187.79/187.89 ! [V_x,V_z,V_d] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 187.79/187.89 => 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)))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 187.79/187.89 ! [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)))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 187.79/187.89 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 187.79/187.89 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.89 & class_Groups_Ocomm__monoid__mult(T_b) )
% 187.79/187.89 => ( V_A_2 = V_B_2
% 187.79/187.89 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.79/187.89 => ( ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 187.79/187.89 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 187.79/187.89 => 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) ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_int__val__lemma,axiom,
% 187.79/187.89 ! [V_k_2,V_f_2,V_n_2] :
% 187.79/187.89 ( ! [B_i] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 187.79/187.89 => 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))) )
% 187.79/187.89 => ( 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))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 187.79/187.89 => ? [B_i] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 187.79/187.89 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_nat0__intermed__int__val,axiom,
% 187.79/187.89 ! [V_k_2,V_f_2,V_n_2] :
% 187.79/187.89 ( ! [B_i] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 187.79/187.89 => 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))) )
% 187.79/187.89 => ( 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))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 187.79/187.89 => ? [B_i] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 187.79/187.89 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__le__eq__Un0,axiom,
% 187.79/187.89 ! [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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SUP1__I,axiom,
% 187.79/187.89 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__o,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SUP1__iff,axiom,
% 187.79/187.89 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.89 ( 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))
% 187.79/187.89 <=> ? [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.89 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_finite__UN,axiom,
% 187.79/187.89 ! [V_B_2,T_c,V_A_2,T_b] :
% 187.79/187.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.89 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SUP__UN__eq,axiom,
% 187.79/187.89 ! [V_x_2,V_r_2,T_c,T_b] :
% 187.79/187.89 ( 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))
% 187.79/187.89 <=> 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__lessThan__UNIV,axiom,
% 187.79/187.89 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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__atMost__UNIV,axiom,
% 187.79/187.89 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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__atLeast__UNIV,axiom,
% 187.79/187.89 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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__UN__finite__eq,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__le__add__shift,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__I,axiom,
% 187.79/187.89 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 187.79/187.89 => 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))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_vimage__eq__UN,axiom,
% 187.79/187.89 ! [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))))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_image__eq__UN,axiom,
% 187.79/187.89 ! [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)))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__insert,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__simps_I3_J,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 187.79/187.89 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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)) )
% 187.79/187.89 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ball__UN,axiom,
% 187.79/187.89 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.89 ( ! [B_x] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.79/187.89 <=> ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.79/187.89 => ! [B_xa] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 187.79/187.89 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SUP__commute,axiom,
% 187.79/187.89 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 187.79/187.89 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.89 => 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__UN__flatten,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__simps_I9_J,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__extend__simps_I9_J,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SUP__le__iff,axiom,
% 187.79/187.89 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 187.79/187.89 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.89 => ( 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))
% 187.79/187.89 <=> ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.79/187.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_less__SUP__iff,axiom,
% 187.79/187.89 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 187.79/187.89 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.89 & class_Orderings_Olinorder(T_b) )
% 187.79/187.89 => ( 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)))
% 187.79/187.89 <=> ? [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.79/187.89 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__iff,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 187.79/187.89 ( 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)))
% 187.79/187.89 <=> ? [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.79/187.89 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SUP__const,axiom,
% 187.79/187.89 ! [V_M_2,T_b,V_A_2,T_c] :
% 187.79/187.89 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 187.79/187.89 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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 ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UNION__empty__conv_I1_J,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.89 ( 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)
% 187.79/187.89 <=> ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.79/187.89 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__empty2,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__constant,axiom,
% 187.79/187.89 ! [V_ca_2,T_c,T_b,V_A_2] :
% 187.79/187.89 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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)) )
% 187.79/187.89 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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 ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UNION__empty__conv_I2_J,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.89 ( 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))
% 187.79/187.89 <=> ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.79/187.89 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__subset__iff,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 187.79/187.89 ( 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))
% 187.79/187.89 <=> ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__extend__simps_I10_J,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_image__UN,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__simps_I10_J,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__Un__distrib,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__Un,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Int__UN__distrib2,axiom,
% 187.79/187.89 ! [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))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__extend__simps_I4_J,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_Int__UN__distrib,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__extend__simps_I5_J,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__simps_I4_J,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__simps_I5_J,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SUPR__apply,axiom,
% 187.79/187.89 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 187.79/187.89 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__extend__simps_I6_J,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__simps_I6_J,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_vimage__UN,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SUP__subset,axiom,
% 187.79/187.89 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.89 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.89 => 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))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_le__SUPI,axiom,
% 187.79/187.89 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 187.79/187.89 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 187.79/187.89 => 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))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__insert__distrib,axiom,
% 187.79/187.89 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__upper,axiom,
% 187.79/187.89 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.89 => 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__absorb,axiom,
% 187.79/187.89 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__extend__simps_I1_J,axiom,
% 187.79/187.89 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 187.79/187.89 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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))) )
% 187.79/187.89 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__singleton,axiom,
% 187.79/187.89 ! [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 ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__simps_I1_J,axiom,
% 187.79/187.89 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 187.79/187.89 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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)) )
% 187.79/187.89 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__extend__simps_I2_J,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 187.79/187.89 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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 )
% 187.79/187.89 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__extend__simps_I3_J,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 187.79/187.89 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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 )
% 187.79/187.89 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__simps_I2_J,axiom,
% 187.79/187.89 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 187.79/187.89 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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)) )
% 187.79/187.89 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.89 => 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) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__finite2__subset,axiom,
% 187.79/187.89 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 187.79/187.89 ( ! [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)))
% 187.79/187.89 => 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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__finite2__eq,axiom,
% 187.79/187.89 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 187.79/187.89 ( ! [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)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_UN__finite__subset,axiom,
% 187.79/187.89 ! [V_C_2,V_A_2,T_b] :
% 187.79/187.89 ( ! [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))
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_finite__UN__I,axiom,
% 187.79/187.89 ! [V_B_2,T_c,V_A_2,T_b] :
% 187.79/187.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.89 => ( ! [B_a] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 187.79/187.89 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 187.79/187.89 => 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))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SUP2__I,axiom,
% 187.79/187.89 ! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ex__bij__betw__nat__finite__1,axiom,
% 187.79/187.89 ! [V_M_2,T_b] :
% 187.79/187.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 187.79/187.89 => ? [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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_finite__map__freshness,axiom,
% 187.79/187.89 ! [V_f_2,T_c,T_b] :
% 187.79/187.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2)))
% 187.79/187.89 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 187.79/187.89 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_diff__nat__eq__if,axiom,
% 187.79/187.89 ! [V_z_2,V_z_H_2] :
% 187.79/187.89 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 187.79/187.89 => 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) )
% 187.79/187.89 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 187.79/187.89 => 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)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_setsum__SucD,axiom,
% 187.79/187.89 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 187.79/187.89 ( 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)
% 187.79/187.89 => ? [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.89 & 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))) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_SUP2__iff,axiom,
% 187.79/187.89 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 187.79/187.89 ( 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))
% 187.79/187.89 <=> ? [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.89 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_not__neg__0,axiom,
% 187.79/187.89 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_not__neg__int,axiom,
% 187.79/187.89 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_not__neg__1,axiom,
% 187.79/187.89 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_not__neg__eq__ge__0,axiom,
% 187.79/187.89 ! [V_x_2] :
% 187.79/187.89 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_neg__def,axiom,
% 187.79/187.89 ! [V_Z_2] :
% 187.79/187.89 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 187.79/187.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_neg__nat,axiom,
% 187.79/187.89 ! [V_z] :
% 187.79/187.89 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 187.79/187.89 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_not__neg__nat,axiom,
% 187.79/187.89 ! [V_z] :
% 187.79/187.89 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 187.79/187.89 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_neg__zminus__int,axiom,
% 187.79/187.89 ! [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))))) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ex__bij__betw__nat__finite,axiom,
% 187.79/187.89 ! [V_M_2,T_b] :
% 187.79/187.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 187.79/187.89 => ? [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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_setprod_Oremove,axiom,
% 187.79/187.89 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 187.79/187.89 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.89 => 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)))))) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_ex__bij__betw__finite__nat,axiom,
% 187.79/187.89 ! [V_M_2,T_b] :
% 187.79/187.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 187.79/187.89 => ? [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))) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_fold__image__1,axiom,
% 187.79/187.89 ! [V_f_2,V_S_2,T_b,T_c] :
% 187.79/187.89 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.89 => ( ! [B_x] :
% 187.79/187.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 187.79/187.89 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 187.79/187.89 => 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) ) ) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_int__setprod,axiom,
% 187.79/187.89 ! [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) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__nat__setprod,axiom,
% 187.79/187.89 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.89 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 187.79/187.89 & class_Rings_Osemiring__1(T_b) )
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 187.79/187.89 ! [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)) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_of__int__setprod,axiom,
% 187.79/187.89 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.89 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 187.79/187.89 & class_Rings_Oring__1(T_b) )
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_setprod__1,axiom,
% 187.79/187.89 ! [V_A_2,T_c,T_b] :
% 187.79/187.89 ( class_Groups_Ocomm__monoid__mult(T_b)
% 187.79/187.89 => 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) ) ).
% 187.79/187.89
% 187.79/187.89 fof(fact_setprod__timesf,axiom,
% 187.79/187.89 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 187.79/187.89 ( class_Groups_Ocomm__monoid__mult(T_b)
% 187.79/187.89 => 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)) ) ).
% 187.79/187.89
% 187.79/187.90 fof(fact_abs__setprod,axiom,
% 187.79/187.90 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_b)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 187.79/187.90 ! [V_A_2,V_f_2,T_b] :
% 187.79/187.90 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.90 & class_Groups_Ocomm__monoid__mult(T_b) )
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__zero,axiom,
% 187.79/187.90 ! [V_f_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Rings_Ocomm__semiring__1(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => ( ? [B_x] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.90 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 187.79/187.90 => 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) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__zero__iff,axiom,
% 187.79/187.90 ! [V_f_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 187.79/187.90 & class_Rings_Ono__zero__divisors(T_c) )
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => ( 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)
% 187.79/187.90 <=> ? [B_x] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.90 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod_Oempty,axiom,
% 187.79/187.90 ! [V_g_2,T_c,T_b] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_b)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__empty,axiom,
% 187.79/187.90 ! [V_f_2,T_c,T_b] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_b)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod_Oinfinite,axiom,
% 187.79/187.90 ! [V_g_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__infinite,axiom,
% 187.79/187.90 ! [V_f_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__eq__1__iff,axiom,
% 187.79/187.90 ! [V_f_2,V_F_2,T_b] :
% 187.79/187.90 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 187.79/187.90 => ( 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)
% 187.79/187.90 <=> ! [B_x] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 187.79/187.90 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 187.79/187.90 ! [V_f_2,V_A_2,T_b] :
% 187.79/187.90 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.90 & class_Groups_Ocomm__monoid__mult(T_b) )
% 187.79/187.90 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod_Odistrib,axiom,
% 187.79/187.90 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__pos__nat__iff,axiom,
% 187.79/187.90 ! [V_f_2,V_S_2,T_b] :
% 187.79/187.90 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> ! [B_x] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__reindex__cong,axiom,
% 187.79/187.90 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_d)
% 187.79/187.90 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.79/187.90 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 187.79/187.90 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 187.79/187.90 => 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) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__reindex,axiom,
% 187.79/187.90 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_d)
% 187.79/187.90 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__delta,axiom,
% 187.79/187.90 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.90 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 187.79/187.90 => 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) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 187.79/187.90 => 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) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__delta_H,axiom,
% 187.79/187.90 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.90 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 187.79/187.90 => 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) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 187.79/187.90 => 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) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod_Oinsert,axiom,
% 187.79/187.90 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.90 => 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)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__insert,axiom,
% 187.79/187.90 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.90 => 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)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__Un__Int,axiom,
% 187.79/187.90 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.90 => 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)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod_Ounion__inter,axiom,
% 187.79/187.90 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.90 => 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)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod_Oreindex,axiom,
% 187.79/187.90 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 187.79/187.90 => 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) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod_Oeq__fold,axiom,
% 187.79/187.90 ! [V_g_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod_OF__eq,axiom,
% 187.79/187.90 ! [V_g_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => 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) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => 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) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod_Oinsert__remove,axiom,
% 187.79/187.90 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => 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)))))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod_Ounion__disjoint,axiom,
% 187.79/187.90 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.90 => ( 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))
% 187.79/187.90 => 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)) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__Un__disjoint,axiom,
% 187.79/187.90 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.90 => ( 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))
% 187.79/187.90 => 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)) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 187.79/187.90 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.90 => ( ! [B_x] :
% 187.79/187.90 ( 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)))
% 187.79/187.90 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 187.79/187.90 => 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)) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__Un__one,axiom,
% 187.79/187.90 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 187.79/187.90 => ( ! [B_x] :
% 187.79/187.90 ( 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)))
% 187.79/187.90 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 187.79/187.90 => 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)) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__gen__delta,axiom,
% 187.79/187.90 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.90 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 187.79/187.90 => 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)))) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 187.79/187.90 => 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)) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__diff1,axiom,
% 187.79/187.90 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Fields_Ofield(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 187.79/187.90 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.90 => 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)) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.90 => 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) ) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 187.79/187.90 ! [V_n,V_x] :
% 187.79/187.90 ( c_Nat__Transfer_Ois__nat(V_x)
% 187.79/187.90 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_of__int__power,axiom,
% 187.79/187.90 ! [V_n,V_z,T_a] :
% 187.79/187.90 ( class_Rings_Oring__1(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 187.79/187.90 ! [V_x,T_a] :
% 187.79/187.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.90 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zpower__int,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_int__power,axiom,
% 187.79/187.90 ! [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) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__zero,axiom,
% 187.79/187.90 ! [V_a,T_a] :
% 187.79/187.90 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__zero__left,axiom,
% 187.79/187.90 ! [V_a,T_a] :
% 187.79/187.90 ( class_Rings_Odivision__ring(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_add__divide__distrib,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Odivision__ring(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_times__divide__eq__right,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Odivision__ring(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 187.79/187.90 ! [V_q,V_p,V_x,T_a] :
% 187.79/187.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_minus__divide__left,axiom,
% 187.79/187.90 ! [V_b,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Odivision__ring(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__1,axiom,
% 187.79/187.90 ! [V_a,T_a] :
% 187.79/187.90 ( class_Rings_Odivision__ring(T_a)
% 187.79/187.90 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 187.79/187.90 ! [V_q,V_y,V_x,T_a] :
% 187.79/187.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_diff__divide__distrib,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Odivision__ring(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zpower__zpower,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nat__power__eq,axiom,
% 187.79/187.90 ! [V_n,V_z] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 187.79/187.90 ! [V_n,V_x] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setsum__divide__distrib,axiom,
% 187.79/187.90 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.90 ( class_Fields_Ofield(T_b)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_eq__divide__imp,axiom,
% 187.79/187.90 ! [V_b,V_a,V_c,T_a] :
% 187.79/187.90 ( class_Rings_Odivision__ring(T_a)
% 187.79/187.90 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 187.79/187.90 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__eq__imp,axiom,
% 187.79/187.90 ! [V_a,V_b,V_c,T_a] :
% 187.79/187.90 ( class_Rings_Odivision__ring(T_a)
% 187.79/187.90 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 187.79/187.90 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nonzero__divide__eq__eq,axiom,
% 187.79/187.90 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 187.79/187.90 ( class_Rings_Odivision__ring(T_b)
% 187.79/187.90 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.90 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
% 187.79/187.90 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nonzero__eq__divide__eq,axiom,
% 187.79/187.90 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 187.79/187.90 ( class_Rings_Odivision__ring(T_b)
% 187.79/187.90 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.90 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 187.79/187.90 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_right__inverse__eq,axiom,
% 187.79/187.90 ! [V_a_2,V_b_2,T_b] :
% 187.79/187.90 ( class_Rings_Odivision__ring(T_b)
% 187.79/187.90 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.90 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 187.79/187.90 <=> V_a_2 = V_b_2 ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__self,axiom,
% 187.79/187.90 ! [V_a,T_a] :
% 187.79/187.90 ( class_Rings_Odivision__ring(T_a)
% 187.79/187.90 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__self__if,axiom,
% 187.79/187.90 ! [V_a,T_a] :
% 187.79/187.90 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 187.79/187.90 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 187.79/187.90 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nonzero__minus__divide__divide,axiom,
% 187.79/187.90 ! [V_a,V_b,T_a] :
% 187.79/187.90 ( class_Rings_Odivision__ring(T_a)
% 187.79/187.90 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nonzero__minus__divide__right,axiom,
% 187.79/187.90 ! [V_a,V_b,T_a] :
% 187.79/187.90 ( class_Rings_Odivision__ring(T_a)
% 187.79/187.90 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 187.79/187.90 ! [V_q,V_x,T_a] :
% 187.79/187.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 187.79/187.90 ! [V_q,V_x,T_a] :
% 187.79/187.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 187.79/187.90 ! [V_q,V_x,T_a] :
% 187.79/187.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 187.79/187.90 ! [V_x,T_a] :
% 187.79/187.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 187.79/187.90 ! [V_q,V_p,V_x,T_a] :
% 187.79/187.90 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 187.79/187.90 ! [V_n,V_x] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.90 => 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))) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zpower__zadd__distrib,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Ints__power,axiom,
% 187.79/187.90 ! [V_n_2,V_a_2,T_b] :
% 187.79/187.90 ( class_Rings_Oring__1(T_b)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 187.79/187.90 => 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))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__dividef,axiom,
% 187.79/187.90 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Fields_Ofield__inverse__zero(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_geometric__sum,axiom,
% 187.79/187.90 ! [V_n_2,V_x_2,T_b] :
% 187.79/187.90 ( class_Fields_Ofield(T_b)
% 187.79/187.90 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 187.79/187.90 => 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))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zero__le__zpower__abs,axiom,
% 187.79/187.90 ! [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))) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__constant,axiom,
% 187.79/187.90 ! [V_y_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__eq__if,axiom,
% 187.79/187.90 ! [V_p,V_m] :
% 187.79/187.90 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.90 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 187.79/187.90 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.90 => 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)))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zero__less__zpower__abs__iff,axiom,
% 187.79/187.90 ! [V_n_2,V_x_2] :
% 187.79/187.90 ( 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)))
% 187.79/187.90 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.90 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__strict__mono,axiom,
% 187.79/187.90 ! [V_n,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.90 => 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))) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__diff,axiom,
% 187.79/187.90 ! [V_m,V_n,V_a,T_a] :
% 187.79/187.90 ( class_Fields_Ofield(T_a)
% 187.79/187.90 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.79/187.90 => 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)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_one__less__power,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__le__imp__le__exp,axiom,
% 187.79/187.90 ! [V_n,V_m,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_field__power__not__zero,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 187.79/187.90 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 187.79/187.90 ! [V_m_2,V_x_2] :
% 187.79/187.90 ( 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))
% 187.79/187.90 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.90 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__Suc__0,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nat__power__less__imp__less,axiom,
% 187.79/187.90 ! [V_n,V_m,V_i] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nat__zero__less__power__iff,axiom,
% 187.79/187.90 ! [V_n_2,V_x_2] :
% 187.79/187.90 ( 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)))
% 187.79/187.90 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 187.79/187.90 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__commutes,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Groups_Omonoid__mult(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__mult__distrib,axiom,
% 187.79/187.90 ! [V_n,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__one,axiom,
% 187.79/187.90 ! [V_n,T_a] :
% 187.79/187.90 ( class_Groups_Omonoid__mult(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_of__nat__power,axiom,
% 187.79/187.90 ! [V_n,V_m,T_a] :
% 187.79/187.90 ( class_Rings_Osemiring__1(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__mult,axiom,
% 187.79/187.90 ! [V_n,V_m,V_a,T_a] :
% 187.79/187.90 ( class_Groups_Omonoid__mult(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__divide,axiom,
% 187.79/187.90 ! [V_n,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Fields_Ofield__inverse__zero(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__abs,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__one__right,axiom,
% 187.79/187.90 ! [V_a,T_a] :
% 187.79/187.90 ( class_Groups_Omonoid__mult(T_a)
% 187.79/187.90 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__mono,axiom,
% 187.79/187.90 ! [V_n,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zero__le__power,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.90 => 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))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zero__less__power,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.90 => 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))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__eq__0__iff,axiom,
% 187.79/187.90 ! [V_n_2,V_a_2,T_b] :
% 187.79/187.90 ( ( class_Power_Opower(T_b)
% 187.79/187.90 & class_Rings_Omult__zero(T_b)
% 187.79/187.90 & class_Rings_Ono__zero__divisors(T_b)
% 187.79/187.90 & class_Rings_Ozero__neq__one(T_b) )
% 187.79/187.90 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.90 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.90 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_one__le__power,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 187.79/187.90 => 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))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__0__Suc,axiom,
% 187.79/187.90 ! [V_n,T_a] :
% 187.79/187.90 ( ( class_Power_Opower(T_a)
% 187.79/187.90 & class_Rings_Osemiring__0(T_a) )
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__inject__exp,axiom,
% 187.79/187.90 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_b)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 187.79/187.90 => ( 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)
% 187.79/187.90 <=> V_m_2 = V_n_2 ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__Suc,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Power_Opower(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__Suc2,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Groups_Omonoid__mult(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nat__one__le__power,axiom,
% 187.79/187.90 ! [V_n,V_i] :
% 187.79/187.90 ( 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))
% 187.79/187.90 => 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))) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__0,axiom,
% 187.79/187.90 ! [V_a,T_a] :
% 187.79/187.90 ( class_Power_Opower(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__add,axiom,
% 187.79/187.90 ! [V_n,V_m,V_a,T_a] :
% 187.79/187.90 ( class_Groups_Omonoid__mult(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nonzero__power__divide,axiom,
% 187.79/187.90 ! [V_n,V_a,V_b,T_a] :
% 187.79/187.90 ( class_Fields_Ofield(T_a)
% 187.79/187.90 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__one__over,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Fields_Ofield__inverse__zero(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_abs__power__minus,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__less__imp__less__base,axiom,
% 187.79/187.90 ! [V_b,V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( 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)))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__inject__base,axiom,
% 187.79/187.90 ! [V_b,V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( 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))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.90 => V_a = V_b ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__le__imp__le__base,axiom,
% 187.79/187.90 ! [V_b,V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( 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))))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__less__power__Suc,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 187.79/187.90 => 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)))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__gt1__lemma,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 187.79/187.90 => 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)))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__0__left,axiom,
% 187.79/187.90 ! [V_n,T_a] :
% 187.79/187.90 ( ( class_Power_Opower(T_a)
% 187.79/187.90 & class_Rings_Osemiring__0(T_a) )
% 187.79/187.90 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.90 => 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) )
% 187.79/187.90 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.90 => 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) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__gt1,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 187.79/187.90 => 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)))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__strict__increasing__iff,axiom,
% 187.79/187.90 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_b)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__less__imp__less__exp,axiom,
% 187.79/187.90 ! [V_n,V_m,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__strict__increasing,axiom,
% 187.79/187.90 ! [V_a,V_N,V_n,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zero__le__power__abs,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.90 => 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))) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__increasing,axiom,
% 187.79/187.90 ! [V_a,V_N,V_n,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__minus,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Oring__1(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__Suc__less,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__eq__imp__eq__base,axiom,
% 187.79/187.90 ! [V_b,V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( 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)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.90 => V_a = V_b ) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__Suc__less__one,axiom,
% 187.79/187.90 ! [V_n,V_a,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__strict__decreasing,axiom,
% 187.79/187.90 ! [V_a,V_N,V_n,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 187.79/187.90 => 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))) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__decreasing,axiom,
% 187.79/187.90 ! [V_a,V_N,V_n,T_a] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 187.79/187.90 => 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))) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__increasing__iff,axiom,
% 187.79/187.90 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 187.79/187.90 ( class_Rings_Olinordered__semidom(T_b)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__left__mono__neg,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 => 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))) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__left__mono,axiom,
% 187.79/187.90 ! [V_c,V_a,V_b,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 => 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))) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_neg__divide__le__eq,axiom,
% 187.79/187.90 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_b)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 => ( 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))
% 187.79/187.90 <=> 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)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_neg__le__divide__eq,axiom,
% 187.79/187.90 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_b)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_times__divide__times__eq,axiom,
% 187.79/187.90 ! [V_w,V_z,V_y,V_x,T_a] :
% 187.79/187.90 ( class_Fields_Ofield__inverse__zero(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_minus__divide__right,axiom,
% 187.79/187.90 ! [V_b,V_a,T_a] :
% 187.79/187.90 ( class_Fields_Ofield__inverse__zero(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_minus__divide__divide,axiom,
% 187.79/187.90 ! [V_b,V_a,T_a] :
% 187.79/187.90 ( class_Fields_Ofield__inverse__zero(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_abs__divide,axiom,
% 187.79/187.90 ! [V_b,V_a,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zero__le__divide__iff,axiom,
% 187.79/187.90 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 187.79/187.90 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__le__0__iff,axiom,
% 187.79/187.90 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 187.79/187.90 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__right__mono,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__right__mono__neg,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zero__less__divide__iff,axiom,
% 187.79/187.90 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 187.79/187.90 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__less__0__iff,axiom,
% 187.79/187.90 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 187.79/187.90 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__pos__pos,axiom,
% 187.79/187.90 ! [V_y,V_x,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__pos__neg,axiom,
% 187.79/187.90 ! [V_y,V_x,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__neg__pos,axiom,
% 187.79/187.90 ! [V_y,V_x,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__neg__neg,axiom,
% 187.79/187.90 ! [V_y,V_x,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__strict__right__mono,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__strict__right__mono__neg,axiom,
% 187.79/187.90 ! [V_c,V_a,V_b,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_frac__eq__eq,axiom,
% 187.79/187.90 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 187.79/187.90 ( class_Fields_Ofield(T_b)
% 187.79/187.90 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.90 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.90 => ( 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)
% 187.79/187.90 <=> 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) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mult__divide__mult__cancel__left,axiom,
% 187.79/187.90 ! [V_b,V_a,V_c,T_a] :
% 187.79/187.90 ( class_Fields_Ofield__inverse__zero(T_a)
% 187.79/187.90 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mult__divide__mult__cancel__right,axiom,
% 187.79/187.90 ! [V_b,V_a,V_c,T_a] :
% 187.79/187.90 ( class_Fields_Ofield__inverse__zero(T_a)
% 187.79/187.90 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__eq__eq,axiom,
% 187.79/187.90 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 187.79/187.90 ( class_Fields_Ofield__inverse__zero(T_b)
% 187.79/187.90 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
% 187.79/187.90 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.90 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) )
% 187.79/187.90 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.90 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_eq__divide__eq,axiom,
% 187.79/187.90 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.90 ( class_Fields_Ofield__inverse__zero(T_b)
% 187.79/187.90 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 187.79/187.90 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.90 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 )
% 187.79/187.90 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.90 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nonzero__abs__divide,axiom,
% 187.79/187.90 ! [V_a,V_b,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__nonpos__neg,axiom,
% 187.79/187.90 ! [V_y,V_x,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__nonpos__pos,axiom,
% 187.79/187.90 ! [V_y,V_x,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_frac__le,axiom,
% 187.79/187.90 ! [V_z,V_w,V_y,V_x,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 187.79/187.90 => 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))) ) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_frac__less,axiom,
% 187.79/187.90 ! [V_z,V_w,V_y,V_x,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 187.79/187.90 => 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))) ) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_frac__less2,axiom,
% 187.79/187.90 ! [V_z,V_w,V_y,V_x,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 187.79/187.90 => 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))) ) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__nonneg__neg,axiom,
% 187.79/187.90 ! [V_y,V_x,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__nonneg__pos,axiom,
% 187.79/187.90 ! [V_y,V_x,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__strict__left__mono__neg,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 => 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))) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__strict__left__mono,axiom,
% 187.79/187.90 ! [V_c,V_a,V_b,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 => 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))) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_neg__divide__less__eq,axiom,
% 187.79/187.90 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_b)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 => ( 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))
% 187.79/187.90 <=> 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)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_neg__less__divide__eq,axiom,
% 187.79/187.90 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_b)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mult__imp__less__div__pos,axiom,
% 187.79/187.90 ! [V_x,V_z,V_y,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.79/187.90 => ( 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))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mult__imp__div__pos__less,axiom,
% 187.79/187.90 ! [V_z,V_x,V_y,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 => 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)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_pos__divide__less__eq,axiom,
% 187.79/187.90 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_b)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.90 => ( 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))
% 187.79/187.90 <=> 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_pos__less__divide__eq,axiom,
% 187.79/187.90 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_b)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> 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)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__less__eq,axiom,
% 187.79/187.90 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.90 => ( 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))
% 187.79/187.90 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.90 => 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))) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.90 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 => 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)) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_less__divide__eq,axiom,
% 187.79/187.90 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.90 => 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)) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.90 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 => 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))) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_add__num__frac,axiom,
% 187.79/187.90 ! [V_x,V_z,V_y,T_a] :
% 187.79/187.90 ( class_Fields_Ofield__inverse__zero(T_a)
% 187.79/187.90 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_add__divide__eq__iff,axiom,
% 187.79/187.90 ! [V_y,V_x,V_z,T_a] :
% 187.79/187.90 ( class_Fields_Ofield(T_a)
% 187.79/187.90 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_add__frac__num,axiom,
% 187.79/187.90 ! [V_z,V_x,V_y,T_a] :
% 187.79/187.90 ( class_Fields_Ofield__inverse__zero(T_a)
% 187.79/187.90 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__add__eq__iff,axiom,
% 187.79/187.90 ! [V_y,V_x,V_z,T_a] :
% 187.79/187.90 ( class_Fields_Ofield(T_a)
% 187.79/187.90 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_add__frac__eq,axiom,
% 187.79/187.90 ! [V_w,V_x,V_z,V_y,T_a] :
% 187.79/187.90 ( class_Fields_Ofield(T_a)
% 187.79/187.90 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_diff__frac__eq,axiom,
% 187.79/187.90 ! [V_w,V_x,V_z,V_y,T_a] :
% 187.79/187.90 ( class_Fields_Ofield(T_a)
% 187.79/187.90 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__diff__eq__iff,axiom,
% 187.79/187.90 ! [V_y,V_x,V_z,T_a] :
% 187.79/187.90 ( class_Fields_Ofield(T_a)
% 187.79/187.90 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_diff__divide__eq__iff,axiom,
% 187.79/187.90 ! [V_y,V_x,V_z,T_a] :
% 187.79/187.90 ( class_Fields_Ofield(T_a)
% 187.79/187.90 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_less__half__sum,axiom,
% 187.79/187.90 ! [V_b,V_a,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.90 => 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))))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_gt__half__sum,axiom,
% 187.79/187.90 ! [V_b,V_a,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_abs__div__pos,axiom,
% 187.79/187.90 ! [V_x,V_y,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_le__divide__eq,axiom,
% 187.79/187.90 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.90 => 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)) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.90 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 => 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))) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divide__le__eq,axiom,
% 187.79/187.90 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.90 => ( 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))
% 187.79/187.90 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.90 => 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))) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.90 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 => 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)) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_pos__le__divide__eq,axiom,
% 187.79/187.90 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_b)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> 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)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_pos__divide__le__eq,axiom,
% 187.79/187.90 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_b)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.90 => ( 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))
% 187.79/187.90 <=> 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mult__imp__div__pos__le,axiom,
% 187.79/187.90 ! [V_z,V_x,V_y,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 => 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)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mult__imp__le__div__pos,axiom,
% 187.79/187.90 ! [V_x,V_z,V_y,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field(T_a)
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.79/187.90 => ( 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))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 187.79/187.90 ! [V_f_2,V_A_2,T_b] :
% 187.79/187.90 ( ! [B_x] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.90 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__Un,axiom,
% 187.79/187.90 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.90 ( class_Fields_Ofield(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.79/187.90 => ( ! [B_x] :
% 187.79/187.90 ( 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)))
% 187.79/187.90 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 187.79/187.90 => 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))) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power__power__power,axiom,
% 187.79/187.90 ! [T_b] :
% 187.79/187.90 ( class_Power_Opower(T_b)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_int__power__div__base,axiom,
% 187.79/187.90 ! [V_k,V_m] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 187.79/187.90 => 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)))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__by__1,axiom,
% 187.79/187.90 ! [V_a,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 187.79/187.90 ! [V_y,V_x] :
% 187.79/187.90 ( c_Nat__Transfer_Ois__nat(V_x)
% 187.79/187.90 => ( c_Nat__Transfer_Ois__nat(V_y)
% 187.79/187.90 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__by__0,axiom,
% 187.79/187.90 ! [V_a,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__0,axiom,
% 187.79/187.90 ! [V_a,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zdiv__zminus__zminus,axiom,
% 187.79/187.90 ! [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) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zdiv__zminus2,axiom,
% 187.79/187.90 ! [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) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zdiv__zero,axiom,
% 187.79/187.90 ! [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) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 187.79/187.90 ! [V_y,V_x] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.79/187.90 => 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))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 187.79/187.90 ! [V_a_2,V_b_2] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 187.79/187.90 ! [V_a_2,V_b_2] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__neg__pos__less0,axiom,
% 187.79/187.90 ! [V_b,V_a] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.90 => 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))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zdiv__self,axiom,
% 187.79/187.90 ! [V_a] :
% 187.79/187.90 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.90 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__mult__mult1,axiom,
% 187.79/187.90 ! [V_b,V_a,V_c,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__mult__mult2,axiom,
% 187.79/187.90 ! [V_b,V_a,V_c,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__mult__self1__is__id,axiom,
% 187.79/187.90 ! [V_a,V_b,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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 ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__mult__self2__is__id,axiom,
% 187.79/187.90 ! [V_a,V_b,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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 ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__mult__mult1__if,axiom,
% 187.79/187.90 ! [V_b,V_a,V_c,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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) )
% 187.79/187.90 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__self,axiom,
% 187.79/187.90 ! [V_a,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zdiv__eq__0__iff,axiom,
% 187.79/187.90 ! [V_k_2,V_i_2] :
% 187.79/187.90 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.90 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.90 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 187.79/187.90 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 187.79/187.90 ! [V_a_2,V_b_2] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 187.79/187.90 ! [V_i_2,V_k_2] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 187.79/187.90 ! [V_b_2,V_a_2] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zdiv__mono2,axiom,
% 187.79/187.90 ! [V_b,V_b_H,V_a] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__nonneg__neg__le0,axiom,
% 187.79/187.90 ! [V_b,V_a] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.90 => 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))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__pos__pos__trivial,axiom,
% 187.79/187.90 ! [V_b,V_a] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 187.79/187.90 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 187.79/187.90 ! [V_a_2,V_b_2] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.90 => ( 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)))
% 187.79/187.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__nonpos__pos__le0,axiom,
% 187.79/187.90 ! [V_b,V_a] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.90 => 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))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zdiv__mono2__neg,axiom,
% 187.79/187.90 ! [V_b,V_b_H,V_a] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 187.79/187.90 => 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))) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__neg__neg__trivial,axiom,
% 187.79/187.90 ! [V_b,V_a] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 187.79/187.90 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zdiv__mono1,axiom,
% 187.79/187.90 ! [V_b,V_a_H,V_a] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.90 => 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))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zdiv__mono1__neg,axiom,
% 187.79/187.90 ! [V_b,V_a_H,V_a] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.90 => 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))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_int__div__less__self,axiom,
% 187.79/187.90 ! [V_k,V_x] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zdiv__zmult2__eq,axiom,
% 187.79/187.90 ! [V_b,V_a,V_c] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power_Opower_Opower__0,axiom,
% 187.79/187.90 ! [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 ).
% 187.79/187.90
% 187.79/187.90 fof(fact_power_Opower_Opower__Suc,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__mult__self1,axiom,
% 187.79/187.90 ! [V_c,V_a,V_b,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__mult__self2,axiom,
% 187.79/187.90 ! [V_c,V_a,V_b,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__add__self2,axiom,
% 187.79/187.90 ! [V_a,V_b,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__add__self1,axiom,
% 187.79/187.90 ! [V_a,V_b,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_divmod__int__rel__div__eq,axiom,
% 187.79/187.90 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 187.79/187.90 ( 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)
% 187.79/187.90 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 187.79/187.90 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.90 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_split__zdiv,axiom,
% 187.79/187.90 ! [V_k_2,V_n_2,V_Pa_2] :
% 187.79/187.90 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 187.79/187.90 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.90 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.79/187.90 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 187.79/187.90 => ! [B_i] :
% 187.79/187.90 ( ? [B_j] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 187.79/187.90 & 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) )
% 187.79/187.90 => hBOOL(hAPP(V_Pa_2,B_i)) ) )
% 187.79/187.90 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.90 => ! [B_i] :
% 187.79/187.90 ( ? [B_j] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.90 & 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) )
% 187.79/187.90 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_z3div__def,axiom,
% 187.79/187.90 ! [V_k,V_l] :
% 187.79/187.90 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 187.79/187.90 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 187.79/187.90 => 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))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_strong__setprod__reindex__cong,axiom,
% 187.79/187.90 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_d)
% 187.79/187.90 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.79/187.90 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 187.79/187.90 => ( ! [B_x] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.90 => 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) )
% 187.79/187.90 => 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) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__mono__one__left,axiom,
% 187.79/187.90 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 187.79/187.90 => ( ! [B_x] :
% 187.79/187.90 ( 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)))
% 187.79/187.90 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 187.79/187.90 => 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) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_setprod__mono__one__right,axiom,
% 187.79/187.90 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 187.79/187.90 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 187.79/187.90 => ( ! [B_x] :
% 187.79/187.90 ( 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)))
% 187.79/187.90 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 187.79/187.90 => 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) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__le__mono,axiom,
% 187.79/187.90 ! [V_k,V_n,V_m] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 187.79/187.90 => 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))) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__le__dividend,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__mult2__eq,axiom,
% 187.79/187.90 ! [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) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__1,axiom,
% 187.79/187.90 ! [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 ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__less,axiom,
% 187.79/187.90 ! [V_n,V_m] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.90 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nat__mult__div__cancel__disj,axiom,
% 187.79/187.90 ! [V_n,V_m,V_k] :
% 187.79/187.90 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.90 => 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) )
% 187.79/187.90 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zdiv__int,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__le__mono2,axiom,
% 187.79/187.90 ! [V_k,V_n,V_m] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 187.79/187.90 => 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))) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__mult__self__is__m,axiom,
% 187.79/187.90 ! [V_m,V_n] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.90 => 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 ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__mult__self1__is__m,axiom,
% 187.79/187.90 ! [V_m,V_n] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.90 => 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 ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nat__mult__div__cancel1,axiom,
% 187.79/187.90 ! [V_n,V_m,V_k] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__less__dividend,axiom,
% 187.79/187.90 ! [V_m,V_n] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__if,axiom,
% 187.79/187.90 ! [V_m,V_n] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.90 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.90 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.79/187.90 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.90 => 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)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_div__geq,axiom,
% 187.79/187.90 ! [V_m,V_n] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.90 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_split__div,axiom,
% 187.79/187.90 ! [V_k_2,V_n_2,V_Pa_2] :
% 187.79/187.90 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 187.79/187.90 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.90 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 187.79/187.90 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.90 => ! [B_i,B_j] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 187.79/187.90 => ( 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)
% 187.79/187.90 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 187.79/187.90 ! [V_y,V_x] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_nat__div__distrib,axiom,
% 187.79/187.90 ! [V_y,V_x] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_le__div__geq,axiom,
% 187.79/187.90 ! [V_m,V_n] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.79/187.90 => 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)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_split__div__lemma,axiom,
% 187.79/187.90 ! [V_m_2,V_q_2,V_n_2] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 187.79/187.90 => ( ( 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))
% 187.79/187.90 & 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)))) )
% 187.79/187.90 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_split__div_H,axiom,
% 187.79/187.90 ! [V_n_2,V_m_2,V_Pa_2] :
% 187.79/187.90 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 187.79/187.90 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.90 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 187.79/187.90 | ? [B_q] :
% 187.79/187.90 ( 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))
% 187.79/187.90 & 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))))
% 187.79/187.90 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_card__Pow,axiom,
% 187.79/187.90 ! [V_A_2,T_b] :
% 187.79/187.90 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_field__le__mult__one__interval,axiom,
% 187.79/187.90 ! [V_y,V_x,T_a] :
% 187.79/187.90 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.79/187.90 => ( ! [B_z] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 187.79/187.90 => 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)) ) )
% 187.79/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 187.79/187.90 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 187.79/187.90 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.90 & class_Groups_Ocomm__monoid__mult(T_b) )
% 187.79/187.90 => ( V_A_2 = V_B_2
% 187.79/187.90 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.79/187.90 => ( ! [B_x] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 187.79/187.90 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 187.79/187.90 => 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) ) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_PowI,axiom,
% 187.79/187.90 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.90 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Pow__iff,axiom,
% 187.79/187.90 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 187.79/187.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_PowD,axiom,
% 187.79/187.90 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 187.79/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Pow__mono,axiom,
% 187.79/187.90 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.90 => 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))) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_image__Pow__surj,axiom,
% 187.79/187.90 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 187.79/187.90 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Pow__UNIV,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Un__Pow__subset,axiom,
% 187.79/187.90 ! [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)))) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Pow__Int__eq,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Pow__empty,axiom,
% 187.79/187.90 ! [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))) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Pow__bottom,axiom,
% 187.79/187.90 ! [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))) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Cantors__paradox,axiom,
% 187.79/187.90 ! [V_A_2,T_b] :
% 187.79/187.90 ~ ? [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) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Pow__top,axiom,
% 187.79/187.90 ! [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))) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Pow__not__empty,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Pow__insert,axiom,
% 187.79/187.90 ! [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))) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_UN__Pow__subset,axiom,
% 187.79/187.90 ! [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)))) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_image__Pow__mono,axiom,
% 187.79/187.90 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.90 ( 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))
% 187.79/187.90 => 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))) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Pow__def,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_finite__Pow__iff,axiom,
% 187.79/187.90 ! [V_A_2,T_b] :
% 187.79/187.90 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 187.79/187.90 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Pow__Compl,axiom,
% 187.79/187.90 ! [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))))) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 187.79/187.90 ! [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)))) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Powp__Pow__eq,axiom,
% 187.79/187.90 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.90 ( 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))
% 187.79/187.90 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_split__neg__lemma,axiom,
% 187.79/187.90 ! [V_n_2,V_Pa_2,V_k_2] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 187.79/187.90 <=> ! [B_i,B_j] :
% 187.79/187.90 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.90 & 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) )
% 187.79/187.90 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_split__pos__lemma,axiom,
% 187.79/187.90 ! [V_n_2,V_Pa_2,V_k_2] :
% 187.79/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 187.79/187.90 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 187.79/187.90 <=> ! [B_i,B_j] :
% 187.79/187.90 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 187.79/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 187.79/187.90 & 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) )
% 187.79/187.90 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zpower__zmod,axiom,
% 187.79/187.90 ! [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) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 187.79/187.90 ! [V_y,V_x] :
% 187.79/187.90 ( c_Nat__Transfer_Ois__nat(V_x)
% 187.79/187.90 => ( c_Nat__Transfer_Ois__nat(V_y)
% 187.79/187.90 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zdiff__zmod__left,axiom,
% 187.79/187.90 ! [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) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zdiff__zmod__right,axiom,
% 187.79/187.90 ! [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) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zmod__zminus2,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zmod__zminus__zminus,axiom,
% 187.79/187.90 ! [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)) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zminus__zmod,axiom,
% 187.79/187.90 ! [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) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__mod__trivial,axiom,
% 187.79/187.90 ! [V_b,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__diff__right__eq,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Oring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__diff__left__eq,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Oring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__diff__eq,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Oring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__diff__cong,axiom,
% 187.79/187.90 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Oring__div(T_a)
% 187.79/187.90 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 187.79/187.90 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 187.79/187.90 => 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) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__minus__cong,axiom,
% 187.79/187.90 ! [V_a_H,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Oring__div(T_a)
% 187.79/187.90 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 187.79/187.90 => 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) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__minus__eq,axiom,
% 187.79/187.90 ! [V_b,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Oring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__mult__right__eq,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__mult__left__eq,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__mult__eq,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__mult__mult1,axiom,
% 187.79/187.90 ! [V_b,V_a,V_c,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => 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)) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__mult__mult2,axiom,
% 187.79/187.90 ! [V_b,V_c,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_zmod__simps_I4_J,axiom,
% 187.79/187.90 ! [V_b,V_c,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__mult__cong,axiom,
% 187.79/187.90 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 187.79/187.90 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 187.79/187.90 => 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) ) ) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__add__self2,axiom,
% 187.79/187.90 ! [V_b,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__add__self1,axiom,
% 187.79/187.90 ! [V_a,V_b,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.90 fof(fact_mod__add__right__eq,axiom,
% 187.79/187.90 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.90 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.90 => 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) ) ).
% 187.79/187.90
% 187.79/187.91 fof(fact_mod__add__left__eq,axiom,
% 187.79/187.91 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__add__eq,axiom,
% 187.79/187.91 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__simps_I2_J,axiom,
% 187.79/187.91 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__simps_I1_J,axiom,
% 187.79/187.91 ! [V_b,V_c,V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__add__cong,axiom,
% 187.79/187.91 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 187.79/187.91 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 187.79/187.91 => 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) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__0,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__zero,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__by__0,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__self,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__self,axiom,
% 187.79/187.91 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__zmult1__eq,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__simps_I3_J,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__mult__self2__is__0,axiom,
% 187.79/187.91 ! [V_b,V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__mult__self1__is__0,axiom,
% 187.79/187.91 ! [V_a,V_b,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__mult__self2,axiom,
% 187.79/187.91 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__mult__self1,axiom,
% 187.79/187.91 ! [V_b,V_c,V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__by__1,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__div__trivial,axiom,
% 187.79/187.91 ! [V_b,V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 187.79/187.91 ! [V_y,V_x] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.79/187.91 => 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))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__le__nonneg__dividend,axiom,
% 187.79/187.91 ! [V_k,V_m] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_neg__mod__bound,axiom,
% 187.79/187.91 ! [V_a,V_b] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_pos__mod__bound,axiom,
% 187.79/187.91 ! [V_a,V_b] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__eq__0__iff,axiom,
% 187.79/187.91 ! [V_d_2,V_m_2] :
% 187.79/187.91 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.91 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__zminus2__not__zero,axiom,
% 187.79/187.91 ! [V_l,V_k] :
% 187.79/187.91 ( 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)
% 187.79/187.91 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__zminus1__not__zero,axiom,
% 187.79/187.91 ! [V_l,V_k] :
% 187.79/187.91 ( 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)
% 187.79/187.91 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_DIVISION__BY__ZERO,axiom,
% 187.79/187.91 ! [V_a] :
% 187.79/187.91 ( 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)
% 187.79/187.91 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__zdiv__trivial,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zdiv__zadd1__eq,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 187.79/187.91 ! [V_b,V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => 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 ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__div__equality2,axiom,
% 187.79/187.91 ! [V_a,V_b,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => 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 ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__div__equality,axiom,
% 187.79/187.91 ! [V_b,V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => 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 ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_div__mod__equality2,axiom,
% 187.79/187.91 ! [V_c,V_a,V_b,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_div__mod__equality,axiom,
% 187.79/187.91 ! [V_c,V_b,V_a,T_a] :
% 187.79/187.91 ( class_Divides_Osemiring__div(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__neg__neg__trivial,axiom,
% 187.79/187.91 ! [V_b,V_a] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 187.79/187.91 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_neg__mod__conj,axiom,
% 187.79/187.91 ! [V_a,V_b] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.91 => ( 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)))
% 187.79/187.91 & 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))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_neg__mod__sign,axiom,
% 187.79/187.91 ! [V_a,V_b] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__pos__pos__trivial,axiom,
% 187.79/187.91 ! [V_b,V_a] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 187.79/187.91 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_pos__mod__conj,axiom,
% 187.79/187.91 ! [V_a,V_b] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.91 => ( 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)))
% 187.79/187.91 & 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_pos__mod__sign,axiom,
% 187.79/187.91 ! [V_a,V_b] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__zminus1__eq__if,axiom,
% 187.79/187.91 ! [V_b,V_a] :
% 187.79/187.91 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__zminus2__eq__if,axiom,
% 187.79/187.91 ! [V_b,V_a] :
% 187.79/187.91 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.91 => 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) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__zdiv__equality,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zdiv__zmult1__eq,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zdiv__zmod__equality,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zdiv__zmod__equality2,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmult__div__cancel,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__zdiv__equality_H,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Powp__mono,axiom,
% 187.79/187.91 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__pos__neg__trivial,axiom,
% 187.79/187.91 ! [V_b,V_a] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.91 => ( 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)))
% 187.79/187.91 => 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) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_split__zmod,axiom,
% 187.79/187.91 ! [V_k_2,V_n_2,V_Pa_2] :
% 187.79/187.91 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 187.79/187.91 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.91 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 187.79/187.91 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 187.79/187.91 => ! [B_i,B_j] :
% 187.79/187.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 187.79/187.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 187.79/187.91 & 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) )
% 187.79/187.91 => hBOOL(hAPP(V_Pa_2,B_j)) ) )
% 187.79/187.91 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.91 => ! [B_i,B_j] :
% 187.79/187.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 187.79/187.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.91 & 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) )
% 187.79/187.91 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmult2__lemma__aux3,axiom,
% 187.79/187.91 ! [V_q,V_b,V_r,V_c] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 187.79/187.91 => 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))) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmult2__lemma__aux4,axiom,
% 187.79/187.91 ! [V_q,V_b,V_r,V_c] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 187.79/187.91 => 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))) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmult2__lemma__aux1,axiom,
% 187.79/187.91 ! [V_q,V_r,V_b,V_c] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.91 => 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))) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmult2__lemma__aux2,axiom,
% 187.79/187.91 ! [V_q,V_r,V_b,V_c] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.91 => 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))) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_divmod__int__rel__mod__eq,axiom,
% 187.79/187.91 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 187.79/187.91 ( 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)
% 187.79/187.91 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.79/187.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 187.79/187.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 187.79/187.91 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.91 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__zmult2__eq,axiom,
% 187.79/187.91 ! [V_b,V_a,V_c] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zdiv__zminus1__eq__if,axiom,
% 187.79/187.91 ! [V_a,V_b] :
% 187.79/187.91 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.91 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.91 => 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)) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zdiv__zminus2__eq__if,axiom,
% 187.79/187.91 ! [V_a,V_b] :
% 187.79/187.91 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.91 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.91 => 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)) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_z3mod__def,axiom,
% 187.79/187.91 ! [V_k,V_l] :
% 187.79/187.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 187.79/187.91 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_setprod__pos__nat,axiom,
% 187.79/187.91 ! [V_f_2,V_S_2,T_b] :
% 187.79/187.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 187.79/187.91 => ( ! [B_x] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 187.79/187.91 => 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))) )
% 187.79/187.91 => 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))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_card__quotient__disjoint,axiom,
% 187.79/187.91 ! [V_r_2,V_A_2,T_b] :
% 187.79/187.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.91 => ( 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)
% 187.79/187.91 => 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) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_card_Oneutral,axiom,
% 187.79/187.91 ! [V_A_2,T_b] :
% 187.79/187.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.91 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.91 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.79/187.91 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__mult__distrib2,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__mult__distrib,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__less,axiom,
% 187.79/187.91 ! [V_n,V_m] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.91 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__less__eq__dividend,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_quotient__is__empty,axiom,
% 187.79/187.91 ! [V_r_2,V_A_2,T_b] :
% 187.79/187.91 ( 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))
% 187.79/187.91 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_quotient__is__empty2,axiom,
% 187.79/187.91 ! [V_r_2,V_A_2,T_b] :
% 187.79/187.91 ( 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)
% 187.79/187.91 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_quotient__empty,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__1,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__Suc,axiom,
% 187.79/187.91 ! [V_n,V_m] :
% 187.79/187.91 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 187.79/187.91 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.79/187.91 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__less__divisor,axiom,
% 187.79/187.91 ! [V_m,V_n] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__eq__0__iff,axiom,
% 187.79/187.91 ! [V_d_2,V_m_2] :
% 187.79/187.91 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.91 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__if,axiom,
% 187.79/187.91 ! [V_n,V_m] :
% 187.79/187.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.91 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.91 => 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) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__geq,axiom,
% 187.79/187.91 ! [V_n,V_m] :
% 187.79/187.91 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__mult__self3,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_le__mod__geq,axiom,
% 187.79/187.91 ! [V_m,V_n] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__int,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_div__add1__eq,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__gcd_Osimps,axiom,
% 187.79/187.91 ! [V_x,V_y] :
% 187.79/187.91 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.91 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 187.79/187.91 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__le__divisor,axiom,
% 187.79/187.91 ! [V_m,V_n] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__mult__self4,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__mult2__eq,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_div__mult1__eq,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_div__mod__equality_H,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mult__div__cancel,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Divides_Omod__div__equality_H,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_quotient__diff1,axiom,
% 187.79/187.91 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 187.79/187.91 ( 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)
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__lemma,axiom,
% 187.79/187.91 ! [V_q,V_b,V_r,V_c] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 187.79/187.91 => 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))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_split__mod,axiom,
% 187.79/187.91 ! [V_k_2,V_n_2,V_Pa_2] :
% 187.79/187.91 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 187.79/187.91 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.91 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 187.79/187.91 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.91 => ! [B_i,B_j] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 187.79/187.91 => ( 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)
% 187.79/187.91 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Suc__times__mod__eq,axiom,
% 187.79/187.91 ! [V_m,V_k] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__mod__distrib,axiom,
% 187.79/187.91 ! [V_y,V_x] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 187.79/187.91 ! [V_y,V_x] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_quotient__def,axiom,
% 187.79/187.91 ! [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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_singleton__quotient,axiom,
% 187.79/187.91 ! [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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_quotientI,axiom,
% 187.79/187.91 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_fold__image__cong,axiom,
% 187.79/187.91 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 187.79/187.91 ( class_Groups_Oab__semigroup__mult(T_c)
% 187.79/187.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.91 => ( ! [B_x] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.91 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 187.79/187.91 => 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) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Image__eq__UN,axiom,
% 187.79/187.91 ! [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))))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Image__Int__subset,axiom,
% 187.79/187.91 ! [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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Image__UN,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_quotientE,axiom,
% 187.79/187.91 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 187.79/187.91 ( 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)))
% 187.79/187.91 => ~ ! [B_x] :
% 187.79/187.91 ( 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))))
% 187.79/187.91 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Image__empty,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Image__mono,axiom,
% 187.79/187.91 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 187.79/187.91 ( 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))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 187.79/187.91 => 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))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Image__Un,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Un__Image,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__mod__eq__lemma,axiom,
% 187.79/187.91 ! [V_y,V_n,V_x] :
% 187.79/187.91 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 187.79/187.91 => ? [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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__induct__0,axiom,
% 187.79/187.91 ! [V_i_2,V_Pa_2,V_p_2] :
% 187.79/187.91 ( ! [B_i] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 187.79/187.91 => ( hBOOL(hAPP(V_Pa_2,B_i))
% 187.79/187.91 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 187.79/187.91 => ( hBOOL(hAPP(V_Pa_2,V_i_2))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 187.79/187.91 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Max__eqI,axiom,
% 187.79/187.91 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.91 ( class_Orderings_Olinorder(T_b)
% 187.79/187.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.91 => ( ! [B_y] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 187.79/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.91 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Min__eqI,axiom,
% 187.79/187.91 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.91 ( class_Orderings_Olinorder(T_b)
% 187.79/187.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.91 => ( ! [B_y] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 187.79/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.91 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__by__empty,axiom,
% 187.79/187.91 ! [V_B_2,T_b,V_A_2] :
% 187.79/187.91 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_expand__Suc,axiom,
% 187.79/187.91 ! [V_v] :
% 187.79/187.91 ( 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)))
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_quotient__disj,axiom,
% 187.79/187.91 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 187.79/187.91 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.91 => ( 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)))
% 187.79/187.91 => ( 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)))
% 187.79/187.91 => ( V_X_2 = V_Y_2
% 187.79/187.91 | 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)) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_com_Osize_I11_J,axiom,
% 187.79/187.91 ! [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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_com_Osize_I3_J,axiom,
% 187.79/187.91 ! [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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_of__nat__number__of__lemma,axiom,
% 187.79/187.91 ! [V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => ( ( 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)))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => 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) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_com_Osimps_I22_J,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_com_Osimps_I23_J,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_com_Osimps_I10_J,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_com_Osimps_I11_J,axiom,
% 187.79/187.91 ! [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 ).
% 187.79/187.91
% 187.79/187.91 fof(fact_com_Osimps_I35_J,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_com_Osimps_I34_J,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_of__nat__number__of__eq,axiom,
% 187.79/187.91 ! [V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_number__of__reorient,axiom,
% 187.79/187.91 ! [V_x_2,V_w_2,T_b] :
% 187.79/187.91 ( class_Int_Onumber(T_b)
% 187.79/187.91 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 187.79/187.91 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_eq__number__of,axiom,
% 187.79/187.91 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 & class_Int_Oring__char__0(T_b) )
% 187.79/187.91 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 187.79/187.91 <=> V_x_2 = V_y_2 ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_com_Osimps_I2_J,axiom,
% 187.79/187.91 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 187.79/187.91 ( 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)
% 187.79/187.91 <=> ( V_loc_2 = V_loc_H_2
% 187.79/187.91 & V_fun_2 = V_fun_H_2
% 187.79/187.91 & V_com_2 = V_com_H_2 ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_number__of__eq,axiom,
% 187.79/187.91 ! [V_k,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_of__int__number__of__eq,axiom,
% 187.79/187.91 ! [V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_com_Osimps_I36_J,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_com_Osimps_I37_J,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_com_Osimps_I39_J,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_com_Osimps_I38_J,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_com_Osimps_I66_J,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_le__number__of__eq__not__less,axiom,
% 187.79/187.91 ! [V_w_2,V_v_2,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber(T_b)
% 187.79/187.91 & class_Orderings_Olinorder(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> ~ 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))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_left__distrib__number__of,axiom,
% 187.79/187.91 ! [V_v,V_b,V_a,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber(T_b)
% 187.79/187.91 & class_Rings_Osemiring(T_b) )
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_right__distrib__number__of,axiom,
% 187.79/187.91 ! [V_c,V_b,V_v,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber(T_b)
% 187.79/187.91 & class_Rings_Osemiring(T_b) )
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_left__diff__distrib__number__of,axiom,
% 187.79/187.91 ! [V_v,V_b,V_a,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber(T_b)
% 187.79/187.91 & class_Rings_Oring(T_b) )
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_right__diff__distrib__number__of,axiom,
% 187.79/187.91 ! [V_c,V_b,V_v,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber(T_b)
% 187.79/187.91 & class_Rings_Oring(T_b) )
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_le__number__of,axiom,
% 187.79/187.91 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 & class_Rings_Olinordered__idom(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__number__of,axiom,
% 187.79/187.91 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 & class_Rings_Olinordered__idom(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_min__number__of,axiom,
% 187.79/187.91 ! [V_v,V_u,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber(T_b)
% 187.79/187.91 & class_Orderings_Oord(T_b) )
% 187.79/187.91 => ( ( 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)))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => 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) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_max__number__of,axiom,
% 187.79/187.91 ! [V_v,V_u,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber(T_b)
% 187.79/187.91 & class_Orderings_Oord(T_b) )
% 187.79/187.91 => ( ( 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)))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => 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) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__number__of__left,axiom,
% 187.79/187.91 ! [V_z,V_w,V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__number__of__eq,axiom,
% 187.79/187.91 ! [V_w,V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_number__of__add,axiom,
% 187.79/187.91 ! [V_w,V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mult__number__of__left,axiom,
% 187.79/187.91 ! [V_z,V_w,V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_arith__simps_I32_J,axiom,
% 187.79/187.91 ! [V_w,V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_number__of__mult,axiom,
% 187.79/187.91 ! [V_w,V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_number__of__diff,axiom,
% 187.79/187.91 ! [V_w,V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_arith__simps_I30_J,axiom,
% 187.79/187.91 ! [V_w,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_number__of__minus,axiom,
% 187.79/187.91 ! [V_w,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Ints__number__of,axiom,
% 187.79/187.91 ! [V_w_2,T_b] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_eq__divide__eq__number__of1,axiom,
% 187.79/187.91 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 187.79/187.91 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 187.79/187.91 & class_Int_Onumber(T_b) )
% 187.79/187.91 => ( 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))
% 187.79/187.91 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.91 => 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 )
% 187.79/187.91 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.91 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_eq__divide__eq__number__of,axiom,
% 187.79/187.91 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 187.79/187.91 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 187.79/187.91 & class_Int_Onumber(T_b) )
% 187.79/187.91 => ( 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)
% 187.79/187.91 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.91 => 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 )
% 187.79/187.91 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.91 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_divide__eq__eq__number__of,axiom,
% 187.79/187.91 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 187.79/187.91 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 187.79/187.91 & class_Int_Onumber(T_b) )
% 187.79/187.91 => ( 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)
% 187.79/187.91 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.91 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_divide__eq__eq__number__of1,axiom,
% 187.79/187.91 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 187.79/187.91 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 187.79/187.91 & class_Int_Onumber(T_b) )
% 187.79/187.91 => ( 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
% 187.79/187.91 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.91 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__number__of__diff1,axiom,
% 187.79/187.91 ! [V_c,V_w,V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_minus__number__of__mult,axiom,
% 187.79/187.91 ! [V_z,V_w,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_diff__number__of__eq,axiom,
% 187.79/187.91 ! [V_w,V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__divide__eq__number__of1,axiom,
% 187.79/187.91 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 187.79/187.91 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.91 & class_Int_Onumber(T_b) )
% 187.79/187.91 => ( 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))))
% 187.79/187.91 <=> ( ( 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)))
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => ( ( 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)))
% 187.79/187.91 => 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)))) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__divide__eq__number__of,axiom,
% 187.79/187.91 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 187.79/187.91 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.91 & class_Int_Onumber(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.91 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.91 => 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))) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.91 => 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))) ) ) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_divide__less__eq__number__of,axiom,
% 187.79/187.91 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 187.79/187.91 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.91 & class_Int_Onumber(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.91 => 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))) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.91 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.91 => 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))) ) ) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_divide__less__eq__number__of1,axiom,
% 187.79/187.91 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 187.79/187.91 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.91 & class_Int_Onumber(T_b) )
% 187.79/187.91 => ( 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))
% 187.79/187.91 <=> ( ( 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)))
% 187.79/187.91 => 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)))) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => ( ( 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)))
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_abs__number__of,axiom,
% 187.79/187.91 ! [V_x,T_a] :
% 187.79/187.91 ( ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 & class_Rings_Olinordered__idom(T_a) )
% 187.79/187.91 => ( ( 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)))
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => 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) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__number__of__diff2,axiom,
% 187.79/187.91 ! [V_w,V_c,V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_divide__le__eq__number__of1,axiom,
% 187.79/187.91 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 187.79/187.91 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.91 & class_Int_Onumber(T_b) )
% 187.79/187.91 => ( 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))
% 187.79/187.91 <=> ( ( 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)))
% 187.79/187.91 => 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)))) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => ( ( 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)))
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_divide__le__eq__number__of,axiom,
% 187.79/187.91 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 187.79/187.91 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.91 & class_Int_Onumber(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.91 => 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))) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.91 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.91 => 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))) ) ) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_le__divide__eq__number__of,axiom,
% 187.79/187.91 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 187.79/187.91 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.91 & class_Int_Onumber(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 187.79/187.91 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.91 => 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))) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 187.79/187.91 => 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))) ) ) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_le__divide__eq__number__of1,axiom,
% 187.79/187.91 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 187.79/187.91 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.91 & class_Int_Onumber(T_b) )
% 187.79/187.91 => ( 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))))
% 187.79/187.91 <=> ( ( 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)))
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => ( ( 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)))
% 187.79/187.91 => 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)))) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_equiv__class__self,axiom,
% 187.79/187.91 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 187.79/187.91 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.91 => 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)))))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_UN__equiv__class2,axiom,
% 187.79/187.91 ! [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] :
% 187.79/187.91 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 187.79/187.91 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 187.79/187.91 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 187.79/187.91 => 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) ) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_UN__equiv__class,axiom,
% 187.79/187.91 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 187.79/187.91 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.91 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.91 => 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) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_one__mod__nat__number__of,axiom,
% 187.79/187.91 ! [V_v_H] :
% 187.79/187.91 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 187.79/187.91 => 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))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_one__div__nat__number__of,axiom,
% 187.79/187.91 ! [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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__eq__number__of__int__code,axiom,
% 187.79/187.91 ! [V_l_2,V_k_2] :
% 187.79/187.91 ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_plus__numeral__code_I9_J,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_times__numeral__code_I5_J,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_minus__numeral__code_I5_J,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_number__of__is__id,axiom,
% 187.79/187.91 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__number__of__int__code,axiom,
% 187.79/187.91 ! [V_l_2,V_k_2] :
% 187.79/187.91 ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_int__number__of__def,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__number__of__def,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__number__of,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_congruent2__implies__congruent,axiom,
% 187.79/187.91 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 187.79/187.91 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 187.79/187.91 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.91 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_minus__numeral__code_I6_J,axiom,
% 187.79/187.91 ! [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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_neg__imp__number__of__eq__0,axiom,
% 187.79/187.91 ! [V_v] :
% 187.79/187.91 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_int__eq__iff__number__of,axiom,
% 187.79/187.91 ! [V_v_2,V_m_2] :
% 187.79/187.91 ( 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)
% 187.79/187.91 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 187.79/187.91 & 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))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_eq__nat__number__of,axiom,
% 187.79/187.91 ! [V_v_H_2,V_v_2] :
% 187.79/187.91 ( 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)
% 187.79/187.91 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 187.79/187.91 => 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))) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 187.79/187.91 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 187.79/187.91 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 187.79/187.91 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__number__of__add__left,axiom,
% 187.79/187.91 ! [V_k,V_v_H,V_v] :
% 187.79/187.91 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 187.79/187.91 => 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) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_int__nat__number__of,axiom,
% 187.79/187.91 ! [V_v] :
% 187.79/187.91 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__nat__number__of,axiom,
% 187.79/187.91 ! [V_v_H,V_v] :
% 187.79/187.91 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 187.79/187.91 => 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))) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_congruent2__implies__congruent__UN,axiom,
% 187.79/187.91 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 187.79/187.91 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 187.79/187.91 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 187.79/187.91 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 187.79/187.91 => 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)) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_div__nat__number__of,axiom,
% 187.79/187.91 ! [V_v_H,V_v] :
% 187.79/187.91 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power__nat__number__of__number__of,axiom,
% 187.79/187.91 ! [V_w,V_v] :
% 187.79/187.91 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power__nat__number__of,axiom,
% 187.79/187.91 ! [V_n,V_v] :
% 187.79/187.91 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Suc__nat__number__of__add,axiom,
% 187.79/187.91 ! [V_n,V_v] :
% 187.79/187.91 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_diff__nat__number__of,axiom,
% 187.79/187.91 ! [V_v_2,V_v_H_2] :
% 187.79/187.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_min__number__of__Suc,axiom,
% 187.79/187.91 ! [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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_min__Suc__number__of,axiom,
% 187.79/187.91 ! [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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I19_J,axiom,
% 187.79/187.91 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_diff__bin__simps_I1_J,axiom,
% 187.79/187.91 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 187.79/187.91
% 187.79/187.91 fof(fact_minus__Pls,axiom,
% 187.79/187.91 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Pls__def,axiom,
% 187.79/187.91 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I2_J,axiom,
% 187.79/187.91 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__Pls__right,axiom,
% 187.79/187.91 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__Pls,axiom,
% 187.79/187.91 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 187.79/187.91
% 187.79/187.91 fof(fact_succ__pred,axiom,
% 187.79/187.91 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mult__Pls,axiom,
% 187.79/187.91 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 187.79/187.91
% 187.79/187.91 fof(fact_semiring__norm_I112_J,axiom,
% 187.79/187.91 ! [T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_number__of__Pls,axiom,
% 187.79/187.91 ! [T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__numeral__0,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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 ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__numeral__0__right,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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 ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_bin__less__0__simps_I1_J,axiom,
% 187.79/187.91 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_semiring__norm_I113_J,axiom,
% 187.79/187.91 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__number__of__Pls,axiom,
% 187.79/187.91 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zero__is__num__zero,axiom,
% 187.79/187.91 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Suc__diff__number__of,axiom,
% 187.79/187.91 ! [V_m,V_v] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_not__neg__number__of__Pls,axiom,
% 187.79/187.91 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__1__add__number__of,axiom,
% 187.79/187.91 ! [V_v] :
% 187.79/187.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__number__of__add__1,axiom,
% 187.79/187.91 ! [V_v] :
% 187.79/187.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_le__iff__pred__less,axiom,
% 187.79/187.91 ! [V_l_2,V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_pred__def,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__number__of__diff__1,axiom,
% 187.79/187.91 ! [V_v] :
% 187.79/187.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_divide__Numeral0,axiom,
% 187.79/187.91 ! [V_x,T_a] :
% 187.79/187.91 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 187.79/187.91 & class_Int_Onumber__ring(T_a) )
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_eq__number__of__0,axiom,
% 187.79/187.91 ! [V_v_2] :
% 187.79/187.91 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_eq__0__number__of,axiom,
% 187.79/187.91 ! [V_v_2] :
% 187.79/187.91 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_number__of2,axiom,
% 187.79/187.91 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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__nat__number__of,axiom,
% 187.79/187.91 ! [V_v_H_2,V_v_2] :
% 187.79/187.91 ( 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)))
% 187.79/187.91 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 187.79/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 187.79/187.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_le__nat__number__of,axiom,
% 187.79/187.91 ! [V_v_H_2,V_v_2] :
% 187.79/187.91 ( 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)))
% 187.79/187.91 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 187.79/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_succ__def,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_le__special_I3_J,axiom,
% 187.79/187.91 ! [V_x_2,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 & class_Rings_Olinordered__idom(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_le__special_I1_J,axiom,
% 187.79/187.91 ! [V_y_2,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 & class_Rings_Olinordered__idom(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__special_I3_J,axiom,
% 187.79/187.91 ! [V_x_2,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 & class_Rings_Olinordered__idom(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__special_I1_J,axiom,
% 187.79/187.91 ! [V_y_2,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 & class_Rings_Olinordered__idom(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__0__number__of,axiom,
% 187.79/187.91 ! [V_v_2] :
% 187.79/187.91 ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__nat__number__of,axiom,
% 187.79/187.91 ! [V_v_H,V_v] :
% 187.79/187.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.79/187.91 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 187.79/187.91 => 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)) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_number__of__succ,axiom,
% 187.79/187.91 ! [V_k,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_number__of__pred,axiom,
% 187.79/187.91 ! [V_w,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mult__nat__number__of,axiom,
% 187.79/187.91 ! [V_v_H,V_v] :
% 187.79/187.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__number__of__mult__left,axiom,
% 187.79/187.91 ! [V_k,V_v_H,V_v] :
% 187.79/187.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.79/187.91 => 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) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.79/187.91 => 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) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_neg__number__of__pred__iff__0,axiom,
% 187.79/187.91 ! [V_v_2] :
% 187.79/187.91 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 187.79/187.91 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Suc__eq__number__of,axiom,
% 187.79/187.91 ! [V_v_2,V_n_2] :
% 187.79/187.91 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 187.79/187.91 <=> 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))))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_eq__number__of__Suc,axiom,
% 187.79/187.91 ! [V_n_2,V_v_2] :
% 187.79/187.91 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 187.79/187.91 <=> 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))))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__case__number__of,axiom,
% 187.79/187.91 ! [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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__number__of__Suc,axiom,
% 187.79/187.91 ! [V_n_2,V_v_2] :
% 187.79/187.91 ( 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)))
% 187.79/187.91 <=> 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)))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__Suc__number__of,axiom,
% 187.79/187.91 ! [V_v_2,V_n_2] :
% 187.79/187.91 ( 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)))
% 187.79/187.91 <=> 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))))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_le__number__of__Suc,axiom,
% 187.79/187.91 ! [V_n_2,V_v_2] :
% 187.79/187.91 ( 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)))
% 187.79/187.91 <=> 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)))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_le__Suc__number__of,axiom,
% 187.79/187.91 ! [V_v_2,V_n_2] :
% 187.79/187.91 ( 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)))
% 187.79/187.91 <=> 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))))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Suc__nat__number__of,axiom,
% 187.79/187.91 ! [V_v] :
% 187.79/187.91 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_max__Suc__number__of,axiom,
% 187.79/187.91 ! [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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_max__number__of__Suc,axiom,
% 187.79/187.91 ! [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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__case__add__eq__if,axiom,
% 187.79/187.91 ! [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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__rec__add__eq__if,axiom,
% 187.79/187.91 ! [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))))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__rec__number__of,axiom,
% 187.79/187.91 ! [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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_UN__equiv__class__type2,axiom,
% 187.79/187.91 ! [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] :
% 187.79/187.91 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 187.79/187.91 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 187.79/187.91 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 187.79/187.91 => ( 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)))
% 187.79/187.91 => ( 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)))
% 187.79/187.91 => ( ! [B_x1] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 187.79/187.91 => ! [B_x2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 187.79/187.91 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 187.79/187.91 => 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)) ) ) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_UN__equiv__class__type,axiom,
% 187.79/187.91 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 187.79/187.91 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.91 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 187.79/187.91 => ( 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)))
% 187.79/187.91 => ( ! [B_x] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.91 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 187.79/187.91 => 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)) ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__rec__0,axiom,
% 187.79/187.91 ! [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 ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__rec__Suc,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_eq__special_I3_J,axiom,
% 187.79/187.91 ! [V_x_2,T_b] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.91 <=> 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)))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_eq__special_I1_J,axiom,
% 187.79/187.91 ! [V_y_2,T_b] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 187.79/187.91 <=> 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)))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power__number__of__odd__number__of,axiom,
% 187.79/187.91 ! [V_v_2,V_w_2,T_b] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 => ( ( 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)))
% 187.79/187.91 => 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))) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => 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) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_iszero__number__of__Bit1,axiom,
% 187.79/187.91 ! [V_w,T_a] :
% 187.79/187.91 ( ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 & class_Int_Oring__char__0(T_a) )
% 187.79/187.91 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__eq__int__code_I16_J,axiom,
% 187.79/187.91 ! [V_k2_2,V_k1_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I34_J,axiom,
% 187.79/187.91 ! [V_l_2,V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__int__code_I16_J,axiom,
% 187.79/187.91 ! [V_k2_2,V_k1_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I17_J,axiom,
% 187.79/187.91 ! [V_l_2,V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I51_J,axiom,
% 187.79/187.91 ! [V_l_2,V_k_2] :
% 187.79/187.91 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 187.79/187.91 <=> V_k_2 = V_l_2 ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I46_J,axiom,
% 187.79/187.91 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I39_J,axiom,
% 187.79/187.91 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_not__iszero__Numeral1,axiom,
% 187.79/187.91 ! [T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_iszero__def,axiom,
% 187.79/187.91 ! [V_z_2,T_b] :
% 187.79/187.91 ( class_Rings_Osemiring__1(T_b)
% 187.79/187.91 => ( c_Int_Oiszero(T_b,V_z_2)
% 187.79/187.91 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_iszero__0,axiom,
% 187.79/187.91 ! [T_a] :
% 187.79/187.91 ( class_Rings_Osemiring__1(T_a)
% 187.79/187.91 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_not__iszero__1,axiom,
% 187.79/187.91 ! [T_a] :
% 187.79/187.91 ( class_Rings_Osemiring__1(T_a)
% 187.79/187.91 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_bin__less__0__simps_I4_J,axiom,
% 187.79/187.91 ! [V_w_2] :
% 187.79/187.91 ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I22_J,axiom,
% 187.79/187.91 ! [V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I12_J,axiom,
% 187.79/187.91 ! [V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Bit1__def,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_neg__number__of__Bit1,axiom,
% 187.79/187.91 ! [V_w_2] :
% 187.79/187.91 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 187.79/187.91 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_minus__Bit1,axiom,
% 187.79/187.91 ! [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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_succ__Pls,axiom,
% 187.79/187.91 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_number__of__Bit1,axiom,
% 187.79/187.91 ! [V_w,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mult__numeral__1,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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 ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mult__numeral__1__right,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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 ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_semiring__norm_I110_J,axiom,
% 187.79/187.91 ! [T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_numeral__1__eq__1,axiom,
% 187.79/187.91 ! [T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I5_J,axiom,
% 187.79/187.91 ! [V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I29_J,axiom,
% 187.79/187.91 ! [V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_divide__Numeral1,axiom,
% 187.79/187.91 ! [V_x,T_a] :
% 187.79/187.91 ( ( class_Fields_Ofield(T_a)
% 187.79/187.91 & class_Int_Onumber__ring(T_a) )
% 187.79/187.91 => 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 ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_divide__numeral__1,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( ( class_Fields_Ofield(T_a)
% 187.79/187.91 & class_Int_Onumber__ring(T_a) )
% 187.79/187.91 => 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 ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_eq__special_I2_J,axiom,
% 187.79/187.91 ! [V_y_2,T_b] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 187.79/187.91 <=> 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)))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_eq__special_I4_J,axiom,
% 187.79/187.91 ! [V_x_2,T_b] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 187.79/187.91 <=> 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))))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_one__is__num__one,axiom,
% 187.79/187.91 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__numeral__1__eq__1,axiom,
% 187.79/187.91 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Numeral1__eq1__nat,axiom,
% 187.79/187.91 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 187.79/187.91 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_iszero__Numeral0,axiom,
% 187.79/187.91 ! [T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_numeral__3__eq__3,axiom,
% 187.79/187.91 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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_numeral__1__eq__Suc__0,axiom,
% 187.79/187.91 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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power3__eq__cube,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Groups_Omonoid__mult(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 187.79/187.91 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))))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Suc3__eq__add__3,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 187.79/187.91 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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 187.79/187.91 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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_le__special_I2_J,axiom,
% 187.79/187.91 ! [V_y_2,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 & class_Rings_Olinordered__idom(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_le__special_I4_J,axiom,
% 187.79/187.91 ! [V_x_2,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 & class_Rings_Olinordered__idom(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__special_I4_J,axiom,
% 187.79/187.91 ! [V_x_2,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 & class_Rings_Olinordered__idom(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__special_I2_J,axiom,
% 187.79/187.91 ! [V_y_2,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 & class_Rings_Olinordered__idom(T_b) )
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__special_I2_J,axiom,
% 187.79/187.91 ! [V_w,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__special_I3_J,axiom,
% 187.79/187.91 ! [V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 187.79/187.91 ! [V_m,V_n] :
% 187.79/187.91 ( 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))
% 187.79/187.91 => 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)))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_div__Suc__eq__div__add3,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Suc__div__eq__add3__div,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_eq__number__of__eq,axiom,
% 187.79/187.91 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 187.79/187.91 <=> 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)))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_diff__special_I1_J,axiom,
% 187.79/187.91 ! [V_w,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_diff__special_I2_J,axiom,
% 187.79/187.91 ! [V_v,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__number__of__Bit1,axiom,
% 187.79/187.91 ! [V_w_2] :
% 187.79/187.91 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 187.79/187.91 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.79/187.91 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 187.79/187.91 => 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)))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power__number__of__odd,axiom,
% 187.79/187.91 ! [V_z_2,V_w_2,T_b] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 => ( ( 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)))
% 187.79/187.91 => 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))) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => 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) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zpower__number__of__odd,axiom,
% 187.79/187.91 ! [V_z_2,V_w_2] :
% 187.79/187.91 ( ( 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)))
% 187.79/187.91 => 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))) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => 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) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__number__of__Bit1,axiom,
% 187.79/187.91 ! [V_v,V_w] :
% 187.79/187.91 ( ( 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)))
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_neg__zmod__mult__2,axiom,
% 187.79/187.91 ! [V_b,V_a] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_arith__series__int,axiom,
% 187.79/187.91 ! [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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I49_J,axiom,
% 187.79/187.91 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I50_J,axiom,
% 187.79/187.91 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Bit0__Pls,axiom,
% 187.79/187.91 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I38_J,axiom,
% 187.79/187.91 ! [V_l_2] :
% 187.79/187.91 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 187.79/187.91 <=> c_Int_OPls = V_l_2 ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I44_J,axiom,
% 187.79/187.91 ! [V_k_2] :
% 187.79/187.91 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 187.79/187.91 <=> V_k_2 = c_Int_OPls ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_minus__Bit0,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I48_J,axiom,
% 187.79/187.91 ! [V_l_2,V_k_2] :
% 187.79/187.91 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 187.79/187.91 <=> V_k_2 = V_l_2 ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Bit0__def,axiom,
% 187.79/187.91 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__Bit0__Bit0,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mult__Bit0,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I14_J,axiom,
% 187.79/187.91 ! [V_l_2,V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__int__code_I13_J,axiom,
% 187.79/187.91 ! [V_k2_2,V_k1_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_diff__bin__simps_I7_J,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I31_J,axiom,
% 187.79/187.91 ! [V_l_2,V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__eq__int__code_I13_J,axiom,
% 187.79/187.91 ! [V_k2_2,V_k1_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_bin__less__0__simps_I3_J,axiom,
% 187.79/187.91 ! [V_w_2] :
% 187.79/187.91 ( 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)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I27_J,axiom,
% 187.79/187.91 ! [V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I21_J,axiom,
% 187.79/187.91 ! [V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__eq__int__code_I14_J,axiom,
% 187.79/187.91 ! [V_k2_2,V_k1_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I32_J,axiom,
% 187.79/187.91 ! [V_l_2,V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I4_J,axiom,
% 187.79/187.91 ! [V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I10_J,axiom,
% 187.79/187.91 ! [V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I16_J,axiom,
% 187.79/187.91 ! [V_l_2,V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__int__code_I15_J,axiom,
% 187.79/187.91 ! [V_k2_2,V_k1_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__Bit0__Bit1,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__Bit1__Bit0,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_diff__bin__simps_I3_J,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_diff__bin__simps_I10_J,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_diff__bin__simps_I9_J,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zdiv__number__of__Bit0,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_neg__number__of__Bit0,axiom,
% 187.79/187.91 ! [V_w_2] :
% 187.79/187.91 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 187.79/187.91 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_pred__Bit1,axiom,
% 187.79/187.91 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_pred__Bit0,axiom,
% 187.79/187.91 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_iszero__number__of__Bit0,axiom,
% 187.79/187.91 ! [V_w_2,T_b] :
% 187.79/187.91 ( ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 & class_Int_Oring__char__0(T_b) )
% 187.79/187.91 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 187.79/187.91 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_succ__Bit0,axiom,
% 187.79/187.91 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_succ__Bit1,axiom,
% 187.79/187.91 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__number__of__Bit0,axiom,
% 187.79/187.91 ! [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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_number__of__Bit0,axiom,
% 187.79/187.91 ! [V_w,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__eq__int__code_I15_J,axiom,
% 187.79/187.91 ! [V_k2_2,V_k1_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I33_J,axiom,
% 187.79/187.91 ! [V_l_2,V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__int__code_I14_J,axiom,
% 187.79/187.91 ! [V_k2_2,V_k1_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_rel__simps_I15_J,axiom,
% 187.79/187.91 ! [V_l_2,V_k_2] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_card__UNIV__bool,axiom,
% 187.79/187.91 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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mult__Bit1,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_diff__bin__simps_I8_J,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__Bit1__Bit1,axiom,
% 187.79/187.91 ! [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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power__number__of__even,axiom,
% 187.79/187.91 ! [V_w_2,V_z_2,T_b] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zpower__number__of__even,axiom,
% 187.79/187.91 ! [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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_double__number__of__Bit0,axiom,
% 187.79/187.91 ! [V_w,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_number__of1,axiom,
% 187.79/187.91 ! [V_n] :
% 187.79/187.91 ( 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)))
% 187.79/187.91 => ( 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))))
% 187.79/187.91 & 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)))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 187.79/187.91 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power__number__of__even__number__of,axiom,
% 187.79/187.91 ! [V_w_2,V_v_2,T_b] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_b)
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mult__2__right,axiom,
% 187.79/187.91 ! [V_z,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mult__2,axiom,
% 187.79/187.91 ! [V_z,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_one__add__one__is__two,axiom,
% 187.79/187.91 ! [T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zero__eq__power2,axiom,
% 187.79/187.91 ! [V_a_2,T_b] :
% 187.79/187.91 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 187.79/187.91 => ( 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)
% 187.79/187.91 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zero__power2,axiom,
% 187.79/187.91 ! [T_a] :
% 187.79/187.91 ( class_Rings_Osemiring__1(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_semiring__norm_I115_J,axiom,
% 187.79/187.91 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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_numeral__2__eq__2,axiom,
% 187.79/187.91 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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 187.79/187.91 ! [V_x,T_a] :
% 187.79/187.91 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.91 => 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)))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power2__eq__square,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Groups_Omonoid__mult(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 187.79/187.91 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))))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__2__eq__Suc_H,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__2__eq__Suc,axiom,
% 187.79/187.91 ! [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)) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_one__power2,axiom,
% 187.79/187.91 ! [T_a] :
% 187.79/187.91 ( class_Rings_Osemiring__1(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power2__minus,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Rings_Oring__1(T_a)
% 187.79/187.91 => 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)))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__mult__2__right,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__mult__2,axiom,
% 187.79/187.91 ! [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) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power__even__eq,axiom,
% 187.79/187.91 ! [V_n,V_a,T_a] :
% 187.79/187.91 ( class_Groups_Omonoid__mult(T_a)
% 187.79/187.91 => 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)))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 187.79/187.91 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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 187.79/187.91 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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power2__abs,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.91 => 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)))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_abs__power2,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.91 => 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)))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__1__add__1,axiom,
% 187.79/187.91 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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod2__Suc__Suc,axiom,
% 187.79/187.91 ! [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)))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_div2__Suc__Suc,axiom,
% 187.79/187.91 ! [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))))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zmod__number__of__Bit0,axiom,
% 187.79/187.91 ! [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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_add__self__div__2,axiom,
% 187.79/187.91 ! [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 ).
% 187.79/187.91
% 187.79/187.91 fof(fact_half__gt__zero__iff,axiom,
% 187.79/187.91 ! [V_r_2,T_b] :
% 187.79/187.91 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 187.79/187.91 & class_Int_Onumber__ring(T_b) )
% 187.79/187.91 => ( 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))))))
% 187.79/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_half__gt__zero,axiom,
% 187.79/187.91 ! [V_r,T_a] :
% 187.79/187.91 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.79/187.91 & class_Int_Onumber__ring(T_a) )
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 187.79/187.91 => 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)))))) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zero__le__power2,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.91 => 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)))))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power2__le__imp__le,axiom,
% 187.79/187.91 ! [V_y,V_x,T_a] :
% 187.79/187.91 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.91 => ( 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))))))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.79/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power2__eq__imp__eq,axiom,
% 187.79/187.91 ! [V_y,V_x,T_a] :
% 187.79/187.91 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.91 => ( 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))))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.79/187.91 => V_x = V_y ) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zero__less__power2,axiom,
% 187.79/187.91 ! [V_a_2,T_b] :
% 187.79/187.91 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.91 => ( 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))))))
% 187.79/187.91 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power2__less__0,axiom,
% 187.79/187.91 ! [V_a,T_a] :
% 187.79/187.91 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.91 => ~ 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_sum__power2__eq__zero__iff,axiom,
% 187.79/187.91 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.91 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.91 => ( 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)
% 187.79/187.91 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.91 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power2__eq__square__number__of,axiom,
% 187.79/187.91 ! [V_w,T_b] :
% 187.79/187.91 ( ( class_Groups_Omonoid__mult(T_b)
% 187.79/187.91 & class_Int_Onumber(T_b) )
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_less__2__cases,axiom,
% 187.79/187.91 ! [V_n] :
% 187.79/187.91 ( 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)))))
% 187.79/187.91 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.91 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_nat__2,axiom,
% 187.79/187.91 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))) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power2__eq__1__iff,axiom,
% 187.79/187.91 ! [V_a_2,T_b] :
% 187.79/187.91 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 187.79/187.91 => ( 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)
% 187.79/187.91 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 187.79/187.91 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 187.79/187.91 ! [V_n,V_x,T_a] :
% 187.79/187.91 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power__minus__even,axiom,
% 187.79/187.91 ! [V_n,V_a,T_a] :
% 187.79/187.91 ( class_Rings_Oring__1(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power2__less__imp__less,axiom,
% 187.79/187.91 ! [V_y,V_x,T_a] :
% 187.79/187.91 ( class_Rings_Olinordered__semidom(T_a)
% 187.79/187.91 => ( 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))))))
% 187.79/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.79/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_sum__power2__ge__zero,axiom,
% 187.79/187.91 ! [V_y,V_x,T_a] :
% 187.79/187.91 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.91 => 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))))))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_sum__power2__le__zero__iff,axiom,
% 187.79/187.91 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.91 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.91 => ( 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)))
% 187.79/187.91 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.91 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_sum__power2__gt__zero__iff,axiom,
% 187.79/187.91 ! [V_y_2,V_x_2,T_b] :
% 187.79/187.91 ( class_Rings_Olinordered__idom(T_b)
% 187.79/187.91 => ( 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)))))))
% 187.79/187.91 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 187.79/187.91 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_not__sum__power2__lt__zero,axiom,
% 187.79/187.91 ! [V_y,V_x,T_a] :
% 187.79/187.91 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.91 => ~ 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power2__sum,axiom,
% 187.79/187.91 ! [V_y,V_x,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zero__le__even__power_H,axiom,
% 187.79/187.91 ! [V_n,V_a,T_a] :
% 187.79/187.91 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.91 => 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)))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 187.79/187.91 ! [V_n,V_x,T_a] :
% 187.79/187.91 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.79/187.91 => 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))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power__odd__eq,axiom,
% 187.79/187.91 ! [V_n,V_a,T_a] :
% 187.79/187.91 ( class_Groups_Omonoid__mult(T_a)
% 187.79/187.91 => 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))))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power__minus1__even,axiom,
% 187.79/187.91 ! [V_n,T_a] :
% 187.79/187.91 ( class_Rings_Oring__1(T_a)
% 187.79/187.91 => 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_zdiv__number__of__Bit1,axiom,
% 187.79/187.91 ! [V_v,V_w] :
% 187.79/187.91 ( ( 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)))
% 187.79/187.91 => 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)) )
% 187.79/187.91 & ( ~ 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)))
% 187.79/187.91 => 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)) ) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_mod2__gr__0,axiom,
% 187.79/187.91 ! [V_m_2] :
% 187.79/187.91 ( 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))))))
% 187.79/187.91 <=> 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) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_div__2__gt__zero,axiom,
% 187.79/187.91 ! [V_n] :
% 187.79/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 187.79/187.91 => 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)))))) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_power2__diff,axiom,
% 187.79/187.91 ! [V_y,V_x,T_a] :
% 187.79/187.91 ( class_Int_Onumber__ring(T_a)
% 187.79/187.91 => 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)) ) ).
% 187.79/187.91
% 187.79/187.91 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 187.79/187.91 ! [V_n,V_a,T_a] :
% 187.79/187.91 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.91 => ( 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)))))
% 187.79/187.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_odd__power__less__zero,axiom,
% 187.79/187.92 ! [V_n,V_a,T_a] :
% 187.79/187.92 ( class_Rings_Olinordered__idom(T_a)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.79/187.92 => 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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_power__minus1__odd,axiom,
% 187.79/187.92 ! [V_n,T_a] :
% 187.79/187.92 ( class_Rings_Oring__1(T_a)
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 187.79/187.92 ! [V_n] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.92 => 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)))))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_of__nat__double,axiom,
% 187.79/187.92 ! [V_x,T_a] :
% 187.79/187.92 ( class_Rings_Osemiring__1(T_a)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.79/187.92 => 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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pos__zmod__mult__2,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_neg__zdiv__mult__2,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pos__zdiv__mult__2,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_int__of__code,axiom,
% 187.79/187.92 ! [V_k] :
% 187.79/187.92 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.79/187.92 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 187.79/187.92 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.79/187.92 => ( ( 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)
% 187.79/187.92 => 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)))))) )
% 187.79/187.92 & ( 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)
% 187.79/187.92 => 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)) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_of__int__num,axiom,
% 187.79/187.92 ! [V_k_2,T_b] :
% 187.79/187.92 ( class_Rings_Oring__1(T_b)
% 187.79/187.92 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 187.79/187.92 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => 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))) )
% 187.79/187.92 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => 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))))) ) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_power__m1__odd,axiom,
% 187.79/187.92 ! [V_n,T_a] :
% 187.79/187.92 ( class_Int_Onumber__ring(T_a)
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I45_J,axiom,
% 187.79/187.92 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I42_J,axiom,
% 187.79/187.92 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I24_J,axiom,
% 187.79/187.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_code__numeral__zero__minus__one,axiom,
% 187.79/187.92 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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I7_J,axiom,
% 187.79/187.92 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I37_J,axiom,
% 187.79/187.92 c_Int_OPls != c_Int_OMin ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I40_J,axiom,
% 187.79/187.92 c_Int_OMin != c_Int_OPls ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I47_J,axiom,
% 187.79/187.92 ! [V_k_2] :
% 187.79/187.92 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 187.79/187.92 <=> V_k_2 = c_Int_OMin ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I43_J,axiom,
% 187.79/187.92 ! [V_l_2] :
% 187.79/187.92 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 187.79/187.92 <=> c_Int_OMin = V_l_2 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Bit1__Min,axiom,
% 187.79/187.92 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 187.79/187.92
% 187.79/187.92 fof(fact_bin__less__0__simps_I2_J,axiom,
% 187.79/187.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I23_J,axiom,
% 187.79/187.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I20_J,axiom,
% 187.79/187.92 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I26_J,axiom,
% 187.79/187.92 ! [V_k_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 187.79/187.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I30_J,axiom,
% 187.79/187.92 ! [V_k_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 187.79/187.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I3_J,axiom,
% 187.79/187.92 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I6_J,axiom,
% 187.79/187.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I13_J,axiom,
% 187.79/187.92 ! [V_k_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 187.79/187.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I9_J,axiom,
% 187.79/187.92 ! [V_k_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 187.79/187.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I28_J,axiom,
% 187.79/187.92 ! [V_k_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 187.79/187.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I8_J,axiom,
% 187.79/187.92 ! [V_k_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 187.79/187.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_eq__number__of__Pls__Min,axiom,
% 187.79/187.92 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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Int_OMin__def,axiom,
% 187.79/187.92 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mult__Min,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_neg__number__of__Min,axiom,
% 187.79/187.92 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pred__Pls,axiom,
% 187.79/187.92 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 187.79/187.92
% 187.79/187.92 fof(fact_add__Min__right,axiom,
% 187.79/187.92 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_add__Min,axiom,
% 187.79/187.92 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pred__Min,axiom,
% 187.79/187.92 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_nonzero__number__of__Min,axiom,
% 187.79/187.92 ! [T_a] :
% 187.79/187.92 ( class_Int_Onumber__ring(T_a)
% 187.79/187.92 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_succ__Min,axiom,
% 187.79/187.92 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 187.79/187.92
% 187.79/187.92 fof(fact_diff__bin__simps_I2_J,axiom,
% 187.79/187.92 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mult__minus1__right,axiom,
% 187.79/187.92 ! [V_z,T_a] :
% 187.79/187.92 ( class_Int_Onumber__ring(T_a)
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mult__minus1,axiom,
% 187.79/187.92 ! [V_z,T_a] :
% 187.79/187.92 ( class_Int_Onumber__ring(T_a)
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_number__of__Min,axiom,
% 187.79/187.92 ! [T_a] :
% 187.79/187.92 ( class_Int_Onumber__ring(T_a)
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_arith__simps_I31_J,axiom,
% 187.79/187.92 ! [T_a] :
% 187.79/187.92 ( class_Int_Onumber__ring(T_a)
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_abs__minus__one,axiom,
% 187.79/187.92 ! [T_a] :
% 187.79/187.92 ( ( class_Int_Onumber__ring(T_a)
% 187.79/187.92 & class_Rings_Olinordered__idom(T_a) )
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divide__minus1,axiom,
% 187.79/187.92 ! [V_x,T_a] :
% 187.79/187.92 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 187.79/187.92 & class_Int_Onumber__ring(T_a) )
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I25_J,axiom,
% 187.79/187.92 ! [V_k_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 187.79/187.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rel__simps_I11_J,axiom,
% 187.79/187.92 ! [V_k_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 187.79/187.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zmod__minus1__right,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_diff__bin__simps_I4_J,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_minus__Min,axiom,
% 187.79/187.92 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zmult__eq__1__iff,axiom,
% 187.79/187.92 ! [V_n_2,V_m_2] :
% 187.79/187.92 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 187.79/187.92 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 187.79/187.92 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 187.79/187.92 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 187.79/187.92 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 187.79/187.92 ! [V_n,V_m] :
% 187.79/187.92 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 187.79/187.92 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 187.79/187.92 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_diff__bin__simps_I6_J,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_diff__bin__simps_I5_J,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_of__int__m1,axiom,
% 187.79/187.92 ! [T_a] :
% 187.79/187.92 ( class_Int_Onumber__ring(T_a)
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zdiv__minus1__right,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zero__code__numeral__code,axiom,
% 187.79/187.92 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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_minus1__divide,axiom,
% 187.79/187.92 ! [V_x,T_a] :
% 187.79/187.92 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 187.79/187.92 & class_Int_Onumber__ring(T_a) )
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_abs__power__minus__one,axiom,
% 187.79/187.92 ! [V_n,T_a] :
% 187.79/187.92 ( ( class_Int_Onumber__ring(T_a)
% 187.79/187.92 & class_Rings_Olinordered__idom(T_a) )
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_div__eq__minus1,axiom,
% 187.79/187.92 ! [V_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_div__pos__neg__trivial,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => 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) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zmod__minus1,axiom,
% 187.79/187.92 ! [V_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_one__code__numeral__code,axiom,
% 187.79/187.92 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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_power__m1__even,axiom,
% 187.79/187.92 ! [V_n,T_a] :
% 187.79/187.92 ( class_Int_Onumber__ring(T_a)
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Nitpick_OFrac__def,axiom,
% 187.79/187.92 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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_small__int__def,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_int__ge__less__than2__def,axiom,
% 187.79/187.92 ! [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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_inj__graph,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_int__ge__less__than__def,axiom,
% 187.79/187.92 ! [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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Nitpick_Oprod__def,axiom,
% 187.79/187.92 ! [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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_nat__of__aux__code,axiom,
% 187.79/187.92 ! [V_n,V_i] :
% 187.79/187.92 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.79/187.92 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 187.79/187.92 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__int__rel__def,axiom,
% 187.79/187.92 ! [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))))))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_finite__psubset__def,axiom,
% 187.79/187.92 ! [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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_full__small__int__def,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__int__correct,axiom,
% 187.79/187.92 ! [V_a,V_b] :
% 187.79/187.92 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zmult2__lemma,axiom,
% 187.79/187.92 ! [V_c,V_r,V_q,V_b,V_a] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 187.79/187.92 => 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)))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_code__numeral_Osize_I1_J,axiom,
% 187.79/187.92 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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Nats__number__of,axiom,
% 187.79/187.92 ! [V_w_2,T_b] :
% 187.79/187.92 ( class_Int_Onumber__ring(T_b)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 187.79/187.92 => 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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_sup__Un__eq2,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 <=> 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pred__subset__eq2,axiom,
% 187.79/187.92 ! [V_S_2,V_R_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 <=> 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pred__equals__eq2,axiom,
% 187.79/187.92 ! [V_S_2,V_R_2,T_c,T_b] :
% 187.79/187.92 ( 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)
% 187.79/187.92 <=> V_R_2 = V_S_2 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_inf__Int__eq2,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 <=> 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_bot__empty__eq2,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,T_c,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 <=> 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)))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_congruentD,axiom,
% 187.79/187.92 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 187.79/187.92 => ( 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))
% 187.79/187.92 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_congruent2D,axiom,
% 187.79/187.92 ! [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] :
% 187.79/187.92 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 187.79/187.92 => ( 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))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_enum__ex__prod__def,axiom,
% 187.79/187.92 ! [V_Pa_2,T_b,T_c] :
% 187.79/187.92 ( ( class_Enum_Oenum(T_c)
% 187.79/187.92 & class_Enum_Oenum(T_b) )
% 187.79/187.92 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_2))
% 187.79/187.92 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_enum__all__prod__def,axiom,
% 187.79/187.92 ! [V_Pa_2,T_b,T_c] :
% 187.79/187.92 ( ( class_Enum_Oenum(T_c)
% 187.79/187.92 & class_Enum_Oenum(T_b) )
% 187.79/187.92 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_2))
% 187.79/187.92 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_small__prod__def,axiom,
% 187.79/187.92 ! [V_d_2,V_f_2,T_b,T_c] :
% 187.79/187.92 ( ( class_Smallcheck_Osmall(T_c)
% 187.79/187.92 & class_Smallcheck_Osmall(T_b) )
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Image__iff,axiom,
% 187.79/187.92 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 187.79/187.92 <=> ? [B_x] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.79/187.92 & 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rev__ImageI,axiom,
% 187.79/187.92 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__int__rel__0,axiom,
% 187.79/187.92 ! [V_b] :
% 187.79/187.92 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => 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)))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_self__remainder,axiom,
% 187.79/187.92 ! [V_r,V_q,V_a] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_unique__quotient,axiom,
% 187.79/187.92 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => V_q = V_q_H ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_unique__remainder,axiom,
% 187.79/187.92 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => V_r = V_r_H ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_SUP__UN__eq2,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 <=> 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_self__quotient,axiom,
% 187.79/187.92 ! [V_r,V_q,V_a] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__int__rel__mod,axiom,
% 187.79/187.92 ! [V_r,V_q,V_b,V_a] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__int__rel__div,axiom,
% 187.79/187.92 ! [V_r,V_q,V_b,V_a] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Nats__0,axiom,
% 187.79/187.92 ! [T_b] :
% 187.79/187.92 ( class_Rings_Osemiring__1(T_b)
% 187.79/187.92 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__int__mod__div,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Nats__add,axiom,
% 187.79/187.92 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.92 ( class_Rings_Osemiring__1(T_b)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 187.79/187.92 => 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))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Nats__mult,axiom,
% 187.79/187.92 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.92 ( class_Rings_Osemiring__1(T_b)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 187.79/187.92 => 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))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Nats__1,axiom,
% 187.79/187.92 ! [T_b] :
% 187.79/187.92 ( class_Rings_Osemiring__1(T_b)
% 187.79/187.92 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_of__nat__in__Nats,axiom,
% 187.79/187.92 ! [V_n_2,T_b] :
% 187.79/187.92 ( class_Rings_Osemiring__1(T_b)
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Image__singleton__iff,axiom,
% 187.79/187.92 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 187.79/187.92 ( 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))))))
% 187.79/187.92 <=> 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_equiv__class__eq,axiom,
% 187.79/187.92 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.92 => ( 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))
% 187.79/187.92 => 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)))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_quotient__eqI,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_quotient__eq__iff,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 187.79/187.92 => ( V_X_2 = V_Y_2
% 187.79/187.92 <=> 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)) ) ) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__int__rel__div__mod,axiom,
% 187.79/187.92 ! [V_a,V_b] :
% 187.79/187.92 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => 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)))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Image__singleton,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_equiv__class__eq__iff,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.92 => ( 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))
% 187.79/187.92 <=> ( 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))))
% 187.79/187.92 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.92 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_eq__equiv__class__iff,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 187.79/187.92 => ( 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))))
% 187.79/187.92 <=> 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)) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_eq__equiv__class,axiom,
% 187.79/187.92 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 187.79/187.92 ( 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))))
% 187.79/187.92 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 187.79/187.92 => 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)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_equiv__class__subset,axiom,
% 187.79/187.92 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.92 => ( 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))
% 187.79/187.92 => 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)))))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_eq__equiv__class__iff2,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 187.79/187.92 => ( 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)
% 187.79/187.92 <=> 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)) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zadd1__lemma,axiom,
% 187.79/187.92 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => 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)))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zminus1__lemma,axiom,
% 187.79/187.92 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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))))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_subset__equiv__class,axiom,
% 187.79/187.92 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.92 => ( 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))))))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 187.79/187.92 => 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)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_equiv__class__nondisjoint,axiom,
% 187.79/187.92 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.92 => ( 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)))))))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__int__relI,axiom,
% 187.79/187.92 ! [V_r,V_q,V_b,V_a] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 187.79/187.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 187.79/187.92 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 187.79/187.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 187.79/187.92 => 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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zmult1__lemma,axiom,
% 187.79/187.92 ! [V_a,V_r,V_q,V_c,V_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => 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)))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pair__imageI,axiom,
% 187.79/187.92 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_norm__frac_Osimps,axiom,
% 187.79/187.92 ! [V_a_2,V_b_2] :
% 187.79/187.92 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 187.79/187.92 => 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))) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_adjust__def,axiom,
% 187.79/187.92 ! [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))))))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_sup2CI,axiom,
% 187.79/187.92 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 187.79/187.92 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_sup2E,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_inf2I,axiom,
% 187.79/187.92 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_inf2E,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 187.79/187.92 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mem__splitI,axiom,
% 187.79/187.92 ! [T_d,T_c,V_b_2,V_a_2,V_ca_2,V_z_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2)))
% 187.79/187.92 => 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)))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_splitI,axiom,
% 187.79/187.92 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_prod__caseI,axiom,
% 187.79/187.92 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_bot2E,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_splitD_H,axiom,
% 187.79/187.92 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_swap__inj__on,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_inf2D1,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_inf2D2,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rev__predicate2D,axiom,
% 187.79/187.92 ! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Qa_2))
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_predicate2D,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_c,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Qa_2))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_sup2I2,axiom,
% 187.79/187.92 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_sup2I1,axiom,
% 187.79/187.92 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_split__paired__All,axiom,
% 187.79/187.92 ! [T_c,T_b,V_Pa_2] :
% 187.79/187.92 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 187.79/187.92 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Pair__eq,axiom,
% 187.79/187.92 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 187.79/187.92 ( 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)
% 187.79/187.92 <=> ( V_a_2 = V_a_H_2
% 187.79/187.92 & V_b_2 = V_b_H_2 ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Pair__inject,axiom,
% 187.79/187.92 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => ~ ( V_a = V_a_H
% 187.79/187.92 => V_b != V_b_H ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_split__weak__cong,axiom,
% 187.79/187.92 ! [V_ca_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 187.79/187.92 ( V_p_2 = V_q_2
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_in__finite__psubset,axiom,
% 187.79/187.92 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.92 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_split__twice,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_split__conv,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_prod_Osimps_I2_J,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_splitD,axiom,
% 187.79/187.92 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_split__eta,axiom,
% 187.79/187.92 ! [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 ).
% 187.79/187.92
% 187.79/187.92 fof(fact_split__paired__The,axiom,
% 187.79/187.92 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_The__split__eq,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_adjust__eq,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_in__rel__def,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 187.79/187.92 <=> 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_div__mod__code__numeral__def,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 187.79/187.92 ! [V_w] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ( 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))))
% 187.79/187.92 => 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))) )
% 187.79/187.92 & ( ~ 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))))
% 187.79/187.92 => 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)))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_negDivAlg__correct,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_negDivAlg__div__mod,axiom,
% 187.79/187.92 ! [V_l,V_k] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_negDivAlg__minus1,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_negDivAlg_Osimps,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( ( ( 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)))
% 187.79/187.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( ~ ( 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)))
% 187.79/187.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.79/187.92 => 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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_negDivAlg__eqn__number__of,axiom,
% 187.79/187.92 ! [V_w,V_v] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ( 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))))
% 187.79/187.92 => 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))) )
% 187.79/187.92 & ( ~ 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))))
% 187.79/187.92 => 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)))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_negDivAlg__eqn,axiom,
% 187.79/187.92 ! [V_a,V_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => ( ( 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)))
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( ~ 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)))
% 187.79/187.92 => 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))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Nitpick_Orefl_H__def,axiom,
% 187.79/187.92 ! [V_r_2,T_b] :
% 187.79/187.92 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 187.79/187.92 <=> ! [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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 187.79/187.92 ! [V_w] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ( 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)))
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( ~ 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)))
% 187.79/187.92 => 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)))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_posDivAlg_Osimps,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 187.79/187.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.79/187.92 => 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) )
% 187.79/187.92 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 187.79/187.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.79/187.92 => 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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_posDivAlg__0,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_posDivAlg__correct,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_posDivAlg__div__mod,axiom,
% 187.79/187.92 ! [V_l,V_k] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_posDivAlg__eqn,axiom,
% 187.79/187.92 ! [V_a,V_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 187.79/187.92 => 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) )
% 187.79/187.92 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 187.79/187.92 => 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))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_posDivAlg__eqn__number__of,axiom,
% 187.79/187.92 ! [V_w,V_v] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ( 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)))
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( ~ 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)))
% 187.79/187.92 => 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)))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__int__def,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.92 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 187.79/187.92 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => 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))) ) ) ) ) )
% 187.79/187.92 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.92 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 187.79/187.92 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => 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))) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__nat__step,axiom,
% 187.79/187.92 ! [V_m,V_n] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__int__pdivmod,axiom,
% 187.79/187.92 ! [V_l_2,V_k_2] :
% 187.79/187.92 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => 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) )
% 187.79/187.92 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => 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)))) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_apsnd__compose,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_negateSnd__def,axiom,
% 187.79/187.92 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_apsnd__conv,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__nat__zero,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__nat__base,axiom,
% 187.79/187.92 ! [V_n,V_m] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_negateSnd__eq,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__nat__div__mod,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__int__rel__neg,axiom,
% 187.79/187.92 ! [V_qr,V_b,V_a] :
% 187.79/187.92 ( 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))
% 187.79/187.92 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__nat__if,axiom,
% 187.79/187.92 ! [V_m_2,V_n_2] :
% 187.79/187.92 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 187.79/187.92 => 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) )
% 187.79/187.92 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pdivmod__def,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pdivmod__posDivAlg,axiom,
% 187.79/187.92 ! [V_k,V_l] :
% 187.79/187.92 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__int__code,axiom,
% 187.79/187.92 ! [V_l_2,V_k_2] :
% 187.79/187.92 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => 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) )
% 187.79/187.92 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 => 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)))) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_UN__equiv__class__inject,axiom,
% 187.79/187.92 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.92 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 187.79/187.92 => ( 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)
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => ( ! [B_x] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.92 => ! [B_y] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 187.79/187.92 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 187.79/187.92 => 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)) ) ) )
% 187.79/187.92 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 187.79/187.92 ! [V_a,V_r,V_q,V_c,V_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 187.79/187.92 => 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)))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 187.79/187.92 ! [V_c,V_r,V_q,V_b,V_a] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 187.79/187.92 => 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)))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__nat__rel__unique,axiom,
% 187.79/187.92 ! [V_qr_H,V_qr,V_n,V_m] :
% 187.79/187.92 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 187.79/187.92 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 187.79/187.92 => V_qr = V_qr_H ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__nat__eq,axiom,
% 187.79/187.92 ! [V_qr,V_n,V_m] :
% 187.79/187.92 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 187.79/187.92 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 187.79/187.92 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__nat__def,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mod__eq,axiom,
% 187.79/187.92 ! [V_r,V_q,V_n,V_m] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_div__eq,axiom,
% 187.79/187.92 ! [V_r,V_q,V_n,V_m] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__nat__rel,axiom,
% 187.79/187.92 ! [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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 187.79/187.92 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 187.79/187.92 => 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)))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_negDivAlg_Opsimps,axiom,
% 187.79/187.92 ! [V_b_2,V_a_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ( ( 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)))
% 187.79/187.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( ~ ( 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)))
% 187.79/187.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.79/187.92 => 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))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_small_H_Opsimps,axiom,
% 187.79/187.92 ! [V_i_2,V_d_2,V_f_2] :
% 187.79/187.92 ( 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))))
% 187.79/187.92 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 187.79/187.92 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 187.79/187.92 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 187.79/187.92 => 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)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_posDivAlg_Opsimps,axiom,
% 187.79/187.92 ! [V_b_2,V_a_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 187.79/187.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.79/187.92 => 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) )
% 187.79/187.92 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 187.79/187.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.79/187.92 => 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))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_accp_Osimps,axiom,
% 187.79/187.92 ! [V_a_2,V_r_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 187.79/187.92 <=> ! [B_x] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 187.79/187.92 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_accp_Oequations,axiom,
% 187.79/187.92 ! [V_a_2,V_r_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 187.79/187.92 <=> ! [B_x] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 187.79/187.92 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_accp__downward,axiom,
% 187.79/187.92 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 187.79/187.92 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_accp__subset,axiom,
% 187.79/187.92 ! [V_R2_2,V_R1_2,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_norm__frac_Opsimps,axiom,
% 187.79/187.92 ! [V_b_2,V_a_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.79/187.92 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 187.79/187.92 => 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))) ) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_negDivAlg_Opinduct,axiom,
% 187.79/187.92 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ! [B_a,B_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ( ~ ( 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)))
% 187.79/187.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_posDivAlg_Opinduct,axiom,
% 187.79/187.92 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ! [B_a,B_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 187.79/187.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_nat__gcd_Opsimps,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.92 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 187.79/187.92 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.92 => 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)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_small_H_Opinduct,axiom,
% 187.79/187.92 ! [V_Pa_2,V_a2_2,V_a1_2,V_a0_2] :
% 187.79/187.92 ( 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))))
% 187.79/187.92 => ( ! [B_f,B_d,B_i] :
% 187.79/187.92 ( 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))))
% 187.79/187.92 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 187.79/187.92 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 187.79/187.92 => hBOOL(hAPP(hAPP(hAPP(V_Pa_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)))) ) )
% 187.79/187.92 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,B_f),B_d),B_i)) ) )
% 187.79/187.92 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mod__pos__neg__1__number__of,axiom,
% 187.79/187.92 ! [V_w] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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))))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_snd__apsnd,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_apsnd__eq__conv,axiom,
% 187.79/187.92 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 187.79/187.92 ( 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)
% 187.79/187.92 <=> 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_snd__def,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_snd__conv,axiom,
% 187.79/187.92 ! [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 ).
% 187.79/187.92
% 187.79/187.92 fof(fact_snd__eqD,axiom,
% 187.79/187.92 ! [V_a,V_y,V_x,T_a,T_b] :
% 187.79/187.92 ( 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
% 187.79/187.92 => V_y = V_a ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mod__int__def,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mod__neg__pos,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mod__pos__pos,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mod__pos__pos__1__number__of,axiom,
% 187.79/187.92 ! [V_w] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mod__pos__neg,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => 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)))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mod__neg__neg,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => 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)))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_in__measure,axiom,
% 187.79/187.92 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 <=> 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_irrefl__def,axiom,
% 187.79/187.92 ! [V_r_2,T_b] :
% 187.79/187.92 ( c_Relation_Oirrefl(T_b,V_r_2)
% 187.79/187.92 <=> ! [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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_norm__frac_Opinduct,axiom,
% 187.79/187.92 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ! [B_a,B_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mod__nat__def,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_div__pos__neg__1__number__of,axiom,
% 187.79/187.92 ! [V_w] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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))))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_nat__def,axiom,
% 187.79/187.92 ! [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)))))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_nat__gcd_Opinduct,axiom,
% 187.79/187.92 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ! [B_x,B_y] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) )
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Pair__fst__snd__eq,axiom,
% 187.79/187.92 ! [T_c,T_b,V_t_2,V_s_2] :
% 187.79/187.92 ( V_s_2 = V_t_2
% 187.79/187.92 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 187.79/187.92 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_prod__eqI,axiom,
% 187.79/187.92 ! [V_q,V_p,T_b,T_a] :
% 187.79/187.92 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 187.79/187.92 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 187.79/187.92 => V_p = V_q ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_fst__apsnd,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_fst__def,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Rep__Integ__inject,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2] :
% 187.79/187.92 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 187.79/187.92 <=> V_x_2 = V_y_2 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_fst__conv,axiom,
% 187.79/187.92 ! [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 ).
% 187.79/187.92
% 187.79/187.92 fof(fact_fst__eqD,axiom,
% 187.79/187.92 ! [V_a,V_y,V_x,T_b,T_a] :
% 187.79/187.92 ( 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
% 187.79/187.92 => V_x = V_a ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_surjective__pairing,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pair__collapse,axiom,
% 187.79/187.92 ! [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 ).
% 187.79/187.92
% 187.79/187.92 fof(fact_prod__case__beta,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_div__int__def,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_split__beta,axiom,
% 187.79/187.92 ! [V_z_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_split__comp__eq,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_split__def,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_split__comp,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_The__split,axiom,
% 187.79/187.92 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_div__neg__pos,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_div__pos__pos,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_div__pos__pos__1__number__of,axiom,
% 187.79/187.92 ! [V_w] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_div__pos__neg,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => 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)))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_div__neg__neg,axiom,
% 187.79/187.92 ! [V_b,V_a] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.79/187.92 => 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)))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_prod__size__simp,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_conjI__realizer,axiom,
% 187.79/187.92 ! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_Pa_2] :
% 187.79/187.92 ( hBOOL(hAPP(V_Pa_2,V_p_2))
% 187.79/187.92 => ( hBOOL(hAPP(V_Qa_2,V_q_2))
% 187.79/187.92 => ( hBOOL(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
% 187.79/187.92 & 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)))) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_exI__realizer,axiom,
% 187.79/187.92 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2))
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_div__nat__def,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_divmod__nat__rel__def,axiom,
% 187.79/187.92 ! [V_qr_2,V_n_2,V_m_2] :
% 187.79/187.92 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 187.79/187.92 <=> ( 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))
% 187.79/187.92 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.92 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.79/187.92 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.92 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 & 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)) ) )
% 187.79/187.92 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 & 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))) ) ) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_inv__image__def,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mlex__leq,axiom,
% 187.79/187.92 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => 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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_code__numeral_Osize_I2_J,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_code__numeral_Oinject,axiom,
% 187.79/187.92 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 187.79/187.92 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 187.79/187.92 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 187.79/187.92 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_in__inv__image,axiom,
% 187.79/187.92 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 <=> 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Suc__code__numeral__minus__one,axiom,
% 187.79/187.92 ! [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 ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mlex__less,axiom,
% 187.79/187.92 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_code__numeral_Osize_I4_J,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rp__inv__image__def,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_prod_Orecs,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_code__numeral_Osize_I3_J,axiom,
% 187.79/187.92 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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__add__map__of__foldr,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_in__lex__prod,axiom,
% 187.79/187.92 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 <=> ( 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))
% 187.79/187.92 | ( V_a_2 = V_a_H_2
% 187.79/187.92 & 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)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_equivp__equiv,axiom,
% 187.79/187.92 ! [V_A_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 187.79/187.92 <=> 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_identity__equivp,axiom,
% 187.79/187.92 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_equivp__def,axiom,
% 187.79/187.92 ! [V_R_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 187.79/187.92 <=> ! [B_x,B_y] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 187.79/187.92 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_equivp__reflp,axiom,
% 187.79/187.92 ! [V_x_2,V_R_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_equivp__symp,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_equivp__transp,axiom,
% 187.79/187.92 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 187.79/187.92 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_same__fstI,axiom,
% 187.79/187.92 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] :
% 187.79/187.92 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_apsnd__apfst,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_apfst__apsnd,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_apfst__conv,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_fst__apfst,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_apfst__eq__conv,axiom,
% 187.79/187.92 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 187.79/187.92 ( 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)
% 187.79/187.92 <=> 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_snd__apfst,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_apfst__compose,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_apsnd__apfst__commute,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pair__lessI2,axiom,
% 187.79/187.92 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_ImageE,axiom,
% 187.79/187.92 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 187.79/187.92 => ~ ! [B_x] :
% 187.79/187.92 ( 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))
% 187.79/187.92 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mlex__prod__def,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pair__less__def,axiom,
% 187.79/187.92 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_measure__def,axiom,
% 187.79/187.92 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_less__than__iff,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2] :
% 187.79/187.92 ( 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))
% 187.79/187.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pair__lessI1,axiom,
% 187.79/187.92 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pair__leqI2,axiom,
% 187.79/187.92 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_smax__insertI,axiom,
% 187.79/187.92 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => 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)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_smin__insertI,axiom,
% 187.79/187.92 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => 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)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_smin__emptyI,axiom,
% 187.79/187.92 ! [V_X_2] :
% 187.79/187.92 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_smax__emptyI,axiom,
% 187.79/187.92 ! [V_Y_2] :
% 187.79/187.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 187.79/187.92 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_pair__leqI1,axiom,
% 187.79/187.92 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_wmin__insertI,axiom,
% 187.79/187.92 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => 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)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_wmax__insertI,axiom,
% 187.79/187.92 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => 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)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Field__insert,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Field__empty,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mono__Field,axiom,
% 187.79/187.92 ! [V_s_2,V_r_2,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Field__Un,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_finite__Field,axiom,
% 187.79/187.92 ! [V_r_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 187.79/187.92 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_wmax__emptyI,axiom,
% 187.79/187.92 ! [V_X_2] :
% 187.79/187.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_wmin__emptyI,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_min__weak__def,axiom,
% 187.79/187.92 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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_max__weak__def,axiom,
% 187.79/187.92 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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Id__on__def,axiom,
% 187.79/187.92 ! [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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Id__on__def_H,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Id__on__empty,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Image__Id__on,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Id__on__eqI,axiom,
% 187.79/187.92 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 187.79/187.92 ( V_a_2 = V_b_2
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.92 => 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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Id__on__iff,axiom,
% 187.79/187.92 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 <=> ( V_x_2 = V_y_2
% 187.79/187.92 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_max__strict__def,axiom,
% 187.79/187.92 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_max__ext__additive,axiom,
% 187.79/187.92 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => 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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_min__strict__def,axiom,
% 187.79/187.92 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_max__extp__max__ext__eq,axiom,
% 187.79/187.92 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 187.79/187.92 ( 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)
% 187.79/187.92 <=> 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_min__rpair__set,axiom,
% 187.79/187.92 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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_max__rpair__set,axiom,
% 187.79/187.92 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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_rp__inv__image__rp,axiom,
% 187.79/187.92 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 187.79/187.92 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 187.79/187.92 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_equiv__intrel__iff,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2] :
% 187.79/187.92 ( 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))))
% 187.79/187.92 <=> 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_intrel__iff,axiom,
% 187.79/187.92 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 187.79/187.92 ( 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))
% 187.79/187.92 <=> 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Id__onE,axiom,
% 187.79/187.92 ! [V_A_2,V_ca_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_2),c_Relation_OId__on(T_b,V_A_2)))
% 187.79/187.92 => ~ ! [B_x] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.92 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_equiv__intrel,axiom,
% 187.79/187.92 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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_of__int,axiom,
% 187.79/187.92 ! [V_j_2,V_i_2,T_b] :
% 187.79/187.92 ( class_Rings_Oring__1(T_b)
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_One__int__def,axiom,
% 187.79/187.92 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))))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_mult,axiom,
% 187.79/187.92 ! [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))))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Rep__Integ__inverse,axiom,
% 187.79/187.92 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 187.79/187.92
% 187.79/187.92 fof(fact_minus,axiom,
% 187.79/187.92 ! [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))))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Zero__int__def,axiom,
% 187.79/187.92 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))))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_int__def,axiom,
% 187.79/187.92 ! [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))))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_add,axiom,
% 187.79/187.92 ! [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))))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_nat,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_minus__int__def,axiom,
% 187.79/187.92 ! [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))))))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_less,axiom,
% 187.79/187.92 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 187.79/187.92 ( 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)))))))
% 187.79/187.92 <=> 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_le,axiom,
% 187.79/187.92 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 187.79/187.92 ( 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)))))))
% 187.79/187.92 <=> 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_eq__Abs__Integ,axiom,
% 187.79/187.92 ! [V_z_2] :
% 187.79/187.92 ~ ! [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))))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Integ__def,axiom,
% 187.79/187.92 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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__mapk__SomeI,axiom,
% 187.79/187.92 ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] :
% 187.79/187.92 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.79/187.92 => ( 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)
% 187.79/187.92 => 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) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_inj__mapI,axiom,
% 187.79/187.92 ! [V_f_2,T_c,T_b] :
% 187.79/187.92 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_inj__map,axiom,
% 187.79/187.92 ! [V_f_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_inj__map__eq__map,axiom,
% 187.79/187.92 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 187.79/187.92 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.79/187.92 => ( 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)
% 187.79/187.92 <=> V_xs_2 = V_ys_2 ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_inj__mapD,axiom,
% 187.79/187.92 ! [V_f_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__injective,axiom,
% 187.79/187.92 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 187.79/187.92 => V_xs_2 = V_ys_2 ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__ident,axiom,
% 187.79/187.92 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 187.79/187.92
% 187.79/187.92 fof(fact_List_Omap_Ocomp,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__comp__map,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_List_Omap_Ocompositionality,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__map,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_foldr__map,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Rep__Integ,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__map,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__map__restrict,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_type__definition__Integ,axiom,
% 187.79/187.92 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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_finite__set,axiom,
% 187.79/187.92 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__eq__conv,axiom,
% 187.79/187.92 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 187.79/187.92 ( 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)
% 187.79/187.92 <=> ! [B_x] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 187.79/187.92 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_infinite__UNIV__listI,axiom,
% 187.79/187.92 ! [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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__map,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__inj__on,axiom,
% 187.79/187.92 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => V_xs_2 = V_ys_2 ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_inj__on__map__eq__map,axiom,
% 187.79/187.92 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( 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)
% 187.79/187.92 <=> V_xs_2 = V_ys_2 ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__fun__upd,axiom,
% 187.79/187.92 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 187.79/187.92 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__eq__dom,axiom,
% 187.79/187.92 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 187.79/187.92 ( hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2) = hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2)
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__is__SomeD,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__SomeD,axiom,
% 187.79/187.92 ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_dom__map__of__conv__image__fst,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__eq__None__iff,axiom,
% 187.79/187.92 ! [V_x_2,V_xys_2,T_b,T_c] :
% 187.79/187.92 ( hAPP(hAPP(c_Map_Omap__of(T_c,T_b),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b)
% 187.79/187.92 <=> ~ 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)))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 187.79/187.92 ! [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 ).
% 187.79/187.92
% 187.79/187.92 fof(fact_type__definition_ORep__range,axiom,
% 187.79/187.92 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 187.79/187.92 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 187.79/187.92 => 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 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_type__definition_OAbs__image,axiom,
% 187.79/187.92 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 187.79/187.92 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__map__keys,axiom,
% 187.79/187.92 ! [V_m_2,T_c,V_xs_2,T_b] :
% 187.79/187.92 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Map_Odom(T_b,T_c,V_m_2)
% 187.79/187.92 => 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 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_the_Osimps,axiom,
% 187.79/187.92 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 187.79/187.92
% 187.79/187.92 fof(fact_type__definition_ORep__inverse,axiom,
% 187.79/187.92 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 187.79/187.92 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 187.79/187.92 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_type__definition_ORep__inject,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 187.79/187.92 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 187.79/187.92 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 187.79/187.92 <=> V_x_2 = V_y_2 ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_type__definition_ORep,axiom,
% 187.79/187.92 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 187.79/187.92 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 187.79/187.92 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_type__definition_OAbs__inverse,axiom,
% 187.79/187.92 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 187.79/187.92 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 187.79/187.92 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_type__definition_OAbs__inject,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 187.79/187.92 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 187.79/187.92 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 187.79/187.92 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_ran__distinct,axiom,
% 187.79/187.92 ! [V_al_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__map__of__compr,axiom,
% 187.79/187.92 ! [V_xs_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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)))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__is__SomeI,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => 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) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__map,axiom,
% 187.79/187.92 ! [V_xs_2,V_f_2,T_c,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 187.79/187.92 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 187.79/187.92 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__inject__set,axiom,
% 187.79/187.92 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => ( hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2) = hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2)
% 187.79/187.92 <=> 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) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Some__eq__map__of__iff,axiom,
% 187.79/187.92 ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( 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)
% 187.79/187.92 <=> 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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__eq__Some__iff,axiom,
% 187.79/187.92 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( 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)
% 187.79/187.92 <=> 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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_greaterThanLessThan__upto,axiom,
% 187.79/187.92 ! [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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_weak__map__of__SomeI,axiom,
% 187.79/187.92 ! [V_l_2,V_x_2,V_k_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ? [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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__remove1__eq,axiom,
% 187.79/187.92 ! [V_x_2,V_xs_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.92 => 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)))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__upto,axiom,
% 187.79/187.92 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__remove1,axiom,
% 187.79/187.92 ! [V_x,V_xs,T_a] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.79/187.92 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_remove1__commute,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_atLeastAtMost__upto,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__upto,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_in__set__remove1,axiom,
% 187.79/187.92 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 187.79/187.92 ( V_a_2 != V_b_2
% 187.79/187.92 => ( 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))))
% 187.79/187.92 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_notin__set__remove1,axiom,
% 187.79/187.92 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.92 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => ~ 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)))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_remove1__idem,axiom,
% 187.79/187.92 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.92 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__remove1__subset,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_atLeastLessThan__upto,axiom,
% 187.79/187.92 ! [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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_greaterThanAtMost__upto,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_nat__list__def,axiom,
% 187.79/187.92 ! [V_l_2] :
% 187.79/187.92 ( c_List_Onat__list(V_l_2)
% 187.79/187.92 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_sorted__list__of__set__remove,axiom,
% 187.79/187.92 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.92 ( class_Orderings_Olinorder(T_b)
% 187.79/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__zip__map,axiom,
% 187.79/187.92 ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 187.79/187.92 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => 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) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__zipI2,axiom,
% 187.79/187.92 ! [V_xs,T_b,V_ys,T_a] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 187.79/187.92 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__zipI1,axiom,
% 187.79/187.92 ! [V_ys,T_b,V_xs,T_a] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.79/187.92 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zip__same__conv__map,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zip__map__fst__snd,axiom,
% 187.79/187.92 ! [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 ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__zip__map,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__zip__map2,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zip__same,axiom,
% 187.79/187.92 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 187.79/187.92 ( 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))))
% 187.79/187.92 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 & V_a_2 = V_b_2 ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__zip__leftD,axiom,
% 187.79/187.92 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 187.79/187.92 ( 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))))
% 187.79/187.92 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__zip__rightD,axiom,
% 187.79/187.92 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 187.79/187.92 ( 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))))
% 187.79/187.92 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_in__set__zipE,axiom,
% 187.79/187.92 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 187.79/187.92 ( 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))))
% 187.79/187.92 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zip__map__map,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zip__map1,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zip__map2,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_sorted__list__of__set__insert,axiom,
% 187.79/187.92 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.92 ( class_Orderings_Olinorder(T_b)
% 187.79/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.92 => 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)))))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__zip__upd,axiom,
% 187.79/187.92 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => ( 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)
% 187.79/187.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => 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)) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__removeAll__inj__on,axiom,
% 187.79/187.92 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_length__zip,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__removeAll,axiom,
% 187.79/187.92 ! [V_x,V_xs,T_a] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.79/187.92 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_length__map,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__eq__imp__length__eq,axiom,
% 187.79/187.92 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_insort__left__comm,axiom,
% 187.79/187.92 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 187.79/187.92 ( class_Orderings_Olinorder(T_b)
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_insort__key__left__comm,axiom,
% 187.79/187.92 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 187.79/187.92 ( class_Orderings_Olinorder(T_b)
% 187.79/187.92 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_neq__if__length__neq,axiom,
% 187.79/187.92 ! [V_ys,V_xs,T_a] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => V_xs != V_ys ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_length__insort,axiom,
% 187.79/187.92 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 187.79/187.92 ( class_Orderings_Olinorder(T_c)
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_remove1__insort,axiom,
% 187.79/187.92 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.92 ( class_Orderings_Olinorder(T_b)
% 187.79/187.92 => 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 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__insort,axiom,
% 187.79/187.92 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 187.79/187.92 ( class_Orderings_Olinorder(T_c)
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_card__length,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_removeAll__id,axiom,
% 187.79/187.92 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.92 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__card,axiom,
% 187.79/187.92 ! [V_xs_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_card__distinct,axiom,
% 187.79/187.92 ! [V_xs_2,T_b] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__zip__inject,axiom,
% 187.79/187.92 ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => ( 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)
% 187.79/187.92 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__fst__zip,axiom,
% 187.79/187.92 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => 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 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__snd__zip,axiom,
% 187.79/187.92 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => 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 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__remove1__removeAll,axiom,
% 187.79/187.92 ! [V_x,V_xs,T_a] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.79/187.92 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__insort,axiom,
% 187.79/187.92 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 187.79/187.92 ( class_Orderings_Olinorder(T_c)
% 187.79/187.92 => ( 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)))
% 187.79/187.92 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_length__pos__if__in__set,axiom,
% 187.79/187.92 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zip__eq__conv,axiom,
% 187.79/187.92 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 187.79/187.92 <=> ( 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
% 187.79/187.92 & 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 ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__removeAll__inj,axiom,
% 187.79/187.92 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 187.79/187.92 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_finite__lists__length__eq,axiom,
% 187.79/187.92 ! [V_n_2,V_A_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.92 => 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))))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__zip__is__None,axiom,
% 187.79/187.92 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => ( 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)
% 187.79/187.92 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__zip__is__Some,axiom,
% 187.79/187.92 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 <=> ? [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) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_length__remove1,axiom,
% 187.79/187.92 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.92 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => 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)) )
% 187.79/187.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => 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) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_dom__map__of__zip,axiom,
% 187.79/187.92 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.92 => 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) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_finite__lists__length__le,axiom,
% 187.79/187.92 ! [V_n_2,V_A_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.92 => 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))))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__removeAll,axiom,
% 187.79/187.92 ! [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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_length__sublists,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_length__sublist,axiom,
% 187.79/187.92 ! [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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_insort__insert__insort__key,axiom,
% 187.79/187.92 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 187.79/187.92 ( class_Orderings_Olinorder(T_b)
% 187.79/187.92 => ( ~ 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))))
% 187.79/187.92 => 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) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__sublistI,axiom,
% 187.79/187.92 ! [V_I_2,V_xs_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.92 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__insort__insert,axiom,
% 187.79/187.92 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 187.79/187.92 ( class_Orderings_Olinorder(T_c)
% 187.79/187.92 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.92 => 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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_in__set__sublistD,axiom,
% 187.79/187.92 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.92 ( 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))))
% 187.79/187.92 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_notin__set__sublistI,axiom,
% 187.79/187.92 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.92 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => ~ 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)))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__sublist__subset,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_insort__insert__triv,axiom,
% 187.79/187.92 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.92 ( class_Orderings_Olinorder(T_b)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__insort__insert,axiom,
% 187.79/187.92 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.92 ( class_Orderings_Olinorder(T_b)
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__set__sublists,axiom,
% 187.79/187.92 ! [V_xs_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.92 => 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)))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_sublists__powset,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_insort__insert__key__triv,axiom,
% 187.79/187.92 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 187.79/187.92 ( class_Orderings_Olinorder(T_b)
% 187.79/187.92 => ( 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))))
% 187.79/187.92 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_insort__insert__insort,axiom,
% 187.79/187.92 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.92 ( class_Orderings_Olinorder(T_b)
% 187.79/187.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => 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) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__n__lists,axiom,
% 187.79/187.92 ! [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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__zip,axiom,
% 187.79/187.92 ! [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)))))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__zip__enum__inject,axiom,
% 187.79/187.92 ! [V_ys_2,V_xs_2,T_b,T_c] :
% 187.79/187.92 ( ( class_Enum_Oenum(T_c)
% 187.79/187.92 & class_Enum_Oenum(T_b) )
% 187.79/187.92 => ( 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))
% 187.79/187.92 => ( 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))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => V_xs_2 = V_ys_2 ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_nth__zip,axiom,
% 187.79/187.92 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_list__eq__iff__nth__eq,axiom,
% 187.79/187.92 ! [T_b,V_ys_2,V_xs_2] :
% 187.79/187.92 ( V_xs_2 = V_ys_2
% 187.79/187.92 <=> ( 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)
% 187.79/187.92 & ! [B_i] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_length__n__lists__elem,axiom,
% 187.79/187.92 ! [V_xs_2,V_n_2,V_ys_2,T_b] :
% 187.79/187.92 ( 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))))
% 187.79/187.92 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_enum__distinct,axiom,
% 187.79/187.92 ! [T_a] :
% 187.79/187.92 ( class_Enum_Oenum(T_a)
% 187.79/187.92 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__n__lists,axiom,
% 187.79/187.92 ! [V_n,V_xs,T_a] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.79/187.92 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_enum__fun__code,axiom,
% 187.79/187.92 ! [T_c,T_b] :
% 187.79/187.92 ( ( class_Enum_Oenum(T_b)
% 187.79/187.92 & class_HOL_Oequal(T_b)
% 187.79/187.92 & class_Enum_Oenum(T_c) )
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_enum__fun__def,axiom,
% 187.79/187.92 ! [T_c,T_b] :
% 187.79/187.92 ( ( class_Enum_Oenum(T_b)
% 187.79/187.92 & class_Enum_Oenum(T_c) )
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_in__enum,axiom,
% 187.79/187.92 ! [V_x_2,T_b] :
% 187.79/187.92 ( class_Enum_Oenum(T_b)
% 187.79/187.92 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_Enum_Oenum__class_Oenum(T_b)))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_UNIV__enum,axiom,
% 187.79/187.92 ! [T_b] :
% 187.79/187.92 ( class_Enum_Oenum(T_b)
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_enum__UNIV,axiom,
% 187.79/187.92 ! [T_b] :
% 187.79/187.92 ( class_Enum_Oenum(T_b)
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_all__set__conv__all__nth,axiom,
% 187.79/187.92 ! [V_Pa_2,V_xs_2,T_b] :
% 187.79/187.92 ( ! [B_x] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.79/187.92 <=> ! [B_i] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_nth__map,axiom,
% 187.79/187.92 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__conv__nth,axiom,
% 187.79/187.92 ! [V_xs_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.92 <=> ! [B_i] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ! [B_j] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( B_i != B_j
% 187.79/187.92 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_nth__eq__iff__index__eq,axiom,
% 187.79/187.92 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => ( 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)))
% 187.79/187.92 => ( 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)
% 187.79/187.92 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_in__set__conv__nth,axiom,
% 187.79/187.92 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 <=> ? [B_i] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_nth__mem,axiom,
% 187.79/187.92 ! [V_xs_2,T_b,V_n_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__conv__nth,axiom,
% 187.79/187.92 ! [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))))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_length__n__lists,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__sublist,axiom,
% 187.79/187.92 ! [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))))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_enum__ex__fun__code,axiom,
% 187.79/187.92 ! [V_Pa_2,T_b,T_c] :
% 187.79/187.92 ( ( class_Enum_Oenum(T_c)
% 187.79/187.92 & class_Enum_Oenum(T_b)
% 187.79/187.92 & class_HOL_Oequal(T_b) )
% 187.79/187.92 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_b,T_c)),V_Pa_2))
% 187.79/187.92 <=> 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_Pa_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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_enum__ex__fun__def,axiom,
% 187.79/187.92 ! [V_Pa_2,T_b,T_c] :
% 187.79/187.92 ( ( class_Enum_Oenum(T_c)
% 187.79/187.92 & class_Enum_Oenum(T_b) )
% 187.79/187.92 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_b,T_c)),V_Pa_2))
% 187.79/187.92 <=> 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_Pa_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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_enum__all__fun__code,axiom,
% 187.79/187.92 ! [V_Pa_2,T_b,T_c] :
% 187.79/187.92 ( ( class_Enum_Oenum(T_c)
% 187.79/187.92 & class_Enum_Oenum(T_b)
% 187.79/187.92 & class_HOL_Oequal(T_b) )
% 187.79/187.92 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_b,T_c)),V_Pa_2))
% 187.79/187.92 <=> 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_Pa_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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_all__n__lists__def,axiom,
% 187.79/187.92 ! [V_n_2,V_Pa_2,T_b] :
% 187.79/187.92 ( class_Enum_Oenum(T_b)
% 187.79/187.92 => ( c_Enum_Oall__n__lists(T_b,V_Pa_2,V_n_2)
% 187.79/187.92 <=> ! [B_x] :
% 187.79/187.92 ( 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)))))
% 187.79/187.92 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_ex__n__lists__def,axiom,
% 187.79/187.92 ! [V_n_2,V_Pa_2,T_b] :
% 187.79/187.92 ( class_Enum_Oenum(T_b)
% 187.79/187.92 => ( c_Enum_Oex__n__lists(T_b,V_Pa_2,V_n_2)
% 187.79/187.92 <=> ? [B_x] :
% 187.79/187.92 ( 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)))))
% 187.79/187.92 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_enum__all__fun__def,axiom,
% 187.79/187.92 ! [V_Pa_2,T_b,T_c] :
% 187.79/187.92 ( ( class_Enum_Oenum(T_c)
% 187.79/187.92 & class_Enum_Oenum(T_b) )
% 187.79/187.92 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_b,T_c)),V_Pa_2))
% 187.79/187.92 <=> 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_Pa_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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__list__update,axiom,
% 187.79/187.92 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.92 => ( ~ 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))))))
% 187.79/187.92 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_distinct__product,axiom,
% 187.79/187.92 ! [V_ys,T_b,V_xs,T_a] :
% 187.79/187.92 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.79/187.92 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 187.79/187.92 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__of__zip__enum__is__Some,axiom,
% 187.79/187.92 ! [V_x,V_ys,T_b,T_a] :
% 187.79/187.92 ( class_Enum_Oenum(T_a)
% 187.79/187.92 => ( 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))
% 187.79/187.92 => ? [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) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__update,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_nth__list__update__neq,axiom,
% 187.79/187.92 ! [V_x,V_xs,T_a,V_j,V_i] :
% 187.79/187.92 ( V_i != V_j
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_list__update__id,axiom,
% 187.79/187.92 ! [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 ).
% 187.79/187.92
% 187.79/187.92 fof(fact_length__list__update,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_update__zip,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_zip__update,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_list__update__swap,axiom,
% 187.79/187.92 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 187.79/187.92 ( V_i != V_i_H
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_list__update__overwrite,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_list__update__beyond,axiom,
% 187.79/187.92 ! [V_x,V_i,V_xs,T_a] :
% 187.79/187.92 ( 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))
% 187.79/187.92 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_enum__prod__def,axiom,
% 187.79/187.92 ! [T_b,T_a] :
% 187.79/187.92 ( ( class_Enum_Oenum(T_a)
% 187.79/187.92 & class_Enum_Oenum(T_b) )
% 187.79/187.92 => 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)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__update__subsetI,axiom,
% 187.79/187.92 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__update__subset__insert,axiom,
% 187.79/187.92 ! [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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_nth__list__update__eq,axiom,
% 187.79/187.92 ! [V_x,V_xs,T_a,V_i] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_list__update__same__conv,axiom,
% 187.79/187.92 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 187.79/187.92 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_nth__list__update,axiom,
% 187.79/187.92 ! [V_x,V_j,V_xs,T_a,V_i] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => ( ( V_i = V_j
% 187.79/187.92 => 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 )
% 187.79/187.92 & ( V_i != V_j
% 187.79/187.92 => 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) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_set__update__memI,axiom,
% 187.79/187.92 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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)))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_inj__on__mapI,axiom,
% 187.79/187.92 ! [V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_listsum__setsum__nth,axiom,
% 187.79/187.92 ! [V_xs_2,T_b] :
% 187.79/187.92 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_restrict__map__upds,axiom,
% 187.79/187.92 ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] :
% 187.79/187.92 ( 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)
% 187.79/187.92 => ( 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))
% 187.79/187.92 => 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) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_UnionI,axiom,
% 187.79/187.92 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 187.79/187.92 => 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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Field__Union,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_image__Union,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 187.79/187.92 ! [V_ns_2] :
% 187.79/187.92 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.92 <=> ! [B_x] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 187.79/187.92 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Union__disjoint,axiom,
% 187.79/187.92 ! [V_A_2,V_C_2,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 <=> ! [B_x] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 187.79/187.92 => 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)) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Int__Union2,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Int__Union,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_UN__simps_I8_J,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_UN__extend__simps_I8_J,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Union__def,axiom,
% 187.79/187.92 ! [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))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_vimage__Union,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Sup__le__iff,axiom,
% 187.79/187.92 ! [V_b_2,V_A_2,T_b] :
% 187.79/187.92 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.92 => ( 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))
% 187.79/187.92 <=> ! [B_x] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_less__Sup__iff,axiom,
% 187.79/187.92 ! [V_S_2,V_a_2,T_b] :
% 187.79/187.92 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.92 & class_Orderings_Olinorder(T_b) )
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 187.79/187.92 <=> ? [B_x] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 187.79/187.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Union__Pow__eq,axiom,
% 187.79/187.92 ! [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 ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__add__upds,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Union__upper,axiom,
% 187.79/187.92 ! [V_A_2,V_B_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Union__empty,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Union__mono,axiom,
% 187.79/187.92 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.92 ( 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))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_elem__le__listsum__nat,axiom,
% 187.79/187.92 ! [V_ns,V_k] :
% 187.79/187.92 ( 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)))
% 187.79/187.92 => 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))) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Union__insert,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Union__quotient,axiom,
% 187.79/187.92 ! [V_r_2,V_A_2,T_b] :
% 187.79/187.92 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.92 => 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 ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_finite__UnionD,axiom,
% 187.79/187.92 ! [V_A_2,T_b] :
% 187.79/187.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 187.79/187.92 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_subset__Pow__Union,axiom,
% 187.79/187.92 ! [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)))) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_map__upds__apply__nontin,axiom,
% 187.79/187.92 ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 187.79/187.92 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Union__UNIV,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Union__Un__distrib,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Union__image__eq,axiom,
% 187.79/187.92 ! [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) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_UNION__eq__Union__image,axiom,
% 187.79/187.92 ! [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)) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_Sup__upper,axiom,
% 187.79/187.92 ! [V_A_2,V_x_2,T_b] :
% 187.79/187.92 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.92 => 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))) ) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_listsum__0,axiom,
% 187.79/187.92 ! [V_xs_2,T_c,T_b] :
% 187.79/187.92 ( class_Groups_Omonoid__add(T_b)
% 187.79/187.92 => 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) ) ).
% 187.79/187.92
% 187.79/187.92 fof(fact_listsum__addf,axiom,
% 187.79/187.93 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 187.79/187.93 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__const__mult,axiom,
% 187.79/187.93 ! [V_xs_2,V_f_2,V_ca_2,T_c,T_b] :
% 187.79/187.93 ( class_Rings_Osemiring__0(T_b)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__mult__const,axiom,
% 187.79/187.93 ! [V_xs_2,V_ca_2,V_f_2,T_c,T_b] :
% 187.79/187.93 ( class_Rings_Osemiring__0(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__subtractf,axiom,
% 187.79/187.93 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 187.79/187.93 ( class_Groups_Oab__group__add(T_b)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sup__empty,axiom,
% 187.79/187.93 ! [T_b] :
% 187.79/187.93 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sup__singleton,axiom,
% 187.79/187.93 ! [V_a_2,T_b] :
% 187.79/187.93 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.93 => 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 ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sup__insert,axiom,
% 187.79/187.93 ! [V_A_2,V_a_2,T_b] :
% 187.79/187.93 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sup__UNIV,axiom,
% 187.79/187.93 ! [T_b] :
% 187.79/187.93 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__update__nat,axiom,
% 187.79/187.93 ! [V_n,V_ns,V_k] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__abs,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 187.79/187.93 => 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)))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_uminus__listsum__map,axiom,
% 187.79/187.93 ! [V_xs_2,V_f_2,T_c,T_b] :
% 187.79/187.93 ( class_Groups_Oab__group__add(T_b)
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Un__eq__Union,axiom,
% 187.79/187.93 ! [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))))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Un__Union__image,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Union__Int__subset,axiom,
% 187.79/187.93 ! [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)))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.93 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sup__binary,axiom,
% 187.79/187.93 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.93 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sup__fin__Sup,axiom,
% 187.79/187.93 ! [V_A_2,T_b] :
% 187.79/187.93 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.93 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 187.79/187.93 ! [V_f_2,V_xs_2,T_b,T_c] :
% 187.79/187.93 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.93 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 187.79/187.93 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 187.79/187.93 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 187.79/187.93 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 187.79/187.93 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__upds__list__update2__drop,axiom,
% 187.79/187.93 ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => ( 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)))
% 187.79/187.93 => 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) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__triv,axiom,
% 187.79/187.93 ! [V_xs_2,V_r_2,T_c,T_b] :
% 187.79/187.93 ( class_Rings_Osemiring__1(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__upds__twist,axiom,
% 187.79/187.93 ! [V_bs_2,V_b_2,V_m_2,T_c,V_as_2,V_a_2,T_b] :
% 187.79/187.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2)))
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__map__remove1,axiom,
% 187.79/187.93 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 187.79/187.93 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => 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)))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 187.79/187.93 ! [V_f_2,V_A_2,T_b,T_c] :
% 187.79/187.93 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.93 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.93 => 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))))) )
% 187.79/187.93 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.93 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_finite__Union,axiom,
% 187.79/187.93 ! [V_A_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 187.79/187.93 => ( ! [B_M] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 187.79/187.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 187.79/187.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_insert__partition,axiom,
% 187.79/187.93 ! [V_F_2,V_x_2,T_b] :
% 187.79/187.93 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 187.79/187.93 => ( ! [B_x] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => ! [B_xa] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => ( B_x != B_xa
% 187.79/187.93 => 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)) ) ) )
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_someI,axiom,
% 187.79/187.93 ! [T_b,V_x_2,V_Pa_2] :
% 187.79/187.93 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_tfl__some,axiom,
% 187.79/187.93 ! [T_b,B_P] :
% 187.79/187.93 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 187.79/187.93 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_someI__ex,axiom,
% 187.79/187.93 ! [T_b,V_Pa_2] :
% 187.79/187.93 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 187.79/187.93 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_some__eq__ex,axiom,
% 187.79/187.93 ! [T_b,V_Pa_2] :
% 187.79/187.93 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
% 187.79/187.93 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_some__eq__trivial,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_some__sym__eq__trivial,axiom,
% 187.79/187.93 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_exE__some,axiom,
% 187.79/187.93 ! [T_b,V_ca_2,V_Pa_2] :
% 187.79/187.93 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 187.79/187.93 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2)
% 187.79/187.93 => hBOOL(hAPP(V_Pa_2,V_ca_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_inv__into__def,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_inv__def,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Nitpick_Ocard_H__def,axiom,
% 187.79/187.93 ! [V_A_2,T_b] :
% 187.79/187.93 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.93 => 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)))) )
% 187.79/187.93 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.93 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__mono,axiom,
% 187.79/187.93 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 187.79/187.93 ( ( class_Groups_Omonoid__add(T_c)
% 187.79/187.93 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 187.79/187.93 => ( ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 187.79/187.93 => 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)))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__transpose,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose__map__map,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Eps__split__eq,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_split__paired__Eps,axiom,
% 187.79/187.93 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Eps__split,axiom,
% 187.79/187.93 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__transpose,axiom,
% 187.79/187.93 ! [V_xs_2,T_b,V_i_2] :
% 187.79/187.93 ( 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))))
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_card__partition,axiom,
% 187.79/187.93 ! [V_k_2,V_C_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 187.79/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 187.79/187.93 => ( ! [B_c] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 187.79/187.93 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 187.79/187.93 => ( ! [B_c1] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 187.79/187.93 => ! [B_c2] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 187.79/187.93 => ( B_c1 != B_c2
% 187.79/187.93 => 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)) ) ) )
% 187.79/187.93 => 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)) ) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_all__nth__imp__all__set,axiom,
% 187.79/187.93 ! [V_x_2,V_Pa_2,V_xs_2,T_b] :
% 187.79/187.93 ( ! [B_i] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct__filter,axiom,
% 187.79/187.93 ! [V_Pa_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.93 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_filter__filter,axiom,
% 187.79/187.93 ! [V_xs_2,V_Qa_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Qa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Qa_2)),V_Pa_2)),V_xs_2) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_filter__remove1,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_remove1__filter__not,axiom,
% 187.79/187.93 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 187.79/187.93 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_removeAll__filter__not,axiom,
% 187.79/187.93 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 187.79/187.93 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_filter__insort__triv,axiom,
% 187.79/187.93 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_c)
% 187.79/187.93 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_removeAll__filter__not__eq,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_filter__id__conv,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] :
% 187.79/187.93 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2
% 187.79/187.93 <=> ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_filter__is__subset,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__filter__le,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_filter__map,axiom,
% 187.79/187.93 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sum__length__filter__compl,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__filter,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_Pa_2)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__filter__map,axiom,
% 187.79/187.93 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__filter__less,axiom,
% 187.79/187.93 ! [V_Pa_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__minus__filter__out,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_filter__in__sublist,axiom,
% 187.79/187.93 ! [V_s_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__filter__conv__card,axiom,
% 187.79/187.93 ! [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))))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__filter__def,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__filter__map__filter,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_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_Pa_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_Pa_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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose__max__length,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_filter_Osimps_I1_J,axiom,
% 187.79/187.93 ! [V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__is__Nil__conv,axiom,
% 187.79/187.93 ! [V_xs_2,V_f_2,T_b,T_c] :
% 187.79/187.93 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 187.79/187.93 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map_Osimps_I1_J,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Nil__is__map__conv,axiom,
% 187.79/187.93 ! [V_xs_2,V_f_2,T_c,T_b] :
% 187.79/187.93 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 187.79/187.93 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list__update__code_I1_J,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list__update_Osimps_I1_J,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list__update__nonempty,axiom,
% 187.79/187.93 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 187.79/187.93 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 187.79/187.93 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__empty,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.93 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__empty2,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 187.79/187.93 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__0__conv,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list_Osize_I3_J,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_product_Osimps_I1_J,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_removeAll_Osimps_I1_J,axiom,
% 187.79/187.93 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_insort__not__Nil,axiom,
% 187.79/187.93 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_c)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_remove1_Osimps_I1_J,axiom,
% 187.79/187.93 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__filter__simps_I2_J,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_zip_Osimps_I1_J,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_zip__Nil,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sublist__nil,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct_Osimps_I1_J,axiom,
% 187.79/187.93 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__upds__Nil2,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__upds__Nil1,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldr_Osimps_I1_J,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose_Osimps_I1_J,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose__empty,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 187.79/187.93 <=> ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 187.79/187.93 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__simps_I1_J,axiom,
% 187.79/187.93 ! [T_a] :
% 187.79/187.93 ( class_Groups_Omonoid__add(T_a)
% 187.79/187.93 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_filter__empty__conv,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] :
% 187.79/187.93 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 187.79/187.93 <=> ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__of__Cons__code_I1_J,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upto__empty,axiom,
% 187.79/187.93 ! [V_i,V_j] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 187.79/187.93 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__list__of__set__empty,axiom,
% 187.79/187.93 ! [T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sublist__empty,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__of_Osimps_I1_J,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__greater__0__conv,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__of__filter__in,axiom,
% 187.79/187.93 ! [V_Pa_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] :
% 187.79/187.93 ( 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)
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_k_2),V_z_2))
% 187.79/187.93 => 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_Pa_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sublist__shift__lemma__Suc,axiom,
% 187.79/187.93 ! [V_is_2,V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose__aux__max,axiom,
% 187.79/187.93 ! [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)))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sublist__def,axiom,
% 187.79/187.93 ! [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))))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sublist__shift__lemma,axiom,
% 187.79/187.93 ! [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))))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upt__conv__Nil,axiom,
% 187.79/187.93 ! [V_i,V_j] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 187.79/187.93 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upt__0,axiom,
% 187.79/187.93 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct__upt,axiom,
% 187.79/187.93 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__list__of__set__range,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__Suc__upt,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upt__eq__Nil__conv,axiom,
% 187.79/187.93 ! [V_j_2,V_i_2] :
% 187.79/187.93 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 187.79/187.93 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_atLeastLessThan__upt,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__upt,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__upt,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__nth,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_atLeastAtMost__upt,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_atLeast__upt,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 187.79/187.93 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 187.79/187.93 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 187.79/187.93 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 187.79/187.93 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__upt,axiom,
% 187.79/187.93 ! [V_j,V_k,V_i] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_greaterThanAtMost__upt,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_greaterThanLessThan__upt,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__map__upt,axiom,
% 187.79/187.93 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_atMost__upto,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose__rectangle,axiom,
% 187.79/187.93 ! [V_n_2,T_b,V_xs_2] :
% 187.79/187.93 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 187.79/187.93 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.79/187.93 => ( ! [B_i] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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 )
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list__size__conv__listsum,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list__size__map,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list_Osize_I1_J,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list__size__estimation,axiom,
% 187.79/187.93 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 187.79/187.93 => 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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list__size__estimation_H,axiom,
% 187.79/187.93 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 187.79/187.93 => 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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 187.79/187.93 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose_Opsimps_I1_J,axiom,
% 187.79/187.93 ! [T_b] :
% 187.79/187.93 ( 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))))
% 187.79/187.93 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_return__list__def,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 187.79/187.93 ! [V_l] :
% 187.79/187.93 ( c_List_Onat__list(V_l)
% 187.79/187.93 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__map__filter,axiom,
% 187.79/187.93 ! [V_f_2,V_Pa_2,V_xs_2,T_b,T_c] :
% 187.79/187.93 ( class_Groups_Omonoid__add(T_c)
% 187.79/187.93 => ( ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => ( ~ hBOOL(hAPP(V_Pa_2,B_x))
% 187.79/187.93 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
% 187.79/187.93 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_embed__list__def,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upto__rec__number__of,axiom,
% 187.79/187.93 ! [V_n,V_m] :
% 187.79/187.93 ( ( 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)))
% 187.79/187.93 => 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))) )
% 187.79/187.93 & ( ~ 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)))
% 187.79/187.93 => 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) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_last__list__update,axiom,
% 187.79/187.93 ! [V_x,V_k,T_a,V_xs] :
% 187.79/187.93 ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.93 => ( ( 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))
% 187.79/187.93 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 187.79/187.93 & ( 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))
% 187.79/187.93 => 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) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list_Osimps_I3_J,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_last_Osimps,axiom,
% 187.79/187.93 ! [V_x,T_a,V_xs] :
% 187.79/187.93 ( ( V_xs = c_List_Olist_ONil(T_a)
% 187.79/187.93 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 187.79/187.93 & ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.93 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_last__ConsR,axiom,
% 187.79/187.93 ! [V_x,T_a,V_xs] :
% 187.79/187.93 ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.93 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_last__ConsL,axiom,
% 187.79/187.93 ! [V_x,T_a,V_xs] :
% 187.79/187.93 ( V_xs = c_List_Olist_ONil(T_a)
% 187.79/187.93 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_insort__key_Osimps_I1_J,axiom,
% 187.79/187.93 ! [V_x_2,V_f_2,T_b,T_c] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_c)
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__filter__simps_I1_J,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldr_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list_Oinject,axiom,
% 187.79/187.93 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 187.79/187.93 ( 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)
% 187.79/187.93 <=> ( V_a_2 = V_a_H_2
% 187.79/187.93 & V_list_2 = V_list_H_2 ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_not__Cons__self2,axiom,
% 187.79/187.93 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 187.79/187.93
% 187.79/187.93 fof(fact_not__Cons__self,axiom,
% 187.79/187.93 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_remove1_Osimps_I2_J,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_y,V_x] :
% 187.79/187.93 ( ( V_x = V_y
% 187.79/187.93 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 187.79/187.93 & ( V_x != V_y
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_removeAll_Osimps_I2_J,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_y,V_x] :
% 187.79/187.93 ( ( V_x = V_y
% 187.79/187.93 => 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) )
% 187.79/187.93 & ( V_x != V_y
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_insort__key_Osimps_I2_J,axiom,
% 187.79/187.93 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( ( 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)))
% 187.79/187.93 => 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)) )
% 187.79/187.93 & ( ~ 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)))
% 187.79/187.93 => 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)) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list__update__code_I3_J,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list__update__code_I2_J,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__subset__Cons,axiom,
% 187.79/187.93 ! [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)))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_impossible__Cons,axiom,
% 187.79/187.93 ! [V_x,V_ys,V_xs,T_a] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__ConsD,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 187.79/187.93 ( 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))))
% 187.79/187.93 => ( V_y_2 = V_x_2
% 187.79/187.93 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__simps_I2_J,axiom,
% 187.79/187.93 ! [V_xs,V_x,T_a] :
% 187.79/187.93 ( class_Groups_Omonoid__add(T_a)
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list__update_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__Cons__0,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__Cons__Suc,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_zip__Cons__Cons,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_filter_Osimps_I2_J,axiom,
% 187.79/187.93 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 187.79/187.93 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) )
% 187.79/187.93 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth_Osimps,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_last__map,axiom,
% 187.79/187.93 ! [V_f_2,T_c,T_b,V_xs_2] :
% 187.79/187.93 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct_Osimps_I2_J,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 187.79/187.93 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__upds__Cons,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_last__in__set,axiom,
% 187.79/187.93 ! [T_b,V_as_2] :
% 187.79/187.93 ( V_as_2 != c_List_Olist_ONil(T_b)
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list_Osize_I4_J,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__Cons_H,axiom,
% 187.79/187.93 ! [V_xs,V_x,T_a,V_n] :
% 187.79/187.93 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 187.79/187.93 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 => 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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list_Osize_I2_J,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sublist__singleton,axiom,
% 187.79/187.93 ! [V_x_2,T_b,V_A_2] :
% 187.79/187.93 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 187.79/187.93 => 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)) )
% 187.79/187.93 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 187.79/187.93 => 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) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__Cons__number__of,axiom,
% 187.79/187.93 ! [V_xs,V_x,T_a,V_v] :
% 187.79/187.93 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 => 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 )
% 187.79/187.93 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 => 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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_last__upt,axiom,
% 187.79/187.93 ! [V_j,V_i] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upto_Osimps,axiom,
% 187.79/187.93 ! [V_j,V_i] :
% 187.79/187.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 187.79/187.93 => 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)) )
% 187.79/187.93 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 187.79/187.93 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_last__conv__nth,axiom,
% 187.79/187.93 ! [T_a,V_xs] :
% 187.79/187.93 ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upto_Opsimps,axiom,
% 187.79/187.93 ! [V_j_2,V_i_2] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 187.79/187.93 => 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)) )
% 187.79/187.93 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 187.79/187.93 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__Cons__def,axiom,
% 187.79/187.93 ! [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)))))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upt__conv__Cons,axiom,
% 187.79/187.93 ! [V_j,V_i] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__of__Cons__code_I2_J,axiom,
% 187.79/187.93 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 187.79/187.93 ( ( V_l = V_k
% 187.79/187.93 => 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) )
% 187.79/187.93 & ( V_l != V_k
% 187.79/187.93 => 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) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_enum__option__def,axiom,
% 187.79/187.93 ! [T_b] :
% 187.79/187.93 ( class_Enum_Oenum(T_b)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sublists_Osimps_I1_J,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upt__eq__Cons__conv,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 187.79/187.93 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 187.79/187.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 187.79/187.93 & V_i_2 = V_x_2
% 187.79/187.93 & 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 ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upt__rec,axiom,
% 187.79/187.93 ! [V_j,V_i] :
% 187.79/187.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.79/187.93 => 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)) )
% 187.79/187.93 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.79/187.93 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_n__lists__Nil,axiom,
% 187.79/187.93 ! [T_a,V_n] :
% 187.79/187.93 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 => 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))) )
% 187.79/187.93 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_n__lists_Osimps_I1_J,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__of_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upt__rec__number__of,axiom,
% 187.79/187.93 ! [V_n,V_m] :
% 187.79/187.93 ( ( 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)))
% 187.79/187.93 => 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))) )
% 187.79/187.93 & ( ~ 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)))
% 187.79/187.93 => 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) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose_Opsimps_I2_J,axiom,
% 187.79/187.93 ! [V_xss_2,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__Cons__sing__Nil,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_zip__Cons1,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_zip__Cons,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list_Osimps_I5_J,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list_Osimps_I4_J,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listset_Osimps_I1_J,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_anamorph_Osimps,axiom,
% 187.79/187.93 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 187.79/187.93 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.79/187.93 => 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) )
% 187.79/187.93 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listset_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel__Cons,axiom,
% 187.79/187.93 ! [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))))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upto_Opinduct,axiom,
% 187.79/187.93 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => ( ! [B_i,B_j] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 187.79/187.93 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
% 187.79/187.93 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) )
% 187.79/187.93 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel__Nil2,axiom,
% 187.79/187.93 ! [V_r_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel__Nil1,axiom,
% 187.79/187.93 ! [V_r_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel__eq__len,axiom,
% 187.79/187.93 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel_ONil,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel__mono,axiom,
% 187.79/187.93 ! [V_s_2,V_r_2,T_b] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel_OCons,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel__Nil,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel__iff__nth,axiom,
% 187.79/187.93 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 <=> ( 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)
% 187.79/187.93 & ! [B_n] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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)) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__upds__append1,axiom,
% 187.79/187.93 ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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)))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sublist__Cons,axiom,
% 187.79/187.93 ! [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)))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__eq__Cons__conv,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 187.79/187.93 ( 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)
% 187.79/187.93 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 187.79/187.93 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 187.79/187.93 | ? [B_ys_H] :
% 187.79/187.93 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 187.79/187.93 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Cons__eq__append__conv,axiom,
% 187.79/187.93 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( 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)
% 187.79/187.93 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 187.79/187.93 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 187.79/187.93 | ? [B_ys_H] :
% 187.79/187.93 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 187.79/187.93 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append1__eq__conv,axiom,
% 187.79/187.93 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 <=> ( V_xs_2 = V_ys_2
% 187.79/187.93 & V_x_2 = V_y_2 ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__Cons,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Cons__eq__appendI,axiom,
% 187.79/187.93 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 187.79/187.93 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 187.79/187.93 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 187.79/187.93 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__append,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_filter__append,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_zip__append,axiom,
% 187.79/187.93 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 187.79/187.93 ( 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)
% 187.79/187.93 => ( 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)
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__append,axiom,
% 187.79/187.93 ! [V_ys,V_xs,T_a] :
% 187.79/187.93 ( class_Groups_Omonoid__add(T_a)
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__append,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__append,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_fun__upds__append__drop,axiom,
% 187.79/187.93 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 187.79/187.93 ( 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)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_fun__upds__append2__drop,axiom,
% 187.79/187.93 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 187.79/187.93 ( 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)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_removeAll__append,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__assoc,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__eq__append__conv2,axiom,
% 187.79/187.93 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( 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)
% 187.79/187.93 <=> ? [B_us] :
% 187.79/187.93 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 187.79/187.93 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 )
% 187.79/187.93 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 187.79/187.93 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_same__append__eq,axiom,
% 187.79/187.93 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( 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)
% 187.79/187.93 <=> V_ys_2 = V_zs_2 ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__same__eq,axiom,
% 187.79/187.93 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 187.79/187.93 ( 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)
% 187.79/187.93 <=> V_ys_2 = V_zs_2 ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__eq__appendI,axiom,
% 187.79/187.93 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 187.79/187.93 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 187.79/187.93 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 187.79/187.93 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldr__append,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__of__append,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_last__append,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_ys] :
% 187.79/187.93 ( ( V_ys = c_List_Olist_ONil(T_a)
% 187.79/187.93 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 187.79/187.93 & ( V_ys != c_List_Olist_ONil(T_a)
% 187.79/187.93 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_last__appendR,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_ys] :
% 187.79/187.93 ( V_ys != c_List_Olist_ONil(T_a)
% 187.79/187.93 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_last__appendL,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_ys] :
% 187.79/187.93 ( V_ys = c_List_Olist_ONil(T_a)
% 187.79/187.93 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__Nil,axiom,
% 187.79/187.93 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Nil__is__append__conv,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 187.79/187.93 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 187.79/187.93 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__Nil2,axiom,
% 187.79/187.93 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 187.79/187.93
% 187.79/187.93 fof(fact_self__append__conv,axiom,
% 187.79/187.93 ! [V_ys_2,T_b,V_xs_2] :
% 187.79/187.93 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 187.79/187.93 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_self__append__conv2,axiom,
% 187.79/187.93 ! [V_xs_2,T_b,V_ys_2] :
% 187.79/187.93 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 187.79/187.93 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__is__Nil__conv,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 187.79/187.93 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 187.79/187.93 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__self__conv,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 187.79/187.93 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__self__conv2,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 187.79/187.93 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_eq__Nil__appendI,axiom,
% 187.79/187.93 ! [T_a,V_ys,V_xs] :
% 187.79/187.93 ( V_xs = V_ys
% 187.79/187.93 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__append__length,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__append__length__plus,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list__update__append1,axiom,
% 187.79/187.93 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list__update__length,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_remove1__append,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => 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) )
% 187.79/187.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upt__add__eq__append,axiom,
% 187.79/187.93 ! [V_k,V_j,V_i] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_last__snoc,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct__append,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 187.79/187.93 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.93 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 187.79/187.93 & 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__append,axiom,
% 187.79/187.93 ! [V_ys,V_xs,T_a,V_n] :
% 187.79/187.93 ( ( 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)))
% 187.79/187.93 => 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) )
% 187.79/187.93 & ( ~ 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)))
% 187.79/187.93 => 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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list__update__append,axiom,
% 187.79/187.93 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 187.79/187.93 ( ( 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)))
% 187.79/187.93 => 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) )
% 187.79/187.93 & ( ~ 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)))
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sublists_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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))))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_product_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sublist__append,axiom,
% 187.79/187.93 ! [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)))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upt__Suc,axiom,
% 187.79/187.93 ! [V_j,V_i] :
% 187.79/187.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.79/187.93 => 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))) )
% 187.79/187.93 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.79/187.93 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upt__Suc__append,axiom,
% 187.79/187.93 ! [V_j,V_i] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Cons__in__lex,axiom,
% 187.79/187.93 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 <=> ( ( 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))
% 187.79/187.93 & 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) )
% 187.79/187.93 | ( V_x_2 = V_y_2
% 187.79/187.93 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrelp__listrel__eq,axiom,
% 187.79/187.93 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 187.79/187.93 ( 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)
% 187.79/187.93 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrelp_ONil,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrelp_Oequations_I1_J,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrelp_OCons,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 187.79/187.93 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrelp_Oequations_I2_J,axiom,
% 187.79/187.93 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 187.79/187.93 ( 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))
% 187.79/187.93 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 187.79/187.93 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Nil2__notin__lex,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Nil__notin__lex,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_lenlex__conv,axiom,
% 187.79/187.93 ! [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)))))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_lenlex__def,axiom,
% 187.79/187.93 ! [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)))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel__Cons2,axiom,
% 187.79/187.93 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 => ~ ! [B_x,B_xs] :
% 187.79/187.93 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 187.79/187.93 => ( 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))
% 187.79/187.93 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel__Cons1,axiom,
% 187.79/187.93 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 => ~ ! [B_y,B_ys] :
% 187.79/187.93 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 187.79/187.93 => ( 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))
% 187.79/187.93 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel__iff__zip,axiom,
% 187.79/187.93 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 <=> ( 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)
% 187.79/187.93 & ! [B_x] :
% 187.79/187.93 ( 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))))
% 187.79/187.93 => 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)) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_lexord__append__left__rightI,axiom,
% 187.79/187.93 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_ball__empty,axiom,
% 187.79/187.93 ! [V_Pa_2,T_b,B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 187.79/187.93 => hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Powp__def,axiom,
% 187.79/187.93 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 187.79/187.93 <=> ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 187.79/187.93 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_congruent__def,axiom,
% 187.79/187.93 ! [V_f_2,V_r_2,T_c,T_b] :
% 187.79/187.93 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 187.79/187.93 <=> ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_list__eq__iff__zip__eq,axiom,
% 187.79/187.93 ! [T_b,V_ys_2,V_xs_2] :
% 187.79/187.93 ( V_xs_2 = V_ys_2
% 187.79/187.93 <=> ( 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)
% 187.79/187.93 & ! [B_x] :
% 187.79/187.93 ( 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))))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_lexord__Nil__right,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_lexord__append__leftI,axiom,
% 187.79/187.93 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_lexord__lex,axiom,
% 187.79/187.93 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 & 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) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_lexord__cons__cons,axiom,
% 187.79/187.93 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 <=> ( 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))
% 187.79/187.93 | ( V_a_2 = V_b_2
% 187.79/187.93 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_lexord__take__index__conv,axiom,
% 187.79/187.93 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 <=> ( ( 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)))
% 187.79/187.93 & 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 )
% 187.79/187.93 | ? [B_i] :
% 187.79/187.93 ( 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))))
% 187.79/187.93 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 187.79/187.93 & 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)) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 187.79/187.93 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 & V_x_2 = V_y_2 )
% 187.79/187.93 | ( V_xs_2 = V_ys_2
% 187.79/187.93 & 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)) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_in__set__takeD,axiom,
% 187.79/187.93 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 187.79/187.93 ( 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))))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__all,axiom,
% 187.79/187.93 ! [V_n,V_xs,T_a] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__take__subset,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__eq__Nil,axiom,
% 187.79/187.93 ! [V_xs_2,V_n_2,T_b] :
% 187.79/187.93 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 187.79/187.93 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__0,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__Nil,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct__take,axiom,
% 187.79/187.93 ! [V_i,V_xs,T_a] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.79/187.93 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__take,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__take,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_n,V_i] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__take,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__zip,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__map,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__Suc__Cons,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sublist__upt__eq__take,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__take__subset__set__take,axiom,
% 187.79/187.93 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.93 => 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)))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__append,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__1__Cons,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel1__mono,axiom,
% 187.79/187.93 ! [V_s_2,V_r_2,T_b] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__upt,axiom,
% 187.79/187.93 ! [V_n,V_m,V_i] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel1I2,axiom,
% 187.79/187.93 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel1__eq__len,axiom,
% 187.79/187.93 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_not__listrel1__Nil,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_not__Nil__listrel1,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__listrel1I,axiom,
% 187.79/187.93 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 & V_us_2 = V_vs_2 )
% 187.79/187.93 | ( V_xs_2 = V_ys_2
% 187.79/187.93 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) )
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__Cons,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__Cons_H,axiom,
% 187.79/187.93 ! [V_xs,V_x,T_a,V_n] :
% 187.79/187.93 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 => 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) )
% 187.79/187.93 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_dom__map__upds,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel1I1,axiom,
% 187.79/187.93 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Cons__listrel1__Cons,axiom,
% 187.79/187.93 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 <=> ( ( 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))
% 187.79/187.93 & V_xs_2 = V_ys_2 )
% 187.79/187.93 | ( V_x_2 = V_y_2
% 187.79/187.93 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__Cons__number__of,axiom,
% 187.79/187.93 ! [V_xs,V_x,T_a,V_v] :
% 187.79/187.93 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 => 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) )
% 187.79/187.93 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__upd__upds__conv__if,axiom,
% 187.79/187.93 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] :
% 187.79/187.93 ( ( 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))))
% 187.79/187.93 => 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) )
% 187.79/187.93 & ( ~ 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))))
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__Suc__conv__app__nth,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_i] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel1I,axiom,
% 187.79/187.93 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => ( 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))
% 187.79/187.93 => ( 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))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel1__iff__update,axiom,
% 187.79/187.93 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 <=> ? [B_y,B_n] :
% 187.79/187.93 ( 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))
% 187.79/187.93 & 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)))
% 187.79/187.93 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel1E,axiom,
% 187.79/187.93 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 => ~ ! [B_x,B_y] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => ! [B_us,B_vs] :
% 187.79/187.93 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 187.79/187.93 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_lexord__append__leftD,axiom,
% 187.79/187.93 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 => ( ! [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))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate1__def,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate1__is__Nil__conv,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 187.79/187.93 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct1__rotate,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 187.79/187.93 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__rotate1,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__rotate1,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate__simps,axiom,
% 187.79/187.93 ! [V_xs,V_x,T_b,T_a] :
% 187.79/187.93 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 187.79/187.93 & 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate1__length01,axiom,
% 187.79/187.93 ! [V_xs,T_a] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listrel1__subset__listrel,axiom,
% 187.79/187.93 ! [V_r_H_2,V_r_2,T_b] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 187.79/187.93 => 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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_lexn__length,axiom,
% 187.79/187.93 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.93 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 187.79/187.93 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_refl__on__Id__on,axiom,
% 187.79/187.93 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_lexn_Osimps_I1_J,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_refl__on__empty,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_refl__on__Un,axiom,
% 187.79/187.93 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 187.79/187.93 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 187.79/187.93 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_refl__on__Int,axiom,
% 187.79/187.93 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 187.79/187.93 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 187.79/187.93 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_refl__onD,axiom,
% 187.79/187.93 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 187.79/187.93 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_refl__onD1,axiom,
% 187.79/187.93 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 187.79/187.93 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 187.79/187.93 => ( 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))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_refl__onD2,axiom,
% 187.79/187.93 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 187.79/187.93 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 187.79/187.93 => ( 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))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_lex__def,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_refl__on__def_H,axiom,
% 187.79/187.93 ! [V_r_2,V_A_2,T_b] :
% 187.79/187.93 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 187.79/187.93 <=> ( ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 187.79/187.93 => 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)) )
% 187.79/187.93 & ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.93 => 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)) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_lexn_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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)))))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_reflp__def,axiom,
% 187.79/187.93 ! [V_r_2,T_b] :
% 187.79/187.93 ( c_Predicate_Oreflp(T_b,V_r_2)
% 187.79/187.93 <=> 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__pair__imageI,axiom,
% 187.79/187.93 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__pair__simp,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_reflpE,axiom,
% 187.79/187.93 ! [V_x_2,V_r_2,T_b] :
% 187.79/187.93 ( c_Predicate_Oreflp(T_b,V_r_2)
% 187.79/187.93 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__pair__ident,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_snd__prod__fun,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_fst__map__pair,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_snd__comp__map__pair,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_fst__comp__map__pair,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__pair_Ocomp,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__pair__compose,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__pair_Ocompositionality,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__pair__def,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__pair__surj,axiom,
% 187.79/187.93 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => ( 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))
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_partition__filter__conv,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose_Opsimps_I3_J,axiom,
% 187.79/187.93 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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))))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_partition__filter1,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_concat_Osimps_I1_J,axiom,
% 187.79/187.93 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_concat_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_concat__eq__Nil__conv,axiom,
% 187.79/187.93 ! [V_xss_2,T_b] :
% 187.79/187.93 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 187.79/187.93 <=> ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 187.79/187.93 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Nil__eq__concat__conv,axiom,
% 187.79/187.93 ! [V_xss_2,T_b] :
% 187.79/187.93 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 187.79/187.93 <=> ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 187.79/187.93 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__concat,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_filter__concat,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__concat,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__concat,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_concat__append,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_partition__P,axiom,
% 187.79/187.93 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 187.79/187.93 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 187.79/187.93 => ( ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 187.79/187.93 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.79/187.93 & ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 187.79/187.93 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_partition_Osimps_I1_J,axiom,
% 187.79/187.93 ! [V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_partition_Osimps_I2_J,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_Pa_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose_Osimps_I3_J,axiom,
% 187.79/187.93 ! [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))))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_partition__filter2,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_Pa_2)),V_xs_2) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_concat__injective,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 187.79/187.93 => ( 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)
% 187.79/187.93 => ( ! [B_x] :
% 187.79/187.93 ( 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))))
% 187.79/187.93 => 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)) )
% 187.79/187.93 => V_xs_2 = V_ys_2 ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_concat__eq__concat__iff,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( ! [B_x] :
% 187.79/187.93 ( 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))))
% 187.79/187.93 => 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)) )
% 187.79/187.93 => ( 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)
% 187.79/187.93 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 187.79/187.93 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_concat__map__singleton,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_n__lists_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_partition__set,axiom,
% 187.79/187.93 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 187.79/187.93 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose__aux__filter__tail,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose__aux__filter__head,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__tl,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_tl_Osimps_I1_J,axiom,
% 187.79/187.93 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct__tl,axiom,
% 187.79/187.93 ! [V_xs,T_a] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.79/187.93 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_tl_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_hd_Osimps,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__Suc,axiom,
% 187.79/187.93 ! [V_n,T_a,V_xs] :
% 187.79/187.93 ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_tl__append2,axiom,
% 187.79/187.93 ! [V_ys,T_a,V_xs] :
% 187.79/187.93 ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate1__hd__tl,axiom,
% 187.79/187.93 ! [T_a,V_xs] :
% 187.79/187.93 ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__tl,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_hd__map,axiom,
% 187.79/187.93 ! [V_f_2,T_c,T_b,V_xs_2] :
% 187.79/187.93 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_hd__append2,axiom,
% 187.79/187.93 ! [V_ys,T_a,V_xs] :
% 187.79/187.93 ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_hd__append,axiom,
% 187.79/187.93 ! [V_ys,T_a,V_xs] :
% 187.79/187.93 ( ( V_xs = c_List_Olist_ONil(T_a)
% 187.79/187.93 => 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) )
% 187.79/187.93 & ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.93 => 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) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_hd__upt,axiom,
% 187.79/187.93 ! [V_j,V_i] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.79/187.93 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_tl__append,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__tl,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_hd__in__set,axiom,
% 187.79/187.93 ! [T_b,V_xs_2] :
% 187.79/187.93 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_tl__take,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_hd__conv__nth,axiom,
% 187.79/187.93 ! [T_a,V_xs] :
% 187.79/187.93 ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__remdups__concat,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_insort__key__remove1,axiom,
% 187.79/187.93 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_c)
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 187.79/187.93 => ( 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
% 187.79/187.93 => 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 ) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted_ONil,axiom,
% 187.79/187.93 ! [T_a] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_a)
% 187.79/187.93 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct__remdups,axiom,
% 187.79/187.93 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__single,axiom,
% 187.79/187.93 ! [V_x,T_a] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_a)
% 187.79/187.93 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__remdups__leq,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__filter,axiom,
% 187.79/187.93 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 187.79/187.93 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_remdups__map__remdups,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__map__remove1,axiom,
% 187.79/187.93 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 187.79/187.93 => 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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__insort__key,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( 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)))
% 187.79/187.93 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__distinct__set__unique,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 187.79/187.93 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 187.79/187.93 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 187.79/187.93 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 187.79/187.93 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__tl,axiom,
% 187.79/187.93 ! [V_xs,T_a] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_a)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 187.79/187.93 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__remdups,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__same,axiom,
% 187.79/187.93 ! [V_xs_2,V_g_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_remdups__filter,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oremdups(T_b,V_xs_2)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__upt,axiom,
% 187.79/187.93 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__remdups__eq,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( 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)
% 187.79/187.93 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__insort,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( 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))
% 187.79/187.93 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__remove1,axiom,
% 187.79/187.93 ! [V_a,V_xs,T_a] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_a)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 187.79/187.93 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__upto,axiom,
% 187.79/187.93 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_remdups__remdups,axiom,
% 187.79/187.93 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__remdups,axiom,
% 187.79/187.93 ! [V_l,T_a] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_a)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 187.79/187.93 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__insort__insert,axiom,
% 187.79/187.93 ! [V_x_2,V_xs_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_remdups__id__iff__distinct,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 187.79/187.93 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct__remdups__id,axiom,
% 187.79/187.93 ! [V_xs,T_a] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.79/187.93 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_remdups_Osimps_I1_J,axiom,
% 187.79/187.93 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted_Oequations_I1_J,axiom,
% 187.79/187.93 ! [T_a] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_a)
% 187.79/187.93 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_remdups__eq__nil__right__iff,axiom,
% 187.79/187.93 ! [V_x_2,T_b] :
% 187.79/187.93 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 187.79/187.93 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_remdups__eq__nil__iff,axiom,
% 187.79/187.93 ! [V_x_2,T_b] :
% 187.79/187.93 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 187.79/187.93 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__many__eq,axiom,
% 187.79/187.93 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( 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)))
% 187.79/187.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 187.79/187.93 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__many,axiom,
% 187.79/187.93 ! [V_zs,V_y,V_x,T_a] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_a)
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 187.79/187.93 => 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))) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__take,axiom,
% 187.79/187.93 ! [V_n,V_xs,T_a] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_a)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 187.79/187.93 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__insort__insert__key,axiom,
% 187.79/187.93 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 187.79/187.93 => 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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__map__same,axiom,
% 187.79/187.93 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_remove1__remdups,axiom,
% 187.79/187.93 ! [V_x,V_xs,T_a] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__Cons,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 187.79/187.93 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 187.79/187.93 & ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__append,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 187.79/187.93 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 187.79/187.93 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 187.79/187.93 & ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => ! [B_xa] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_filter__insort,axiom,
% 187.79/187.93 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 187.79/187.93 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_remdups_Osimps_I2_J,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => 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) )
% 187.79/187.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__remdups__card__conv,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted_Oequations_I2_J,axiom,
% 187.79/187.93 ! [V_a1_2,V_a2_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 187.79/187.93 <=> ( ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 187.79/187.93 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__list__of__set,axiom,
% 187.79/187.93 ! [V_A_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.93 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 187.79/187.93 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 187.79/187.93 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_insort__remove1,axiom,
% 187.79/187.93 ! [V_xs_2,V_a_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 187.79/187.93 => 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 ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__nth__mono,axiom,
% 187.79/187.93 ! [V_j,V_i,V_xs,T_a] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_a)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.79/187.93 => ( 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)))
% 187.79/187.93 => 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))) ) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__equals__nth__mono,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 187.79/187.93 <=> ! [B_j] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => ! [B_i] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 187.79/187.93 => 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))) ) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__sorted__distinct__set__unique,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_c)
% 187.79/187.93 => ( 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)))
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 187.79/187.93 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 187.79/187.93 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 187.79/187.93 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 187.79/187.93 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose__column,axiom,
% 187.79/187.93 ! [V_i_2,V_xs_2,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => ( 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)))
% 187.79/187.93 => 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) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__nth__transpose__sorted,axiom,
% 187.79/187.93 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => ( 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))))
% 187.79/187.93 => ( 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))))
% 187.79/187.93 => 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) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_inj__on__rev,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__is__Nil__conv,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 187.79/187.93 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Nil__is__rev__conv,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 187.79/187.93 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev_Osimps_I1_J,axiom,
% 187.79/187.93 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct__rev,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 187.79/187.93 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__is__rev__conv,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 187.79/187.93 <=> V_xs_2 = V_ys_2 ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__swap,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 187.79/187.93 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__rev__ident,axiom,
% 187.79/187.93 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__rev,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__rev,axiom,
% 187.79/187.93 ! [V_xs,T_a] :
% 187.79/187.93 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__filter,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_singleton__rev__conv,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( 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)
% 187.79/187.93 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__singleton__conv,axiom,
% 187.79/187.93 ! [V_x_2,V_xs_2,T_b] :
% 187.79/187.93 ( 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))
% 187.79/187.93 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__append,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_zip__rev,axiom,
% 187.79/187.93 ! [V_ys,T_b,V_xs,T_a] :
% 187.79/187.93 ( 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)
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__rev,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__map,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__concat,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__eq__Cons__iff,axiom,
% 187.79/187.93 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 187.79/187.93 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 187.79/187.93 <=> 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev_Osimps_I2_J,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_last__rev,axiom,
% 187.79/187.93 ! [T_a,V_xs] :
% 187.79/187.93 ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.93 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_hd__rev,axiom,
% 187.79/187.93 ! [T_a,V_xs] :
% 187.79/187.93 ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.93 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__transpose,axiom,
% 187.79/187.93 ! [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)))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__nth,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_n] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__update,axiom,
% 187.79/187.93 ! [V_y,V_xs,T_a,V_k] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__rev__nth__mono,axiom,
% 187.79/187.93 ! [V_j,V_i,V_xs,T_a] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_a)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.79/187.93 => ( 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)))
% 187.79/187.93 => 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))) ) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldr__max__sorted,axiom,
% 187.79/187.93 ! [V_y_2,V_xs_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 187.79/187.93 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 187.79/187.93 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 187.79/187.93 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 187.79/187.93 => 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) ) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__transpose__sorted,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 187.79/187.93 => 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) )
% 187.79/187.93 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 187.79/187.93 => 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))) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose__column__length,axiom,
% 187.79/187.93 ! [V_i_2,V_xs_2,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => ( 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)))
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_transpose__transpose,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__hd__drop,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_n] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__drop,axiom,
% 187.79/187.93 ! [V_n,V_xs,T_a] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_a)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 187.79/187.93 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__takeWhile,axiom,
% 187.79/187.93 ! [V_Pa_2,V_xs_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 187.79/187.93 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_takeWhile__tail,axiom,
% 187.79/187.93 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] :
% 187.79/187.93 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__map,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_zip__takeWhile__snd,axiom,
% 187.79/187.93 ! [V_ys_2,V_Pa_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_zip__takeWhile__fst,axiom,
% 187.79/187.93 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__takeWhileD,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,V_x_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_in__set__dropD,axiom,
% 187.79/187.93 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 187.79/187.93 ( 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))))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__drop__subset,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__tl,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_tl__drop,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__Suc,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_takeWhile__eq__all__conv,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] :
% 187.79/187.93 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2
% 187.79/187.93 <=> ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__zip,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 187.79/187.93 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 187.79/187.93 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) )
% 187.79/187.93 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__via__drop,axiom,
% 187.79/187.93 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 187.79/187.93 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 187.79/187.93 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__1__Cons,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__Suc__Cons,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__upt,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__drop,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__drop,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__0,axiom,
% 187.79/187.93 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct__drop,axiom,
% 187.79/187.93 ! [V_i,V_xs,T_a] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.79/187.93 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct__takeWhile,axiom,
% 187.79/187.93 ! [V_Pa_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.93 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__Nil,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 187.79/187.93 ! [V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__take__drop__id,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__take,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__drop,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__takeWhile__le,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_takeWhile__eq__take,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_takeWhile__map,axiom,
% 187.79/187.93 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__drop__subset__set__drop,axiom,
% 187.79/187.93 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 187.79/187.93 => 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)))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__eq__Nil,axiom,
% 187.79/187.93 ! [V_xs_2,V_n_2,T_b] :
% 187.79/187.93 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 187.79/187.93 <=> 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__all,axiom,
% 187.79/187.93 ! [V_n,V_xs,T_a] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__append,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__eq__conv__conj,axiom,
% 187.79/187.93 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 187.79/187.93 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 187.79/187.93 <=> ( 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)
% 187.79/187.93 & 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) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_last__drop,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_n] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__Cons,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_takeWhile__append1,axiom,
% 187.79/187.93 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__length__takeWhile,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 187.79/187.93 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_takeWhile__nth,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
% 187.79/187.93 => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__Cons_H,axiom,
% 187.79/187.93 ! [V_xs,V_x,T_a,V_n] :
% 187.79/187.93 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 => 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) )
% 187.79/187.93 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 => 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) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__drop,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_i,V_n] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_append__eq__append__conv__if,axiom,
% 187.79/187.93 ! [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] :
% 187.79/187.93 ( 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)
% 187.79/187.93 <=> ( ( 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)))
% 187.79/187.93 => ( 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)
% 187.79/187.93 & 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) ) )
% 187.79/187.93 & ( ~ 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)))
% 187.79/187.93 => ( 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
% 187.79/187.93 & 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 ) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__drop,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__take,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__upds__def,axiom,
% 187.79/187.93 ! [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)))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_nth__drop_H,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_i] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_drop__Cons__number__of,axiom,
% 187.79/187.93 ! [V_xs,V_x,T_a,V_v] :
% 187.79/187.93 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 => 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) )
% 187.79/187.93 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 => 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) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_take__add,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_j,V_i] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_hd__drop__conv__nth,axiom,
% 187.79/187.93 ! [V_n,T_a,V_xs] :
% 187.79/187.93 ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.93 => ( 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)))
% 187.79/187.93 => 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) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_zip__append1,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_zip__append2,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 187.79/187.93 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( 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)))
% 187.79/187.93 => 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) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_id__take__nth__drop,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_i] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_upd__conv__take__nth__drop,axiom,
% 187.79/187.93 ! [V_a,V_xs,T_a,V_i] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_takeWhile__neq__rev,axiom,
% 187.79/187.93 ! [V_x_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => 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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_dropWhile__neq__rev,axiom,
% 187.79/187.93 ! [V_x_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => 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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 187.79/187.93 ! [V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct__dropWhile,axiom,
% 187.79/187.93 ! [V_Pa_2,V_xs_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.93 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 187.79/187.93 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 187.79/187.93 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) )
% 187.79/187.93 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__dropWhile,axiom,
% 187.79/187.93 ! [V_Pa_2,V_xs_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 187.79/187.93 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] :
% 187.79/187.93 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b)
% 187.79/187.93 <=> ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__dropWhile__le,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_takeWhile__dropWhile__id,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) = V_xs_2 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_hd__dropWhile,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] :
% 187.79/187.93 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 187.79/187.93 => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_dropWhile__map,axiom,
% 187.79/187.93 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_dropWhile__append1,axiom,
% 187.79/187.93 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.93 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.93 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 187.79/187.93 ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] :
% 187.79/187.93 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 187.79/187.93 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
% 187.79/187.93 & ~ hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_dropWhile__eq__drop,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_dropWhile__nth,axiom,
% 187.79/187.93 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))
% 187.79/187.93 => hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sorted__nth__monoI,axiom,
% 187.79/187.93 ! [V_xs,T_a] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_a)
% 187.79/187.93 => ( ! [B_i,B_j] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 187.79/187.93 => ( 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)))
% 187.79/187.93 => 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))) ) )
% 187.79/187.93 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_prod__fun__imageE,axiom,
% 187.79/187.93 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_ca_2,T_c,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => ~ ! [B_x,B_y] :
% 187.79/187.93 ( 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))
% 187.79/187.93 => ~ 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_fold1__set,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 187.79/187.93 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_hd__rotate__conv__nth,axiom,
% 187.79/187.93 ! [V_n,T_a,V_xs] :
% 187.79/187.93 ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldr__conv__foldl,axiom,
% 187.79/187.93 ! [V_a_2,V_xs_2,T_b] :
% 187.79/187.93 ( class_Groups_Oab__semigroup__add(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldl__conv__concat,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_start__le__sum,axiom,
% 187.79/187.93 ! [V_ns_2,V_n_2,V_m_2] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldl__Nil,axiom,
% 187.79/187.93 ! [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 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate__is__Nil__conv,axiom,
% 187.79/187.93 ! [V_xs_2,V_n_2,T_b] :
% 187.79/187.93 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 187.79/187.93 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_distinct__rotate,axiom,
% 187.79/187.93 ! [V_xs_2,V_n_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 187.79/187.93 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldl__absorb0,axiom,
% 187.79/187.93 ! [V_zs_2,V_x_2,T_b] :
% 187.79/187.93 ( class_Groups_Omonoid__add(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate__rotate,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldl__assoc,axiom,
% 187.79/187.93 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 187.79/187.93 ( class_Groups_Osemigroup__add(T_b)
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_length__rotate,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldl__Cons,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldl__append,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate1__rotate__swap,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_set__rotate,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldl__map,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate__map,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate__conv__mod,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldl__foldr,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldr__foldl,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate__Suc,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_listsum__foldl,axiom,
% 187.79/187.93 ! [T_b] :
% 187.79/187.93 ( class_Groups_Omonoid__add(T_b)
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_concat__conv__foldl,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldl__foldr1__lemma,axiom,
% 187.79/187.93 ! [V_xs_2,V_a_2,T_b] :
% 187.79/187.93 ( class_Groups_Omonoid__add(T_b)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_foldl__foldr1,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( class_Groups_Omonoid__add(T_b)
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_sum__eq__0__conv,axiom,
% 187.79/187.93 ! [V_ns_2,V_m_2] :
% 187.79/187.93 ( 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)
% 187.79/187.93 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.79/187.93 & ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 187.79/187.93 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rev__foldl__cons,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate__add,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate__id,axiom,
% 187.79/187.93 ! [V_xs,T_a,V_n] :
% 187.79/187.93 ( 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)
% 187.79/187.93 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate__length01,axiom,
% 187.79/187.93 ! [V_n,V_xs,T_a] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sup__set__fold,axiom,
% 187.79/187.93 ! [V_xs_2,T_b] :
% 187.79/187.93 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sup__fin__set__fold,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( class_Lattices_Olattice(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Inf__fin__set__fold,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( class_Lattices_Olattice(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Min__fin__set__fold,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Max__fin__set__fold,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 187.79/187.93 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.93 ( class_Orderings_Olinorder(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_SUPR__set__fold,axiom,
% 187.79/187.93 ! [V_f_2,V_xs_2,T_c,T_b] :
% 187.79/187.93 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.93 => 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) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__upds__fold__map__upd,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate__rev,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_elem__le__sum,axiom,
% 187.79/187.93 ! [V_ns_2,V_n_2] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_rotate__drop__take,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_image__split__eq__Sigma,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_lexord__append__rightI,axiom,
% 187.79/187.93 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 187.79/187.93 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_SigmaI,axiom,
% 187.79/187.93 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 187.79/187.93 => 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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_UNIV__Times__UNIV,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_SigmaE2,axiom,
% 187.79/187.93 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.93 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_SigmaD2,axiom,
% 187.79/187.93 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_SigmaD1,axiom,
% 187.79/187.93 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_mem__Sigma__iff,axiom,
% 187.79/187.93 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 187.79/187.93 ( 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)))
% 187.79/187.93 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.93 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sigma__Union,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_setprod__cartesian__product,axiom,
% 187.79/187.93 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 187.79/187.93 ( class_Groups_Ocomm__monoid__mult(T_b)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_setsum__cartesian__product,axiom,
% 187.79/187.93 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 187.79/187.93 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.79/187.93 => 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sigma__empty2,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Times__empty,axiom,
% 187.79/187.93 ! [V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.93 ( 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))
% 187.79/187.93 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.93 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sigma__empty1,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sigma__Int__distrib1,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Times__Int__distrib1,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sigma__Int__distrib2,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_equiv__type,axiom,
% 187.79/187.93 ! [V_r_2,V_A_2,T_b] :
% 187.79/187.93 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.93 => 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)))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Compl__Times__UNIV2,axiom,
% 187.79/187.93 ! [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)))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Compl__Times__UNIV1,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sigma__Diff__distrib1,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Times__Diff__distrib1,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sigma__Diff__distrib2,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_card__cartesian__product,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sigma__Un__distrib2,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Times__Un__distrib1,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sigma__Un__distrib1,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_finite__cartesian__product,axiom,
% 187.79/187.93 ! [V_B_2,T_c,V_A_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 187.79/187.93 => 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)))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Times__eq__cancel2,axiom,
% 187.79/187.93 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 187.79/187.93 => ( 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))
% 187.79/187.93 <=> V_A_2 = V_B_2 ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Id__on__subset__Times,axiom,
% 187.79/187.93 ! [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)))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_card__cartesian__product__singleton,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Times__subset__cancel2,axiom,
% 187.79/187.93 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 187.79/187.93 => ( 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))))
% 187.79/187.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Image__subset,axiom,
% 187.79/187.93 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 187.79/187.93 ( 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))))
% 187.79/187.93 => 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)) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_finite__cartesian__productD1,axiom,
% 187.79/187.93 ! [V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.93 ( 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))))
% 187.79/187.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 187.79/187.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_finite__cartesian__productD2,axiom,
% 187.79/187.93 ! [V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.93 ( 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))))
% 187.79/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Collect__split,axiom,
% 187.79/187.93 ! [V_Qa_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Qa_2))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_SetCompr__Sigma__eq,axiom,
% 187.79/187.93 ! [V_Qa_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Qa_2)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_fst__image__times,axiom,
% 187.79/187.93 ! [V_A_2,T_c,T_b,V_B_2] :
% 187.79/187.93 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.93 => 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)) )
% 187.79/187.93 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.93 => 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 ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_snd__image__times,axiom,
% 187.79/187.93 ! [V_B_2,T_c,T_b,V_A_2] :
% 187.79/187.93 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.93 => 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)) )
% 187.79/187.93 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.93 => 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 ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__pair__surj__on,axiom,
% 187.79/187.93 ! [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] :
% 187.79/187.93 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 187.79/187.93 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 187.79/187.93 => 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)) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_product__list__set,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_swap__product,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_refl__on__def,axiom,
% 187.79/187.93 ! [V_r_2,V_A_2,T_b] :
% 187.79/187.93 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 187.79/187.93 <=> ( 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))))
% 187.79/187.93 & ! [B_x] :
% 187.79/187.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.93 => 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)) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_insert__times__insert,axiom,
% 187.79/187.93 ! [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)))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_finite__equiv__class,axiom,
% 187.79/187.93 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.93 => ( 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))))
% 187.79/187.93 => ( 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)))
% 187.79/187.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__pair__inj__on,axiom,
% 187.79/187.93 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 187.79/187.93 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.79/187.93 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 187.79/187.93 => 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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_UN__Times__distrib,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Sigma__def,axiom,
% 187.79/187.93 ! [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))))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_finite__quotient,axiom,
% 187.79/187.93 ! [V_r_2,V_A_2,T_b] :
% 187.79/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.93 => ( 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))))
% 187.79/187.93 => 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))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_vimage__Times,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 187.79/187.93 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 187.79/187.93 ( class_Rings_Osemiring__0(T_d)
% 187.79/187.93 => ( 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)))
% 187.79/187.93 => 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))))))) ) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 187.79/187.93 ! [V_A_2,V_I_2,T_c,T_b] :
% 187.79/187.93 ? [B_f] :
% 187.79/187.93 ( 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))
% 187.79/187.93 & 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))) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_bij__betw__id,axiom,
% 187.79/187.93 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_image__id,axiom,
% 187.79/187.93 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_surj__id,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__pair_Oidentity,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_map__pair_Oid,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_inv__id,axiom,
% 187.79/187.93 ! [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) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_of__int__eq__id,axiom,
% 187.79/187.93 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_inj__on__id,axiom,
% 187.79/187.93 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_id__apply,axiom,
% 187.79/187.93 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Option_Omap_Oid,axiom,
% 187.79/187.93 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_id__def,axiom,
% 187.79/187.93 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_vimage__id,axiom,
% 187.79/187.93 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 187.79/187.93
% 187.79/187.93 fof(fact_bij__betw__id__iff,axiom,
% 187.79/187.93 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.93 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
% 187.79/187.93 <=> V_A_2 = V_B_2 ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_Option_Omap_Oidentity,axiom,
% 187.79/187.93 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_apsnd__id,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_apfst__id,axiom,
% 187.79/187.93 ! [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)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_bij__id,axiom,
% 187.79/187.93 ! [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))) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_List_Omap_Oidentity,axiom,
% 187.79/187.93 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_List_Omap_Oid,axiom,
% 187.79/187.93 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_folding_Oempty,axiom,
% 187.79/187.93 ! [V_F_2,V_f_2,T_c,T_b] :
% 187.79/187.93 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 187.79/187.93 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 187.79/187.93
% 187.79/187.93 fof(fact_o__eq__id__dest,axiom,
% 187.79/187.93 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 187.79/187.94 ( 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)
% 187.79/187.94 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_o__id,axiom,
% 187.79/187.94 ! [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 ).
% 187.79/187.94
% 187.79/187.94 fof(fact_id__o,axiom,
% 187.79/187.94 ! [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 ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rotate0,axiom,
% 187.79/187.94 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_apsnd__def,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_apfst__def,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_split__Pair,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_setsum__reindex__id,axiom,
% 187.79/187.94 ! [V_B_2,V_f_2,T_b,T_c] :
% 187.79/187.94 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.94 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_setprod__reindex__id,axiom,
% 187.79/187.94 ! [V_B_2,V_f_2,T_b,T_c] :
% 187.79/187.94 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.79/187.94 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_surj__iff,axiom,
% 187.79/187.94 ! [V_f_2,T_b,T_c] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_inj__iff,axiom,
% 187.79/187.94 ! [V_f_2,T_c,T_b] :
% 187.79/187.94 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.79/187.94 <=> 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_inv__o__cancel,axiom,
% 187.79/187.94 ! [V_f_2,T_c,T_b] :
% 187.79/187.94 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_setprod__Sigma,axiom,
% 187.79/187.94 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 187.79/187.94 ( class_Groups_Ocomm__monoid__mult(T_d)
% 187.79/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.94 => ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 187.79/187.94 => 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)) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_refl__onI,axiom,
% 187.79/187.94 ! [V_A_2,V_r_2,T_b] :
% 187.79/187.94 ( 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))))
% 187.79/187.94 => ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.94 => 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)) )
% 187.79/187.94 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_setsum__Sigma,axiom,
% 187.79/187.94 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 187.79/187.94 ( class_Groups_Ocomm__monoid__add(T_d)
% 187.79/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.94 => ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 187.79/187.94 => 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)) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_fold__image__Sigma,axiom,
% 187.79/187.94 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 187.79/187.94 ( class_Groups_Ocomm__monoid__mult(T_d)
% 187.79/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.94 => ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 187.79/187.94 => 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)) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_card__SigmaI,axiom,
% 187.79/187.94 ! [V_B_2,T_c,V_A_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.94 => ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 187.79/187.94 => 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) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_finite__SigmaI,axiom,
% 187.79/187.94 ! [V_B_2,T_c,V_A_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.94 => ( ! [B_a] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 187.79/187.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listrel__subset,axiom,
% 187.79/187.94 ! [V_A_2,V_r_2,T_b] :
% 187.79/187.94 ( 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))))
% 187.79/187.94 => 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))))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_sort__foldl__insort,axiom,
% 187.79/187.94 ! [V_xs_2,T_b] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_b)
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_lists_ONil,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_lists__mono,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_sort__key__simps_I1_J,axiom,
% 187.79/187.94 ! [V_f_2,T_b,T_c] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_c)
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_distinct__sort,axiom,
% 187.79/187.94 ! [V_xs_2,V_f_2,T_b,T_c] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_c)
% 187.79/187.94 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
% 187.79/187.94 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_length__sort,axiom,
% 187.79/187.94 ! [V_xs_2,V_f_2,T_b,T_c] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_c)
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_filter__sort,axiom,
% 187.79/187.94 ! [V_xs_2,V_f_2,V_Pa_2,T_b,T_c] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_c)
% 187.79/187.94 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_set__sort,axiom,
% 187.79/187.94 ! [V_xs_2,V_f_2,T_b,T_c] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_c)
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_sorted__sort,axiom,
% 187.79/187.94 ! [V_xs_2,T_b] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_b)
% 187.79/187.94 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_append__in__lists__conv,axiom,
% 187.79/187.94 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 187.79/187.94 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_lists__UNIV,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_equiv__listrel,axiom,
% 187.79/187.94 ! [V_r_2,V_A_2,T_b] :
% 187.79/187.94 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 187.79/187.94 => 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listrel__refl__on,axiom,
% 187.79/187.94 ! [V_r_2,V_A_2,T_b] :
% 187.79/187.94 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 187.79/187.94 => 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_sorted__sort__key,axiom,
% 187.79/187.94 ! [V_xs_2,V_f_2,T_c,T_b] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_b)
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_sort__key__simps_I2_J,axiom,
% 187.79/187.94 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_c)
% 187.79/187.94 => 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Cons__in__lists__iff,axiom,
% 187.79/187.94 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.94 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_in__lists__conv__set,axiom,
% 187.79/187.94 ! [V_A_2,V_xs_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 187.79/187.94 <=> ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_lists__eq__set,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 187.79/187.94 ! [V_xs_2,T_b] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_b)
% 187.79/187.94 => 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_lists__empty,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_lexord__Nil__left,axiom,
% 187.79/187.94 ! [V_r_2,V_y_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.94 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_takeWhile__eq__filter,axiom,
% 187.79/187.94 ! [V_xs_2,V_Pa_2,T_b] :
% 187.79/187.94 ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))
% 187.79/187.94 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.79/187.94 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_lexord__irreflexive,axiom,
% 187.79/187.94 ! [V_y_2,V_r_2,T_b] :
% 187.79/187.94 ( ! [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))
% 187.79/187.94 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_lexord__linear,axiom,
% 187.79/187.94 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 187.79/187.94 ( ! [B_a,B_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 | B_a = B_b
% 187.79/187.94 | 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)) )
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 187.79/187.94 | V_x_2 = V_y_2
% 187.79/187.94 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_lists_Osimps,axiom,
% 187.79/187.94 ! [V_A_2,V_a_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 187.79/187.94 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 187.79/187.94 | ? [B_a,B_l] :
% 187.79/187.94 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 187.79/187.94 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 187.79/187.94 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 187.79/187.94 ! [V_Pa_2,V_xs_2,T_b,V_n_2] :
% 187.79/187.94 ( ! [B_i] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
% 187.79/187.94 => ( ( 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)))
% 187.79/187.94 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
% 187.79/187.94 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__size__pointwise,axiom,
% 187.79/187.94 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 187.79/187.94 ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_butlast__take,axiom,
% 187.79/187.94 ! [V_xs,T_a,V_n] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_distinct__butlast,axiom,
% 187.79/187.94 ! [T_a,V_xs] :
% 187.79/187.94 ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.94 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.79/187.94 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_butlast_Osimps_I2_J,axiom,
% 187.79/187.94 ! [V_x,T_a,V_xs] :
% 187.79/187.94 ( ( V_xs = c_List_Olist_ONil(T_a)
% 187.79/187.94 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 187.79/187.94 & ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_butlast_Osimps_I1_J,axiom,
% 187.79/187.94 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_map__butlast,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_in__set__butlastD,axiom,
% 187.79/187.94 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_drop__butlast,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_butlast__drop,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_butlast__append,axiom,
% 187.79/187.94 ! [V_xs,T_a,V_ys] :
% 187.79/187.94 ( ( V_ys = c_List_Olist_ONil(T_a)
% 187.79/187.94 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 187.79/187.94 & ( V_ys != c_List_Olist_ONil(T_a)
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_sorted__butlast,axiom,
% 187.79/187.94 ! [V_xs,T_a] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_a)
% 187.79/187.94 => ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.94 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 187.79/187.94 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_in__set__butlast__appendI,axiom,
% 187.79/187.94 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.94 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 187.79/187.94 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 187.79/187.94 => 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))))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_butlast__snoc,axiom,
% 187.79/187.94 ! [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 ).
% 187.79/187.94
% 187.79/187.94 fof(fact_take__butlast,axiom,
% 187.79/187.94 ! [V_xs,T_a,V_n] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_length__butlast,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_butlast__conv__take,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_butlast__list__update,axiom,
% 187.79/187.94 ! [V_x,V_xs,T_a,V_k] :
% 187.79/187.94 ( ( 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))
% 187.79/187.94 => 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) )
% 187.79/187.94 & ( 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))
% 187.79/187.94 => 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) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_append__butlast__last__id,axiom,
% 187.79/187.94 ! [T_a,V_xs] :
% 187.79/187.94 ( V_xs != c_List_Olist_ONil(T_a)
% 187.79/187.94 => 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 ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_snoc__eq__iff__butlast,axiom,
% 187.79/187.94 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 187.79/187.94 ( 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
% 187.79/187.94 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 187.79/187.94 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 187.79/187.94 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_takeWhile__not__last,axiom,
% 187.79/187.94 ! [T_b,V_xs_2] :
% 187.79/187.94 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 187.79/187.94 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.79/187.94 => 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) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_length__takeWhile__less__P__nth,axiom,
% 187.79/187.94 ! [V_xs_2,T_b,V_Pa_2,V_j_2] :
% 187.79/187.94 ( ! [B_i] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 187.79/187.94 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INFI__set__fold,axiom,
% 187.79/187.94 ! [V_f_2,V_xs_2,T_c,T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__D,axiom,
% 187.79/187.94 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__E,axiom,
% 187.79/187.94 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 187.79/187.94 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INF1__D,axiom,
% 187.79/187.94 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.94 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INF1__E,axiom,
% 187.79/187.94 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 187.79/187.94 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INF2__D,axiom,
% 187.79/187.94 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.94 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INF2__E,axiom,
% 187.79/187.94 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 187.79/187.94 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_finite__INT,axiom,
% 187.79/187.94 ! [V_A_2,T_c,V_I_2,T_b] :
% 187.79/187.94 ( ? [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 187.79/187.94 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_vimage__INT,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Compl__UN,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Compl__INT,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_UN__extend__simps_I7_J,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_UN__simps_I7_J,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__extend__simps_I9_J,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__simps_I9_J,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Collect__ball__eq,axiom,
% 187.79/187.94 ! [V_Pa_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_Pa_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_Pa_2))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INFI__bool__eq,axiom,
% 187.79/187.94 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__absorb,axiom,
% 187.79/187.94 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__Int__distrib,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__Un,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__empty,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__constant,axiom,
% 187.79/187.94 ! [V_ca_2,T_c,T_b,V_A_2] :
% 187.79/187.94 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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)) )
% 187.79/187.94 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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 ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__extend__simps_I1_J,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 187.79/187.94 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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 )
% 187.79/187.94 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__extend__simps_I2_J,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 187.79/187.94 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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 )
% 187.79/187.94 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__insert,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INF__const,axiom,
% 187.79/187.94 ! [V_M_2,T_b,V_A_2,T_c] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 187.79/187.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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 ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__extend__simps_I5_J,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__simps_I5_J,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__simps_I8_J,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__extend__simps_I8_J,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INF__less__iff,axiom,
% 187.79/187.94 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 187.79/187.94 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 & class_Orderings_Olinorder(T_b) )
% 187.79/187.94 => ( 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))
% 187.79/187.94 <=> ? [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.79/187.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__simps_I7_J,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__simps_I6_J,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__extend__simps_I7_J,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Un__INT__distrib,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__extend__simps_I6_J,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Un__INT__distrib2,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INFI__apply,axiom,
% 187.79/187.94 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INF__commute,axiom,
% 187.79/187.94 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Pow__INT__eq,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.94 ( 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)
% 187.79/187.94 <=> ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.79/187.94 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.79/187.94 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__iff,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 <=> ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INF__INT__eq,axiom,
% 187.79/187.94 ! [V_x_2,V_r_2,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__insert__distrib,axiom,
% 187.79/187.94 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 187.79/187.94 => 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INF__INT__eq2,axiom,
% 187.79/187.94 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__extend__simps_I10_J,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__simps_I10_J,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Image__INT__subset,axiom,
% 187.79/187.94 ! [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)))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_le__INF__iff,axiom,
% 187.79/187.94 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => ( 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)))
% 187.79/187.94 <=> ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__subset__iff,axiom,
% 187.79/187.94 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 <=> ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__lower,axiom,
% 187.79/187.94 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INF__subset,axiom,
% 187.79/187.94 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INTER__def,axiom,
% 187.79/187.94 ! [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)))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__simps_I2_J,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 187.79/187.94 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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)) )
% 187.79/187.94 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__simps_I1_J,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 187.79/187.94 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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)) )
% 187.79/187.94 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__simps_I3_J,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 187.79/187.94 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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)) )
% 187.79/187.94 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__extend__simps_I3_J,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 187.79/187.94 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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) )
% 187.79/187.94 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__extend__simps_I4_J,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 187.79/187.94 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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 )
% 187.79/187.94 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_bij__image__INT,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INF__leI,axiom,
% 187.79/187.94 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__greaterThan__UNIV,axiom,
% 187.79/187.94 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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INT__simps_I4_J,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 187.79/187.94 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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)) )
% 187.79/187.94 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_nth__take__lemma,axiom,
% 187.79/187.94 ! [V_ys,V_xs,T_a,V_k] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => ( ! [B_i] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 187.79/187.94 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 187.79/187.94 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_lists__IntI,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,V_l_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listsp_ONil,axiom,
% 187.79/187.94 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INF2__iff,axiom,
% 187.79/187.94 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.94 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INF1__iff,axiom,
% 187.79/187.94 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.94 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listsp_Oequations_I1_J,axiom,
% 187.79/187.94 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listsp__conj__eq,axiom,
% 187.79/187.94 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2))
% 187.79/187.94 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listsp_Oequations_I2_J,axiom,
% 187.79/187.94 ! [V_a2_2,V_a1_2,V_A_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
% 187.79/187.94 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 187.79/187.94 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_append__in__listsp__conv,axiom,
% 187.79/187.94 ! [V_ys_2,V_xs_2,V_A_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 187.79/187.94 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 187.79/187.94 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listsp__infI,axiom,
% 187.79/187.94 ! [V_B_2,V_l_2,V_A_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
% 187.79/187.94 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listsp__inf__eq,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_in__listsp__conv__set,axiom,
% 187.79/187.94 ! [V_xs_2,V_A_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 187.79/187.94 <=> ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.94 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listsp__mono,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listsp__lists__eq,axiom,
% 187.79/187.94 ! [V_x_2,V_A_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_lists__Int__eq,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_image__INT,axiom,
% 187.79/187.94 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 187.79/187.94 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 187.79/187.94 => ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 187.79/187.94 => 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)) )
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 187.79/187.94 => 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)) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inf__Sup,axiom,
% 187.79/187.94 ! [V_A_2,T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => 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))))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_finite__Inter,axiom,
% 187.79/187.94 ! [V_M_2,T_b] :
% 187.79/187.94 ( ? [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 187.79/187.94 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 187.79/187.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_InterE,axiom,
% 187.79/187.94 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_InterD,axiom,
% 187.79/187.94 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inter__def,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inter__UNIV,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inf__lower,axiom,
% 187.79/187.94 ! [V_A_2,V_x_2,T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inter__empty,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inter__eq,axiom,
% 187.79/187.94 ! [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)))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inf__less__iff,axiom,
% 187.79/187.94 ! [V_a_2,V_S_2,T_b] :
% 187.79/187.94 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 & class_Orderings_Olinorder(T_b) )
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 187.79/187.94 <=> ? [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 187.79/187.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inter__insert,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_le__Inf__iff,axiom,
% 187.79/187.94 ! [V_A_2,V_b_2,T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => ( 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)))
% 187.79/187.94 <=> ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inter__lower,axiom,
% 187.79/187.94 ! [V_A_2,V_B_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.79/187.94 => 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inter__anti__mono,axiom,
% 187.79/187.94 ! [V_A_2,V_B_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inter__Un__distrib,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inf__singleton,axiom,
% 187.79/187.94 ! [V_a_2,T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => 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 ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inf__empty,axiom,
% 187.79/187.94 ! [T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inf__UNIV,axiom,
% 187.79/187.94 ! [T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inf__insert,axiom,
% 187.79/187.94 ! [V_A_2,V_a_2,T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_INTER__eq__Inter__image,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inter__image__eq,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Un__Inter,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Int__eq__Inter,axiom,
% 187.79/187.94 ! [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))))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Int__Inter__image,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inter__Un__subset,axiom,
% 187.79/187.94 ! [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)))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inf__binary,axiom,
% 187.79/187.94 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inf__fin__Inf,axiom,
% 187.79/187.94 ! [V_A_2,T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inf__set__fold,axiom,
% 187.79/187.94 ! [V_xs_2,T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Sup__Inf,axiom,
% 187.79/187.94 ! [V_A_2,T_b] :
% 187.79/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.79/187.94 => 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)))))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__def,axiom,
% 187.79/187.94 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 187.79/187.94 <=> ( 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)
% 187.79/187.94 & ! [B_x] :
% 187.79/187.94 ( 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))))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_sorted_Osimps,axiom,
% 187.79/187.94 ! [V_a_2,T_b] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_b)
% 187.79/187.94 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
% 187.79/187.94 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 187.79/187.94 | ? [B_xs,B_x] :
% 187.79/187.94 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 187.79/187.94 & ! [B_xa] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
% 187.79/187.94 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__rev,axiom,
% 187.79/187.94 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2))
% 187.79/187.94 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__rev1,axiom,
% 187.79/187.94 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
% 187.79/187.94 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__takeI,axiom,
% 187.79/187.94 ! [V_n_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 187.79/187.94 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_ys_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__Nil2,axiom,
% 187.79/187.94 ! [V_xs_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_c))
% 187.79/187.94 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__Nil,axiom,
% 187.79/187.94 ! [V_ys_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,c_List_Olist_ONil(T_b),V_ys_2)
% 187.79/187.94 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__eq,axiom,
% 187.79/187.94 ! [T_b,V_ys_2,V_xs_2] :
% 187.79/187.94 ( V_xs_2 = V_ys_2
% 187.79/187.94 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__lengthD,axiom,
% 187.79/187.94 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__Cons,axiom,
% 187.79/187.94 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))
% 187.79/187.94 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 187.79/187.94 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__appendI,axiom,
% 187.79/187.94 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2)
% 187.79/187.94 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_ca_2,V_d_2)
% 187.79/187.94 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__append,axiom,
% 187.79/187.94 ! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
% 187.79/187.94 ( 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)
% 187.79/187.94 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2))
% 187.79/187.94 <=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 187.79/187.94 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_us_2,V_vs_2) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__map2,axiom,
% 187.79/187.94 ! [V_bs_2,V_f_2,T_d,V_as_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2))
% 187.79/187.94 <=> c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_Pa_2)),V_f_2),V_as_2,V_bs_2) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__map1,axiom,
% 187.79/187.94 ! [V_bs_2,V_as_2,V_f_2,T_d,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2)
% 187.79/187.94 <=> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_Pa_2),V_f_2),V_as_2,V_bs_2) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__dropI,axiom,
% 187.79/187.94 ! [V_n_2,V_bs_2,V_as_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,V_bs_2)
% 187.79/187.94 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_bs_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__conv__all__nth,axiom,
% 187.79/187.94 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 187.79/187.94 <=> ( 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)
% 187.79/187.94 & ! [B_i] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i))) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__nthD,axiom,
% 187.79/187.94 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__nthD2,axiom,
% 187.79/187.94 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__update__cong,axiom,
% 187.79/187.94 ! [V_y_2,V_x_2,V_ys_2,V_Pa_2,T_c,V_xs_2,T_b,V_i_2] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 187.79/187.94 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__update__cong2,axiom,
% 187.79/187.94 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 187.79/187.94 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2I,axiom,
% 187.79/187.94 ! [V_Pa_2,V_b_2,V_a_2,T_c,T_b] :
% 187.79/187.94 ( ! [B_x] :
% 187.79/187.94 ( 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))))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) )
% 187.79/187.94 => ( 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)
% 187.79/187.94 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_SigmaE,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,V_ca_2,T_c,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ~ ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.94 => ! [B_y] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 187.79/187.94 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_not__in__set__insert,axiom,
% 187.79/187.94 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.94 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_List_Oinsert__def,axiom,
% 187.79/187.94 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.94 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.94 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 )
% 187.79/187.94 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.94 => 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) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_distinct__insert,axiom,
% 187.79/187.94 ! [V_x,V_xs,T_a] :
% 187.79/187.94 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.79/187.94 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_insert__remdups,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_in__set__insert,axiom,
% 187.79/187.94 ! [V_xs_2,V_x_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.94 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_List_Oset__insert,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_insert__Nil,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_maps__def,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_concat__map__maps,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_maps__simps_I2_J,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_maps__simps_I1_J,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_distinct__concat,axiom,
% 187.79/187.94 ! [V_xs_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
% 187.79/187.94 => ( ! [B_ys] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 187.79/187.94 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
% 187.79/187.94 => ( ! [B_ys] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 187.79/187.94 => ! [B_zs] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 187.79/187.94 => ( B_ys != B_zs
% 187.79/187.94 => 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)) ) ) )
% 187.79/187.94 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_accp__acc__eq,axiom,
% 187.79/187.94 ! [V_x_2,V_r_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Cons__acc__listrel1I,axiom,
% 187.79/187.94 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 187.79/187.94 => ( 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))))
% 187.79/187.94 => 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)))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_acc__subset,axiom,
% 187.79/187.94 ! [V_R2_2,V_R1_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_lists__accI,axiom,
% 187.79/187.94 ! [V_r_2,V_xs_2,T_b] :
% 187.79/187.94 ( 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))))
% 187.79/187.94 => 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)))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_lists__accD,axiom,
% 187.79/187.94 ! [V_r_2,V_xs_2,T_b] :
% 187.79/187.94 ( 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))))
% 187.79/187.94 => 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)))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_acc_Osimps,axiom,
% 187.79/187.94 ! [V_r_2,V_a_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 187.79/187.94 <=> ! [B_x] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_acc__downward,axiom,
% 187.79/187.94 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 187.79/187.94 => ( 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))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_measures__lesseq,axiom,
% 187.79/187.94 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => 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)))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rel__comp__def,axiom,
% 187.79/187.94 ! [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))))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rel__compI,axiom,
% 187.79/187.94 ! [V_s_2,V_ca_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( 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))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rel__comp__UNION__distrib2,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rel__comp__UNION__distrib,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_union__comp__emptyR,axiom,
% 187.79/187.94 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( 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))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_union__comp__emptyL,axiom,
% 187.79/187.94 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( 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))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rel__comp__empty1,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rel__comp__empty2,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rel__comp__distrib2,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rel__comp__distrib,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_O__assoc,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rel__comp__mono,axiom,
% 187.79/187.94 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( 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))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rel__comp__subset__Sigma,axiom,
% 187.79/187.94 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 187.79/187.94 ( 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))))
% 187.79/187.94 => ( 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))))
% 187.79/187.94 => 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)))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_in__measures_I1_J,axiom,
% 187.79/187.94 ! [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))))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_measures__def,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_max__ext__compat,axiom,
% 187.79/187.94 ! [V_S_2,V_R_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_min__ext__compat,axiom,
% 187.79/187.94 ! [V_S_2,V_R_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_measures__less,axiom,
% 187.79/187.94 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => 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)))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_in__measures_I2_J,axiom,
% 187.79/187.94 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
% 187.79/187.94 ( 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))))
% 187.79/187.94 <=> ( 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)))
% 187.79/187.94 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 187.79/187.94 & 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))) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_pred__comp__rel__comp__eq,axiom,
% 187.79/187.94 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_reduction__pairI,axiom,
% 187.79/187.94 ! [V_S_2,V_R_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_R_2)
% 187.79/187.94 => ( 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))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__less__than,axiom,
% 187.79/187.94 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_pred__comp_Ointros,axiom,
% 187.79/187.94 ! [T_d,T_c,T_b,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__empty,axiom,
% 187.79/187.94 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__inv__image,axiom,
% 187.79/187.94 ! [V_f_2,T_c,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__lex,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__lex__prod,axiom,
% 187.79/187.94 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 187.79/187.94 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 187.79/187.94 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__lenlex,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__measure,axiom,
% 187.79/187.94 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__acc__iff,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_acc__wfD,axiom,
% 187.79/187.94 ! [V_x_2,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__no__loop,axiom,
% 187.79/187.94 ! [V_R_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__union__merge,axiom,
% 187.79/187.94 ! [V_S_2,V_R_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__comp__self,axiom,
% 187.79/187.94 ! [V_R_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_R_2)
% 187.79/187.94 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__measures,axiom,
% 187.79/187.94 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__Int2,axiom,
% 187.79/187.94 ! [V_r_H_2,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__Int1,axiom,
% 187.79/187.94 ! [V_r_H_2,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__subset,axiom,
% 187.79/187.94 ! [V_p_2,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => ( 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))
% 187.79/187.94 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__lexn,axiom,
% 187.79/187.94 ! [V_n_2,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__not__refl,axiom,
% 187.79/187.94 ! [V_a_2,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => ~ 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__not__sym,axiom,
% 187.79/187.94 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => ( 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))
% 187.79/187.94 => ~ 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__asym,axiom,
% 187.79/187.94 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => ( 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))
% 187.79/187.94 => ~ 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__irrefl,axiom,
% 187.79/187.94 ! [V_a_2,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => ~ 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__int__ge__less__than,axiom,
% 187.79/187.94 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__int__ge__less__than2,axiom,
% 187.79/187.94 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_max__ext__wf,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__pair__less,axiom,
% 187.79/187.94 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__mlex,axiom,
% 187.79/187.94 ! [V_f_2,V_R_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_R_2)
% 187.79/187.94 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_pred__comp_Oequations,axiom,
% 187.79/187.94 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> ? [B_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 187.79/187.94 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__finite__psubset,axiom,
% 187.79/187.94 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_min__ext__wf,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__less,axiom,
% 187.79/187.94 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)))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 <=> ~ ? [B_f] :
% 187.79/187.94 ! [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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wfE__pf,axiom,
% 187.79/187.94 ! [V_A_2,V_R_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_R_2)
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__union__compatible,axiom,
% 187.79/187.94 ! [V_S_2,V_R_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_R_2)
% 187.79/187.94 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 187.79/187.94 => ( 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))
% 187.79/187.94 => 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)) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf,axiom,
% 187.79/187.94 ! [T_b] :
% 187.79/187.94 ( class_Orderings_Owellorder(T_b)
% 187.79/187.94 => 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)))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_reduction__pair__def,axiom,
% 187.79/187.94 ! [V_Pa_2,T_b] :
% 187.79/187.94 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 187.79/187.94 <=> ( c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))
% 187.79/187.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_reduction__pair__lemma,axiom,
% 187.79/187.94 ! [V_S_2,V_R_2,V_Pa_2,T_b] :
% 187.79/187.94 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)))
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)))
% 187.79/187.94 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 187.79/187.94 => 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)) ) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__map__pair__image,axiom,
% 187.79/187.94 ! [V_f_2,T_c,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__if__measure,axiom,
% 187.79/187.94 ! [T_b,V_g_2,V_f_2,V_Pa_2] :
% 187.79/187.94 ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(V_Pa_2,B_x))
% 187.79/187.94 => 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))) )
% 187.79/187.94 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_max__extp_Oequations,axiom,
% 187.79/187.94 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 187.79/187.94 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 187.79/187.94 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 187.79/187.94 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 & ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 187.79/187.94 => ? [B_xa] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 187.79/187.94 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_pred__nat__def,axiom,
% 187.79/187.94 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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__same__fst,axiom,
% 187.79/187.94 ! [T_b,V_R_2,T_c,V_Pa_2] :
% 187.79/187.94 ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(V_Pa_2,B_x))
% 187.79/187.94 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 187.79/187.94 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__pred__nat,axiom,
% 187.79/187.94 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_max__ext_Ointros,axiom,
% 187.79/187.94 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 187.79/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 187.79/187.94 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 187.79/187.94 => ? [B_xa] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 187.79/187.94 & 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)) ) )
% 187.79/187.94 => 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))) ) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Nitpick_Oone__frac__def,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Nitpick_Ofrac__def,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_inj__on__Inter,axiom,
% 187.79/187.94 ! [V_f_2,T_c,T_b,V_S_2] :
% 187.79/187.94 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 187.79/187.94 => ( ! [B_A] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 187.79/187.94 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Range__Collect__split,axiom,
% 187.79/187.94 ! [V_Pa_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Inter__subset,axiom,
% 187.79/187.94 ! [V_B_2,V_A_2,T_b] :
% 187.79/187.94 ( ! [B_X] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 187.79/187.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_RangeI,axiom,
% 187.79/187.94 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_snd__eq__Range,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Range__Id__on,axiom,
% 187.79/187.94 ! [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 ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Range__Union,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_finite__Range,axiom,
% 187.79/187.94 ! [V_r_2,T_c,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 187.79/187.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Range__Un__eq,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Range__empty,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Range__empty__iff,axiom,
% 187.79/187.94 ! [V_r_2,T_b,T_c] :
% 187.79/187.94 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Range__iff,axiom,
% 187.79/187.94 ! [V_r_2,T_c,V_a_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 187.79/187.94 <=> ? [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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Range__insert,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Range__Int__subset,axiom,
% 187.79/187.94 ! [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)))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Range__Diff__subset,axiom,
% 187.79/187.94 ! [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)))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_RangeP__Range__eq,axiom,
% 187.79/187.94 ! [V_x_2,V_r_2,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_RangeE,axiom,
% 187.79/187.94 ! [V_r_2,T_c,V_b_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 187.79/187.94 => ~ ! [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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_RangeP_Ointros,axiom,
% 187.79/187.94 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 187.79/187.94 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_RangeP_Oequations,axiom,
% 187.79/187.94 ! [V_a2_2,V_r_2,T_c,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 187.79/187.94 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__Un,axiom,
% 187.79/187.94 ! [V_s_2,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 187.79/187.94 => ( 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))
% 187.79/187.94 => 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)) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_foldl__apply,axiom,
% 187.79/187.94 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
% 187.79/187.94 ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.94 => 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)) )
% 187.79/187.94 => 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_DomainI,axiom,
% 187.79/187.94 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_fst__eq__Domain,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_finite__Domain,axiom,
% 187.79/187.94 ! [V_r_2,T_c,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 187.79/187.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Domain__Id__on,axiom,
% 187.79/187.94 ! [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 ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Domain__Un__eq,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Domain__empty,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Domain__empty__iff,axiom,
% 187.79/187.94 ! [V_r_2,T_c,T_b] :
% 187.79/187.94 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Domain__mono,axiom,
% 187.79/187.94 ! [V_s_2,V_r_2,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Domain__iff,axiom,
% 187.79/187.94 ! [V_r_2,T_c,V_a_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 187.79/187.94 <=> ? [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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Domain__insert,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Domain__Int__subset,axiom,
% 187.79/187.94 ! [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)))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Domain__Diff__subset,axiom,
% 187.79/187.94 ! [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)))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Field__def,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Domain__Union,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Domain__Collect__split,axiom,
% 187.79/187.94 ! [V_Pa_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_Pa_2)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_DomainP__Domain__eq,axiom,
% 187.79/187.94 ! [V_x_2,V_r_2,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_DomainE,axiom,
% 187.79/187.94 ! [V_r_2,T_c,V_a_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 187.79/187.94 => ~ ! [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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_DomainP_Ointros,axiom,
% 187.79/187.94 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 187.79/187.94 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_DomainP_Oequations,axiom,
% 187.79/187.94 ! [V_a1_2,V_r_2,T_c,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 187.79/187.94 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wfP__def,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 187.79/187.94 <=> 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Rep__Integ__cases,axiom,
% 187.79/187.94 ! [V_y_2] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 187.79/187.94 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wfP__empty,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_accp__wfPD,axiom,
% 187.79/187.94 ! [V_x_2,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 187.79/187.94 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wfP__accp__iff,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 187.79/187.94 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wfP__subset,axiom,
% 187.79/187.94 ! [V_p_2,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 187.79/187.94 => ( 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))
% 187.79/187.94 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__in__rel,axiom,
% 187.79/187.94 ! [V_R_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_R_2)
% 187.79/187.94 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wfP__wf__eq,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wfP__acyclicP,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Rep__Integ__induct,axiom,
% 187.79/187.94 ! [V_Pa_2,V_y_2] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 187.79/187.94 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x)))
% 187.79/187.94 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_acyclic__subset,axiom,
% 187.79/187.94 ! [V_r_2,V_s_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 187.79/187.94 => ( 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))
% 187.79/187.94 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__acyclic,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 187.79/187.94 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_finite__acyclic__wf,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 187.79/187.94 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 187.79/187.94 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Nitpick_Owf_H__def,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 187.79/187.94 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 187.79/187.94 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 187.79/187.94 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_inj__on__INTER,axiom,
% 187.79/187.94 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 187.79/187.94 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 => ( ! [B_i] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 187.79/187.94 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_zip__obtain__same__length,axiom,
% 187.79/187.94 ! [V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
% 187.79/187.94 ( ( 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))
% 187.79/187.94 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2)))) )
% 187.79/187.94 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_map__of__eqI,axiom,
% 187.79/187.94 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( ! [B_x] :
% 187.79/187.94 ( 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))))
% 187.79/187.94 => 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) )
% 187.79/187.94 => hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2) = hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Abs__Integ__induct,axiom,
% 187.79/187.94 ! [V_x_2,V_Pa_2] :
% 187.79/187.94 ( ! [B_y] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 187.79/187.94 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 187.79/187.94 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Abs__Integ__cases,axiom,
% 187.79/187.94 ! [V_x_2] :
% 187.79/187.94 ~ ! [B_y] :
% 187.79/187.94 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 187.79/187.94 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wfP__SUP,axiom,
% 187.79/187.94 ! [T_b,V_r_2,T_c] :
% 187.79/187.94 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 187.79/187.94 => ( ! [B_i,B_j] :
% 187.79/187.94 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 187.79/187.94 => 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)) )
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_dropWhile__append2,axiom,
% 187.79/187.94 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
% 187.79/187.94 ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.94 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.79/187.94 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_ys_2) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__all2__all__nthI,axiom,
% 187.79/187.94 ! [V_Pa_2,V_b_2,T_c,V_a_2,T_b] :
% 187.79/187.94 ( 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)
% 187.79/187.94 => ( ! [B_n] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_b_2),B_n))) )
% 187.79/187.94 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_mem__splitI2,axiom,
% 187.79/187.94 ! [V_ca_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 187.79/187.94 ( ! [B_a,B_b] :
% 187.79/187.94 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) )
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_mem__splitE,axiom,
% 187.79/187.94 ! [V_p_2,V_ca_2,T_d,T_c,V_z_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ~ ! [B_x,B_y] :
% 187.79/187.94 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 187.79/187.94 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_finite__sorted__distinct__unique,axiom,
% 187.79/187.94 ! [V_A_2,T_b] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_b)
% 187.79/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.79/187.94 => ? [B_x] :
% 187.79/187.94 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2
% 187.79/187.94 & c_List_Olinorder__class_Osorted(T_b,B_x)
% 187.79/187.94 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
% 187.79/187.94 & ! [B_y] :
% 187.79/187.94 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2
% 187.79/187.94 & c_List_Olinorder__class_Osorted(T_b,B_y)
% 187.79/187.94 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) )
% 187.79/187.94 => B_y = B_x ) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_takeWhile__append2,axiom,
% 187.79/187.94 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
% 187.79/187.94 ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.94 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.79/187.94 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_OtakeWhile(T_b,V_Pa_2,V_ys_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_insort__is__Cons,axiom,
% 187.79/187.94 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_c)
% 187.79/187.94 => ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 187.79/187.94 => 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) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wfI__pf,axiom,
% 187.79/187.94 ! [V_R_2,T_b] :
% 187.79/187.94 ( ! [B_A] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 187.79/187.94 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Cons__eq__filter__iff,axiom,
% 187.79/187.94 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 187.79/187.94 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)
% 187.79/187.94 <=> ? [B_us,B_vs] :
% 187.79/187.94 ( 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))
% 187.79/187.94 & ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 187.79/187.94 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.79/187.94 & hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.94 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_filter__eq__Cons__iff,axiom,
% 187.79/187.94 ! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_b] :
% 187.79/187.94 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
% 187.79/187.94 <=> ? [B_us,B_vs] :
% 187.79/187.94 ( 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))
% 187.79/187.94 & ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 187.79/187.94 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.79/187.94 & hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.94 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Sigma__mono,axiom,
% 187.79/187.94 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 187.79/187.94 => ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.79/187.94 => 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))) )
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_not__acc__down,axiom,
% 187.79/187.94 ! [V_R_2,V_x_2,T_b] :
% 187.79/187.94 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 187.79/187.94 => ~ ! [B_z] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_acc_OaccI,axiom,
% 187.79/187.94 ! [V_r_2,V_x_2,T_b] :
% 187.79/187.94 ( ! [B_y] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__ball__nth,axiom,
% 187.79/187.94 ! [V_Pa_2,V_xs_2,T_b,V_n_2] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.94 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 187.79/187.94 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_max__ext_Osimps,axiom,
% 187.79/187.94 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 187.79/187.94 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 187.79/187.94 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.79/187.94 & ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 187.79/187.94 => ? [B_xa] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 187.79/187.94 & 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)) ) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_sorted_OCons,axiom,
% 187.79/187.94 ! [V_x_2,V_xs_2,T_b] :
% 187.79/187.94 ( class_Orderings_Olinorder(T_b)
% 187.79/187.94 => ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
% 187.79/187.94 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 187.79/187.94 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_InterI,axiom,
% 187.79/187.94 ! [V_A_2,V_C_2,T_b] :
% 187.79/187.94 ( ! [B_X] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__no__infinite__down__chainE,axiom,
% 187.79/187.94 ! [V_f_2,V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => ~ ! [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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__ex__length,axiom,
% 187.79/187.94 ! [V_xs_2,V_Pa_2,T_b] :
% 187.79/187.94 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 187.79/187.94 <=> ? [B_n] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__ex__simps_I1_J,axiom,
% 187.79/187.94 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 187.79/187.94 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 187.79/187.94 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 187.79/187.94 | c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__ex__rev,axiom,
% 187.79/187.94 ! [V_xs_2,V_Pa_2,T_b] :
% 187.79/187.94 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 187.79/187.94 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__ex__append,axiom,
% 187.79/187.94 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
% 187.79/187.94 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 187.79/187.94 <=> ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 187.79/187.94 | c_List_Olist__ex(T_b,V_Pa_2,V_ys_2) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__ex__iff,axiom,
% 187.79/187.94 ! [V_xs_2,V_Pa_2,T_b] :
% 187.79/187.94 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 187.79/187.94 <=> ? [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.79/187.94 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_list__ex__simps_I2_J,axiom,
% 187.79/187.94 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_setsum__reindex__cong,axiom,
% 187.79/187.94 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 187.79/187.94 ( class_Groups_Ocomm__monoid__add(T_d)
% 187.79/187.94 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 187.79/187.94 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 187.79/187.94 => ( ! [B_a] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 187.79/187.94 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 187.79/187.94 => 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) ) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_scomp__unfold,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_scomp__scomp,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Pair__scomp,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_scomp__Pair,axiom,
% 187.79/187.94 ! [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 ).
% 187.79/187.94
% 187.79/187.94 fof(fact_scomp__def,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_scomp__apply,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_iterate_Osimps,axiom,
% 187.79/187.94 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 187.79/187.94 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.79/187.94 => 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) )
% 187.79/187.94 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_setsum__ivl__cong,axiom,
% 187.79/187.94 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_b,T_c] :
% 187.79/187.94 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 187.79/187.94 & class_Orderings_Oord(T_b) )
% 187.79/187.94 => ( V_a_2 = V_ca_2
% 187.79/187.94 => ( V_b_2 = V_d_2
% 187.79/187.94 => ( ! [B_x] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x))
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 187.79/187.94 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 187.79/187.94 => 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)) ) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_log_Osimps,axiom,
% 187.79/187.94 ! [V_i,V_b] :
% 187.79/187.94 ( ( ( 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)))
% 187.79/187.94 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 187.79/187.94 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 187.79/187.94 & ( ~ ( 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)))
% 187.79/187.94 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_minus__shift__def,axiom,
% 187.79/187.94 ! [V_r,V_l,V_k] :
% 187.79/187.94 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 187.79/187.94 => 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) )
% 187.79/187.94 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 187.79/187.94 => 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) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_inc__shift__def,axiom,
% 187.79/187.94 ! [V_k,V_v] :
% 187.79/187.94 ( ( V_v = V_k
% 187.79/187.94 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 187.79/187.94 & ( V_v != V_k
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_select,axiom,
% 187.79/187.94 ! [V_s_2,T_b,V_xs_2] :
% 187.79/187.94 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_select__weight__member,axiom,
% 187.79/187.94 ! [V_s_2,V_xs_2,T_b] :
% 187.79/187.94 ( 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))))
% 187.79/187.94 => 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)))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_select__weigth__select,axiom,
% 187.79/187.94 ! [T_b,V_xs_2] :
% 187.79/187.94 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_select__weight__cons__zero,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_select__weigth__drop__zero,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_pick__member,axiom,
% 187.79/187.94 ! [V_xs_2,T_b,V_i_2] :
% 187.79/187.94 ( 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))))
% 187.79/187.94 => 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)))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_pick_Osimps,axiom,
% 187.79/187.94 ! [V_xs,V_x,T_a,V_i] :
% 187.79/187.94 ( ( 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)))
% 187.79/187.94 => 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) )
% 187.79/187.94 & ( ~ 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)))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_pick__drop__zero,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_select__weight__def,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_pick__same,axiom,
% 187.79/187.94 ! [V_xs_2,T_b,V_l_2] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => 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) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_one__code__numeral__def,axiom,
% 187.79/187.94 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_zero__code__numeral__def,axiom,
% 187.79/187.94 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 187.79/187.94 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_times__code__numeral__code,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 187.79/187.94 ! [V_m_2,V_n_2] :
% 187.79/187.94 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 187.79/187.94 <=> V_n_2 = V_m_2 ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 187.79/187.94 ! [V_y_2,V_x_2] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 187.79/187.94 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 187.79/187.94 <=> V_x_2 = V_y_2 ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_number__of__code__numeral__def,axiom,
% 187.79/187.94 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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_less__code__numeral__code,axiom,
% 187.79/187.94 ! [V_m_2,V_n_2] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_plus__code__numeral__code,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_less__eq__code__numeral__code,axiom,
% 187.79/187.94 ! [V_m_2,V_n_2] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_code__numeral__not__eq__zero,axiom,
% 187.79/187.94 ! [V_i_2] :
% 187.79/187.94 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 187.79/187.94 <=> 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_range,axiom,
% 187.79/187.94 ! [V_s,V_k] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => 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)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_select__def,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_subtract__code__numeral__code,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_type__definition__code__numeral,axiom,
% 187.79/187.94 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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_times__code__numeral__def,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_nat__of__of__nat,axiom,
% 187.79/187.94 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 187.79/187.94
% 187.79/187.94 fof(fact_of__nat__nat__of,axiom,
% 187.79/187.94 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 187.79/187.94
% 187.79/187.94 fof(fact_nat__of__inverse,axiom,
% 187.79/187.94 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 187.79/187.94
% 187.79/187.94 fof(fact_less__code__numeral__def,axiom,
% 187.79/187.94 ! [V_m_2,V_n_2] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 187.79/187.94 <=> 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_int__of__def,axiom,
% 187.79/187.94 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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_nat__of__number,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_code__numeral_Onat__of__inject,axiom,
% 187.79/187.94 ! [V_y_2,V_x_2] :
% 187.79/187.94 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 187.79/187.94 <=> V_x_2 = V_y_2 ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 187.79/187.94 ! [V_l_2,V_k_2] :
% 187.79/187.94 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 187.79/187.94 <=> V_k_2 = V_l_2 ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_nat__of,axiom,
% 187.79/187.94 ! [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)))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_less__eq__code__numeral__def,axiom,
% 187.79/187.94 ! [V_m_2,V_n_2] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 187.79/187.94 <=> 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_nat__of__code,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_nat__of__aux__def,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Suc__code__numeral__def,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_minus__code__numeral__def,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_of__nat__inverse,axiom,
% 187.79/187.94 ! [V_y_2] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 187.79/187.94 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_plus__code__numeral__def,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_div__code__numeral__def,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_minus__code__numeral__code,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_subtract__code__numeral__def,axiom,
% 187.79/187.94 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_mod__code__numeral__def,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_code__numeral__decr,axiom,
% 187.79/187.94 ! [V_k] :
% 187.79/187.94 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_less__eq,axiom,
% 187.79/187.94 ! [V_n_2,V_m_2] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_less__than__def,axiom,
% 187.79/187.94 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_wf__trancl,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Owf(T_b,V_r_2)
% 187.79/187.94 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_acyclic__def,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 187.79/187.94 <=> ! [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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl_Or__into__trancl,axiom,
% 187.79/187.94 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__subset__Field2,axiom,
% 187.79/187.94 ! [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))))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_r__into__trancl_H,axiom,
% 187.79/187.94 ! [V_r_2,V_p_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__empty,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__domain,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__range,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_finite__trancl,axiom,
% 187.79/187.94 ! [V_r_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 187.79/187.94 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__trans,axiom,
% 187.79/187.94 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 187.79/187.94 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( 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))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__into__trancl2,axiom,
% 187.79/187.94 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_r__r__into__trancl,axiom,
% 187.79/187.94 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( 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))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__mono,axiom,
% 187.79/187.94 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 187.79/187.94 => ( 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))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__unfold,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__subset__Sigma,axiom,
% 187.79/187.94 ! [V_A_2,V_r_2,T_b] :
% 187.79/187.94 ( 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))))
% 187.79/187.94 => 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)))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__Int__subset,axiom,
% 187.79/187.94 ! [V_s_2,V_r_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( 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))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__insert,axiom,
% 187.79/187.94 ! [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)))))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_reflcl__set__eq,axiom,
% 187.79/187.94 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 <=> 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)))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_r__into__rtrancl,axiom,
% 187.79/187.94 ! [V_r_2,V_p_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_IdI,axiom,
% 187.79/187.94 ! [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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__into__rtrancl,axiom,
% 187.79/187.94 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listrel__rtrancl__refl,axiom,
% 187.79/187.94 ! [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)))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__unfold__right,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__unfold__left,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_reflcl__trancl,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__reflcl,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__rtrancl__absorb,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__trancl__absorb,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__eq__or__trancl,axiom,
% 187.79/187.94 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 <=> ( V_x_2 = V_y_2
% 187.79/187.94 | ( V_x_2 != V_y_2
% 187.79/187.94 & 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))) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__into__trancl2,axiom,
% 187.79/187.94 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtranclD,axiom,
% 187.79/187.94 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( V_a_2 = V_b_2
% 187.79/187.94 | ( V_a_2 != V_b_2
% 187.79/187.94 & 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))) ) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__into__trancl1,axiom,
% 187.79/187.94 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( 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))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_trancl__rtrancl__trancl,axiom,
% 187.79/187.94 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__trancl__trancl,axiom,
% 187.79/187.94 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__trans,axiom,
% 187.79/187.94 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 187.79/187.94 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( 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))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 187.79/187.94 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => 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))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__Int__subset,axiom,
% 187.79/187.94 ! [V_r_2,V_s_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( 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))
% 187.79/187.94 => 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)) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__subset__rtrancl,axiom,
% 187.79/187.94 ! [V_s_2,V_r_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__subset,axiom,
% 187.79/187.94 ! [V_S_2,V_R_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => ( 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)))
% 187.79/187.94 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__mono,axiom,
% 187.79/187.94 ! [V_s_2,V_r_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => 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))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__Un__subset,axiom,
% 187.79/187.94 ! [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)))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Image__closed__trancl,axiom,
% 187.79/187.94 ! [V_X_2,V_r_2,T_b] :
% 187.79/187.94 ( 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))
% 187.79/187.94 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_refl__rtrancl,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__idemp,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__r__diff__Id,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__empty,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__reflcl,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__Un__rtrancl,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__reflcl__absorb,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_in__rtrancl__UnI,axiom,
% 187.79/187.94 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 187.79/187.94 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 187.79/187.94 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 187.79/187.94 => 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)))) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_r__comp__rtrancl__eq,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__idemp__self__comp,axiom,
% 187.79/187.94 ! [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) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__unfold,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Range__rtrancl,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Domain__rtrancl,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listrel__rtrancl__trans,axiom,
% 187.79/187.94 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 187.79/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Domain__Id,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Range__Id,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Id__O__R,axiom,
% 187.79/187.94 ! [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 ).
% 187.79/187.94
% 187.79/187.94 fof(fact_R__O__Id,axiom,
% 187.79/187.94 ! [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 ).
% 187.79/187.94
% 187.79/187.94 fof(fact_refl__Id,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 187.79/187.94 ! [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)) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Image__Id,axiom,
% 187.79/187.94 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 187.79/187.94 ! [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)))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_pair__in__Id__conv,axiom,
% 187.79/187.94 ! [V_b_2,V_a_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 <=> V_a_2 = V_b_2 ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 187.79/187.94 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 187.79/187.94 ( 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)))
% 187.79/187.94 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 187.79/187.94 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 187.79/187.94 ! [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)))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_pair__leq__def,axiom,
% 187.79/187.94 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))) ).
% 187.79/187.94
% 187.79/187.94 fof(fact_Not__Domain__rtrancl,axiom,
% 187.79/187.94 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 188.07/187.94 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 188.07/187.94 => ( 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)))
% 188.07/187.94 <=> V_x_2 = V_y_2 ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_acc__downwards,axiom,
% 188.07/187.94 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 188.07/187.94 => ( 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)))
% 188.07/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_acc__downwards__aux,axiom,
% 188.07/187.94 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 188.07/187.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_wf__insert,axiom,
% 188.07/187.94 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 188.07/187.94 ( 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))
% 188.07/187.94 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 188.07/187.94 & ~ 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))) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 188.07/187.94 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 188.07/187.94 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 188.07/187.94 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 188.07/187.94 => 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) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_acyclic__insert,axiom,
% 188.07/187.94 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 188.07/187.94 ( 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))
% 188.07/187.94 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 188.07/187.94 & ~ 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))) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 188.07/187.94 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 188.07/187.94 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 188.07/187.94 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 188.07/187.94 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_refl__reflcl,axiom,
% 188.07/187.94 ! [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))) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_Id__def,axiom,
% 188.07/187.94 ! [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))))) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_irrefl__diff__Id,axiom,
% 188.07/187.94 ! [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))) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_pred__nat__trancl__eq__le,axiom,
% 188.07/187.94 ! [V_n_2,V_m_2] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_trancl__subset__Sigma__aux,axiom,
% 188.07/187.94 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => ( 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))))
% 188.07/187.94 => ( V_a_2 = V_b_2
% 188.07/187.94 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_irrefl__tranclI,axiom,
% 188.07/187.94 ! [V_x_2,V_r_2,T_b] :
% 188.07/187.94 ( 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))
% 188.07/187.94 => ~ 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))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_sequence__trans,axiom,
% 188.07/187.94 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 188.07/187.94 ( ! [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)))
% 188.07/187.94 => 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))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rtrancl__converseD,axiom,
% 188.07/187.94 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 188.07/187.94 ( 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))))
% 188.07/187.94 => 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))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rtrancl__converseI,axiom,
% 188.07/187.94 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => 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)))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rtrancl__converse,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_converse__Id,axiom,
% 188.07/187.94 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_trancl__converseD,axiom,
% 188.07/187.94 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 188.07/187.94 ( 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))))
% 188.07/187.94 => 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)))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_trancl__converseI,axiom,
% 188.07/187.94 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 188.07/187.94 ( 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))))
% 188.07/187.94 => 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)))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_converseD,axiom,
% 188.07/187.94 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => 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)) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_converseI,axiom,
% 188.07/187.94 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 188.07/187.94 ( 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))
% 188.07/187.94 => 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))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_converse__iff,axiom,
% 188.07/187.94 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 <=> 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)) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_in__listrel1__converse,axiom,
% 188.07/187.94 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 188.07/187.94 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_acyclic__converse,axiom,
% 188.07/187.94 ! [V_r_2,T_b] :
% 188.07/187.94 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 188.07/187.94 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_converse__UNION,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_converse__Int,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_refl__on__converse,axiom,
% 188.07/187.94 ! [V_r_2,V_A_2,T_b] :
% 188.07/187.94 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 188.07/187.94 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_Field__converse,axiom,
% 188.07/187.94 ! [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) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_converse__converse,axiom,
% 188.07/187.94 ! [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 ).
% 188.07/187.94
% 188.07/187.94 fof(fact_converse__Id__on,axiom,
% 188.07/187.94 ! [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) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_finite__converse,axiom,
% 188.07/187.94 ! [V_r_2,T_c,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 188.07/187.94 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_listrel1__converse,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_converse__INTER,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_converse__Un,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_converse__inv__image,axiom,
% 188.07/187.94 ! [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) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_equiv__comp__eq,axiom,
% 188.07/187.94 ! [V_r_2,V_A_2,T_b] :
% 188.07/187.94 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 188.07/187.94 => 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 ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_converse__rel__comp,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_Range__def,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_Domain__converse,axiom,
% 188.07/187.94 ! [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) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_Range__converse,axiom,
% 188.07/187.94 ! [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) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_wf__converse__trancl,axiom,
% 188.07/187.94 ! [V_r_2,T_b] :
% 188.07/187.94 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 188.07/187.94 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_trancl__converse,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_Image__subset__eq,axiom,
% 188.07/187.94 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 188.07/187.94 ( 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))
% 188.07/187.94 <=> 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))))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_refl__on__comp__subset,axiom,
% 188.07/187.94 ! [V_r_2,V_A_2,T_b] :
% 188.07/187.94 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 188.07/187.94 => 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))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_comp__equivI,axiom,
% 188.07/187.94 ! [V_A_2,V_r_2,T_b] :
% 188.07/187.94 ( 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
% 188.07/187.94 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 188.07/187.94 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_finite__acyclic__wf__converse,axiom,
% 188.07/187.94 ! [V_r_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 188.07/187.94 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 188.07/187.94 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_converse__def,axiom,
% 188.07/187.94 ! [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))) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_Image__INT__eq,axiom,
% 188.07/187.94 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 188.07/187.94 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 188.07/187.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 188.07/187.94 => 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)) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_total__on__diff__Id,axiom,
% 188.07/187.94 ! [V_r_2,V_A_2,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_single__valued__Id,axiom,
% 188.07/187.94 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_total__on__converse,axiom,
% 188.07/187.94 ! [V_r_2,V_A_2,T_b] :
% 188.07/187.94 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 188.07/187.94 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_single__valued__rel__comp,axiom,
% 188.07/187.94 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 188.07/187.94 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 188.07/187.94 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 188.07/187.94 => 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)) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_total__on__empty,axiom,
% 188.07/187.94 ! [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) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_single__valued__Id__on,axiom,
% 188.07/187.94 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_single__valued__subset,axiom,
% 188.07/187.94 ! [V_s_2,V_r_2,T_c,T_b] :
% 188.07/187.94 ( 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))
% 188.07/187.94 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 188.07/187.94 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_single__valued__def,axiom,
% 188.07/187.94 ! [V_r_2,T_c,T_b] :
% 188.07/187.94 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 188.07/187.94 <=> ! [B_x,B_y] :
% 188.07/187.94 ( 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))
% 188.07/187.94 => ! [B_z] :
% 188.07/187.94 ( 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))
% 188.07/187.94 => B_y = B_z ) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_single__valuedD,axiom,
% 188.07/187.94 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 188.07/187.94 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 188.07/187.94 => ( 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))
% 188.07/187.94 => ( 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))
% 188.07/187.94 => V_y_2 = V_z_2 ) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_total__on__def,axiom,
% 188.07/187.94 ! [V_r_2,V_A_2,T_b] :
% 188.07/187.94 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 188.07/187.94 <=> ! [B_x] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 188.07/187.94 => ! [B_xa] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 188.07/187.94 => ( B_x != B_xa
% 188.07/187.94 => ( 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))
% 188.07/187.94 | 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)) ) ) ) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_single__valued__confluent,axiom,
% 188.07/187.94 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 188.07/187.94 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 188.07/187.94 => ( 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)))
% 188.07/187.94 => ( 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)))
% 188.07/187.94 => ( 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)))
% 188.07/187.94 | 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))) ) ) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_Image__Int__eq,axiom,
% 188.07/187.94 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 188.07/187.94 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 188.07/187.94 => 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)) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 188.07/187.94 ! [V_R_2,V_p_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 188.07/187.94 => 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)))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_acyclicI,axiom,
% 188.07/187.94 ! [V_r_2,T_b] :
% 188.07/187.94 ( ! [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)))
% 188.07/187.94 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_single__valued__rel__pow,axiom,
% 188.07/187.94 ! [V_n_2,V_R_2,T_b] :
% 188.07/187.94 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 188.07/187.94 => 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)) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rel__pow__0__E,axiom,
% 188.07/187.94 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => V_x_2 = V_y_2 ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rel__pow__0__I,axiom,
% 188.07/187.94 ! [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))) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rel__pow__Suc__I,axiom,
% 188.07/187.94 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => ( 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))
% 188.07/187.94 => 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))) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rel__pow__Suc__I2,axiom,
% 188.07/187.94 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 188.07/187.94 ( 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))
% 188.07/187.94 => ( 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)))
% 188.07/187.94 => 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))) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_comp__funpow,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_wf__exp,axiom,
% 188.07/187.94 ! [V_R_2,V_n_2,T_b] :
% 188.07/187.94 ( 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))
% 188.07/187.94 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_funpow__swap1,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_funpow__mult,axiom,
% 188.07/187.94 ! [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) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rel__pow__commute,axiom,
% 188.07/187.94 ! [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) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_relpow_Osimps_I2_J,axiom,
% 188.07/187.94 ! [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) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rel__pow__1,axiom,
% 188.07/187.94 ! [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 ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rel__pow__add,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_relpow_Osimps_I1_J,axiom,
% 188.07/187.94 ! [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) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rel__pow__imp__rtrancl,axiom,
% 188.07/187.94 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rtrancl__power,axiom,
% 188.07/187.94 ! [V_R_2,V_p_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 188.07/187.94 <=> ? [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))) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_funpow_Osimps_I2_J,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_funpow__add,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_funpow_Osimps_I1_J,axiom,
% 188.07/187.94 ! [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) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_trancl__power,axiom,
% 188.07/187.94 ! [V_R_2,V_p_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 188.07/187.94 <=> ? [B_n] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 188.07/187.94 & 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))) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_funpow__code__def,axiom,
% 188.07/187.94 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rel__pow__E2,axiom,
% 188.07/187.94 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 188.07/187.94 => V_x_2 != V_z_2 )
% 188.07/187.94 => ~ ! [B_y,B_m] :
% 188.07/187.94 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 188.07/187.94 => ( 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))
% 188.07/187.94 => ~ 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))) ) ) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rotate__def,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rel__pow__E,axiom,
% 188.07/187.94 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 188.07/187.94 => V_x_2 != V_z_2 )
% 188.07/187.94 => ~ ! [B_y,B_m] :
% 188.07/187.94 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 188.07/187.94 => ( 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)))
% 188.07/187.94 => ~ 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)) ) ) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_pos__not__random__dseq__def,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 188.07/187.94 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Qa_2))))
% 188.07/187.94 => ( ! [B_x] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
% 188.07/187.94 => ! [B_y] :
% 188.07/187.94 ( 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))
% 188.07/187.94 => B_y = B_x ) )
% 188.07/187.94 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rtrancl__Un__separatorE,axiom,
% 188.07/187.94 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Qa_2))))
% 188.07/187.94 => ( ! [B_x] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
% 188.07/187.94 => ! [B_y] :
% 188.07/187.94 ( 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))
% 188.07/187.94 => B_x = B_y ) )
% 188.07/187.94 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rel__pow__Suc__D2,axiom,
% 188.07/187.94 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => ? [B_y] :
% 188.07/187.94 ( 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))
% 188.07/187.94 & 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))) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rel__pow__Suc__E2,axiom,
% 188.07/187.94 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => ~ ! [B_y] :
% 188.07/187.94 ( 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))
% 188.07/187.94 => ~ 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))) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_rel__pow__Suc__E,axiom,
% 188.07/187.94 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => ~ ! [B_y] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => ~ 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)) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_tranclD2,axiom,
% 188.07/187.94 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => ? [B_z] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 & 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)) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_tranclD,axiom,
% 188.07/187.94 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 188.07/187.94 ( 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)))
% 188.07/187.94 => ? [B_z] :
% 188.07/187.94 ( 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))
% 188.07/187.94 & 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))) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_IdE,axiom,
% 188.07/187.94 ! [V_p_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 188.07/187.94 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_nat__intermed__int__val,axiom,
% 188.07/187.94 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 188.07/187.94 ( ! [B_i] :
% 188.07/187.94 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 188.07/187.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 188.07/187.94 => 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))) )
% 188.07/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 188.07/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 188.07/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 188.07/187.94 => ? [B_i] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 188.07/187.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 188.07/187.94 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_in__set__conv__decomp,axiom,
% 188.07/187.94 ! [V_xs_2,V_x_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 188.07/187.94 <=> ? [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)) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_in__set__conv__decomp__first,axiom,
% 188.07/187.94 ! [V_xs_2,V_x_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 188.07/187.94 <=> ? [B_ys] :
% 188.07/187.94 ( ? [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))
% 188.07/187.94 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_in__set__conv__decomp__last,axiom,
% 188.07/187.94 ! [V_xs_2,V_x_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 188.07/187.94 <=> ? [B_ys,B_zs] :
% 188.07/187.94 ( 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))
% 188.07/187.94 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_mod__div__decomp,axiom,
% 188.07/187.94 ! [V_b,V_a,T_a] :
% 188.07/187.94 ( class_Divides_Osemiring__div(T_a)
% 188.07/187.94 => 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)) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 188.07/187.94 ! [V_x_2,V_A_2,T_b] :
% 188.07/187.94 ( class_Orderings_Olinorder(T_b)
% 188.07/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 188.07/187.94 => 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) ) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_fold__sup__insert,axiom,
% 188.07/187.94 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 188.07/187.94 ( class_Lattices_Osemilattice__sup(T_b)
% 188.07/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.94 => 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)) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_union__fold__insert,axiom,
% 188.07/187.94 ! [V_B_2,V_A_2,T_b] :
% 188.07/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.94 => 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) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_sup__Sup__fold__sup,axiom,
% 188.07/187.94 ! [V_B_2,V_A_2,T_b] :
% 188.07/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 188.07/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.94 => 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) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 188.07/187.94 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 188.07/187.94 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 188.07/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.94 => 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) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 188.07/187.94 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 188.07/187.94 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 188.07/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.94 => 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)) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_inf__Inf__fold__inf,axiom,
% 188.07/187.94 ! [V_B_2,V_A_2,T_b] :
% 188.07/187.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 188.07/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.94 => 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) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_fold__inf__insert,axiom,
% 188.07/187.94 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 188.07/187.94 ( class_Lattices_Osemilattice__inf(T_b)
% 188.07/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.94 => 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)) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_fold__empty,axiom,
% 188.07/187.94 ! [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 ).
% 188.07/187.94
% 188.07/187.94 fof(fact_fold__image__def,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_folding_Oeq__fold,axiom,
% 188.07/187.94 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 188.07/187.94 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 188.07/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.94 => 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) ) ) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_fold__def,axiom,
% 188.07/187.94 ! [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)) ).
% 188.07/187.94
% 188.07/187.94 fof(fact_min__max_Ofold__sup__insert,axiom,
% 188.07/187.94 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Orderings_Olinorder(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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)) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_min__max_Ofold__inf__insert,axiom,
% 188.07/187.95 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Orderings_Olinorder(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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)) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_sup__SUPR__fold__sup,axiom,
% 188.07/187.95 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 188.07/187.95 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_inf__INFI__fold__inf,axiom,
% 188.07/187.95 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 188.07/187.95 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 188.07/187.95 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 188.07/187.95 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 188.07/187.95 => 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) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_sup__le__fold__sup,axiom,
% 188.07/187.95 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Lattices_Osemilattice__sup(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 188.07/187.95 => 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))) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fold__inf__le__inf,axiom,
% 188.07/187.95 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Lattices_Osemilattice__inf(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 188.07/187.95 => 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))) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 188.07/187.95 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Orderings_Olinorder(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 188.07/187.95 => 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))) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 188.07/187.95 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Orderings_Olinorder(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 188.07/187.95 => 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))) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Sup__fold__sup,axiom,
% 188.07/187.95 ! [V_A_2,T_b] :
% 188.07/187.95 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Inf__fold__inf,axiom,
% 188.07/187.95 ! [V_A_2,T_b] :
% 188.07/187.95 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fold1__eq__fold__idem,axiom,
% 188.07/187.95 ! [V_a_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 188.07/187.95 ! [V_a_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Lattices_Olattice(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 188.07/187.95 ! [V_a_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Lattices_Olattice(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 188.07/187.95 ! [V_a_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Orderings_Olinorder(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 188.07/187.95 ! [V_a_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Orderings_Olinorder(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 188.07/187.95 ! [V_a_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Orderings_Olinorder(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 188.07/187.95 ! [V_a_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Orderings_Olinorder(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_minus__fold__remove,axiom,
% 188.07/187.95 ! [V_B_2,V_A_2,T_b] :
% 188.07/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_folding__one_Oeq__fold_H,axiom,
% 188.07/187.95 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 188.07/187.95 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_SUPR__fold__sup,axiom,
% 188.07/187.95 ! [V_f_2,V_A_2,T_b,T_c] :
% 188.07/187.95 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_INFI__fold__inf,axiom,
% 188.07/187.95 ! [V_f_2,V_A_2,T_b,T_c] :
% 188.07/187.95 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fold1__eq__fold,axiom,
% 188.07/187.95 ! [V_a_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Groups_Oab__semigroup__mult(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 188.07/187.95 => 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) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 188.07/187.95 ! [V_x_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Lattices_Olattice(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 188.07/187.95 => 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) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 188.07/187.95 ! [V_x_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Lattices_Olattice(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 188.07/187.95 => 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) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Min_Oeq__fold_H,axiom,
% 188.07/187.95 ! [V_x_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Orderings_Olinorder(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 188.07/187.95 => 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) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Max_Oeq__fold_H,axiom,
% 188.07/187.95 ! [V_x_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Orderings_Olinorder(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 188.07/187.95 => 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) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 188.07/187.95 ! [V_x_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Orderings_Olinorder(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 188.07/187.95 => 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) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 188.07/187.95 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 188.07/187.95 => 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)))))) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 188.07/187.95 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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)))))) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 188.07/187.95 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 188.07/187.95 => 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)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm__insort,axiom,
% 188.07/187.95 ! [T_b] :
% 188.07/187.95 ( class_Orderings_Olinorder(T_b)
% 188.07/187.95 => 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))) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 188.07/187.95 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 188.07/187.95 => 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)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 188.07/187.95 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 188.07/187.95 => 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)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 188.07/187.95 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 188.07/187.95 => V_y_2 = V_x_2 ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm,axiom,
% 188.07/187.95 ! [T_b] :
% 188.07/187.95 ( class_Groups_Oab__semigroup__mult(T_b)
% 188.07/187.95 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 188.07/187.95 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 188.07/187.95 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 188.07/187.95 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 188.07/187.95 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => 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))) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 188.07/187.95 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 188.07/187.95 => 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) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 188.07/187.95 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 188.07/187.95 => 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)) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 188.07/187.95 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 188.07/187.95 => 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)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 188.07/187.95 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 188.07/187.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 188.07/187.95 => ? [B_y_H] :
% 188.07/187.95 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 188.07/187.95 & 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)) ) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 188.07/187.95 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 188.07/187.95 => ( 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))
% 188.07/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 188.07/187.95 => ~ ! [B_y] :
% 188.07/187.95 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 188.07/187.95 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 188.07/187.95 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Orderings_Olinorder(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( ! [B_x] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 188.07/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 188.07/187.95 => 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))) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 188.07/187.95 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Orderings_Olinorder(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( ! [B_x] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 188.07/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 188.07/187.95 => 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))) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_inf__le__fold__inf,axiom,
% 188.07/187.95 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Lattices_Osemilattice__inf(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( ! [B_x] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 188.07/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 188.07/187.95 => 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))) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_fold__sup__le__sup,axiom,
% 188.07/187.95 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 188.07/187.95 ( class_Lattices_Osemilattice__sup(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 188.07/187.95 => ( ! [B_x] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 188.07/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 188.07/187.95 => 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))) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_wf__eq__minimal,axiom,
% 188.07/187.95 ! [V_r_2,T_b] :
% 188.07/187.95 ( c_Wellfounded_Owf(T_b,V_r_2)
% 188.07/187.95 <=> ! [B_Q] :
% 188.07/187.95 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 188.07/187.95 => ? [B_x] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 188.07/187.95 & ! [B_y] :
% 188.07/187.95 ( 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))
% 188.07/187.95 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 188.07/187.95 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 188.07/187.95 => 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)) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 188.07/187.95 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 188.07/187.95 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 188.07/187.95 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 188.07/187.95 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 188.07/187.95 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 188.07/187.95 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 188.07/187.95 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 188.07/187.95 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 188.07/187.95 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 188.07/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 188.07/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 188.07/187.95 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_transfer__nat__int__set__cong,axiom,
% 188.07/187.95 ! [V_P_H_2,V_Pa_2] :
% 188.07/187.95 ( ! [B_x] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 188.07/187.95 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 188.07/187.95 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 188.07/187.95 => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_UnionE,axiom,
% 188.07/187.95 ! [V_C_2,V_A_2,T_b] :
% 188.07/187.95 ( 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)))
% 188.07/187.95 => ~ ! [B_X] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 188.07/187.95 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_rel__compE,axiom,
% 188.07/187.95 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 188.07/187.95 ( 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)))
% 188.07/187.95 => ~ ! [B_x,B_y,B_z] :
% 188.07/187.95 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 188.07/187.95 => ( 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))
% 188.07/187.95 => ~ 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)) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_converseE,axiom,
% 188.07/187.95 ! [V_r_2,V_yx_2,T_c,T_b] :
% 188.07/187.95 ( 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)))
% 188.07/187.95 => ~ ! [B_x,B_y] :
% 188.07/187.95 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 188.07/187.95 => ~ 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)) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 188.07/187.95 ! [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))) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_setprod__pos,axiom,
% 188.07/187.95 ! [V_f_2,V_A_2,T_b,T_c] :
% 188.07/187.95 ( class_Rings_Olinordered__semidom(T_c)
% 188.07/187.95 => ( ! [B_x] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 188.07/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 188.07/187.95 => 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))) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 188.07/187.95 ! [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))) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Nitpick_Oof__frac__def,axiom,
% 188.07/187.95 ! [V_q,T_a,T_b] :
% 188.07/187.95 ( ( class_Rings_Oinverse(T_b)
% 188.07/187.95 & class_Rings_Oring__1(T_b) )
% 188.07/187.95 => 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))) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 188.07/187.95 ! [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))) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Nitpick_Oless__frac__def,axiom,
% 188.07/187.95 ! [V_r_2,V_q_2,T_b] :
% 188.07/187.95 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 188.07/187.95 <=> 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))) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 188.07/187.95 ! [V_r_2,V_q_2,T_b] :
% 188.07/187.95 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 188.07/187.95 <=> 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))) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Nitpick_Onum__def,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Nitpick_Odenom__def,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_list__all__length,axiom,
% 188.07/187.95 ! [V_xs_2,V_Pa_2,T_b] :
% 188.07/187.95 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 188.07/187.95 <=> ! [B_n] :
% 188.07/187.95 ( 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)))
% 188.07/187.95 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_internal__split__def,axiom,
% 188.07/187.95 ! [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) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Ball__set__list__all,axiom,
% 188.07/187.95 ! [V_Pa_2,V_xs_2,T_b] :
% 188.07/187.95 ( ! [B_x] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 188.07/187.95 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 188.07/187.95 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_list__all__rev,axiom,
% 188.07/187.95 ! [V_xs_2,V_Pa_2,T_b] :
% 188.07/187.95 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 188.07/187.95 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_list__all__append,axiom,
% 188.07/187.95 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
% 188.07/187.95 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 188.07/187.95 <=> ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 188.07/187.95 & c_List_Olist__all(T_b,V_Pa_2,V_ys_2) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_list__all__iff,axiom,
% 188.07/187.95 ! [V_xs_2,V_Pa_2,T_b] :
% 188.07/187.95 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 188.07/187.95 <=> ! [B_x] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 188.07/187.95 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_list__all__simps_I2_J,axiom,
% 188.07/187.95 ! [V_Pa_2,T_b] : c_List_Olist__all(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_list__all__simps_I1_J,axiom,
% 188.07/187.95 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 188.07/187.95 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 188.07/187.95 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 188.07/187.95 & c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_list__all__iff__raw,axiom,
% 188.07/187.95 ! [V_xs_2,V_Pa_2,T_b] :
% 188.07/187.95 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 188.07/187.95 <=> ! [B_x] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 188.07/187.95 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_internal__split__conv,axiom,
% 188.07/187.95 ! [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) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_list__ex1__simps_I2_J,axiom,
% 188.07/187.95 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 188.07/187.95 ( c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 188.07/187.95 <=> ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 188.07/187.95 => c_List_Olist__all(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))),hAPP(c_fequal,V_x_2)),V_xs_2) )
% 188.07/187.95 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 188.07/187.95 => c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_setprod__nonneg,axiom,
% 188.07/187.95 ! [V_f_2,V_A_2,T_b,T_c] :
% 188.07/187.95 ( class_Rings_Olinordered__semidom(T_c)
% 188.07/187.95 => ( ! [B_x] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 188.07/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 188.07/187.95 => 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))) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_list__ex1__simps_I1_J,axiom,
% 188.07/187.95 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_exists1__code,axiom,
% 188.07/187.95 ! [V_Pa_2,T_b] :
% 188.07/187.95 ( class_Enum_Oenum(T_b)
% 188.07/187.95 => ( ? [B_x] :
% 188.07/187.95 ( hBOOL(hAPP(V_Pa_2,B_x))
% 188.07/187.95 & ! [B_y] :
% 188.07/187.95 ( hBOOL(hAPP(V_Pa_2,B_y))
% 188.07/187.95 => B_y = B_x ) )
% 188.07/187.95 <=> c_List_Olist__ex1(T_b,V_Pa_2,c_Enum_Oenum__class_Oenum(T_b)) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_list__ex1__iff,axiom,
% 188.07/187.95 ! [V_xs_2,V_Pa_2,T_b] :
% 188.07/187.95 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
% 188.07/187.95 <=> ? [B_x] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 188.07/187.95 & hBOOL(hAPP(V_Pa_2,B_x))
% 188.07/187.95 & ! [B_y] :
% 188.07/187.95 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 188.07/187.95 & hBOOL(hAPP(V_Pa_2,B_y)) )
% 188.07/187.95 => B_y = B_x ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_bool_Osize_I2_J,axiom,
% 188.07/187.95 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_bool_Osize_I1_J,axiom,
% 188.07/187.95 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_finite__less__ub,axiom,
% 188.07/187.95 ! [V_u_2,V_f_2] :
% 188.07/187.95 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 188.07/187.95 => 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)))) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_measure__function__int,axiom,
% 188.07/187.95 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))) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_measure__fst,axiom,
% 188.07/187.95 ! [T_c,V_f_2,T_b] :
% 188.07/187.95 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 188.07/187.95 => 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))) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_measure__size,axiom,
% 188.07/187.95 ! [T_b] :
% 188.07/187.95 ( class_Nat_Osize(T_b)
% 188.07/187.95 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_is__measure_Ointros,axiom,
% 188.07/187.95 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_is__measure_Oequations,axiom,
% 188.07/187.95 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_is__measure_Osimps,axiom,
% 188.07/187.95 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_measure__snd,axiom,
% 188.07/187.95 ! [T_c,V_f_2,T_b] :
% 188.07/187.95 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 188.07/187.95 => 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))) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_finite__induct,axiom,
% 188.07/187.95 ! [V_Pa_2,V_F_2,T_b] :
% 188.07/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 188.07/187.95 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 188.07/187.95 => ( ! [B_x,B_F] :
% 188.07/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 188.07/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
% 188.07/187.95 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 188.07/187.95 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
% 188.07/187.95 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_equal__fun__def,axiom,
% 188.07/187.95 ! [V_g_2,V_f_2,T_b,T_c] :
% 188.07/187.95 ( ( class_HOL_Oequal(T_c)
% 188.07/187.95 & class_Enum_Oenum(T_b) )
% 188.07/187.95 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 188.07/187.95 <=> ! [B_x] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_Enum_Oenum__class_Oenum(T_b))))
% 188.07/187.95 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__equal,axiom,
% 188.07/187.95 ! [T_b] :
% 188.07/187.95 ( class_HOL_Oequal(T_b)
% 188.07/187.95 => c_fequal = c_HOL_Oequal__class_Oequal(T_b) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_equal__eq,axiom,
% 188.07/187.95 ! [V_y_2,V_x_2,T_b] :
% 188.07/187.95 ( class_HOL_Oequal(T_b)
% 188.07/187.95 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_b),V_x_2),V_y_2))
% 188.07/187.95 <=> V_x_2 = V_y_2 ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_equal__refl,axiom,
% 188.07/187.95 ! [V_x,T_a] :
% 188.07/187.95 ( class_HOL_Oequal(T_a)
% 188.07/187.95 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_equal,axiom,
% 188.07/187.95 ! [T_b] :
% 188.07/187.95 ( class_HOL_Oequal(T_b)
% 188.07/187.95 => c_HOL_Oequal__class_Oequal(T_b) = c_fequal ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_bool_Osize_I3_J,axiom,
% 188.07/187.95 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_bool_Osize_I4_J,axiom,
% 188.07/187.95 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_size__code,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_transfer__morphism__int__nat,axiom,
% 188.07/187.95 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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I2_J,axiom,
% 188.07/187.95 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I5_J,axiom,
% 188.07/187.95 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I12_J,axiom,
% 188.07/187.95 ! [V_k1_2] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin))
% 188.07/187.95 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I8_J,axiom,
% 188.07/187.95 ! [V_k2_2] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2)))
% 188.07/187.95 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I11_J,axiom,
% 188.07/187.95 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I7_J,axiom,
% 188.07/187.95 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I10_J,axiom,
% 188.07/187.95 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I4_J,axiom,
% 188.07/187.95 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I9_J,axiom,
% 188.07/187.95 ! [V_k1_2] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls))
% 188.07/187.95 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I3_J,axiom,
% 188.07/187.95 ! [V_k2_2] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2)))
% 188.07/187.95 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I15_J,axiom,
% 188.07/187.95 ! [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))) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I14_J,axiom,
% 188.07/187.95 ! [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))) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__number__of__int__code,axiom,
% 188.07/187.95 ! [V_l_2,V_k_2] :
% 188.07/187.95 ( 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)))
% 188.07/187.95 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I6_J,axiom,
% 188.07/187.95 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I16_J,axiom,
% 188.07/187.95 ! [V_k2_2,V_k1_2] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 188.07/187.95 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I1_J,axiom,
% 188.07/187.95 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__code_I13_J,axiom,
% 188.07/187.95 ! [V_k2_2,V_k1_2] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 188.07/187.95 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_equal__int__def,axiom,
% 188.07/187.95 ! [V_l_2,V_k_2] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2))
% 188.07/187.95 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_lazy__sequence__size__code,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_seq__case,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_eq__int__refl,axiom,
% 188.07/187.95 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_yieldn__def,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 188.07/187.95 ! [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))) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 188.07/187.95 ! [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) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_lazy__sequence_Oinject,axiom,
% 188.07/187.95 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
% 188.07/187.95 ( 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)
% 188.07/187.95 <=> ( V_a_2 = V_a_H_2
% 188.07/187.95 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact__01,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 188.07/187.95 ! [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))) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 188.07/187.95 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 188.07/187.95 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 188.07/187.95 => 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) )
% 188.07/187.95 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 188.07/187.95 => 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)) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 188.07/187.95 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 188.07/187.95 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 188.07/187.95 => 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) )
% 188.07/187.95 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 188.07/187.95 => 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)) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 188.07/187.95 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_pos__empty__def,axiom,
% 188.07/187.95 ! [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) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_neg__bind__def,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_neg__map__def,axiom,
% 188.07/187.95 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_neg__single__def,axiom,
% 188.07/187.95 ! [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) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_pos__bind__def,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 188.07/187.95 ! [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) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_pos__map__def,axiom,
% 188.07/187.95 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_pos__single__def,axiom,
% 188.07/187.95 ! [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) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_length__splice,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_splice_Osimps_I3_J,axiom,
% 188.07/187.95 ! [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))) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_splice_Osimps_I1_J,axiom,
% 188.07/187.95 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 188.07/187.95
% 188.07/187.95 fof(fact_splice__Nil2,axiom,
% 188.07/187.95 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 188.07/187.95
% 188.07/187.95 fof(fact_splice_Osimps_I2_J,axiom,
% 188.07/187.95 ! [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) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_New__DSequence_Opos__single__def,axiom,
% 188.07/187.95 ! [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) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_acyclicP__converse,axiom,
% 188.07/187.95 ! [V_r_2,T_b] :
% 188.07/187.95 ( 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))))
% 188.07/187.95 <=> 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))) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_converse__meet,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_conversepD,axiom,
% 188.07/187.95 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 188.07/187.95 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_conversep_Ointros,axiom,
% 188.07/187.95 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 188.07/187.95 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_conversep_Oequations,axiom,
% 188.07/187.95 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
% 188.07/187.95 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_conversep__iff,axiom,
% 188.07/187.95 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 188.07/187.95 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_conversep__conversep,axiom,
% 188.07/187.95 ! [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 ).
% 188.07/187.95
% 188.07/187.95 fof(fact_conversep__eq,axiom,
% 188.07/187.95 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ).
% 188.07/187.95
% 188.07/187.95 fof(fact_conversep__noteq,axiom,
% 188.07/187.95 ! [V_y_2,V_x_2,T_b] :
% 188.07/187.95 ( 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))
% 188.07/187.95 <=> V_x_2 != V_y_2 ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_converse__pred__comp,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_converse__join,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_conversep__converse__eq,axiom,
% 188.07/187.95 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 188.07/187.95 ( 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))
% 188.07/187.95 <=> 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))) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact__02,axiom,
% 188.07/187.95 ! [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)))) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_tl__replicate,axiom,
% 188.07/187.95 ! [V_x,T_a,V_n] :
% 188.07/187.95 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 188.07/187.95 => 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) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_zip__replicate,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_replicate__app__Cons__same,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_replicate__Suc,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_filter__replicate,axiom,
% 188.07/187.95 ! [V_n_2,T_b,V_x_2,V_Pa_2] :
% 188.07/187.95 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 188.07/187.95 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,V_x_2) )
% 188.07/187.95 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 188.07/187.95 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_replicate__0,axiom,
% 188.07/187.95 ! [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) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_empty__replicate,axiom,
% 188.07/187.95 ! [V_x_2,V_n_2,T_b] :
% 188.07/187.95 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
% 188.07/187.95 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_replicate__empty,axiom,
% 188.07/187.95 ! [V_x_2,V_n_2,T_b] :
% 188.07/187.95 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
% 188.07/187.95 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_concat__replicate__trivial,axiom,
% 188.07/187.95 ! [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) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_drop__replicate,axiom,
% 188.07/187.95 ! [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) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_take__replicate,axiom,
% 188.07/187.95 ! [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) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_last__replicate,axiom,
% 188.07/187.95 ! [V_x,T_a,V_n] :
% 188.07/187.95 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 188.07/187.95 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Bex__set__replicate,axiom,
% 188.07/187.95 ! [V_Pa_2,V_a_2,V_n_2,T_b] :
% 188.07/187.95 ( ? [B_x] :
% 188.07/187.95 ( 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))))
% 188.07/187.95 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 188.07/187.95 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 188.07/187.95 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_Ball__set__replicate,axiom,
% 188.07/187.95 ! [V_Pa_2,V_a_2,V_n_2,T_b] :
% 188.07/187.95 ( ! [B_x] :
% 188.07/187.95 ( 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))))
% 188.07/187.95 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 188.07/187.95 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 188.07/187.95 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_append__replicate__commute,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_replicate__eq__replicate,axiom,
% 188.07/187.95 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
% 188.07/187.95 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
% 188.07/187.95 <=> ( V_m_2 = V_n_2
% 188.07/187.95 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 188.07/187.95 => V_x_2 = V_y_2 ) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_hd__replicate,axiom,
% 188.07/187.95 ! [V_x,T_a,V_n] :
% 188.07/187.95 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 188.07/187.95 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_rev__replicate,axiom,
% 188.07/187.95 ! [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) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_nth__replicate,axiom,
% 188.07/187.95 ! [V_x,T_a,V_n,V_i] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 188.07/187.95 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_replicate__add,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_map__replicate,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_in__set__replicate,axiom,
% 188.07/187.95 ! [V_y_2,V_n_2,V_x_2,T_b] :
% 188.07/187.95 ( 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))))
% 188.07/187.95 <=> ( V_x_2 = V_y_2
% 188.07/187.95 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 188.07/187.95
% 188.07/187.95 fof(fact_replicate__append__same,axiom,
% 188.07/187.95 ! [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)) ).
% 188.07/187.95
% 188.07/187.95 %----Arity declarations (233)
% 188.07/187.95 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 188.07/187.95 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Lattices_Obounded__lattice(T_1)
% 188.07/187.95 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 188.07/187.95 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Lattices_Obounded__lattice(T_1)
% 188.07/187.95 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Lattices_Obounded__lattice(T_1)
% 188.07/187.95 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Lattices_Olattice(T_1)
% 188.07/187.95 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Lattices_Olattice(T_1)
% 188.07/187.95 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Lattices_Odistrib__lattice(T_1)
% 188.07/187.95 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Lattices_Oboolean__algebra(T_1)
% 188.07/187.95 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Orderings_Opreorder,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Orderings_Opreorder(T_1)
% 188.07/187.95 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 188.07/187.95 ! [T_1,T_2] :
% 188.07/187.95 ( ( class_Finite__Set_Ofinite(T_2)
% 188.07/187.95 & class_Finite__Set_Ofinite(T_1) )
% 188.07/187.95 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Lattices_Olattice,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Lattices_Olattice(T_1)
% 188.07/187.95 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Orderings_Oorder,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Orderings_Oorder(T_1)
% 188.07/187.95 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Orderings_Otop,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Orderings_Otop(T_1)
% 188.07/187.95 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Orderings_Oord,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Orderings_Oord(T_1)
% 188.07/187.95 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Orderings_Obot,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Orderings_Obot(T_1)
% 188.07/187.95 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Groups_Ouminus,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Groups_Ouminus(T_1)
% 188.07/187.95 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Groups_Ominus,axiom,
% 188.07/187.95 ! [T_2,T_1] :
% 188.07/187.95 ( class_Groups_Ominus(T_1)
% 188.07/187.95 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__HOL_Oequal,axiom,
% 188.07/187.95 ! [T_1,T_2] :
% 188.07/187.95 ( ( class_Enum_Oenum(T_2)
% 188.07/187.95 & class_HOL_Oequal(T_1) )
% 188.07/187.95 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_fun__Enum_Oenum,axiom,
% 188.07/187.95 ! [T_1,T_2] :
% 188.07/187.95 ( ( class_Enum_Oenum(T_2)
% 188.07/187.95 & class_Enum_Oenum(T_1) )
% 188.07/187.95 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Com__Ocom__HOL_Oequal,axiom,
% 188.07/187.95 class_HOL_Oequal(tc_Com_Ocom) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Com__Ocom__Nat_Osize,axiom,
% 188.07/187.95 class_Nat_Osize(tc_Com_Ocom) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 188.07/187.95 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 188.07/187.95 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 188.07/187.95 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 188.07/187.95 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 188.07/187.95 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 188.07/187.95 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 188.07/187.95 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 188.07/187.95 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 188.07/187.95 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 188.07/187.95 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 188.07/187.95 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 188.07/187.95 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 188.07/187.95 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 188.07/187.95 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 188.07/187.95 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 188.07/187.95 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 188.07/187.95 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 188.07/187.95 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 188.07/187.95 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 188.07/187.95 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 188.07/187.95 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 188.07/187.95 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 188.07/187.95 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 188.07/187.95 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 188.07/187.95 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 188.07/187.95 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 188.07/187.95 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 188.07/187.95 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 188.07/187.95 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 188.07/187.95 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 188.07/187.95 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 188.07/187.95 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 188.07/187.95 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 188.07/187.95 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 188.07/187.95 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 188.07/187.95 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 188.07/187.95 class_Orderings_Opreorder(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 188.07/187.95 class_Orderings_Olinorder(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 188.07/187.95 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 188.07/187.95 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 188.07/187.95 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 188.07/187.95 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 188.07/187.95 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 188.07/187.95 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 188.07/187.95 class_Lattices_Olattice(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 188.07/187.95 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 188.07/187.95 class_Divides_Oring__div(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 188.07/187.95 class_Rings_Omult__zero(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 188.07/187.95 class_Orderings_Oorder(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 188.07/187.95 class_Int_Oring__char__0(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 188.07/187.95 class_Int_Onumber__ring(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 188.07/187.95 class_Rings_Osemiring(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 188.07/187.95 class_Orderings_Oord(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 188.07/187.95 class_Groups_Ouminus(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 188.07/187.95 class_Groups_Osgn__if(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 188.07/187.95 class_Groups_Oabs__if(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 188.07/187.95 class_Rings_Oring__1(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 188.07/187.95 class_Groups_Ominus(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Power_Opower,axiom,
% 188.07/187.95 class_Power_Opower(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 188.07/187.95 class_Groups_Ozero(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Oring,axiom,
% 188.07/187.95 class_Rings_Oring(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 188.07/187.95 class_Rings_Oidom(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Int_Onumber,axiom,
% 188.07/187.95 class_Int_Onumber(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__Groups_Oone,axiom,
% 188.07/187.95 class_Groups_Oone(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Int__Oint__HOL_Oequal,axiom,
% 188.07/187.95 class_HOL_Oequal(tc_Int_Oint) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 188.07/187.95 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 188.07/187.95 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 188.07/187.95 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 188.07/187.95 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 188.07/187.95 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 188.07/187.95 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 188.07/187.95 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 188.07/187.95 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 188.07/187.95 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 188.07/187.95 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 188.07/187.95 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 188.07/187.95 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 188.07/187.95 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 188.07/187.95 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 188.07/187.95 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 188.07/187.95 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 188.07/187.95 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 188.07/187.95 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 188.07/187.95 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 188.07/187.95 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 188.07/187.95 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 188.07/187.95 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 188.07/187.95 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 188.07/187.95 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 188.07/187.95 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 188.07/187.95 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 188.07/187.95 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 188.07/187.95 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 188.07/187.95 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 188.07/187.95 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 188.07/187.95 class_Lattices_Olattice(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 188.07/187.95 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 188.07/187.95 class_Orderings_Oorder(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 188.07/187.95 class_Rings_Osemiring(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 188.07/187.95 class_Orderings_Oord(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 188.07/187.95 class_Orderings_Obot(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 188.07/187.95 class_Groups_Ominus(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Power_Opower,axiom,
% 188.07/187.95 class_Power_Opower(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 188.07/187.95 class_Groups_Ozero(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 188.07/187.95 class_Int_Onumber(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 188.07/187.95 class_Groups_Oone(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__HOL_Oequal,axiom,
% 188.07/187.95 class_HOL_Oequal(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 188.07/187.95 class_Nat_Osize(tc_Nat_Onat) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 188.07/187.95 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 188.07/187.95 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 188.07/187.95 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 188.07/187.95 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 188.07/187.95 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 188.07/187.95 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 188.07/187.95 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 188.07/187.95 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 188.07/187.95 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 188.07/187.95 class_Lattices_Olattice(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 188.07/187.95 class_Orderings_Oorder(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 188.07/187.95 class_Orderings_Otop(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 188.07/187.95 class_Orderings_Oord(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 188.07/187.95 class_Orderings_Obot(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 188.07/187.95 class_Groups_Ouminus(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 188.07/187.95 class_Groups_Ominus(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__HOL_Oequal,axiom,
% 188.07/187.95 class_HOL_Oequal(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 188.07/187.95 class_Enum_Oenum(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 188.07/187.95 class_Nat_Osize(tc_HOL_Obool) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Com__Ostate__HOL_Oequal,axiom,
% 188.07/187.95 class_HOL_Oequal(tc_Com_Ostate) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Com__Ostate__Nat_Osize,axiom,
% 188.07/187.95 class_Nat_Osize(tc_Com_Ostate) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Com__Ovname__HOL_Oequal,axiom,
% 188.07/187.95 class_HOL_Oequal(tc_Com_Ovname) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Com__Ovname__Nat_Osize,axiom,
% 188.07/187.95 class_Nat_Osize(tc_Com_Ovname) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_List__Olist__HOL_Oequal,axiom,
% 188.07/187.95 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_List__Olist__Nat_Osize,axiom,
% 188.07/187.95 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 188.07/187.95 ! [T_1,T_2] :
% 188.07/187.95 ( ( class_Finite__Set_Ofinite(T_2)
% 188.07/187.95 & class_Finite__Set_Ofinite(T_1) )
% 188.07/187.95 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_sum__HOL_Oequal,axiom,
% 188.07/187.95 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_sum__Enum_Oenum,axiom,
% 188.07/187.95 ! [T_1,T_2] :
% 188.07/187.95 ( ( class_Enum_Oenum(T_2)
% 188.07/187.95 & class_Enum_Oenum(T_1) )
% 188.07/187.95 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_sum__Nat_Osize,axiom,
% 188.07/187.95 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 188.07/187.95 ! [T_1] :
% 188.07/187.95 ( class_Finite__Set_Ofinite(T_1)
% 188.07/187.95 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Option__Ooption__HOL_Oequal,axiom,
% 188.07/187.95 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 188.07/187.95 ! [T_1] :
% 188.07/187.95 ( class_Enum_Oenum(T_1)
% 188.07/187.95 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 188.07/187.95 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 188.07/187.95 ! [T_1,T_2] :
% 188.07/187.95 ( ( class_Finite__Set_Ofinite(T_2)
% 188.07/187.95 & class_Finite__Set_Ofinite(T_1) )
% 188.07/187.95 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_prod__Smallcheck_Osmall,axiom,
% 188.07/187.95 ! [T_1,T_2] :
% 188.07/187.95 ( ( class_Smallcheck_Osmall(T_2)
% 188.07/187.95 & class_Smallcheck_Osmall(T_1) )
% 188.07/187.95 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_prod__HOL_Oequal,axiom,
% 188.07/187.95 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_prod__Enum_Oenum,axiom,
% 188.07/187.95 ! [T_1,T_2] :
% 188.07/187.95 ( ( class_Enum_Oenum(T_2)
% 188.07/187.95 & class_Enum_Oenum(T_1) )
% 188.07/187.95 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_prod__Nat_Osize,axiom,
% 188.07/187.95 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 188.07/187.95 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 188.07/187.95 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom,
% 188.07/187.95 class_HOL_Oequal(tc_Product__Type_Ounit) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 188.07/187.95 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 188.07/187.95 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom,
% 188.07/187.95 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 188.07/187.95 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom,
% 188.07/187.95 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 188.07/187.95 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 188.07/187.95 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 188.07/187.95 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 188.07/187.95 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 188.07/187.95 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 188.07/187.95 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 188.07/187.95 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 188.07/187.95 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 188.07/187.95 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 188.07/187.95 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 188.07/187.95 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 188.07/187.95 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 188.07/187.95 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 188.07/187.95 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 188.07/187.95 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 188.07/187.95 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 188.07/187.95 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 188.07/187.95 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 188.07/187.95 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 188.07/187.95 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 188.07/187.95 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 188.07/187.95 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 188.07/187.95 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 188.07/187.95 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 188.07/187.95 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 188.07/187.95 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 188.07/187.95 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 188.07/187.95 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 188.07/187.95 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 188.07/187.95 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 188.07/187.95 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 188.07/187.95 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 188.07/187.95 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 188.07/187.95 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 188.07/187.95 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 188.07/187.95 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom,
% 188.07/187.95 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 188.07/187.95 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom,
% 188.07/187.95 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 188.07/187.95
% 188.07/187.95 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 188.07/187.95 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 188.07/187.95
% 188.07/187.95 %----Helper facts (20)
% 188.07/187.95 fof(help_c__COMBI__1,axiom,
% 188.07/187.95 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__COMBK__1,axiom,
% 188.07/187.95 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__COMBB__1,axiom,
% 188.07/187.95 ! [V_R_2,V_Qa_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Qa_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Qa_2,V_R_2)) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__COMBC__1,axiom,
% 188.07/187.95 ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__COMBS__1,axiom,
% 188.07/187.95 ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_2,V_R_2)) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fequal__1,axiom,
% 188.07/187.95 ! [V_y_2,V_x_2] :
% 188.07/187.95 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 188.07/187.95 | V_x_2 = V_y_2 ) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fequal__2,axiom,
% 188.07/187.95 ! [V_y_2,V_x_2] :
% 188.07/187.95 ( V_x_2 != V_y_2
% 188.07/187.95 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fFalse__1,axiom,
% 188.07/187.95 ~ hBOOL(c_fFalse) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fTrue__1,axiom,
% 188.07/187.95 hBOOL(c_fTrue) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fNot__1,axiom,
% 188.07/187.95 ! [V_Pa_2] :
% 188.07/187.95 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2))
% 188.07/187.95 | ~ hBOOL(V_Pa_2) ) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fNot__2,axiom,
% 188.07/187.95 ! [V_Pa_2] :
% 188.07/187.95 ( ~ ~ hBOOL(V_Pa_2)
% 188.07/187.95 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fconj__1,axiom,
% 188.07/187.95 ! [V_Qa_2,V_Pa_2] :
% 188.07/187.95 ( ~ hBOOL(V_Pa_2)
% 188.07/187.95 | ~ hBOOL(V_Qa_2)
% 188.07/187.95 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fconj__2,axiom,
% 188.07/187.95 ! [V_Qa_2,V_Pa_2] :
% 188.07/187.95 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
% 188.07/187.95 | hBOOL(V_Pa_2) ) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fconj__3,axiom,
% 188.07/187.95 ! [V_Qa_2,V_Pa_2] :
% 188.07/187.95 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
% 188.07/187.95 | hBOOL(V_Qa_2) ) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fdisj__1,axiom,
% 188.07/187.95 ! [V_Qa_2,V_Pa_2] :
% 188.07/187.95 ( ~ hBOOL(V_Pa_2)
% 188.07/187.95 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fdisj__2,axiom,
% 188.07/187.95 ! [V_Pa_2,V_Qa_2] :
% 188.07/187.95 ( ~ hBOOL(V_Qa_2)
% 188.07/187.95 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fdisj__3,axiom,
% 188.07/187.95 ! [V_Qa_2,V_Pa_2] :
% 188.07/187.95 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
% 188.07/187.95 | hBOOL(V_Pa_2)
% 188.07/187.95 | hBOOL(V_Qa_2) ) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fimplies__1,axiom,
% 188.07/187.95 ! [V_Qa_2,V_Pa_2] :
% 188.07/187.95 ( hBOOL(V_Pa_2)
% 188.07/187.95 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fimplies__2,axiom,
% 188.07/187.95 ! [V_Pa_2,V_Qa_2] :
% 188.07/187.95 ( ~ hBOOL(V_Qa_2)
% 188.07/187.95 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ).
% 188.07/187.95
% 188.07/187.95 fof(help_c__fimplies__3,axiom,
% 188.07/187.95 ! [V_Qa_2,V_Pa_2] :
% 188.07/187.95 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
% 188.07/187.95 | ~ hBOOL(V_Pa_2)
% 188.07/187.95 | hBOOL(V_Qa_2) ) ).
% 188.07/187.95
% 188.07/187.95 %----Conjectures (2)
% 188.07/187.95 fof(conj_0,hypothesis,
% 188.07/187.95 ! [B_s_H] : 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(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,B_s_H)))),v_P)),v_c),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ).
% 188.07/187.95
% 188.07/187.95 fof(conj_1,conjecture,
% 188.07/187.95 ! [B_Z,B_s] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(v_P,B_Z),B_s))
% 188.07/187.95 => ? [B_P_H,B_Q_H] :
% 188.07/187.95 ( 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),B_P_H),v_c),B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
% 188.07/187.95 & ! [B_s_H] :
% 188.07/187.95 ( ! [B_Z_H] :
% 188.07/187.95 ( hBOOL(hAPP(hAPP(B_P_H,B_Z_H),B_s))
% 188.07/187.95 => hBOOL(hAPP(hAPP(B_Q_H,B_Z_H),B_s_H)) )
% 188.07/187.95 => hBOOL(hAPP(hAPP(v_Q,B_Z),B_s_H)) ) ) ) ).
% 188.07/187.95
% 188.07/187.95 %------------------------------------------------------------------------------
% 188.07/187.95 %-------------------------------------------
% 188.07/187.95 % Proof found
% 188.07/187.95 % SZS status Theorem for theBenchmark
% 188.07/187.95 % SZS output start Proof
% 188.07/187.95 %ClaNum:10164(EqnAxiom:2872)
% 188.07/187.95 %VarNum:70272(SingletonVarNum:20521)
% 188.07/187.95 %MaxLitNum:8
% 188.07/187.95 %MaxfuncDepth:13
% 188.07/187.95 %SharedTerms:1037
% 188.07/187.95 %goalClause: 3240 8560 8599
% 188.07/187.95 %singleGoalClaCount:1
% 188.07/187.95 [2876]P1(a860)
% 188.07/187.95 [2877]P1(a865)
% 188.07/187.95 [2878]P101(a187)
% 188.07/187.95 [2879]P2(a860)
% 188.07/187.95 [2880]P2(a865)
% 188.07/187.95 [2881]P2(a1)
% 188.07/187.95 [2882]P3(a860)
% 188.07/187.95 [2883]P97(a860)
% 188.07/187.95 [2884]P97(a865)
% 188.07/187.95 [2885]P97(a1)
% 188.07/187.95 [2886]P4(a860)
% 188.07/187.95 [2887]P4(a865)
% 188.07/187.95 [2888]P4(a1)
% 188.07/187.95 [2889]P4(a99)
% 188.07/187.95 [2890]P102(a860)
% 188.07/187.95 [2891]P102(a865)
% 188.07/187.95 [2892]P102(a1)
% 188.07/187.96 [2893]P102(a99)
% 188.07/187.96 [2894]P98(a860)
% 188.07/187.96 [2895]P98(a865)
% 188.07/187.96 [2896]P98(a1)
% 188.07/187.96 [2897]P103(a865)
% 188.07/187.96 [2898]P103(a1)
% 188.07/187.96 [2899]P103(a99)
% 188.07/187.96 [2900]P104(a860)
% 188.07/187.96 [2901]P104(a865)
% 188.07/187.96 [2902]P104(a1)
% 188.07/187.96 [2903]P104(a99)
% 188.07/187.96 [2904]P105(a860)
% 188.07/187.96 [2905]P105(a865)
% 188.07/187.96 [2906]P105(a1)
% 188.07/187.96 [2907]P105(a99)
% 188.07/187.96 [2908]P106(a860)
% 188.07/187.96 [2909]P95(a860)
% 188.07/187.96 [2910]P96(a860)
% 188.07/187.96 [2911]P96(a865)
% 188.07/187.96 [2912]P96(a1)
% 188.07/187.96 [2913]P75(a1)
% 188.07/187.96 [2914]P5(a860)
% 188.07/187.96 [2915]P5(a868)
% 188.07/187.96 [2916]P79(a860)
% 188.07/187.96 [2917]P79(a1)
% 188.07/187.96 [2918]P87(a860)
% 188.07/187.96 [2919]P59(a1)
% 188.07/187.96 [2920]P60(a1)
% 188.07/187.96 [2921]P66(a865)
% 188.07/187.96 [2922]P66(a1)
% 188.07/187.96 [2923]P66(a99)
% 188.07/187.96 [2924]P107(a1)
% 188.07/187.96 [2925]P108(a1)
% 188.07/187.96 [2926]P116(a1)
% 188.07/187.96 [2927]P61(a860)
% 188.07/187.96 [2928]P61(a868)
% 188.07/187.96 [2929]P68(a865)
% 188.07/187.96 [2930]P68(a1)
% 188.07/187.96 [2931]P68(a99)
% 188.07/187.96 [2932]P76(a865)
% 188.07/187.96 [2933]P76(a1)
% 188.07/187.96 [2934]P76(a99)
% 188.07/187.96 [2935]P77(a865)
% 188.07/187.96 [2936]P77(a1)
% 188.07/187.96 [2937]P77(a99)
% 188.07/187.96 [2938]P119(a865)
% 188.07/187.96 [2939]P119(a1)
% 188.07/187.96 [2940]P119(a99)
% 188.07/187.96 [2941]P133(a1)
% 188.07/187.96 [2942]P109(a1)
% 188.07/187.96 [2943]P112(a865)
% 188.07/187.96 [2944]P112(a1)
% 188.07/187.96 [2945]P112(a99)
% 188.07/187.96 [2946]P135(a865)
% 188.07/187.96 [2947]P135(a1)
% 188.07/187.96 [2948]P67(a865)
% 188.07/187.96 [2949]P67(a1)
% 188.07/187.96 [2950]P67(a99)
% 188.07/187.96 [2951]P69(a865)
% 188.07/187.96 [2952]P69(a1)
% 188.07/187.96 [2953]P69(a99)
% 188.07/187.96 [2954]P70(a865)
% 188.07/187.96 [2955]P70(a1)
% 188.07/187.96 [2956]P70(a99)
% 188.07/187.96 [2957]P80(a865)
% 188.07/187.96 [2958]P80(a1)
% 188.07/187.96 [2959]P80(a99)
% 188.07/187.96 [2960]P81(a865)
% 188.07/187.96 [2961]P81(a1)
% 188.07/187.96 [2962]P81(a99)
% 188.07/187.96 [2963]P83(a865)
% 188.07/187.96 [2964]P83(a1)
% 188.07/187.96 [2965]P83(a99)
% 188.07/187.96 [2966]P113(a865)
% 188.07/187.96 [2967]P113(a1)
% 188.07/187.96 [2968]P113(a99)
% 188.07/187.96 [2969]P136(a865)
% 188.07/187.96 [2970]P136(a1)
% 188.07/187.96 [2971]P136(a99)
% 188.07/187.96 [2972]P122(a1)
% 188.07/187.96 [2973]P73(a865)
% 188.07/187.96 [2974]P73(a1)
% 188.07/187.96 [2975]P73(a99)
% 188.07/187.96 [2976]P88(a865)
% 188.07/187.96 [2977]P88(a1)
% 188.07/187.96 [2978]P88(a99)
% 188.07/187.96 [2979]P78(a865)
% 188.07/187.96 [2980]P78(a1)
% 188.07/187.96 [2981]P78(a99)
% 188.07/187.96 [2982]P72(a865)
% 188.07/187.96 [2983]P72(a1)
% 188.07/187.96 [2984]P72(a99)
% 188.07/187.96 [2985]P74(a1)
% 188.07/187.96 [2986]P123(a865)
% 188.07/187.96 [2987]P123(a1)
% 188.07/187.96 [2988]P123(a99)
% 188.07/187.96 [2989]P137(a1)
% 188.07/187.96 [2990]P124(a865)
% 188.07/187.96 [2991]P124(a1)
% 188.07/187.96 [2992]P124(a99)
% 188.07/187.96 [2993]P138(a865)
% 188.07/187.96 [2994]P138(a1)
% 188.07/187.96 [2995]P138(a99)
% 188.07/187.96 [2996]P120(a1)
% 188.07/187.96 [2997]P121(a1)
% 188.07/187.96 [2998]P84(a865)
% 188.07/187.96 [2999]P84(a1)
% 188.07/187.96 [3000]P84(a99)
% 188.07/187.96 [3001]P129(a865)
% 188.07/187.96 [3002]P129(a1)
% 188.07/187.96 [3003]P129(a99)
% 188.07/187.96 [3004]P131(a865)
% 188.07/187.96 [3005]P131(a1)
% 188.07/187.96 [3006]P131(a99)
% 188.07/187.96 [3007]P130(a865)
% 188.07/187.96 [3008]P130(a1)
% 188.07/187.96 [3009]P130(a99)
% 188.07/187.96 [3010]P125(a865)
% 188.07/187.96 [3011]P125(a1)
% 188.07/187.96 [3012]P125(a99)
% 188.07/187.96 [3013]P117(a865)
% 188.07/187.96 [3014]P117(a1)
% 188.07/187.96 [3015]P117(a99)
% 188.07/187.96 [3016]P126(a865)
% 188.07/187.96 [3017]P126(a1)
% 188.07/187.96 [3018]P126(a99)
% 188.07/187.96 [3019]P127(a1)
% 188.07/187.96 [3020]P128(a1)
% 188.07/187.96 [3021]P134(a1)
% 188.07/187.96 [3022]P89(a1)
% 188.07/187.96 [3023]P85(a1)
% 188.07/187.96 [3024]P139(a865)
% 188.07/187.96 [3025]P139(a1)
% 188.07/187.96 [3026]P139(a99)
% 188.07/187.96 [3027]P99(a865)
% 188.07/187.96 [3028]P99(a1)
% 188.07/187.96 [3029]P99(a99)
% 188.07/187.96 [3030]P140(a865)
% 188.07/187.96 [3031]P140(a1)
% 188.07/187.96 [3032]P140(a99)
% 188.07/187.96 [3033]P82(a1)
% 188.07/187.96 [3034]P132(a1)
% 188.07/187.96 [3035]P71(a1)
% 188.07/187.96 [3036]P6(a860)
% 188.07/187.96 [3037]P110(a865)
% 188.07/187.96 [3038]P110(a1)
% 188.07/187.96 [3039]P110(a99)
% 188.07/187.96 [3040]P57(a865)
% 188.07/187.96 [3041]P57(a1)
% 188.07/187.96 [3042]P57(a99)
% 188.07/187.96 [3043]P58(a1)
% 188.07/187.96 [3044]P90(a1)
% 188.07/187.96 [3045]P91(a865)
% 188.07/187.96 [3046]P91(a1)
% 188.07/187.96 [3047]P91(a99)
% 188.07/187.96 [3048]P141(a868)
% 188.07/187.96 [3049]P141(a1)
% 188.07/187.96 [3050]P92(a860)
% 188.07/187.96 [3051]P92(a861)
% 188.07/187.96 [3052]P92(a865)
% 188.07/187.96 [3053]P92(a863)
% 188.07/187.96 [3054]P92(a862)
% 188.07/187.96 [3055]P92(a868)
% 188.07/187.96 [3056]P92(a1)
% 188.07/187.96 [3057]P92(a319)
% 188.07/187.96 [3058]P92(a99)
% 188.07/187.96 [3059]P86(a865)
% 188.07/187.96 [3060]P86(a1)
% 188.07/187.96 [3061]P86(a99)
% 188.07/187.96 [3062]P111(a865)
% 188.07/187.96 [3063]P100(a860)
% 188.07/187.96 [3064]P100(a861)
% 188.07/187.96 [3065]P100(a865)
% 188.07/187.96 [3066]P100(a863)
% 188.07/187.96 [3067]P100(a862)
% 188.07/187.96 [3068]P100(a868)
% 188.07/187.96 [3069]P100(a319)
% 188.07/187.96 [3070]P100(a99)
% 188.07/187.96 [3071]P94(a860)
% 188.07/187.96 [3091]P38(a865,a242)
% 188.07/187.96 [3092]P38(a865,a313)
% 188.07/187.96 [4469]~E(a97,a81)
% 188.07/187.96 [4470]~P101(a241)
% 188.07/187.96 [2873]E(f2(a1),a81)
% 188.07/187.96 [2874]E(f100(a99),a3)
% 188.07/187.96 [2875]E(f22(a99),a23)
% 188.07/187.96 [3072]E(f188(a865),f2(a865))
% 188.07/187.96 [3073]E(f28(a24),f2(a865))
% 188.07/187.96 [3074]E(f101(a865),f235(a865))
% 188.07/187.96 [3075]E(f110(a865),f236(a865))
% 188.07/187.96 [3076]E(f102(a1),f32(a1))
% 188.07/187.96 [3077]E(f82(a187),f2(a865))
% 188.07/187.96 [3078]E(f82(a241),f2(a865))
% 188.07/187.96 [3079]P7(f76(a1))
% 188.07/187.96 [3080]P7(f2(a1))
% 188.07/187.96 [3139]P38(f871(a865,a865),a33)
% 188.07/187.96 [3490]E(f315(a865,a865,a242,a242),a33)
% 188.07/187.96 [4471]~E(f76(a1),f2(a1))
% 188.07/187.96 [3081]E(f111(f2(a865)),f2(a865))
% 188.07/187.96 [3082]E(f4(f2(a99)),f2(a865))
% 188.07/187.96 [3094]E(f323(f77(a1),a81),a81)
% 188.07/187.96 [3097]E(f323(a112,f2(a865)),f76(a865))
% 188.07/187.96 [3098]E(f323(a104,f76(a1)),f76(a865))
% 188.07/187.96 [3099]E(f323(a3,f76(a865)),f76(a99))
% 188.07/187.96 [3101]E(f323(a3,f2(a865)),f2(a99))
% 188.07/187.96 [3103]E(f323(f103(a1),a81),f2(a1))
% 188.07/187.96 [3104]E(f323(f103(a99),a81),f2(a99))
% 188.07/187.96 [3105]E(f323(a104,f2(a1)),f2(a865))
% 188.07/187.96 [3106]E(f323(f189(a860),a187),f2(a865))
% 188.07/187.96 [3107]E(f323(f189(a860),a241),f2(a865))
% 188.07/187.96 [3108]E(f323(f189(a862),a24),f2(a865))
% 188.07/187.96 [3109]E(f323(f103(a865),a81),f2(a865))
% 188.07/187.96 [3113]E(f323(f77(a1),f76(a1)),a97)
% 188.07/187.96 [3120]E(f323(f77(a1),f2(a1)),f2(a1))
% 188.07/187.96 [3122]E(f323(f189(a99),f2(a99)),f2(a865))
% 188.07/187.96 [3123]E(f323(f100(a1),f76(a865)),f76(a1))
% 188.07/187.96 [3124]E(f323(f100(a1),f2(a865)),f2(a1))
% 188.07/187.96 [3135]E(f323(a104,f76(a1)),f323(a112,f2(a865)))
% 188.07/187.96 [3137]E(f314(f871(a865,a865),a33),a34)
% 188.07/187.96 [3138]E(f316(f871(a865,a865),a33),a66)
% 188.07/187.96 [3159]E(f323(f244(a865),f2(a865)),f188(f872(a865,a860)))
% 188.07/187.96 [3160]E(f323(f245(a865),f2(a865)),f246(f872(a865,a860)))
% 188.07/187.96 [3169]P39(f188(f872(a1,a860)))
% 188.07/187.96 [3205]E(f323(f323(f22(a99),f2(a99)),f76(a99)),f2(a99))
% 188.07/187.96 [3240]P101(f323(f323(a873,a687),a796))
% 188.07/187.96 [3284]P101(f323(f323(f238(a1),a97),f2(a1)))
% 188.07/187.96 [3309]P101(f323(f323(f237(a1),f2(a1)),f76(a1)))
% 188.07/187.96 [3311]P101(f323(f323(f238(a1),f2(a1)),f76(a1)))
% 188.07/187.96 [3520]E(f323(f323(f280(a865,a865,a865),a313),f299(a865,a313)),a242)
% 188.07/187.96 [3559]P41(a1,a865,a104,f323(f237(a1),f2(a1)))
% 188.07/187.96 [3563]E(f323(f323(f39(a865,f872(a865,a860)),f246(f872(a865,a860))),f244(a865)),f246(f872(a865,a860)))
% 188.07/187.96 [3564]E(f323(f323(f39(a865,f872(a865,a860)),f246(f872(a865,a860))),f245(a865)),f246(f872(a865,a860)))
% 188.07/187.96 [3565]E(f323(f323(f39(a865,f872(a865,a860)),f246(f872(a865,a860))),f292(a865)),f246(f872(a865,a860)))
% 188.07/187.96 [3566]E(f323(f323(f40(a865,f872(a865,a860)),f246(f872(a865,a860))),f295(a865)),f188(f872(a865,a860)))
% 188.07/187.96 [3582]P27(a865,a1,f100(a1),f246(f872(a865,a860)))
% 188.07/187.96 [3596]P41(a865,a1,f100(a1),f323(f16(a860,a865),a187))
% 188.07/187.96 [3728]E(f323(f71(a865,a99,a1,a3),a104),f103(a99))
% 188.07/187.96 [3957]P53(a99,a865,a19,a3,f246(f872(a865,a860)))
% 188.07/187.96 [3966]P53(a1,f872(f871(a865,a865),a860),a107,a87,a98)
% 188.07/187.96 [4233]E(f263(a1,a1,a1,a1,f32(a1),f77(a1)),a48)
% 188.07/187.96 [4494]~E(f323(f103(a1),a97),f323(f103(a1),a81))
% 188.07/187.96 [4495]~P101(f323(a193,f76(a1)))
% 188.07/187.96 [4496]~P101(f323(a193,f2(a1)))
% 188.07/187.96 [4537]~P101(f323(f323(f238(a1),a81),f2(a1)))
% 188.07/187.96 [3152]E(f323(f323(f22(a1),a97),a97),a81)
% 188.07/187.96 [3167]E(f323(f100(a1),f323(a112,f2(a865))),f76(a1))
% 188.07/187.96 [3234]E(f323(f35(a868),f246(f872(a868,a860))),f76(a865))
% 188.07/187.96 [3256]P101(f323(a193,f323(f103(a1),a97)))
% 188.07/187.96 [3258]P101(f323(f323(f237(a1),a97),a81))
% 188.07/187.96 [3260]P101(f323(f323(f238(a1),a97),a81))
% 188.07/187.96 [3320]E(f323(f323(f301(a865),f2(a865)),f188(f872(a865,a860))),f323(f292(a865),f2(a865)))
% 188.07/187.96 [3375]P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),a81)))
% 188.07/187.96 [3387]E(f323(f302(a865,a865,a112),f246(f872(a865,a860))),f323(f295(a865),f2(a865)))
% 188.07/187.96 [3427]P9(f871(a865,a865),f246(f872(f871(a865,a865),a860)),a108)
% 188.07/187.96 [3736]E(f323(f71(a865,a1,a99,f100(a1)),a19),a20)
% 188.07/187.96 [3797]P38(a865,f323(f243(f871(a865,a865)),f323(f262(a865,a865,a860),f238(a865))))
% 188.07/187.96 [4526]~P101(f323(a193,f323(f103(a1),a81)))
% 188.07/187.96 [4527]~P101(f323(f323(f237(a1),a81),a97))
% 188.07/187.96 [4528]~P101(f323(f323(f238(a1),a81),a81))
% 188.07/187.96 [4529]~P101(f323(f323(f238(a1),a81),a97))
% 188.07/187.96 [4530]~P101(f323(f323(f238(a1),a97),a97))
% 188.07/187.96 [4531]~P101(f323(f323(f89(a1),a81),a97))
% 188.07/187.96 [4532]~P101(f323(f323(f89(a1),a97),a81))
% 188.07/187.96 [4543]~P101(f323(f59(a865),f246(f872(a865,a860))))
% 188.07/187.96 [4544]~P101(f323(f59(a1),f246(f872(a1,a860))))
% 188.07/187.96 [4406]E(f323(f262(a1,a1,a860),f323(f323(f8(f872(a1,a860),f872(a1,a860),a1),f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f238(a1),f2(a1))))),f323(f323(f7(a1,a1,f872(a1,a860)),f323(f323(f8(f872(a1,f872(a1,a860)),f872(a1,f872(a1,a860)),a1),f7(a1,a1,a860)),f323(f323(f8(f872(a1,a1),f872(a1,f872(a1,a860)),a1),f323(f8(a1,f872(a1,a860),a1),a320)),a219))),f76(a1)))),a215)
% 188.07/187.96 [3465]E(f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97),f323(f77(a1),a97))
% 188.07/187.96 [3503]E(f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97),f323(f323(f22(a1),a81),a97))
% 188.07/187.96 [3662]E(f323(f323(f58(f871(a865,a865)),f246(f872(f871(a865,a865),a860))),a108),a98)
% 188.07/187.96 [3691]E(f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f76(a1))
% 188.07/187.96 [3692]E(f323(f103(a99),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f76(a99))
% 188.07/187.96 [3693]E(f323(f103(a865),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f76(a865))
% 188.07/187.96 [3697]E(f323(f103(a865),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(a112,f2(a865)))
% 188.07/187.96 [4092]E(f323(f323(f110(f872(f871(f871(a865,a865),f871(a865,a865)),a860)),a33),f299(f871(a865,a865),f188(f872(f871(f871(a865,a865),f871(a865,a865)),a860)))),a68)
% 188.07/187.96 [4162]E(f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),f76(a865)),f2(a865))),f188(f872(f871(a865,a865),a860))))),f76(a1))
% 188.07/187.96 [4163]E(f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),f2(a865)),f2(a865))),f188(f872(f871(a865,a865),a860))))),f2(a1))
% 188.07/187.96 [4178]E(f323(f243(f871(a865,a865)),f323(f262(a865,a865,a860),f323(f323(f8(a865,f872(a865,a860),a865),f323(f7(a865,a865,a860),a320)),a112))),a313)
% 188.07/187.96 [4148]E(f323(f103(a865),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(a865))))
% 188.07/187.96 [4151]E(f323(f103(a865),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(a865),f76(a865)),f76(a865)))
% 188.07/187.96 [4152]E(f323(f103(a865),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(a860),f246(f872(a860,a860))))
% 188.07/187.96 [4219]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))))
% 188.07/187.96 [4291]P29(f872(f871(a865,a865),a860),f323(f323(f258(f872(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),a860),f872(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),a860)),a34),a67))
% 188.07/187.96 [4292]P29(f872(f871(a865,a865),a860),f323(f323(f258(f872(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),a860),f872(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),a860)),a66),a69))
% 188.07/187.96 [4333]E(f323(f323(f110(f872(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),a860)),f316(f871(a865,a865),a68)),f323(f323(f301(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f258(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),f188(f872(f871(a865,a865),a860))),f188(f872(f871(a865,a865),a860)))),f188(f872(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),a860)))),a69)
% 188.07/187.96 [4334]E(f323(f323(f110(f872(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),a860)),f314(f871(a865,a865),a68)),f323(f323(f301(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f258(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),f188(f872(f871(a865,a865),a860))),f188(f872(f871(a865,a865),a860)))),f188(f872(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),a860)))),a67)
% 188.07/187.96 [4221]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(a865))))
% 188.07/187.96 [4268]E(f323(f100(a1),f323(f103(a865),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))))
% 188.07/187.96 [4304]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)))))
% 188.07/187.96 [4305]E(f323(f103(a865),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(a865)))))
% 188.07/187.96 [4348]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)))
% 188.07/187.96 [4376]E(f323(f100(a1),f323(f103(a865),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)))
% 188.07/187.96 [4391]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))))
% 188.07/187.96 [3093]P8(x30931,a320)
% 188.07/187.96 [3491]P27(a865,a865,a112,x34911)
% 188.07/187.96 [3083]P92(f864(x30831))
% 188.07/187.96 [3084]P92(f869(x30841))
% 188.07/187.96 [3085]P92(f866(x30851))
% 188.07/187.96 [3086]P92(f867(x30861))
% 188.07/187.96 [3087]P100(f864(x30871))
% 188.07/187.96 [3088]P100(f869(x30881))
% 188.07/187.96 [3089]P100(f866(x30891))
% 188.07/187.96 [3090]P100(f867(x30901))
% 188.07/187.96 [3110]P38(a1,f105(x31101))
% 188.07/187.96 [3111]P38(a1,f106(x31111))
% 188.07/187.96 [3156]P38(f872(x31561,a860),f298(x31561))
% 188.07/187.96 [3181]E(f247(x31811,x31811,a320),a320)
% 188.07/187.96 [3196]E(f42(a1,x31961,x31961),f2(a1))
% 188.07/187.96 [3253]P17(x32531,f872(x32531,a860),f301(x32531))
% 188.07/187.96 [4473]~E(f323(a112,x44731),x44731)
% 188.07/187.96 [4485]~E(f323(a112,x44851),f2(a865))
% 188.07/187.96 [3095]E(f323(f189(a865),x30951),x30951)
% 188.07/187.96 [3096]E(f323(f103(a1),x30961),x30961)
% 188.07/187.96 [3112]E(f323(a87,f324(x31121)),x31121)
% 188.07/187.96 [3125]E(f145(x31251,f113(x31251)),f113(x31251))
% 188.07/187.96 [3126]E(f114(x31261,f113(x31261)),f113(x31261))
% 188.07/187.96 [3132]E(f323(f161(x31321),f113(x31321)),f113(x31321))
% 188.07/187.96 [3133]E(f323(f165(x31331),f113(x31331)),f113(x31331))
% 188.07/187.96 [3134]E(f323(f162(x31341),f113(x31341)),f113(x31341))
% 188.07/187.96 [3140]E(f323(f103(a1),x31401),f323(f102(a1),x31401))
% 188.07/187.96 [3141]E(f323(a87,f323(a107,x31411)),x31411)
% 188.07/187.96 [3143]E(f323(a3,f323(a19,x31431)),x31431)
% 188.07/187.96 [3144]E(f323(a19,f323(a3,x31441)),x31441)
% 188.07/187.96 [3145]P7(f323(f100(a1),x31451))
% 188.07/187.96 [3150]E(f323(f189(f869(x31501)),f200(x31501)),f2(a865))
% 188.07/187.96 [3151]E(f323(f189(f866(x31511)),f113(x31511)),f2(a865))
% 188.07/187.96 [3165]E(f229(x31651,f200(x31651)),f188(f872(x31651,a860)))
% 188.07/187.96 [3172]E(f323(f323(f22(a865),x31721),f2(a865)),x31721)
% 188.07/187.96 [3173]E(f323(f323(f79(a865),x31731),f76(a865)),x31731)
% 188.07/187.96 [3174]E(f323(f323(f79(a1),x31741),f76(a1)),x31741)
% 188.07/187.96 [3175]E(f323(f323(f78(a865),x31751),f2(a865)),x31751)
% 188.07/187.96 [3176]E(f323(f323(f78(a1),x31761),f2(a1)),x31761)
% 188.07/187.96 [3177]E(f323(f323(f236(a865),x31771),f2(a865)),x31771)
% 188.07/187.96 [3178]E(f323(f323(f79(a865),x31781),f2(a865)),f2(a865))
% 188.07/187.96 [3179]E(f323(f323(f235(a865),x31791),f2(a865)),f2(a865))
% 188.07/187.96 [3180]E(f323(f323(f36(a1),x31801),f2(a1)),f2(a1))
% 188.07/187.96 [3187]E(f323(f166(x31871),f113(x31871)),f188(f872(x31871,a860)))
% 188.07/187.96 [3191]P101(f323(f130(x31911),f113(x31911)))
% 188.07/187.96 [3197]E(f323(f201(x31971,x31971),f5(x31971)),f32(f869(x31971)))
% 188.07/187.96 [3198]E(f323(f201(x31981,x31981),f32(x31981)),f32(f869(x31981)))
% 188.07/187.96 [3199]E(f323(f147(x31991,x31991),f5(x31991)),f32(f866(x31991)))
% 188.07/187.96 [3200]E(f323(f147(x32001,x32001),f32(x32001)),f32(f866(x32001)))
% 188.07/187.96 [3201]E(f42(a1,x32011,f2(a1)),x32011)
% 188.07/187.96 [3202]E(f323(f237(a865),f323(a112,x32021)),f323(f238(a865),x32021))
% 188.07/187.96 [3203]E(f323(f244(a865),f323(a112,x32031)),f323(f292(a865),x32031))
% 188.07/187.96 [3204]E(f323(f245(a865),f323(a112,x32041)),f323(f295(a865),x32041))
% 188.07/187.96 [3206]E(f42(a1,f2(a1),x32061),f2(a1))
% 188.07/187.96 [3218]E(f323(f323(f78(a865),x32181),f76(a865)),f323(a112,x32181))
% 188.07/187.96 [3228]E(f323(f293(a865,x32281),f2(a865)),f188(f872(a865,a860)))
% 188.07/187.96 [3241]E(f294(a865,f2(a865),x32411),f323(f292(a865),x32411))
% 188.07/187.96 [3287]E(f323(f323(f22(a865),f323(a112,x32871)),f76(a865)),x32871)
% 188.07/187.96 [3300]E(f44(f2(a1),x33001),f323(f323(f258(a1,a1),f2(a1)),f2(a1)))
% 188.07/187.96 [3349]P101(f323(f323(f238(a865),x33491),f323(a112,x33491)))
% 188.07/187.96 [3361]P101(f323(f323(f238(a865),f2(a865)),f323(a112,x33611)))
% 188.07/187.96 [3595]E(f91(x35951,x35951,f246(f872(x35951,a860)),f32(x35951)),f32(x35951))
% 188.07/187.96 [3649]E(f323(f323(f22(a99),f323(a3,f323(a112,f323(a19,x36491)))),f76(a99)),x36491)
% 188.07/187.96 [3720]P101(f323(f323(f237(a1),f323(f77(a1),f323(f100(a1),x37201))),f2(a1)))
% 188.07/187.96 [3872]P101(f323(f323(f238(a1),f323(f77(a1),f323(f100(a1),f323(a112,x38721)))),f2(a1)))
% 188.07/187.96 [4501]~E(f246(f872(x45011,a860)),f188(f872(x45011,a860)))
% 188.07/187.96 [4540]~P101(f323(f323(f238(a865),x45401),f2(a865)))
% 188.07/187.96 [4552]~P101(f323(f323(f238(a1),f323(f100(a1),x45521)),f2(a1)))
% 188.07/187.96 [3155]E(f173(x31551,f113(f866(x31551))),f113(f866(x31551)))
% 188.07/187.96 [3157]E(f323(f323(f79(a1),a81),x31571),a81)
% 188.07/187.96 [3158]E(f323(f323(f78(a1),a81),x31581),x31581)
% 188.07/187.96 [3161]E(f323(a104,f323(f100(a1),x31611)),x31611)
% 188.07/187.96 [3162]E(f323(f323(f22(a1),x31621),a81),x31621)
% 188.07/187.96 [3163]E(f323(f323(f78(a1),x31631),a81),x31631)
% 188.07/187.96 [3166]E(f323(f323(f22(a865),x31661),x31661),f2(a865))
% 188.07/187.96 [3170]E(f323(f77(a1),f323(f77(a1),x31701)),x31701)
% 188.07/187.96 [3171]E(f323(f35(a865),f323(f244(a865),x31711)),x31711)
% 188.07/187.96 [3182]E(f323(f323(f79(a865),f76(a865)),x31821),x31821)
% 188.07/187.96 [3183]E(f323(f323(f79(a1),f76(a1)),x31831),x31831)
% 188.07/187.96 [3184]E(f323(f323(f78(a865),f2(a865)),x31841),x31841)
% 188.07/187.96 [3185]E(f323(f323(f78(a1),f2(a1)),x31851),x31851)
% 188.07/187.96 [3186]E(f323(f323(f236(a865),f2(a865)),x31861),x31861)
% 188.07/187.96 [3192]E(f323(f323(f22(a865),f2(a865)),x31921),f2(a865))
% 188.07/187.96 [3193]E(f323(f323(f79(a865),f2(a865)),x31931),f2(a865))
% 188.07/187.96 [3194]E(f323(f323(f235(a865),f2(a865)),x31941),f2(a865))
% 188.07/187.96 [3195]E(f323(f323(f36(a1),f2(a1)),x31951),f2(a1))
% 188.07/187.96 [3212]E(f323(f293(a865,f2(a865)),x32121),f323(f244(a865),x32121))
% 188.07/187.96 [3213]E(f323(f323(f79(a1),a97),x32131),f323(f77(a1),x32131))
% 188.07/187.96 [3220]E(f323(a104,f323(f103(a1),x32201)),f323(f103(a865),x32201))
% 188.07/187.96 [3221]E(f323(a19,f323(f103(a99),x32211)),f323(f103(a865),x32211))
% 188.07/187.96 [3222]E(f323(f35(a865),f323(f292(a865),x32221)),f323(a112,x32221))
% 188.07/187.96 [3232]E(f323(f323(f78(a865),f76(a865)),x32321),f323(a112,x32321))
% 188.07/187.96 [3236]E(f323(f102(a1),f323(f100(a1),x32361)),f323(f100(a1),x32361))
% 188.07/187.96 [3237]E(f323(f73(a1),f323(f100(a1),x32371)),f323(f100(a1),x32371))
% 188.07/187.96 [3243]E(f323(f35(x32431),f188(f872(x32431,a860))),f2(a865))
% 188.07/187.96 [3245]E(f323(f323(f36(a865),x32451),f323(a112,f2(a865))),x32451)
% 188.07/187.96 [3254]E(f42(a865,x32541,f323(a112,f2(a865))),f2(a865))
% 188.07/187.96 [3255]E(f42(a1,x32551,f323(f103(a1),a97)),f2(a1))
% 188.07/187.96 [3271]E(f323(f323(f36(a1),x32711),f323(f103(a1),a97)),f323(f77(a1),x32711))
% 188.07/187.96 [3275]E(f132(a865,f323(f293(a865,x32751),f2(a865))),f113(a865))
% 188.07/187.96 [3276]E(f323(f323(f78(a1),x32761),f76(a1)),f323(f323(f22(a1),x32761),a97))
% 188.07/187.96 [3277]E(f323(f323(f22(a1),x32771),f76(a1)),f323(f323(f78(a1),x32771),a97))
% 188.07/187.96 [3281]P101(f323(f323(f237(a865),x32811),x32811))
% 188.07/187.96 [3282]P101(f323(f323(f237(a1),x32821),x32821))
% 188.07/187.96 [3283]P101(f323(f323(f89(a1),x32831),x32831))
% 188.07/187.96 [3288]E(f323(f77(a1),f323(f103(a1),x32881)),f323(f103(a1),f323(f77(a1),x32881)))
% 188.07/187.96 [3289]P101(f323(f59(a865),f323(f244(a865),x32891)))
% 188.07/187.96 [3290]P101(f323(f59(a865),f323(f292(a865),x32901)))
% 188.07/187.96 [3298]E(f154(x32981,f246(f872(x32981,a860))),f246(f872(f866(x32981),a860)))
% 188.07/187.96 [3303]P101(f323(f323(f237(a865),f2(a865)),x33031))
% 188.07/187.96 [3313]E(f323(f323(f78(a865),f111(x33131)),f323(a112,f2(a865))),f111(f323(a112,x33131)))
% 188.07/187.96 [3314]E(f323(f243(x33141),f323(f16(a860,x33141),a241)),f188(f872(x33141,a860)))
% 188.07/187.96 [3315]E(f323(f243(x33151),f323(f16(a860,x33151),a187)),f246(f872(x33151,a860)))
% 188.07/187.96 [3319]E(f323(f323(f301(a865),x33191),f323(f244(a865),x33191)),f323(f244(a865),f323(a112,x33191)))
% 188.07/187.96 [3331]E(f323(f323(f78(a1),f76(a1)),f323(f100(a1),x33311)),f323(f100(a1),f323(a112,x33311)))
% 188.07/187.96 [3333]E(f323(f323(f144(f866(x33331)),f113(x33331)),f113(f866(x33331))),f51(x33331,f113(x33331)))
% 188.07/187.96 [3352]E(f188(f872(f871(x33521,x33521),a860)),f255(x33521,f188(f872(x33521,a860))))
% 188.07/187.96 [3353]E(f323(f300(x33531),f246(f872(x33531,a860))),f246(f872(f872(x33531,a860),a860)))
% 188.07/187.96 [3354]E(f323(f77(f872(x33541,a860)),f188(f872(x33541,a860))),f246(f872(x33541,a860)))
% 188.07/187.96 [3355]E(f323(f77(f872(x33551,a860)),f246(f872(x33551,a860))),f188(f872(x33551,a860)))
% 188.07/187.96 [3357]P101(f323(f59(x33571),f188(f872(x33571,a860))))
% 188.07/187.96 [3359]E(f323(f293(a865,x33591),f323(a112,x33591)),f323(f323(f301(a865),x33591),f188(f872(a865,a860))))
% 188.07/187.96 [3360]E(f83(f871(a865,a865),f45(x33601,f2(a865))),f323(f323(f258(a865,a865),f2(a865)),x33601))
% 188.07/187.96 [3374]E(f323(f323(f301(a865),f323(a112,x33741)),f323(f292(a865),x33741)),f323(f292(a865),f323(a112,x33741)))
% 188.07/187.96 [3378]P38(x33781,f188(f872(f871(x33781,x33781),a860)))
% 188.07/187.96 [3381]P101(f323(f323(f237(a1),f2(a1)),f323(f100(a1),x33811)))
% 188.07/187.96 [3389]E(f323(f323(f78(a865),f323(f189(a865),x33891)),f323(a112,f2(a865))),f323(f189(a865),f323(a112,x33891)))
% 188.07/187.96 [3498]P39(f323(f302(a865,a1,f100(a1)),x34981))
% 188.07/187.96 [3536]P40(x35361,f188(f872(x35361,a860)),f188(f872(f871(x35361,x35361),a860)))
% 188.07/187.96 [3555]E(f323(f323(f258(a1,a1),f323(f103(a1),a97)),f323(f323(f22(a1),x35551),f76(a1))),f47(f323(f103(a1),a97),x35551))
% 188.07/187.96 [3608]P56(x36081,f323(f16(f872(x36081,a860),x36081),f323(f16(a860,x36081),a241)))
% 188.07/187.96 [3809]P101(f323(f323(f325(f872(f871(a865,a865),a860)),f324(x38091)),a98))
% 188.07/187.96 [3836]P101(f323(f323(f325(f872(f871(a865,a865),a860)),f323(a107,x38361)),a98))
% 188.07/187.96 [3976]P27(x39761,f872(x39761,a860),f323(f323(f7(x39761,f872(x39761,a860),f872(x39761,a860)),f301(x39761)),f188(f872(x39761,a860))),f246(f872(x39761,a860)))
% 188.07/187.96 [4498]~E(f323(f323(f78(a1),x44981),x44981),a97)
% 188.07/187.96 [4525]~E(f323(a3,f323(a112,f323(a19,x45251))),f2(a99))
% 188.07/187.96 [4533]~P101(f323(a193,f323(f100(a1),x45331)))
% 188.07/187.96 [4536]~P101(f323(f323(f238(a865),x45361),x45361))
% 188.07/187.96 [4545]~P101(f323(f323(f237(a865),f323(a112,x45451)),x45451))
% 188.07/187.96 [3305]E(f323(a104,f323(f77(a1),f323(f100(a1),x33051))),f2(a865))
% 188.07/187.96 [3308]E(f323(f323(f78(a1),f323(f77(a1),x33081)),x33081),f2(a1))
% 188.07/187.96 [3312]E(f323(f35(a1),f323(f293(a1,f2(a1)),x33121)),f323(a104,x33121))
% 188.07/187.96 [3324]E(f323(f323(f248(a865),f323(a112,f2(a865))),x33241),f323(a112,f2(a865)))
% 188.07/187.96 [3424]E(f323(f276(x34241),f188(f872(f871(x34241,x34241),a860))),f188(f872(x34241,a860)))
% 188.07/187.96 [3432]E(f37(f872(x34321,a860),f188(f872(f872(x34321,a860),a860))),f188(f872(x34321,a860)))
% 188.07/187.96 [3433]E(f37(f872(x34331,a860),f246(f872(f872(x34331,a860),a860))),f246(f872(x34331,a860)))
% 188.07/187.96 [3434]E(f38(f872(x34341,a860),f188(f872(f872(x34341,a860),a860))),f246(f872(x34341,a860)))
% 188.07/187.96 [3435]E(f38(f872(x34351,a860),f246(f872(f872(x34351,a860),a860))),f188(f872(x34351,a860)))
% 188.07/187.96 [3481]E(f323(f323(f301(f866(x34811)),f113(x34811)),f188(f872(f866(x34811),a860))),f155(x34811,f113(f872(x34811,a860))))
% 188.07/187.96 [3482]E(f323(f323(f301(f866(x34821)),f113(x34821)),f188(f872(f866(x34821),a860))),f154(x34821,f188(f872(x34821,a860))))
% 188.07/187.96 [3519]E(f323(f323(f78(a865),f4(x35191)),f323(a112,f2(a865))),f4(f323(a3,f323(a112,f323(a19,x35191)))))
% 188.07/187.96 [3547]E(f323(f35(a1),f323(f302(a865,a1,f100(a1)),x35471)),f323(f35(a865),x35471))
% 188.07/187.96 [3548]P101(f323(f323(f237(a865),x35481),f323(f323(f79(a865),x35481),x35481)))
% 188.07/187.96 [3586]E(f323(f302(a1,a865,a104),f294(a1,f2(a1),f323(f100(a1),x35861))),f323(f292(a865),x35861))
% 188.07/187.96 [3603]E(f323(f323(f36(a865),f323(a112,f2(a865))),f323(f103(a865),x36031)),f323(a104,f323(f323(f36(a1),f76(a1)),f323(f103(a1),x36031))))
% 188.07/187.96 [3605]E(f323(f166(a865),f132(a865,f323(f293(a865,f2(a865)),f323(a112,x36051)))),f323(f292(a865),x36051))
% 188.07/187.96 [3606]E(f323(f323(f78(a865),f323(f189(a99),x36061)),f323(a112,f2(a865))),f323(f189(a99),f323(a3,f323(a112,f323(a19,x36061)))))
% 188.07/187.96 [3623]E(f323(f302(a1,a865,a104),f323(f302(a865,a1,f100(a1)),x36231)),x36231)
% 188.07/187.96 [3655]E(f323(f323(f301(a865),f2(a865)),f323(f302(a865,a865,a112),f323(f244(a865),x36551))),f323(f244(a865),f323(a112,x36551)))
% 188.07/187.96 [3661]P51(x36611,x36611,f299(x36611,f188(f872(f871(x36611,x36611),a860))))
% 188.07/187.96 [3667]P101(f323(a193,f323(f77(a1),f323(f100(a1),f323(a112,x36671)))))
% 188.07/187.96 [3678]E(f323(f323(f22(f872(a865,a860)),f323(f245(a865),x36781)),f323(f323(f301(a865),x36781),f188(f872(a865,a860)))),f323(f245(a865),f323(a112,x36781)))
% 188.07/187.96 [3694]E(f323(f323(f78(a1),f323(f323(f22(a1),a81),x36941)),f323(f323(f22(a1),a81),x36941)),f323(f323(f22(a1),a81),f323(f323(f78(a1),x36941),x36941)))
% 188.07/187.96 [3710]E(f323(f323(f301(f872(x37101,a860)),f188(f872(x37101,a860))),f188(f872(f872(x37101,a860),a860))),f323(f300(x37101),f188(f872(x37101,a860))))
% 188.07/187.96 [3737]E(f323(f323(f22(f872(a865,a860)),f323(f295(a865),x37371)),f323(f323(f301(a865),f323(a112,x37371)),f188(f872(a865,a860)))),f323(f295(a865),f323(a112,x37371)))
% 188.07/187.96 [3746]E(f323(f323(f301(f869(x37461)),f200(x37461)),f323(f302(x37461,f869(x37461),f230(x37461)),f246(f872(x37461,a860)))),f246(f872(f869(x37461),a860)))
% 188.07/187.96 [3848]E(f323(f103(a865),f323(f323(f78(a1),x38481),x38481)),f323(f323(f84(a865,a865),f323(f103(a865),x38481)),f323(f323(f18(a865,a865,a865),f78(a865)),f5(a865))))
% 188.07/187.96 [4242]P17(x42421,f872(x42421,a860),f323(f323(f8(f872(x42421,a860),f872(f872(x42421,a860),f872(x42421,a860)),x42421),f323(f7(f872(x42421,a860),f872(x42421,a860),f872(x42421,a860)),f22(f872(x42421,a860)))),f323(f323(f7(x42421,f872(x42421,a860),f872(x42421,a860)),f301(x42421)),f188(f872(x42421,a860)))))
% 188.07/187.96 [4332]E(f323(f243(f871(a1,a1)),f323(f262(a1,a1,a860),f323(f323(f8(f872(a1,a860),f872(a1,a860),a1),f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f237(a1),x43321)))),f238(a1)))),f105(x43321))
% 188.07/187.96 [4366]E(f323(f243(f871(a1,a1)),f323(f262(a1,a1,a860),f323(f323(f18(a1,f872(a1,a860),f872(a1,a860)),f323(f323(f8(f872(a860,a860),f872(f872(a1,a860),f872(a1,a860)),a1),f8(a860,a860,a1)),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f237(a1),x43661)))),f238(a1)))),f106(x43661))
% 188.07/187.96 [4421]E(f323(f243(f871(f872(x44211,a860),f872(x44211,a860))),f323(f262(f872(x44211,a860),f872(x44211,a860),a860),f323(f323(f7(f872(x44211,a860),f872(f872(x44211,a860),a860),f872(f872(x44211,a860),a860)),f323(f323(f8(f872(f872(x44211,a860),f872(a860,a860)),f872(f872(f872(x44211,a860),a860),f872(f872(x44211,a860),a860)),f872(x44211,a860)),f18(f872(x44211,a860),a860,a860)),f323(f323(f8(f872(f872(x44211,a860),a860),f872(f872(x44211,a860),f872(a860,a860)),f872(x44211,a860)),f323(f8(a860,f872(a860,a860),f872(x44211,a860)),a322)),f238(f872(x44211,a860))))),f59(x44211)))),f298(x44211))
% 188.07/187.96 [4435]P26(a859,a874,f323(f323(f301(f864(a859)),f323(f323(f323(f90(a859),f323(f323(f8(f872(a861,a860),f872(a861,a860),a859),f323(f18(a861,a860,a860),f323(f323(f8(a860,f872(a860,a860),a861),a322),f323(a320,x44351)))),a873)),a875),a876)),f188(f872(f864(a859),a860))))
% 188.07/187.96 [4549]~P101(f323(f59(f866(x45491)),f246(f872(f866(x45491),a860))))
% 188.07/187.96 [4554]~P101(f323(f323(f89(a1),a97),f323(f323(f78(a1),x45541),x45541)))
% 188.07/187.96 [4564]~P101(f323(f323(f237(a1),f2(a1)),f323(f77(a1),f323(f100(a1),f323(a112,x45641)))))
% 188.07/187.96 [3459]E(f323(f323(f22(a1),f323(f323(f78(a1),x34591),a97)),a97),x34591)
% 188.07/187.96 [3475]E(f323(f166(a865),f132(a865,f323(f293(a865,f2(a865)),x34751))),f323(f244(a865),x34751))
% 188.07/187.96 [3716]E(f323(f323(f78(a1),f323(f323(f78(a1),f76(a1)),x37161)),x37161),f323(f323(f22(a1),f323(f323(f78(a1),x37161),x37161)),a97))
% 188.07/187.96 [3764]E(f323(f278(x37641,x37641),f299(x37641,f188(f872(f871(x37641,x37641),a860)))),f299(x37641,f188(f872(f871(x37641,x37641),a860))))
% 188.07/187.96 [3812]P101(f323(f323(f237(a865),x38121),f323(f323(f79(a865),x38121),f323(f323(f79(a865),x38121),x38121))))
% 188.07/187.96 [4096]P101(f323(f59(a865),f323(f243(a865),f323(f323(f7(a865,a865,a860),f237(a865)),x40961))))
% 188.07/187.96 [4097]P101(f323(f59(a865),f323(f243(a865),f323(f323(f7(a865,a865,a860),f238(a865)),x40971))))
% 188.07/187.96 [4386]E(f323(f243(f871(x43861,x43861)),f323(f323(f8(f872(x43861,a860),a860,f871(x43861,x43861)),f85(x43861)),f323(f323(f7(f871(x43861,x43861),f872(x43861,f871(x43861,x43861)),f872(x43861,a860)),f323(f323(f8(f872(f871(x43861,x43861),a860),f872(f872(x43861,f871(x43861,x43861)),f872(x43861,a860)),f871(x43861,x43861)),f8(f871(x43861,x43861),a860,x43861)),a320)),f323(f323(f18(x43861,x43861,f871(x43861,x43861)),f258(x43861,x43861)),f5(x43861))))),f299(x43861,f188(f872(f871(x43861,x43861),a860))))
% 188.07/187.96 [4551]~E(f323(f323(f22(a1),f323(f323(f78(a1),x45511),x45511)),a97),a81)
% 188.07/187.96 [4553]~E(f323(f323(f78(a1),f323(f323(f78(a1),f76(a1)),x45531)),x45531),f2(a1))
% 188.07/187.96 [4561]~P101(f323(f323(f89(a1),f323(f323(f78(a1),x45611),x45611)),a97))
% 188.07/187.96 [3861]E(f323(f323(f78(a1),f323(f323(f22(a1),a97),x38611)),f323(f323(f22(a1),a97),x38611)),f323(f323(f22(a1),a97),f323(f323(f22(a1),f323(f323(f78(a1),x38611),x38611)),a97)))
% 188.07/187.96 [3985]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),a97),x39851)),f323(f323(f22(a1),a97),x39851))),a97),f323(f323(f22(a1),a97),f323(f323(f78(a1),x39851),x39851)))
% 188.07/187.96 [4020]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f78(a1),x40201),a97)),f323(f323(f78(a1),x40201),a97))),a97),f323(f323(f78(a1),f323(f323(f78(a1),x40201),x40201)),a97))
% 188.07/187.96 [4058]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),a97),x40581)),f323(f323(f22(a1),a97),x40581))),a97),f323(f323(f22(a1),a81),f323(f323(f22(a1),f323(f323(f78(a1),x40581),x40581)),a97)))
% 188.07/187.96 [4158]E(f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x41581),f2(a865))),f188(f872(f871(a865,a865),a860))))),f323(f100(a1),x41581))
% 188.07/187.96 [4168]E(f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),f328(x41681)),f530(x41681))),f188(f872(f871(a865,a865),a860))))),x41681)
% 188.07/187.96 [4204]E(f323(f243(a1),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f237(a1),f2(a1)))),x42041)),f323(f302(a865,a1,f100(a1)),f323(f243(a865),f323(f323(f8(a1,a860,a865),x42041),f100(a1)))))
% 188.07/187.96 [4250]P39(f323(f243(a1),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f237(a1),f2(a1)))),x42501)))
% 188.07/187.96 [4271]P101(f323(f323(f325(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f258(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),x42711),f188(f872(f871(a865,a865),a860)))),a69))
% 188.07/187.96 [4277]E(f323(f302(a1,a865,a104),f323(f243(a1),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f237(a1),f2(a1)))),f323(f323(f8(a865,a860,a1),x42771),a104)))),f323(f243(a865),x42771))
% 188.07/187.96 [4436]E(f304(a865,f323(f323(f39(f871(a865,a865),f872(a865,a860)),f323(a107,x44361)),f323(f262(a865,a865,f872(a865,a860)),f323(f323(f7(a865,f872(a865,a860),f872(a865,f872(a865,a860))),f323(f323(f8(f872(a865,f872(f872(a865,a860),f872(a865,a860))),f872(f872(a865,a860),f872(a865,f872(a865,a860))),a865),f7(a865,f872(a865,a860),f872(a865,a860))),f323(f323(f8(f872(a865,a865),f872(a865,f872(f872(a865,a860),f872(a865,a860))),a865),f323(f8(a865,f872(f872(a865,a860),f872(a865,a860)),a865),f301(a865))),f22(a865)))),f188(f872(a865,a860)))))),f323(a104,x44361))
% 188.07/187.96 [4566]~P101(f323(f323(f89(a1),a81),f323(f323(f22(a1),f323(f323(f78(a1),x45661),x45661)),a97)))
% 188.07/187.96 [3906]E(f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),x39061),x39061)),a97)),a97),f323(f323(f78(a1),x39061),x39061))
% 188.07/187.96 [3958]E(f323(f323(f22(a1),f323(f323(f22(a1),f323(f323(f78(a1),x39581),x39581)),a97)),a97),f323(f323(f78(a1),f323(f323(f22(a1),x39581),a97)),f323(f323(f22(a1),x39581),a97)))
% 188.07/187.96 [4176]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f78(a1),f323(f77(a1),x41761)),a97)),f323(f323(f78(a1),f323(f77(a1),x41761)),a97))),a97),f323(f77(a1),f323(f323(f22(a1),f323(f323(f78(a1),x41761),x41761)),a97)))
% 188.07/187.96 [4574]~P101(f323(f323(f89(a1),f323(f323(f22(a1),f323(f323(f78(a1),x45741),x45741)),a97)),a81))
% 188.07/187.96 [4222]E(f323(f323(f78(a865),x42221),f323(f103(a865),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,x42221)))
% 188.07/187.96 [4223]E(f323(f323(f79(a865),x42231),f323(f103(a865),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(a865),x42231),x42231))
% 188.07/187.96 [4224]E(f323(f323(f36(a865),f323(f323(f78(a865),x42241),x42241)),f323(f103(a865),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)))),x42241)
% 188.07/187.96 [4307]E(f42(a865,f323(a112,f323(a112,x43071)),f323(f103(a865),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(a865,x43071,f323(f103(a865),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)))))
% 188.07/187.96 [4453]E(f323(a87,f323(f323(f39(f871(a865,a865),f872(f871(a865,a865),a860)),f323(a107,x44531)),f323(f262(a865,a865,f872(f871(a865,a865),a860)),f323(f323(f8(f872(a865,f872(f871(a865,a865),a860)),f872(a865,f872(f871(a865,a865),a860)),a865),f323(f8(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860),a865),f277(f871(a865,a865),f871(a865,a865),a108))),f323(f323(f7(a865,f872(f871(a865,a865),a860),f872(a865,f872(f871(a865,a865),a860))),f323(f323(f8(f872(a865,f872(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f872(f872(f871(a865,a865),a860),f872(a865,f872(f871(a865,a865),a860))),a865),f7(a865,f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f8(f872(a865,f871(a865,a865)),f872(a865,f872(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),a865),f323(f8(f871(a865,a865),f872(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),a865),f301(f871(a865,a865)))),f323(f7(a865,a865,f871(a865,a865)),f258(a865,a865))))),f188(f872(f871(a865,a865),a860))))))),f323(f77(a1),x44531))
% 188.07/187.96 [4302]E(f323(f323(f78(a865),f323(f103(a865),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)))),x43021),f323(a112,f323(a112,x43021)))
% 188.07/187.96 [4303]E(f323(f323(f79(a865),f323(f103(a865),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)))),x43031),f323(f323(f78(a865),x43031),x43031))
% 188.07/187.96 [4338]E(f323(f323(f36(a865),f323(a112,f323(a112,x43381))),f323(f103(a865),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(a865),x43381),f323(f103(a865),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))))))
% 188.07/187.96 [4392]E(f323(f323(f78(a865),f323(f103(a865),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))),x43921),f323(a112,f323(a112,f323(a112,x43921))))
% 188.07/187.96 [4467]E(f323(f262(a1,a1,f871(a1,a1)),f323(f323(f18(a1,f872(a1,f871(a1,a1)),f872(a1,f871(a1,a1))),f323(f323(f8(f872(a1,f872(f871(a1,a1),f871(a1,a1))),f872(f872(a1,f871(a1,a1)),f872(a1,f871(a1,a1))),a1),f18(a1,f871(a1,a1),f871(a1,a1))),f323(f323(f8(f872(a1,f871(a1,a1)),f872(a1,f872(f871(a1,a1),f871(a1,a1))),a1),f323(f18(a1,f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),f323(f323(f8(a860,f872(f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),a1),f96(f871(a1,a1))),f323(f323(f8(a1,a860,a1),f323(f237(a1),f2(a1))),f323(f323(f7(a1,a1,a1),f22(a1)),x44671))))),f323(f323(f7(a1,f872(a1,a1),f872(a1,f871(a1,a1))),f323(f323(f8(f872(a1,f871(a1,a1)),f872(f872(a1,a1),f872(a1,f871(a1,a1))),a1),f8(a1,f871(a1,a1),a1)),f323(f323(f8(a1,f872(a1,f871(a1,a1)),a1),f258(a1,a1)),f323(f323(f7(a1,a1,a1),f323(f323(f8(a1,f872(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)),x44671))))),f323(f323(f8(a1,f872(a1,f871(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(x44671))
% 188.07/187.96 [3128]P92(f870(x31281,x31282))
% 188.07/187.96 [3129]P92(f871(x31291,x31292))
% 188.07/187.96 [3130]P100(f870(x31301,x31302))
% 188.07/187.96 [3131]P100(f871(x31311,x31312))
% 188.07/187.96 [3148]P16(a1,f172(x31481,x31482))
% 188.07/187.96 [3149]P38(x31491,f146(x31491,x31492))
% 188.07/187.96 [3214]P32(x32141,x32142,f113(x32141))
% 188.07/187.96 [3249]P40(x32491,x32492,f255(x32491,x32492))
% 188.07/187.96 [3250]P51(x32501,x32501,f255(x32501,x32502))
% 188.07/187.96 [3522]P27(x35221,x35221,f5(x35221),x35222)
% 188.07/187.96 [3523]P27(x35231,x35231,f32(x35231),x35232)
% 188.07/187.96 [3531]P33(x35311,x35312,f113(x35311),f113(x35311))
% 188.07/187.96 [3532]P27(x35321,f869(x35321),f230(x35321),x35322)
% 188.07/187.96 [3541]P27(f866(x35411),f866(x35411),f162(x35411),x35412)
% 188.07/187.96 [3949]P28(x39491,x39491,f32(x39491),x39492,x39492)
% 188.07/187.96 [4477]~E(f30(x44771,x44772),a24)
% 188.07/187.96 [4478]~E(f29(x44781,x44782),a24)
% 188.07/187.96 [4479]~E(f25(x44791,x44792),a24)
% 188.07/187.96 [4508]~P34(x45081,x45082,f113(x45081))
% 188.07/187.96 [4509]~P36(x45091,x45092,f113(x45091))
% 188.07/187.96 [3114]E(f323(f243(x31141),x31142),x31142)
% 188.07/187.96 [3115]E(f323(f5(x31151),x31152),x31152)
% 188.07/187.96 [3117]E(f323(f32(x31171),x31172),x31172)
% 188.07/187.96 [3127]E(f323(f191(x31271),x31272),f115(x31271))
% 188.07/187.96 [3136]E(f28(f25(x31361,x31362)),f2(a865))
% 188.07/187.96 [3146]E(f83(x31461,f323(a320,x31462)),x31462)
% 188.07/187.96 [3147]E(f88(x31471,f323(a320,x31472)),x31472)
% 188.07/187.96 [3164]E(f323(f189(a862),f25(x31641,x31642)),f2(a865))
% 188.07/187.96 [3168]E(f323(f129(x31681,x31682),f113(x31681)),f113(x31681))
% 188.07/187.96 [3188]E(f145(x31881,f145(x31881,x31882)),f145(x31881,x31882))
% 188.07/187.96 [3189]E(f299(x31891,f299(x31891,x31892)),f299(x31891,x31892))
% 188.07/187.96 [3209]E(f323(f323(f121(x32091),x32092),f113(x32091)),x32092)
% 188.07/187.96 [3215]E(f167(x32151,x32152,f113(x32151)),x32152)
% 188.07/187.96 [3216]E(f167(x32161,f113(x32161),x32162),x32162)
% 188.07/187.96 [3217]E(f163(x32171,f2(a865),x32172),f113(x32171))
% 188.07/187.96 [3223]E(f323(f323(f169(x32231),x32232),f113(x32231)),f113(x32231))
% 188.07/187.96 [3224]E(f323(f323(f131(x32241),x32242),f113(x32241)),f113(x32241))
% 188.07/187.96 [3226]E(f231(x32261,x32262,f200(x32261)),f2(a865))
% 188.07/187.96 [3227]E(f148(x32271,x32272,f113(x32271)),f2(a865))
% 188.07/187.96 [3229]E(f164(x32291,x32292,f113(x32291)),f113(x32291))
% 188.07/187.96 [3230]E(f171(x32301,x32302,f113(x32301)),f113(x32301))
% 188.07/187.96 [3231]E(f170(x32311,f113(x32311),x32312),f113(x32311))
% 188.07/187.96 [3235]E(f323(f166(x32351),f145(x32351,x32352)),f323(f166(x32351),x32352))
% 188.07/187.96 [3238]E(f323(f254(x32381,x32381),f255(x32381,x32382)),x32382)
% 188.07/187.96 [3239]E(f323(f256(x32391,x32391),f255(x32391,x32392)),x32392)
% 188.07/187.96 [3248]E(f323(f278(x32481,x32481),f255(x32481,x32482)),f255(x32481,x32482))
% 188.07/187.96 [3263]E(f299(f866(x32631),f150(x32631,x32632)),f151(x32631,f299(x32631,x32632)))
% 188.07/187.96 [3265]P101(f323(f130(a1),f172(x32651,x32652)))
% 188.07/187.96 [3273]E(f323(f254(x32731,x32731),f299(x32731,x32732)),f246(f872(x32731,a860)))
% 188.07/187.96 [3274]E(f323(f256(x32741,x32741),f299(x32741,x32742)),f246(f872(x32741,a860)))
% 188.07/187.96 [3278]P101(f323(f130(x32781),f145(x32781,x32782)))
% 188.07/187.96 [3280]P101(f323(f153(x32801,x32802),f113(x32801)))
% 188.07/187.96 [3286]E(f323(f166(a1),f172(x32861,x32862)),f294(a1,x32861,x32862))
% 188.07/187.96 [3301]P52(x33011,f188(f872(x33011,a860)),x33012)
% 188.07/187.96 [3306]E(f323(f261(a1,a1),f43(x33061,x33062)),f42(a1,x33061,x33062))
% 188.07/187.96 [3307]E(f323(f293(a865,x33071),f323(a112,x33072)),f294(a865,x33071,x33072))
% 188.07/187.96 [3323]E(f323(f323(f144(x33231),x33232),f113(x33231)),f133(x33231,x33232,f113(x33231)))
% 188.07/187.96 [3335]E(f294(a865,f323(a112,x33351),x33352),f296(a865,x33351,x33352))
% 188.07/187.96 [3338]P40(x33381,f246(f872(x33381,a860)),f299(x33381,x33382))
% 188.07/187.96 [3401]E(f323(f323(f22(a865),x34011),f323(a112,x34012)),f323(f35(a865),f297(a865,x34012,x34011)))
% 188.07/187.96 [3460]E(f160(x34601,x34602,f113(x34601)),f323(f323(f258(f866(x34601),f866(x34601)),f113(x34601)),f113(x34601)))
% 188.07/187.96 [3479]E(f323(f262(x34791,x34792,f871(x34791,x34792)),f258(x34791,x34792)),f32(f871(x34791,x34792)))
% 188.07/187.96 [3483]P101(f323(f323(f325(f866(x34831)),f113(x34831)),f154(x34831,x34832)))
% 188.07/187.96 [3484]E(f323(f189(f866(x34841)),f114(x34841,x34842)),f323(f323(f22(a865),f323(f189(f866(x34841)),x34842)),f76(a865)))
% 188.07/187.96 [3492]P101(f323(f59(a865),f294(a865,x34921,x34922)))
% 188.07/187.96 [3493]P101(f323(f59(a865),f297(a865,x34931,x34932)))
% 188.07/187.96 [3494]P101(f323(f59(a865),f296(a865,x34941,x34942)))
% 188.07/187.96 [3495]P101(f323(f59(a1),f294(a1,x34951,x34952)))
% 188.07/187.96 [3496]P101(f323(f59(a1),f297(a1,x34961,x34962)))
% 188.07/187.96 [3497]P101(f323(f59(a1),f296(a1,x34971,x34972)))
% 188.07/187.96 [3602]E(f323(f302(a865,a865,a112),f294(a865,x36021,x36022)),f294(a865,f323(a112,x36021),f323(a112,x36022)))
% 188.07/187.96 [3620]E(f323(f323(f280(x36201,x36201,x36201),f299(x36201,x36202)),f299(x36201,x36202)),f299(x36201,x36202))
% 188.07/187.96 [3653]E(f323(f323(f258(a1,a1),f323(f323(f36(a1),x36531),x36532)),f42(a1,x36531,x36532)),f43(x36531,x36532))
% 188.07/187.96 [3654]E(f323(f323(f258(a99,a99),f323(f323(f36(a99),x36541),x36542)),f42(a99,x36541,x36542)),f21(x36541,x36542))
% 188.07/187.96 [3682]E(f323(f323(f258(a865,a865),f323(f323(f36(a865),x36821),x36822)),f42(a865,x36821,x36822)),f83(f871(a865,a865),f45(x36821,x36822)))
% 188.07/187.96 [3733]P101(f323(f323(f238(a865),f323(f323(f22(a865),x37331),x37332)),f323(a112,x37331)))
% 188.07/187.96 [3835]E(f323(f323(f78(a1),f323(f323(f79(a1),x38351),f323(f323(f36(a1),x38352),x38351))),f42(a1,x38352,x38351)),x38352)
% 188.07/187.96 [3839]E(f323(f323(f39(a865,f872(f871(f866(x38391),f866(x38391)),a860)),f246(f872(a865,a860))),f136(x38391,x38392)),f138(x38391,x38392))
% 188.07/187.96 [4071]P101(f323(f323(f325(f871(f866(x40711),f866(x40711))),f323(f323(f258(f866(x40711),f866(x40711)),f113(x40711)),f113(x40711))),f151(x40711,x40712)))
% 188.07/187.96 [4235]E(f263(x42351,x42351,x42352,x42352,f5(x42351),f5(x42352)),f32(f871(x42351,x42352)))
% 188.07/187.96 [4237]E(f263(x42371,x42371,x42372,x42372,f32(x42371),f32(x42372)),f32(f871(x42371,x42372)))
% 188.07/187.96 [4487]~E(f323(f230(x44871),x44872),f200(x44871))
% 188.07/187.96 [3207]E(f323(f234(x32071),f323(f230(x32071),x32072)),x32072)
% 188.07/187.96 [3208]E(f323(f162(x32081),f323(f162(x32081),x32082)),x32082)
% 188.07/187.96 [3210]E(f323(f323(f131(x32101),f2(a865)),x32102),x32102)
% 188.07/187.96 [3225]E(f323(f323(f169(x32251),f2(a865)),x32252),f113(x32251))
% 188.07/187.96 [3233]E(f323(f323(f121(x32331),f113(x32331)),x32332),x32332)
% 188.07/187.96 [3242]E(f323(f189(f869(x32421)),f323(f230(x32421),x32422)),f2(a865))
% 188.07/187.96 [3244]E(f37(f872(x32441,a860),f323(f300(x32441),x32442)),x32442)
% 188.07/187.96 [3246]E(f323(f166(x32461),f323(f161(x32461),x32462)),f323(f166(x32461),x32462))
% 188.07/187.96 [3247]E(f323(f166(x32471),f323(f162(x32471),x32472)),f323(f166(x32471),x32472))
% 188.07/187.96 [3252]E(f323(f323(f22(a99),x32521),x32522),f323(f323(a23,x32521),x32522))
% 188.07/187.96 [3267]E(f323(f323(f79(a865),x32671),x32672),f323(f323(f79(a865),x32672),x32671))
% 188.07/187.96 [3268]E(f323(f323(f79(a1),x32681),x32682),f323(f323(f79(a1),x32682),x32681))
% 188.07/187.96 [3269]E(f323(f323(f78(a865),x32691),x32692),f323(f323(f78(a865),x32692),x32691))
% 188.07/187.96 [3270]E(f323(f323(f78(a1),x32701),x32702),f323(f323(f78(a1),x32702),x32701))
% 188.07/187.96 [3293]E(f323(f323(f183(x32931,x32931),f2(a865)),x32932),f32(x32931))
% 188.07/187.96 [3294]E(f323(f189(f866(x32941)),f323(f161(x32941),x32942)),f323(f189(f866(x32941)),x32942))
% 188.07/187.96 [3295]E(f323(f189(f866(x32951)),f323(f162(x32951),x32952)),f323(f189(f866(x32951)),x32952))
% 188.07/187.96 [3296]E(f170(x32961,x32962,f188(f872(a865,a860))),f113(x32961))
% 188.07/187.96 [3297]E(f323(f323(f147(x32971,x32971),f5(x32971)),x32972),x32972)
% 188.07/187.96 [3299]E(f323(f257(a1,a1),f43(x32991,x32992)),f323(f323(f36(a1),x32991),x32992))
% 188.07/187.96 [3316]E(f323(f189(f866(x33161)),f145(x33161,x33162)),f323(f35(x33161),f323(f166(x33161),x33162)))
% 188.07/187.96 [3317]E(f28(f29(x33171,x33172)),f323(f323(f78(a865),f28(x33172)),f323(a112,f2(a865))))
% 188.07/187.96 [3318]E(f323(f276(x33181),f323(f278(x33181,x33181),x33182)),f323(f276(x33181),x33182))
% 188.07/187.96 [3322]P101(f323(f59(x33221),f323(f166(x33221),x33222)))
% 188.07/187.96 [3330]E(f323(f323(f78(a1),x33301),f323(f77(a1),x33302)),f323(f323(f22(a1),x33301),x33302))
% 188.07/187.96 [3337]P26(x33371,x33372,f188(f872(f864(x33371),a860)))
% 188.07/187.96 [3339]E(f323(f302(x33391,x33391,f5(x33391)),x33392),x33392)
% 188.07/187.96 [3340]E(f323(f302(x33401,x33401,f32(x33401)),x33402),x33402)
% 188.07/187.96 [3341]E(f323(f303(x33411,x33411,f5(x33411)),x33412),x33412)
% 188.07/187.96 [3342]E(f323(f303(x33421,x33421,f32(x33421)),x33422),x33422)
% 188.07/187.96 [3343]P101(f323(f246(f872(x33431,a860)),x33432))
% 188.07/187.96 [3345]E(f323(f35(a865),f323(f293(a865,x33451),x33452)),f323(f323(f22(a865),x33452),x33451))
% 188.07/187.96 [3346]E(f323(f293(a865,f323(a112,x33461)),x33462),f297(a865,x33461,x33462))
% 188.07/187.96 [3358]E(f323(f323(f301(x33581),x33582),f188(f872(x33581,a860))),f323(f243(x33581),f323(a320,x33582)))
% 188.07/187.96 [3362]E(f323(f323(f301(x33621),x33622),f188(f872(x33621,a860))),f229(x33621,f323(f230(x33621),x33622)))
% 188.07/187.96 [3365]E(f299(x33651,f323(f278(x33651,x33651),x33652)),f323(f278(x33651,x33651),f299(x33651,x33652)))
% 188.07/187.96 [3369]E(f323(f323(f78(a865),f323(a112,x33691)),x33692),f323(f323(f78(a865),x33691),f323(a112,x33692)))
% 188.07/187.96 [3370]E(f323(f323(f22(a865),f323(a112,x33701)),f323(a112,x33702)),f323(f323(f22(a865),x33701),x33702))
% 188.07/187.96 [3376]E(f52(x33761,f2(a865),x33762),f323(f323(f144(f866(x33761)),f113(x33761)),f113(f866(x33761))))
% 188.07/187.96 [3377]E(f323(f35(a865),f296(a865,x33771,x33772)),f323(f323(f22(a865),x33772),x33771))
% 188.07/187.96 [3386]P38(x33861,f323(f323(f279(a865,x33861),a242),x33862))
% 188.07/187.96 [3388]P16(a865,f132(a865,f323(f293(a865,x33881),x33882)))
% 188.07/187.96 [3390]P101(f323(f59(a865),f323(f293(a865,x33901),x33902)))
% 188.07/187.96 [3391]P101(f323(f59(a1),f323(f293(a1,x33911),x33912)))
% 188.07/187.96 [3394]E(f323(f278(f866(x33941),f866(x33941)),f150(x33941,x33942)),f150(x33941,f323(f278(x33941,x33941),x33942)))
% 188.07/187.96 [3395]E(f323(f189(a862),f29(x33951,x33952)),f323(f323(f78(a865),f323(f189(a862),x33952)),f323(a112,f2(a865))))
% 188.07/187.96 [3397]E(f323(f293(a1,x33971),f323(f323(f78(a1),x33972),f76(a1))),f294(a1,x33971,x33972))
% 188.07/187.96 [3400]E(f323(f323(f36(a1),f323(f77(a1),x34001)),f323(f77(a1),x34002)),f323(f323(f36(a1),x34001),x34002))
% 188.07/187.96 [3408]E(f177(x34081,x34082,f323(f16(f869(x34082),x34081),f200(x34082))),f188(f872(x34081,a860)))
% 188.07/187.96 [3409]E(f178(x34091,x34092,f323(f16(f869(x34092),x34091),f200(x34092))),f188(f872(x34092,a860)))
% 188.07/187.96 [3410]E(f323(f323(f183(f871(x34101,x34101),a860),f76(a865)),x34102),x34102)
% 188.07/187.96 [3412]E(f323(f323(f110(f872(x34121,a860)),x34122),f188(f872(x34121,a860))),x34122)
% 188.07/187.96 [3413]E(f323(f323(f22(f872(x34131,a860)),x34132),f188(f872(x34131,a860))),x34132)
% 188.07/187.96 [3414]E(f323(f323(f101(f872(x34141,a860)),x34142),f246(f872(x34141,a860))),x34142)
% 188.07/187.96 [3415]E(f323(f257(a865,a865),f83(f871(a865,a865),f45(x34151,x34152))),f323(f323(f36(a865),x34151),x34152))
% 188.07/187.96 [3422]E(f305(x34221,f323(a20,x34222),f323(f77(a1),f323(a20,x34222))),f323(f323(f308(a1),x34221),x34222))
% 188.07/187.96 [3423]E(f294(a1,f323(f323(f78(a1),x34231),f76(a1)),x34232),f296(a1,x34231,x34232))
% 188.07/187.96 [3428]E(f323(f261(a865,a865),f83(f871(a865,a865),f45(x34281,x34282))),f42(a865,x34281,x34282))
% 188.07/187.96 [3436]E(f306(x34361,f323(a20,x34362),f323(f77(a1),f323(a20,x34362))),f307(a1,x34361,x34362))
% 188.07/187.96 [3439]P101(f323(f323(f325(x34391),x34392),f246(f872(x34391,a860))))
% 188.07/187.96 [3444]E(f323(f323(f22(a865),f323(a112,x34441)),x34442),f323(f35(a865),f294(a865,x34442,x34441)))
% 188.07/187.96 [3471]E(f323(f323(f110(f872(x34711,a860)),x34712),f246(f872(x34711,a860))),f246(f872(x34711,a860)))
% 188.07/187.96 [3472]E(f323(f323(f22(f872(x34721,a860)),x34722),f246(f872(x34721,a860))),f188(f872(x34721,a860)))
% 188.07/187.96 [3473]E(f323(f323(f101(f872(x34731,a860)),x34732),f188(f872(x34731,a860))),f188(f872(x34731,a860)))
% 188.07/187.96 [3487]E(f42(a1,f323(f77(a1),x34871),f323(f77(a1),x34872)),f323(f77(a1),f42(a1,x34871,x34872)))
% 188.07/187.96 [3488]E(f42(a1,f323(f100(a1),x34881),f323(f100(a1),x34882)),f323(f100(a1),f42(a865,x34881,x34882)))
% 188.07/187.96 [3499]E(f323(f189(f866(x34991)),f323(f165(x34991),x34992)),f323(f323(f22(a865),f323(f189(f866(x34991)),x34992)),f76(a865)))
% 188.07/187.96 [3524]E(f323(f323(f36(a1),f42(a1,x35241,x35242)),x35242),f2(a1))
% 188.07/187.96 [3534]E(f323(a3,f42(a865,f323(a19,x35341),f323(a19,x35342))),f42(a99,x35341,x35342))
% 188.07/187.96 [3568]E(f323(a3,f323(f323(f22(a865),f323(a19,x35681)),f323(a19,x35682))),f323(f323(f22(a99),x35681),x35682))
% 188.07/187.96 [3569]E(f323(a3,f323(f323(f79(a865),f323(a19,x35691)),f323(a19,x35692))),f323(f323(f79(a99),x35691),x35692))
% 188.07/187.96 [3570]E(f323(a3,f323(f323(f78(a865),f323(a19,x35701)),f323(a19,x35702))),f323(f323(f78(a99),x35701),x35702))
% 188.07/187.96 [3571]E(f323(a3,f323(f323(f36(a865),f323(a19,x35711)),f323(a19,x35712))),f323(f323(f36(a99),x35711),x35712))
% 188.07/187.96 [3580]E(f323(f302(a865,a865,a112),f323(f293(a865,x35801),x35802)),f323(f293(a865,f323(a112,x35801)),f323(a112,x35802)))
% 188.07/187.96 [3607]P101(f323(f45(x36071,x36072),f83(f871(a865,a865),f45(x36071,x36072))))
% 188.07/187.96 [3626]E(f323(f323(f78(a865),f323(f323(f78(a865),f28(x36261)),f28(x36262))),f323(a112,f2(a865))),f28(f30(x36261,x36262)))
% 188.07/187.96 [3627]E(f42(a865,f323(a112,f42(a865,x36271,x36272)),x36272),f42(a865,f323(a112,x36271),x36272))
% 188.07/187.96 [3641]E(f323(f323(f39(f872(x36411,a860),f872(x36411,a860)),x36412),f5(f872(x36411,a860))),f37(f872(x36411,a860),x36412))
% 188.07/187.96 [3642]E(f323(f323(f40(f872(x36421,a860),f872(x36421,a860)),x36422),f5(f872(x36421,a860))),f38(f872(x36421,a860),x36422))
% 188.07/187.96 [3643]E(f323(f302(f866(x36431),f872(x36431,a860),f166(x36431)),f323(f166(f866(x36431)),f51(x36431,x36432))),f323(f300(x36431),f323(f166(x36431),x36432)))
% 188.07/187.96 [3646]P101(f323(f323(f325(f872(x36461,a860)),x36462),f323(f300(x36461),x36462)))
% 188.07/187.96 [3652]E(f42(a1,f323(f77(a1),f42(a1,x36521,x36522)),x36522),f42(a1,f323(f77(a1),x36521),x36522))
% 188.07/187.96 [3663]P101(f323(f323(f237(f872(x36631,a860)),x36632),f246(f872(x36631,a860))))
% 188.07/187.96 [3665]E(f323(f323(f280(x36651,x36651,x36651),f299(x36651,x36652)),f299(x36651,f299(x36651,x36652))),f299(x36651,x36652))
% 188.07/187.96 [3666]E(f323(f323(f110(f872(x36661,a860)),f323(f256(x36661,x36661),x36662)),f323(f254(x36661,x36661),x36662)),f323(f276(x36661),x36662))
% 188.07/187.96 [3687]E(f310(x36871,x36872,f246(f872(x36871,a860)),f246(f872(x36872,a860))),f246(f872(f870(x36871,x36872),a860)))
% 188.07/187.96 [3738]P101(f323(f323(f237(a865),f42(a865,x37381,x37382)),x37381))
% 188.07/187.96 [3762]P101(f323(f323(f237(a1),f323(f77(a1),f323(f100(a1),x37621))),f323(f100(a1),x37622)))
% 188.07/187.96 [3788]P101(f323(f323(f325(f872(x37881,a860)),f188(f872(x37881,a860))),f323(f300(x37881),x37882)))
% 188.07/187.96 [3793]E(f299(x37931,f323(f323(f280(x37931,x37931,x37931),x37932),f299(x37931,x37932))),f299(x37931,x37932))
% 188.07/187.96 [3796]E(f323(f323(f280(x37961,x37961,x37961),f299(x37961,x37962)),x37962),f323(f323(f280(x37961,x37961,x37961),x37962),f299(x37961,x37962)))
% 188.07/187.96 [3798]E(f323(a104,f323(f323(f78(a1),f323(f323(f22(a1),x37981),x37982)),f76(a1))),f323(f35(a1),f294(a1,x37982,x37981)))
% 188.07/187.96 [3813]E(f323(f254(x38131,x38131),f323(f323(f280(x38131,x38131,x38131),x38132),f299(x38131,x38132))),f323(f254(x38131,x38131),x38132))
% 188.07/187.96 [3814]E(f323(f256(x38141,x38141),f323(f323(f280(x38141,x38141,x38141),x38142),f299(x38141,x38142))),f323(f256(x38141,x38141),x38142))
% 188.07/187.96 [3831]E(f323(f323(f78(a865),f323(f323(f78(a865),f323(f189(a862),x38311)),f323(f189(a862),x38312))),f323(a112,f2(a865))),f323(f189(a862),f30(x38311,x38312)))
% 188.07/187.96 [3834]E(f323(f135(f866(x38341),f866(x38341),f121(x38341),f113(x38341)),f163(f866(x38341),x38342,f113(x38341))),f113(x38341))
% 188.07/187.96 [3843]P27(a865,a865,f323(f323(f7(a865,a865,a865),f78(a865)),x38431),x38432)
% 188.07/187.96 [3845]P16(a865,f323(f162(a865),f323(f323(f147(f866(x38451),a865),f189(f866(x38451))),f173(x38451,x38452))))
% 188.07/187.96 [3892]P101(f323(f323(f238(a1),f323(f77(a1),f323(f100(a1),f323(a112,x38921)))),f323(f100(a1),x38922)))
% 188.07/187.96 [3938]E(f323(f135(f866(x39381),x39381,f323(f7(x39381,f866(x39381),f866(x39381)),f144(x39381)),f113(x39381)),x39382),f323(f162(x39381),x39382))
% 188.07/187.96 [3992]P101(f323(f323(f237(f872(f871(f866(x39921),f866(x39921)),a860)),f151(x39921,x39922)),f299(f866(x39921),f150(x39921,x39922))))
% 188.07/187.96 [4024]P101(f323(f45(x40241,x40242),f323(f323(f258(a865,a865),f323(f323(f36(a865),x40241),x40242)),f42(a865,x40241,x40242))))
% 188.07/187.96 [4035]P101(f323(f323(f237(f872(f871(f866(x40351),f866(x40351)),a860)),f150(x40351,f299(x40351,x40352))),f299(f866(x40351),f150(x40351,x40352))))
% 188.07/187.96 [4261]E(f323(f323(f264(f871(a99,a99),a99,f871(a99,a99),f871(x42611,f871(a99,a99))),f268(f323(f159(a99),f323(f323(f147(f871(a99,x42611),a99),f257(a99,x42611)),x42612)))),f323(f323(f8(x42611,f872(f871(a99,a99),f871(x42611,f871(a99,a99))),a99),f258(x42611,f871(a99,a99))),f269(x42611,x42612))),f267(x42611,x42612))
% 188.07/187.96 [4374]E(f323(f232(a865,f871(x43741,f867(x43741)),f2(a865),f323(f262(x43741,f867(x43741),a865),f323(f16(f872(f867(x43741),a865),x43741),f323(f323(f7(f867(x43741),a865,a865),f323(f323(f8(a865,f872(a865,a865),f867(x43741)),f78(a865)),f189(f867(x43741)))),f76(a865))))),f323(f128(x43741),x43742)),f323(f189(f867(x43741)),x43742))
% 188.07/187.96 [4452]E(f323(f262(f872(f871(x44521,x44521),a860),f872(f871(x44521,x44521),a860),f872(f872(x44522,x44521),f871(f872(f871(x44522,x44522),a860),f872(f871(x44522,x44522),a860)))),f323(f323(f7(f872(f871(x44521,x44521),a860),f872(f872(f871(x44521,x44521),a860),f872(f872(x44522,x44521),f872(f871(x44522,x44522),a860))),f872(f872(f871(x44521,x44521),a860),f872(f872(x44522,x44521),f871(f872(f871(x44522,x44522),a860),f872(f871(x44522,x44522),a860))))),f323(f323(f8(f872(f872(f872(x44522,x44521),f872(f871(x44522,x44522),a860)),f872(f872(x44522,x44521),f871(f872(f871(x44522,x44522),a860),f872(f871(x44522,x44522),a860)))),f872(f872(f872(f871(x44521,x44521),a860),f872(f872(x44522,x44521),f872(f871(x44522,x44522),a860))),f872(f872(f871(x44521,x44521),a860),f872(f872(x44522,x44521),f871(f872(f871(x44522,x44522),a860),f872(f871(x44522,x44522),a860))))),f872(f871(x44521,x44521),a860)),f8(f872(f872(x44522,x44521),f872(f871(x44522,x44522),a860)),f872(f872(x44522,x44521),f871(f872(f871(x44522,x44522),a860),f872(f871(x44522,x44522),a860))),f872(f871(x44521,x44521),a860))),f323(f323(f8(f872(f872(x44522,x44521),f872(f872(f871(x44522,x44522),a860),f871(f872(f871(x44522,x44522),a860),f872(f871(x44522,x44522),a860)))),f872(f872(f872(x44522,x44521),f872(f871(x44522,x44522),a860)),f872(f872(x44522,x44521),f871(f872(f871(x44522,x44522),a860),f872(f871(x44522,x44522),a860)))),f872(f871(x44521,x44521),a860)),f18(f872(x44522,x44521),f872(f871(x44522,x44522),a860),f871(f872(f871(x44522,x44522),a860),f872(f871(x44522,x44522),a860)))),f323(f323(f8(f872(f872(x44522,x44521),f872(f871(x44522,x44522),a860)),f872(f872(x44522,x44521),f872(f872(f871(x44522,x44522),a860),f871(f872(f871(x44522,x44522),a860),f872(f871(x44522,x44522),a860)))),f872(f871(x44521,x44521),a860)),f323(f8(f872(f871(x44522,x44522),a860),f872(f872(f871(x44522,x44522),a860),f871(f872(f871(x44522,x44522),a860),f872(f871(x44522,x44522),a860))),f872(x44522,x44521)),f258(f872(f871(x44522,x44522),a860),f872(f871(x44522,x44522),a860)))),f279(x44521,x44522))))),f279(x44521,x44522))),f72(x44521,x44522))
% 188.07/187.96 [4534]~E(f323(f300(x45341),x45342),f188(f872(f872(x45341,a860),a860)))
% 188.07/187.96 [4548]~P101(f323(f323(f325(x45481),x45482),f188(f872(x45481,a860))))
% 188.07/187.96 [4558]~P101(f323(f323(f238(f872(x45581,a860)),x45582),f188(f872(x45581,a860))))
% 188.07/187.96 [3348]E(f323(f323(f22(a865),x33481),f323(f323(f78(a865),x33481),x33482)),f2(a865))
% 188.07/187.96 [3350]E(f323(f323(f110(f872(x33501,a860)),x33502),x33502),x33502)
% 188.07/187.96 [3351]E(f323(f323(f101(f872(x33511,a860)),x33512),x33512),x33512)
% 188.07/187.96 [3379]E(f323(f323(f22(f872(x33791,a860)),x33792),x33792),f188(f872(x33791,a860)))
% 188.07/187.96 [3382]E(f323(f136(x33821,x33822),f2(a865)),f188(f872(f871(f866(x33821),f866(x33821)),a860)))
% 188.07/187.96 [3383]E(f323(f323(f78(a865),x33831),f323(a112,x33832)),f323(a112,f323(f323(f78(a865),x33831),x33832)))
% 188.07/187.96 [3396]E(f194(f323(f100(a1),x33961),f323(f100(a1),x33962)),f323(f100(a1),f323(f323(f22(a865),x33961),x33962)))
% 188.07/187.96 [3399]E(f323(f323(f36(a1),f323(f77(a1),x33991)),x33992),f323(f323(f36(a1),x33991),f323(f77(a1),x33992)))
% 188.07/187.96 [3403]E(f323(f35(a1),f323(f293(a1,x34031),x34032)),f323(a104,f323(f323(f22(a1),x34032),x34031)))
% 188.07/187.96 [3406]E(f323(f323(f78(a865),f323(a112,x34061)),x34062),f323(a112,f323(f323(f78(a865),x34061),x34062)))
% 188.07/187.96 [3411]E(f323(f77(f872(x34111,a860)),f323(f77(f872(x34111,a860)),x34112)),x34112)
% 188.07/187.96 [3425]E(f173(x34251,f323(f323(f144(f866(x34251)),f113(x34251)),x34252)),f173(x34251,x34252))
% 188.07/187.96 [3429]E(f323(f323(f78(a865),x34291),f323(f323(f79(a865),x34291),x34292)),f323(f323(f79(a865),x34291),f323(a112,x34292)))
% 188.07/187.96 [3437]E(f323(f323(a23,f323(a3,x34371)),f323(a3,x34372)),f323(a3,f323(f323(f22(a865),x34371),x34372)))
% 188.07/187.96 [3451]E(f323(f323(f79(a1),f323(f77(a1),x34511)),x34512),f323(f77(a1),f323(f323(f79(a1),x34511),x34512)))
% 188.07/187.96 [3453]E(f323(f323(f248(a1),f323(f100(a1),x34531)),x34532),f323(f100(a1),f323(f323(f248(a865),x34531),x34532)))
% 188.07/187.96 [3454]E(f323(f323(f79(a99),f323(a3,x34541)),f323(a3,x34542)),f323(a3,f323(f323(f79(a865),x34541),x34542)))
% 188.07/187.96 [3455]E(f323(f323(f78(a99),f323(a3,x34551)),f323(a3,x34552)),f323(a3,f323(f323(f78(a865),x34551),x34552)))
% 188.07/187.96 [3456]E(f323(f323(f235(a865),f323(a112,x34561)),f323(a112,x34562)),f323(a112,f323(f323(f235(a865),x34561),x34562)))
% 188.07/187.96 [3457]E(f323(f323(f236(a865),f323(a112,x34571)),f323(a112,x34572)),f323(a112,f323(f323(f236(a865),x34571),x34572)))
% 188.07/187.96 [3463]E(f323(f166(a865),f132(a865,f323(f293(a865,x34631),x34632))),f323(f293(a865,x34631),x34632))
% 188.07/187.96 [3464]E(f304(x34641,f323(f323(f301(x34641),x34642),f188(f872(x34641,a860)))),x34642)
% 188.07/187.96 [3469]E(f323(f254(x34691,x34692),f188(f872(f871(x34691,x34692),a860))),f188(f872(x34692,a860)))
% 188.07/187.96 [3470]E(f323(f256(x34701,x34702),f188(f872(f871(x34701,x34702),a860))),f188(f872(x34701,a860)))
% 188.07/187.96 [3474]E(f323(a104,f323(f323(f22(a1),x34741),x34742)),f323(f35(a1),f296(a1,x34742,x34741)))
% 188.07/187.96 [3478]E(f323(f323(f78(a865),x34781),f323(f323(f79(a865),x34782),x34781)),f323(f323(f79(a865),f323(a112,x34782)),x34781))
% 188.07/187.96 [3480]E(f323(f323(f58(x34801),f188(f872(x34801,a860))),x34802),f188(f872(f872(x34801,a860),a860)))
% 188.07/187.96 [3489]E(f323(f189(f866(a865)),f132(a865,f323(f293(a865,x34891),x34892))),f323(f323(f22(a865),x34892),x34891))
% 188.07/187.96 [3504]E(f323(f323(f110(f872(x35041,a860)),f188(f872(x35041,a860))),x35042),x35042)
% 188.07/187.96 [3505]E(f323(f323(f101(f872(x35051,a860)),f246(f872(x35051,a860))),x35052),x35052)
% 188.07/187.96 [3506]E(f323(f323(f78(a1),f323(f77(a1),x35061)),f323(f77(a1),x35062)),f323(f77(a1),f323(f323(f78(a1),x35061),x35062)))
% 188.07/187.96 [3511]E(f323(f323(f79(a1),f323(f100(a1),x35111)),f323(f100(a1),x35112)),f323(f100(a1),f323(f323(f79(a865),x35111),x35112)))
% 188.07/187.96 [3512]E(f323(f323(f79(a1),f323(f103(a1),x35121)),f323(f103(a1),x35122)),f323(f103(a1),f323(f323(f79(a1),x35121),x35122)))
% 188.07/187.96 [3514]E(f323(f323(f78(a1),f323(f100(a1),x35141)),f323(f100(a1),x35142)),f323(f100(a1),f323(f323(f78(a865),x35141),x35142)))
% 188.07/187.96 [3515]E(f323(f323(f78(a1),f323(f103(a1),x35151)),f323(f103(a1),x35152)),f323(f103(a1),f323(f323(f78(a1),x35151),x35152)))
% 188.07/187.96 [3516]E(f323(f323(f36(a1),f323(f100(a1),x35161)),f323(f100(a1),x35162)),f323(f100(a1),f323(f323(f36(a865),x35161),x35162)))
% 188.07/187.96 [3535]E(f323(f323(f6(x35351,a865),f323(f16(a865,x35351),f76(a865))),x35352),f323(f35(x35351),x35352))
% 188.07/187.96 [3542]E(f323(f77(a1),f42(a1,f323(f77(a1),x35421),x35422)),f42(a1,x35421,f323(f77(a1),x35422)))
% 188.07/187.96 [3544]E(f323(f166(a1),f172(x35441,f323(f323(f22(a1),x35442),f76(a1)))),f323(f293(a1,x35441),x35442))
% 188.07/187.96 [3549]P101(f323(f323(f237(a865),x35491),f323(f323(f78(a865),x35492),x35491)))
% 188.07/187.96 [3550]P101(f323(f323(f237(a865),x35501),f323(f323(f78(a865),x35501),x35502)))
% 188.07/187.96 [3552]E(f323(f323(f110(f872(x35521,a860)),f246(f872(x35521,a860))),x35522),f246(f872(x35521,a860)))
% 188.07/187.96 [3553]E(f323(f323(f22(f872(x35531,a860)),f188(f872(x35531,a860))),x35532),f188(f872(x35531,a860)))
% 188.07/187.96 [3554]E(f323(f323(f101(f872(x35541,a860)),f188(f872(x35541,a860))),x35542),f188(f872(x35541,a860)))
% 188.07/187.96 [3560]E(f323(f323(f258(a1,a1),x35601),f323(f77(a1),x35602)),f323(a48,f323(f323(f258(a1,a1),x35601),x35602)))
% 188.07/187.96 [3561]E(f323(f293(a1,f323(f323(f78(a1),x35611),f76(a1))),x35612),f297(a1,x35611,x35612))
% 188.07/187.96 [3572]E(f323(f323(f79(a865),x35721),f323(f323(f36(a865),x35722),x35721)),f323(f323(f22(a865),x35722),f42(a865,x35722,x35721)))
% 188.07/187.96 [3573]E(f323(f323(f79(a1),x35731),f323(f323(f36(a1),x35732),x35731)),f323(f323(f22(a1),x35732),f42(a1,x35732,x35731)))
% 188.07/187.96 [3577]E(f323(f166(a1),f172(f323(f323(f78(a1),x35771),f76(a1)),x35772)),f296(a1,x35771,x35772))
% 188.07/187.96 [3581]P101(f323(f323(f237(f872(x35811,a860)),x35812),x35812))
% 188.07/187.96 [3584]E(f323(f323(f110(f872(x35841,a860)),x35842),f323(f77(f872(x35841,a860)),x35842)),f246(f872(x35841,a860)))
% 188.07/187.96 [3585]E(f323(f323(f101(f872(x35851,a860)),x35852),f323(f77(f872(x35851,a860)),x35852)),f188(f872(x35851,a860)))
% 188.07/187.96 [3593]E(f323(f323(f22(a865),f323(f323(f22(a865),x35931),f76(a865))),x35932),f323(f323(f22(a865),x35931),f323(a112,x35932)))
% 188.07/187.96 [3599]E(f323(f323(f22(f872(x35991,a860)),f246(f872(x35991,a860))),x35992),f323(f77(f872(x35991,a860)),x35992))
% 188.07/187.96 [3600]E(f323(f323(f22(a1),f323(f103(a1),x36001)),f323(f103(a1),x36002)),f323(f103(a1),f323(f323(f78(a1),x36001),f323(f77(a1),x36002))))
% 188.07/187.96 [3612]E(f323(f166(a865),f132(a865,f323(f293(a865,x36121),f323(a112,x36122)))),f294(a865,x36121,x36122))
% 188.07/187.96 [3624]E(f323(f189(f866(f866(x36241))),f51(x36241,x36242)),f323(f323(f248(a865),f323(a112,f323(a112,f2(a865)))),f323(f189(f866(x36241)),x36242)))
% 188.07/187.96 [3644]E(f323(f323(f183(f871(x36441,x36441),a860),f2(a865)),x36442),f299(x36441,f188(f872(f871(x36441,x36441),a860))))
% 188.07/187.96 [3648]P101(f323(f130(a865),f132(a865,f323(f293(a865,x36481),x36482))))
% 188.07/187.96 [3664]E(f323(f302(a1,a865,a104),f294(a1,f323(f100(a1),x36641),f323(f100(a1),x36642))),f294(a865,x36641,x36642))
% 188.07/187.96 [3674]E(f185(a865,f2(a865),f5(a865),f323(f323(f22(a865),x36741),x36742)),f323(f323(f22(a865),x36741),f323(a112,x36742)))
% 188.07/187.96 [3675]E(f323(a104,f323(f323(f22(a1),x36751),f323(f323(f78(a1),x36752),f76(a1)))),f323(f35(a1),f297(a1,x36752,x36751)))
% 188.07/187.96 [3711]E(f323(f323(f147(a865,a865),a112),f132(a865,f323(f293(a865,x37111),x37112))),f132(a865,f323(f293(a865,f323(a112,x37111)),f323(a112,x37112))))
% 188.07/187.96 [3718]E(f323(f166(a1),f172(f323(f323(f78(a1),x37181),f76(a1)),f323(f323(f22(a1),x37182),f76(a1)))),f297(a1,x37181,x37182))
% 188.07/187.96 [3729]P101(f323(f323(f237(f872(x37291,a860)),f188(f872(x37291,a860))),x37292))
% 188.07/187.96 [3734]E(f83(x37341,f323(f323(f7(x37341,x37341,a860),a320),x37342)),x37342)
% 188.07/187.96 [3735]E(f88(x37351,f323(f323(f7(x37351,x37351,a860),a320),x37352)),x37352)
% 188.07/187.96 [3739]E(f323(f166(a865),f132(a865,f323(f293(a865,f323(a112,x37391)),f323(a112,x37392)))),f296(a865,x37391,x37392))
% 188.07/187.96 [3765]E(f323(f323(f260(x37651,x37652),f246(f872(x37651,a860))),f323(f16(f872(x37652,a860),x37651),f246(f872(x37652,a860)))),f246(f872(f871(x37651,x37652),a860)))
% 188.07/187.96 [3800]E(f323(f243(x38001),f323(f323(f8(a860,a860,x38001),a318),x38002)),f323(f77(f872(x38001,a860)),f323(f243(x38001),x38002)))
% 188.07/187.96 [3803]E(f323(f243(x38031),f323(f323(f7(x38031,x38031,a860),a320),x38032)),f323(f323(f301(x38031),x38032),f188(f872(x38031,a860))))
% 188.07/187.96 [3810]E(f323(f323(f78(a1),f323(f323(f22(a1),x38101),x38102)),f323(f323(f22(a1),x38101),x38102)),f323(f323(f22(a1),f323(f323(f78(a1),x38101),x38101)),f323(f323(f78(a1),x38102),x38102)))
% 188.07/187.96 [3811]E(f323(f323(f78(a1),f323(f323(f78(a1),x38111),x38111)),f323(f323(f78(a1),x38112),x38112)),f323(f323(f78(a1),f323(f323(f78(a1),x38111),x38112)),f323(f323(f78(a1),x38111),x38112)))
% 188.07/187.96 [3823]P26(x38231,f323(f323(f301(f864(x38231)),x38232),f188(f872(f864(x38231),a860))),f323(f323(f301(f864(x38231)),x38232),f188(f872(f864(x38231),a860))))
% 188.07/187.96 [3828]P101(f323(f323(f237(a865),f323(f35(x38281),f323(f166(x38281),x38282))),f323(f189(f866(x38281)),x38282)))
% 188.07/187.96 [3829]P101(f323(f323(f237(a865),f323(f189(f866(x38291)),f145(x38291,x38292))),f323(f189(f866(x38291)),x38292)))
% 188.07/187.96 [3840]E(f323(f243(x38401),f323(f323(f7(x38401,f872(x38401,a860),a860),f325(x38401)),x38402)),x38402)
% 188.07/187.96 [3856]E(f323(f323(f169(x38561),f323(f323(f22(a865),f323(f189(f866(x38561)),x38562)),f76(a865))),x38562),f114(x38561,x38562))
% 188.07/187.96 [3879]E(f185(a865,f2(a865),f323(f323(f8(a865,a865,a865),a112),f323(f235(a865),x38791)),x38792),f323(f323(f235(a865),f323(a112,x38791)),x38792))
% 188.07/187.96 [3883]E(f37(f872(x38831,a860),f323(f302(f872(f871(x38831,x38831),a860),f872(x38831,a860),f276(x38831)),x38832)),f323(f276(x38831),f37(f872(f871(x38831,x38831),a860),x38832)))
% 188.07/187.96 [3884]E(f185(a865,f323(a112,x38841),f323(f323(f8(a865,a865,a865),a112),f323(f236(a865),x38841)),x38842),f323(f323(f236(a865),f323(a112,x38841)),x38842))
% 188.07/187.96 [3886]E(f323(f323(f258(a1,a1),f323(f323(f36(a1),f323(f73(a1),x38861)),f323(f73(a1),x38862))),f42(a1,f323(f73(a1),x38861),f323(f73(a1),x38862))),f50(x38861,x38862))
% 188.07/187.96 [3909]P101(f323(f323(f237(f872(f872(x39091,a860),a860)),x39092),f323(f300(x39091),f37(f872(x39091,a860),x39092))))
% 188.07/187.96 [3943]E(f323(f323(f39(x39431,f872(x39431,a860)),x39432),f323(f323(f7(x39431,f872(x39431,a860),f872(x39431,a860)),f301(x39431)),f188(f872(x39431,a860)))),x39432)
% 188.07/187.96 [3944]E(f323(f323(f280(x39441,x39441,x39441),f323(f278(x39441,x39441),x39442)),f299(x39441,f323(f278(x39441,x39441),x39442))),f323(f278(x39441,x39441),f323(f323(f280(x39441,x39441,x39441),x39442),f299(x39441,x39442))))
% 188.07/187.96 [4015]E(f323(f166(x40151),f323(f135(f866(x40151),f866(x40151),f121(x40151),f113(x40151)),x40152)),f323(f323(f39(f866(x40151),f872(x40151,a860)),f323(f166(f866(x40151)),x40152)),f166(x40151)))
% 188.07/187.96 [4047]E(f323(f323(f110(f872(f871(x40471,x40471),a860)),f299(x40471,f188(f872(f871(x40471,x40471),a860)))),f323(f323(f280(x40471,x40471,x40471),f299(x40471,x40472)),x40472)),f299(x40471,x40472))
% 188.07/187.96 [4081]E(f323(f323(f175(x40811,x40811),x40812),x40812),f323(f323(f147(x40811,f871(x40811,x40811)),f323(f323(f18(x40811,x40811,f871(x40811,x40811)),f258(x40811,x40811)),f5(x40811))),x40812))
% 188.07/187.96 [4198]E(f323(f135(a865,f866(x41981),f323(f7(f866(x41981),a865,a865),f323(f323(f8(a865,f872(a865,a865),f866(x41981)),f236(a865)),f189(f866(x41981)))),f2(a865)),f323(f162(f866(x41981)),x41982)),f323(f189(f866(f866(x41981))),f173(x41981,x41982)))
% 188.07/187.96 [4276]E(f323(f323(f279(f871(a865,f866(x42761)),f866(x42761)),f315(a865,f866(x42761),a242,f138(x42761,x42762))),f323(f323(f18(f866(x42761),f866(x42761),f871(a865,f866(x42761))),f323(f323(f8(a865,f872(f866(x42761),f871(a865,f866(x42761))),f866(x42761)),f258(a865,f866(x42761))),f189(f866(x42761)))),f5(f866(x42761)))),f139(x42761,x42762))
% 188.07/187.96 [4408]E(f323(f243(x44081),f323(f323(f8(f872(f872(x44081,a860),a860),a860,x44081),f86(f872(x44081,a860))),f323(f323(f8(f872(f872(x44081,a860),a860),f872(f872(x44081,a860),a860),x44081),f323(f18(f872(x44081,a860),a860,a860),f323(f323(f8(a860,f872(a860,a860),f872(x44081,a860)),a326),f323(f323(f7(f872(x44081,a860),f872(f872(x44081,a860),a860),a860),f325(f872(x44081,a860))),x44082)))),f325(x44081)))),f38(f872(x44081,a860),x44082))
% 188.07/187.96 [4559]~P101(f323(f323(f238(a1),f323(f100(a1),x45591)),f323(f77(a1),f323(f100(a1),x45592))))
% 188.07/187.96 [4575]~P101(f323(f323(f89(a1),f323(f323(f22(a1),f323(f323(f78(a1),x45751),x45751)),a97)),f323(f323(f78(a1),x45752),x45752)))
% 188.07/187.96 [3476]E(f323(f323(f22(a865),f323(f323(f78(a865),x34761),x34762)),x34762),x34761)
% 188.07/187.96 [3477]E(f323(f323(f22(a865),f323(f323(f78(a865),x34771),x34772)),x34771),x34772)
% 188.07/187.96 [3543]E(f323(f323(f78(a865),f323(f323(f22(a865),x35431),x35432)),x35432),f323(f323(f236(a865),x35431),x35432))
% 188.07/187.96 [3651]E(f323(f323(f79(a865),f323(f323(f36(a865),x36511),x36512)),x36512),f323(f323(f22(a865),x36511),f42(a865,x36511,x36512)))
% 188.07/187.96 [3679]E(f323(f166(a865),f132(a865,f323(f293(a865,f323(a112,x36791)),x36792))),f297(a865,x36791,x36792))
% 188.07/187.96 [3686]E(f323(f100(a1),f218(f323(a104,f323(f73(a1),x36861)),f323(a104,f323(f73(a1),x36862)))),f323(f323(a219,x36861),x36862))
% 188.07/187.96 [3688]E(f323(f323(f110(f872(x36881,a860)),f323(f77(f872(x36881,a860)),x36882)),x36882),f246(f872(x36881,a860)))
% 188.07/187.96 [3689]E(f323(f323(f101(f872(x36891,a860)),f323(f77(f872(x36891,a860)),x36892)),x36892),f188(f872(x36891,a860)))
% 188.07/187.96 [3707]P101(f323(f323(f237(a865),f323(f323(f22(a865),x37071),x37072)),x37071))
% 188.07/187.96 [3708]P101(f323(f323(f237(a865),f323(f323(f36(a865),x37081),x37082)),x37081))
% 188.07/187.96 [3731]P101(f323(f323(f238(a865),x37311),f323(a112,f323(f323(f78(a865),x37312),x37311))))
% 188.07/187.96 [3732]P101(f323(f323(f238(a865),x37321),f323(a112,f323(f323(f78(a865),x37321),x37322))))
% 188.07/187.96 [3750]E(f323(f323(f79(a865),f323(a104,f323(f73(a1),x37501))),f323(a104,f323(f73(a1),x37502))),f323(a104,f323(f73(a1),f323(f323(f79(a1),x37501),x37502))))
% 188.07/187.96 [3761]P101(f323(f323(f237(a1),f2(a1)),f323(f323(f248(a1),f323(f73(a1),x37611)),x37612)))
% 188.07/187.96 [3833]E(f323(f277(f866(x38331),f866(x38331),f151(x38331,x38332)),f323(f323(f301(f866(x38331)),f113(x38331)),f188(f872(f866(x38331),a860)))),f323(f323(f301(f866(x38331)),f113(x38331)),f188(f872(f866(x38331),a860))))
% 188.07/187.96 [3854]E(f323(f323(f110(f872(f871(x38541,x38541),a860)),f299(x38541,x38542)),f299(x38541,f188(f872(f871(x38541,x38541),a860)))),f299(x38541,x38542))
% 188.07/187.96 [3869]E(f323(f323(f36(a1),f323(f103(a1),f323(f323(f78(a1),x38691),x38691))),f323(f103(a1),f323(f323(f78(a1),x38692),x38692))),f323(f323(f36(a1),f323(f103(a1),x38691)),f323(f103(a1),x38692)))
% 188.07/187.96 [3933]E(f323(f323(f248(a1),x39331),f323(f103(a865),f323(f323(f78(a1),x39332),x39332))),f323(f323(f84(a1,a1),f323(f323(f248(a1),x39331),f323(f103(a865),x39332))),f323(f323(f18(a1,a1,a1),f79(a1)),f5(a1))))
% 188.07/187.96 [3939]E(f323(f243(f872(x39391,a860)),f323(f323(f7(f872(x39391,a860),f872(x39391,a860),a860),f237(f872(x39391,a860))),x39392)),f323(f300(x39391),x39392))
% 188.07/187.96 [3955]E(f323(f323(f147(a1,a865),a104),f323(f323(f121(a1),f323(f323(f147(a865,a1),f100(a1)),x39551)),f323(f323(f147(a865,a1),f100(a1)),x39552))),f323(f323(f121(a865),x39551),x39552))
% 188.07/187.96 [3991]E(f323(f302(a1,a1,f323(f323(f7(a1,a1,a1),f78(a1)),x39911)),f323(f293(a1,f2(a1)),f323(f323(f22(a1),x39912),x39911))),f323(f293(a1,x39911),x39912))
% 188.07/187.96 [3993]P42(x39931,f323(f323(f22(f872(f871(x39931,x39931),a860)),x39932),f299(x39931,f188(f872(f871(x39931,x39931),a860)))))
% 188.07/187.96 [4013]E(f323(f189(f866(x40131)),f323(f135(f866(x40131),f866(x40131),f121(x40131),f113(x40131)),x40132)),f323(f159(a865),f323(f323(f147(f866(x40131),a865),f189(f866(x40131))),x40132)))
% 188.07/187.96 [4018]P40(x40181,f246(f872(x40181,a860)),f323(f323(f110(f872(f871(x40181,x40181),a860)),x40182),f299(x40181,f188(f872(f871(x40181,x40181),a860)))))
% 188.07/187.96 [4061]E(f185(a865,f2(a865),f323(f323(f8(a865,a865,a865),a112),f323(f323(f7(a865,a865,a865),f235(a865)),x40611)),x40612),f323(f323(f235(a865),x40612),f323(a112,x40611)))
% 188.07/187.96 [4064]E(f185(a865,f323(a112,x40641),f323(f323(f8(a865,a865,a865),a112),f323(f323(f7(a865,a865,a865),f236(a865)),x40641)),x40642),f323(f323(f236(a865),x40642),f323(a112,x40641)))
% 188.07/187.96 [4067]E(f323(f302(x40671,f866(x40671),f323(f323(f7(x40671,f866(x40671),f866(x40671)),f144(x40671)),f113(x40671))),x40672),f168(x40671,x40672,f323(f323(f301(f866(x40671)),f113(x40671)),f188(f872(f866(x40671),a860)))))
% 188.07/187.96 [4068]E(f323(f323(f110(f872(f871(x40681,x40681),a860)),f323(f323(f280(x40681,x40681,x40681),x40682),f299(x40681,x40682))),f299(x40681,f188(f872(f871(x40681,x40681),a860)))),f299(x40681,x40682))
% 188.07/187.96 [4076]P101(f323(f323(f237(f872(f871(x40761,x40761),a860)),f255(x40761,x40762)),f323(f323(f260(x40761,x40761),x40762),f323(f16(f872(x40761,a860),x40761),x40762))))
% 188.07/187.96 [4079]E(f323(f302(a1,a865,a104),f323(f323(f110(f872(a1,a860)),f323(f302(a865,a1,f100(a1)),x40791)),f323(f302(a865,a1,f100(a1)),x40792))),f323(f323(f110(f872(a865,a860)),x40791),x40792))
% 188.07/187.96 [4080]E(f323(f302(a1,a865,a104),f323(f323(f101(f872(a1,a860)),f323(f302(a865,a1,f100(a1)),x40801)),f323(f302(a865,a1,f100(a1)),x40802))),f323(f323(f101(f872(a865,a860)),x40801),x40802))
% 188.07/187.96 [4084]E(f323(f243(x40841),f323(f323(f8(a860,a860,x40841),a318),f323(f323(f7(x40841,f872(x40841,a860),a860),f325(x40841)),x40842))),f323(f77(f872(x40841,a860)),x40842))
% 188.07/187.96 [4111]E(f323(f135(f866(x41111),f866(x41111),f121(x41111),f113(x41111)),f323(f323(f147(f866(x41111),f866(x41111)),f162(x41111)),f323(f162(f866(x41111)),x41112))),f323(f162(x41111),f323(f135(f866(x41111),f866(x41111),f121(x41111),f113(x41111)),x41112)))
% 188.07/187.96 [4139]E(f323(f323(f39(a865,f872(f871(x41391,x41391),a860)),f246(f872(a865,a860))),f323(f323(f7(a865,f872(f871(x41391,x41391),a860),f872(f871(x41391,x41391),a860)),f183(f871(x41391,x41391),a860)),x41392)),f299(x41391,x41392))
% 188.07/187.96 [4159]E(f83(x41591,f323(f323(f8(f872(x41591,a860),a860,x41591),f323(a320,x41592)),f323(f323(f7(x41591,f872(x41591,a860),f872(x41591,a860)),f301(x41591)),f188(f872(x41591,a860))))),f304(x41591,x41592))
% 188.07/187.96 [4167]E(f323(f189(f866(x41671)),f145(x41671,f323(f135(f866(x41671),f866(x41671),f121(x41671),f113(x41671)),x41672))),f323(f35(x41671),f323(f323(f39(f866(x41671),f872(x41671,a860)),f323(f166(f866(x41671)),x41672)),f166(x41671))))
% 188.07/187.96 [4183]E(f323(f323(f110(f872(f871(x41831,x41831),a860)),x41832),f323(f323(f280(x41831,x41831,x41831),f323(f323(f280(x41831,x41831,x41831),x41832),f299(x41831,x41832))),x41832)),f323(f323(f280(x41831,x41831,x41831),x41832),f299(x41831,x41832)))
% 188.07/187.96 [4208]P101(f323(f323(f237(f872(f871(x42081,x42081),a860)),f323(f323(f280(x42081,x42081,x42081),x42082),f299(x42081,x42082))),f323(f323(f260(x42081,x42081),f323(f276(x42081),x42082)),f323(f16(f872(x42081,a860),x42081),f323(f276(x42081),x42082)))))
% 188.07/187.96 [4251]E(f323(f243(f866(x42511)),f323(f323(f7(f866(x42511),f872(x42511,a860),a860),f323(f323(f8(f872(x42511,a860),f872(f872(x42511,a860),a860),f866(x42511)),f237(f872(x42511,a860))),f166(x42511))),x42512)),f154(x42511,x42512))
% 188.07/187.96 [4263]E(f323(f149(f866(x42631),x42631,f113(x42631),f323(f323(f8(f866(x42631),f872(f866(x42631),f866(x42631)),x42631),f323(f7(f866(x42631),f866(x42631),f866(x42631)),f121(x42631))),f323(f323(f7(x42631,f866(x42631),f866(x42631)),f144(x42631)),f113(x42631)))),x42632),f323(f161(x42631),x42632))
% 188.07/187.96 [4306]P27(f872(x43061,x43062),f872(f871(x43061,x43062),a860),f323(f323(f8(f872(f871(x43061,x43062),a860),f872(f871(x43061,x43062),a860),f872(x43061,x43062)),f243(f871(x43061,x43062))),f323(f323(f8(f872(x43061,f872(x43062,a860)),f872(f871(x43061,x43062),a860),f872(x43061,x43062)),f262(x43061,x43062,a860)),f323(f8(x43062,f872(x43062,a860),x43061),f323(f7(x43062,x43062,a860),a320)))),f246(f872(f872(x43061,x43062),a860)))
% 188.07/187.96 [4311]E(f42(a1,f323(f103(a1),f323(f323(f78(a1),x43111),x43111)),f323(f103(a1),f323(f323(f78(a1),x43112),x43112))),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),x43111),f323(f103(a1),x43112))))
% 188.07/187.96 [4355]E(f323(f323(f39(x43551,f872(f871(x43551,x43551),a860)),x43552),f323(f323(f7(x43551,f872(f871(x43551,x43551),a860),f872(f871(x43551,x43551),a860)),f323(f323(f8(f871(x43551,x43551),f872(f872(f871(x43551,x43551),a860),f872(f871(x43551,x43551),a860)),x43551),f301(f871(x43551,x43551))),f323(f323(f18(x43551,x43551,f871(x43551,x43551)),f258(x43551,x43551)),f5(x43551)))),f188(f872(f871(x43551,x43551),a860)))),f255(x43551,x43552))
% 188.07/187.96 [4363]E(f205(x43631,f323(f323(f258(a1,a1),f323(f77(a1),f323(f323(f71(f871(a1,a1),a1,x43631,f257(a1,a1)),f214(x43631)),x43632))),f323(f323(f71(f871(a1,a1),a1,x43631,f261(a1,a1)),f214(x43631)),x43632))),f222(x43631,x43632))
% 188.07/187.96 [4447]E(f323(f243(f872(x44471,a860)),f323(f323(f8(f872(f872(x44471,a860),a860),a860,f872(x44471,a860)),f85(f872(x44471,a860))),f323(f323(f7(f872(x44471,a860),f872(f872(x44471,a860),a860),f872(f872(x44471,a860),a860)),f323(f323(f8(f872(f872(x44471,a860),f872(a860,a860)),f872(f872(f872(x44471,a860),a860),f872(f872(x44471,a860),a860)),f872(x44471,a860)),f18(f872(x44471,a860),a860,a860)),f323(f323(f8(f872(f872(x44471,a860),a860),f872(f872(x44471,a860),f872(a860,a860)),f872(x44471,a860)),f323(f8(a860,f872(a860,a860),f872(x44471,a860)),a322)),f323(f323(f7(f872(x44471,a860),f872(f872(x44471,a860),f872(x44471,a860)),f872(f872(x44471,a860),a860)),f323(f323(f8(f872(f872(x44471,a860),a860),f872(f872(f872(x44471,a860),f872(x44471,a860)),f872(f872(x44471,a860),a860)),f872(x44471,a860)),f8(f872(x44471,a860),a860,f872(x44471,a860))),a320)),f77(f872(x44471,a860)))))),f323(f323(f8(f872(f872(x44471,a860),a860),a860,f872(x44471,a860)),f323(f325(f872(x44471,a860)),x44472)),f300(x44471))))),f323(f300(x44471),f323(f77(f872(x44471,a860)),x44472)))
% 188.07/187.96 [4556]~E(f323(f323(f78(a1),x45561),x45561),f323(f323(f22(a1),f323(f323(f78(a1),x45562),x45562)),a97))
% 188.07/187.96 [4562]~P101(f323(f323(f238(a865),f323(f323(f78(a865),x45621),x45622)),x45622))
% 188.07/187.96 [4563]~P101(f323(f323(f238(a865),f323(f323(f78(a865),x45631),x45632)),x45631))
% 188.07/187.96 [3766]E(f323(f323(f22(a865),x37661),f323(f323(f79(a865),f323(f323(f36(a865),x37661),x37662)),x37662)),f42(a865,x37661,x37662))
% 188.07/187.96 [3767]E(f323(f323(f22(a1),x37671),f323(f323(f79(a1),f323(f323(f36(a1),x37671),x37672)),x37672)),f42(a1,x37671,x37672))
% 188.07/187.96 [3801]E(f323(f323(f147(a865,x38011),f323(f158(x38011),x38012)),f132(a865,f323(f293(a865,f2(a865)),f323(f189(f866(x38011)),x38012)))),x38012)
% 188.07/187.96 [3865]E(f323(f277(x38651,x38651,f299(x38651,f188(f872(f871(x38651,x38651),a860)))),x38652),x38652)
% 188.07/187.96 [3996]E(f299(x39961,f323(f323(f110(f872(f871(x39961,x39961),a860)),x39962),f299(x39961,f188(f872(f871(x39961,x39961),a860))))),f299(x39961,x39962))
% 188.07/187.96 [3997]E(f299(x39971,f323(f323(f22(f872(f871(x39971,x39971),a860)),x39972),f299(x39971,f188(f872(f871(x39971,x39971),a860))))),f299(x39971,x39972))
% 188.07/187.96 [4050]E(f323(f323(f22(a1),f323(f323(f22(a1),f323(f323(f78(a1),x40501),x40501)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x40502),x40502)),a97)),f323(f323(f78(a1),f323(f323(f22(a1),x40501),x40502)),f323(f323(f22(a1),x40501),x40502)))
% 188.07/187.96 [4089]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f78(a1),x40891),x40892)),f323(f323(f78(a1),x40891),x40892))),a97),f323(f323(f78(a1),f323(f323(f78(a1),x40891),x40891)),f323(f323(f22(a1),f323(f323(f78(a1),x40892),x40892)),a97)))
% 188.07/187.96 [4115]E(f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),x41151),x41151)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x41152),x41152)),a97)),f323(f323(f78(a1),f323(f323(f78(a1),x41151),f323(f323(f22(a1),x41152),a97))),f323(f323(f78(a1),x41151),f323(f323(f22(a1),x41152),a97))))
% 188.07/187.96 [4125]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),x41251),x41252)),f323(f323(f22(a1),x41251),x41252))),a97),f323(f323(f22(a1),f323(f323(f22(a1),f323(f323(f78(a1),x41251),x41251)),a97)),f323(f323(f78(a1),x41252),x41252)))
% 188.07/187.96 [4126]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f78(a1),x41261),x41262)),f323(f323(f78(a1),x41261),x41262))),a97),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),x41261),x41261)),a97)),f323(f323(f78(a1),x41262),x41262)))
% 188.07/187.96 [4180]E(f323(f100(a1),f323(f323(f36(a865),f323(f323(f79(a865),f323(a104,f323(f73(a1),x41801))),f323(a104,f323(f73(a1),x41802)))),f218(f323(a104,f323(f73(a1),x41801)),f323(a104,f323(f73(a1),x41802))))),f220(x41801,x41802))
% 188.07/187.96 [4228]E(f323(f323(f264(f871(a99,a99),a99,f871(a99,a99),f871(x42281,f871(a99,a99))),f268(f323(a3,f323(f189(f866(x42281)),x42282)))),f323(f323(f8(x42281,f872(f871(a99,a99),f871(x42281,f871(a99,a99))),a99),f258(x42281,f871(a99,a99))),f323(f323(f8(a865,x42281,a99),f323(f158(x42281),x42282)),a19))),f274(x42281,x42282))
% 188.07/187.96 [4312]E(f323(f135(a865,f866(x43121),f323(f7(f866(x43121),a865,a865),f323(f323(f8(a865,f872(a865,a865),f866(x43121)),f236(a865)),f189(f866(x43121)))),f2(a865)),f323(f162(f866(x43121)),f173(x43121,x43122))),f323(f189(f866(f866(x43121))),f323(f129(f866(x43121),f323(f323(f8(a860,a860,f866(x43121)),a318),f323(f323(f7(f866(x43121),f866(x43121),a860),a320),f113(x43121)))),x43122)))
% 188.07/187.96 [4318]E(f323(f323(f39(a865,f872(x43181,a860)),f246(f872(a865,a860))),f323(f323(f7(a865,f872(a865,f872(x43181,a860)),f872(x43181,a860)),f323(f323(f8(f872(a865,a860),f872(f872(a865,f872(x43181,a860)),f872(x43181,a860)),a865),f39(a865,f872(x43181,a860))),f293(a865,f2(a865)))),x43182)),f323(f323(f39(a865,f872(x43181,a860)),f246(f872(a865,a860))),x43182))
% 188.07/187.96 [4339]P101(f323(f59(a865),f323(f243(a865),f323(f323(f18(a865,a860,a860),f323(f323(f8(a860,f872(a860,a860),a865),a322),x43391)),f323(f323(f7(a865,a865,a860),f238(a865)),x43392)))))
% 188.07/187.96 [4458]E(f323(f243(f871(f866(x44581),f866(x44581))),f323(f262(f866(x44581),f866(x44581),a860),f323(f323(f18(f866(x44581),f872(f866(x44581),a860),f872(f866(x44581),a860)),f323(f323(f8(f872(f866(x44581),f872(a860,a860)),f872(f872(f866(x44581),a860),f872(f866(x44581),a860)),f866(x44581)),f18(f866(x44581),a860,a860)),f323(f323(f8(f872(f866(x44581),a860),f872(f866(x44581),f872(a860,a860)),f866(x44581)),f323(f8(a860,f872(a860,a860),f866(x44581)),a321)),f323(f323(f7(f866(x44581),f872(f866(x44581),a865),f872(f866(x44581),a860)),f323(f323(f8(f872(a865,a860),f872(f872(f866(x44581),a865),f872(f866(x44581),a860)),f866(x44581)),f8(a865,a860,f866(x44581))),f323(f323(f8(a865,f872(a865,a860),f866(x44581)),f238(a865)),f189(f866(x44581))))),f189(f866(x44581)))))),f323(f323(f18(f866(x44581),f872(f866(x44581),a860),f872(f866(x44581),a860)),f323(f323(f8(f872(f866(x44581),f872(a860,a860)),f872(f872(f866(x44581),a860),f872(f866(x44581),a860)),f866(x44581)),f18(f866(x44581),a860,a860)),f323(f323(f8(f872(f866(x44581),a860),f872(f866(x44581),f872(a860,a860)),f866(x44581)),f323(f8(a860,f872(a860,a860),f866(x44581)),a322)),f323(f323(f7(f866(x44581),f872(f866(x44581),a865),f872(f866(x44581),a860)),f323(f323(f8(f872(a865,a860),f872(f872(f866(x44581),a865),f872(f866(x44581),a860)),f866(x44581)),f8(a865,a860,f866(x44581))),f323(f323(f8(a865,f872(a865,a860),f866(x44581)),a320),f189(f866(x44581))))),f189(f866(x44581)))))),f323(f323(f7(f866(x44581),f872(f871(f866(x44581),f866(x44581)),a860),f872(f866(x44581),a860)),f323(f323(f8(f872(f866(x44581),f872(f872(f871(f866(x44581),f866(x44581)),a860),a860)),f872(f872(f871(f866(x44581),f866(x44581)),a860),f872(f866(x44581),a860)),f866(x44581)),f7(f866(x44581),f872(f871(f866(x44581),f866(x44581)),a860),a860)),f323(f323(f8(f872(f866(x44581),f871(f866(x44581),f866(x44581))),f872(f866(x44581),f872(f872(f871(f866(x44581),f866(x44581)),a860),a860)),f866(x44581)),f323(f8(f871(f866(x44581),f866(x44581)),f872(f872(f871(f866(x44581),f866(x44581)),a860),a860),f866(x44581)),f325(f871(f866(x44581),f866(x44581))))),f258(f866(x44581),f866(x44581))))),f138(x44581,x44582)))))),f139(x44581,x44582))
% 188.07/187.96 [4568]~P101(f323(f323(f89(a1),f323(f323(f78(a1),x45681),x45681)),f323(f323(f22(a1),f323(f323(f78(a1),x45682),x45682)),a97)))
% 188.07/187.96 [4118]E(f323(f323(f78(a1),f323(f323(f78(a1),f323(f323(f79(a1),x41181),x41182)),f323(f323(f79(a1),x41181),x41182))),x41182),f323(f323(f79(a1),f323(f323(f22(a1),f323(f323(f78(a1),x41181),x41181)),a97)),x41182))
% 188.07/187.96 [4226]E(f323(a104,f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x42261),x42262)),f188(f872(f871(a865,a865),a860)))))),f323(f323(f22(a865),x42261),x42262))
% 188.07/187.96 [4231]E(f323(f323(f280(x42311,x42311,x42311),f323(f323(f110(f872(f871(x42311,x42311),a860)),x42312),f299(x42311,f188(f872(f871(x42311,x42311),a860))))),f299(x42311,f323(f323(f110(f872(f871(x42311,x42311),a860)),x42312),f299(x42311,f188(f872(f871(x42311,x42311),a860)))))),f299(x42311,x42312))
% 188.07/187.96 [4269]E(f267(x42691,f323(f129(f871(a99,x42691),f323(f262(a99,x42691,a860),f323(f323(f8(a860,f872(x42691,a860),a99),f16(a860,x42691)),f323(f238(a99),f2(a99))))),x42692)),f267(x42691,x42692))
% 188.07/187.96 [4270]E(f269(x42701,f323(f129(f871(a99,x42701),f323(f262(a99,x42701,a860),f323(f323(f8(a860,f872(x42701,a860),a99),f16(a860,x42701)),f323(f238(a99),f2(a99))))),x42702)),f269(x42701,x42702))
% 188.07/187.96 [4272]E(f323(f77(a1),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x42721),x42722)),f188(f872(f871(a865,a865),a860)))))),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x42722),x42721)),f188(f872(f871(a865,a865),a860))))))
% 188.07/187.96 [4330]E(f323(f323(f279(f866(a865),x43301),f138(a865,a242)),f323(f323(f7(x43301,f866(f872(x43301,a865)),f866(a865)),f323(f323(f8(f872(f872(x43301,a865),a865),f872(f866(f872(x43301,a865)),f866(a865)),x43301),f147(f872(x43301,a865),a865)),f323(f7(f872(x43301,a865),x43301,a865),f5(f872(x43301,a865))))),x43302)),f146(x43301,x43302))
% 188.07/187.96 [4352]E(f323(f323(f84(a1,a865),f323(f103(a1),f323(f323(f78(a1),x43521),a97))),f323(f323(f18(a1,a865,a865),f323(f323(f7(a1,a865,f872(a865,a865)),f323(f323(f8(a860,f872(a865,f872(a865,a865)),a1),f96(a865)),a193)),f2(a865))),f323(f323(f8(a865,a865,a1),a112),f323(f323(f8(a865,a865,a1),f323(f235(a865),x43522)),a104)))),f323(f323(f235(a865),f323(a112,x43522)),f323(f103(a865),x43521)))
% 188.07/187.96 [4353]E(f323(f323(f84(a1,a865),f323(f103(a1),f323(f323(f78(a1),x43531),a97))),f323(f323(f18(a1,a865,a865),f323(f323(f7(a1,a865,f872(a865,a865)),f323(f323(f8(a860,f872(a865,f872(a865,a865)),a1),f96(a865)),a193)),f323(a112,x43532))),f323(f323(f8(a865,a865,a1),a112),f323(f323(f8(a865,a865,a1),f323(f236(a865),x43532)),a104)))),f323(f323(f236(a865),f323(a112,x43532)),f323(f103(a865),x43531)))
% 188.07/187.96 [4373]E(f323(f135(f866(x43731),f866(x43731),f121(x43731),f113(x43731)),f323(f323(f147(f866(x43731),f866(x43731)),f149(f866(x43731),x43731,f113(x43731),f323(f323(f8(f866(x43731),f872(f866(x43731),f866(x43731)),x43731),f16(f866(x43731),f866(x43731))),f323(f323(f7(x43731,f866(x43731),f866(x43731)),f144(x43731)),f113(x43731))))),x43732)),f323(f323(f147(f866(x43731),x43731),f134(x43731)),f323(f129(f866(x43731),f323(f323(f8(a860,a860,f866(x43731)),a318),f323(f323(f7(f866(x43731),f866(x43731),a860),a320),f113(x43731)))),x43732)))
% 188.07/187.96 [4437]E(f323(f262(a1,a1,a860),f323(f323(f7(a1,f872(a1,a860),f872(a1,a860)),f323(f323(f8(f872(a1,f872(a860,a860)),f872(f872(a1,a860),f872(a1,a860)),a1),f18(a1,a860,a860)),f323(f323(f8(f872(a1,a860),f872(a1,f872(a860,a860)),a1),f323(f8(a860,f872(a860,a860),a1),a322)),f323(f323(f8(f872(a1,a1),f872(a1,a860),a1),f323(f8(a1,a860,a1),f323(a320,x44371))),f323(f323(f8(a1,f872(a1,a1),a1),f78(a1)),f323(f79(a1),x44372)))))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f323(f8(a860,a860,a1),f323(a326,f323(f323(f238(a1),f2(a1)),x44372))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f237(a1),f2(a1)))),f323(f323(f7(a1,a1,a860),f238(a1)),x44372))))),f323(f323(f8(a860,a860,a1),f323(a326,f323(a318,f323(f323(f238(a1),f2(a1)),x44372)))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f238(a1),x44372))),f323(f323(f7(a1,a1,a860),f237(a1)),f2(a1))))))),f46(x44371,x44372))
% 188.07/187.96 [4439]E(f323(f243(x44391),f323(f323(f8(f872(a865,a860),a860,x44391),f85(a865)),f323(f323(f7(x44391,f872(a865,a860),f872(a865,a860)),f323(f323(f8(f872(a865,f872(a860,a860)),f872(f872(a865,a860),f872(a865,a860)),x44391),f18(a865,a860,a860)),f323(f323(f8(f872(a865,a860),f872(a865,f872(a860,a860)),x44391),f323(f8(a860,f872(a860,a860),a865),a322)),f323(f323(f7(x44391,f872(a865,x44391),f872(a865,a860)),f323(f323(f8(f872(x44391,a860),f872(f872(a865,x44391),f872(a865,a860)),x44391),f8(x44391,a860,a865)),a320)),f323(f158(x44391),x44392))))),f323(f323(f7(a865,a865,a860),f238(a865)),f323(f189(f866(x44391)),x44392))))),f323(f166(x44391),x44392))
% 188.07/187.96 [4241]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),x42411),a97)),x42412)),f323(f323(f22(a1),f323(f323(f78(a1),x42411),a97)),x42412))),a97),f323(f323(f22(a1),f323(f323(f78(a1),x42411),x42411)),f323(f323(f22(a1),f323(f323(f78(a1),x42412),x42412)),a97)))
% 188.07/187.96 [4368]E(f323(f135(f866(f866(x43681)),f866(f866(x43681)),f121(f866(x43681)),f113(f866(x43681))),f323(f323(f147(f866(x43681),f866(f866(x43681))),f149(f866(f866(x43681)),x43681,f113(f866(x43681)),f323(f16(f872(f866(x43681),f866(f866(x43681))),x43681),f323(f323(f7(f866(x43681),f866(f866(x43681)),f866(f866(x43681))),f144(f866(x43681))),f113(f866(x43681)))))),x43682)),f323(f323(f147(f866(x43681),f866(x43681)),f165(x43681)),f323(f129(f866(x43681),f323(f323(f8(a860,a860,f866(x43681)),a318),f323(f323(f7(f866(x43681),f866(x43681),a860),a320),f113(x43681)))),x43682)))
% 188.07/187.96 [4379]E(f323(f323(f84(a1,a865),f323(f103(a1),f323(f323(f78(a1),x43791),a97))),f323(f323(f18(a1,a865,a865),f323(f323(f7(a1,a865,f872(a865,a865)),f323(f323(f8(a860,f872(a865,f872(a865,a865)),a1),f96(a865)),a193)),f2(a865))),f323(f323(f8(a865,a865,a1),a112),f323(f323(f7(a1,a865,a865),f323(f323(f8(a865,f872(a865,a865),a1),f235(a865)),a104)),x43792)))),f323(f323(f235(a865),f323(f103(a865),x43791)),f323(a112,x43792)))
% 188.07/187.96 [4380]E(f323(f323(f84(a1,a865),f323(f103(a1),f323(f323(f78(a1),x43801),a97))),f323(f323(f18(a1,a865,a865),f323(f323(f7(a1,a865,f872(a865,a865)),f323(f323(f8(a860,f872(a865,f872(a865,a865)),a1),f96(a865)),a193)),f323(a112,x43802))),f323(f323(f8(a865,a865,a1),a112),f323(f323(f7(a1,a865,a865),f323(f323(f8(a865,f872(a865,a865),a1),f236(a865)),a104)),x43802)))),f323(f323(f236(a865),f323(f103(a865),x43801)),f323(a112,x43802)))
% 188.07/187.96 [4367]E(f323(f262(x43671,x43671,a860),f323(f323(f18(x43671,a860,f872(x43671,a860)),f323(f323(f8(f872(x43671,f872(a860,a860)),f872(a860,f872(x43671,a860)),x43671),f7(x43671,a860,a860)),f323(f323(f8(f872(x43671,a860),f872(x43671,f872(a860,a860)),x43671),f323(f8(a860,f872(a860,a860),x43671),a322)),a320))),x43672)),f255(x43671,x43672))
% 188.07/187.96 [4414]E(f323(f323(f36(a865),x44141),f323(f323(f78(a865),f323(f103(a865),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))),x44142)),f323(f323(f36(a865),x44141),f323(a112,f323(a112,f323(a112,x44142)))))
% 188.07/187.96 [4415]E(f42(a865,x44151,f323(f323(f78(a865),f323(f103(a865),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))),x44152)),f42(a865,x44151,f323(a112,f323(a112,f323(a112,x44152)))))
% 188.07/187.96 [4416]E(f42(a865,f323(f323(f78(a865),f323(f103(a865),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))),x44161),x44162),f42(a865,f323(a112,f323(a112,f323(a112,x44161))),x44162))
% 188.07/187.96 [4429]E(f120(f323(x44291,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))),x44292))),f323(f203(x44291),x44292))
% 188.07/187.96 [4430]E(f323(f323(f36(a865),f323(f323(f78(a865),f323(f103(a865),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))),x44301)),x44302),f323(f323(f36(a865),f323(a112,f323(a112,f323(a112,x44301)))),x44302))
% 188.07/187.96 [4504]~E(f27(x45041,x45042,x45043),a24)
% 188.07/187.96 [4505]~E(f26(x45051,x45052,x45053),a24)
% 188.07/187.96 [3190]E(f323(f192(x31901,x31902),x31903),f118(x31901,x31902))
% 188.07/187.96 [3211]E(f323(f202(x32111,x32112),x32113),f323(f122(x32111),x32112))
% 188.07/187.96 [3291]E(f323(f323(f201(x32911,x32912),x32913),f200(x32911)),f200(x32912))
% 188.07/187.96 [3292]E(f323(f323(f147(x32921,x32922),x32923),f113(x32921)),f113(x32922))
% 188.07/187.96 [3332]E(f323(f184(x33321,x33322,x33323),f2(a865)),x33322)
% 188.07/187.96 [3334]E(f323(f323(f175(x33341,x33342),x33343),f113(x33342)),f113(f871(x33341,x33342)))
% 188.07/187.96 [3368]E(f83(x33681,f60(x33681,x33682,x33683)),f323(f61(x33681,x33682),x33683))
% 188.07/187.96 [3372]E(f247(x33721,x33722,f247(x33722,x33721,x33723)),x33723)
% 188.07/187.96 [3392]E(f323(f162(x33921),f163(x33921,x33922,x33923)),f163(x33921,x33922,x33923))
% 188.07/187.96 [3421]E(f133(x34211,x34212,f145(x34211,x34213)),f145(x34211,f133(x34211,x34212,x34213)))
% 188.07/187.96 [3440]E(f323(f257(f866(x34401),f866(x34401)),f160(x34401,x34402,x34403)),f323(f129(x34401,x34402),x34403))
% 188.07/187.96 [3485]E(f323(f323(f144(x34851),x34852),f163(x34851,x34853,x34852)),f163(x34851,f323(a112,x34853),x34852))
% 188.07/187.96 [3517]E(f185(x35171,x35172,x35173,f2(a865)),x35172)
% 188.07/187.96 [3518]E(f17(x35181,x35182,x35183,f2(a99)),x35182)
% 188.07/187.96 [3525]E(f156(x35251,x35252,x35253,f113(x35251)),f113(x35252))
% 188.07/187.96 [3526]E(f157(x35261,x35262,x35263,f113(x35261)),f113(x35262))
% 188.07/187.96 [3533]E(f323(f323(f158(x35331),f323(f323(f144(x35331),x35332),x35333)),f2(a865)),x35332)
% 188.07/187.96 [3562]E(f57(x35621,x35622,f113(x35621),x35623),f113(f871(x35621,x35622)))
% 188.07/187.96 [3583]P27(x35831,x35832,x35833,f188(f872(x35831,a860)))
% 188.07/187.96 [3740]E(f323(f71(x37401,x37402,x37401,x37403),f32(x37401)),x37403)
% 188.07/187.96 [3924]P101(f323(f323(f325(f871(x39241,x39241)),f323(f323(f258(x39241,x39241),x39242),x39242)),f299(x39241,x39243)))
% 188.07/187.96 [4569]~P101(f323(f323(f325(f871(f866(x45691),f866(x45691))),f323(f323(f258(f866(x45691),f866(x45691)),x45692),f113(x45691))),f138(x45691,x45693)))
% 188.07/187.96 [4570]~P101(f323(f323(f325(f871(f866(x45701),f866(x45701))),f323(f323(f258(f866(x45701),f866(x45701)),x45702),f113(x45701))),f140(x45701,x45703)))
% 188.07/187.96 [4571]~P101(f323(f323(f325(f871(f866(x45711),f866(x45711))),f323(f323(f258(f866(x45711),f866(x45711)),x45712),f113(x45711))),f150(x45711,x45713)))
% 188.07/187.96 [4572]~P101(f323(f323(f325(f871(f866(x45721),f866(x45721))),f323(f323(f258(f866(x45721),f866(x45721)),f113(x45721)),x45722)),f138(x45721,x45723)))
% 188.07/187.96 [4573]~P101(f323(f323(f325(f871(f866(x45731),f866(x45731))),f323(f323(f258(f866(x45731),f866(x45731)),f113(x45731)),x45732)),f150(x45731,x45733)))
% 188.07/187.96 [3266]E(f323(f323(f204(x32661),x32662),x32663),f205(x32661,f217(x32662,x32663)))
% 188.07/187.96 [3321]E(f323(f278(x33211,x33212),f323(f278(x33212,x33211),x33213)),x33213)
% 188.07/187.96 [3344]E(f323(f323(f175(x33441,x33442),f113(x33441)),x33443),f113(f871(x33441,x33442)))
% 188.07/187.96 [3347]E(f170(x33471,x33472,f323(f244(a865),x33473)),f323(f323(f169(x33471),x33473),x33472))
% 188.07/187.96 [3364]E(f145(x33641,f323(f129(x33641,x33642),x33643)),f323(f129(x33641,x33642),f145(x33641,x33643)))
% 188.07/187.96 [3366]E(f323(f254(x33661,x33662),f323(f278(x33662,x33661),x33663)),f323(f256(x33662,x33661),x33663))
% 188.07/187.96 [3367]E(f323(f256(x33671,x33672),f323(f278(x33672,x33671),x33673)),f323(f254(x33672,x33671),x33673))
% 188.07/187.96 [3384]E(f323(f129(x33841,x33842),f323(f162(x33841),x33843)),f323(f162(x33841),f323(f129(x33841,x33842),x33843)))
% 188.07/187.96 [3398]E(f323(f323(f131(x33981),x33982),f323(f165(x33981),x33983)),f323(f323(f131(x33981),f323(a112,x33982)),x33983))
% 188.07/187.96 [3416]E(f28(f26(x34161,x34162,x34163)),f323(f323(f78(a865),f28(x34163)),f323(a112,f2(a865))))
% 188.07/187.96 [3417]E(f323(f302(x34171,x34172,x34173),f188(f872(x34171,a860))),f188(f872(x34172,a860)))
% 188.07/187.96 [3418]E(f323(f303(x34181,x34182,x34183),f188(f872(x34182,a860))),f188(f872(x34181,a860)))
% 188.07/187.96 [3419]E(f323(f303(x34191,x34192,x34193),f246(f872(x34192,a860))),f246(f872(x34191,a860)))
% 188.07/187.96 [3420]E(f323(f277(x34201,x34202,x34203),f188(f872(x34201,a860))),f188(f872(x34202,a860)))
% 188.07/187.96 [3449]E(f323(f323(f301(x34491),x34492),f323(f166(x34491),x34493)),f323(f166(x34491),f133(x34491,x34492,x34493)))
% 188.07/187.96 [3461]E(f231(x34611,x34612,f323(f230(x34611),x34613)),f323(f323(f78(a865),f323(x34612,x34613)),f323(a112,f2(a865))))
% 188.07/187.96 [3537]E(f323(f189(a862),f26(x35371,x35372,x35373)),f323(f323(f78(a865),f323(f189(a862),x35373)),f323(a112,f2(a865))))
% 188.07/187.96 [3538]E(f323(f302(f871(x35381,x35382),x35382,f261(x35381,x35382)),x35383),f323(f254(x35381,x35382),x35383))
% 188.07/187.96 [3539]E(f323(f302(f871(x35391,x35392),x35391,f257(x35391,x35392)),x35393),f323(f256(x35391,x35392),x35393))
% 188.07/187.96 [3611]E(f323(f323(f258(x36111,x36112),f323(f257(x36111,x36112),x36113)),f323(f261(x36111,x36112),x36113)),x36113)
% 188.07/187.96 [3618]E(f323(f189(f867(x36181)),f123(x36181,x36182,x36183)),f323(f323(f78(a865),f323(f189(f867(x36181)),x36183)),f323(a112,f2(a865))))
% 188.07/187.96 [3619]E(f323(f323(f262(x36191,x36192,x36191),f16(x36191,x36192)),x36193),f323(f257(x36191,x36192),x36193))
% 188.07/187.96 [3639]E(f180(x36391,x36392,x36393,f323(f16(f869(x36392),x36391),f200(x36392))),x36393)
% 188.07/187.96 [3640]E(f180(x36401,x36402,f323(f16(f869(x36402),x36401),f200(x36402)),x36403),x36403)
% 188.07/187.96 [3695]E(f28(f27(x36951,x36952,x36953)),f323(f323(f78(a865),f323(f323(f78(a865),f28(x36952)),f28(x36953))),f323(a112,f2(a865))))
% 188.07/187.96 [3745]E(f323(f71(x37451,x37451,x37452,f32(x37451)),x37453),x37453)
% 188.07/187.96 [3753]E(f323(f323(f121(x37531),f163(x37531,x37532,x37533)),f323(f323(f144(x37531),x37533),f113(x37531))),f323(f323(f144(x37531),x37533),f163(x37531,x37532,x37533)))
% 188.07/187.96 [3857]E(f323(f189(a862),f27(x38571,x38572,x38573)),f323(f323(f78(a865),f323(f323(f78(a865),f323(f189(a862),x38572)),f323(f189(a862),x38573))),f323(a112,f2(a865))))
% 188.07/187.96 [3934]P101(f323(f323(f237(f872(x39341,a860)),f323(f166(x39341),f323(f129(x39341,x39342),x39343))),f323(f166(x39341),x39343)))
% 188.07/187.96 [3981]P101(f323(f323(f237(f872(x39811,a860)),f323(f166(x39811),f323(f323(f169(x39811),x39812),x39813))),f323(f166(x39811),x39813)))
% 188.07/187.96 [3982]P101(f323(f323(f237(f872(x39821,a860)),f323(f166(x39821),f323(f323(f131(x39821),x39822),x39823))),f323(f166(x39821),x39823)))
% 188.07/187.96 [3987]P101(f323(f323(f237(f872(x39871,a860)),f323(f166(x39871),f164(x39871,x39872,x39873))),f323(f166(x39871),x39873)))
% 188.07/187.96 [3988]P101(f323(f323(f237(f872(x39881,a860)),f323(f166(x39881),f170(x39881,x39882,x39883))),f323(f166(x39881),x39882)))
% 188.07/187.96 [4011]P27(f871(x40111,x40112),f871(x40112,x40111),f323(f262(x40111,x40112,f871(x40112,x40111)),f323(f7(x40112,x40111,f871(x40112,x40111)),f258(x40112,x40111))),x40113)
% 188.07/187.96 [4023]E(f323(f323(f323(f183(f866(x40231),f866(x40231)),f42(a865,x40232,f323(f189(f866(x40231)),x40233))),f161(x40231)),x40233),f323(f323(f323(f183(f866(x40231),f866(x40231)),x40232),f161(x40231)),x40233))
% 188.07/187.96 [4065]P101(f323(f323(f325(f871(f866(x40651),f866(x40651))),f323(f323(f258(f866(x40651),f866(x40651)),x40652),x40652)),f151(x40651,f299(x40651,x40653))))
% 188.07/187.96 [4211]E(f83(f871(x42111,x42112),f323(f323(f18(f871(x42111,x42112),x42112,a860),f323(f323(f8(x42111,f872(x42112,a860),f871(x42111,x42112)),x42113),f257(x42111,x42112))),f261(x42111,x42112))),f83(f871(x42111,x42112),f323(f262(x42111,x42112,a860),x42113)))
% 188.07/187.96 [4212]E(f88(f871(x42121,x42122),f323(f323(f18(f871(x42121,x42122),x42122,a860),f323(f323(f8(x42121,f872(x42122,a860),f871(x42121,x42122)),x42123),f257(x42121,x42122))),f261(x42121,x42122))),f88(f871(x42121,x42122),f323(f262(x42121,x42122,a860),x42123)))
% 188.07/187.96 [4248]E(f323(f323(f279(f871(a865,x42481),x42481),f315(a865,x42481,a242,x42482)),f323(f323(f18(x42481,x42481,f871(a865,x42481)),f323(f323(f8(a865,f872(x42481,f871(a865,x42481)),x42481),f258(a865,x42481)),x42483)),f5(x42481))),f317(x42481,x42483,x42482))
% 188.07/187.96 [4314]E(f323(f263(x43141,x43141,x43142,x43142,f5(x43141),f5(x43142)),x43143),x43143)
% 188.07/187.96 [4390]E(f323(f135(f866(f866(x43901)),f866(f866(x43901)),f121(f866(x43901)),f113(f866(x43901))),f323(f323(f147(f866(x43901),f866(f866(x43901))),f323(f323(f7(f866(x43901),f866(x43901),f866(f866(x43901))),f323(f323(f8(f872(x43901,f866(x43901)),f872(f866(x43901),f866(f866(x43901))),f866(x43901)),f147(x43901,f866(x43901))),f323(f7(x43901,f866(x43901),f866(x43901)),f144(x43901)))),x43902)),f52(x43901,x43903,x43902))),f52(x43901,f323(a112,x43903),x43902))
% 188.07/187.96 [4454]E(f323(f232(a865,f871(x44541,f867(x44541)),f2(a865),f323(f262(x44541,f867(x44541),a865),f323(f323(f7(x44541,a865,f872(f867(x44541),a865)),f323(f323(f8(f872(f867(x44541),f872(a865,a865)),f872(a865,f872(f867(x44541),a865)),x44541),f7(f867(x44541),a865,a865)),f323(f323(f8(f872(f867(x44541),a865),f872(f867(x44541),f872(a865,a865)),x44541),f323(f8(a865,f872(a865,a865),f867(x44541)),f78(a865))),f323(f323(f7(x44541,f872(f867(x44541),a865),f872(f867(x44541),a865)),f323(f323(f8(f872(a865,a865),f872(f872(f867(x44541),a865),f872(f867(x44541),a865)),x44541),f8(a865,a865,f867(x44541))),f323(f323(f8(a865,f872(a865,a865),x44541),f78(a865)),x44542))),f125(x44541,x44542))))),f76(a865)))),f323(f128(x44541),x44543)),f323(f125(x44541,x44542),x44543))
% 188.07/187.96 [4457]E(f323(f323(f84(a1,x44571),f220(f323(f323(f71(f871(a1,a1),a1,x44571,f261(a1,a1)),f214(x44571)),x44572),f323(f323(f71(f871(a1,a1),a1,x44571,f261(a1,a1)),f214(x44571)),x44573))),f323(f323(f18(a1,a1,x44571),f323(f323(f8(a1,f872(a1,x44571),a1),f204(x44571)),f323(f323(f18(a1,a1,a1),f323(f323(f8(a1,f872(a1,a1),a1),f78(a1)),f323(f323(f8(a1,a1,a1),f323(f79(a1),f323(f323(f71(f871(a1,a1),a1,x44571,f257(a1,a1)),f214(x44571)),x44572))),f323(f323(f7(a1,a1,a1),f36(a1)),f323(f323(f71(f871(a1,a1),a1,x44571,f261(a1,a1)),f214(x44571)),x44572))))),f323(f323(f8(a1,a1,a1),f323(f79(a1),f323(f323(f71(f871(a1,a1),a1,x44571,f257(a1,a1)),f214(x44571)),x44573))),f323(f323(f7(a1,a1,a1),f36(a1)),f323(f323(f71(f871(a1,a1),a1,x44571,f261(a1,a1)),f214(x44571)),x44573)))))),f5(a1))),f225(x44571,x44572,x44573))
% 188.07/187.96 [4500]~E(f323(f323(f144(x45001),x45002),x45003),x45003)
% 188.07/187.96 [4507]~E(f323(f323(f144(x45071),x45072),x45073),f113(x45071))
% 188.07/187.96 [4523]~E(f323(f323(f301(x45231),x45232),x45233),f188(f872(x45231,a860)))
% 188.07/187.96 [4546]~E(f323(f302(x45461,f872(x45461,a860),x45462),x45463),f323(f300(x45461),x45463))
% 188.07/187.96 [3326]E(f323(f323(f152(x33261,f113(x33261)),x33262),x33263),f113(x33261))
% 188.07/187.96 [3327]E(f323(f165(x33271),f323(f323(f144(x33271),x33272),x33273)),x33273)
% 188.07/187.96 [3328]E(f323(f134(x33281),f323(f323(f144(x33281),x33282),x33283)),x33282)
% 188.07/187.96 [3371]E(f323(f323(f131(x33711),f76(a865)),f323(f323(f144(x33711),x33712),x33713)),x33713)
% 188.07/187.96 [3405]E(f114(x34051,f323(f323(f131(x34051),x34052),x34053)),f323(f323(f131(x34051),x34052),f114(x34051,x34053)))
% 188.07/187.96 [3407]E(f323(f323(f152(x34071,x34072),x34073),f323(f323(f158(x34071),x34072),x34073)),x34072)
% 188.07/187.96 [3431]E(f323(f323(f301(x34311),x34312),f323(f323(f301(x34311),x34312),x34313)),f323(f323(f301(x34311),x34312),x34313))
% 188.07/187.96 [3442]E(f323(f323(f179(x34421,x34422),f113(f871(x34421,x34422))),x34423),f200(x34422))
% 188.07/187.96 [3445]E(f323(f323(f301(x34451),x34452),f323(f166(x34451),x34453)),f323(f166(x34451),f323(f323(f144(x34451),x34452),x34453)))
% 188.07/187.96 [3447]E(f323(f323(f131(x34471),x34472),f323(f165(x34471),x34473)),f323(f165(x34471),f323(f323(f131(x34471),x34472),x34473)))
% 188.07/187.96 [3458]E(f323(f323(f169(x34581),f76(a865)),f323(f323(f144(x34581),x34582),x34583)),f323(f323(f144(x34581),x34582),f113(x34581)))
% 188.07/187.96 [3502]E(f323(f61(x35021,x35022),f323(f323(f301(x35021),x35023),f188(f872(x35021,a860)))),x35023)
% 188.07/187.96 [3545]E(f323(f323(f78(a865),x35451),f323(f323(f78(a865),x35452),x35453)),f323(f323(f78(a865),x35452),f323(f323(f78(a865),x35451),x35453)))
% 188.07/187.96 [3546]E(f323(f323(f78(a1),x35461),f323(f323(f78(a1),x35462),x35463)),f323(f323(f78(a1),x35462),f323(f323(f78(a1),x35461),x35463)))
% 188.07/187.96 [3551]E(f323(f323(f260(x35511,x35512),f188(f872(x35511,a860))),x35513),f188(f872(f871(x35511,x35512),a860)))
% 188.07/187.96 [3575]E(f323(f323(f110(f872(x35751,a860)),x35752),x35753),f323(f323(f110(f872(x35751,a860)),x35753),x35752))
% 188.07/187.96 [3576]E(f323(f323(f101(f872(x35761,a860)),x35762),x35763),f323(f323(f101(f872(x35761,a860)),x35763),x35762))
% 188.07/187.96 [3578]E(f323(f323(f121(x35781),x35782),f323(f323(f144(x35781),x35783),f113(x35781))),f323(f161(x35781),f323(f323(f144(x35781),x35783),x35782)))
% 188.07/187.96 [3579]E(f323(f323(f121(x35791),f323(f162(x35791),x35792)),f323(f162(x35791),x35793)),f323(f162(x35791),f323(f323(f121(x35791),x35793),x35792)))
% 188.07/187.96 [3589]E(f323(f165(x35891),f323(f323(f169(x35891),f323(a112,x35892)),x35893)),f323(f323(f169(x35891),x35892),f323(f165(x35891),x35893)))
% 188.07/187.96 [3597]P101(f323(f323(f325(x35971),x35972),f323(f323(f301(x35971),x35972),x35973)))
% 188.07/187.96 [3601]E(f323(f323(f40(x36011,f872(x36012,a860)),f188(f872(x36011,a860))),x36013),f246(f872(x36012,a860)))
% 188.07/187.96 [3604]E(f323(f277(x36041,x36041,f255(x36041,x36042)),x36043),f323(f323(f101(f872(x36041,a860)),x36042),x36043))
% 188.07/187.96 [3617]E(f323(f189(f866(x36171)),f323(f323(f144(x36171),x36172),x36173)),f323(f323(f78(a865),f323(f189(f866(x36171)),x36173)),f323(a112,f2(a865))))
% 188.07/187.96 [3621]E(f137(x36211,f323(f323(f121(x36211),x36212),f323(f323(f144(x36211),x36213),f113(x36211)))),x36213)
% 188.07/187.96 [3622]E(f114(x36221,f323(f323(f121(x36221),x36222),f323(f323(f144(x36221),x36223),f113(x36221)))),x36222)
% 188.07/187.96 [3628]E(f323(f323(f121(x36281),f323(f323(f169(x36281),x36282),x36283)),f323(f323(f131(x36281),x36282),x36283)),x36283)
% 188.07/187.96 [3637]E(f323(f323(f22(a865),f323(f323(f78(a865),x36371),x36372)),f323(f323(f78(a865),x36373),x36372)),f323(f323(f22(a865),x36371),x36373))
% 188.07/187.96 [3638]E(f323(f323(f22(a865),f323(f323(f78(a865),x36381),x36382)),f323(f323(f78(a865),x36381),x36383)),f323(f323(f22(a865),x36382),x36383))
% 188.07/187.96 [3645]E(f323(f323(f121(x36451),f323(f162(x36451),x36452)),f323(f323(f144(x36451),x36453),f113(x36451))),f323(f162(x36451),f323(f323(f144(x36451),x36453),x36452)))
% 188.07/187.96 [3647]E(f323(f323(f78(a865),f323(f189(f866(x36471)),x36472)),f323(f189(f866(x36471)),x36473)),f323(f189(f866(x36471)),f323(f323(f121(x36471),x36472),x36473)))
% 188.07/187.96 [3650]E(f323(f323(f78(a865),f323(f189(f866(x36501)),x36502)),f323(f189(f866(x36501)),x36503)),f323(f189(f866(x36501)),f167(x36501,x36502,x36503)))
% 188.07/187.96 [3657]E(f323(f323(f110(f872(x36571,a860)),f323(f166(x36571),x36572)),f323(f166(x36571),x36573)),f323(f166(x36571),f323(f323(f121(x36571),x36572),x36573)))
% 188.07/187.96 [3658]E(f42(a865,f323(f323(f79(a865),x36581),x36582),f323(f323(f79(a865),x36581),x36583)),f323(f323(f79(a865),x36581),f42(a865,x36582,x36583)))
% 188.07/187.96 [3671]E(f323(f323(f169(x36711),f323(f323(f22(a865),x36712),f76(a865))),f323(f165(x36711),x36713)),f323(f165(x36711),f323(f323(f169(x36711),x36712),x36713)))
% 188.07/187.96 [3676]E(f323(f323(f101(f872(x36761,a860)),x36762),f323(f77(f872(x36761,a860)),x36763)),f323(f323(f22(f872(x36761,a860)),x36762),x36763))
% 188.07/187.96 [3677]E(f323(f323(f22(f872(x36771,a860)),x36772),f323(f77(f872(x36771,a860)),x36773)),f323(f323(f101(f872(x36771,a860)),x36772),x36773))
% 188.07/187.96 [3699]E(f323(f323(f260(x36991,x36992),x36993),f323(f16(f872(x36992,a860),x36991),f188(f872(x36992,a860)))),f188(f872(f871(x36991,x36992),a860)))
% 188.07/187.96 [3701]E(f323(f323(f22(a865),f323(f323(f79(a865),x37011),x37012)),f323(f323(f79(a865),x37011),x37013)),f323(f323(f79(a865),x37011),f323(f323(f22(a865),x37012),x37013)))
% 188.07/187.96 [3702]E(f323(f323(f78(a865),f323(f323(f79(a865),x37021),x37022)),f323(f323(f79(a865),x37021),x37023)),f323(f323(f79(a865),x37021),f323(f323(f78(a865),x37022),x37023)))
% 188.07/187.96 [3703]E(f323(f323(f22(a1),f323(f323(f79(a1),x37031),x37032)),f323(f323(f79(a1),x37031),x37033)),f323(f323(f79(a1),x37031),f323(f323(f22(a1),x37032),x37033)))
% 188.07/187.96 [3704]E(f323(f323(f78(a1),f323(f323(f79(a1),x37041),x37042)),f323(f323(f79(a1),x37041),x37043)),f323(f323(f79(a1),x37041),f323(f323(f78(a1),x37042),x37043)))
% 188.07/187.96 [3705]E(f323(f323(f79(a1),f323(f323(f248(a1),x37051),x37052)),f323(f323(f248(a1),x37051),x37053)),f323(f323(f248(a1),x37051),f323(f323(f78(a865),x37052),x37053)))
% 188.07/187.96 [3719]E(f323(f323(f39(x37191,f872(x37192,a860)),x37193),f323(f16(f872(x37192,a860),x37191),f188(f872(x37192,a860)))),f188(f872(x37192,a860)))
% 188.07/187.96 [3721]E(f42(a865,f323(f323(f79(a865),x37211),x37212),f323(f323(f79(a865),x37213),x37212)),f323(f323(f79(a865),f42(a865,x37211,x37213)),x37212))
% 188.07/187.96 [3725]E(f42(a1,f323(f323(f22(a1),x37251),f42(a1,x37252,x37253)),x37253),f42(a1,f323(f323(f22(a1),x37251),x37252),x37253))
% 188.07/187.96 [3726]E(f42(a1,f323(f323(f79(a1),x37261),f42(a1,x37262,x37263)),x37263),f42(a1,f323(f323(f79(a1),x37261),x37262),x37263))
% 188.07/187.96 [3727]P101(f323(f323(f237(f872(x37271,a860)),x37272),f323(f323(f301(x37271),x37273),x37272)))
% 188.07/187.96 [3730]E(f323(f302(f871(x37301,x37302),x37301,f257(x37301,x37302)),f323(f166(f871(x37301,x37302)),x37303)),f177(x37301,x37302,f323(f179(x37301,x37302),x37303)))
% 188.07/187.96 [3780]P101(f323(f59(x37801),f177(x37801,x37802,f323(f179(x37801,x37802),x37803))))
% 188.07/187.96 [3805]E(f323(f323(f40(f872(x38051,a860),f872(x38051,a860)),x38052),f323(f110(f872(x38051,a860)),x38053)),f323(f323(f110(f872(x38051,a860)),x38053),f38(f872(x38051,a860),x38052)))
% 188.07/187.96 [3806]E(f323(f323(f39(f872(x38061,a860),f872(x38061,a860)),x38062),f323(f101(f872(x38061,a860)),x38063)),f323(f323(f101(f872(x38061,a860)),x38063),f37(f872(x38061,a860),x38062)))
% 188.07/187.96 [3817]E(f323(f166(x38171),f323(f323(f323(f183(f866(x38171),f866(x38171)),x38172),f161(x38171)),x38173)),f323(f166(x38171),x38173))
% 188.07/187.96 [3821]E(f323(f323(f169(x38211),f323(f189(f866(x38211)),f171(x38211,x38212,x38213))),x38213),f171(x38211,x38212,x38213))
% 188.07/187.96 [3822]E(f177(x38221,x38222,f323(f323(f8(x38222,f869(x38222),x38221),f230(x38222)),x38223)),f246(f872(x38221,a860)))
% 188.07/187.96 [3827]E(f323(f189(f866(x38271)),f323(f323(f323(f183(f866(x38271),f866(x38271)),x38272),f161(x38271)),x38273)),f323(f189(f866(x38271)),x38273))
% 188.07/187.96 [3830]E(f323(f323(f262(x38301,x38302,x38302),f323(f16(f872(x38302,x38302),x38301),f5(x38302))),x38303),f323(f261(x38301,x38302),x38303))
% 188.07/187.96 [3837]E(f42(a1,f323(f323(f22(a1),f42(a1,x38371,x38372)),x38373),x38372),f42(a1,f323(f323(f22(a1),x38371),x38373),x38372))
% 188.07/187.96 [3838]E(f42(a1,f323(f323(f248(a1),f42(a1,x38381,x38382)),x38383),x38382),f42(a1,f323(f323(f248(a1),x38381),x38383),x38382))
% 188.07/187.96 [3841]E(f323(f323(f39(f872(f871(x38411,x38412),a860),f872(x38412,a860)),x38413),f254(x38411,x38412)),f323(f254(x38411,x38412),f37(f872(f871(x38411,x38412),a860),x38413)))
% 188.07/187.96 [3842]E(f323(f323(f39(f872(f871(x38421,x38422),a860),f872(x38421,a860)),x38423),f256(x38421,x38422)),f323(f256(x38421,x38422),f37(f872(f871(x38421,x38422),a860),x38423)))
% 188.07/187.96 [3870]E(f323(f71(x38701,x38701,x38701,x38702),f323(f323(f183(x38701,x38701),x38703),x38702)),f323(f323(f183(x38701,x38701),f323(a112,x38703)),x38702))
% 188.07/187.96 [3880]E(f232(f869(x38801),x38802,f200(x38801),f323(f323(f8(x38801,f869(x38801),x38802),f230(x38801)),x38803)),f323(f201(x38802,x38801),x38803))
% 188.07/187.96 [3887]E(f323(f323(f131(x38871),f323(f323(f22(a865),f323(f189(f866(x38871)),x38872)),x38873)),f323(f162(x38871),x38872)),f323(f162(x38871),f323(f323(f169(x38871),x38873),x38872)))
% 188.07/187.96 [3888]E(f323(f323(f169(x38881),f323(f323(f22(a865),f323(f189(f866(x38881)),x38882)),x38883)),f323(f162(x38881),x38882)),f323(f162(x38881),f323(f323(f131(x38881),x38883),x38882)))
% 188.07/187.96 [3891]E(f323(f323(f78(a865),f323(f159(a865),f323(f323(f147(x38911,a865),x38912),x38913))),f323(f189(f866(x38911)),x38913)),f148(x38911,x38912,x38913))
% 188.07/187.96 [3910]E(f323(f161(x39101),f323(f323(f323(f183(f866(x39101),f866(x39101)),x39102),f161(x39101)),x39103)),f323(f323(f323(f183(f866(x39101),f866(x39101)),f323(a112,x39102)),f161(x39101)),x39103))
% 188.07/187.96 [3925]P101(f323(f323(f237(a865),f323(f189(f866(x39251)),f323(f129(x39251,x39252),x39253))),f323(f189(f866(x39251)),x39253)))
% 188.07/187.96 [3942]E(f323(f323(f110(f872(f872(x39421,a860),a860)),f323(f300(x39421),x39422)),f323(f302(f872(x39421,a860),f872(x39421,a860),f323(f301(x39421),x39423)),f323(f300(x39421),x39422))),f323(f300(x39421),f323(f323(f301(x39421),x39423),x39422)))
% 188.07/187.96 [3962]P26(x39621,x39622,f323(f323(f301(f864(x39621)),f323(f323(f323(f90(x39621),x39623),a24),x39623)),f188(f872(f864(x39621),a860))))
% 188.07/187.96 [3978]P101(f323(f323(f237(a865),f323(f189(f866(x39781)),f171(x39781,x39782,x39783))),f323(f189(f866(x39781)),x39783)))
% 188.07/187.96 [3986]E(f323(f256(x39861,x39862),f323(f243(f871(x39861,x39862)),f323(f262(x39861,x39862,a860),x39863))),f323(f243(x39861),f323(f323(f8(f872(x39862,a860),a860,x39861),f85(x39862)),x39863)))
% 188.07/187.96 [3998]E(f323(f302(a865,a865,f323(f323(f7(a865,a865,a865),f78(a865)),x39981)),f294(a865,x39982,x39983)),f294(a865,f323(f323(f78(a865),x39982),x39981),f323(f323(f78(a865),x39983),x39981)))
% 188.07/187.96 [4001]P101(f323(f59(f869(x40011)),f323(f302(x40012,f869(x40011),f323(f179(x40012,x40011),x40013)),f246(f872(x40012,a860)))))
% 188.07/187.96 [4014]E(f323(f302(a865,a865,f323(f323(f7(a865,a865,a865),f78(a865)),x40141)),f323(f293(a865,x40142),x40143)),f323(f293(a865,f323(f323(f78(a865),x40142),x40141)),f323(f323(f78(a865),x40143),x40141)))
% 188.07/187.96 [4032]E(f323(f323(f175(x40321,x40322),f323(f323(f147(f871(x40321,x40322),x40321),f257(x40321,x40322)),x40323)),f323(f323(f147(f871(x40321,x40322),x40322),f261(x40321,x40322)),x40323)),x40323)
% 188.07/187.96 [4037]E(f323(f323(f78(a865),f323(f323(f79(a865),x40371),f42(a865,f323(f323(f36(a865),x40372),x40371),x40373))),f42(a865,x40372,x40371)),f42(a865,x40372,f323(f323(f79(a865),x40371),x40373)))
% 188.07/187.96 [4051]E(f323(f323(f121(x40511),x40512),f323(f135(f866(x40511),f866(x40511),f121(x40511),f113(x40511)),x40513)),f323(f135(f866(x40511),f866(x40511),f121(x40511),x40512),x40513))
% 188.07/187.96 [4069]P101(f323(f323(f325(f871(x40691,x40691)),f323(f323(f258(x40691,x40691),x40692),x40692)),f323(f323(f183(f871(x40691,x40691),a860),f2(a865)),x40693)))
% 188.07/187.96 [4075]E(f323(f243(x40751),f323(f323(f8(f872(x40752,a860),a860,x40751),f85(x40752)),f323(f7(x40752,x40751,a860),x40753))),f323(f254(x40752,x40751),f323(f243(f871(x40752,x40751)),f323(f262(x40752,x40751,a860),x40753))))
% 188.07/187.96 [4093]E(f323(f323(f110(f872(x40931,a860)),f323(f323(f39(a865,f872(x40931,a860)),f294(a865,f76(a865),x40932)),x40933)),f323(x40933,f2(a865))),f323(f323(f39(a865,f872(x40931,a860)),f323(f292(a865),x40932)),x40933))
% 188.07/187.96 [4108]E(f323(f135(f866(x41081),f866(x41081),f121(x41081),f113(x41081)),f323(f323(f147(f866(x41081),f866(x41081)),f129(x41081,x41082)),x41083)),f323(f129(x41081,x41082),f323(f135(f866(x41081),f866(x41081),f121(x41081),f113(x41081)),x41083)))
% 188.07/187.96 [4113]E(f323(f261(f866(x41131),f866(x41131)),f160(x41131,x41132,x41133)),f323(f129(x41131,f323(f71(a860,a860,x41131,a318),x41132)),x41133))
% 188.07/187.96 [4161]E(f323(f323(f78(a1),f323(f323(f78(a1),f323(f323(f79(a1),x41611),f323(f323(f36(a1),x41612),x41611))),f42(a1,x41612,x41611))),x41613),f323(f323(f78(a1),x41612),x41613))
% 188.07/187.96 [4200]E(f323(f323(f78(a1),f323(f323(f78(a1),f323(f323(f79(a1),f323(f323(f36(a1),x42001),x42002)),x42002)),f42(a1,x42001,x42002))),x42003),f323(f323(f78(a1),x42001),x42003))
% 188.07/187.96 [4229]E(f83(f871(x42291,x42292),f323(f262(x42291,x42292,a860),f323(f323(f8(f872(x42292,f871(x42291,x42292)),f872(x42292,a860),x42291),f323(f8(f871(x42291,x42292),a860,x42292),x42293)),f258(x42291,x42292)))),f83(f871(x42291,x42292),x42293))
% 188.07/187.96 [4230]E(f88(f871(x42301,x42302),f323(f262(x42301,x42302,a860),f323(f323(f8(f872(x42302,f871(x42301,x42302)),f872(x42302,a860),x42301),f323(f8(f871(x42301,x42302),a860,x42302),x42303)),f258(x42301,x42302)))),f88(f871(x42301,x42302),x42303))
% 188.07/187.96 [4258]P101(f323(f323(f237(f872(x42581,a860)),f37(f872(x42581,a860),f323(f323(f101(f872(f872(x42581,a860),a860)),x42582),x42583))),f323(f323(f101(f872(x42581,a860)),f37(f872(x42581,a860),x42582)),f37(f872(x42581,a860),x42583))))
% 188.07/187.96 [4259]E(f323(f162(x42591),f323(f323(f323(f183(f866(x42591),f866(x42591)),f323(f323(f22(a865),f323(f189(f866(x42591)),x42592)),f42(a865,x42593,f323(f189(f866(x42591)),x42592)))),f161(x42591)),x42592)),f323(f323(f323(f183(f866(x42591),f866(x42591)),x42593),f161(x42591)),f323(f162(x42591),x42592)))
% 188.07/187.96 [4273]E(f323(f243(x42731),f323(f323(f8(a860,a860,x42731),a318),f323(f323(f7(x42731,f869(x42732),a860),f323(f323(f8(f869(x42732),f872(f869(x42732),a860),x42731),a320),x42733)),f200(x42732)))),f177(x42731,x42732,x42733))
% 188.07/187.96 [4298]P101(f323(f323(f237(a865),f323(f189(f866(x42981)),f323(f323(f131(x42981),f323(f189(f866(x42981)),f171(x42981,x42982,x42983))),x42983))),f323(f189(f866(x42981)),x42983)))
% 188.07/187.96 [4341]E(f323(f243(x43411),f323(f323(f8(f872(x43412,a860),a860,x43411),f85(x43412)),f323(f323(f8(f869(x43411),f872(x43412,a860),x43411),f323(f7(x43412,f869(x43411),a860),f323(f323(f8(f869(x43411),f872(f869(x43411),a860),x43412),a320),x43413))),f230(x43411)))),f178(x43412,x43411,x43413))
% 188.07/187.96 [4560]~P101(f323(f60(x45601,x45602,f188(f872(x45601,a860))),x45603))
% 188.07/187.96 [4567]~P101(f323(f323(f325(f871(x45671,x45671)),f323(f323(f258(x45671,x45671),x45672),x45673)),f146(x45671,f113(f872(x45671,a865)))))
% 188.07/187.96 [3590]E(f323(f189(f866(x35901)),f323(f323(f169(x35901),x35902),x35903)),f323(f323(f235(a865),f323(f189(f866(x35901)),x35903)),x35902))
% 188.07/187.96 [3591]E(f323(f189(f866(x35911)),f323(f323(f131(x35911),x35912),x35913)),f323(f323(f22(a865),f323(f189(f866(x35911)),x35913)),x35912))
% 188.07/187.96 [3616]E(f323(f189(f866(f866(x36161))),f52(x36161,x36162,x36163)),f323(f323(f248(a865),f323(f189(f866(x36161)),x36163)),x36162))
% 188.07/187.96 [3630]E(f323(f323(f36(a865),f323(f323(f36(a865),x36301),x36302)),x36303),f323(f323(f36(a865),x36301),f323(f323(f79(a865),x36302),x36303)))
% 188.07/187.96 [3631]E(f323(f323(f22(a865),f323(f323(f22(a865),x36311),x36312)),x36313),f323(f323(f22(a865),x36311),f323(f323(f78(a865),x36312),x36313)))
% 188.07/187.96 [3632]E(f323(f323(f79(a865),f323(f323(f79(a865),x36321),x36322)),x36323),f323(f323(f79(a865),x36321),f323(f323(f79(a865),x36322),x36323)))
% 188.07/187.96 [3633]E(f323(f323(f79(a1),f323(f323(f79(a1),x36331),x36332)),x36333),f323(f323(f79(a1),x36331),f323(f323(f79(a1),x36332),x36333)))
% 188.07/187.96 [3634]E(f323(f323(f78(a865),f323(f323(f78(a865),x36341),x36342)),x36343),f323(f323(f78(a865),x36341),f323(f323(f78(a865),x36342),x36343)))
% 188.07/187.96 [3635]E(f323(f323(f78(a1),f323(f323(f78(a1),x36351),x36352)),x36353),f323(f323(f78(a1),x36351),f323(f323(f78(a1),x36352),x36353)))
% 188.07/187.96 [3636]E(f323(f323(f248(a1),f323(f323(f248(a1),x36361),x36362)),x36363),f323(f323(f248(a1),x36361),f323(f323(f79(a865),x36362),x36363)))
% 188.07/187.96 [3656]E(f155(x36561,f323(f323(f144(f872(x36561,a860)),x36562),x36563)),f168(x36561,x36562,f155(x36561,x36563)))
% 188.07/187.96 [3700]E(f323(f323(f22(a865),f323(f323(f22(a865),x37001),x37002)),x37003),f323(f323(f22(a865),f323(f323(f22(a865),x37001),x37003)),x37002))
% 188.07/187.96 [3706]E(f323(f230(f871(x37061,f867(x37061))),f323(f323(f258(x37061,f867(x37061)),x37062),x37063)),f323(f128(x37061),f123(x37061,x37062,x37063)))
% 188.07/187.96 [3709]E(f323(f323(f101(f872(x37091,a860)),x37092),f323(f323(f22(f872(x37091,a860)),x37093),x37092)),f188(f872(x37091,a860)))
% 188.07/187.96 [3751]E(f37(f872(x37511,a860),f323(f323(f301(f872(x37511,a860)),x37512),x37513)),f323(f323(f110(f872(x37511,a860)),x37512),f37(f872(x37511,a860),x37513)))
% 188.07/187.96 [3752]E(f38(f872(x37521,a860),f323(f323(f301(f872(x37521,a860)),x37522),x37523)),f323(f323(f101(f872(x37521,a860)),x37522),f38(f872(x37521,a860),x37523)))
% 188.07/187.96 [3755]E(f323(f323(f22(a865),f323(f323(f79(a865),x37551),x37552)),f323(f323(f79(a865),x37553),x37552)),f323(f323(f79(a865),f323(f323(f22(a865),x37551),x37553)),x37552))
% 188.07/187.96 [3756]E(f323(f323(f78(a865),f323(f323(f79(a865),x37561),x37562)),f323(f323(f79(a865),x37563),x37562)),f323(f323(f79(a865),f323(f323(f78(a865),x37561),x37563)),x37562))
% 188.07/187.96 [3757]E(f323(f323(f22(a1),f323(f323(f79(a1),x37571),x37572)),f323(f323(f79(a1),x37573),x37572)),f323(f323(f79(a1),f323(f323(f22(a1),x37571),x37573)),x37572))
% 188.07/187.96 [3758]E(f323(f323(f78(a1),f323(f323(f79(a1),x37581),x37582)),f323(f323(f79(a1),x37583),x37582)),f323(f323(f79(a1),f323(f323(f78(a1),x37581),x37583)),x37582))
% 188.07/187.96 [3760]E(f323(f323(f235(a865),f323(f323(f22(a865),x37601),x37602)),f323(f323(f22(a865),x37603),x37602)),f323(f323(f22(a865),f323(f323(f235(a865),x37601),x37603)),x37602))
% 188.07/187.96 [3783]E(f323(f323(f101(f872(f866(x37831),a860)),f153(x37831,x37832)),f153(x37831,x37833)),f153(x37831,f323(f323(f101(f872(x37831,a860)),x37832),x37833)))
% 188.07/187.96 [3785]E(f323(f323(f110(f872(x37851,a860)),x37852),f323(f323(f110(f872(x37851,a860)),x37852),x37853)),f323(f323(f110(f872(x37851,a860)),x37852),x37853))
% 188.07/187.96 [3786]E(f323(f323(f110(f872(x37861,a860)),x37862),f323(f323(f22(f872(x37861,a860)),x37863),x37862)),f323(f323(f110(f872(x37861,a860)),x37862),x37863))
% 188.07/187.96 [3787]E(f323(f323(f101(f872(x37871,a860)),x37872),f323(f323(f101(f872(x37871,a860)),x37872),x37873)),f323(f323(f101(f872(x37871,a860)),x37872),x37873))
% 188.07/187.96 [3799]E(f323(f323(f280(x37991,x37992,x37992),x37993),f299(x37992,f188(f872(f871(x37992,x37992),a860)))),x37993)
% 188.07/187.96 [3802]E(f323(f323(f110(f872(x38021,a860)),f323(f323(f301(x38021),x38022),f188(f872(x38021,a860)))),x38023),f323(f323(f301(x38021),x38022),x38023))
% 188.07/187.96 [3820]E(f323(f323(f22(a865),f323(f323(f22(a865),f323(a112,x38201)),x38202)),f323(a112,x38203)),f323(f323(f22(a865),f323(f323(f22(a865),x38201),x38202)),x38203))
% 188.07/187.96 [3851]E(f323(f323(f101(f872(f872(x38511,a860),a860)),f323(f300(x38511),x38512)),f323(f300(x38511),x38513)),f323(f300(x38511),f323(f323(f101(f872(x38511,a860)),x38512),x38513)))
% 188.07/187.96 [3855]E(f323(f323(f110(f872(x38551,a860)),f323(f77(f872(x38551,a860)),x38552)),x38553),f323(f77(f872(x38551,a860)),f323(f323(f22(f872(x38551,a860)),x38552),x38553)))
% 188.07/187.96 [3867]E(f323(f323(f301(x38671),x38672),f323(f323(f22(f872(x38671,a860)),x38673),f323(f323(f301(x38671),x38672),f188(f872(x38671,a860))))),f323(f323(f301(x38671),x38672),x38673))
% 188.07/187.96 [3877]P101(f323(f323(f237(f872(x38771,a860)),x38772),f323(f323(f110(f872(x38771,a860)),x38773),x38772)))
% 188.07/187.96 [3878]P101(f323(f323(f237(f872(x38781,a860)),x38782),f323(f323(f110(f872(x38781,a860)),x38782),x38783)))
% 188.07/187.96 [3881]E(f323(f323(f101(f872(x38811,a860)),f323(f77(f872(x38811,a860)),x38812)),f323(f77(f872(x38811,a860)),x38813)),f323(f77(f872(x38811,a860)),f323(f323(f110(f872(x38811,a860)),x38812),x38813)))
% 188.07/187.96 [3882]E(f323(f323(f110(f872(x38821,a860)),f323(f77(f872(x38821,a860)),x38822)),f323(f77(f872(x38821,a860)),x38823)),f323(f77(f872(x38821,a860)),f323(f323(f101(f872(x38821,a860)),x38822),x38823)))
% 188.07/187.96 [3896]P101(f323(f323(f237(f872(x38961,a860)),f323(f166(x38961),x38962)),f323(f166(x38961),f323(f323(f144(x38961),x38963),x38962))))
% 188.07/187.96 [3907]E(f323(f323(f110(f872(x39071,a860)),f323(f323(f22(f872(x39071,a860)),x39072),x39073)),f323(f323(f101(f872(x39071,a860)),x39072),x39073)),x39072)
% 188.07/187.96 [3964]E(f323(f323(f6(x39641,a1),f323(f323(f8(a865,a1,x39641),f100(a1)),x39642)),x39643),f323(f100(a1),f323(f323(f6(x39641,a865),x39642),x39643)))
% 188.07/187.96 [3965]E(f323(f323(f9(x39651,a1),f323(f323(f8(a865,a1,x39651),f100(a1)),x39652)),x39653),f323(f100(a1),f323(f323(f9(x39651,a865),x39652),x39653)))
% 188.07/187.96 [4016]E(f323(f323(f121(x40161),f171(x40161,x40162,x40163)),f323(f323(f131(x40161),f323(f189(f866(x40161)),f171(x40161,x40162,x40163))),x40163)),x40163)
% 188.07/187.96 [4021]E(f323(f77(f872(f871(x40211,x40212),a860)),f323(f323(f260(x40211,x40212),x40213),f323(f16(f872(x40212,a860),x40211),f246(f872(x40212,a860))))),f323(f323(f260(x40211,x40212),f323(f77(f872(x40211,a860)),x40213)),f323(f16(f872(x40212,a860),x40211),f246(f872(x40212,a860)))))
% 188.07/187.96 [4022]E(f323(f77(f872(f871(x40221,x40222),a860)),f323(f323(f260(x40221,x40222),f246(f872(x40221,a860))),f323(f16(f872(x40222,a860),x40221),x40223))),f323(f323(f260(x40221,x40222),f246(f872(x40221,a860))),f323(f16(f872(x40222,a860),x40221),f323(f77(f872(x40222,a860)),x40223))))
% 188.07/187.96 [4070]E(f323(f323(f39(f872(x40701,a860),f872(x40701,a860)),x40702),f323(f323(f7(f872(x40701,a860),f872(x40701,a860),f872(x40701,a860)),f101(f872(x40701,a860))),x40703)),f323(f323(f101(f872(x40701,a860)),f37(f872(x40701,a860),x40702)),x40703))
% 188.07/187.96 [4077]E(f323(f135(f866(x40771),f866(x40771),f121(x40771),f113(x40771)),f323(f323(f144(f866(x40771)),x40772),x40773)),f323(f323(f121(x40771),x40772),f323(f135(f866(x40771),f866(x40771),f121(x40771),f113(x40771)),x40773)))
% 188.07/187.96 [4099]E(f323(f323(f301(f872(x40991,a860)),f323(f277(x40991,x40991,x40992),f323(f323(f301(x40991),x40993),f188(f872(x40991,a860))))),f188(f872(f872(x40991,a860),a860))),f323(f323(f58(x40991),f323(f323(f301(x40991),x40993),f188(f872(x40991,a860)))),x40992))
% 188.07/187.96 [4109]E(f323(f323(f78(a865),f323(f323(f79(a865),x41091),f323(f323(f36(a865),x41092),x41093))),f323(f323(f36(a865),f323(f323(f79(a865),x41091),f42(a865,x41092,x41093))),x41093)),f323(f323(f36(a865),f323(f323(f79(a865),x41091),x41092)),x41093))
% 188.07/187.96 [4110]E(f323(f323(f78(a1),f323(f323(f79(a1),x41101),f323(f323(f36(a1),x41102),x41103))),f323(f323(f36(a1),f323(f323(f79(a1),x41101),f42(a1,x41102,x41103))),x41103)),f323(f323(f36(a1),f323(f323(f79(a1),x41101),x41102)),x41103))
% 188.07/187.96 [4146]E(f323(f323(f22(f872(x41461,a860)),f323(f166(x41461),x41462)),f323(f323(f301(x41461),x41463),f188(f872(x41461,a860)))),f323(f166(x41461),f323(f129(x41461,f323(f323(f8(a860,a860,x41461),a318),f323(a320,x41463))),x41462)))
% 188.07/187.96 [4197]E(f323(f323(f121(x41971),f323(f135(f866(x41971),f866(x41971),f121(x41971),f113(x41971)),x41972)),f323(f135(f866(x41971),f866(x41971),f121(x41971),f113(x41971)),x41973)),f323(f135(f866(x41971),f866(x41971),f121(x41971),f113(x41971)),f323(f323(f121(f866(x41971)),x41972),x41973)))
% 188.07/187.96 [4202]E(f323(f323(f258(f866(x42021),f866(x42021)),f323(f129(x42021,x42022),x42023)),f323(f129(x42021,f323(f71(a860,a860,x42021,a318),x42022)),x42023)),f160(x42021,x42022,x42023))
% 188.07/187.96 [4205]E(f323(f323(f78(a865),f323(f323(f78(a865),f323(f323(f36(a865),x42051),x42052)),f323(f323(f36(a865),x42053),x42052))),f323(f323(f36(a865),f323(f323(f78(a865),f42(a865,x42051,x42052)),f42(a865,x42053,x42052))),x42052)),f323(f323(f36(a865),f323(f323(f78(a865),x42051),x42053)),x42052))
% 188.07/187.96 [4206]E(f323(f323(f78(a1),f323(f323(f78(a1),f323(f323(f36(a1),x42061),x42062)),f323(f323(f36(a1),x42063),x42062))),f323(f323(f36(a1),f323(f323(f78(a1),f42(a1,x42061,x42062)),f42(a1,x42063,x42062))),x42062)),f323(f323(f36(a1),f323(f323(f78(a1),x42061),x42063)),x42062))
% 188.07/187.96 [4262]E(f323(f323(f101(f872(f866(x42621),a860)),f323(f323(f7(f866(x42621),f872(f866(x42621),a860),a860),f325(f866(x42621))),f154(x42621,x42622))),f323(f323(f7(f866(x42621),f872(f866(x42621),a860),a860),f325(f866(x42621))),f154(x42621,x42623))),f153(x42621,f323(f323(f101(f872(x42621,a860)),f323(f323(f7(x42621,f872(x42621,a860),a860),f325(x42621)),x42622)),f323(f323(f7(x42621,f872(x42621,a860),a860),f325(x42621)),x42623))))
% 188.07/187.96 [4275]E(f323(f243(x42751),f323(f323(f18(x42751,a860,a860),f323(f323(f8(a860,f872(a860,a860),x42751),a321),f323(f323(f7(x42751,x42751,a860),a320),x42752))),f323(f323(f7(x42751,f872(x42751,a860),a860),f325(x42751)),x42753))),f323(f323(f301(x42751),x42752),x42753))
% 188.07/187.96 [4295]E(f323(f323(f84(f866(f866(x42951)),f866(f866(x42951))),f51(x42951,x42952)),f323(f323(f18(f866(f866(x42951)),f866(f866(x42951)),f866(f866(x42951))),f323(f323(f8(f866(f866(x42951)),f872(f866(f866(x42951)),f866(f866(x42951))),f866(f866(x42951))),f121(f866(x42951))),f323(f147(f866(x42951),f866(x42951)),f323(f144(x42951),x42953)))),f5(f866(f866(x42951))))),f51(x42951,f323(f323(f144(x42951),x42953),x42952)))
% 188.07/187.96 [4299]E(f323(f243(x42991),f323(f323(f18(x42991,a860,a860),f323(f323(f8(a860,f872(a860,a860),x42991),a321),f323(f323(f7(x42991,f872(x42991,a860),a860),f325(x42991)),x42992))),f323(f323(f7(x42991,f872(x42991,a860),a860),f325(x42991)),x42993))),f323(f323(f110(f872(x42991,a860)),x42992),x42993))
% 188.07/187.96 [4300]E(f323(f243(x43001),f323(f323(f18(x43001,a860,a860),f323(f323(f8(a860,f872(a860,a860),x43001),a322),f323(f323(f7(x43001,f872(x43001,a860),a860),f325(x43001)),x43002))),f323(f323(f7(x43001,f872(x43001,a860),a860),f325(x43001)),x43003))),f323(f323(f101(f872(x43001,a860)),x43002),x43003))
% 188.07/187.96 [4393]E(f323(f323(f39(x43931,f872(f872(x43931,a860),a860)),x43932),f323(f323(f7(x43931,f872(f872(x43931,a860),a860),f872(f872(x43931,a860),a860)),f323(f323(f8(f872(x43931,a860),f872(f872(f872(x43931,a860),a860),f872(f872(x43931,a860),a860)),x43931),f301(f872(x43931,a860))),f323(f323(f8(f872(x43931,a860),f872(x43931,a860),x43931),f277(x43931,x43931,x43933)),f323(f323(f7(x43931,f872(x43931,a860),f872(x43931,a860)),f301(x43931)),f188(f872(x43931,a860)))))),f188(f872(f872(x43931,a860),a860)))),f323(f323(f58(x43931),x43932),x43933))
% 188.07/187.96 [4395]E(f323(f323(f204(x43951),f323(f323(f79(a1),f323(f323(f71(f871(a1,a1),a1,x43951,f257(a1,a1)),f214(x43951)),x43952)),f323(f323(f71(f871(a1,a1),a1,x43951,f257(a1,a1)),f214(x43951)),x43953))),f323(f323(f79(a1),f323(f323(f71(f871(a1,a1),a1,x43951,f261(a1,a1)),f214(x43951)),x43952)),f323(f323(f71(f871(a1,a1),a1,x43951,f261(a1,a1)),f214(x43951)),x43953))),f223(x43951,x43952,x43953))
% 188.07/187.96 [4398]E(f323(f243(f866(x43981)),f323(f323(f18(f866(x43981),a860,a860),f323(f323(f8(a860,f872(a860,a860),f866(x43981)),a322),f323(f323(f7(f866(x43981),a865,a860),f323(f323(f8(a865,f872(a865,a860),f866(x43981)),a320),f189(f866(x43981)))),x43982))),f323(f323(f7(f866(x43981),f872(x43981,a860),a860),f323(f323(f8(f872(x43981,a860),f872(f872(x43981,a860),a860),f866(x43981)),f237(f872(x43981,a860))),f166(x43981))),f323(f166(x43981),x43983)))),f323(f166(f866(x43981)),f52(x43981,x43982,x43983)))
% 188.07/187.96 [3773]E(f42(a865,f323(f323(f78(a865),f323(f323(f79(a865),x37731),x37732)),x37733),x37732),f42(a865,x37733,x37732))
% 188.07/187.96 [3819]E(f132(a865,f323(f293(a865,f323(f323(f78(a865),x38191),x38192)),x38193)),f323(f323(f131(a865),x38192),f132(a865,f323(f293(a865,x38191),x38193))))
% 188.07/187.96 [3866]E(f323(f323(f78(a1),f323(f100(a1),x38661)),f323(f323(f78(a1),f323(f100(a1),x38662)),x38663)),f323(f323(f78(a1),f323(f100(a1),f323(f323(f78(a865),x38661),x38662))),x38663))
% 188.07/187.96 [3873]E(f323(f323(f110(f872(x38731,a860)),f323(f323(f22(f872(x38731,a860)),x38732),x38733)),x38733),f323(f323(f110(f872(x38731,a860)),x38732),x38733))
% 188.07/187.96 [3874]E(f323(f323(f22(f872(x38741,a860)),f323(f323(f22(f872(x38741,a860)),x38742),x38743)),x38743),f323(f323(f22(f872(x38741,a860)),x38742),x38743))
% 188.07/187.96 [3897]E(f323(f323(f280(x38971,x38971,x38972),f299(x38971,f188(f872(f871(x38971,x38971),a860)))),x38973),x38973)
% 188.07/187.96 [3904]E(f323(f323(f110(f872(x39041,a860)),f323(f276(x39041),x39042)),f323(f276(x39041),x39043)),f323(f276(x39041),f323(f323(f110(f872(f871(x39041,x39041),a860)),x39042),x39043)))
% 188.07/187.96 [3915]E(f267(x39151,f323(f323(f144(f871(a99,x39151)),f323(f323(f258(a99,x39151),f2(a99)),x39152)),x39153)),f267(x39151,x39153))
% 188.07/187.96 [3918]E(f323(f323(f110(f872(x39181,a860)),f37(f872(x39181,a860),x39182)),f37(f872(x39181,a860),x39183)),f37(f872(x39181,a860),f323(f323(f110(f872(f872(x39181,a860),a860)),x39182),x39183)))
% 188.07/187.96 [3919]E(f323(f323(f101(f872(x39191,a860)),f38(f872(x39191,a860),x39192)),f38(f872(x39191,a860),x39193)),f38(f872(x39191,a860),f323(f323(f110(f872(f872(x39191,a860),a860)),x39192),x39193)))
% 188.07/187.96 [3956]E(f323(f323(f280(x39561,x39561,x39561),f323(f323(f183(f871(x39561,x39561),a860),x39562),x39563)),x39563),f323(f323(f183(f871(x39561,x39561),a860),f323(a112,x39562)),x39563))
% 188.07/187.96 [4007]P101(f323(f323(f237(f872(x40071,a860)),f323(f323(f22(f872(x40071,a860)),x40072),x40073)),x40072))
% 188.07/187.96 [4008]P101(f323(f323(f237(f872(x40081,a860)),f323(f323(f101(f872(x40081,a860)),x40082),x40083)),x40083))
% 188.07/187.96 [4009]P101(f323(f323(f237(f872(x40091,a860)),f323(f323(f101(f872(x40091,a860)),x40092),x40093)),x40092))
% 188.07/187.96 [4034]E(f299(x40341,f323(f323(f110(f872(f871(x40341,x40341),a860)),f299(x40341,x40342)),f299(x40341,x40343))),f299(x40341,f323(f323(f110(f872(f871(x40341,x40341),a860)),x40342),x40343)))
% 188.07/187.96 [4038]E(f37(f872(x40381,a860),f323(f323(f301(f872(x40381,a860)),x40382),f323(f323(f301(f872(x40381,a860)),x40383),f188(f872(f872(x40381,a860),a860))))),f323(f323(f110(f872(x40381,a860)),x40382),x40383))
% 188.07/187.96 [4039]E(f38(f872(x40391,a860),f323(f323(f301(f872(x40391,a860)),x40392),f323(f323(f301(f872(x40391,a860)),x40393),f188(f872(f872(x40391,a860),a860))))),f323(f323(f101(f872(x40391,a860)),x40392),x40393))
% 188.07/187.96 [4045]E(f323(f323(f280(x40451,x40451,x40451),f323(f323(f183(f871(x40451,x40451),a860),x40452),x40453)),x40453),f323(f323(f280(x40451,x40451,x40451),x40453),f323(f323(f183(f871(x40451,x40451),a860),x40452),x40453)))
% 188.07/187.96 [4114]E(f323(f323(f110(f872(x41141,a860)),f323(f243(x41141),f323(f323(f7(x41141,x41141,a860),a320),x41142))),x41143),f323(f323(f301(x41141),x41142),x41143))
% 188.07/187.96 [4116]E(f323(a104,f323(f323(f6(x41161,a1),f323(f323(f8(a865,a1,x41161),f100(a1)),x41162)),x41163)),f323(f323(f6(x41161,a865),x41162),x41163))
% 188.07/187.96 [4117]E(f323(a104,f323(f323(f9(x41171,a1),f323(f323(f8(a865,a1,x41171),f100(a1)),x41172)),x41173)),f323(f323(f9(x41171,a865),x41172),x41173))
% 188.07/187.96 [4194]E(f323(f149(f866(x41941),x41941,f323(f165(x41941),x41942),f323(f16(f872(f866(x41941),f866(x41941)),x41941),f323(f323(f7(f866(x41941),f866(x41941),f866(x41941)),f121(x41941)),x41942))),x41943),f323(f165(x41941),f323(f323(f121(x41941),x41943),x41942)))
% 188.07/187.96 [4225]P101(f323(f323(f237(f872(f872(x42251,a860),a860)),f323(f323(f110(f872(f872(x42251,a860),a860)),f323(f300(x42251),x42252)),f323(f300(x42251),x42253))),f323(f300(x42251),f323(f323(f110(f872(x42251,a860)),x42252),x42253))))
% 188.07/187.96 [4319]E(f323(f243(x43191),f323(f323(f18(x43191,a860,a860),f323(f323(f8(a860,f872(a860,a860),x43191),a322),f323(f323(f7(x43191,f872(x43191,a860),a860),f325(x43191)),x43192))),f323(f323(f8(a860,a860,x43191),a318),f323(f323(f7(x43191,f872(x43191,a860),a860),f325(x43191)),x43193)))),f323(f323(f22(f872(x43191,a860)),x43192),x43193))
% 188.07/187.96 [4342]E(f323(f35(a865),f323(f243(a865),f323(f323(f18(a865,a860,a860),f323(f323(f8(a860,f872(a860,a860),a865),a322),f323(f323(f7(a865,a865,a860),f238(a865)),f323(f189(f866(x43421)),x43422)))),f323(f323(f8(x43421,a860,a865),x43423),f323(f158(x43421),x43422))))),f323(f189(f866(x43421)),f323(f129(x43421,x43423),x43422)))
% 188.07/187.96 [4344]E(f323(f189(f866(x43441)),f170(x43441,x43442,x43443)),f323(f35(a865),f323(f243(a865),f323(f323(f18(a865,a860,a860),f323(f323(f8(a860,f872(a860,a860),a865),a322),f323(f323(f7(a865,a865,a860),f238(a865)),f323(f189(f866(x43441)),x43442)))),f323(f323(f7(a865,f872(a865,a860),a860),f325(a865)),x43443)))))
% 188.07/187.96 [4442]E(f323(f323(f101(f872(f871(f866(x44421),f866(x44421)),a860)),f323(f302(f871(f871(x44421,f866(x44421)),f871(x44421,f866(x44421))),f871(f866(x44421),f866(x44421)),f263(f871(x44421,f866(x44421)),f866(x44421),f871(x44421,f866(x44421)),f866(x44421),f323(f262(x44421,f866(x44421),f866(x44421)),f144(x44421)),f323(f262(x44421,f866(x44421),f866(x44421)),f144(x44421)))),f315(x44421,f866(x44421),x44422,f323(f136(x44421,x44422),x44423)))),f323(f243(f871(f866(x44421),f866(x44421))),f323(f262(f866(x44421),f866(x44421),a860),f323(f323(f7(f866(x44421),f872(f866(x44421),a860),f872(f866(x44421),a860)),f323(f323(f8(f872(a860,a860),f872(f872(f866(x44421),a860),f872(f866(x44421),a860)),f866(x44421)),f8(a860,a860,f866(x44421))),f323(f323(f8(a860,f872(a860,a860),f866(x44421)),a322),f323(f323(f7(f866(x44421),a865,a860),f323(f323(f8(a865,f872(a865,a860),f866(x44421)),a320),f189(f866(x44421)))),f323(a112,x44423))))),f323(f323(f7(f866(x44421),a865,a860),f323(f323(f8(a865,f872(a865,a860),f866(x44421)),a320),f189(f866(x44421)))),f323(a112,x44423)))))),f323(f136(x44421,x44422),f323(a112,x44423)))
% 188.07/187.96 [3920]E(f42(a865,f323(a112,f323(f323(f78(a865),f323(f323(f79(a865),x39201),x39202)),x39203)),x39202),f42(a865,f323(a112,x39203),x39202))
% 188.07/187.96 [4181]E(f323(f243(x41811),f323(f323(f18(x41811,a860,a860),f323(f323(f8(a860,f872(a860,a860),x41811),a321),x41812)),x41813)),f323(f323(f110(f872(x41811,a860)),f323(f243(x41811),x41812)),f323(f243(x41811),x41813)))
% 188.07/187.96 [4182]E(f323(f243(x41821),f323(f323(f18(x41821,a860,a860),f323(f323(f8(a860,f872(a860,a860),x41821),a322),x41822)),x41823)),f323(f323(f101(f872(x41821,a860)),f323(f243(x41821),x41822)),f323(f243(x41821),x41823)))
% 188.07/187.96 [4184]E(f323(f323(f121(x41841),f323(f323(f131(x41841),f42(a865,x41842,f323(f189(f866(x41841)),x41843))),x41843)),f323(f323(f169(x41841),f42(a865,x41842,f323(f189(f866(x41841)),x41843))),x41843)),f323(f323(f323(f183(f866(x41841),f866(x41841)),x41842),f161(x41841)),x41843))
% 188.07/187.96 [4190]E(f323(f243(x41901),f323(f323(f18(x41901,a860,a860),f323(f323(f8(a860,f872(a860,a860),x41901),a326),x41902)),x41903)),f323(f323(f110(f872(x41901,a860)),f323(f77(f872(x41901,a860)),f323(f243(x41901),x41902))),f323(f243(x41901),x41903)))
% 188.07/187.96 [4207]E(f323(f323(f78(a865),f323(f189(f866(x42071)),f323(f129(x42071,x42072),x42073))),f323(f189(f866(x42071)),f323(f129(x42071,f323(f323(f8(a860,a860,x42071),a318),x42072)),x42073))),f323(f189(f866(x42071)),x42073))
% 188.07/187.96 [4232]P101(f323(f323(f237(f872(x42321,a860)),f323(f323(f110(f872(x42321,a860)),f38(f872(x42321,a860),x42322)),f38(f872(x42321,a860),x42323))),f38(f872(x42321,a860),f323(f323(f101(f872(f872(x42321,a860),a860)),x42322),x42323))))
% 188.07/187.96 [4246]E(f323(f166(x42461),f323(f129(x42461,f323(f323(f8(a860,a860,x42461),a318),f323(f323(f7(x42461,x42461,a860),a320),x42462))),x42463)),f323(f323(f22(f872(x42461,a860)),f323(f166(x42461),x42463)),f323(f323(f301(x42461),x42462),f188(f872(x42461,a860)))))
% 188.07/187.96 [4255]P101(f323(f323(f237(f872(f871(x42551,x42551),a860)),f323(f323(f110(f872(f871(x42551,x42551),a860)),f299(x42551,x42552)),f299(x42551,x42553))),f299(x42551,f323(f323(f110(f872(f871(x42551,x42551),a860)),x42552),x42553))))
% 188.07/187.96 [4280]E(f323(f323(f79(a865),f323(a112,f323(a112,f2(a865)))),f323(f323(f6(a865,a865),f323(f323(f8(a865,a865,a865),f323(f78(a865),x42801)),f323(f323(f7(a865,a865,a865),f79(a865)),x42802))),f323(f244(a865),x42803))),f323(f323(f79(a865),x42803),f323(f323(f78(a865),x42801),f323(f323(f78(a865),x42801),f323(f323(f79(a865),f323(f323(f22(a865),x42803),f76(a865))),x42802)))))
% 188.07/187.96 [4290]E(f323(f243(x42901),f323(f323(f18(x42901,a860,a860),f323(f323(f8(a860,f872(a860,a860),x42901),a322),f323(f323(f7(x42901,f872(x42901,a860),a860),f325(x42901)),f323(f166(x42901),x42902)))),x42903)),f323(f166(x42901),f323(f129(x42901,x42903),x42902)))
% 188.07/187.96 [4441]E(f323(f243(x44411),f323(f323(f8(f872(a865,a860),a860,x44411),f85(a865)),f323(f323(f7(x44411,f872(a865,a860),f872(a865,a860)),f323(f323(f8(f872(a865,f872(a860,a860)),f872(f872(a865,a860),f872(a865,a860)),x44411),f18(a865,a860,a860)),f323(f323(f8(f872(a865,a860),f872(a865,f872(a860,a860)),x44411),f323(f8(a860,f872(a860,a860),a865),a322)),f323(f323(f7(x44411,f872(a865,x44411),f872(a865,a860)),f323(f323(f8(f872(x44411,a860),f872(f872(a865,x44411),f872(a865,a860)),x44411),f8(x44411,a860,a865)),a320)),f323(f158(x44411),x44412))))),f323(f323(f18(a865,a860,a860),f323(f323(f8(a860,f872(a860,a860),a865),a322),f323(f323(f7(a865,a865,a860),f238(a865)),f323(f189(f866(x44411)),x44412)))),f323(f323(f7(a865,f872(a865,a860),a860),f325(a865)),x44413))))),f323(f166(x44411),f170(x44411,x44412,x44413)))
% 188.07/187.96 [4331]E(f323(f243(x43311),f323(f323(f18(x43311,a860,a860),f323(f323(f8(a860,f872(a860,a860),x43311),a326),f323(f323(f8(a860,a860,x43311),a318),f323(f323(f7(x43311,x43311,a860),a320),x43312)))),x43313)),f323(f323(f301(x43311),x43312),f323(f243(x43311),x43313)))
% 188.07/187.96 [4364]E(f323(f323(f147(f871(x43641,a865),x43641),f257(x43641,a865)),f323(f129(f871(x43641,a865),f323(f323(f7(f871(x43641,a865),f872(a865,a860),a860),f323(f323(f8(a865,f872(f872(a865,a860),a860),f871(x43641,a865)),f325(a865)),f261(x43641,a865))),x43642)),f323(f323(f175(x43641,a865),x43643),f132(a865,f323(f293(a865,f2(a865)),f323(f189(f866(x43641)),x43643)))))),f170(x43641,x43643,x43642))
% 188.07/187.96 [4394]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(a865,a1),f323(f323(f8(a1,a1,a865),f323(f78(a1),x43941)),f323(f323(f7(a865,a1,a1),f323(f323(f8(a1,f872(a1,a1),a865),f79(a1)),f100(a1))),x43942))),f323(f244(a865),x43943))),f323(f323(f79(a1),f323(f100(a1),x43943)),f323(f323(f78(a1),x43941),f323(f323(f78(a1),x43941),f323(f323(f79(a1),f323(f100(a1),f323(f323(f22(a865),x43943),f76(a865)))),x43942)))))
% 188.07/187.96 [4434]E(f323(f243(f871(x44341,x44342)),f323(f262(x44341,x44342,a860),f323(f323(f7(x44341,f872(f871(x44342,x44341),a860),f872(x44342,a860)),f323(f323(f8(f872(x44342,f872(f872(f871(x44342,x44341),a860),a860)),f872(f872(f871(x44342,x44341),a860),f872(x44342,a860)),x44341),f7(x44342,f872(f871(x44342,x44341),a860),a860)),f323(f323(f8(f872(x44342,f871(x44342,x44341)),f872(x44342,f872(f872(f871(x44342,x44341),a860),a860)),x44341),f323(f8(f871(x44342,x44341),f872(f872(f871(x44342,x44341),a860),a860),x44342),f325(f871(x44342,x44341)))),f323(f7(x44342,x44341,f871(x44342,x44341)),f258(x44342,x44341))))),x44343))),f323(f278(x44342,x44341),x44343))
% 188.07/187.96 [4465]E(f323(f243(f866(x44651)),f323(f323(f8(f872(x44651,a860),a860,f866(x44651)),f85(x44651)),f323(f323(f8(f872(x44651,f872(f866(x44651),a860)),f872(x44651,a860),f866(x44651)),f323(f8(f872(f866(x44651),a860),a860,x44651),f85(f866(x44651)))),f323(f323(f7(f866(x44651),f872(x44651,f872(f866(x44651),a860)),f872(x44651,f872(f866(x44651),a860))),f323(f323(f8(f872(x44651,f872(f872(f866(x44651),a860),f872(f866(x44651),a860))),f872(f872(x44651,f872(f866(x44651),a860)),f872(x44651,f872(f866(x44651),a860))),f866(x44651)),f18(x44651,f872(f866(x44651),a860),f872(f866(x44651),a860))),f323(f323(f8(f872(x44651,f872(f866(x44651),f872(a860,a860))),f872(x44651,f872(f872(f866(x44651),a860),f872(f866(x44651),a860))),f866(x44651)),f323(f8(f872(f866(x44651),f872(a860,a860)),f872(f872(f866(x44651),a860),f872(f866(x44651),a860)),x44651),f18(f866(x44651),a860,a860))),f323(f323(f8(f872(x44651,f872(f866(x44651),a860)),f872(x44651,f872(f866(x44651),f872(a860,a860))),f866(x44651)),f323(f8(f872(f866(x44651),a860),f872(f866(x44651),f872(a860,a860)),x44651),f323(f8(a860,f872(a860,a860),f866(x44651)),a322))),f323(f323(f7(f866(x44651),f872(x44651,f872(f866(x44651),f866(x44651))),f872(x44651,f872(f866(x44651),a860))),f323(f323(f8(f872(f872(f866(x44651),f866(x44651)),f872(f866(x44651),a860)),f872(f872(x44651,f872(f866(x44651),f866(x44651))),f872(x44651,f872(f866(x44651),a860))),f866(x44651)),f8(f872(f866(x44651),f866(x44651)),f872(f866(x44651),a860),x44651)),f323(f323(f8(f872(f866(x44651),a860),f872(f872(f866(x44651),f866(x44651)),f872(f866(x44651),a860)),f866(x44651)),f8(f866(x44651),a860,f866(x44651))),a320))),f144(x44651)))))),f323(f323(f7(x44651,f872(f866(x44651),a860),f872(f866(x44651),a860)),f323(f323(f8(f872(a860,a860),f872(f872(f866(x44651),a860),f872(f866(x44651),a860)),x44651),f8(a860,a860,f866(x44651))),f323(f323(f8(a860,f872(a860,a860),x44651),a322),f323(f323(f7(x44651,f872(x44651,a860),a860),f325(x44651)),x44652)))),f323(f323(f7(f866(x44651),f872(f866(x44651),a860),a860),f325(f866(x44651))),x44653)))))),f168(x44651,x44652,x44653))
% 188.07/187.96 [4456]E(f323(f323(f84(a1,f871(a1,a1)),f323(f323(f22(a1),x44561),x44562)),f323(f323(f7(a1,f871(a1,a1),f871(a1,a1)),f323(f323(f18(a1,f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),f323(f323(f8(a860,f872(f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),a1),f96(f871(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)))),x44563)),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)))),x44563)),x44561))),f323(f41(x44562),f323(f323(f258(a1,a1),x44563),x44561)))
% 188.07/187.96 [4489]~E(f29(x44891,x44892),f30(x44893,x44894))
% 188.07/187.96 [4492]~E(f25(x44921,x44922),f30(x44923,x44924))
% 188.07/187.96 [4493]~E(f25(x44931,x44932),f29(x44933,x44934))
% 188.07/187.96 [3468]E(f323(f323(f323(f70(x34681,x34682),x34683),x34684),f323(x34683,x34684)),x34683)
% 188.07/187.96 [3527]E(f323(f323(f249(x35271,x35272,x35273),x35274),f2(a865)),x35272)
% 188.07/187.96 [3567]E(f185(x35671,x35672,x35673,f323(a112,x35674)),f323(x35673,x35674))
% 188.07/187.96 [3609]E(f164(x36091,x36092,f164(x36091,x36093,x36094)),f164(x36091,x36093,f164(x36091,x36092,x36094)))
% 188.07/187.96 [3741]E(f323(f232(x37411,x37412,x37413,x37414),f200(x37412)),x37413)
% 188.07/187.96 [3742]E(f323(f149(x37421,x37422,x37423,x37424),f113(x37422)),x37423)
% 188.07/187.96 [3743]E(f323(f135(x37431,x37432,x37433,x37434),f113(x37432)),x37434)
% 188.07/187.96 [3850]E(f323(f323(f121(x38501),f163(x38501,x38502,x38503)),f163(x38501,x38504,x38503)),f323(f323(f121(x38501),f163(x38501,x38504,x38503)),f163(x38501,x38502,x38503)))
% 188.07/187.96 [3863]E(f323(f232(f869(x38631),x38632,f200(x38631),f323(f16(f869(x38631),x38632),f200(x38631))),f323(x38633,x38634)),f200(x38631))
% 188.07/187.96 [3908]E(f323(f323(f110(f872(x39081,a860)),f177(x39081,x39082,x39083)),f177(x39081,x39082,x39084)),f177(x39081,x39082,f180(x39081,x39082,x39084,x39083)))
% 188.07/187.96 [3940]E(f323(f323(f264(x39401,x39402,x39403,f871(x39402,x39403)),x39404),f258(x39402,x39403)),x39404)
% 188.07/187.96 [3950]E(f233(x39501,x39502,x39503,x39504,f200(x39502)),x39503)
% 188.07/187.96 [3951]E(f181(x39511,x39512,x39513,x39514,f113(x39512)),x39513)
% 188.07/187.96 [3952]E(f181(x39521,x39522,x39523,f113(x39521),x39524),x39523)
% 188.07/187.96 [4239]P43(x42391,x42392,x42393,x42394,f188(f872(x42391,a860)),x42394)
% 188.07/187.96 [3272]E(f323(f323(f16(x32721,x32722),x32723),x32724),x32723)
% 188.07/187.96 [3385]E(f323(f323(f201(x33851,x33852),x33853),f323(f230(x33851),x33854)),f323(f230(x33852),f323(x33853,x33854)))
% 188.07/187.96 [3557]E(f164(x35571,x35572,f323(f129(x35571,x35573),x35574)),f323(f129(x35571,x35573),f164(x35571,x35572,x35574)))
% 188.07/187.96 [3592]E(f323(f323(f62(x35921,x35922,x35923),x35924),f188(f872(x35921,a860))),x35924)
% 188.07/187.96 [3615]E(f323(f323(f158(x36151),f323(f323(f144(x36151),x36152),x36153)),f323(a112,x36154)),f323(f323(f158(x36151),x36153),x36154))
% 188.07/187.96 [3681]E(f323(f323(x36811,x36812),f323(f184(x36813,x36814,x36811),x36812)),f323(f184(x36813,x36814,x36811),f323(a112,x36812)))
% 188.07/187.96 [3778]E(f323(f323(f152(x37781,f323(f323(f144(x37781),x37782),x37783)),f2(a865)),x37784),f323(f323(f144(x37781),x37784),x37783))
% 188.07/187.96 [3789]E(f323(f323(f39(f872(x37891,a860),f872(x37892,a860)),x37893),f302(x37891,x37892,x37894)),f323(f302(x37891,x37892,x37894),f37(f872(x37891,a860),x37893)))
% 188.07/187.96 [3790]E(f323(f323(f39(f872(x37901,a860),f872(x37902,a860)),x37903),f303(x37902,x37901,x37904)),f323(f303(x37902,x37901,x37904),f37(f872(x37901,a860),x37903)))
% 188.07/187.96 [3890]E(f177(x38901,x38902,f182(x38901,x38902,x38903,x38904)),f323(f323(f101(f872(x38901,a860)),f177(x38901,x38902,x38903)),x38904))
% 188.07/187.96 [3894]E(f323(f125(x38941,x38942),f123(x38941,x38943,x38944)),f323(f323(f78(a865),f323(f323(f78(a865),f323(x38942,x38943)),f323(f125(x38941,x38942),x38944))),f323(a112,f2(a865))))
% 188.07/187.96 [3914]E(f323(f135(x39141,x39142,f323(f7(x39142,x39141,x39141),x39143),x39144),f323(f162(x39142),f113(x39142))),x39144)
% 188.07/187.96 [3963]E(f74(x39631,x39632,x39633,x39634,f188(f872(x39631,a860))),x39633)
% 188.07/187.96 [4010]E(f323(f323(f323(f323(f70(x40101,f869(x40102)),f323(f16(f869(x40102),x40101),f200(x40102))),x40103),f200(x40102)),x40104),f200(x40102))
% 188.07/187.96 [4164]E(f323(f262(x41641,x41642,x41643),f323(f323(f8(f872(x41642,f871(x41641,x41642)),f872(x41642,x41643),x41641),f323(f8(f871(x41641,x41642),x41643,x41642),x41644)),f258(x41641,x41642))),x41644)
% 188.07/187.96 [3466]E(f323(f261(x34661,x34662),f323(f323(f258(x34661,x34662),x34663),x34664)),x34664)
% 188.07/187.96 [3467]E(f323(f257(x34671,x34672),f323(f323(f258(x34671,x34672),x34673),x34674)),x34673)
% 188.07/187.96 [3500]E(f323(f189(f866(x35001)),f323(f323(f147(x35002,x35001),x35003),x35004)),f323(f189(f866(x35002)),x35004))
% 188.07/187.96 [3501]E(f323(f189(f866(x35011)),f323(f323(f152(x35011,x35012),x35013),x35014)),f323(f189(f866(x35011)),x35012))
% 188.07/187.96 [3521]E(f323(f323(f131(x35211),f323(a112,x35212)),f323(f323(f144(x35211),x35213),x35214)),f323(f323(f131(x35211),x35212),x35214))
% 188.07/187.96 [3587]E(f323(f323(f169(x35871),x35872),f163(x35871,x35873,x35874)),f163(x35871,f323(f323(f235(a865),x35872),x35873),x35874))
% 188.07/187.96 [3588]E(f323(f323(f131(x35881),x35882),f163(x35881,x35883,x35884)),f163(x35881,f323(f323(f22(a865),x35883),x35882),x35884))
% 188.07/187.96 [3594]E(f323(f323(f301(x35941),x35942),f323(f323(f301(x35941),x35943),x35944)),f323(f323(f301(x35941),x35943),f323(f323(f301(x35941),x35942),x35944)))
% 188.07/187.96 [3598]E(f323(f323(f147(x35981,x35982),x35983),f114(x35981,x35984)),f114(x35982,f323(f323(f147(x35981,x35982),x35983),x35984)))
% 188.07/187.96 [3613]E(f323(f162(x36131),f323(f323(f147(x36132,x36131),x36133),x36134)),f323(f323(f147(x36132,x36131),x36133),f323(f162(x36132),x36134)))
% 188.07/187.96 [3614]E(f323(f323(f147(x36141,x36142),x36143),f323(f165(x36141),x36144)),f323(f165(x36142),f323(f323(f147(x36141,x36142),x36143),x36144)))
% 188.07/187.96 [3625]E(f323(f323(f169(x36251),f323(a112,x36252)),f323(f323(f144(x36251),x36253),x36254)),f323(f323(f144(x36251),x36253),f323(f323(f169(x36251),x36252),x36254)))
% 188.07/187.96 [3629]E(f323(f166(x36291),f323(f323(f147(x36292,x36291),x36293),x36294)),f323(f302(x36292,x36291,x36293),f323(f166(x36292),x36294)))
% 188.07/187.96 [3680]E(f17(x36801,x36802,x36803,f323(a3,f323(a112,f323(a19,x36804)))),f323(x36803,x36804))
% 188.07/187.96 [3683]E(f323(f323(f121(x36831),f323(f129(x36831,x36832),x36833)),f323(f129(x36831,x36832),x36834)),f323(f129(x36831,x36832),f323(f323(f121(x36831),x36833),x36834)))
% 188.07/187.96 [3696]E(f145(x36961,f323(f323(f147(x36962,x36961),x36963),f145(x36962,x36964))),f145(x36961,f323(f323(f147(x36962,x36961),x36963),x36964)))
% 188.07/187.96 [3712]E(f323(f278(x37121,x37121),f323(f323(f279(x37122,x37121),x37123),x37124)),f323(f323(f279(x37122,x37121),f323(f278(x37122,x37122),x37123)),x37124))
% 188.07/187.96 [3722]E(f323(f323(f280(x37221,x37222,x37223),x37224),f188(f872(f871(x37222,x37223),a860))),f188(f872(f871(x37221,x37223),a860)))
% 188.07/187.96 [3723]E(f323(f323(f169(x37231),f323(f323(f22(a865),x37232),x37233)),f323(f323(f131(x37231),x37233),x37234)),f323(f323(f131(x37231),x37233),f323(f323(f169(x37231),x37232),x37234)))
% 188.07/187.96 [3744]E(f323(f323(f121(x37441),f163(x37441,x37442,x37443)),f163(x37441,x37444,x37443)),f163(x37441,f323(f323(f78(a865),x37442),x37444),x37443))
% 188.07/187.96 [3770]E(f37(f872(x37701,a860),f323(f302(x37702,f872(x37701,a860),x37703),x37704)),f323(f323(f39(x37702,f872(x37701,a860)),x37704),x37703))
% 188.07/187.96 [3771]E(f38(f872(x37711,a860),f323(f302(x37712,f872(x37711,a860),x37713),x37714)),f323(f323(f40(x37712,f872(x37711,a860)),x37714),x37713))
% 188.07/187.96 [3772]E(f323(f189(f866(f871(x37721,x37722))),f323(f323(f175(x37721,x37722),x37723),x37724)),f323(f323(f235(a865),f323(f189(f866(x37721)),x37723)),f323(f189(f866(x37722)),x37724)))
% 188.07/187.96 [3774]E(f323(f303(x37741,x37742,x37743),f323(f77(f872(x37742,a860)),x37744)),f323(f77(f872(x37741,a860)),f323(f303(x37741,x37742,x37743),x37744)))
% 188.07/187.96 [3804]E(f323(f182(x38041,x38042,x38043,f188(f872(x38041,a860))),x38044),f200(x38042))
% 188.07/187.96 [3826]E(f323(f303(x38261,x38262,x38263),f323(f243(x38262),x38264)),f323(f243(x38261),f323(f323(f8(x38262,a860,x38261),x38264),x38263)))
% 188.07/187.96 [3844]E(f323(f323(f158(x38441),f323(f323(f121(x38441),x38442),f323(f323(f144(x38441),x38443),x38444))),f323(f189(f866(x38441)),x38442)),x38443)
% 188.07/187.96 [3849]E(f323(f182(x38491,x38492,f323(f16(f869(x38492),x38491),f200(x38492)),x38493),x38494),f200(x38492))
% 188.07/187.96 [3871]E(f323(f302(x38711,x38712,x38713),f323(f303(x38711,x38712,x38713),x38714)),f323(f323(f101(f872(x38712,a860)),x38714),f323(f302(x38711,x38712,x38713),f246(f872(x38711,a860)))))
% 188.07/187.96 [3889]P101(f323(f323(f325(x38891),f323(x38892,x38893)),f323(f302(x38894,x38891,x38892),f246(f872(x38894,a860)))))
% 188.07/187.96 [3901]E(f323(f323(f121(x39011),f163(x39011,x39012,x39013)),f323(f323(f144(x39011),x39013),x39014)),f323(f323(f144(x39011),x39013),f323(f323(f121(x39011),f163(x39011,x39012,x39013)),x39014)))
% 188.07/187.96 [3903]E(f323(f323(f260(x39031,x39032),f323(f166(x39031),x39033)),f323(f16(f872(x39032,a860),x39031),f323(f166(x39032),x39034))),f323(f166(f871(x39031,x39032)),f57(x39031,x39032,x39033,x39034)))
% 188.07/187.96 [3917]E(f148(x39171,x39172,f323(f323(f144(x39171),x39173),x39174)),f323(f323(f78(a865),f323(f323(f78(a865),f323(x39172,x39173)),f148(x39171,x39172,x39174))),f323(a112,f2(a865))))
% 188.07/187.96 [3931]E(f185(f866(x39311),f323(f323(f144(x39311),x39312),x39313),f323(f323(f7(a865,f866(x39311),f866(x39311)),f131(x39311)),x39313),x39314),f323(f323(f131(x39311),x39314),f323(f323(f144(x39311),x39312),x39313)))
% 188.07/187.96 [3932]P27(x39321,f871(x39322,x39321),f327(x39323,x39324,x39322,x39321),f323(f323(f39(x39322,f872(x39321,a860)),x39324),x39323))
% 188.07/187.96 [3941]E(f323(f323(f22(f872(x39411,a860)),f323(f323(f22(f872(x39411,a860)),x39412),x39413)),f323(f323(f301(x39411),x39414),f188(f872(x39411,a860)))),f323(f323(f22(f872(x39411,a860)),x39412),f323(f323(f301(x39411),x39414),x39413)))
% 188.07/187.96 [3954]E(f323(f323(f183(f872(x39541,x39542),f872(x39541,x39542)),x39543),f71(x39542,x39542,x39541,x39544)),f71(x39542,x39542,x39541,f323(f323(f183(x39542,x39542),x39543),x39544)))
% 188.07/187.96 [4033]E(f323(f323(f323(f183(f866(x40331),f866(x40331)),x40332),f161(x40331)),f323(f323(f323(f183(f866(x40331),f866(x40331)),x40333),f161(x40331)),x40334)),f323(f323(f323(f183(f866(x40331),f866(x40331)),f323(f323(f78(a865),x40332),x40333)),f161(x40331)),x40334))
% 188.07/187.96 [4119]P101(f323(f323(f237(f872(x41191,a860)),f323(f166(x41191),f323(f323(f152(x41191,x41192),x41193),x41194))),f323(f323(f301(x41191),x41194),f323(f166(x41191),x41192))))
% 188.07/187.96 [4154]E(f323(f323(f39(f872(x41541,a860),f872(f871(x41541,x41542),a860)),x41543),f323(f323(f7(f872(x41541,a860),f872(x41541,f872(x41542,a860)),f872(f871(x41541,x41542),a860)),f260(x41541,x41542)),x41544)),f323(f323(f260(x41541,x41542),f37(f872(x41541,a860),x41543)),x41544))
% 188.07/187.96 [4186]P26(x41861,x41862,f323(f323(f301(f864(x41861)),f323(f323(f323(f90(x41861),x41863),x41864),f323(f16(f872(a861,a860),x41861),f323(f16(a860,a861),a187)))),f188(f872(f864(x41861),a860))))
% 188.07/187.96 [4193]E(f211(x41931,x41932,x41933,f323(f71(x41932,f872(a99,f872(a99,f872(f871(a99,a99),f872(a99,f867(x41932))))),x41931,f210(x41932)),x41934)),f212(x41931,x41932,x41934,x41933))
% 188.07/187.96 [4210]E(f207(x42101,x42102,x42103,f323(f71(x42102,f872(a99,f872(a99,f872(f871(a99,a99),f872(a99,f867(f869(x42102)))))),x42101,f206(x42102)),x42104)),f208(x42101,x42102,x42104,x42103))
% 188.07/187.96 [4215]P101(f323(f64(x42151,x42152,x42153,x42154,f188(f872(x42151,a860))),x42154))
% 188.07/187.96 [4257]E(f323(f323(f39(x42571,f872(x42572,a860)),x42573),f323(f323(f7(x42571,f872(x42572,a860),f872(x42572,a860)),f323(f323(f8(x42572,f872(f872(x42572,a860),f872(x42572,a860)),x42571),f301(x42572)),x42574)),f188(f872(x42572,a860)))),f323(f302(x42571,x42572,x42574),x42573))
% 188.07/187.96 [4264]P101(f323(f323(f237(f872(x42641,a860)),f323(f254(x42642,x42641),f323(f323(f101(f872(f871(x42642,x42641),a860)),x42643),x42644))),f323(f323(f101(f872(x42641,a860)),f323(f254(x42642,x42641),x42643)),f323(f254(x42642,x42641),x42644))))
% 188.07/187.96 [4265]P101(f323(f323(f237(f872(x42651,a860)),f323(f256(x42651,x42652),f323(f323(f101(f872(f871(x42651,x42652),a860)),x42653),x42654))),f323(f323(f101(f872(x42651,a860)),f323(f256(x42651,x42652),x42653)),f323(f256(x42651,x42652),x42654))))
% 188.07/187.96 [4301]P26(x43011,x43012,f323(f323(f301(f864(x43011)),f323(f323(f323(f90(x43011),f323(f16(f872(a861,a860),x43011),f323(f16(a860,a861),a241))),x43013),x43014)),f188(f872(f864(x43011),a860))))
% 188.07/187.96 [4328]P101(f323(f323(f237(f872(f871(x43281,x43282),a860)),f323(f302(x43282,f871(x43281,x43282),f327(x43283,x43284,x43281,x43282)),f323(f323(f39(x43281,f872(x43282,a860)),x43284),x43283))),f323(f323(f260(x43281,x43282),x43284),x43283)))
% 188.07/187.96 [4329]E(f323(f116(x43291,f871(x43291,x43292),x43293),f323(f323(f8(f872(x43292,f867(f871(x43291,x43292))),f867(f871(x43291,x43292)),x43291),f116(x43292,f871(x43291,x43292),x43294)),f323(f323(f8(f872(x43292,f871(x43291,x43292)),f872(x43292,f867(f871(x43291,x43292))),x43291),f323(f8(f871(x43291,x43292),f867(f871(x43291,x43292)),x43292),f122(f871(x43291,x43292)))),f258(x43291,x43292)))),f127(x43291,x43292,x43293,x43294))
% 188.07/187.96 [4370]E(f83(f871(x43701,x43702),f323(f262(x43701,x43702,a860),f323(f323(f7(x43701,f872(x43702,a860),f872(x43702,a860)),f323(f323(f8(f872(a860,a860),f872(f872(x43702,a860),f872(x43702,a860)),x43701),f8(a860,a860,x43702)),f323(f323(f8(a860,f872(a860,a860),x43701),a322),f323(a320,x43703)))),f323(a320,x43704)))),f323(f323(f258(x43701,x43702),x43703),x43704))
% 188.07/187.96 [4371]E(f88(f871(x43711,x43712),f323(f262(x43711,x43712,a860),f323(f323(f7(x43711,f872(x43712,a860),f872(x43712,a860)),f323(f323(f8(f872(a860,a860),f872(f872(x43712,a860),f872(x43712,a860)),x43711),f8(a860,a860,x43712)),f323(f323(f8(a860,f872(a860,a860),x43711),a322),f323(a320,x43713)))),f323(a320,x43714)))),f323(f323(f258(x43711,x43712),x43713),x43714))
% 188.07/187.96 [4445]E(f323(f323(f262(f866(x44451),f866(x44451),f871(f866(x44451),f866(x44451))),f323(f323(f18(f866(x44451),f872(f866(x44451),f871(f866(x44451),f866(x44451))),f872(f866(x44451),f871(f866(x44451),f866(x44451)))),f323(f323(f8(f872(f866(x44451),f872(f871(f866(x44451),f866(x44451)),f871(f866(x44451),f866(x44451)))),f872(f872(f866(x44451),f871(f866(x44451),f866(x44451))),f872(f866(x44451),f871(f866(x44451),f866(x44451)))),f866(x44451)),f18(f866(x44451),f871(f866(x44451),f866(x44451)),f871(f866(x44451),f866(x44451)))),f323(f323(f8(f872(f866(x44451),f871(f866(x44451),f866(x44451))),f872(f866(x44451),f872(f871(f866(x44451),f866(x44451)),f871(f866(x44451),f866(x44451)))),f866(x44451)),f323(f8(f871(f866(x44451),f866(x44451)),f872(f871(f866(x44451),f866(x44451)),f871(f866(x44451),f866(x44451))),f866(x44451)),f323(f96(f871(f866(x44451),f866(x44451))),f323(x44452,x44453)))),f323(f323(f8(f866(x44451),f872(f866(x44451),f871(f866(x44451),f866(x44451))),f866(x44451)),f258(f866(x44451),f866(x44451))),f323(f144(x44451),x44453))))),f323(f323(f7(f866(x44451),f872(f866(x44451),f866(x44451)),f872(f866(x44451),f871(f866(x44451),f866(x44451)))),f323(f323(f8(f872(f866(x44451),f871(f866(x44451),f866(x44451))),f872(f872(f866(x44451),f866(x44451)),f872(f866(x44451),f871(f866(x44451),f866(x44451)))),f866(x44451)),f8(f866(x44451),f871(f866(x44451),f866(x44451)),f866(x44451))),f258(f866(x44451),f866(x44451)))),f323(f144(x44451),x44453)))),f160(x44451,x44452,x44454)),f160(x44451,x44452,f323(f323(f144(x44451),x44453),x44454)))
% 188.07/187.96 [4451]E(f323(f135(f872(x44511,f869(x44512)),f871(x44511,x44512),f323(f7(f871(x44511,x44512),f872(x44511,f869(x44512)),f872(x44511,f869(x44512))),f323(f262(x44511,x44512,f872(f872(x44511,f869(x44512)),f872(x44511,f869(x44512)))),f323(f323(f7(x44511,f872(x44512,f869(x44512)),f872(x44512,f872(f872(x44511,f869(x44512)),f872(x44511,f869(x44512))))),f323(f323(f8(f872(f869(x44512),f872(f872(x44511,f869(x44512)),f872(x44511,f869(x44512)))),f872(f872(x44512,f869(x44512)),f872(x44512,f872(f872(x44511,f869(x44512)),f872(x44511,f869(x44512))))),x44511),f8(f869(x44512),f872(f872(x44511,f869(x44512)),f872(x44511,f869(x44512))),x44512)),f323(f323(f8(f872(f872(x44511,f869(x44512)),f872(f869(x44512),f872(x44511,f869(x44512)))),f872(f869(x44512),f872(f872(x44511,f869(x44512)),f872(x44511,f869(x44512)))),x44511),f7(f872(x44511,f869(x44512)),f869(x44512),f872(x44511,f869(x44512)))),f323(f7(f872(x44511,f869(x44512)),x44511,f872(f869(x44512),f872(x44511,f869(x44512)))),f70(x44511,f869(x44512)))))),f230(x44512)))),x44513),f323(f162(f871(x44511,x44512)),x44514)),f180(x44511,x44512,x44513,f323(f179(x44511,x44512),x44514)))
% 188.07/187.96 [3540]E(f323(f189(f864(x35401)),f323(f323(f323(f90(x35401),x35402),x35403),x35404)),f2(a865))
% 188.07/187.96 [3659]E(f323(f323(f169(x36591),x36592),f323(f323(f169(x36591),x36593),x36594)),f323(f323(f169(x36591),f323(f323(f235(a865),x36592),x36593)),x36594))
% 188.07/187.96 [3660]E(f323(f323(f131(x36601),x36602),f323(f323(f131(x36601),x36603),x36604)),f323(f323(f131(x36601),f323(f323(f78(a865),x36602),x36603)),x36604))
% 188.07/187.96 [3672]E(f323(f323(f121(x36721),f323(f323(f144(x36721),x36722),x36723)),x36724),f323(f323(f144(x36721),x36722),f323(f323(f121(x36721),x36723),x36724)))
% 188.07/187.96 [3673]E(f323(f323(f121(x36731),f323(f323(f121(x36731),x36732),x36733)),x36734),f323(f323(f121(x36731),x36732),f323(f323(f121(x36731),x36733),x36734)))
% 188.07/187.96 [3754]E(f323(f323(f158(x37541),f323(f323(f144(x37541),x37542),x37543)),x37544),f185(x37541,x37542,f323(f158(x37541),x37543),x37544))
% 188.07/187.96 [3763]E(f323(f323(f183(x37631,x37631),x37632),f323(f323(f183(x37631,x37631),x37633),x37634)),f323(f323(f183(x37631,x37631),f323(f323(f79(a865),x37633),x37632)),x37634))
% 188.07/187.96 [3792]E(f323(f323(f110(f872(x37921,a860)),x37922),f323(f323(f301(x37921),x37923),x37924)),f323(f323(f301(x37921),x37923),f323(f323(f110(f872(x37921,a860)),x37922),x37924)))
% 188.07/187.96 [3807]E(f323(f323(f323(f183(x38071,x38071),x38072),x38073),f323(x38073,x38074)),f323(x38073,f323(f323(f323(f183(x38071,x38071),x38072),x38073),x38074)))
% 188.07/187.96 [3815]E(f323(f323(f280(x38151,x38152,x38153),f188(f872(f871(x38151,x38152),a860))),x38154),f188(f872(f871(x38151,x38153),a860)))
% 188.07/187.96 [3832]E(f323(f323(f110(f872(x38321,a860)),f323(f323(f301(x38321),x38322),x38323)),x38324),f323(f323(f301(x38321),x38322),f323(f323(f110(f872(x38321,a860)),x38323),x38324)))
% 188.07/187.96 [3852]E(f180(x38521,x38522,f323(f179(x38521,x38522),x38523),f323(f179(x38521,x38522),x38524)),f323(f179(x38521,x38522),f323(f323(f121(f871(x38521,x38522)),x38524),x38523)))
% 188.07/187.96 [3853]E(f323(f35(f871(x38531,x38532)),f323(f323(f260(x38531,x38532),x38533),f323(f16(f872(x38532,a860),x38531),x38534))),f323(f323(f79(a865),f323(f35(x38531),x38533)),f323(f35(x38532),x38534)))
% 188.07/187.96 [3860]E(f323(f323(f101(f872(x38601,a860)),f323(f323(f301(x38601),x38602),x38603)),f323(f323(f301(x38601),x38602),x38604)),f323(f323(f301(x38601),x38602),f323(f323(f101(f872(x38601,a860)),x38603),x38604)))
% 188.07/187.96 [3875]E(f323(f323(f110(f872(x38751,a860)),x38752),f323(f323(f110(f872(x38751,a860)),x38753),x38754)),f323(f323(f110(f872(x38751,a860)),x38753),f323(f323(f110(f872(x38751,a860)),x38752),x38754)))
% 188.07/187.96 [3876]E(f323(f323(f101(f872(x38761,a860)),x38762),f323(f323(f101(f872(x38761,a860)),x38763),x38764)),f323(f323(f101(f872(x38761,a860)),x38763),f323(f323(f101(f872(x38761,a860)),x38762),x38764)))
% 188.07/187.96 [3885]E(f62(x38851,x38852,f323(f323(f8(x38852,f872(x38852,x38852),x38851),x38853),x38854)),f323(f63(x38852,x38851,x38853),x38854))
% 188.07/187.96 [3895]E(f173(x38951,f323(f323(f147(f866(x38952),f866(x38951)),f323(f147(x38952,x38951),x38953)),x38954)),f323(f323(f147(f866(x38952),f866(x38951)),f323(f147(x38952,x38951),x38953)),f173(x38952,x38954)))
% 188.07/187.96 [3913]E(f323(f135(f866(x39131),f866(x39131),f121(x39131),f113(x39131)),f323(f323(f147(x39132,f866(x39131)),x39133),x39134)),f157(x39132,x39131,x39133,x39134))
% 188.07/187.96 [3916]E(f182(x39161,x39162,x39163,f323(f77(f872(x39161,a860)),f323(f323(f301(x39161),x39164),f188(f872(x39161,a860))))),f323(f323(f323(f70(x39161,f869(x39162)),x39163),x39164),f200(x39162)))
% 188.07/187.96 [3959]E(f323(f323(f323(f70(x39591,f869(x39592)),f323(f179(x39591,x39592),x39593)),f323(f257(x39591,x39592),x39594)),f323(f230(x39592),f323(f261(x39591,x39592),x39594))),f323(f179(x39591,x39592),f323(f323(f144(f871(x39591,x39592)),x39594),x39593)))
% 188.07/187.96 [3977]E(f323(f71(x39771,x39771,x39771,f323(f323(f183(x39771,x39771),x39772),x39773)),f323(f323(f183(x39771,x39771),x39774),x39773)),f323(f323(f183(x39771,x39771),f323(f323(f78(a865),x39772),x39774)),x39773))
% 188.07/187.96 [4002]E(f323(f323(f101(f872(x40021,a860)),f323(f323(f110(f872(x40021,a860)),x40022),x40023)),f323(f323(f110(f872(x40021,a860)),x40022),x40024)),f323(f323(f110(f872(x40021,a860)),x40022),f323(f323(f101(f872(x40021,a860)),x40023),x40024)))
% 188.07/187.96 [4003]E(f323(f323(f101(f872(x40031,a860)),f323(f323(f22(f872(x40031,a860)),x40032),x40033)),f323(f323(f22(f872(x40031,a860)),x40032),x40034)),f323(f323(f22(f872(x40031,a860)),x40032),f323(f323(f110(f872(x40031,a860)),x40033),x40034)))
% 188.07/187.96 [4004]E(f323(f323(f110(f872(x40041,a860)),f323(f323(f22(f872(x40041,a860)),x40042),x40043)),f323(f323(f22(f872(x40041,a860)),x40042),x40044)),f323(f323(f22(f872(x40041,a860)),x40042),f323(f323(f101(f872(x40041,a860)),x40043),x40044)))
% 188.07/187.96 [4005]E(f323(f323(f110(f872(x40051,a860)),f323(f323(f101(f872(x40051,a860)),x40052),x40053)),f323(f323(f101(f872(x40051,a860)),x40052),x40054)),f323(f323(f101(f872(x40051,a860)),x40052),f323(f323(f110(f872(x40051,a860)),x40053),x40054)))
% 188.07/187.96 [4006]E(f323(f323(f22(f872(x40061,a860)),f323(f323(f101(f872(x40061,a860)),x40062),x40063)),f323(f323(f101(f872(x40061,a860)),x40062),x40064)),f323(f323(f101(f872(x40061,a860)),x40062),f323(f323(f22(f872(x40061,a860)),x40063),x40064)))
% 188.07/187.96 [4012]E(f323(f35(f871(x40121,x40122)),f323(f323(f260(x40121,x40122),f323(f323(f301(x40121),x40123),f188(f872(x40121,a860)))),f323(f16(f872(x40122,a860),x40121),x40124))),f323(f35(x40122),x40124))
% 188.07/187.96 [4048]E(f323(f323(f40(x40481,f872(x40482,a860)),x40483),f323(f323(f8(f872(x40482,a860),f872(x40482,a860),x40481),f77(f872(x40482,a860))),x40484)),f323(f77(f872(x40482,a860)),f323(f323(f39(x40481,f872(x40482,a860)),x40483),x40484)))
% 188.07/187.96 [4049]E(f323(f323(f39(x40491,f872(x40492,a860)),x40493),f323(f323(f8(f872(x40492,a860),f872(x40492,a860),x40491),f77(f872(x40492,a860))),x40494)),f323(f77(f872(x40492,a860)),f323(f323(f40(x40491,f872(x40492,a860)),x40493),x40494)))
% 188.07/187.96 [4063]E(f323(f323(f280(x40631,x40631,x40631),f323(f323(f183(f871(x40631,x40631),a860),x40632),x40633)),f323(f323(f183(f871(x40631,x40631),a860),x40634),x40633)),f323(f323(f183(f871(x40631,x40631),a860),f323(f323(f78(a865),x40632),x40634)),x40633))
% 188.07/187.96 [4094]E(f323(f323(f40(x40941,f872(f872(x40942,a860),a860)),x40943),f323(f323(f8(f872(x40942,a860),f872(f872(x40942,a860),a860),x40941),f300(x40942)),x40944)),f323(f300(x40942),f323(f323(f40(x40941,f872(x40942,a860)),x40943),x40944)))
% 188.07/187.96 [4123]E(f323(f323(f39(f872(x41231,a860),f872(x41232,a860)),x41233),f323(f323(f7(f872(x41231,a860),f872(x41231,f872(x41232,a860)),f872(x41232,a860)),f39(x41231,f872(x41232,a860))),x41234)),f323(f323(f39(x41231,f872(x41232,a860)),f37(f872(x41231,a860),x41233)),x41234))
% 188.07/187.96 [4124]E(f323(f323(f40(f872(x41241,a860),f872(x41242,a860)),x41243),f323(f323(f7(f872(x41241,a860),f872(x41241,f872(x41242,a860)),f872(x41242,a860)),f40(x41241,f872(x41242,a860))),x41244)),f323(f323(f40(x41241,f872(x41242,a860)),f37(f872(x41241,a860),x41243)),x41244))
% 188.07/187.96 [4129]E(f323(f323(f147(x41291,x41292),x41293),f323(f135(f866(x41291),f866(x41291),f121(x41291),f113(x41291)),x41294)),f323(f135(f866(x41292),f866(x41292),f121(x41292),f113(x41292)),f323(f323(f147(f866(x41291),f866(x41292)),f323(f147(x41291,x41292),x41293)),x41294)))
% 188.07/187.96 [4132]E(f185(f866(x41321),f113(x41321),f323(f323(f8(f866(x41321),f866(x41321),a865),f323(f144(x41321),x41322)),f323(f323(f7(a865,f866(x41321),f866(x41321)),f169(x41321)),x41323)),x41324),f323(f323(f169(x41321),x41324),f323(f323(f144(x41321),x41322),x41323)))
% 188.07/187.96 [4174]P101(f323(f323(f237(f872(x41741,a860)),f323(f302(x41742,x41741,x41743),f323(f303(x41742,x41741,x41743),x41744))),x41744))
% 188.07/187.96 [4177]E(f323(f302(f871(x41771,x41772),f871(x41772,x41771),f323(f262(x41771,x41772,f871(x41772,x41771)),f323(f7(x41772,x41771,f871(x41772,x41771)),f258(x41772,x41771)))),f323(f323(f260(x41771,x41772),x41773),f323(f16(f872(x41772,a860),x41771),x41774))),f323(f323(f260(x41772,x41771),x41774),f323(f16(f872(x41771,a860),x41772),x41773)))
% 188.07/187.96 [4187]E(f323(f323(f39(x41871,f872(x41872,a860)),x41873),f323(f323(f8(f872(x41871,a860),f872(x41872,a860),x41871),f303(x41872,x41871,x41874)),f323(f323(f7(x41871,f872(x41871,a860),f872(x41871,a860)),f301(x41871)),f188(f872(x41871,a860))))),f323(f303(x41872,x41871,x41874),x41873))
% 188.07/187.96 [4188]E(f323(f323(f39(x41881,f872(x41882,a860)),x41883),f323(f323(f8(f872(x41881,a860),f872(x41882,a860),x41881),f277(x41881,x41882,x41884)),f323(f323(f7(x41881,f872(x41881,a860),f872(x41881,a860)),f301(x41881)),f188(f872(x41881,a860))))),f323(f277(x41881,x41882,x41884),x41883))
% 188.07/187.96 [4279]E(f323(f323(f110(f872(x42791,a860)),f323(f323(f110(f872(x42791,a860)),f323(f323(f101(f872(x42791,a860)),x42792),x42793)),f323(f323(f101(f872(x42791,a860)),x42793),x42794))),f323(f323(f101(f872(x42791,a860)),x42794),x42792)),f323(f323(f101(f872(x42791,a860)),f323(f323(f101(f872(x42791,a860)),f323(f323(f110(f872(x42791,a860)),x42792),x42793)),f323(f323(f110(f872(x42791,a860)),x42793),x42794))),f323(f323(f110(f872(x42791,a860)),x42794),x42792)))
% 188.07/187.96 [4343]E(f323(f135(f866(x43431),f866(x43431),f121(x43431),f113(x43431)),f323(f323(f147(x43432,f866(x43431)),f323(f323(f7(x43432,f866(x43431),f866(x43431)),f323(f323(f8(x43431,f872(f866(x43431),f866(x43431)),x43432),f144(x43431)),x43433)),f113(x43431))),x43434)),f323(f323(f147(x43432,x43431),x43433),x43434))
% 188.07/187.96 [4354]E(f323(f323(f84(a1,x43541),f323(f103(a1),f323(f323(f78(a1),x43542),a97))),f323(f323(f18(a1,x43541,x43541),f323(f323(f7(a1,x43541,f872(x43541,x43541)),f323(f323(f8(a860,f872(x43541,f872(x43541,x43541)),a1),f96(x43541)),a193)),x43543)),f323(f323(f8(a865,x43541,a1),x43544),a104))),f185(x43541,x43543,x43544,f323(f103(a865),x43542)))
% 188.07/187.96 [4565]~P101(f323(f323(f188(f872(x45651,f872(x45652,a860))),x45653),x45654))
% 188.07/187.96 [3818]E(f323(f323(f158(x38181),f323(f323(f121(x38181),x38182),x38183)),f323(f323(f78(a865),f323(f189(f866(x38181)),x38182)),x38184)),f323(f323(f158(x38181),x38183),x38184))
% 188.07/187.96 [3825]E(f323(f323(f131(x38251),x38252),f323(f323(f169(x38251),f323(f323(f78(a865),x38253),x38252)),x38254)),f323(f323(f169(x38251),x38253),f323(f323(f131(x38251),x38252),x38254)))
% 188.07/187.96 [3929]E(f323(f323(f110(f872(x39291,a860)),f323(f254(x39292,x39291),x39293)),f323(f254(x39292,x39291),x39294)),f323(f254(x39292,x39291),f323(f323(f110(f872(f871(x39292,x39291),a860)),x39293),x39294)))
% 188.07/187.96 [3930]E(f323(f323(f110(f872(x39301,a860)),f323(f256(x39301,x39302),x39303)),f323(f256(x39301,x39302),x39304)),f323(f256(x39301,x39302),f323(f323(f110(f872(f871(x39301,x39302),a860)),x39303),x39304)))
% 188.07/187.96 [3935]E(f323(f323(f110(f872(x39351,a860)),f323(f323(f110(f872(x39351,a860)),x39352),x39353)),x39354),f323(f323(f110(f872(x39351,a860)),x39352),f323(f323(f110(f872(x39351,a860)),x39353),x39354)))
% 188.07/187.96 [3936]E(f323(f323(f22(f872(x39361,a860)),f323(f323(f101(f872(x39361,a860)),x39362),x39363)),x39364),f323(f323(f101(f872(x39361,a860)),x39362),f323(f323(f22(f872(x39361,a860)),x39363),x39364)))
% 188.07/187.96 [3937]E(f323(f323(f101(f872(x39371,a860)),f323(f323(f101(f872(x39371,a860)),x39372),x39373)),x39374),f323(f323(f101(f872(x39371,a860)),x39372),f323(f323(f101(f872(x39371,a860)),x39373),x39374)))
% 188.07/187.96 [3979]E(f323(f323(f110(f872(f871(x39791,x39792),a860)),f323(f278(x39792,x39791),x39793)),f323(f278(x39792,x39791),x39794)),f323(f278(x39792,x39791),f323(f323(f110(f872(f871(x39792,x39791),a860)),x39793),x39794)))
% 188.07/187.96 [3980]E(f323(f323(f101(f872(f871(x39801,x39802),a860)),f323(f278(x39802,x39801),x39803)),f323(f278(x39802,x39801),x39804)),f323(f278(x39802,x39801),f323(f323(f101(f872(f871(x39802,x39801),a860)),x39803),x39804)))
% 188.07/187.96 [3994]E(f323(f323(f110(f872(x39941,f872(x39942,a860))),f247(x39942,x39941,x39943)),f247(x39942,x39941,x39944)),f247(x39942,x39941,f323(f323(f110(f872(x39942,f872(x39941,a860))),x39943),x39944)))
% 188.07/187.96 [3995]E(f323(f323(f101(f872(x39951,f872(x39952,a860))),f247(x39952,x39951,x39953)),f247(x39952,x39951,x39954)),f247(x39952,x39951,f323(f323(f101(f872(x39952,f872(x39951,a860))),x39953),x39954)))
% 188.07/187.96 [4052]E(f323(f323(f101(f872(x40521,a860)),f323(f323(f110(f872(x40521,a860)),x40522),x40523)),f323(f323(f110(f872(x40521,a860)),x40524),x40523)),f323(f323(f110(f872(x40521,a860)),f323(f323(f101(f872(x40521,a860)),x40522),x40524)),x40523))
% 188.07/187.96 [4053]E(f323(f323(f110(f872(x40531,a860)),f323(f323(f22(f872(x40531,a860)),x40532),x40533)),f323(f323(f22(f872(x40531,a860)),x40534),x40533)),f323(f323(f22(f872(x40531,a860)),f323(f323(f110(f872(x40531,a860)),x40532),x40534)),x40533))
% 188.07/187.96 [4054]E(f323(f323(f110(f872(x40541,a860)),f323(f323(f101(f872(x40541,a860)),x40542),x40543)),f323(f323(f101(f872(x40541,a860)),x40544),x40543)),f323(f323(f101(f872(x40541,a860)),f323(f323(f110(f872(x40541,a860)),x40542),x40544)),x40543))
% 188.07/187.96 [4055]E(f323(f323(f22(f872(x40551,a860)),f323(f323(f101(f872(x40551,a860)),x40552),x40553)),f323(f323(f101(f872(x40551,a860)),x40554),x40553)),f323(f323(f101(f872(x40551,a860)),f323(f323(f22(f872(x40551,a860)),x40552),x40554)),x40553))
% 188.07/187.96 [4056]E(f323(f323(f22(f872(x40561,a860)),f323(f323(f101(f872(x40561,a860)),x40562),x40563)),f323(f323(f101(f872(x40561,a860)),x40564),x40563)),f323(f323(f22(f872(x40561,a860)),f323(f323(f101(f872(x40561,a860)),x40562),x40563)),x40564))
% 188.07/187.96 [4066]E(f323(f323(f22(f872(x40661,a860)),f323(f323(f22(f872(x40661,a860)),x40662),f323(f323(f301(x40661),x40663),f188(f872(x40661,a860))))),x40664),f323(f323(f22(f872(x40661,a860)),x40662),f323(f323(f301(x40661),x40663),x40664)))
% 188.07/187.96 [4120]E(f323(f323(f110(f872(x41201,a860)),f323(f323(f301(x41201),x41202),f323(f323(f301(x41201),x41203),f188(f872(x41201,a860))))),f323(f276(x41201),x41204)),f323(f276(x41201),f323(f323(f301(f871(x41201,x41201)),f323(f323(f258(x41201,x41201),x41202),x41203)),x41204)))
% 188.07/187.96 [4149]E(f323(f323(f39(a865,f872(x41491,a860)),f323(f292(a865),x41492)),f323(f323(f8(a865,f872(x41491,a860),a865),x41493),f323(f323(f7(a865,a865,a865),f78(a865)),x41494))),f323(f323(f39(a865,f872(x41491,a860)),f294(a865,x41494,f323(f323(f78(a865),x41492),x41494))),x41493))
% 188.07/187.96 [4150]E(f168(x41501,f323(f277(x41501,x41501,x41502),f323(f323(f301(x41501),x41503),f188(f872(x41501,a860)))),f323(f277(f866(x41501),f866(x41501),f151(x41501,x41502)),f323(f323(f301(f866(x41501)),x41504),f188(f872(f866(x41501),a860))))),f323(f277(f866(x41501),f866(x41501),f151(x41501,x41502)),f323(f323(f301(f866(x41501)),f323(f323(f144(x41501),x41503),x41504)),f188(f872(f866(x41501),a860)))))
% 188.07/187.96 [4213]E(f323(f179(x42131,x42132),f323(f323(f147(x42131,f871(x42131,x42132)),f323(f323(f18(x42131,x42132,f871(x42131,x42132)),f258(x42131,x42132)),x42133)),x42134)),f182(x42131,x42132,f323(f71(x42132,f869(x42132),x42131,f230(x42132)),x42133),f323(f166(x42131),x42134)))
% 188.07/187.96 [4218]E(f323(f243(x42181),f323(f323(f7(x42181,f872(x42182,a860),a860),f323(f323(f8(x42182,f872(f872(x42182,a860),a860),x42181),f325(x42182)),x42183)),x42184)),f323(f303(x42181,x42182,x42183),x42184))
% 188.07/187.96 [4313]E(f323(f243(x43131),f323(f323(f7(x43131,f872(f871(x43132,x43131),a860),a860),f323(f323(f8(f871(x43132,x43131),f872(f872(f871(x43132,x43131),a860),a860),x43131),f325(f871(x43132,x43131))),f323(f258(x43132,x43131),x43133))),x43134)),f323(f277(x43132,x43131,x43134),f323(f323(f301(x43132),x43133),f188(f872(x43132,a860)))))
% 188.07/187.96 [4327]E(f323(f323(f147(f871(x43271,a865),x43271),f257(x43271,a865)),f323(f129(f871(x43271,a865),f323(f323(f8(a865,a860,f871(x43271,a865)),x43272),f323(f323(f8(a865,a865,f871(x43271,a865)),a112),f261(x43271,a865)))),f323(f323(f175(x43271,a865),x43273),x43274))),f323(f323(f147(f871(x43271,a865),x43271),f257(x43271,a865)),f323(f129(f871(x43271,a865),f323(f323(f8(a865,a860,f871(x43271,a865)),x43272),f261(x43271,a865))),f323(f323(f175(x43271,a865),x43273),f323(f323(f147(a865,a865),a112),x43274)))))
% 188.07/187.96 [4335]P101(f323(f323(f237(f872(f872(x43351,a860),a860)),f323(f323(f39(x43352,f872(f872(x43351,a860),a860)),x43353),f323(f323(f8(f872(x43351,a860),f872(f872(x43351,a860),a860),x43352),f300(x43351)),x43354))),f323(f300(x43351),f323(f323(f39(x43352,f872(x43351,a860)),x43353),x43354))))
% 188.07/187.96 [4378]E(f323(f323(f84(a1,x43781),f323(f103(a1),f323(f323(f78(a1),x43782),a97))),f323(f323(f18(a1,x43781,x43781),f323(f323(f7(a1,x43781,f872(x43781,x43781)),f323(f323(f8(a860,f872(x43781,f872(x43781,x43781)),a1),f96(x43781)),a193)),x43783)),f323(f323(f18(a1,x43781,x43781),f323(f323(f8(a865,f872(x43781,x43781),a1),x43784),a104)),f323(f323(f8(a865,x43781,a1),f184(x43781,x43783,x43784)),a104)))),f323(f184(x43781,x43783,x43784),f323(f103(a865),x43782)))
% 188.07/187.96 [4381]E(f323(f323(f147(x43811,x43812),f323(f71(f869(x43812),x43812,x43811,f234(x43812)),x43813)),f323(f129(x43811,f323(f323(f8(a860,a860,x43811),a318),f323(f323(f7(x43811,f869(x43812),a860),f323(f323(f8(f869(x43812),f872(f869(x43812),a860),x43811),a320),x43813)),f200(x43812)))),x43814)),f156(x43811,x43812,x43813,x43814))
% 188.07/187.96 [4404]E(f323(f243(f871(x44041,x44042)),f323(f262(x44041,x44042,a860),f323(f323(f7(x44041,f872(x44042,a860),f872(x44042,a860)),f323(f323(f8(f872(a860,a860),f872(f872(x44042,a860),f872(x44042,a860)),x44041),f8(a860,a860,x44042)),f323(f323(f8(a860,f872(a860,a860),x44041),a322),f323(f323(f7(x44041,f872(x44041,a860),a860),f325(x44041)),x44043)))),f323(f323(f7(x44042,f872(x44042,a860),a860),f325(x44042)),x44044)))),f224(x44041,x44042,x44043,x44044))
% 188.07/187.96 [4438]E(f323(f323(f39(x44381,f872(f871(x44381,x44382),a860)),x44383),f323(f323(f18(x44381,f872(x44382,f872(f871(x44381,x44382),a860)),f872(f871(x44381,x44382),a860)),f323(f323(f8(f872(x44382,a860),f872(f872(x44382,f872(f871(x44381,x44382),a860)),f872(f871(x44381,x44382),a860)),x44381),f39(x44382,f872(f871(x44381,x44382),a860))),x44384)),f323(f323(f7(x44381,f872(f871(x44381,x44382),a860),f872(x44382,f872(f871(x44381,x44382),a860))),f323(f323(f8(f872(x44382,f872(f872(f871(x44381,x44382),a860),f872(f871(x44381,x44382),a860))),f872(f872(f871(x44381,x44382),a860),f872(x44382,f872(f871(x44381,x44382),a860))),x44381),f7(x44382,f872(f871(x44381,x44382),a860),f872(f871(x44381,x44382),a860))),f323(f323(f8(f872(x44382,f871(x44381,x44382)),f872(x44382,f872(f872(f871(x44381,x44382),a860),f872(f871(x44381,x44382),a860))),x44381),f323(f8(f871(x44381,x44382),f872(f872(f871(x44381,x44382),a860),f872(f871(x44381,x44382),a860)),x44382),f301(f871(x44381,x44382)))),f258(x44381,x44382)))),f188(f872(f871(x44381,x44382),a860))))),f323(f323(f260(x44381,x44382),x44383),x44384))
% 188.07/187.96 [3989]E(f323(f323(f121(x39891),f323(f323(f169(x39891),x39892),x39893)),f323(f323(f169(x39891),f323(f323(f22(a865),x39892),f323(f189(f866(x39891)),x39893))),x39894)),f323(f323(f169(x39891),x39892),f323(f323(f121(x39891),x39893),x39894)))
% 188.07/187.96 [3990]E(f323(f323(f121(x39901),f323(f323(f131(x39901),x39902),x39903)),f323(f323(f131(x39901),f323(f323(f22(a865),x39902),f323(f189(f866(x39901)),x39903))),x39904)),f323(f323(f131(x39901),x39902),f323(f323(f121(x39901),x39903),x39904)))
% 188.07/187.96 [4042]E(f323(f323(f78(a865),f323(f323(f79(a865),x40421),x40422)),f323(f323(f78(a865),f323(f323(f79(a865),x40423),x40422)),x40424)),f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f78(a865),x40421),x40423)),x40422)),x40424))
% 188.07/187.96 [4191]E(f88(x41911,f323(f323(f7(x41911,x41912,a860),f323(f323(f8(x41912,f872(x41912,a860),x41911),a320),x41913)),x41914)),f323(f91(x41911,x41912,f246(f872(x41911,a860)),x41913),x41914))
% 188.07/187.96 [4243]P101(f323(f323(f237(f872(x42431,a860)),f323(f323(f22(f872(x42431,a860)),f323(f254(x42432,x42431),x42433)),f323(f254(x42432,x42431),x42434))),f323(f254(x42432,x42431),f323(f323(f22(f872(f871(x42432,x42431),a860)),x42433),x42434))))
% 188.07/187.96 [4244]P101(f323(f323(f237(f872(x42441,a860)),f323(f323(f22(f872(x42441,a860)),f323(f256(x42441,x42442),x42443)),f323(f256(x42441,x42442),x42444))),f323(f256(x42441,x42442),f323(f323(f22(f872(f871(x42441,x42442),a860)),x42443),x42444))))
% 188.07/187.96 [4356]E(f323(f323(f78(a1),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x43561),x43562)),f188(f872(f871(a865,a865),a860)))))),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x43563),x43564)),f188(f872(f871(a865,a865),a860)))))),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),f323(f323(f78(a865),x43561),x43563)),f323(f323(f78(a865),x43562),x43564))),f188(f872(f871(a865,a865),a860))))))
% 188.07/187.96 [4399]E(f323(f323(f79(a1),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x43991),x43992)),f188(f872(f871(a865,a865),a860)))))),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x43993),x43994)),f188(f872(f871(a865,a865),a860)))))),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),f323(f323(f78(a865),f323(f323(f79(a865),x43991),x43993)),f323(f323(f79(a865),x43992),x43994))),f323(f323(f78(a865),f323(f323(f79(a865),x43991),x43994)),f323(f323(f79(a865),x43992),x43993)))),f188(f872(f871(a865,a865),a860))))))
% 188.07/187.96 [4419]E(f323(f243(x44191),f323(f323(f8(f872(x44192,a860),a860,x44191),f86(x44192)),f323(f323(f8(f872(x44192,a860),f872(x44192,a860),x44191),f323(f18(x44192,a860,a860),f323(f323(f8(a860,f872(a860,a860),x44192),a326),f323(f323(f7(x44192,f872(x44192,a860),a860),f325(x44192)),x44193)))),f323(f323(f7(x44191,f872(x44192,f872(x44191,a860)),f872(x44192,a860)),f323(f323(f8(f872(f872(x44191,a860),a860),f872(f872(x44192,f872(x44191,a860)),f872(x44192,a860)),x44191),f8(f872(x44191,a860),a860,x44192)),f325(x44191))),x44194)))),f323(f323(f40(x44192,f872(x44191,a860)),x44193),x44194))
% 188.07/187.96 [4455]E(f323(f323(f280(x44551,x44551,x44551),f323(f323(f301(f871(x44551,x44551)),f323(f323(f258(x44551,x44551),x44552),x44553)),x44554)),f299(x44551,f323(f323(f301(f871(x44551,x44551)),f323(f323(f258(x44551,x44551),x44552),x44553)),x44554))),f323(f323(f110(f872(f871(x44551,x44551),a860)),f323(f323(f280(x44551,x44551,x44551),x44554),f299(x44551,x44554))),f323(f243(f871(x44551,x44551)),f323(f262(x44551,x44551,a860),f323(f323(f7(x44551,f872(x44551,a860),f872(x44551,a860)),f323(f323(f8(f872(a860,a860),f872(f872(x44551,a860),f872(x44551,a860)),x44551),f8(a860,a860,x44551)),f323(f323(f8(a860,f872(a860,a860),x44551),a322),f323(f323(f7(x44551,f872(f871(x44551,x44551),a860),a860),f323(f323(f8(f871(x44551,x44551),f872(f872(f871(x44551,x44551),a860),a860),x44551),f325(f871(x44551,x44551))),f323(f323(f7(x44551,x44551,f871(x44551,x44551)),f258(x44551,x44551)),x44552))),f299(x44551,x44554))))),f323(f323(f7(x44551,f872(f871(x44551,x44551),a860),a860),f323(f323(f8(f871(x44551,x44551),f872(f872(f871(x44551,x44551),a860),a860),x44551),f325(f871(x44551,x44551))),f323(f258(x44551,x44551),x44553))),f299(x44551,x44554)))))))
% 188.07/187.96 [4245]E(f323(f129(x42451,f323(f323(f18(x42451,a860,a860),f323(f323(f8(a860,f872(a860,a860),x42451),a322),x42452)),x42453)),x42454),f323(f129(x42451,x42453),f323(f129(x42451,x42452),x42454)))
% 188.07/187.96 [4350]E(f323(f323(f121(x43501),f323(f323(f323(f96(f866(x43501)),f323(f323(f325(a865),f2(a865)),x43502)),f323(f323(f144(x43501),x43503),f113(x43501))),f113(x43501))),f170(x43501,x43504,f323(f243(a865),f323(f323(f7(a865,f872(a865,a860),a860),f323(f323(f8(a865,f872(f872(a865,a860),a860),a865),f325(a865)),a112)),x43502)))),f170(x43501,f323(f323(f144(x43501),x43503),x43504),x43502))
% 188.07/187.96 [4449]E(f323(f243(f871(x44491,x44492)),f323(f323(f8(f872(a865,a860),a860,f871(x44491,x44492)),f85(a865)),f323(f323(f7(f871(x44491,x44492),f872(a865,a860),f872(a865,a860)),f323(f323(f8(f872(a865,f872(a860,a860)),f872(f872(a865,a860),f872(a865,a860)),f871(x44491,x44492)),f18(a865,a860,a860)),f323(f323(f8(f872(a865,a860),f872(a865,f872(a860,a860)),f871(x44491,x44492)),f323(f8(a860,f872(a860,a860),a865),a322)),f323(f323(f7(f871(x44491,x44492),f872(a865,f871(x44491,x44492)),f872(a865,a860)),f323(f323(f8(f872(f871(x44491,x44492),a860),f872(f872(a865,f871(x44491,x44492)),f872(a865,a860)),f871(x44491,x44492)),f8(f871(x44491,x44492),a860,a865)),a320)),f323(f323(f18(a865,x44492,f871(x44491,x44492)),f323(f323(f8(x44491,f872(x44492,f871(x44491,x44492)),a865),f258(x44491,x44492)),f323(f158(x44491),x44493))),f323(f158(x44492),x44494)))))),f323(f323(f7(a865,a865,a860),f238(a865)),f323(f323(f235(a865),f323(f189(f866(x44491)),x44493)),f323(f189(f866(x44492)),x44494)))))),f323(f166(f871(x44491,x44492)),f323(f323(f175(x44491,x44492),x44493),x44494)))
% 188.07/187.96 [4369]E(f323(f243(f871(x43691,x43692)),f323(f262(x43691,x43692,a860),f323(f323(f7(x43691,f872(x43692,a860),f872(x43692,a860)),f323(f323(f8(f872(a860,a860),f872(f872(x43692,a860),f872(x43692,a860)),x43691),f8(a860,a860,x43692)),f323(f323(f8(a860,f872(a860,a860),x43691),a322),x43693))),x43694))),f323(f323(f260(x43691,x43692),f323(f243(x43691),x43693)),f323(f16(f872(x43692,a860),x43691),f323(f243(x43692),x43694))))
% 188.07/187.96 [4372]E(f323(f243(f871(x43721,x43722)),f323(f262(x43721,x43722,a860),f323(f323(f18(x43721,f872(x43722,a860),f872(x43722,a860)),f323(f323(f8(f872(a860,a860),f872(f872(x43722,a860),f872(x43722,a860)),x43721),f8(a860,a860,x43722)),f323(f323(f8(a860,f872(a860,a860),x43721),a322),x43723))),x43724))),f323(f323(f260(x43721,x43722),f323(f243(x43721),x43723)),f323(f323(f8(f872(x43722,a860),f872(x43722,a860),x43721),f243(x43722)),x43724)))
% 188.07/187.96 [4388]E(f323(f243(x43881),f323(f323(f8(f872(x43882,a860),a860,x43881),f86(x43882)),f323(f323(f8(f872(x43882,a860),f872(x43882,a860),x43881),f323(f18(x43882,a860,a860),f323(f323(f8(a860,f872(a860,a860),x43882),a326),f323(f323(f7(x43882,f872(x43882,a860),a860),f325(x43882)),x43883)))),x43884))),f323(f323(f40(x43882,f872(x43881,a860)),x43883),f323(f323(f8(f872(x43881,a860),f872(x43881,a860),x43882),f243(x43881)),f323(f7(x43881,x43882,a860),x43884))))
% 188.07/187.96 [4432]E(f323(f323(f147(f871(x44321,a865),x44321),f257(x44321,a865)),f323(f129(f871(x44321,a865),f323(f323(f7(f871(x44321,a865),f872(a865,a860),a860),f323(f323(f8(a865,f872(f872(a865,a860),a860),f871(x44321,a865)),f325(a865)),f261(x44321,a865))),x44322)),f323(f323(f175(x44321,a865),x44323),f132(a865,f323(f293(a865,x44324),f323(f323(f78(a865),x44324),f323(f189(f866(x44321)),x44323))))))),f323(f323(f147(f871(x44321,a865),x44321),f257(x44321,a865)),f323(f129(f871(x44321,a865),f323(f323(f7(f871(x44321,a865),f872(a865,a860),a860),f323(f323(f8(a865,f872(f872(a865,a860),a860),f871(x44321,a865)),f325(a865)),f323(f323(f7(f871(x44321,a865),a865,a865),f323(f323(f8(a865,f872(a865,a865),f871(x44321,a865)),f78(a865)),f261(x44321,a865))),x44324))),x44322)),f323(f323(f175(x44321,a865),x44323),f132(a865,f323(f293(a865,f2(a865)),f323(f189(f866(x44321)),x44323)))))))
% 188.07/187.96 [4433]E(f323(a112,f323(f323(f236(a865),f323(f189(f866(x44331)),x44332)),f323(f135(a865,f866(x44333),f323(f7(f866(x44333),a865,a865),f323(f323(f8(a865,f872(a865,a865),f866(x44333)),f236(a865)),f323(f323(f7(f866(x44333),a865,a865),f323(f323(f8(a865,f872(a865,a865),f866(x44333)),f22(a865)),f189(f866(x44333)))),f323(a112,f2(a865))))),f2(a865)),f323(f162(f866(x44333)),f323(f129(f866(x44333),f323(f323(f8(a860,a860,f866(x44333)),a318),f323(f323(f7(f866(x44333),f866(x44333),a860),a320),f113(x44333)))),x44334))))),f323(f323(f236(a865),f323(a112,f323(f189(f866(x44331)),x44332))),f323(f135(a865,f866(x44333),f323(f7(f866(x44333),a865,a865),f323(f323(f8(a865,f872(a865,a865),f866(x44333)),f236(a865)),f189(f866(x44333)))),f2(a865)),f323(f162(f866(x44333)),x44334))))
% 188.07/187.96 [4387]E(f323(f323(f121(x43871),f170(x43871,x43872,x43873)),f170(x43871,x43874,f323(f243(a865),f323(f323(f7(a865,f872(a865,a860),a860),f323(f323(f8(a865,f872(f872(a865,a860),a860),a865),f325(a865)),f323(f323(f7(a865,a865,a865),f78(a865)),f323(f189(f866(x43871)),x43872)))),x43873)))),f170(x43871,f323(f323(f121(x43871),x43872),x43874),x43873))
% 188.07/187.96 [4440]E(f323(f323(f144(f866(x44401)),f323(f323(f144(x44401),x44402),f323(f135(f866(x44401),f866(x44401),f121(x44401),f113(x44401)),f323(f323(f147(f866(x44401),f866(x44401)),f149(f866(x44401),x44401,f113(x44401),f323(f323(f8(f866(x44401),f872(f866(x44401),f866(x44401)),x44401),f16(f866(x44401),f866(x44401))),f323(f323(f7(x44401,f866(x44401),f866(x44401)),f144(x44401)),f113(x44401))))),x44403)))),f173(x44401,f323(f323(f144(f866(x44401)),x44404),f323(f135(f866(f866(x44401)),f866(f866(x44401)),f121(f866(x44401)),f113(f866(x44401))),f323(f323(f147(f866(x44401),f866(f866(x44401))),f149(f866(f866(x44401)),x44401,f113(f866(x44401)),f323(f16(f872(f866(x44401),f866(f866(x44401))),x44401),f323(f323(f7(f866(x44401),f866(f866(x44401)),f866(f866(x44401))),f144(f866(x44401))),f113(f866(x44401)))))),x44403))))),f173(x44401,f323(f323(f144(f866(x44401)),f323(f323(f144(x44401),x44402),x44404)),x44403)))
% 188.07/187.96 [4450]E(f323(f243(f871(x44501,x44501)),f323(f262(x44501,x44501,a860),f323(f323(f7(x44501,f872(f871(x44502,x44502),a860),f872(x44501,a860)),f323(f323(f8(f872(x44501,f872(f872(f871(x44502,x44502),a860),a860)),f872(f872(f871(x44502,x44502),a860),f872(x44501,a860)),x44501),f7(x44501,f872(f871(x44502,x44502),a860),a860)),f323(f323(f8(f872(x44501,f871(x44502,x44502)),f872(x44501,f872(f872(f871(x44502,x44502),a860),a860)),x44501),f323(f8(f871(x44502,x44502),f872(f872(f871(x44502,x44502),a860),a860),x44501),f325(f871(x44502,x44502)))),f323(f323(f7(x44501,f872(x44501,x44502),f872(x44501,f871(x44502,x44502))),f323(f323(f8(f872(x44502,f871(x44502,x44502)),f872(f872(x44501,x44502),f872(x44501,f871(x44502,x44502))),x44501),f8(x44502,f871(x44502,x44502),x44501)),f323(f323(f8(x44502,f872(x44502,f871(x44502,x44502)),x44501),f258(x44502,x44502)),x44503))),x44503)))),x44504))),f323(f323(f279(x44502,x44501),x44504),x44503))
% 188.07/187.96 [4510]~E(f30(x45101,x45102),f27(x45103,x45104,x45105))
% 188.07/187.96 [4511]~E(f30(x45111,x45112),f26(x45113,x45114,x45115))
% 188.07/187.96 [4512]~E(f29(x45121,x45122),f27(x45123,x45124,x45125))
% 188.07/187.96 [4513]~E(f29(x45131,x45132),f26(x45133,x45134,x45135))
% 188.07/187.96 [4514]~E(f25(x45141,x45142),f27(x45143,x45144,x45145))
% 188.07/187.96 [4515]~E(f25(x45151,x45152),f26(x45153,x45154,x45155))
% 188.07/187.96 [4516]~E(f27(x45161,x45162,x45163),f30(x45164,x45165))
% 188.07/187.96 [4517]~E(f27(x45171,x45172,x45173),f29(x45174,x45175))
% 188.07/187.96 [4518]~E(f27(x45181,x45182,x45183),f25(x45184,x45185))
% 188.07/187.96 [4519]~E(f26(x45191,x45192,x45193),f30(x45194,x45195))
% 188.07/187.96 [4520]~E(f26(x45201,x45202,x45203),f29(x45204,x45205))
% 188.07/187.96 [4521]~E(f26(x45211,x45212,x45213),f25(x45214,x45215))
% 188.07/187.96 [3558]E(f323(f323(f147(x35581,x35582),x35583),f163(x35581,x35584,x35585)),f163(x35582,x35584,f323(x35583,x35585)))
% 188.07/187.96 [3927]E(f323(f180(x39271,x39272,x39273,x39274),x39275),f323(f232(f869(x39272),x39272,f323(x39273,x39275),f230(x39272)),f323(x39274,x39275)))
% 188.07/187.96 [4017]E(f180(x40171,x40172,f180(x40171,x40172,x40173,x40174),x40175),f180(x40171,x40172,x40173,f180(x40171,x40172,x40174,x40175)))
% 188.07/187.96 [4192]E(f259(x41921,x41922,x41923,f247(x41922,x41921,x41924),f247(x41923,x41922,x41925)),f247(x41923,x41921,f259(x41923,x41922,x41921,x41925,x41924)))
% 188.07/187.96 [4199]E(f323(f323(f110(f872(x41991,a860)),f323(f166(x41991),f323(f323(f169(x41991),f323(f189(f866(x41992)),x41993)),x41994))),f177(x41991,x41992,x41995)),f177(x41991,x41992,f181(x41991,x41992,x41995,x41994,x41993)))
% 188.07/187.96 [3749]E(f323(f323(f262(x37491,x37492,x37493),x37494),x37495),f323(f323(x37494,f323(f257(x37491,x37492),x37495)),f323(f261(x37491,x37492),x37495)))
% 188.07/187.96 [3775]E(f323(f232(x37751,x37752,x37753,x37754),f323(f230(x37752),x37755)),f323(x37754,x37755))
% 188.07/187.96 [3784]E(f323(f323(f323(f63(x37841,x37842,x37843),x37844),x37845),f188(f872(x37842,a860))),x37845)
% 188.07/187.96 [3960]E(f233(x39601,x39602,x39603,x39604,f323(f230(x39602),x39605)),f323(x39604,x39605))
% 188.07/187.96 [4072]E(f323(f71(f869(x40721),f869(x40722),f869(x40723),f323(f201(x40721,x40722),x40724)),f323(f201(x40723,x40721),x40725)),f323(f201(x40723,x40722),f323(f71(x40721,x40722,x40723,x40724),x40725)))
% 188.07/187.96 [4074]E(f323(f71(f866(x40741),f866(x40742),f866(x40743),f323(f147(x40741,x40742),x40744)),f323(f147(x40743,x40741),x40745)),f323(f147(x40743,x40742),f323(f71(x40741,x40742,x40743,x40744),x40745)))
% 188.07/187.96 [4130]E(f323(f232(x41301,f871(x41302,f867(x41302)),x41303,f323(f262(x41302,f867(x41302),x41301),x41304)),f323(f128(x41302),x41305)),f126(x41301,x41302,x41303,x41304,x41305))
% 188.07/187.96 [4153]E(f83(x41531,f64(x41532,x41531,x41533,x41534,x41535)),f323(f323(f62(x41532,x41531,x41533),x41534),x41535))
% 188.07/187.96 [4189]E(f323(f323(f78(a865),f323(f323(f78(a865),f323(x41891,f323(f257(x41892,x41893),x41894))),f323(x41895,f323(f261(x41892,x41893),x41894)))),f323(a112,f2(a865))),f266(x41892,x41893,x41891,x41895,x41894))
% 188.07/187.96 [4383]E(f156(x43831,x43832,f323(f323(f7(x43831,f869(x43832),f869(x43832)),f323(f323(f18(x43831,f869(x43832),f872(f869(x43832),f869(x43832))),f323(f323(f8(a860,f872(f869(x43832),f872(f869(x43832),f869(x43832))),x43831),f96(f869(x43832))),x43833)),f323(f323(f8(x43832,f869(x43832),x43831),f230(x43832)),x43834))),f200(x43832)),x43835),f323(f323(f147(x43831,x43832),x43834),f323(f129(x43831,x43833),x43835)))
% 188.07/187.96 [4557]~E(f323(f323(f323(f70(x45571,f869(x45572)),x45573),x45574),f323(f230(x45572),x45575)),f323(f16(f869(x45572),x45571),f200(x45572)))
% 188.07/187.96 [3684]E(f323(f323(f169(x36841),x36842),f323(f323(f147(x36843,x36841),x36844),x36845)),f323(f323(f147(x36843,x36841),x36844),f323(f323(f169(x36843),x36842),x36845)))
% 188.07/187.96 [3685]E(f323(f323(f131(x36851),x36852),f323(f323(f147(x36853,x36851),x36854),x36855)),f323(f323(f147(x36853,x36851),x36854),f323(f323(f131(x36853),x36852),x36855)))
% 188.07/187.96 [3717]E(f323(f323(f147(x37171,x37172),x37173),f323(f323(f144(x37171),x37174),x37175)),f323(f323(f144(x37172),f323(x37173,x37174)),f323(f323(f147(x37171,x37172),x37173),x37175)))
% 188.07/187.96 [3779]E(f323(f302(x37791,x37792,x37793),f323(f323(f301(x37791),x37794),x37795)),f323(f323(f301(x37792),f323(x37793,x37794)),f323(f302(x37791,x37792,x37793),x37795)))
% 188.07/187.96 [3808]E(f167(x38081,f323(f323(f144(x38081),x38082),x38083),f323(f323(f144(x38081),x38084),x38085)),f323(f323(f144(x38081),x38082),f323(f323(f144(x38081),x38084),f167(x38081,x38083,x38085))))
% 188.07/187.96 [3846]E(f323(f323(f175(x38461,x38462),f323(f323(f169(x38461),x38463),x38464)),f323(f323(f169(x38462),x38463),x38465)),f323(f323(f169(f871(x38461,x38462)),x38463),f323(f323(f175(x38461,x38462),x38464),x38465)))
% 188.07/187.96 [3847]E(f323(f323(f175(x38471,x38472),f323(f323(f131(x38471),x38473),x38474)),f323(f323(f131(x38472),x38473),x38475)),f323(f323(f131(f871(x38471,x38472)),x38473),f323(f323(f175(x38471,x38472),x38474),x38475)))
% 188.07/187.96 [3859]E(f323(f323(f152(x38591,f323(f323(f144(x38591),x38592),x38593)),f323(a112,x38594)),x38595),f323(f323(f144(x38591),x38592),f323(f323(f152(x38591,x38593),x38594),x38595)))
% 188.07/187.96 [3862]E(f323(f232(f869(x38621),x38622,f200(x38621),x38623),f323(f323(f16(f869(x38622),x38624),f200(x38622)),x38625)),f200(x38621))
% 188.07/187.96 [3864]E(f323(f323(f121(x38641),f323(f323(f147(x38642,x38641),x38643),x38644)),f323(f323(f147(x38642,x38641),x38643),x38645)),f323(f323(f147(x38642,x38641),x38643),f323(f323(f121(x38642),x38644),x38645)))
% 188.07/187.96 [3868]E(f323(f323(x38681,x38682),f323(f323(f249(x38683,x38684,x38681),x38682),x38685)),f323(f323(f249(x38683,x38684,x38681),x38682),f323(a112,x38685)))
% 188.07/187.96 [3898]E(f157(x38981,x38982,x38983,f323(f323(f144(x38981),x38984),x38985)),f323(f323(f121(x38982),f323(x38983,x38984)),f157(x38981,x38982,x38983,x38985)))
% 188.07/187.96 [3911]E(f323(f323(f280(x39111,x39112,x39113),f323(f278(x39112,x39111),x39114)),f323(f278(x39113,x39112),x39115)),f323(f278(x39113,x39111),f323(f323(f280(x39113,x39112,x39111),x39115),x39114)))
% 188.07/187.96 [3945]E(f323(f323(f323(f183(f866(x39451),f866(x39451)),x39452),f161(x39451)),f323(f323(f147(x39453,x39451),x39454),x39455)),f323(f323(f147(x39453,x39451),x39454),f323(f323(f323(f183(f866(x39453),f866(x39453)),x39452),f161(x39453)),x39455)))
% 188.07/187.96 [3946]E(f323(f323(f264(x39461,x39462,x39461,x39463),f323(f258(x39462,x39461),x39464)),x39465),f323(x39465,x39464))
% 188.07/187.96 [3974]E(f148(x39741,x39742,f323(f323(f147(x39743,x39741),x39744),x39745)),f148(x39743,f323(f71(x39741,a865,x39743,x39742),x39744),x39745))
% 188.07/187.96 [4040]E(f323(f323(f71(f869(x40401),f869(x40402),x40403,f323(f201(x40401,x40402),x40404)),f323(f16(f869(x40401),x40403),f200(x40401))),x40405),f200(x40402))
% 188.07/187.96 [4041]E(f171(f871(x40411,x40412),f323(f71(x40412,a860,f871(x40411,x40412),x40413),f261(x40411,x40412)),f323(f323(f175(x40411,x40412),x40414),x40415)),f323(f323(f175(x40411,x40412),x40414),f171(x40412,x40413,x40415)))
% 188.07/187.96 [4046]E(f323(f302(x40461,x40462,f323(f323(f8(x40463,x40462,x40461),x40464),x40465)),f246(f872(x40461,a860))),f323(f302(x40463,x40462,x40464),f323(f302(x40461,x40463,x40465),f246(f872(x40461,a860)))))
% 188.07/187.96 [4059]E(f171(f871(x40591,x40592),f323(f71(x40591,a860,f871(x40591,x40592),x40593),f257(x40591,x40592)),f323(f323(f175(x40591,x40592),x40594),x40595)),f323(f323(f175(x40591,x40592),f171(x40591,x40593,x40594)),x40595))
% 188.07/187.96 [4078]E(f323(f323(f110(f872(x40781,a860)),f323(f303(x40781,x40782,x40783),f323(f323(f301(x40782),x40784),f188(f872(x40782,a860))))),f323(f303(x40781,x40782,x40783),x40785)),f323(f303(x40781,x40782,x40783),f323(f323(f301(x40782),x40784),x40785)))
% 188.07/187.96 [4137]E(f323(f323(f121(f871(x41371,x41372)),f323(f323(f147(x41372,f871(x41371,x41372)),f323(f258(x41371,x41372),x41373)),x41374)),f57(x41371,x41372,x41375,x41374)),f57(x41371,x41372,f323(f323(f144(x41371),x41373),x41375),x41374))
% 188.07/187.96 [4138]E(f323(f323(f147(x41381,x41382),x41383),f171(x41381,f323(f71(x41382,a860,x41381,x41384),x41383),x41385)),f171(x41382,x41384,f323(f323(f147(x41381,x41382),x41383),x41385)))
% 188.07/187.96 [4144]E(f323(f135(x41441,x41442,f323(f7(x41442,x41441,x41441),f323(f7(x41441,x41442,x41441),x41443)),x41444),f323(f162(x41442),f323(f162(x41442),x41445))),f323(f135(x41441,x41442,x41443,x41444),x41445))
% 188.07/187.96 [4145]E(f323(f323(f323(f70(x41451,f869(x41452)),f182(x41451,x41452,x41453,x41454)),x41455),f323(x41453,x41455)),f182(x41451,x41452,x41453,f323(f323(f301(x41451),x41455),x41454)))
% 188.07/187.96 [4216]E(f323(f232(f866(x42161),x42161,f156(x42162,x42161,x42163,x42164),f323(f323(f7(x42161,f866(x42161),f866(x42161)),f144(x42161)),f156(x42162,x42161,x42163,x42164))),f323(x42163,x42165)),f156(x42162,x42161,x42163,f323(f323(f144(x42162),x42165),x42164)))
% 188.07/187.96 [4253]P101(f323(f323(f237(f872(x42531,a860)),f323(f302(x42532,x42531,x42533),f323(f323(f101(f872(x42532,a860)),x42534),x42535))),f323(f323(f101(f872(x42531,a860)),f323(f302(x42532,x42531,x42533),x42534)),f323(f302(x42532,x42531,x42533),x42535))))
% 188.07/187.96 [4254]P101(f323(f323(f237(f872(x42541,a860)),f323(f277(x42542,x42541,x42543),f323(f323(f101(f872(x42542,a860)),x42544),x42545))),f323(f323(f101(f872(x42541,a860)),f323(f277(x42542,x42541,x42543),x42544)),f323(f277(x42542,x42541,x42543),x42545))))
% 188.07/187.96 [4357]E(f323(f261(x43571,x43572),f323(f263(x43573,x43571,x43572,x43572,x43574,f32(x43572)),x43575)),f323(f261(x43573,x43572),x43575))
% 188.07/187.96 [4358]E(f323(f257(x43581,x43582),f323(f263(x43581,x43581,x43583,x43582,f32(x43581),x43584),x43585)),f323(f257(x43581,x43583),x43585))
% 188.07/187.96 [4444]P26(x44441,x44442,f323(f323(f301(f864(x44441)),f323(f323(f323(f90(x44441),f323(f323(f7(x44441,f872(a861,a861),f872(a861,a860)),f323(f323(f8(f872(a861,a860),f872(f872(a861,a861),f872(a861,a860)),x44441),f8(a861,a860,a861)),x44443)),f323(f323(f18(a861,a865,a861),f323(f323(f7(a861,a863,f872(a865,a861)),a196),x44444)),x44445))),f25(x44444,x44445)),x44443)),f188(f872(f864(x44441),a860))))
% 188.07/187.96 [4446]E(f323(f135(f872(x44461,f869(x44462)),f871(x44461,x44462),f323(f323(f8(f872(x44461,f872(x44462,f872(x44461,f869(x44462)))),f872(f871(x44461,x44462),f872(x44461,f869(x44462))),f872(x44461,f869(x44462))),f262(x44461,x44462,f872(x44461,f869(x44462)))),f323(f323(f7(f872(x44461,f869(x44462)),f872(x44462,f869(x44462)),f872(x44461,f872(x44462,f872(x44461,f869(x44462))))),f323(f323(f8(f872(x44461,f872(f872(x44462,f869(x44462)),f872(x44462,f872(x44461,f869(x44462))))),f872(f872(x44462,f869(x44462)),f872(x44461,f872(x44462,f872(x44461,f869(x44462))))),f872(x44461,f869(x44462))),f7(x44461,f872(x44462,f869(x44462)),f872(x44462,f872(x44461,f869(x44462))))),f323(f323(f8(f872(x44461,f872(f869(x44462),f872(x44461,f869(x44462)))),f872(x44461,f872(f872(x44462,f869(x44462)),f872(x44462,f872(x44461,f869(x44462))))),f872(x44461,f869(x44462))),f323(f8(f872(f869(x44462),f872(x44461,f869(x44462))),f872(f872(x44462,f869(x44462)),f872(x44462,f872(x44461,f869(x44462)))),x44461),f8(f869(x44462),f872(x44461,f869(x44462)),x44462))),f70(x44461,f869(x44462))))),f230(x44462))),x44463),f323(f323(f175(x44461,x44462),x44464),x44465)),f181(x44461,x44462,x44463,x44464,x44465))
% 188.07/187.96 [4448]P26(x44481,x44482,f323(f323(f301(f864(x44481)),f323(f323(f323(f90(x44481),f323(f323(f7(x44481,f872(a861,a860),f872(a861,a860)),f323(f323(f8(f872(a861,f872(a860,a860)),f872(f872(a861,a860),f872(a861,a860)),x44481),f18(a861,a860,a860)),f323(f323(f8(f872(a861,a860),f872(a861,f872(a860,a860)),x44481),f323(f8(a860,f872(a860,a860),a861),a322)),x44483))),f323(f323(f8(a860,a860,a861),a318),x44484))),f29(x44484,x44485)),x44483)),f188(f872(f864(x44481),a860))))
% 188.07/187.96 [3528]E(f323(f323(f323(f323(f206(x35281),x35282),x35283),x35284),x35285),f192(x35281,x35282))
% 188.07/187.96 [3529]E(f323(f323(f323(f323(f210(x35291),x35292),x35293),x35294),x35295),f202(x35291,x35292))
% 188.07/187.96 [3574]E(f93(x35741,x35742,f323(f323(f323(f90(x35741),x35743),x35744),x35745)),f2(a865))
% 188.07/187.96 [3668]E(f323(f323(f323(f323(f70(x36681,x36682),x36683),x36684),x36685),x36684),x36685)
% 188.07/187.96 [3899]E(f323(f323(f39(x38991,f872(x38992,a860)),f323(f323(f301(x38991),x38993),x38994)),x38995),f323(f323(f110(f872(x38992,a860)),f323(x38995,x38993)),f323(f323(f39(x38991,f872(x38992,a860)),x38994),x38995)))
% 188.07/187.96 [3900]E(f323(f323(f40(x39001,f872(x39002,a860)),f323(f323(f301(x39001),x39003),x39004)),x39005),f323(f323(f101(f872(x39002,a860)),f323(x39005,x39003)),f323(f323(f40(x39001,f872(x39002,a860)),x39004),x39005)))
% 188.07/187.96 [3953]E(f323(f116(x39531,x39532,f323(x39533,x39534)),f323(f323(f7(x39531,a99,f867(x39532)),x39535),x39534)),f323(f198(x39531,x39532,x39533,x39535),x39534))
% 188.07/187.96 [3967]E(f323(f323(f110(f872(x39671,a860)),f323(f302(x39672,x39671,x39673),x39674)),f323(f302(x39672,x39671,x39673),x39675)),f323(f302(x39672,x39671,x39673),f323(f323(f110(f872(x39672,a860)),x39674),x39675)))
% 188.07/187.96 [3968]E(f323(f323(f110(f872(x39681,a860)),f323(f303(x39681,x39682,x39683),x39684)),f323(f303(x39681,x39682,x39683),x39685)),f323(f303(x39681,x39682,x39683),f323(f323(f110(f872(x39682,a860)),x39684),x39685)))
% 188.07/187.96 [3969]E(f323(f323(f22(f872(x39691,a860)),f323(f303(x39691,x39692,x39693),x39694)),f323(f303(x39691,x39692,x39693),x39695)),f323(f303(x39691,x39692,x39693),f323(f323(f22(f872(x39692,a860)),x39694),x39695)))
% 188.07/187.96 [3970]E(f323(f323(f101(f872(x39701,a860)),f323(f303(x39701,x39702,x39703),x39704)),f323(f303(x39701,x39702,x39703),x39705)),f323(f303(x39701,x39702,x39703),f323(f323(f101(f872(x39702,a860)),x39704),x39705)))
% 188.07/187.96 [3971]E(f323(f323(f110(f872(x39711,a860)),f323(f277(x39712,x39711,x39713),x39714)),f323(f277(x39712,x39711,x39713),x39715)),f323(f277(x39712,x39711,x39713),f323(f323(f110(f872(x39712,a860)),x39714),x39715)))
% 188.07/187.96 [3973]E(f182(x39731,x39732,f182(x39731,x39732,x39733,x39734),x39735),f182(x39731,x39732,x39733,f323(f323(f101(f872(x39731,a860)),x39734),x39735)))
% 188.07/187.96 [4036]E(f323(f323(f152(x40361,f323(f323(f121(x40361),x40362),f323(f323(f144(x40361),x40363),x40364))),f323(f189(f866(x40361)),x40362)),x40365),f323(f323(f121(x40361),x40362),f323(f323(f144(x40361),x40365),x40364)))
% 188.07/187.96 [4044]E(f323(f323(f40(x40441,f872(x40442,a860)),x40443),f323(f323(f8(f872(x40442,a860),f872(x40442,a860),x40441),f323(f301(x40442),x40444)),x40445)),f323(f323(f301(x40442),x40444),f323(f323(f40(x40441,f872(x40442,a860)),x40443),x40445)))
% 188.07/187.96 [4112]E(f182(x41121,x41122,f323(f323(f323(f70(x41121,f869(x41122)),x41123),x41124),f323(f230(x41122),x41125)),f323(f77(f872(x41121,a860)),f323(f323(f301(x41121),x41124),f188(f872(x41121,a860))))),f182(x41121,x41122,x41123,f323(f77(f872(x41121,a860)),f323(f323(f301(x41121),x41124),f188(f872(x41121,a860))))))
% 188.07/187.96 [4203]E(f323(f323(f147(x42031,x42032),x42033),f323(f129(x42031,f323(f71(x42032,a860,x42031,x42034),x42033)),x42035)),f323(f129(x42032,x42034),f323(f323(f147(x42031,x42032),x42033),x42035)))
% 188.07/187.96 [4209]E(f323(f189(f866(x42091)),f323(f129(x42091,x42092),f323(f323(f147(x42093,x42091),x42094),x42095))),f323(f189(f866(x42093)),f323(f129(x42093,f323(f71(x42091,a860,x42093,x42092),x42094)),x42095)))
% 188.07/187.96 [4349]E(f323(f323(f110(f872(x43491,a860)),f323(f323(f22(f872(x43491,a860)),f177(x43491,x43492,x43493)),f323(f243(x43491),f323(f323(f7(x43491,f872(x43491,a860),a860),f325(x43491)),f323(f323(f22(f872(x43491,a860)),x43494),f177(x43491,x43492,x43495)))))),f323(f243(x43491),f323(f323(f7(x43491,f872(x43491,a860),a860),f325(x43491)),f323(f323(f101(f872(x43491,a860)),x43494),f177(x43491,x43492,x43495))))),f177(x43491,x43492,f74(x43491,f869(x43492),x43493,x43495,x43494)))
% 188.07/187.96 [4424]E(f323(f149(f866(f871(x44241,x44242)),x44242,f113(f871(x44241,x44242)),f323(f323(f7(x44242,f872(f866(x44242),f866(f871(x44241,x44242))),f872(f866(x44242),f866(f871(x44241,x44242)))),f323(f323(f8(f872(f866(f871(x44241,x44242)),f866(f871(x44241,x44242))),f872(f872(f866(x44242),f866(f871(x44241,x44242))),f872(f866(x44242),f866(f871(x44241,x44242)))),x44242),f8(f866(f871(x44241,x44242)),f866(f871(x44241,x44242)),f866(x44242))),f323(f323(f8(f871(x44241,x44242),f872(f866(f871(x44241,x44242)),f866(f871(x44241,x44242))),x44242),f144(f871(x44241,x44242))),f323(f258(x44241,x44242),x44243)))),f323(f175(x44241,x44242),x44244))),x44245),f323(f323(f175(x44241,x44242),f323(f323(f144(x44241),x44243),x44244)),x44245))
% 188.07/187.96 [3893]E(f323(f323(f152(x38931,f323(f323(f152(x38931,x38932),x38933),x38934)),x38933),x38935),f323(f323(f152(x38931,x38932),x38933),x38935))
% 188.07/187.96 [3947]E(f323(f254(x39471,x39472),f323(f323(f301(f871(x39471,x39472)),f323(f323(f258(x39471,x39472),x39473),x39474)),x39475)),f323(f323(f301(x39472),x39474),f323(f254(x39471,x39472),x39475)))
% 188.07/187.96 [3948]E(f323(f256(x39481,x39482),f323(f323(f301(f871(x39481,x39482)),f323(f323(f258(x39481,x39482),x39483),x39484)),x39485)),f323(f323(f301(x39481),x39483),f323(f256(x39481,x39482),x39485)))
% 188.07/187.96 [3999]E(f119(x39991,x39992,f323(x39993,x39994),f323(f323(f7(x39991,a99,f867(f869(x39992))),x39995),x39994)),f323(f195(x39991,x39992,x39993,x39995),x39994))
% 188.07/187.96 [4029]E(f323(f323(f110(f872(f871(x40291,x40292),a860)),f323(f323(f260(x40291,x40292),x40293),x40294)),f323(f323(f260(x40291,x40292),x40295),x40294)),f323(f323(f260(x40291,x40292),f323(f323(f110(f872(x40291,a860)),x40293),x40295)),x40294))
% 188.07/187.96 [4030]E(f323(f323(f22(f872(f871(x40301,x40302),a860)),f323(f323(f260(x40301,x40302),x40303),x40304)),f323(f323(f260(x40301,x40302),x40305),x40304)),f323(f323(f260(x40301,x40302),f323(f323(f22(f872(x40301,a860)),x40303),x40305)),x40304))
% 188.07/187.96 [4031]E(f323(f323(f101(f872(f871(x40311,x40312),a860)),f323(f323(f260(x40311,x40312),x40313),x40314)),f323(f323(f260(x40311,x40312),x40315),x40314)),f323(f323(f260(x40311,x40312),f323(f323(f101(f872(x40311,a860)),x40313),x40315)),x40314))
% 188.07/187.96 [4090]E(f323(f323(f110(f872(x40901,a860)),f323(f323(f39(x40902,f872(x40901,a860)),x40903),x40904)),f323(f323(f39(x40902,f872(x40901,a860)),x40905),x40904)),f323(f323(f39(x40902,f872(x40901,a860)),f323(f323(f110(f872(x40902,a860)),x40903),x40905)),x40904))
% 188.07/187.96 [4091]E(f323(f323(f101(f872(x40911,a860)),f323(f323(f40(x40912,f872(x40911,a860)),x40913),x40914)),f323(f323(f40(x40912,f872(x40911,a860)),x40915),x40914)),f323(f323(f40(x40912,f872(x40911,a860)),f323(f323(f110(f872(x40912,a860)),x40913),x40915)),x40914))
% 188.07/187.96 [4105]E(f323(f323(f39(x41051,f872(x41052,a860)),x41053),f323(f323(f8(f872(x41052,a860),f872(x41052,a860),x41051),f323(f22(f872(x41052,a860)),x41054)),x41055)),f323(f323(f22(f872(x41052,a860)),x41054),f323(f323(f40(x41051,f872(x41052,a860)),x41053),x41055)))
% 188.07/187.96 [4106]E(f323(f323(f39(x41061,f872(x41062,a860)),x41063),f323(f323(f8(f872(x41062,a860),f872(x41062,a860),x41061),f323(f101(f872(x41062,a860)),x41064)),x41065)),f323(f323(f101(f872(x41062,a860)),x41064),f323(f323(f39(x41061,f872(x41062,a860)),x41063),x41065)))
% 188.07/187.96 [4107]E(f323(f323(f40(x41071,f872(x41072,a860)),x41073),f323(f323(f8(f872(x41072,a860),f872(x41072,a860),x41071),f323(f110(f872(x41072,a860)),x41074)),x41075)),f323(f323(f110(f872(x41072,a860)),x41074),f323(f323(f40(x41071,f872(x41072,a860)),x41073),x41075)))
% 188.07/187.96 [4143]E(f180(x41431,x41432,x41433,f323(f179(x41431,x41432),f323(f162(f871(x41431,x41432)),f323(f323(f175(x41431,x41432),x41434),x41435)))),f181(x41431,x41432,x41433,x41434,x41435))
% 188.07/187.96 [4165]E(f185(f866(x41651),f323(f323(f144(x41651),x41652),x41653),f323(f323(f8(f866(x41651),f866(x41651),a865),f323(f144(x41651),x41654)),f323(f323(f7(a865,x41651,f866(x41651)),f152(x41651,x41653)),x41652)),x41655),f323(f323(f152(x41651,f323(f323(f144(x41651),x41654),x41653)),x41655),x41652))
% 188.07/187.96 [4169]E(f323(f323(f39(x41691,f872(f871(x41692,x41693),a860)),x41694),f323(f323(f8(f872(f871(x41693,x41692),a860),f872(f871(x41692,x41693),a860),x41691),f278(x41693,x41692)),x41695)),f323(f278(x41693,x41692),f323(f323(f39(x41691,f872(f871(x41693,x41692),a860)),x41694),x41695)))
% 188.07/187.96 [4170]E(f323(f323(f40(x41701,f872(f871(x41702,x41703),a860)),x41704),f323(f323(f8(f872(f871(x41703,x41702),a860),f872(f871(x41702,x41703),a860),x41701),f278(x41703,x41702)),x41705)),f323(f278(x41703,x41702),f323(f323(f40(x41701,f872(f871(x41703,x41702),a860)),x41704),x41705)))
% 188.07/187.96 [4227]E(f177(x42271,x42272,f323(f323(f18(x42271,f869(x42273),f869(x42272)),f323(f323(f8(f872(x42273,x42272),f872(f869(x42273),f869(x42272)),x42271),f201(x42273,x42272)),x42274)),x42275)),f177(x42271,x42273,x42275))
% 188.07/187.96 [4278]P101(f323(f323(f237(f872(x42781,a860)),f323(f323(f22(f872(x42781,a860)),f323(f302(x42782,x42781,x42783),x42784)),f323(f302(x42782,x42781,x42783),x42785))),f323(f302(x42782,x42781,x42783),f323(f323(f22(f872(x42782,a860)),x42784),x42785))))
% 188.07/187.96 [4428]E(f323(f149(f866(f871(x44281,x44282)),x44281,f113(f871(x44281,x44282)),f323(f323(f7(x44281,f872(f866(x44281),f866(f871(x44281,x44282))),f872(f866(x44281),f866(f871(x44281,x44282)))),f323(f323(f8(f872(f866(f871(x44281,x44282)),f866(f871(x44281,x44282))),f872(f872(f866(x44281),f866(f871(x44281,x44282))),f872(f866(x44281),f866(f871(x44281,x44282)))),x44281),f8(f866(f871(x44281,x44282)),f866(f871(x44281,x44282)),f866(x44281))),f323(f323(f8(f871(x44281,x44282),f872(f866(f871(x44281,x44282)),f866(f871(x44281,x44282))),x44281),f144(f871(x44281,x44282))),f323(f323(f7(x44281,x44282,f871(x44281,x44282)),f258(x44281,x44282)),x44283)))),f323(f323(f7(f866(x44281),f866(x44282),f866(f871(x44281,x44282))),f175(x44281,x44282)),x44284))),x44285),f323(f323(f175(x44281,x44282),x44285),f323(f323(f144(x44282),x44283),x44284)))
% 188.07/187.96 [4131]E(f323(f323(f110(f872(x41311,a860)),f323(f277(x41312,x41311,x41313),x41314)),f323(f277(x41312,x41311,x41315),x41314)),f323(f277(x41312,x41311,f323(f323(f110(f872(f871(x41312,x41311),a860)),x41313),x41315)),x41314))
% 188.07/187.96 [4172]E(f323(f323(f121(f871(x41721,x41722)),f323(f323(f175(x41721,x41722),x41723),f323(f323(f169(x41722),f323(f189(f866(x41721)),x41723)),x41724))),f323(f323(f175(x41721,x41722),x41725),f323(f323(f131(x41722),f323(f189(f866(x41721)),x41723)),x41724))),f323(f323(f175(x41721,x41722),f323(f323(f121(x41721),x41723),x41725)),x41724))
% 188.07/187.96 [4281]E(f323(f323(f260(x42811,x42812),x42813),f323(f323(f18(x42811,f872(x42812,a860),f872(x42812,a860)),f323(f323(f8(f872(x42812,a860),f872(f872(x42812,a860),f872(x42812,a860)),x42811),f110(f872(x42812,a860))),x42814)),x42815)),f323(f323(f110(f872(f871(x42811,x42812),a860)),f323(f323(f260(x42811,x42812),x42813),x42814)),f323(f323(f260(x42811,x42812),x42813),x42815)))
% 188.07/187.96 [4282]E(f323(f323(f260(x42821,x42822),x42823),f323(f323(f18(x42821,f872(x42822,a860),f872(x42822,a860)),f323(f323(f8(f872(x42822,a860),f872(f872(x42822,a860),f872(x42822,a860)),x42821),f22(f872(x42822,a860))),x42824)),x42825)),f323(f323(f22(f872(f871(x42821,x42822),a860)),f323(f323(f260(x42821,x42822),x42823),x42824)),f323(f323(f260(x42821,x42822),x42823),x42825)))
% 188.07/187.96 [4283]E(f323(f323(f260(x42831,x42832),x42833),f323(f323(f18(x42831,f872(x42832,a860),f872(x42832,a860)),f323(f323(f8(f872(x42832,a860),f872(f872(x42832,a860),f872(x42832,a860)),x42831),f101(f872(x42832,a860))),x42834)),x42835)),f323(f323(f101(f872(f871(x42831,x42832),a860)),f323(f323(f260(x42831,x42832),x42833),x42834)),f323(f323(f260(x42831,x42832),x42833),x42835)))
% 188.07/187.96 [4287]E(f323(f323(f39(x42871,f872(x42872,a860)),x42873),f323(f323(f7(x42871,f872(x42872,a860),f872(x42872,a860)),f323(f323(f8(f872(x42872,a860),f872(f872(x42872,a860),f872(x42872,a860)),x42871),f22(f872(x42872,a860))),x42874)),x42875)),f323(f323(f22(f872(x42872,a860)),f323(f323(f39(x42871,f872(x42872,a860)),x42873),x42874)),x42875))
% 188.07/187.96 [4288]E(f323(f323(f39(x42881,f872(x42882,a860)),x42883),f323(f323(f7(x42881,f872(x42882,a860),f872(x42882,a860)),f323(f323(f8(f872(x42882,a860),f872(f872(x42882,a860),f872(x42882,a860)),x42881),f101(f872(x42882,a860))),x42884)),x42885)),f323(f323(f101(f872(x42882,a860)),f323(f323(f39(x42881,f872(x42882,a860)),x42883),x42884)),x42885))
% 188.07/187.96 [4289]E(f323(f323(f40(x42891,f872(x42892,a860)),x42893),f323(f323(f7(x42891,f872(x42892,a860),f872(x42892,a860)),f323(f323(f8(f872(x42892,a860),f872(f872(x42892,a860),f872(x42892,a860)),x42891),f110(f872(x42892,a860))),x42894)),x42895)),f323(f323(f110(f872(x42892,a860)),f323(f323(f40(x42891,f872(x42892,a860)),x42893),x42894)),x42895))
% 188.07/187.96 [4293]E(f323(f323(f39(x42931,f872(x42932,a860)),x42933),f323(f323(f18(x42931,f872(x42932,a860),f872(x42932,a860)),f323(f323(f8(f872(x42932,a860),f872(f872(x42932,a860),f872(x42932,a860)),x42931),f110(f872(x42932,a860))),x42934)),x42935)),f323(f323(f110(f872(x42932,a860)),f323(f323(f39(x42931,f872(x42932,a860)),x42933),x42934)),f323(f323(f39(x42931,f872(x42932,a860)),x42933),x42935)))
% 188.07/187.96 [4294]E(f323(f323(f40(x42941,f872(x42942,a860)),x42943),f323(f323(f18(x42941,f872(x42942,a860),f872(x42942,a860)),f323(f323(f8(f872(x42942,a860),f872(f872(x42942,a860),f872(x42942,a860)),x42941),f101(f872(x42942,a860))),x42944)),x42945)),f323(f323(f101(f872(x42942,a860)),f323(f323(f40(x42941,f872(x42942,a860)),x42943),x42944)),f323(f323(f40(x42941,f872(x42942,a860)),x42943),x42945)))
% 188.07/187.96 [4309]E(f323(f323(f39(x43091,f872(x43092,a860)),x43093),f323(f323(f18(x43091,f872(x43092,a860),f872(x43092,a860)),f323(f323(f8(f872(x43092,a860),f872(f872(x43092,a860),f872(x43092,a860)),x43091),f110(f872(x43092,a860))),x43094)),x43095)),f323(f323(f110(f872(x43092,a860)),f37(f872(x43092,a860),f323(f302(x43091,f872(x43092,a860),x43094),x43093))),f37(f872(x43092,a860),f323(f302(x43091,f872(x43092,a860),x43095),x43093))))
% 188.07/187.96 [4310]E(f323(f323(f40(x43101,f872(x43102,a860)),x43103),f323(f323(f18(x43101,f872(x43102,a860),f872(x43102,a860)),f323(f323(f8(f872(x43102,a860),f872(f872(x43102,a860),f872(x43102,a860)),x43101),f101(f872(x43102,a860))),x43104)),x43105)),f323(f323(f101(f872(x43102,a860)),f38(f872(x43102,a860),f323(f302(x43101,f872(x43102,a860),x43104),x43103))),f38(f872(x43102,a860),f323(f302(x43101,f872(x43102,a860),x43105),x43103))))
% 188.07/187.96 [4345]E(f323(f323(f131(x43451),f323(f189(f866(x43451)),f171(x43451,x43452,f323(f323(f147(x43453,x43451),x43454),x43455)))),f323(f323(f147(x43453,x43451),x43454),x43455)),f323(f323(f147(x43453,x43451),x43454),f323(f323(f131(x43453),f323(f189(f866(x43453)),f171(x43453,f323(f71(x43451,a860,x43453,x43452),x43454),x43455))),x43455)))
% 188.07/187.96 [4217]E(f323(f323(f121(f871(x42171,x42172)),f323(f323(f175(x42171,x42172),f323(f323(f169(x42171),f323(f189(f866(x42172)),x42173)),x42174)),x42173)),f323(f323(f175(x42171,x42172),f323(f323(f131(x42171),f323(f189(f866(x42172)),x42173)),x42174)),x42175)),f323(f323(f175(x42171,x42172),x42174),f323(f323(f121(x42172),x42173),x42175)))
% 188.07/187.96 [4336]E(f83(x43361,f323(f323(f18(x43361,a860,a860),f323(f323(f8(a860,f872(a860,a860),x43361),a322),f323(f323(f7(x43361,f872(x43361,a860),a860),f325(x43361)),x43362))),f323(f323(f7(x43361,x43363,a860),f323(f323(f8(x43363,f872(x43363,a860),x43361),a320),x43364)),x43365))),f323(f75(x43361,x43363,x43362,x43364),x43365))
% 188.07/187.96 [4337]E(f88(x43371,f323(f323(f18(x43371,a860,a860),f323(f323(f8(a860,f872(a860,a860),x43371),a322),f323(f323(f7(x43371,f872(x43371,a860),a860),f325(x43371)),x43372))),f323(f323(f7(x43371,x43373,a860),f323(f323(f8(x43373,f872(x43373,a860),x43371),a320),x43374)),x43375))),f323(f91(x43371,x43373,x43372,x43374),x43375))
% 188.07/187.96 [4389]E(f323(f323(f84(a1,x43891),f323(f103(a1),f323(f323(f78(a1),x43892),a97))),f323(f323(f18(a1,x43891,x43891),f323(f323(f7(a1,x43891,f872(x43891,x43891)),f323(f323(f8(a860,f872(x43891,f872(x43891,x43891)),a1),f96(x43891)),a193)),f185(x43891,x43893,x43894,x43895))),f323(f323(f8(a865,x43891,a1),x43894),f323(f323(f7(a1,a865,a865),f323(f323(f8(a865,f872(a865,a865),a1),f78(a865)),a104)),x43895)))),f185(x43891,x43893,x43894,f323(f323(f78(a865),f323(f103(a865),x43892)),x43895)))
% 188.07/187.96 [4425]E(f323(f179(x44251,x44252),f323(f323(f147(f871(x44251,x44253),f871(x44251,x44252)),f323(f262(x44251,x44253,f871(x44251,x44252)),f323(f323(f7(x44251,f872(x44253,x44252),f872(x44253,f871(x44251,x44252))),f323(f323(f8(f872(x44252,f871(x44251,x44252)),f872(f872(x44253,x44252),f872(x44253,f871(x44251,x44252))),x44251),f8(x44252,f871(x44251,x44252),x44253)),f258(x44251,x44252))),x44254))),x44255)),f323(f71(f869(x44253),f869(x44252),x44251,f323(f201(x44253,x44252),x44254)),f323(f179(x44251,x44253),x44255)))
% 188.07/187.96 [4382]E(f177(x43821,x43822,f323(f323(f18(x43821,f869(x43822),f869(x43822)),f323(f323(f18(x43821,f869(x43822),f872(f869(x43822),f869(x43822))),f323(f323(f8(a860,f872(f869(x43822),f872(f869(x43822),f869(x43822))),x43821),f96(f869(x43822))),x43823)),x43824)),x43825)),f323(f323(f110(f872(x43821,a860)),f323(f323(f101(f872(x43821,a860)),f177(x43821,x43822,x43824)),f323(f243(x43821),x43823))),f323(f323(f101(f872(x43821,a860)),f177(x43821,x43822,x43825)),f323(f243(x43821),f323(f323(f8(a860,a860,x43821),a318),x43823)))))
% 188.07/187.96 [4423]E(f323(f323(f84(a1,x44231),f323(f103(a1),f323(f323(f78(a1),x44232),a97))),f323(f323(f18(a1,x44231,x44231),f323(f323(f7(a1,x44231,f872(x44231,x44231)),f323(f323(f8(a860,f872(x44231,f872(x44231,x44231)),a1),f96(x44231)),a193)),f323(f184(x44231,x44233,x44234),x44235))),f323(f323(f18(a1,x44231,x44231),f323(f323(f8(a865,f872(x44231,x44231),a1),x44234),f323(f323(f7(a1,a865,a865),f323(f323(f8(a865,f872(a865,a865),a1),f78(a865)),a104)),x44235))),f323(f323(f8(a865,x44231,a1),f184(x44231,x44233,x44234)),f323(f323(f7(a1,a865,a865),f323(f323(f8(a865,f872(a865,a865),a1),f78(a865)),a104)),x44235))))),f323(f184(x44231,x44233,x44234),f323(f323(f78(a865),f323(f103(a865),x44232)),x44235)))
% 188.07/187.96 [4466]E(f323(f243(f871(x44661,x44662)),f323(f262(x44661,x44662,a860),f323(f323(f8(f872(x44662,f872(x44663,a860)),f872(x44662,a860),x44661),f323(f8(f872(x44663,a860),a860,x44662),f85(x44663))),f323(f323(f7(x44661,f872(x44662,f872(x44663,a860)),f872(x44662,f872(x44663,a860))),f323(f323(f8(f872(f872(x44663,a860),f872(x44663,a860)),f872(f872(x44662,f872(x44663,a860)),f872(x44662,f872(x44663,a860))),x44661),f8(f872(x44663,a860),f872(x44663,a860),x44662)),f323(f323(f8(f872(x44663,f872(a860,a860)),f872(f872(x44663,a860),f872(x44663,a860)),x44661),f18(x44663,a860,a860)),f323(f323(f8(f872(x44663,a860),f872(x44663,f872(a860,a860)),x44661),f323(f8(a860,f872(a860,a860),x44663),a322)),f323(f323(f7(x44661,f872(f871(x44661,x44663),a860),f872(x44663,a860)),f323(f323(f8(f872(x44663,f872(f872(f871(x44661,x44663),a860),a860)),f872(f872(f871(x44661,x44663),a860),f872(x44663,a860)),x44661),f7(x44663,f872(f871(x44661,x44663),a860),a860)),f323(f323(f8(f872(x44663,f871(x44661,x44663)),f872(x44663,f872(f872(f871(x44661,x44663),a860),a860)),x44661),f323(f8(f871(x44661,x44663),f872(f872(f871(x44661,x44663),a860),a860),x44663),f325(f871(x44661,x44663)))),f258(x44661,x44663)))),x44664))))),f323(f323(f7(x44662,f872(f871(x44663,x44662),a860),f872(x44663,a860)),f323(f323(f8(f872(x44663,f872(f872(f871(x44663,x44662),a860),a860)),f872(f872(f871(x44663,x44662),a860),f872(x44663,a860)),x44662),f7(x44663,f872(f871(x44663,x44662),a860),a860)),f323(f323(f8(f872(x44663,f871(x44663,x44662)),f872(x44663,f872(f872(f871(x44663,x44662),a860),a860)),x44662),f323(f8(f871(x44663,x44662),f872(f872(f871(x44663,x44662),a860),a860),x44663),f325(f871(x44663,x44662)))),f323(f7(x44663,x44662,f871(x44663,x44662)),f258(x44663,x44662))))),x44665))))),f323(f323(f280(x44661,x44663,x44662),x44664),x44665))
% 188.07/187.96 [4542]~E(f26(x45421,x45422,x45423),f27(x45424,x45425,x45426))
% 188.07/187.96 [3984]E(f126(x39841,x39842,x39843,x39844,f123(x39842,x39845,x39846)),f323(f323(x39844,x39845),x39846))
% 188.07/187.96 [4201]E(f181(x42011,x42012,f180(x42011,x42012,x42013,x42014),x42015,x42016),f180(x42011,x42012,x42013,f181(x42011,x42012,x42014,x42015,x42016)))
% 188.07/187.96 [4325]E(f323(f71(f871(x43251,x43252),x43252,f871(x43253,x43254),f261(x43251,x43252)),f263(x43253,x43251,x43254,x43252,x43255,x43256)),f323(f71(x43254,x43252,f871(x43253,x43254),x43256),f261(x43253,x43254)))
% 188.07/187.96 [4326]E(f323(f71(f871(x43261,x43262),x43261,f871(x43263,x43264),f257(x43261,x43262)),f263(x43263,x43261,x43264,x43262,x43265,x43266)),f323(f71(x43263,x43261,f871(x43263,x43264),x43265),f257(x43263,x43264)))
% 188.07/187.96 [3922]E(f323(f323(f71(x39221,x39222,x39223,x39224),x39225),x39226),f323(x39224,f323(x39225,x39226)))
% 188.07/187.96 [3715]E(f323(f323(f262(x37151,x37152,x37153),x37154),f323(f323(f258(x37151,x37152),x37155),x37156)),f323(f323(x37154,x37155),x37156))
% 188.07/187.96 [3776]E(f323(f323(f323(f8(x37761,x37762,x37763),x37764),x37765),x37766),f323(x37764,f323(x37765,x37766)))
% 188.07/187.96 [3777]E(f323(f323(f323(f7(x37771,x37772,x37773),x37774),x37775),x37776),f323(f323(x37774,x37776),x37775))
% 188.07/187.96 [3794]E(f323(f323(f323(f18(x37941,x37942,x37943),x37944),x37945),x37946),f323(f323(x37944,x37946),f323(x37945,x37946)))
% 188.07/187.96 [3816]E(f323(f149(x38161,x38162,x38163,x38164),f323(f323(f144(x38162),x38165),x38166)),f323(f323(x38164,x38165),x38166))
% 188.07/187.96 [3858]E(f163(f871(x38581,x38582),f323(f323(f235(a865),x38583),x38584),f323(f323(f258(x38581,x38582),x38585),x38586)),f323(f323(f175(x38581,x38582),f163(x38581,x38583,x38585)),f163(x38582,x38584,x38586)))
% 188.07/187.96 [3926]E(f323(f323(f144(f871(x39261,x39262)),f323(f323(f258(x39261,x39262),x39263),x39264)),f323(f323(f175(x39261,x39262),x39265),x39266)),f323(f323(f175(x39261,x39262),f323(f323(f144(x39261),x39263),x39265)),f323(f323(f144(x39262),x39264),x39266)))
% 188.07/187.96 [3928]E(f323(f323(f147(x39281,x39282),x39283),f323(f323(f152(x39281,x39284),x39285),x39286)),f323(f323(f152(x39282,f323(f323(f147(x39281,x39282),x39283),x39284)),x39285),f323(x39283,x39286)))
% 188.07/187.96 [3972]E(f323(f135(x39721,x39722,x39723,x39724),f323(f323(f144(x39722),x39725),x39726)),f323(f135(x39721,x39722,x39723,f323(f323(x39723,x39724),x39725)),x39726))
% 188.07/187.96 [4000]E(f265(x40001,x40002,x40003,x40004,f323(f323(f258(x40001,x40002),x40005),x40006)),f323(f323(x40004,x40005),x40006))
% 188.07/187.96 [4083]E(f323(f323(f39(x40831,f872(x40832,a860)),x40833),f323(f71(x40834,f872(x40832,a860),x40831,x40835),x40836)),f323(f323(f39(x40834,f872(x40832,a860)),f323(f302(x40831,x40834,x40836),x40833)),x40835))
% 188.07/187.96 [4134]E(f323(f323(f201(x41341,x41342),x41343),f323(f323(f201(x41344,x41341),x41345),x41346)),f323(f323(f201(x41344,x41342),f323(f71(x41341,x41342,x41344,x41343),x41345)),x41346))
% 188.07/187.96 [4136]E(f323(f323(f147(x41361,x41362),x41363),f323(f323(f147(x41364,x41361),x41365),x41366)),f323(f323(f147(x41364,x41362),f323(f71(x41361,x41362,x41364,x41363),x41365)),x41366))
% 188.07/187.96 [4141]E(f323(f302(x41411,x41412,f323(f71(x41413,x41412,x41411,x41414),x41415)),x41416),f323(f302(x41413,x41412,x41414),f323(f302(x41411,x41413,x41415),x41416)))
% 188.07/187.96 [4142]E(f323(f303(x41421,x41422,f323(f71(x41423,x41422,x41421,x41424),x41425)),x41426),f323(f303(x41421,x41423,x41425),f323(f303(x41423,x41422,x41424),x41426)))
% 188.07/187.96 [4171]E(f180(x41711,x41712,x41713,f323(f323(f323(f70(x41711,f869(x41712)),x41714),x41715),f323(f230(x41712),x41716))),f323(f323(f323(f70(x41711,f869(x41712)),f180(x41711,x41712,x41713,x41714)),x41715),f323(f230(x41712),x41716)))
% 188.07/187.96 [4173]E(f323(f135(x41731,x41732,x41733,f323(f135(x41731,x41732,x41733,x41734),x41735)),x41736),f323(f135(x41731,x41732,x41733,x41734),f323(f323(f121(x41732),x41735),x41736)))
% 188.07/187.96 [4315]E(f323(f263(x43151,x43151,x43152,x43153,f32(x43151),x43154),f323(f323(f258(x43151,x43152),x43155),x43156)),f323(f323(f258(x43151,x43153),x43155),f323(x43154,x43156)))
% 188.07/187.96 [4316]E(f323(f263(x43161,x43162,x43163,x43163,x43164,f32(x43163)),f323(f323(f258(x43161,x43163),x43165),x43166)),f323(f323(f258(x43162,x43163),f323(x43164,x43165)),x43166))
% 188.07/187.96 [4407]E(f323(f323(f147(f871(x44071,x44072),f871(x44071,x44073)),f323(f262(x44071,x44072,f871(x44071,x44073)),f323(f323(f7(x44071,f872(x44072,x44073),f872(x44072,f871(x44071,x44073))),f323(f323(f8(f872(x44073,f871(x44071,x44073)),f872(f872(x44072,x44073),f872(x44072,f871(x44071,x44073))),x44071),f8(x44073,f871(x44071,x44073),x44072)),f258(x44071,x44073))),x44074))),f323(f323(f175(x44071,x44072),x44075),x44076)),f323(f323(f175(x44071,x44073),x44075),f323(f323(f147(x44072,x44073),x44074),x44076)))
% 188.07/187.96 [3781]E(f94(x37811,x37812,x37813,f323(f323(f323(f90(x37811),x37814),x37815),x37816)),f323(f323(f323(x37813,x37814),x37815),x37816))
% 188.07/187.96 [3782]E(f95(x37821,x37822,x37823,f323(f323(f323(f90(x37821),x37824),x37825),x37826)),f323(f323(f323(x37823,x37824),x37825),x37826))
% 188.07/187.96 [3983]E(f323(f323(f71(x39831,x39832,x39833,f323(f16(x39832,x39831),x39834)),x39835),x39836),x39834)
% 188.07/187.96 [4019]E(f323(f302(x40191,x40192,x40193),f323(f302(x40194,x40191,x40195),x40196)),f323(f302(x40194,x40192,f323(f323(f8(x40191,x40192,x40194),x40193),x40195)),x40196))
% 188.07/187.96 [4025]E(f323(f323(f39(x40251,f872(x40252,a860)),f323(f302(x40253,x40251,x40254),x40255)),x40256),f323(f323(f39(x40253,f872(x40252,a860)),x40255),f323(f323(f8(x40251,f872(x40252,a860),x40253),x40256),x40254)))
% 188.07/187.96 [4026]E(f323(f323(f40(x40261,f872(x40262,a860)),f323(f302(x40263,x40261,x40264),x40265)),x40266),f323(f323(f40(x40263,f872(x40262,a860)),x40265),f323(f323(f8(x40261,f872(x40262,a860),x40263),x40266),x40264)))
% 188.07/187.96 [4027]E(f323(f323(f39(x40271,f872(x40272,a860)),x40273),f323(f323(f8(x40274,f872(x40272,a860),x40271),x40275),x40276)),f323(f323(f39(x40274,f872(x40272,a860)),f323(f302(x40271,x40274,x40276),x40273)),x40275))
% 188.07/187.96 [4028]E(f323(f323(f40(x40281,f872(x40282,a860)),x40283),f323(f323(f8(x40284,f872(x40282,a860),x40281),x40285),x40286)),f323(f323(f40(x40284,f872(x40282,a860)),f323(f302(x40281,x40284,x40286),x40283)),x40285))
% 188.07/187.96 [4085]E(f323(f323(f39(x40851,f872(x40852,a860)),x40853),f323(f323(f8(f872(x40854,a860),f872(x40852,a860),x40851),f302(x40854,x40852,x40855)),x40856)),f323(f302(x40854,x40852,x40855),f323(f323(f39(x40851,f872(x40854,a860)),x40853),x40856)))
% 188.07/187.96 [4086]E(f323(f323(f39(x40861,f872(x40862,a860)),x40863),f323(f323(f8(f872(x40864,a860),f872(x40862,a860),x40861),f303(x40862,x40864,x40865)),x40866)),f323(f303(x40862,x40864,x40865),f323(f323(f39(x40861,f872(x40864,a860)),x40863),x40866)))
% 188.07/187.96 [4087]E(f323(f323(f40(x40871,f872(x40872,a860)),x40873),f323(f323(f8(f872(x40874,a860),f872(x40872,a860),x40871),f303(x40872,x40874,x40875)),x40876)),f323(f303(x40872,x40874,x40875),f323(f323(f40(x40871,f872(x40874,a860)),x40873),x40876)))
% 188.07/187.96 [4088]E(f323(f323(f39(x40881,f872(x40882,a860)),x40883),f323(f323(f8(f872(x40884,a860),f872(x40882,a860),x40881),f277(x40884,x40882,x40885)),x40886)),f323(f277(x40884,x40882,x40885),f323(f323(f39(x40881,f872(x40884,a860)),x40883),x40886)))
% 188.07/187.96 [4179]E(f323(f135(x41791,x41792,f323(f7(x41792,x41791,x41791),x41793),x41794),f323(f162(x41792),f323(f323(f144(x41792),x41795),x41796))),f323(f323(x41793,x41795),f323(f135(x41791,x41792,f323(f7(x41792,x41791,x41791),x41793),x41794),f323(f162(x41792),x41796))))
% 188.07/187.96 [4240]E(f323(f323(f18(f871(x42401,x42402),x42402,x42403),f323(f323(f8(x42404,f872(x42402,x42403),f871(x42401,x42402)),x42405),f323(f323(f8(x42401,x42404,f871(x42401,x42402)),x42406),f257(x42401,x42402)))),f261(x42401,x42402)),f323(f262(x42401,x42402,x42403),f323(f323(f8(x42404,f872(x42402,x42403),x42401),x42405),x42406)))
% 188.07/187.96 [4247]E(f323(f135(x42471,x42472,f323(f7(x42472,x42471,x42471),x42473),f323(f135(x42471,x42472,f323(f7(x42472,x42471,x42471),x42473),x42474),f323(f162(x42472),x42475))),f323(f162(x42472),x42476)),f323(f135(x42471,x42472,f323(f7(x42472,x42471,x42471),x42473),x42474),f323(f162(x42472),f323(f323(f121(x42472),x42476),x42475))))
% 188.07/187.96 [4249]E(f323(f323(f147(f871(x42491,x42492),f871(x42493,x42492)),f323(f262(x42491,x42492,f871(x42493,x42492)),f323(f323(f8(x42493,f872(x42492,f871(x42493,x42492)),x42491),f258(x42493,x42492)),x42494))),f323(f323(f175(x42491,x42492),x42495),x42496)),f323(f323(f175(x42493,x42492),f323(f323(f147(x42491,x42493),x42494),x42495)),x42496))
% 188.07/187.96 [4297]P101(f323(f323(f237(f872(x42971,a860)),f323(f277(x42972,x42971,x42973),f323(f323(f40(x42974,f872(x42972,a860)),x42975),x42976))),f323(f323(f40(x42974,f872(x42971,a860)),x42975),f323(f323(f8(f872(x42972,a860),f872(x42971,a860),x42974),f277(x42972,x42971,x42973)),x42976))))
% 188.07/187.96 [4098]E(f323(f323(f175(x40981,x40982),f323(f323(f152(x40981,x40983),x40984),f323(f257(x40981,x40982),x40985))),f323(f323(f152(x40982,x40986),x40984),f323(f261(x40981,x40982),x40985))),f323(f323(f152(f871(x40981,x40982),f323(f323(f175(x40981,x40982),x40983),x40986)),x40984),x40985))
% 188.07/187.96 [4160]E(f323(f323(f110(f872(f871(x41601,x41602),a860)),f323(f323(f280(x41601,x41603,x41602),x41604),x41605)),f323(f323(f280(x41601,x41603,x41602),x41604),x41606)),f323(f323(f280(x41601,x41603,x41602),x41604),f323(f323(f110(f872(f871(x41603,x41602),a860)),x41605),x41606)))
% 188.07/187.96 [4260]E(f323(f323(f301(f871(x42601,x42602)),f323(f323(f258(x42601,x42602),x42603),x42604)),f323(f323(f110(f872(f871(x42601,x42602),a860)),f323(f323(f260(x42601,x42602),x42605),f323(f16(f872(x42602,a860),x42601),f323(f323(f301(x42602),x42604),x42606)))),f323(f323(f260(x42601,x42602),f323(f323(f301(x42601),x42603),x42605)),f323(f16(f872(x42602,a860),x42601),x42606)))),f323(f323(f260(x42601,x42602),f323(f323(f301(x42601),x42603),x42605)),f323(f16(f872(x42602,a860),x42601),f323(f323(f301(x42602),x42604),x42606))))
% 188.07/187.96 [4340]E(f323(f323(f101(f872(x43401,a860)),f323(f303(x43401,x43402,f323(f71(f871(x43402,x43403),x43402,x43401,f257(x43402,x43403)),x43404)),x43405)),f323(f303(x43401,x43403,f323(f71(f871(x43402,x43403),x43403,x43401,f261(x43402,x43403)),x43404)),x43406)),f323(f303(x43401,f871(x43402,x43403),x43404),f323(f323(f260(x43402,x43403),x43405),f323(f16(f872(x43403,a860),x43402),x43406))))
% 188.07/187.96 [4082]E(f323(f323(f323(f70(x40821,x40822),f323(f323(f323(f70(x40821,x40822),x40823),x40824),x40825)),x40824),x40826),f323(f323(f323(f70(x40821,x40822),x40823),x40824),x40826))
% 188.07/187.96 [4185]E(f323(f323(f110(f872(f871(x41851,x41852),a860)),f323(f323(f280(x41851,x41853,x41852),x41854),x41855)),f323(f323(f280(x41851,x41853,x41852),x41856),x41855)),f323(f323(f280(x41851,x41853,x41852),f323(f323(f110(f872(f871(x41851,x41853),a860)),x41854),x41856)),x41855))
% 188.07/187.96 [4323]E(f323(f323(f39(x43231,f872(x43232,a860)),x43233),f323(f323(f7(x43231,f872(x43234,f872(x43232,a860)),f872(x43232,a860)),f323(f323(f8(f872(x43234,a860),f872(f872(x43234,f872(x43232,a860)),f872(x43232,a860)),x43231),f39(x43234,f872(x43232,a860))),x43235)),x43236)),f323(f323(f39(x43234,f872(x43232,a860)),f323(f323(f39(x43231,f872(x43234,a860)),x43233),x43235)),x43236))
% 188.07/187.96 [4324]E(f323(f323(f40(x43241,f872(x43242,a860)),x43243),f323(f323(f7(x43241,f872(x43244,f872(x43242,a860)),f872(x43242,a860)),f323(f323(f8(f872(x43244,a860),f872(f872(x43244,f872(x43242,a860)),f872(x43242,a860)),x43241),f40(x43244,f872(x43242,a860))),x43245)),x43246)),f323(f323(f40(x43244,f872(x43242,a860)),f323(f323(f39(x43241,f872(x43244,a860)),x43243),x43245)),x43246))
% 188.07/187.96 [4377]E(f323(f262(x43771,x43772,f871(x43773,x43774)),f323(f323(f7(x43771,f872(x43772,x43774),f872(x43772,f871(x43773,x43774))),f323(f323(f8(f872(x43774,f871(x43773,x43774)),f872(f872(x43772,x43774),f872(x43772,f871(x43773,x43774))),x43771),f8(x43774,f871(x43773,x43774),x43772)),f323(f323(f8(x43773,f872(x43774,f871(x43773,x43774)),x43771),f258(x43773,x43774)),x43775))),x43776)),f263(x43771,x43773,x43772,x43774,x43775,x43776))
% 188.07/187.96 [4296]E(f323(f323(f323(f70(x42961,f869(x42962)),f182(x42961,x42962,x42963,f323(f323(f22(f872(x42961,a860)),x42964),f323(f323(f301(x42961),x42965),f188(f872(x42961,a860)))))),x42965),x42966),f323(f323(f323(f70(x42961,f869(x42962)),f182(x42961,x42962,x42963,x42964)),x42965),x42966))
% 188.07/187.96 [4402]E(f323(f302(x44021,x44022,f323(f323(f18(x44021,x44022,x44022),f323(f323(f18(x44021,x44022,f872(x44022,x44022)),f323(f323(f8(a860,f872(x44022,f872(x44022,x44022)),x44021),f96(x44022)),x44023)),x44024)),x44025)),x44026),f323(f323(f110(f872(x44022,a860)),f323(f302(x44021,x44022,x44024),f323(f323(f101(f872(x44021,a860)),x44026),f323(f243(x44021),x44023)))),f323(f302(x44021,x44022,x44025),f323(f323(f101(f872(x44021,a860)),x44026),f323(f243(x44021),f323(f323(f8(a860,a860,x44021),a318),x44023))))))
% 188.07/187.96 [4413]E(f323(f302(x44131,f871(x44132,x44133),f323(f323(f18(x44131,x44133,f871(x44132,x44133)),f323(f323(f8(x44132,f872(x44133,f871(x44132,x44133)),x44131),f258(x44132,x44133)),x44134)),x44135)),x44136),f323(f323(f260(x44132,x44133),f323(f302(x44131,x44132,x44134),x44136)),f323(f323(f8(f872(x44131,a860),f872(x44133,a860),x44132),f302(x44131,x44133,x44135)),f323(f323(f7(x44132,f872(x44131,a860),f872(x44131,a860)),f323(f323(f8(f872(x44131,a860),f872(f872(x44131,a860),f872(x44131,a860)),x44132),f101(f872(x44131,a860))),f323(f323(f8(f872(x44132,a860),f872(x44131,a860),x44132),f303(x44131,x44132,x44134)),f323(f323(f7(x44132,f872(x44132,a860),f872(x44132,a860)),f301(x44132)),f188(f872(x44132,a860)))))),x44136))))
% 188.07/187.96 [4359]E(f323(f261(x43591,x43592),f323(f263(x43593,x43591,x43594,x43592,x43595,x43596),x43597)),f323(x43596,f323(f261(x43593,x43594),x43597)))
% 188.07/187.96 [4360]E(f323(f257(x43601,x43602),f323(f263(x43603,x43601,x43604,x43602,x43605,x43606),x43607)),f323(x43605,f323(f257(x43603,x43604),x43607)))
% 188.07/187.96 [4060]E(f323(f323(f175(x40601,x40602),f323(f323(f152(x40601,x40603),x40604),x40605)),f323(f323(f152(x40602,x40606),x40604),x40607)),f323(f323(f152(f871(x40601,x40602),f323(f323(f175(x40601,x40602),x40603),x40606)),x40604),f323(f323(f258(x40601,x40602),x40605),x40607)))
% 188.07/187.96 [4128]E(f323(f323(f323(f264(x41281,x41282,x41283,x41284),x41285),x41286),x41287),f323(f323(f262(x41282,x41283,x41284),x41286),f323(x41285,x41287)))
% 188.07/187.96 [4140]E(f323(f323(f323(f264(x41401,x41402,x41403,x41404),x41405),x41406),x41407),f323(f323(x41406,f323(f257(x41402,x41403),f323(x41405,x41407))),f323(f261(x41402,x41403),f323(x41405,x41407))))
% 188.07/187.96 [4175]E(f181(x41751,x41752,f323(f323(f323(f70(x41751,f869(x41752)),x41753),x41754),f323(f230(x41752),x41755)),x41756,x41757),f181(x41751,x41752,x41753,f323(f323(f144(x41751),x41754),x41756),f323(f323(f144(x41752),x41755),x41757)))
% 188.07/187.96 [4195]E(f323(f71(x41951,x41952,x41953,x41954),f323(f71(x41955,x41951,x41953,x41956),x41957)),f323(f71(x41955,x41952,x41953,f323(f71(x41951,x41952,x41955,x41954),x41956)),x41957))
% 188.07/187.96 [4256]E(f323(f71(f869(x42561),f869(x42562),x42563,f323(f201(x42561,x42562),x42564)),f323(f323(f323(f70(x42563,f869(x42561)),x42565),x42566),f323(f230(x42561),x42567))),f323(f323(f323(f70(x42563,f869(x42562)),f323(f71(f869(x42561),f869(x42562),x42563,f323(f201(x42561,x42562),x42564)),x42565)),x42566),f323(f230(x42562),f323(x42564,x42567))))
% 188.07/187.96 [4384]E(f323(f263(x43841,x43842,x43843,x43843,x43844,f32(x43843)),f323(f263(x43841,x43841,x43845,x43843,f32(x43841),x43846),x43847)),f323(f323(f258(x43842,x43843),f323(x43844,f323(f257(x43841,x43845),x43847))),f323(x43846,f323(f261(x43841,x43845),x43847))))
% 188.07/187.96 [4385]E(f323(f263(x43851,x43851,x43852,x43853,f32(x43851),x43854),f323(f263(x43855,x43851,x43852,x43852,x43856,f32(x43852)),x43857)),f323(f323(f258(x43851,x43853),f323(x43856,f323(f257(x43855,x43852),x43857))),f323(x43854,f323(f261(x43855,x43852),x43857))))
% 188.07/187.96 [4400]E(f323(f263(x44001,x44002,x44003,x44003,x44004,f32(x44003)),f323(f263(x44005,x44001,x44003,x44003,x44006,f32(x44003)),x44007)),f323(f263(x44005,x44002,x44003,x44003,f323(f71(x44001,x44002,x44005,x44004),x44006),f32(x44003)),x44007))
% 188.07/187.96 [4401]E(f323(f263(x44011,x44011,x44012,x44013,f32(x44011),x44014),f323(f263(x44011,x44011,x44015,x44012,f32(x44011),x44016),x44017)),f323(f263(x44011,x44011,x44015,x44013,f32(x44011),f323(f71(x44012,x44013,x44015,x44014),x44016)),x44017))
% 188.07/187.96 [4410]E(f323(f263(x44101,x44102,x44103,x44103,x44104,f32(x44103)),f323(f263(x44101,x44101,x44105,x44103,f32(x44101),x44106),x44107)),f323(f263(x44102,x44102,x44105,x44103,f32(x44102),x44106),f323(f263(x44101,x44102,x44105,x44105,x44104,f32(x44105)),x44107)))
% 188.07/187.96 [4095]E(f323(f323(f280(x40951,x40952,x40953),f323(f323(f280(x40951,x40954,x40952),x40955),x40956)),x40957),f323(f323(f280(x40951,x40954,x40953),x40955),f323(f323(f280(x40954,x40952,x40953),x40956),x40957)))
% 188.07/187.96 [4166]E(f323(f323(f262(x41661,x41662,x41663),f323(f71(x41664,f872(x41662,x41663),x41661,x41665),x41666)),x41667),f323(f323(x41665,f323(x41666,f323(f257(x41661,x41662),x41667))),f323(f261(x41661,x41662),x41667)))
% 188.07/187.96 [4220]E(f323(f71(x42201,x42202,x42203,x42204),f323(f323(f323(f70(x42203,x42201),x42205),x42206),x42207)),f323(f323(f323(f70(x42203,x42202),f323(f71(x42201,x42202,x42203,x42204),x42205)),x42206),f323(x42204,x42207)))
% 188.07/187.96 [4252]E(f323(f135(x42521,x42522,f323(f7(x42522,x42521,x42521),x42523),x42524),f323(f162(x42522),f323(f323(f147(x42525,x42522),x42526),x42527))),f323(f135(x42521,x42525,f323(f7(x42525,x42521,x42521),f323(f71(x42522,f872(x42521,x42521),x42525,x42523),x42526)),x42524),f323(f162(x42525),x42527)))
% 188.07/187.96 [4196]E(f323(f323(f39(x41961,f872(f871(x41962,x41963),a860)),x41964),f323(f323(f8(f872(f871(x41965,x41963),a860),f872(f871(x41962,x41963),a860),x41961),f323(f280(x41962,x41965,x41963),x41966)),x41967)),f323(f323(f280(x41962,x41965,x41963),x41966),f323(f323(f39(x41961,f872(f871(x41965,x41963),a860)),x41964),x41967)))
% 188.07/187.96 [4346]E(f323(f323(f39(x43461,f872(f871(x43462,x43463),a860)),x43464),f323(f323(f7(x43461,f872(f871(x43465,x43463),a860),f872(f871(x43462,x43463),a860)),f323(f323(f8(f872(f871(x43462,x43465),a860),f872(f872(f871(x43465,x43463),a860),f872(f871(x43462,x43463),a860)),x43461),f280(x43462,x43465,x43463)),x43466)),x43467)),f323(f323(f280(x43462,x43465,x43463),f323(f323(f39(x43461,f872(f871(x43462,x43465),a860)),x43464),x43466)),x43467))
% 188.07/187.96 [4347]E(f323(f135(x43471,x43472,f323(f323(f7(x43471,f872(x43472,x43473),f872(x43472,x43471)),f323(f323(f8(f872(x43473,x43471),f872(f872(x43472,x43473),f872(x43472,x43471)),x43471),f8(x43473,x43471,x43472)),x43474)),x43475),x43476),x43477),f323(f135(x43471,x43473,x43474,x43476),f323(f323(f147(x43472,x43473),x43475),x43477)))
% 188.07/187.96 [4411]E(f323(f323(f40(x44111,f872(x44112,a860)),x44113),f323(f323(f8(f872(x44114,f872(x44112,a860)),f872(x44112,a860),x44111),f323(f40(x44114,f872(x44112,a860)),x44115)),f323(f323(f7(x44111,f872(x44114,f872(x44112,a860)),f872(x44114,f872(x44112,a860))),f323(f323(f8(f872(f872(x44112,a860),f872(x44112,a860)),f872(f872(x44114,f872(x44112,a860)),f872(x44114,f872(x44112,a860))),x44111),f8(f872(x44112,a860),f872(x44112,a860),x44114)),f323(f323(f8(f872(x44112,a860),f872(f872(x44112,a860),f872(x44112,a860)),x44111),f110(f872(x44112,a860))),x44116))),x44117))),f323(f323(f110(f872(x44112,a860)),f323(f323(f40(x44111,f872(x44112,a860)),x44113),x44116)),f323(f323(f40(x44114,f872(x44112,a860)),x44115),x44117)))
% 188.07/187.96 [4412]E(f323(f323(f39(x44121,f872(x44122,a860)),x44123),f323(f323(f8(f872(x44124,f872(x44122,a860)),f872(x44122,a860),x44121),f323(f39(x44124,f872(x44122,a860)),x44125)),f323(f323(f7(x44121,f872(x44124,f872(x44122,a860)),f872(x44124,f872(x44122,a860))),f323(f323(f8(f872(f872(x44122,a860),f872(x44122,a860)),f872(f872(x44124,f872(x44122,a860)),f872(x44124,f872(x44122,a860))),x44121),f8(f872(x44122,a860),f872(x44122,a860),x44124)),f323(f323(f8(f872(x44122,a860),f872(f872(x44122,a860),f872(x44122,a860)),x44121),f101(f872(x44122,a860))),x44126))),x44127))),f323(f323(f101(f872(x44122,a860)),f323(f323(f39(x44121,f872(x44122,a860)),x44123),x44126)),f323(f323(f39(x44124,f872(x44122,a860)),x44125),x44127)))
% 188.07/187.96 [4405]E(f198(x44051,x44052,f323(f323(f323(x44053,x44054),x44055),x44056),f323(f323(f7(x44051,f871(a99,a99),f872(a99,f867(x44052))),f323(f323(f7(x44051,a99,f872(f871(a99,a99),f872(a99,f867(x44052)))),f323(f323(f7(x44051,a99,f872(a99,f872(f871(a99,a99),f872(a99,f867(x44052))))),x44057),x44054)),x44055)),x44056)),f323(f323(f323(f211(x44051,x44052,x44053,x44057),x44054),x44055),x44056))
% 188.07/187.96 [4418]E(f199(x44181,x44182,f323(f323(f323(x44183,x44184),x44185),x44186),f323(f323(f7(x44181,f871(a99,a99),f872(a99,f867(x44182))),f323(f323(f7(x44181,a99,f872(f871(a99,a99),f872(a99,f867(x44182)))),f323(f323(f7(x44181,a99,f872(a99,f872(f871(a99,a99),f872(a99,f867(x44182))))),x44187),x44184)),x44185)),x44186)),f213(x44181,x44182,x44183,x44187,x44184,x44185,x44186))
% 188.07/187.96 [4409]E(f195(x44091,x44092,f323(f323(f323(x44093,x44094),x44095),x44096),f323(f323(f7(x44091,f871(a99,a99),f872(a99,f867(f869(x44092)))),f323(f323(f7(x44091,a99,f872(f871(a99,a99),f872(a99,f867(f869(x44092))))),f323(f323(f7(x44091,a99,f872(a99,f872(f871(a99,a99),f872(a99,f867(f869(x44092)))))),x44097),x44094)),x44095)),x44096)),f323(f323(f323(f207(x44091,x44092,x44093,x44097),x44094),x44095),x44096))
% 188.07/187.96 [4420]E(f197(x44201,x44202,f323(f323(f323(x44203,x44204),x44205),x44206),f323(f323(f7(x44201,f871(a99,a99),f872(a99,f867(f869(x44202)))),f323(f323(f7(x44201,a99,f872(f871(a99,a99),f872(a99,f867(f869(x44202))))),f323(f323(f7(x44201,a99,f872(a99,f872(f871(a99,a99),f872(a99,f867(f869(x44202)))))),x44207),x44204)),x44205)),x44206)),f209(x44201,x44202,x44203,x44207,x44204,x44205,x44206))
% 188.07/187.96 [4317]E(f323(f263(x43171,x43172,x43173,x43174,x43175,x43176),f323(f323(f258(x43171,x43173),x43177),x43178)),f323(f323(f258(x43172,x43174),f323(x43175,x43177)),f323(x43176,x43178)))
% 188.07/187.96 [4422]E(f323(f323(f147(f871(x44221,x44222),f871(x44223,x44224)),f323(f262(x44221,x44222,f871(x44223,x44224)),f323(f323(f7(x44221,f872(x44222,x44224),f872(x44222,f871(x44223,x44224))),f323(f323(f8(f872(x44224,f871(x44223,x44224)),f872(f872(x44222,x44224),f872(x44222,f871(x44223,x44224))),x44221),f8(x44224,f871(x44223,x44224),x44222)),f323(f323(f8(x44223,f872(x44224,f871(x44223,x44224)),x44221),f258(x44223,x44224)),x44225))),x44226))),f323(f323(f175(x44221,x44222),x44227),x44228)),f323(f323(f175(x44223,x44224),f323(f323(f147(x44221,x44223),x44225),x44227)),f323(f323(f147(x44222,x44224),x44226),x44228)))
% 188.07/187.96 [4426]E(f323(f323(f147(f871(x44261,x44262),x44263),f323(f262(x44261,x44262,x44263),f323(f323(f8(f872(x44262,f871(x44261,x44264)),f872(x44262,x44263),x44261),f323(f8(f871(x44261,x44264),x44263,x44262),x44265)),f323(f323(f7(x44261,f872(x44262,x44264),f872(x44262,f871(x44261,x44264))),f323(f323(f8(f872(x44264,f871(x44261,x44264)),f872(f872(x44262,x44264),f872(x44262,f871(x44261,x44264))),x44261),f8(x44264,f871(x44261,x44264),x44262)),f258(x44261,x44264))),x44266)))),f323(f323(f175(x44261,x44262),x44267),x44268)),f323(f323(f147(f871(x44261,x44264),x44263),x44265),f323(f323(f175(x44261,x44264),x44267),f323(f323(f147(x44262,x44264),x44266),x44268))))
% 188.07/187.96 [4351]E(f323(f323(f147(f871(x43511,x43512),x43513),f323(f262(x43511,x43512,x43513),f323(f323(f8(f872(x43512,f871(x43514,x43512)),f872(x43512,x43513),x43511),f323(f8(f871(x43514,x43512),x43513,x43512),x43515)),f323(f323(f8(x43514,f872(x43512,f871(x43514,x43512)),x43511),f258(x43514,x43512)),x43516)))),f323(f323(f175(x43511,x43512),x43517),x43518)),f323(f323(f147(f871(x43514,x43512),x43513),x43515),f323(f323(f175(x43514,x43512),f323(f323(f147(x43511,x43514),x43516),x43517)),x43518)))
% 188.07/187.96 [4308]E(f323(f323(f262(x43081,x43082,x43083),f323(f323(f8(f872(x43082,f871(x43084,x43085)),f872(x43082,x43083),x43081),f323(f8(f871(x43084,x43085),x43083,x43082),f323(f262(x43084,x43085,x43083),x43086))),x43087)),x43088),f323(f323(f262(x43084,x43085,x43083),x43086),f323(f323(f262(x43081,x43082,f871(x43084,x43085)),x43087),x43088)))
% 188.07/187.96 [4427]E(f323(f323(f39(f871(x44271,x44272),f872(f871(x44273,x44274),a860)),f323(f323(f260(x44271,x44272),x44275),f323(f16(f872(x44272,a860),x44271),x44276))),f323(f262(x44271,x44272,f872(f871(x44273,x44274),a860)),f323(f323(f7(x44271,f872(x44272,f872(x44273,f872(x44274,a860))),f872(x44272,f872(f871(x44273,x44274),a860))),f323(f323(f8(f872(f872(x44273,f872(x44274,a860)),f872(f871(x44273,x44274),a860)),f872(f872(x44272,f872(x44273,f872(x44274,a860))),f872(x44272,f872(f871(x44273,x44274),a860))),x44271),f8(f872(x44273,f872(x44274,a860)),f872(f871(x44273,x44274),a860),x44272)),f323(f323(f8(f872(x44273,a860),f872(f872(x44273,f872(x44274,a860)),f872(f871(x44273,x44274),a860)),x44271),f260(x44273,x44274)),x44277))),f323(f323(f8(f872(x44274,a860),f872(x44273,f872(x44274,a860)),x44272),f16(f872(x44274,a860),x44273)),x44278)))),f323(f323(f260(x44273,x44274),f323(f323(f39(x44271,f872(x44273,a860)),x44275),x44277)),f323(f16(f872(x44274,a860),x44273),f323(f323(f39(x44272,f872(x44274,a860)),x44276),x44278))))
% 188.07/187.96 [4459]E(f31(x44591,x44592,x44593,x44594,x44595,x44596,x44597,x44598,x44599,a24),x44592)
% 188.07/187.96 [4365]E(f323(f323(f264(x43651,x43652,x43653,x43654),f323(f323(f264(x43651,x43655,x43656,f871(x43652,x43653)),x43657),x43658)),x43659),f323(f323(f264(x43651,x43655,x43656,x43654),x43657),f323(f323(f7(x43655,f872(x43652,f872(x43653,x43654)),f872(x43656,x43654)),f323(f323(f8(f872(x43656,f871(x43652,x43653)),f872(f872(x43652,f872(x43653,x43654)),f872(x43656,x43654)),x43655),f264(x43656,x43652,x43653,x43654)),x43658)),x43659)))
% 188.07/187.96 [4397]E(f323(f71(f871(x43971,x43972),f871(x43973,x43974),f871(x43975,x43976),f263(x43971,x43973,x43972,x43974,x43977,x43978)),f263(x43975,x43971,x43976,x43972,x43979,x439710)),f263(x43975,x43973,x43976,x43974,f323(f71(x43971,x43973,x43975,x43977),x43979),f323(f71(x43972,x43974,x43976,x43978),x439710)))
% 188.07/187.96 [4460]E(f31(x44601,x44602,x44603,x44604,x44605,x44606,x44607,x44608,x44609,f30(x446010,x446011)),f323(f323(x44605,x446010),x446011))
% 188.07/187.96 [4461]E(f31(x44611,x44612,x44613,x44614,x44615,x44616,x44617,x44618,x44619,f29(x446110,x446111)),f323(f323(x44617,x446110),x446111))
% 188.07/187.96 [4462]E(f31(x44621,x44622,x44623,x44624,x44625,x44626,x44627,x44628,x44629,f25(x446210,x446211)),f323(f323(x44623,x446210),x446211))
% 188.07/187.96 [4403]E(f323(f263(x44031,x44032,x44033,x44034,x44035,x44036),f323(f263(x44037,x44031,x44038,x44033,x44039,x440310),x440311)),f323(f263(x44037,x44032,x44038,x44034,f323(f71(x44031,x44032,x44037,x44035),x44039),f323(f71(x44033,x44034,x44038,x44036),x440310)),x440311))
% 188.07/187.96 [4463]E(f31(x44631,x44632,x44633,x44634,x44635,x44636,x44637,x44638,x44639,f27(x446310,x446311,x446312)),f323(f323(f323(x44636,x446310),x446311),x446312))
% 188.07/187.96 [4464]E(f31(x44641,x44642,x44643,x44644,x44645,x44646,x44647,x44648,x44649,f26(x446410,x446411,x446412)),f323(f323(f323(x44644,x446410),x446411),x446412))
% 188.07/187.96 [4577]~P92(x45771)+E(f89(x45771),a320)
% 188.07/187.96 [4578]~P5(x45781)+P5(f869(x45781))
% 188.07/187.96 [4579]~P61(x45791)+P61(f869(x45791))
% 188.07/187.96 [4582]~P138(x45821)+~E(f76(x45821),f2(x45821))
% 188.07/187.96 [4584]~E(x45841,f2(a99))+E(f323(a20,x45841),f2(a1))
% 188.07/187.96 [4585]~E(x45851,f2(a1))+E(f80(a1,x45851),f2(a1))
% 188.07/187.96 [4591]~P140(x45911)+P30(x45911,f2(x45911))
% 188.07/187.96 [4593]~P103(x45931)+P16(x45931,f113(x45931))
% 188.07/187.96 [4602]P101(x46021)+P101(f323(a318,x46021))
% 188.07/187.96 [4645]~P140(x46451)+~P30(x46451,f76(x46451))
% 188.07/187.96 [4692]~P101(x46921)+~P101(f323(a318,x46921))
% 188.07/187.96 [4715]E(f323(a104,x47151),f2(a865))+~P101(f323(a193,x47151))
% 188.07/187.96 [4781]~P97(x47811)+P17(x47811,x47811,f110(x47811))
% 188.07/187.96 [4782]~P98(x47821)+P17(x47821,x47821,f101(x47821))
% 188.07/187.96 [4783]~P93(x47831)+P17(x47831,x47831,f79(x47831))
% 188.07/187.96 [4784]~P103(x47841)+P17(x47841,x47841,f235(x47841))
% 188.07/187.96 [4785]~P103(x47851)+P17(x47851,x47851,f236(x47851))
% 188.07/187.96 [4786]~P66(x47861)+P18(x47861,x47861,f79(x47861))
% 188.07/187.96 [4588]~E(x45881,f2(a865))+E(f323(f100(a1),x45881),f2(a1))
% 188.07/187.96 [4595]~P90(x45951)+E(f323(f103(x45951),a81),f2(x45951))
% 188.07/187.96 [4598]~E(f531(x45981),f2(a865))+E(f323(f159(a865),x45981),f2(a865))
% 188.07/187.96 [4599]~P104(x45991)+E(f239(x45991,f237(x45991)),f235(x45991))
% 188.07/187.96 [4600]~P104(x46001)+E(f240(x46001,f237(x46001)),f236(x46001))
% 188.07/187.96 [4601]~P85(x46011)+E(f80(x46011,f2(x46011)),f2(x46011))
% 188.07/187.96 [4610]~P140(x46101)+E(f323(f100(x46101),f76(a865)),f76(x46101))
% 188.07/187.96 [4611]~P140(x46111)+E(f323(f100(x46111),f2(a865)),f2(x46111))
% 188.07/187.96 [4612]~P134(x46121)+E(f323(f102(x46121),f76(a1)),f76(x46121))
% 188.07/187.96 [4613]~P134(x46131)+E(f323(f102(x46131),f2(a1)),f2(x46131))
% 188.07/187.96 [4614]E(x46141,f2(a865))+~E(f323(f100(a1),x46141),f2(a1))
% 188.07/187.96 [4639]~P87(x46391)+E(f323(f77(x46391),f188(x46391)),f246(x46391))
% 188.07/187.96 [4640]~P87(x46401)+E(f323(f77(x46401),f246(x46401)),f188(x46401))
% 188.07/187.96 [4641]~P59(x46411)+E(f323(f77(x46411),f2(x46411)),f2(x46411))
% 188.07/187.96 [4642]~P116(x46421)+E(f323(f73(x46421),f76(x46421)),f76(x46421))
% 188.07/187.96 [4643]~P82(x46431)+E(f323(f73(x46431),f2(x46431)),f2(x46431))
% 188.07/187.96 [4644]~P78(x46441)+E(f323(f159(x46441),f113(x46441)),f2(x46441))
% 188.07/187.96 [4664]~P37(x46641)+P39(f323(f166(a1),x46641))
% 188.07/187.96 [4697]~P90(x46971)+E(f323(f77(x46971),f76(x46971)),f323(f103(x46971),a97))
% 188.07/187.96 [4714]~P90(x47141)+P30(x47141,f323(f103(x47141),a81))
% 188.07/187.96 [4731]~P5(x47311)+E(f323(f166(x47311),f53(x47311)),f246(f872(x47311,a860)))
% 188.07/187.96 [4741]P37(x47411)+~P39(f323(f166(a1),x47411))
% 188.07/187.96 [4742]~P5(x47421)+P101(f323(f130(x47421),f53(x47421)))
% 188.07/187.96 [4787]E(f323(f100(a1),f323(a104,x47871)),x47871)+P101(f323(a193,x47871))
% 188.07/187.96 [4855]~P110(x48551)+E(f249(x48551,f76(x48551),f79(x48551)),f248(x48551))
% 188.07/187.96 [4885]~P90(x48851)+~P30(x48851,f323(f103(x48851),a97))
% 188.07/187.96 [5027]E(f323(f73(a1),x50271),x50271)+P101(f323(f323(f238(a1),x50271),f2(a1)))
% 188.07/187.96 [5045]~E(f323(a104,x50451),f2(a865))+P101(f323(f323(f237(a1),x50451),f2(a1)))
% 188.07/187.96 [5107]~P101(f323(a193,x51071))+P101(f323(f323(f238(a1),x51071),f2(a1)))
% 188.07/187.96 [5147]~P134(x51471)+P101(f323(f323(f325(x51471),f76(x51471)),f109(x51471)))
% 188.07/187.96 [5148]~P140(x51481)+P101(f323(f323(f325(x51481),f76(x51481)),f186(x51481)))
% 188.07/187.96 [5149]~P134(x51491)+P101(f323(f323(f325(x51491),f2(x51491)),f109(x51491)))
% 188.07/187.96 [5150]~P140(x51501)+P101(f323(f323(f325(x51501),f2(x51501)),f186(x51501)))
% 188.07/187.96 [5151]~P119(x51511)+P101(f323(f323(f237(x51511),f2(x51511)),f76(x51511)))
% 188.07/187.96 [5152]~P119(x51521)+P101(f323(f323(f238(x51521),f2(x51521)),f76(x51521)))
% 188.07/187.96 [5201]E(x52011,f2(a865))+~P101(f323(f323(f237(a865),x52011),f2(a865)))
% 188.07/187.96 [5243]E(f323(a104,x52431),f2(a865))+~P101(f323(f323(f237(a1),x52431),f2(a1)))
% 188.07/187.96 [5305]P101(f323(a193,x53051))+~P101(f323(f323(f238(a1),x53051),f2(a1)))
% 188.07/187.96 [5310]~P103(x53101)+P18(x53101,f866(x53101),f141(x53101,x53101,f5(x53101)))
% 188.07/187.96 [5327]P39(x53271)+~P101(f323(f323(f237(a1),f2(a1)),f384(x53271)))
% 188.07/187.96 [5333]E(f323(f73(a1),x53331),f323(f77(a1),x53331))+~P101(f323(f323(f238(a1),x53331),f2(a1)))
% 188.07/187.96 [5505]~P119(x55051)+~P101(f323(f323(f237(x55051),f76(x55051)),f2(x55051)))
% 188.07/187.96 [5506]~P119(x55061)+~P101(f323(f323(f238(x55061),f76(x55061)),f2(x55061)))
% 188.07/187.96 [5516]~E(x55161,f2(a865))+P101(f323(f323(f237(a1),f323(f100(a1),x55161)),f2(a1)))
% 188.07/187.96 [5517]~E(x55171,f2(a1))+P101(f323(f323(f238(a1),f323(f73(a1),x55171)),f76(a1)))
% 188.07/187.96 [5636]~P78(x56361)+E(f135(x56361,x56361,f78(x56361),f2(x56361)),f159(x56361))
% 188.07/187.96 [5806]~P99(x58061)+P27(a865,x58061,f100(x58061),f246(f872(a865,a860)))
% 188.07/187.96 [5995]E(x59951,f2(a865))+~P101(f323(f323(f237(a1),f323(f100(a1),x59951)),f2(a1)))
% 188.07/187.96 [5996]E(x59961,f2(a1))+~P101(f323(f323(f238(a1),f323(f73(a1),x59961)),f76(a1)))
% 188.07/187.96 [6782]~P101(f323(f323(f238(a1),x67821),f2(a1)))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x67821),x67821)),f2(a1)))
% 188.07/187.96 [7323]P101(f323(f323(f238(a1),x73231),f2(a1)))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),x73231),x73231)),f2(a1)))
% 188.07/187.96 [7878]E(x78781,f323(a3,f2(a865)))+P101(f323(f323(f238(a865),f323(f323(f22(a865),f323(a19,x78781)),f323(a112,f2(a865)))),f323(a19,x78781)))
% 188.07/187.96 [8644]~P101(f323(f323(f238(a1),x86441),f2(a1)))+P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x86441),x86441)),a97)),f2(a1)))
% 188.07/187.96 [8741]~P101(f323(f323(f238(a1),x87411),f2(a1)))+P101(f323(f323(f238(a1),f323(f323(f78(a1),f323(f323(f78(a1),f76(a1)),x87411)),x87411)),f2(a1)))
% 188.07/187.96 [9061]P101(f323(f323(f238(a1),x90611),f2(a1)))+~P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90611),x90611)),a97)),f2(a1)))
% 188.07/187.96 [9121]P101(f323(f323(f238(a1),x91211),f2(a1)))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),f323(f323(f78(a1),f76(a1)),x91211)),x91211)),f2(a1)))
% 188.07/187.96 [4685]~E(a81,x46851)+E(f323(f323(f78(a1),x46851),x46851),a81)
% 188.07/187.96 [4686]~E(x46861,a81)+E(f323(f323(f78(a1),x46861),x46861),a81)
% 188.07/187.96 [4700]E(x47001,f2(a1))+E(f323(f323(f36(a1),x47001),x47001),f76(a1))
% 188.07/187.96 [4832]E(x48321,a81)+~E(f323(f323(f78(a1),x48321),x48321),a81)
% 188.07/187.96 [4833]E(a81,x48331)+~E(f323(f323(f78(a1),x48331),x48331),a81)
% 188.07/187.96 [4845]~P103(x48451)+E(f132(x48451,f188(f872(x48451,a860))),f113(x48451))
% 188.07/187.96 [4846]~P6(x48461)+E(f37(x48461,f188(f872(x48461,a860))),f188(x48461))
% 188.07/187.96 [4847]~P6(x48471)+E(f37(x48471,f246(f872(x48471,a860))),f246(x48471))
% 188.07/187.96 [4848]~P6(x48481)+E(f38(x48481,f188(f872(x48481,a860))),f246(x48481))
% 188.07/187.96 [4849]~P6(x48491)+E(f38(x48491,f246(f872(x48491,a860))),f188(x48491))
% 188.07/187.96 [4985]E(x49851,f2(a865))+P101(f323(f323(f238(a865),f2(a865)),x49851))
% 188.07/187.96 [5004]~P7(x50041)+P101(f323(f323(f237(a1),f2(a1)),x50041))
% 188.07/187.96 [5036]~E(f323(f103(a865),x50361),f2(a865))+P101(f323(f323(f237(a1),x50361),a81))
% 188.07/187.96 [5041]P39(x50411)+P101(f323(f323(f325(a1),f384(x50411)),x50411))
% 188.07/187.96 [5042]E(x50421,f323(a3,f2(a865)))+P101(f323(f323(f237(a99),f76(a99)),x50421))
% 188.07/187.96 [5081]P101(f323(a193,x50811))+P101(f323(f323(f237(a1),f2(a1)),x50811))
% 188.07/187.96 [5129]E(f323(f100(a1),f323(a104,x51291)),f2(a1))+P101(f323(f323(f237(a1),f2(a1)),x51291))
% 188.07/187.96 [5188]E(f323(f100(a1),f323(f103(a865),x51881)),f323(f103(a1),x51881))+P101(f323(a193,f323(f103(a1),x51881)))
% 188.07/187.96 [5207]E(f323(f103(a865),x52071),f2(a865))+~P101(f323(a193,f323(f103(a1),x52071)))
% 188.07/187.96 [5208]E(f323(f103(a865),x52081),f2(a865))+~P101(f323(f323(f237(a1),x52081),a81))
% 188.07/187.96 [5240]P7(x52401)+~P101(f323(f323(f237(a1),f2(a1)),x52401))
% 188.07/187.96 [5313]E(f323(a112,f804(x53131)),x53131)+~P101(f323(f323(f238(a865),f2(a865)),x53131))
% 188.07/187.96 [5321]E(f323(a112,f323(f103(a865),x53211)),f76(a865))+~P101(f323(a193,f323(f103(a1),x53211)))
% 188.07/187.96 [5329]E(f323(f100(a1),f426(x53291)),x53291)+~P101(f323(f323(f238(a1),f2(a1)),x53291))
% 188.07/187.96 [5336]~E(x53361,f323(a3,f2(a865)))+~P101(f323(f323(f237(a99),f76(a99)),x53361))
% 188.07/187.96 [5343]E(f323(f100(a1),f323(f103(a865),x53431)),f2(a1))+~P101(f323(a193,f323(f103(a1),x53431)))
% 188.07/187.96 [5369]E(f323(f159(a865),x53691),f2(a865))+P101(f323(f323(f325(a865),f531(x53691)),f323(f166(a865),x53691)))
% 188.07/187.96 [5390]E(f323(f100(a1),f323(a104,x53901)),x53901)+~P101(f323(f323(f237(a1),f2(a1)),x53901))
% 188.07/187.96 [5399]~P101(f323(a193,x53991))+~P101(f323(f323(f237(a1),f2(a1)),x53991))
% 188.07/187.96 [5498]E(f323(f323(f78(a865),f76(a865)),f323(f103(a865),x54981)),f76(a865))+~P101(f323(f323(f238(a1),x54981),a81))
% 188.07/187.96 [5556]E(x55561,f2(a865))+~P101(f323(f323(f238(a865),x55561),f323(a112,f2(a865))))
% 188.07/187.96 [5595]E(f323(f323(f22(a865),f323(f103(a865),x55951)),f76(a865)),f2(a865))+~P101(f323(f323(f237(a1),x55951),a81))
% 188.07/187.96 [5596]E(f323(f323(f78(a865),f323(f103(a865),x55961)),f76(a865)),f76(a865))+~P101(f323(f323(f238(a1),x55961),a81))
% 188.07/187.96 [5606]~P39(x56061)+E(f323(f35(a865),f323(f302(a1,a865,a104),x56061)),f323(f35(a1),x56061))
% 188.07/187.96 [5637]~P103(x56371)+E(f239(x56371,f323(f7(x56371,x56371,a860),f237(x56371))),f236(x56371))
% 188.07/187.96 [5638]~P103(x56381)+E(f240(x56381,f323(f7(x56381,x56381,a860),f237(x56381))),f235(x56381))
% 188.07/187.96 [5648]E(f42(a865,f323(a112,f2(a865)),f323(f103(a865),x56481)),f323(a112,f2(a865)))+~P101(f323(a193,f323(f103(a1),x56481)))
% 188.07/187.96 [5657]~P101(f323(f323(f238(a1),f2(a1)),x56571))+P101(f323(f323(f237(a1),f76(a1)),x56571))
% 188.07/187.96 [5658]P101(f323(f323(f238(a1),f2(a1)),x56581))+~P101(f323(f323(f237(a1),f76(a1)),x56581))
% 188.07/187.96 [5669]E(f323(a112,f323(f323(f22(a865),x56691),f76(a865))),x56691)+~P101(f323(f323(f238(a865),f2(a865)),x56691))
% 188.07/187.96 [5725]P101(f323(f323(f238(a865),f2(a865)),f426(x57251)))+~P101(f323(f323(f238(a1),f2(a1)),x57251))
% 188.07/187.96 [5784]E(f42(a1,f323(f103(a1),a97),x57841),f323(f323(f22(a1),x57841),f76(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x57841))
% 188.07/187.96 [5818]~P101(f323(f323(f238(a1),a81),x58181))+P101(f323(f323(f238(a865),f2(a865)),f323(f103(a865),x58181)))
% 188.07/187.96 [5868]P101(f323(f323(f238(a865),f2(a865)),f323(a104,x58681)))+~P101(f323(f323(f238(a1),f2(a1)),x58681))
% 188.07/187.96 [5917]~P101(f323(f323(f238(a865),f2(a865)),x59171))+P101(f323(f323(f238(a1),f2(a1)),f323(f100(a1),x59171)))
% 188.07/187.96 [5952]~P101(f323(f323(f238(a865),f2(a865)),f323(a104,x59521)))+P101(f323(f323(f238(a1),f2(a1)),x59521))
% 188.07/187.96 [5966]~P39(x59661)+E(f323(f302(a865,a1,f100(a1)),f323(f302(a1,a865,a104),x59661)),x59661)
% 188.07/187.96 [5976]P101(f323(f323(f238(a1),a81),x59761))+~P101(f323(f323(f238(a865),f2(a865)),f323(f103(a865),x59761)))
% 188.07/187.96 [6024]~P5(x60241)+E(f323(f323(f144(f869(x60241)),f200(x60241)),f323(f323(f147(x60241,f869(x60241)),f230(x60241)),f53(x60241))),f53(f869(x60241)))
% 188.07/187.96 [6035]P101(f323(f323(f238(a865),f2(a865)),x60351))+~P101(f323(f323(f238(a1),f2(a1)),f323(f100(a1),x60351)))
% 188.07/187.96 [6144]E(f323(f302(a865,a1,f100(a1)),f323(f244(a865),f323(a104,x61441))),f323(f293(a1,f2(a1)),x61441))+~P101(f323(f323(f237(a1),f2(a1)),x61441))
% 188.07/187.96 [6159]~P119(x61591)+P101(f323(f323(f238(x61591),f2(x61591)),f323(f323(f78(x61591),f76(x61591)),f76(x61591))))
% 188.07/187.96 [6210]P101(f323(f323(f238(a865),f323(a112,f2(a865))),f323(a104,x62101)))+~P101(f323(f323(f238(a1),f76(a1)),x62101))
% 188.07/187.96 [6304]E(x63041,f2(a1))+P101(f323(f46(f2(a1),x63041),f323(f323(f258(a1,a1),f2(a1)),f2(a1))))
% 188.07/187.96 [6467]~P101(f323(f323(f238(a865),f323(a112,f2(a865))),f323(a104,x64671)))+P101(f323(f323(f238(a1),f76(a1)),x64671))
% 188.07/187.96 [6891]~P111(x68911)+P38(x68911,f323(f243(f871(x68911,x68911)),f323(f262(x68911,x68911,a860),f238(x68911))))
% 188.07/187.96 [5543]E(f323(f103(a865),f323(f323(f22(a1),x55431),a97)),f323(a112,f323(f103(a865),x55431)))+P101(f323(a193,f323(f103(a1),x55431)))
% 188.07/187.96 [5559]~P37(x55591)+E(f323(f323(f147(a865,a1),f100(a1)),f323(f323(f147(a1,a865),a104),x55591)),x55591)
% 188.07/187.96 [5675]E(f323(f77(a1),f323(f100(a1),f323(a112,f427(x56751)))),x56751)+~P101(f323(f323(f238(a1),x56751),f2(a1)))
% 188.07/187.96 [5685]E(f323(f323(f78(a865),f76(a865)),f323(f103(a865),x56851)),f323(f103(a865),f323(f323(f22(a1),x56851),a97)))+P101(f323(f323(f238(a1),x56851),a81))
% 188.07/187.96 [5727]E(f323(f323(f36(a1),f323(f103(a1),a97)),x57271),f323(f103(a1),a97))+~P101(f323(f323(f238(a1),f2(a1)),x57271))
% 188.07/187.96 [5814]E(f323(f323(f22(a865),f323(f103(a865),x58141)),f76(a865)),f323(f103(a865),f323(f323(f78(a1),x58141),a97)))+P101(f323(f323(f237(a1),x58141),a81))
% 188.07/187.96 [5815]E(f323(f323(f78(a865),f323(f103(a865),x58151)),f76(a865)),f323(f103(a865),f323(f323(f22(a1),x58151),a97)))+P101(f323(f323(f238(a1),x58151),a81))
% 188.07/187.96 [5856]E(f323(a104,f323(f323(f78(a1),f76(a1)),x58561)),f323(a112,f323(a104,x58561)))+~P101(f323(f323(f237(a1),f2(a1)),x58561))
% 188.07/187.96 [5890]E(f323(a112,f323(f323(f22(a865),x58901),f323(a112,f2(a865)))),x58901)+~P101(f323(f323(f238(a865),f2(a865)),x58901))
% 188.07/187.96 [6095]E(f42(a865,f323(a112,f2(a865)),f323(f103(a865),x60951)),f323(a104,f42(a1,f76(a1),f323(f103(a1),x60951))))+P101(f323(a193,f323(f103(a1),x60951)))
% 188.07/187.96 [6134]~P101(f323(f323(f237(a1),a81),x61341))+P101(f323(f323(f237(a1),a81),f323(f323(f78(a1),x61341),x61341)))
% 188.07/187.96 [6135]~P101(f323(f323(f238(a1),a97),x61351))+P101(f323(f323(f237(a1),a97),f323(f323(f78(a1),x61351),x61351)))
% 188.07/187.96 [6136]~P101(f323(f323(f238(a1),a81),x61361))+P101(f323(f323(f238(a1),a81),f323(f323(f78(a1),x61361),x61361)))
% 188.07/187.96 [6137]~P101(f323(f323(f238(a1),a97),x61371))+P101(f323(f323(f238(a1),a97),f323(f323(f78(a1),x61371),x61371)))
% 188.07/187.96 [6138]~P101(f323(f323(f89(a1),a81),x61381))+P101(f323(f323(f89(a1),a81),f323(f323(f78(a1),x61381),x61381)))
% 188.07/187.96 [6317]~P101(f323(f59(x63171),f246(f872(x63171,a860))))+P101(f323(f59(f869(x63171)),f246(f872(f869(x63171),a860))))
% 188.07/187.96 [6401]~P101(f323(f323(f237(a1),f2(a1)),x64011))+P101(f323(f323(f238(a1),f2(a1)),f323(f323(f78(a1),f76(a1)),x64011)))
% 188.07/187.96 [6408]E(f323(f257(a1,a1),f44(f76(a1),f323(f103(a1),x64081))),f323(f323(f36(a1),f76(a1)),f323(f103(a1),x64081)))+~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x64081)))
% 188.07/187.96 [6428]E(f323(f261(a1,a1),f44(f76(a1),f323(f103(a1),x64281))),f42(a1,f76(a1),f323(f103(a1),x64281)))+~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x64281)))
% 188.07/187.96 [6439]P101(f323(f59(x64391),f246(f872(x64391,a860))))+~P101(f323(f59(f869(x64391)),f246(f872(f869(x64391),a860))))
% 188.07/187.96 [6468]P101(f323(f323(f237(a1),a81),x64681))+~P101(f323(f323(f237(a1),a81),f323(f323(f78(a1),x64681),x64681)))
% 188.07/187.96 [6469]P101(f323(f323(f238(a1),a81),x64691))+~P101(f323(f323(f238(a1),a81),f323(f323(f78(a1),x64691),x64691)))
% 188.07/187.96 [6470]P101(f323(f323(f238(a1),a97),x64701))+~P101(f323(f323(f237(a1),a97),f323(f323(f78(a1),x64701),x64701)))
% 188.07/187.96 [6471]P101(f323(f323(f238(a1),a97),x64711))+~P101(f323(f323(f238(a1),a97),f323(f323(f78(a1),x64711),x64711)))
% 188.07/187.96 [6472]P101(f323(f323(f89(a1),a81),x64721))+~P101(f323(f323(f89(a1),a81),f323(f323(f78(a1),x64721),x64721)))
% 188.07/187.96 [6786]~P101(f323(f59(x67861),f246(f872(x67861,a860))))+P101(f323(f323(f238(a865),f2(a865)),f323(f35(x67861),f246(f872(x67861,a860)))))
% 188.07/187.96 [7365]P101(f323(f59(a865),x73651))+~P101(f323(f59(a1),f323(f302(a865,a1,f100(a1)),x73651)))
% 188.07/187.96 [5473]~E(a97,x54731)+E(f323(f323(f22(a1),f323(f323(f78(a1),x54731),x54731)),a97),a97)
% 188.07/187.96 [5474]~E(x54741,a97)+E(f323(f323(f22(a1),f323(f323(f78(a1),x54741),x54741)),a97),a97)
% 188.07/187.96 [5971]E(x59711,a97)+~E(f323(f323(f22(a1),f323(f323(f78(a1),x59711),x59711)),a97),a97)
% 188.07/187.96 [5972]E(a97,x59721)+~E(f323(f323(f22(a1),f323(f323(f78(a1),x59721),x59721)),a97),a97)
% 188.07/187.96 [6370]~E(f323(f103(a865),x63701),f2(a865))+P101(f323(a193,f323(f103(a1),f323(f323(f78(a1),x63701),a97))))
% 188.07/187.96 [6712]~P101(f323(a193,f323(f103(a1),x67121)))+P101(f323(a193,f323(f103(a1),f323(f323(f78(a1),x67121),x67121))))
% 188.07/187.96 [6713]~P101(f323(f323(f237(a1),x67131),a81))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x67131),x67131)),a81))
% 188.07/187.96 [6714]~P101(f323(f323(f237(a1),x67141),a97))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x67141),x67141)),a97))
% 188.07/187.96 [6715]~P101(f323(f323(f238(a1),x67151),a81))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x67151),x67151)),a81))
% 188.07/187.96 [6716]~P101(f323(f323(f237(a1),x67161),a97))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x67161),x67161)),a97))
% 188.07/187.96 [6717]~P101(f323(f323(f89(a1),x67171),a81))+P101(f323(f323(f89(a1),f323(f323(f78(a1),x67171),x67171)),a81))
% 188.07/187.96 [7036]E(f323(f103(a865),x70361),f2(a865))+~P101(f323(a193,f323(f103(a1),f323(f323(f78(a1),x70361),a97))))
% 188.07/187.96 [7275]~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x72751)))+P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),f323(f323(f78(a1),x72751),x72751))))
% 188.07/187.96 [7276]P101(f323(a193,f323(f103(a1),x72761)))+~P101(f323(a193,f323(f103(a1),f323(f323(f78(a1),x72761),x72761))))
% 188.07/187.96 [7277]P101(f323(f323(f237(a1),x72771),a81))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),x72771),x72771)),a81))
% 188.07/187.96 [7278]P101(f323(f323(f237(a1),x72781),a97))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),x72781),x72781)),a97))
% 188.07/187.96 [7279]P101(f323(f323(f237(a1),x72791),a97))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),x72791),x72791)),a97))
% 188.07/187.96 [7280]P101(f323(f323(f238(a1),x72801),a81))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),x72801),x72801)),a81))
% 188.07/187.96 [7281]P101(f323(f323(f89(a1),x72811),a81))+~P101(f323(f323(f89(a1),f323(f323(f78(a1),x72811),x72811)),a81))
% 188.07/187.96 [7645]E(f323(a107,f681(x76451)),x76451)+~P101(f323(f323(f325(f872(f871(a865,a865),a860)),x76451),a98))
% 188.07/187.96 [6290]~P90(x62901)+E(f323(f103(x62901),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f76(x62901))
% 188.07/187.96 [6764]~P101(f323(a193,f323(f103(a1),x67641)))+E(f323(f103(a865),f323(f323(f22(a1),f323(f323(f78(a1),x67641),x67641)),a97)),f2(a865))
% 188.07/187.96 [7821]~P101(f323(f323(f238(a1),f323(f103(a1),x78211)),f2(a1)))+E(f323(f257(a1,a1),f323(a48,f47(f323(f77(a1),f76(a1)),f323(f77(a1),f323(f103(a1),x78211))))),f323(f323(f36(a1),f76(a1)),f323(f103(a1),x78211)))
% 188.07/187.96 [7835]~P101(f323(f323(f238(a1),f323(f103(a1),x78351)),f2(a1)))+E(f323(f261(a1,a1),f323(a48,f47(f323(f77(a1),f76(a1)),f323(f77(a1),f323(f103(a1),x78351))))),f42(a1,f76(a1),f323(f103(a1),x78351)))
% 188.07/187.96 [7884]~P101(f323(f323(f237(a1),a81),x78841))+P101(f323(f323(f237(a1),a81),f323(f323(f22(a1),f323(f323(f78(a1),x78841),x78841)),a97)))
% 188.07/187.96 [7885]~P101(f323(f323(f237(a1),a97),x78851))+P101(f323(f323(f237(a1),a97),f323(f323(f22(a1),f323(f323(f78(a1),x78851),x78851)),a97)))
% 188.07/187.96 [7886]~P101(f323(f323(f237(a1),a81),x78861))+P101(f323(f323(f238(a1),a81),f323(f323(f22(a1),f323(f323(f78(a1),x78861),x78861)),a97)))
% 188.07/187.96 [7887]~P101(f323(f323(f238(a1),a97),x78871))+P101(f323(f323(f238(a1),a97),f323(f323(f22(a1),f323(f323(f78(a1),x78871),x78871)),a97)))
% 188.07/187.96 [7888]~P101(f323(f323(f89(a1),a97),x78881))+P101(f323(f323(f89(a1),a97),f323(f323(f22(a1),f323(f323(f78(a1),x78881),x78881)),a97)))
% 188.07/187.96 [8186]~P90(x81861)+~P30(x81861,f323(f103(x81861),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))
% 188.07/187.96 [8370]P101(f323(f323(f237(a1),a81),x83701))+~P101(f323(f323(f237(a1),a81),f323(f323(f22(a1),f323(f323(f78(a1),x83701),x83701)),a97)))
% 188.07/187.96 [8371]P101(f323(f323(f237(a1),a81),x83711))+~P101(f323(f323(f238(a1),a81),f323(f323(f22(a1),f323(f323(f78(a1),x83711),x83711)),a97)))
% 188.07/187.96 [8372]P101(f323(f323(f237(a1),a97),x83721))+~P101(f323(f323(f237(a1),a97),f323(f323(f22(a1),f323(f323(f78(a1),x83721),x83721)),a97)))
% 188.07/187.96 [8373]P101(f323(f323(f238(a1),a97),x83731))+~P101(f323(f323(f238(a1),a97),f323(f323(f22(a1),f323(f323(f78(a1),x83731),x83731)),a97)))
% 188.07/187.96 [8374]P101(f323(f323(f89(a1),a97),x83741))+~P101(f323(f323(f89(a1),a97),f323(f323(f22(a1),f323(f323(f78(a1),x83741),x83741)),a97)))
% 188.07/187.96 [8691]E(f323(f103(a865),f323(f323(f22(a1),f323(f323(f78(a1),x86911),x86911)),a97)),f323(f323(f84(a865,a865),f323(f103(a865),x86911)),f323(f323(f8(a865,a865,a865),a112),f323(f323(f18(a865,a865,a865),f78(a865)),f5(a865)))))+P101(f323(a193,f323(f103(a1),x86911)))
% 188.07/187.96 [9538]E(x95381,f188(f872(f871(a865,a865),a860)))+P101(f323(f323(f325(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f258(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),x95381),f188(f872(f871(a865,a865),a860)))),a66))
% 188.07/187.96 [8617]~P101(f323(a193,f323(f103(a1),x86171)))+P101(f323(a193,f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),x86171),x86171)),a97))))
% 188.07/187.96 [8618]~P101(f323(f323(f238(a1),x86181),a81))+P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x86181),x86181)),a97)),a81))
% 188.07/187.96 [8619]~P101(f323(f323(f237(a1),x86191),a97))+P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x86191),x86191)),a97)),a97))
% 188.07/187.96 [8620]~P101(f323(f323(f238(a1),x86201),a81))+P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x86201),x86201)),a97)),a81))
% 188.07/187.96 [8621]~P101(f323(f323(f238(a1),x86211),a97))+P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x86211),x86211)),a97)),a97))
% 188.07/187.96 [8622]~P101(f323(f323(f89(a1),x86221),a97))+P101(f323(f323(f89(a1),f323(f323(f22(a1),f323(f323(f78(a1),x86221),x86221)),a97)),a97))
% 188.07/187.96 [8732]~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x87321)))+P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),x87321),x87321)),a97))))
% 188.07/187.96 [8893]~P90(x88931)+E(f323(f323(f78(x88931),f76(x88931)),f76(x88931)),f323(f103(x88931),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))))
% 188.07/187.96 [9044]P101(f323(a193,f323(f103(a1),x90441)))+~P101(f323(a193,f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90441),x90441)),a97))))
% 188.07/187.96 [9045]P101(f323(f323(f237(a1),x90451),a97))+~P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90451),x90451)),a97)),a97))
% 188.07/187.96 [9046]P101(f323(f323(f238(a1),x90461),a81))+~P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90461),x90461)),a97)),a81))
% 188.07/187.96 [9047]P101(f323(f323(f238(a1),x90471),a81))+~P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90471),x90471)),a97)),a81))
% 188.07/187.96 [9048]P101(f323(f323(f238(a1),x90481),a97))+~P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90481),x90481)),a97)),a97))
% 188.07/187.96 [9049]P101(f323(f323(f89(a1),x90491),a97))+~P101(f323(f323(f89(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90491),x90491)),a97)),a97))
% 188.07/187.96 [9585]~P101(f323(f59(f871(a865,a865)),x95851))+P101(f323(f323(f325(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f258(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),f188(f872(f871(a865,a865),a860))),x95851)),a67))
% 188.07/187.96 [9368]~P140(x93681)+E(f323(f323(f248(x93681),f76(x93681)),f323(f103(a865),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(x93681))
% 188.07/187.96 [9369]~P140(x93691)+E(f323(f323(f248(x93691),f2(x93691)),f323(f103(a865),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(x93691))
% 188.07/187.96 [9815]~P101(f323(f323(f238(a865),f76(a865)),x98151))+P101(f323(f323(f238(a865),f2(a865)),f323(f323(f36(a865),x98151),f323(f103(a865),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))))))
% 188.07/187.96 [9825]~P101(f323(f323(f238(a865),f2(a865)),x98251))+P101(f323(f323(f238(a865),f2(a865)),f323(f323(f36(a865),f323(f323(f78(a865),x98251),f76(a865))),f323(f103(a865),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))))))
% 188.07/187.96 [9867]~E(f42(a865,x98671,f323(f103(a865),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(a865))+P101(f323(f323(f238(a865),f2(a865)),f42(a865,x98671,f323(f103(a865),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))))))
% 188.07/187.96 [9886]E(f42(a865,x98861,f323(f103(a865),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(a865))+~P101(f323(f323(f238(a865),f2(a865)),f42(a865,x98861,f323(f103(a865),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))))))
% 188.07/187.96 [4618]~P38(x46181,x46182)+P54(x46181,x46182)
% 188.07/187.96 [4619]~P44(x46191,x46192)+P54(x46191,x46192)
% 188.07/187.96 [4580]~E(x45801,x45802)+E(f270(x45801,x45802),f76(a99))
% 188.07/187.96 [4583]E(f218(x45831,x45832),x45831)+~E(x45832,f2(a865))
% 188.07/187.96 [4590]~E(x45902,f113(x45901))+E(f145(x45901,x45902),f113(x45901))
% 188.07/187.96 [4609]~E(f145(x46092,x46091),f113(x46092))+E(x46091,f113(x46092))
% 188.07/187.96 [4623]~P1(x46232)+P1(f872(x46231,x46232))
% 188.07/187.96 [4624]~P2(x46242)+P2(f872(x46241,x46242))
% 188.07/187.96 [4625]~P94(x46252)+P3(f872(x46251,x46252))
% 188.07/187.96 [4626]~P2(x46262)+P97(f872(x46261,x46262))
% 188.07/187.96 [4627]~P4(x46272)+P4(f872(x46271,x46272))
% 188.07/187.96 [4628]~P102(x46282)+P102(f872(x46281,x46282))
% 188.07/187.96 [4629]~P2(x46292)+P98(f872(x46291,x46292))
% 188.07/187.96 [4630]~P104(x46302)+P104(f872(x46301,x46302))
% 188.07/187.96 [4631]~P105(x46312)+P105(f872(x46311,x46312))
% 188.07/187.96 [4632]~P106(x46322)+P106(f872(x46321,x46322))
% 188.07/187.96 [4633]~P94(x46332)+P95(f872(x46331,x46332))
% 188.07/187.96 [4634]~P96(x46342)+P96(f872(x46341,x46342))
% 188.07/187.96 [4635]~P79(x46352)+P79(f872(x46351,x46352))
% 188.07/187.96 [4636]~P87(x46362)+P87(f872(x46361,x46362))
% 188.07/187.96 [4637]~P6(x46372)+P6(f872(x46371,x46372))
% 188.07/187.96 [4638]~P94(x46382)+P94(f872(x46381,x46382))
% 188.07/187.96 [4651]E(x46511,x46512)+~E(f323(a112,x46511),f323(a112,x46512))
% 188.07/187.96 [4652]E(x46521,x46522)+~E(f323(a107,x46521),f323(a107,x46522))
% 188.07/187.96 [4653]E(x46531,x46532)+~E(f323(a3,x46531),f323(a3,x46532))
% 188.07/187.96 [4655]E(x46551,x46552)+~E(f323(a19,x46551),f323(a19,x46552))
% 188.07/187.96 [4760]~P57(x47601)+E(f42(x47601,x47602,x47602),f2(x47601))
% 188.07/187.96 [4794]~P38(x47941,x47942)+P38(f866(x47941),f138(x47941,x47942))
% 188.07/187.96 [4795]~P38(x47951,x47952)+P38(f866(x47951),f139(x47951,x47952))
% 188.07/187.96 [4890]~P38(x48901,x48902)+P38(f872(x48901,a860),f316(x48901,x48902))
% 188.07/187.96 [4891]~P38(x48911,x48912)+P38(f872(x48911,a860),f314(x48911,x48912))
% 188.07/187.96 [5010]~P7(x50101)+P39(f294(a1,x50101,x50102))
% 188.07/187.96 [5110]~P38(x51101,x51102)+P56(x51101,f65(x51101,x51101,x51102))
% 188.07/187.96 [5600]~P75(x56001)+P27(x56001,x56001,f77(x56001),x56002)
% 188.07/187.96 [4604]~E(x46042,f113(x46041))+E(f323(f161(x46041),x46042),f113(x46041))
% 188.07/187.96 [4605]~E(x46052,f113(x46051))+E(f323(f162(x46051),x46052),f113(x46051))
% 188.07/187.96 [4659]E(x46591,f323(a104,x46592))+~E(f323(f100(a1),x46591),x46592)
% 188.07/187.96 [4662]E(x46621,f113(x46622))+~E(f323(f161(x46622),x46621),f113(x46622))
% 188.07/187.96 [4663]E(x46631,f113(x46632))+~E(f323(f162(x46632),x46631),f113(x46632))
% 188.07/187.96 [4682]~P90(x46821)+E(f323(f103(x46821),x46822),f323(f102(x46821),x46822))
% 188.07/187.96 [4689]~E(x46892,f200(x46891))+E(f229(x46891,x46892),f188(f872(x46891,a860)))
% 188.07/187.96 [4691]~P61(x46911)+P101(f323(f59(x46911),x46912))
% 188.07/187.96 [4698]E(x46981,f200(x46982))+E(f323(f230(x46982),f688(x46982,x46981)),x46981)
% 188.07/187.96 [4699]E(x46991,f200(x46992))+E(f323(f230(x46992),f797(x46992,x46991)),x46991)
% 188.07/187.96 [4701]~E(f545(x47012,x47011),f113(x47011))+E(f173(x47011,x47012),f113(f866(x47011)))
% 188.07/187.96 [4710]~E(x47102,f113(x47101))+E(f323(f166(x47101),x47102),f188(f872(x47101,a860)))
% 188.07/187.96 [4711]~E(x47112,f113(x47111))+E(f188(f872(x47111,a860)),f323(f166(x47111),x47112))
% 188.07/187.96 [4713]E(x47131,x47132)+~E(f323(f100(a1),x47131),f323(f100(a1),x47132))
% 188.07/187.96 [4716]E(f216(x47161,x47162),f2(a865))+P101(f323(f59(x47161),x47162))
% 188.07/187.96 [4736]~P116(x47361)+E(f80(x47361,f80(x47361,x47362)),f80(x47361,x47362))
% 188.07/187.96 [4749]~P77(x47491)+E(f323(f323(f248(x47491),x47492),f76(a865)),x47492)
% 188.07/187.96 [4750]~P112(x47501)+E(f323(f323(f248(x47501),x47502),f76(a865)),x47502)
% 188.07/187.96 [4754]E(x47541,x47542)+E(f270(x47541,x47542),f323(f323(f78(a99),x47542),f76(a99)))
% 188.07/187.96 [4757]E(f323(f35(x47571),x47572),f2(a865))+P101(f323(f59(x47571),x47572))
% 188.07/187.96 [4761]~E(f145(x47611,x47612),x47612)+P101(f323(f130(x47611),x47612))
% 188.07/187.96 [4764]~P3(x47641)+E(f323(f323(f110(x47641),x47642),f188(x47641)),x47642)
% 188.07/187.96 [4765]~P59(x47651)+E(f323(f323(f22(x47651),x47652),f2(x47651)),x47652)
% 188.07/187.96 [4766]~P95(x47661)+E(f323(f323(f101(x47661),x47662),f246(x47661)),x47662)
% 188.07/187.96 [4767]~P68(x47671)+E(f323(f323(f79(x47671),x47672),f76(x47671)),x47672)
% 188.07/187.96 [4768]~P77(x47681)+E(f323(f323(f79(x47681),x47682),f76(x47681)),x47682)
% 188.07/187.96 [4769]~P112(x47691)+E(f323(f323(f79(x47691),x47692),f76(x47691)),x47692)
% 188.07/187.96 [4770]~P112(x47701)+E(f323(f323(f78(x47701),x47702),f2(x47701)),x47702)
% 188.07/187.96 [4771]~P78(x47711)+E(f323(f323(f78(x47711),x47712),f2(x47711)),x47712)
% 188.07/187.96 [4772]~P72(x47721)+E(f323(f323(f78(x47721),x47722),f2(x47721)),x47722)
% 188.07/187.96 [4773]~P114(x47731)+E(f323(f323(f281(x47731),x47732),f76(x47731)),x47732)
% 188.07/187.96 [4774]~P57(x47741)+E(f323(f323(f36(x47741),x47742),f76(x47741)),x47742)
% 188.07/187.96 [4775]~P112(x47751)+E(f323(f323(f248(x47751),x47752),f2(a865)),f76(x47751))
% 188.07/187.96 [4776]~P110(x47761)+E(f323(f323(f248(x47761),x47762),f2(a865)),f76(x47761))
% 188.07/187.96 [4777]~E(x47772,f188(f872(x47771,a860)))+E(f323(f35(x47771),x47772),f2(a865))
% 188.07/187.96 [4788]~P57(x47881)+E(f42(x47881,x47882,f2(x47881)),x47882)
% 188.07/187.96 [4796]~P95(x47961)+E(f323(f323(f110(x47961),x47962),f246(x47961)),f246(x47961))
% 188.07/187.96 [4797]~P3(x47971)+E(f323(f323(f101(x47971),x47972),f188(x47971)),f188(x47971))
% 188.07/187.96 [4798]~P112(x47981)+E(f323(f323(f79(x47981),x47982),f2(x47981)),f2(x47981))
% 188.07/187.96 [4799]~P124(x47991)+E(f323(f323(f79(x47991),x47992),f2(x47991)),f2(x47991))
% 188.07/187.96 [4800]~P115(x48001)+E(f323(f323(f281(x48001),x48002),f2(x48001)),f2(x48001))
% 188.07/187.96 [4801]~P57(x48011)+E(f323(f323(f36(x48011),x48012),f2(x48011)),f2(x48011))
% 188.07/187.96 [4802]E(x48021,f200(x48022))+~E(f229(x48022,x48021),f188(f872(x48022,a860)))
% 188.07/187.96 [4804]~P57(x48041)+E(f42(x48041,x48042,f76(x48041)),f2(x48041))
% 188.07/187.96 [4805]~P57(x48051)+E(f42(x48051,f2(x48051),x48052),f2(x48051))
% 188.07/187.96 [4834]E(x48341,f2(a865))+E(f52(x48342,x48341,f113(x48342)),f113(f866(x48342)))
% 188.07/187.96 [4857]P38(x48571,x48572)+~E(f689(x48572,x48571),f188(f872(x48571,a860)))
% 188.07/187.96 [4858]E(x48581,f113(x48582))+~E(f323(f166(x48582),x48581),f188(f872(x48582,a860)))
% 188.07/187.96 [4859]E(x48591,f113(x48592))+~E(f188(f872(x48592,a860)),f323(f166(x48592),x48591))
% 188.07/187.96 [4862]~E(x48621,x48622)+P101(f323(f323(a320,x48621),x48622))
% 188.07/187.96 [4872]P101(x48721)+P101(f323(f323(a326,x48721),x48722))
% 188.07/187.96 [4873]E(x48731,f113(x48732))+E(f323(f323(f158(x48732),x48731),f2(a865)),f323(f134(x48732),x48731))
% 188.07/187.96 [4876]E(f145(x48761,x48762),x48762)+~P101(f323(f130(x48761),x48762))
% 188.07/187.96 [4881]~P101(x48812)+P101(f323(f323(a321,x48811),x48812))
% 188.07/187.96 [4882]~P101(x48821)+P101(f323(f323(a321,x48821),x48822))
% 188.07/187.96 [4883]~P101(x48832)+P101(f323(f323(a326,x48831),x48832))
% 188.07/187.96 [4893]~E(f532(x48932,x48931),f540(x48932,x48931))+P101(f323(f130(x48931),x48932))
% 188.07/187.96 [4900]E(f323(f243(x49001),x49002),f188(f872(x49001,a860)))+P101(f323(x49002,f329(x49002)))
% 188.07/187.96 [4901]E(f188(f872(x49011,a860)),f323(f243(x49011),x49012))+P101(f323(x49012,f330(x49012)))
% 188.07/187.96 [4967]~P116(x49671)+E(f323(f323(f79(x49671),x49672),f80(x49671,x49672)),f323(f73(x49671),x49672))
% 188.07/187.96 [4978]~E(x49781,f2(a1))+E(f43(x49781,x49782),f323(f323(f258(a1,a1),f2(a1)),f2(a1)))
% 188.07/187.96 [5009]~P54(x50091,x50092)+P54(x50091,f323(f278(x50091,x50091),x50092))
% 188.07/187.96 [5032]E(x50321,x50322)+~P101(f323(f323(a320,x50321),x50322))
% 188.07/187.96 [5043]P101(x50431)+~P101(f323(f323(a322,x50432),x50431))
% 188.07/187.96 [5044]P101(x50441)+~P101(f323(f323(a322,x50441),x50442))
% 188.07/187.96 [5049]~P106(x50491)+P101(f323(f323(f237(x50491),x50492),f246(x50491)))
% 188.07/187.96 [5053]E(x50531,x50532)+~E(f323(x50531,f425(x50532,x50531)),f323(x50532,f425(x50532,x50531)))
% 188.07/187.96 [5083]E(x50831,f2(a865))+E(f218(x50831,f42(a865,x50832,x50831)),f218(x50832,x50831))
% 188.07/187.96 [5088]~P103(x50881)+P16(x50881,f323(f323(f144(x50881),x50882),f113(x50881)))
% 188.07/187.96 [5090]E(x50901,f2(a1))+P101(f323(f46(x50902,x50901),f43(x50902,x50901)))
% 188.07/187.96 [5108]~E(x51081,x51082)+P101(f323(f323(f238(a865),x51081),f323(a112,x51082)))
% 188.07/187.96 [5118]~E(x51181,f2(a865))+P101(f323(f323(f238(a865),x51181),f323(a112,x51182)))
% 188.07/187.96 [5128]P101(f323(x51281,x51282))+P101(f323(f323(f237(a1),f2(a1)),f421(x51281)))
% 188.07/187.96 [5192]P54(x51921,x51922)+~P54(x51921,f323(f278(x51921,x51921),x51922))
% 188.07/187.96 [5194]~E(f42(a865,x51942,x51941),f2(a865))+E(f323(f323(f79(a865),x51941),f440(x51941,x51942)),x51942)
% 188.07/187.96 [5195]~E(f42(a1,x51952,x51951),f2(a1))+E(f323(f323(f79(a1),x51951),f441(x51951,x51952)),x51952)
% 188.07/187.96 [5219]~P101(f323(x52191,x52192))+P101(f323(f323(f237(a1),f2(a1)),f385(x52191)))
% 188.07/187.96 [5231]E(f323(f323(f22(a865),f323(a104,x52311)),f323(a104,x52312)),f323(a104,x52311))+~P101(f323(a193,x52312))
% 188.07/187.96 [5261]E(f271(x52611,x52612),f76(a99))+~P101(f323(f323(f237(a99),x52611),f76(a99)))
% 188.07/187.96 [5355]E(f323(f323(f158(x53551),x53552),f532(x53552,x53551)),f323(f323(f158(x53551),x53552),f540(x53552,x53551)))+P101(f323(f130(x53551),x53552))
% 188.07/187.96 [5400]~P101(f323(x54001,f88(x54002,x54001)))+P101(f323(x54001,f546(x54002,x54001)))
% 188.07/187.96 [5463]P56(x54631,x54632)+~P101(f323(f311(x54631,x54632),f671(x54632,x54631)))
% 188.07/187.96 [5607]~E(f323(a112,f42(a865,x56071,x56072)),x56072)+E(f42(a865,f323(a112,x56071),x56072),f2(a865))
% 188.07/187.96 [5664]P38(x56641,x56642)+P101(f323(f323(f325(x56641),f734(x56642,x56641)),f735(x56642,x56641)))
% 188.07/187.96 [5671]~P134(x56711)+P101(f323(f323(f325(x56711),f323(f100(x56711),x56712)),f109(x56711)))
% 188.07/187.96 [5672]~P140(x56721)+P101(f323(f323(f325(x56721),f323(f100(x56721),x56722)),f186(x56721)))
% 188.07/187.96 [5673]~P134(x56731)+P101(f323(f323(f325(x56731),f323(f102(x56731),x56732)),f109(x56731)))
% 188.07/187.96 [5674]~P90(x56741)+P101(f323(f323(f325(x56741),f323(f103(x56741),x56742)),f109(x56741)))
% 188.07/187.96 [5817]E(f323(a112,f42(a865,x58171,x58172)),x58172)+E(f42(a865,f323(a112,x58171),x58172),f323(a112,f42(a865,x58171,x58172)))
% 188.07/187.96 [6222]P38(x62221,x62222)+~P101(f323(f323(f325(x62221),f660(x62222,x62221)),f312(x62221,x62222)))
% 188.07/187.96 [6256]~P119(x62561)+~P101(f323(f323(f238(x62561),f323(f100(x62561),x62562)),f2(x62561)))
% 188.07/187.96 [6257]~P82(x62571)+~P101(f323(f323(f238(x62571),f323(f73(x62571),x62572)),f2(x62571)))
% 188.07/187.96 [6344]P101(f323(f323(f238(a1),x63441),f42(a1,x63442,x63441)))+~P101(f323(f323(f238(a1),x63441),f2(a1)))
% 188.07/187.96 [6441]E(f323(f323(f301(a865),f323(a112,x64411)),f294(a865,x64412,x64411)),f294(a865,x64412,f323(a112,x64411)))+~P101(f323(f323(f237(a865),x64412),f323(a112,x64411)))
% 188.07/187.96 [6529]~P103(x65291)+P16(x65291,f143(x65291,x65291,f5(x65291),x65292))
% 188.07/187.96 [6657]E(f323(f161(x66571),x66572),x66572)+~P101(f323(f323(f237(a865),f323(f189(f866(x66571)),x66572)),f76(a865)))
% 188.07/187.96 [6677]~P82(x66771)+P101(f323(f323(f237(x66771),f323(f77(x66771),f323(f73(x66771),x66772))),f2(x66771)))
% 188.07/187.96 [6709]~P38(x67091,x67092)+P38(x67091,f323(f323(f280(x67091,x67091,x67091),x67092),f299(x67091,x67092)))
% 188.07/187.96 [6929]~P101(f323(f323(f238(a1),x69292),f2(a1)))+P101(f323(f323(f237(a1),f42(a1,x69291,x69292)),f2(a1)))
% 188.07/187.96 [7320]~P140(x73201)+E(f190(x73201,f323(f323(f7(x73201,x73201,x73201),f78(x73201)),f76(x73201)),x73202,f2(x73201)),f323(f100(x73201),x73202))
% 188.07/187.96 [7348]~P121(x73481)+~P101(f323(f323(f238(x73481),f323(f323(f79(x73481),x73482),x73482)),f2(x73481)))
% 188.07/187.96 [9976]~P116(x99761)+~P101(f323(f323(f238(x99761),f323(f323(f248(x99761),x99762),f323(f103(a865),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(x99761)))
% 188.07/187.96 [4660]~E(x46602,f113(x46601))+E(f323(f189(f866(x46601)),x46602),f2(a865))
% 188.07/187.96 [4702]~E(x47021,f2(a865))+E(f323(f323(f78(a865),x47021),x47022),x47022)
% 188.07/187.96 [4703]~E(x47032,f2(a865))+E(f323(f323(f79(a865),x47031),x47032),f2(a865))
% 188.07/187.96 [4705]~E(x47051,f2(a865))+E(f323(f323(f79(a865),x47051),x47052),f2(a865))
% 188.07/187.96 [4706]~E(x47062,f2(a865))+E(f323(f323(f248(a865),x47061),x47062),f76(a865))
% 188.07/187.96 [4707]~E(x47072,f2(a1))+E(f323(f323(f36(a1),x47071),x47072),f2(a1))
% 188.07/187.96 [4717]E(x47171,f113(x47172))+~E(f323(f189(f866(x47172)),x47171),f2(a865))
% 188.07/187.96 [4718]~P2(x47181)+E(f323(f323(f110(x47181),x47182),x47182),x47182)
% 188.07/187.96 [4720]~P97(x47201)+E(f323(f323(f110(x47201),x47202),x47202),x47202)
% 188.07/187.96 [4721]~P2(x47211)+E(f323(f323(f101(x47211),x47212),x47212),x47212)
% 188.07/187.96 [4723]~P98(x47231)+E(f323(f323(f101(x47231),x47232),x47232),x47232)
% 188.07/187.96 [4725]~P93(x47251)+E(f323(f323(f79(x47251),x47252),x47252),x47252)
% 188.07/187.96 [4727]~P103(x47271)+E(f323(f323(f235(x47271),x47272),x47272),x47272)
% 188.07/187.96 [4729]~P103(x47291)+E(f323(f323(f236(x47291),x47292),x47292),x47292)
% 188.07/187.96 [4748]~P59(x47481)+E(f323(f323(f22(x47481),x47482),x47482),f2(x47481))
% 188.07/187.96 [4762]~P87(x47621)+E(f323(f77(x47621),f323(f77(x47621),x47622)),x47622)
% 188.07/187.96 [4763]~P59(x47631)+E(f323(f77(x47631),f323(f77(x47631),x47632)),x47632)
% 188.07/187.96 [4780]~E(x47802,f2(a865))+E(f323(f323(f248(a865),x47801),x47802),f323(a112,f2(a865)))
% 188.07/187.96 [4813]~P3(x48131)+E(f323(f323(f110(x48131),f188(x48131)),x48132),x48132)
% 188.07/187.96 [4814]~P95(x48141)+E(f323(f323(f101(x48141),f246(x48141)),x48142),x48142)
% 188.07/187.96 [4815]~P68(x48151)+E(f323(f323(f79(x48151),f76(x48151)),x48152),x48152)
% 188.07/187.96 [4816]~P77(x48161)+E(f323(f323(f79(x48161),f76(x48161)),x48162),x48162)
% 188.07/187.96 [4817]~P112(x48171)+E(f323(f323(f79(x48171),f76(x48171)),x48172),x48172)
% 188.07/187.96 [4818]~P112(x48181)+E(f323(f323(f78(x48181),f2(x48181)),x48182),x48182)
% 188.07/187.96 [4819]~P78(x48191)+E(f323(f323(f78(x48191),f2(x48191)),x48192),x48192)
% 188.07/187.96 [4820]~P72(x48201)+E(f323(f323(f78(x48201),f2(x48201)),x48202),x48202)
% 188.07/187.96 [4838]~P95(x48381)+E(f323(f323(f110(x48381),f246(x48381)),x48382),f246(x48381))
% 188.07/187.96 [4839]~P3(x48391)+E(f323(f323(f101(x48391),f188(x48391)),x48392),f188(x48391))
% 188.07/187.96 [4840]~P112(x48401)+E(f323(f323(f79(x48401),f2(x48401)),x48402),f2(x48401))
% 188.07/187.96 [4841]~P124(x48411)+E(f323(f323(f79(x48411),f2(x48411)),x48412),f2(x48411))
% 188.07/187.96 [4842]~P77(x48421)+E(f323(f323(f248(x48421),f76(x48421)),x48422),f76(x48421))
% 188.07/187.96 [4843]~P114(x48431)+E(f323(f323(f281(x48431),f2(x48431)),x48432),f2(x48431))
% 188.07/187.96 [4844]~P57(x48441)+E(f323(f323(f36(x48441),f2(x48441)),x48442),f2(x48441))
% 188.07/187.96 [4852]E(x48521,f113(x48522))+E(f137(x48522,f323(f162(x48522),x48521)),f323(f134(x48522),x48521))
% 188.07/187.96 [4853]E(x48531,f113(x48532))+E(f323(f134(x48532),f323(f162(x48532),x48531)),f137(x48532,x48531))
% 188.07/187.96 [4854]E(x48541,f2(a865))+~E(f323(f323(f78(a865),x48542),x48541),x48542)
% 188.07/187.96 [4860]~P134(x48601)+E(f323(f102(x48601),f323(f100(a1),x48602)),f323(f100(x48601),x48602))
% 188.07/187.96 [4861]~P90(x48611)+E(f323(f102(x48611),f323(f103(a1),x48612)),f323(f103(x48611),x48612))
% 188.07/187.96 [4868]E(x48681,f76(a865))+~E(f323(f323(f79(a865),x48682),x48681),f76(a865))
% 188.07/187.96 [4869]E(x48691,f76(a865))+~E(f323(f323(f79(a865),x48691),x48692),f76(a865))
% 188.07/187.96 [4870]E(x48701,f2(a865))+~E(f323(f323(f78(a865),x48702),x48701),f2(a865))
% 188.07/187.96 [4871]E(x48711,f2(a865))+~E(f323(f323(f78(a865),x48711),x48712),f2(a865))
% 188.07/187.96 [4886]~P82(x48861)+E(f323(f73(x48861),f323(f77(x48861),x48862)),f323(f73(x48861),x48862))
% 188.07/187.96 [4887]~P116(x48871)+E(f323(f73(x48871),f323(f100(x48871),x48872)),f323(f100(x48871),x48872))
% 188.07/187.96 [4888]~P82(x48881)+E(f323(f73(x48881),f323(f73(x48881),x48882)),f323(f73(x48881),x48882))
% 188.07/187.96 [4889]~P72(x48891)+E(f323(f159(x48891),f323(f162(x48891),x48892)),f323(f159(x48891),x48892))
% 188.07/187.96 [4894]~E(x48941,f323(a112,f2(a865)))+E(f323(f323(f248(a865),x48941),x48942),f323(a112,f2(a865)))
% 188.07/187.96 [4903]~P59(x49031)+E(f323(f323(f22(x49031),f2(x49031)),x49032),f323(f77(x49031),x49032))
% 188.07/187.96 [4904]~E(x49042,f2(a865))+E(f132(a865,f323(f293(a865,x49041),x49042)),f113(a865))
% 188.07/187.96 [4913]~P90(x49131)+E(f323(f323(f78(x49131),x49132),f323(f103(x49131),a81)),x49132)
% 188.07/187.96 [4914]E(x49141,f2(a1))+E(f44(f323(f73(a1),x49142),f323(f73(a1),x49141)),f50(x49142,x49141))
% 188.07/187.96 [4930]~E(x49301,x49302)+P101(f323(f323(f237(a865),x49301),x49302))
% 188.07/187.96 [4937]~E(x49371,f2(a99))+E(f323(f323(f78(a865),f323(a19,x49371)),x49372),x49372)
% 188.07/187.96 [4938]~E(f323(f103(a1),x49382),f323(f100(a1),x49381))+E(x49381,f323(a104,f323(f103(a1),x49382)))
% 188.07/187.96 [4947]~P7(x49471)+P7(f323(f323(f248(a1),x49471),x49472))
% 188.07/187.96 [4948]~P87(x49481)+E(f323(f323(f110(x49481),x49482),f323(f77(x49481),x49482)),f246(x49481))
% 188.07/187.96 [4949]~P87(x49491)+E(f323(f323(f101(x49491),x49492),f323(f77(x49491),x49492)),f188(x49491))
% 188.07/187.96 [4950]~P59(x49501)+E(f323(f323(f78(x49501),x49502),f323(f77(x49501),x49502)),f2(x49501))
% 188.07/187.96 [4975]E(x49751,f2(a865))+~E(f323(f77(a1),f323(f100(a1),x49752)),f323(f100(a1),x49751))
% 188.07/187.96 [4976]E(x49761,f2(a865))+~E(f323(f77(a1),f323(f100(a1),x49761)),f323(f100(a1),x49762))
% 188.07/187.96 [4986]E(f194(x49861,x49862),f2(a1))+P101(f323(f323(f237(a1),x49862),x49861))
% 188.07/187.96 [4987]E(f172(x49871,x49872),f113(a1))+P101(f323(f323(f237(a1),x49871),x49872))
% 188.07/187.96 [5000]E(x50001,f323(a112,f2(a865)))+~E(f323(f323(f79(a865),x50002),x50001),f323(a112,f2(a865)))
% 188.07/187.96 [5001]E(x50011,f323(a112,f2(a865)))+~E(f323(f323(f79(a865),x50011),x50012),f323(a112,f2(a865)))
% 188.07/187.96 [5002]~P102(x50021)+P101(f323(f323(f237(x50021),x50022),x50022))
% 188.07/187.96 [5003]~P92(x50031)+P101(f323(f323(f89(x50031),x50032),x50032))
% 188.07/187.96 [5006]~P90(x50061)+E(f323(f323(f79(x50061),x50062),f323(f103(x50061),a97)),f323(f77(x50061),x50062))
% 188.07/187.96 [5024]~P134(x50241)+E(f323(f77(x50241),f323(f102(x50241),x50242)),f323(f102(x50241),f323(f77(a1),x50242)))
% 188.07/187.96 [5025]~P90(x50251)+E(f323(f77(x50251),f323(f103(x50251),x50252)),f323(f103(x50251),f323(f77(a1),x50252)))
% 188.07/187.96 [5054]~E(x50541,f323(a112,x50542))+P101(f323(f323(f238(a865),f2(a865)),x50541))
% 188.07/187.96 [5071]~P103(x50711)+E(f323(f77(f872(x50711,a860)),f323(f244(x50711),x50712)),f323(f245(x50711),x50712))
% 188.07/187.96 [5072]~P103(x50721)+E(f323(f77(f872(x50721,a860)),f323(f295(x50721),x50722)),f323(f292(x50721),x50722))
% 188.07/187.96 [5073]~P103(x50731)+E(f323(f77(f872(x50731,a860)),f323(f245(x50731),x50732)),f323(f244(x50731),x50732))
% 188.07/187.96 [5074]~P103(x50741)+E(f323(f77(f872(x50741,a860)),f323(f292(x50741),x50742)),f323(f295(x50741),x50742))
% 188.07/187.96 [5082]~E(f323(f100(a1),x50822),x50821)+P101(f323(f323(f237(a1),f2(a1)),x50821))
% 188.07/187.96 [5089]~E(x50892,f2(a1))+E(f50(x50891,x50892),f323(f323(f258(a1,a1),f2(a1)),f323(f73(a1),x50891)))
% 188.07/187.96 [5091]~P1(x50911)+P101(f323(f323(f237(x50911),f188(x50911)),x50912))
% 188.07/187.96 [5123]E(x51231,x51232)+~E(f323(f323(f78(a1),x51231),x51231),f323(f323(f78(a1),x51232),x51232))
% 188.07/187.96 [5127]~P101(f323(x51271,x51272))+P101(f323(x51271,f323(a104,f385(x51271))))
% 188.07/187.96 [5153]~P116(x51531)+E(f323(f323(f79(x51531),f80(x51531,x51532)),f323(f73(x51531),x51532)),x51532)
% 188.07/187.96 [5160]~E(x51602,f2(a865))+E(f83(f871(a865,a865),f45(x51601,x51602)),f323(f323(f258(a865,a865),f2(a865)),x51601))
% 188.07/187.96 [5165]~E(x51651,x51652)+~P101(f323(f323(f238(a865),x51651),x51652))
% 188.07/187.96 [5166]~E(x51661,x51662)+~P101(f323(f323(f238(a1),x51661),x51662))
% 188.07/187.96 [5169]~P140(x51691)+E(f323(f323(f78(x51691),f76(x51691)),f323(f100(x51691),x51692)),f323(f100(x51691),f323(a112,x51692)))
% 188.07/187.96 [5173]~E(x51731,f2(a865))+~P101(f323(f323(f238(a865),x51732),x51731))
% 188.07/187.96 [5189]E(f145(x51891,x51892),x51892)+~E(f323(f189(f866(x51891)),f145(x51891,x51892)),f323(f189(f866(x51891)),x51892))
% 188.07/187.96 [5190]E(f323(f35(x51901),f323(f166(x51901),x51902)),f323(f189(f866(x51901)),x51902))+~P101(f323(f130(x51901),x51902))
% 188.07/187.96 [5199]~P101(f323(x51991,f374(x51991)))+P101(f323(x51991,f323(f100(a1),x51992)))
% 188.07/187.96 [5210]E(f172(x52101,x52102),f113(a1))+~P101(f323(f323(f238(a1),x52102),x52101))
% 188.07/187.96 [5211]E(f271(x52111,x52112),f76(a99))+~P101(f323(f323(f238(a99),x52112),x52111))
% 188.07/187.96 [5212]~P105(x52121)+E(f294(x52121,x52122,x52122),f323(f323(f301(x52121),x52122),f188(f872(x52121,a860))))
% 188.07/187.96 [5234]~E(f323(f323(f22(a865),x52341),x52342),f2(a865))+P101(f323(f323(f237(a865),x52341),x52342))
% 188.07/187.96 [5235]~E(f323(f323(f22(a1),x52351),x52352),f2(a1))+P101(f323(f323(f89(a1),x52351),x52352))
% 188.07/187.96 [5258]~E(x52582,f2(a865))+E(f52(x52581,x52582,f113(x52581)),f323(f323(f144(f866(x52581)),f113(x52581)),f113(f866(x52581))))
% 188.07/187.96 [5262]~P102(x52621)+~P101(f323(f323(f238(x52621),x52622),x52622))
% 188.07/187.96 [5265]~E(f42(a1,x52651,x52652),f2(a1))+E(f42(a1,x52651,f323(f77(a1),x52652)),f2(a1))
% 188.07/187.96 [5267]~E(f42(a1,x52671,x52672),f2(a1))+E(f42(a1,f323(f77(a1),x52671),x52672),f2(a1))
% 188.07/187.96 [5275]E(f323(f293(a865,x52751),f323(a112,x52752)),f188(f872(a865,a860)))+P101(f323(f323(f237(a865),x52751),x52752))
% 188.07/187.96 [5296]E(f132(a865,f323(f293(a865,x52961),x52962)),f113(a865))+P101(f323(f323(f238(a865),x52961),x52962))
% 188.07/187.96 [5301]~E(f323(f35(x53011),f323(f166(x53011),x53012)),f323(f189(f866(x53011)),x53012))+P101(f323(f130(x53011),x53012))
% 188.07/187.96 [5306]~P101(f323(f130(x53061),x53062))+P101(f323(f130(x53061),f323(f161(x53061),x53062)))
% 188.07/187.96 [5307]~P101(f323(f130(x53071),x53072))+P101(f323(f130(x53071),f323(f165(x53071),x53072)))
% 188.07/187.96 [5308]~P101(f323(f130(x53081),x53082))+P101(f323(f130(x53081),f323(f162(x53081),x53082)))
% 188.07/187.96 [5315]P101(f323(x53151,x53152))+~P101(f323(x53151,f323(a104,f421(x53151))))
% 188.07/187.96 [5316]P101(f323(f323(f237(a865),x53162),x53161))+P101(f323(f323(f237(a865),x53161),x53162))
% 188.07/187.96 [5317]P101(f323(f323(f237(a1),x53172),x53171))+P101(f323(f323(f237(a1),x53171),x53172))
% 188.07/187.96 [5319]~P82(x53191)+P101(f323(f323(f237(x53191),x53192),f323(f73(x53191),x53192)))
% 188.07/187.96 [5322]P101(f323(x53221,f381(x53221)))+~P101(f323(x53221,f323(f100(a1),x53222)))
% 188.07/187.96 [5347]E(f323(f323(f22(a865),x53471),x53472),f2(a865))+~P101(f323(f323(f237(a865),x53471),x53472))
% 188.07/187.96 [5348]E(f323(f323(f22(a1),x53481),x53482),f2(a1))+~P101(f323(f323(f89(a1),x53481),x53482))
% 188.07/187.96 [5349]E(f323(f323(f36(a865),x53491),x53492),f2(a865))+~P101(f323(f323(f238(a865),x53491),x53492))
% 188.07/187.96 [5367]E(f42(a865,x53671,x53672),x53671)+~P101(f323(f323(f238(a865),x53671),x53672))
% 188.07/187.96 [5376]E(f42(a1,x53761,f323(f77(a1),x53762)),f282(x53761,x53762))+P101(f323(f323(f237(a1),f2(a1)),x53762))
% 188.07/187.96 [5388]E(f323(f323(f22(a1),x53881),x53882),f194(x53881,x53882))+~P101(f323(f323(f237(a1),x53882),x53881))
% 188.07/187.96 [5407]P101(f323(f323(f237(a1),f2(a1)),f374(x54071)))+P101(f323(x54071,f323(f100(a1),x54072)))
% 188.07/187.96 [5419]~P5(x54191)+P101(f323(f323(f325(x54191),x54192),f323(f166(x54191),f53(x54191))))
% 188.07/187.96 [5421]~P119(x54211)+P101(f323(f323(f237(x54211),f2(x54211)),f323(f100(x54211),x54212)))
% 188.07/187.96 [5422]~P82(x54221)+P101(f323(f323(f237(x54221),f2(x54221)),f323(f73(x54221),x54222)))
% 188.07/187.96 [5449]E(f323(f323(f78(a865),x54491),f805(x54492,x54491)),x54492)+~P101(f323(f323(f237(a865),x54491),x54492))
% 188.07/187.96 [5461]~E(f323(f103(a1),x54611),f323(f100(a1),x54612))+P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x54611)))
% 188.07/187.96 [5464]E(f294(a1,x54641,x54642),f188(f872(a1,a860)))+~P101(f323(f323(f238(a1),x54642),x54641))
% 188.07/187.96 [5467]~P116(x54671)+E(f323(f323(f79(x54671),f323(f73(x54671),x54672)),f323(f73(x54671),x54672)),f323(f323(f79(x54671),x54672),x54672))
% 188.07/187.96 [5472]E(f132(a865,f323(f293(a865,x54721),f323(a112,x54722))),f113(a865))+P101(f323(f323(f237(a865),x54721),x54722))
% 188.07/187.96 [5476]E(f323(f323(f36(a1),x54761),x54762),f283(x54761,x54762))+~P101(f323(f323(f237(a1),f2(a1)),x54762))
% 188.07/187.96 [5496]P101(f323(f130(x54961),x54962))+~P101(f323(f130(x54961),f323(f161(x54961),x54962)))
% 188.07/187.96 [5497]P101(f323(f130(x54971),x54972))+~P101(f323(f130(x54971),f323(f162(x54971),x54972)))
% 188.07/187.96 [5518]P101(f323(f59(a865),x55181))+P101(f323(f323(f325(a865),f806(x55181,x55182)),x55181))
% 188.07/187.96 [5519]P101(f323(f59(a865),x55191))+P101(f323(f323(f325(a865),f817(x55191,x55192)),x55191))
% 188.07/187.96 [5520]P101(f323(f323(f238(a865),x55202),f323(a112,x55201)))+P101(f323(f323(f238(a865),x55201),x55202))
% 188.07/187.96 [5521]E(f42(a1,x55211,x55212),f282(x55211,x55212))+~P101(f323(f323(f237(a1),f2(a1)),x55212))
% 188.07/187.96 [5524]E(f132(a865,f323(f293(a865,x55241),x55242)),f113(a865))+~P101(f323(f323(f237(a865),x55242),x55241))
% 188.07/187.96 [5525]~P75(x55251)+E(f323(f302(x55251,x55251,f77(x55251)),f323(f244(x55251),x55252)),f323(f295(x55251),f323(f77(x55251),x55252)))
% 188.07/187.96 [5526]~P75(x55261)+E(f323(f302(x55261,x55261,f77(x55261)),f323(f295(x55261),x55262)),f323(f244(x55261),f323(f77(x55261),x55262)))
% 188.07/187.96 [5527]~P75(x55271)+E(f323(f302(x55271,x55271,f77(x55271)),f323(f245(x55271),x55272)),f323(f292(x55271),f323(f77(x55271),x55272)))
% 188.07/187.96 [5528]~P75(x55281)+E(f323(f302(x55281,x55281,f77(x55281)),f323(f292(x55281),x55282)),f323(f245(x55281),f323(f77(x55281),x55282)))
% 188.07/187.96 [5539]E(x55391,f188(f872(x55392,a860)))+P101(f323(f323(f325(x55392),f442(x55391,x55392)),x55391))
% 188.07/187.96 [5540]E(x55401,f188(f872(x55402,a860)))+P101(f323(f323(f325(x55402),f464(x55401,x55402)),x55401))
% 188.07/187.96 [5551]~P101(f323(f323(f238(a865),x55511),x55512))+P101(f323(f323(f237(a865),x55511),x55512))
% 188.07/187.96 [5552]~P101(f323(f323(f238(a1),x55521),x55522))+P101(f323(f323(f237(a1),x55521),x55522))
% 188.07/187.96 [5568]E(f44(x55681,x55682),f323(f323(f258(a1,a1),f2(a1)),x55681))+~P101(f323(f323(f238(a1),x55681),x55682))
% 188.07/187.96 [5570]E(f217(f323(f77(a1),x55701),f323(f77(a1),x55702)),f217(x55701,x55702))+~P101(f323(f323(f238(a1),x55702),f2(a1)))
% 188.07/187.96 [5581]E(x55811,x55812)+~E(f323(a3,f323(a112,f323(a19,x55811))),f323(a3,f323(a112,f323(a19,x55812))))
% 188.07/187.96 [5586]E(f44(x55861,x55862),f323(f323(f258(a1,a1),f2(a1)),x55861))+~P101(f323(f323(f237(a1),x55862),f2(a1)))
% 188.07/187.96 [5613]E(f42(a865,f323(f103(a865),x56131),f323(f103(a865),x56132)),f2(a865))+~P101(f323(a193,f323(f103(a1),x56131)))
% 188.07/187.96 [5628]P101(f323(f323(f237(a1),f2(a1)),f381(x56281)))+~P101(f323(x56281,f323(f100(a1),x56282)))
% 188.07/187.96 [5662]P39(f294(a1,x56621,x56622))+~P101(f323(f323(f237(a1),f2(a1)),x56621))
% 188.07/187.96 [5667]~P101(f323(f59(x56671),x56672))+P101(f323(f59(f872(x56671,a860)),f323(f300(x56671),x56672)))
% 188.07/187.96 [5680]E(f323(f323(f78(a1),x56801),f323(f100(a1),f376(x56802,x56801))),x56802)+~P101(f323(f323(f237(a1),x56801),x56802))
% 188.07/187.96 [5688]P101(f323(f323(f237(a865),x56881),x56882))+P101(f323(f323(f237(a865),f323(a112,x56882)),x56881))
% 188.07/187.96 [5731]E(f323(f323(f36(a865),f323(f103(a865),x57311)),f323(f103(a865),x57312)),f2(a865))+~P101(f323(a193,f323(f103(a1),x57311)))
% 188.07/187.96 [5732]E(f323(f323(f79(a865),f323(f103(a865),x57321)),f323(f103(a865),x57322)),f2(a865))+~P101(f323(f323(f238(a1),x57321),a81))
% 188.07/187.96 [5734]P101(f323(f323(f237(a865),x57341),f323(a112,x57342)))+~P101(f323(f323(f237(a865),x57341),x57342))
% 188.07/187.96 [5736]P101(f323(f323(f238(a865),x57361),f323(a112,x57362)))+~P101(f323(f323(f237(a865),x57361),x57362))
% 188.07/187.96 [5738]P101(f323(f323(f238(a865),x57381),f323(a112,x57382)))+~P101(f323(f323(f238(a865),x57381),x57382))
% 188.07/187.96 [5741]~E(x57411,x57412)+P101(f323(f323(f238(a1),x57411),f323(f323(f78(a1),x57412),f76(a1))))
% 188.07/187.96 [5744]E(f42(a1,x57441,x57442),f2(a1))+E(f323(f323(f22(a1),x57442),f42(a1,x57441,x57442)),f42(a1,f323(f77(a1),x57441),x57442))
% 188.07/187.96 [5753]E(x57531,f113(x57532))+P101(f323(f323(f325(x57532),f137(x57532,x57531)),f323(f166(x57532),x57531)))
% 188.07/187.96 [5765]E(f83(f871(a865,a865),f45(x57651,x57652)),f323(f323(f258(a865,a865),f2(a865)),x57651))+~P101(f323(f323(f238(a865),x57651),x57652))
% 188.07/187.96 [5798]E(f323(f323(f22(a865),f323(f103(a865),x57981)),f323(f103(a865),x57982)),f323(f103(a865),x57981))+~P101(f323(f323(f238(a1),x57982),a81))
% 188.07/187.96 [5799]E(f323(f323(f78(a865),f323(f103(a865),x57991)),f323(f103(a865),x57992)),f323(f103(a865),x57992))+~P101(f323(f323(f238(a1),x57991),a81))
% 188.07/187.96 [5804]E(f323(a112,f323(f323(f78(a865),x58041),f820(x58042,x58041))),x58042)+~P101(f323(f323(f238(a865),x58041),x58042))
% 188.07/187.96 [5827]P101(f323(x58271,x58272))+~P101(f323(x58271,f323(a87,f683(x58272,x58271))))
% 188.07/187.96 [5835]~P101(f323(f323(f238(a865),x58351),f323(a112,x58352)))+P101(f323(f323(f237(a865),x58351),x58352))
% 188.07/187.96 [5881]E(f323(f323(f301(a865),x58811),f323(f293(a865,x58812),x58811)),f323(f293(a865,x58812),f323(a112,x58811)))+~P101(f323(f323(f237(a865),x58812),x58811))
% 188.07/187.96 [5883]E(x58831,f113(x58832))+E(f323(f323(f121(x58832),f114(x58832,x58831)),f323(f323(f144(x58832),f137(x58832,x58831)),f113(x58832))),x58831)
% 188.07/187.96 [5897]P101(f323(f59(x58971),x58972))+~P101(f323(f323(f238(a865),f2(a865)),f323(f35(x58971),x58972)))
% 188.07/187.96 [5899]~E(x58991,f188(f872(x58992,a860)))+~P101(f323(f323(f238(a865),f2(a865)),f323(f35(x58992),x58991)))
% 188.07/187.96 [5911]~P101(f323(f323(f238(a865),x59111),x59112))+P101(f323(f323(f237(a865),f323(a112,x59111)),x59112))
% 188.07/187.96 [5918]~P103(x59181)+E(f143(x59181,x59181,f5(x59181),f145(x59181,x59182)),f132(x59181,f323(f166(x59181),x59182)))
% 188.07/187.96 [5921]E(x59211,f113(x59212))+P101(f323(f323(f325(x59212),f323(f134(x59212),x59211)),f323(f166(x59212),x59211)))
% 188.07/187.96 [5927]~P119(x59271)+P101(f323(f323(f238(x59271),x59272),f323(f323(f78(x59271),x59272),f76(x59271))))
% 188.07/187.96 [5929]~P82(x59291)+P101(f323(f323(f237(x59291),f323(f77(x59291),x59292)),f323(f73(x59291),x59292)))
% 188.07/187.96 [5959]P101(f323(f59(a865),x59591))+~P101(f323(f323(f237(a865),f806(x59591,x59592)),x59592))
% 188.07/187.96 [5960]P101(f323(f59(a865),x59601))+~P101(f323(f323(f238(a865),f817(x59601,x59602)),x59602))
% 188.07/187.96 [5963]~P101(f323(f59(f871(x59631,x59631)),x59632))+P101(f323(f59(x59631),f323(f276(x59631),x59632)))
% 188.07/187.96 [6016]~P101(f323(f323(f238(a865),x60162),f323(a112,x60161)))+~P101(f323(f323(f238(a865),x60161),x60162))
% 188.07/187.96 [6017]~P105(x60171)+E(f323(f323(f101(f872(x60171,a860)),f323(f292(x60171),x60172)),f323(f245(x60171),x60172)),f323(f323(f301(x60171),x60172),f188(f872(x60171,a860))))
% 188.07/187.96 [6030]P101(f323(f59(x60301),x60302))+~P101(f323(f59(f872(x60301,a860)),f323(f300(x60301),x60302)))
% 188.07/187.96 [6054]P101(f323(f323(f237(a865),f323(a112,x60541)),f323(a112,x60542)))+~P101(f323(f323(f237(a865),x60541),x60542))
% 188.07/187.96 [6055]P101(f323(f323(f237(a865),f323(a19,x60551)),f323(a19,x60552)))+~P101(f323(f323(f237(a99),x60551),x60552))
% 188.07/187.96 [6056]P101(f323(f323(f237(a99),f323(a3,x60561)),f323(a3,x60562)))+~P101(f323(f323(f237(a865),x60561),x60562))
% 188.07/187.96 [6058]P101(f323(f323(f238(a865),f323(a112,x60581)),f323(a112,x60582)))+~P101(f323(f323(f238(a865),x60581),x60582))
% 188.07/187.96 [6059]P101(f323(f323(f238(a865),f323(a19,x60591)),f323(a19,x60592)))+~P101(f323(f323(f238(a99),x60591),x60592))
% 188.07/187.96 [6060]P101(f323(f323(f238(a99),f323(a3,x60601)),f323(a3,x60602)))+~P101(f323(f323(f238(a865),x60601),x60602))
% 188.07/187.96 [6063]E(x60631,x60632)+~E(f323(f302(a865,a1,f100(a1)),x60631),f323(f302(a865,a1,f100(a1)),x60632))
% 188.07/187.96 [6079]P101(f323(f323(f237(a865),x60791),x60792))+~P101(f323(f323(f237(a865),f323(a112,x60791)),x60792))
% 188.07/187.96 [6082]P101(f323(f323(f238(a865),x60821),x60822))+~P101(f323(f323(f237(a865),f323(a112,x60821)),x60822))
% 188.07/187.96 [6083]P101(f323(f323(f238(a865),x60831),x60832))+~P101(f323(f323(f238(a865),f323(a112,x60831)),x60832))
% 188.07/187.96 [6098]E(f42(a1,x60981,x60982),f2(a1))+E(f323(f323(f22(a1),f42(a1,x60981,x60982)),x60982),f42(a1,x60981,f323(f77(a1),x60982)))
% 188.07/187.96 [6162]E(f323(f35(f872(x61621,a860)),f323(f300(x61621),x61622)),f323(f323(f248(a865),f323(a112,f323(a112,f2(a865)))),f323(f35(x61621),x61622)))+~P101(f323(f59(x61621),x61622))
% 188.07/187.96 [6165]E(x61651,f113(x61652))+E(f323(f323(f158(x61652),x61651),f323(f323(f22(a865),f323(f189(f866(x61652)),x61651)),f76(a865))),f137(x61652,x61651))
% 188.07/187.96 [6190]E(x61901,f113(x61902))+E(f323(f323(f121(x61902),f323(f165(x61902),x61901)),f323(f323(f144(x61902),f323(f134(x61902),x61901)),f113(x61902))),f323(f161(x61902),x61901))
% 188.07/187.96 [6219]~P101(f323(f59(x62191),f37(f872(x62191,a860),x62192)))+P101(f323(f59(f872(x62191,a860)),x62192))
% 188.07/187.96 [6241]P101(f323(f323(f237(a865),f323(f103(a865),x62411)),f323(f103(a865),x62412)))+~P101(f323(f323(f237(a1),x62411),a81))
% 188.07/187.96 [6258]~P101(f323(f323(f238(a1),x62581),x62582))+P101(f323(f323(f237(a1),x62581),f323(f323(f22(a1),x62582),f76(a1))))
% 188.07/187.96 [6259]~P101(f323(f323(f237(a1),x62591),x62592))+P101(f323(f323(f238(a1),x62591),f323(f323(f78(a1),x62592),f76(a1))))
% 188.07/187.96 [6260]~P101(f323(f323(f238(a1),x62601),x62602))+P101(f323(f323(f238(a1),x62601),f323(f323(f78(a1),x62602),f76(a1))))
% 188.07/187.96 [6262]~P101(f323(f323(f237(a1),x62621),x62622))+P101(f323(f323(f237(a865),f323(f103(a865),x62621)),f323(f103(a865),x62622)))
% 188.07/187.96 [6264]~P101(f323(f323(f237(a865),x62641),x62642))+P101(f323(f323(f237(a1),f323(f100(a1),x62641)),f323(f100(a1),x62642)))
% 188.07/187.96 [6265]~P101(f323(f323(f237(a1),x62651),x62652))+P101(f323(f323(f237(a1),f323(f103(a1),x62651)),f323(f103(a1),x62652)))
% 188.07/187.96 [6267]~P101(f323(f323(f238(a865),x62671),x62672))+P101(f323(f323(f238(a1),f323(f100(a1),x62671)),f323(f100(a1),x62672)))
% 188.07/187.96 [6268]~P101(f323(f323(f238(a1),x62681),x62682))+P101(f323(f323(f238(a1),f323(f103(a1),x62681)),f323(f103(a1),x62682)))
% 188.07/187.96 [6269]~P101(f323(f323(f89(a1),x62691),x62692))+P101(f323(f323(f89(a1),f323(f103(a1),x62691)),f323(f103(a1),x62692)))
% 188.07/187.96 [6287]~P101(f323(f323(f237(a865),x62871),x62872))+~P101(f323(f323(f237(a865),f323(a112,x62872)),x62871))
% 188.07/187.96 [6329]~P101(f323(f323(f237(a865),f323(a112,x63291)),f323(a112,x63292)))+P101(f323(f323(f237(a865),x63291),x63292))
% 188.07/187.96 [6330]~P101(f323(f323(f237(a99),f323(a3,x63301)),f323(a3,x63302)))+P101(f323(f323(f237(a865),x63301),x63302))
% 188.07/187.96 [6331]~P101(f323(f323(f237(a865),f323(a19,x63311)),f323(a19,x63312)))+P101(f323(f323(f237(a99),x63311),x63312))
% 188.07/187.96 [6333]~P101(f323(f323(f238(a865),f323(a112,x63331)),f323(a112,x63332)))+P101(f323(f323(f238(a865),x63331),x63332))
% 188.07/187.96 [6334]~P101(f323(f323(f238(a99),f323(a3,x63341)),f323(a3,x63342)))+P101(f323(f323(f238(a865),x63341),x63342))
% 188.07/187.96 [6335]~P101(f323(f323(f238(a865),f323(a104,x63351)),f323(a104,x63352)))+P101(f323(f323(f238(a1),x63351),x63352))
% 188.07/187.96 [6336]~P101(f323(f323(f238(a865),f323(a19,x63361)),f323(a19,x63362)))+P101(f323(f323(f238(a99),x63361),x63362))
% 188.07/187.96 [6376]~P101(f323(f323(f238(a865),f323(a104,x63762)),f323(a104,x63761)))+P101(f323(f323(f238(a1),f2(a1)),x63761))
% 188.07/187.96 [6407]P101(f323(f323(f237(a1),f2(a1)),f42(a1,x64071,x64072)))+~P101(f323(f323(f238(a1),f2(a1)),x64072))
% 188.07/187.96 [6564]P38(x65641,x65642)+~E(f323(f323(f280(x65641,x65641,x65641),x65642),x65642),f188(f872(f871(x65641,x65641),a860)))
% 188.07/187.96 [6576]~P38(x65761,x65762)+P38(x65761,f323(f323(f280(x65761,x65761,x65761),x65762),x65762))
% 188.07/187.96 [6587]P101(f323(f323(f237(a1),x65871),x65872))+~P101(f323(f323(f238(a1),x65871),f323(f323(f78(a1),x65872),f76(a1))))
% 188.07/187.96 [6588]P101(f323(f323(f238(a1),x65881),x65882))+~P101(f323(f323(f237(a1),x65881),f323(f323(f22(a1),x65882),f76(a1))))
% 188.07/187.96 [6591]P101(f323(f323(f237(a865),x65911),x65912))+~P101(f323(f323(f237(a1),f323(f100(a1),x65911)),f323(f100(a1),x65912)))
% 188.07/187.96 [6592]P101(f323(f323(f237(a1),x65921),x65922))+~P101(f323(f323(f237(a1),f323(f103(a1),x65921)),f323(f103(a1),x65922)))
% 188.07/187.96 [6594]P101(f323(f323(f238(a865),x65941),x65942))+~P101(f323(f323(f238(a1),f323(f100(a1),x65941)),f323(f100(a1),x65942)))
% 188.07/187.96 [6595]P101(f323(f323(f238(a1),x65951),x65952))+~P101(f323(f323(f238(a865),f323(f103(a865),x65951)),f323(f103(a865),x65952)))
% 188.07/187.96 [6596]P101(f323(f323(f238(a1),x65961),x65962))+~P101(f323(f323(f238(a1),f323(f103(a1),x65961)),f323(f103(a1),x65962)))
% 188.07/187.96 [6597]P101(f323(f323(f89(a1),x65971),x65972))+~P101(f323(f323(f89(a1),f323(f103(a1),x65971)),f323(f103(a1),x65972)))
% 188.07/187.96 [6690]~E(f581(x66902,x66901),f113(x66901))+E(f323(f135(f866(x66901),f866(x66901),f121(x66901),f113(x66901)),x66902),f113(x66901))
% 188.07/187.96 [6691]~E(f582(x66912,x66911),f113(x66911))+E(f323(f135(f866(x66911),f866(x66911),f121(x66911),f113(x66911)),x66912),f113(x66911))
% 188.07/187.96 [6697]~P6(x66971)+E(f323(f135(x66971,x66971,f110(x66971),f188(x66971)),x66972),f37(x66971,f323(f166(x66971),x66972)))
% 188.07/187.96 [6698]~P6(x66981)+E(f323(f135(x66981,x66981,f101(x66981),f246(x66981)),x66982),f38(x66981,f323(f166(x66981),x66982)))
% 188.07/187.96 [6710]E(x67101,f2(a99))+E(f323(f323(f78(a865),f323(a19,f323(f323(f22(a99),x67101),f76(a99)))),f323(a112,x67102)),f323(f323(f78(a865),f323(a19,x67101)),x67102))
% 188.07/187.96 [6760]P101(f323(f323(f238(a1),f323(f323(f22(a1),x67601),x67602)),f2(a1)))+~P101(f323(f323(f238(a1),x67601),x67602))
% 188.07/187.96 [6788]~P103(x67881)+E(f323(f323(f110(f872(x67881,a860)),f323(f323(f301(x67881),x67882),f188(f872(x67881,a860)))),f323(f295(x67881),x67882)),f323(f245(x67881),x67882))
% 188.07/187.96 [6862]~P56(x68621,x68622)+P38(x68621,f323(f243(f871(x68621,x68621)),f323(f262(x68621,x68621,a860),x68622)))
% 188.07/187.96 [6863]~P56(x68631,x68632)+P54(x68631,f323(f243(f871(x68631,x68631)),f323(f262(x68631,x68631,a860),x68632)))
% 188.07/187.96 [6864]E(x68641,f188(f872(x68642,a860)))+~P101(f323(f323(f237(f872(x68642,a860)),x68641),f188(f872(x68642,a860))))
% 188.07/187.96 [6945]~P101(f323(f323(f238(a865),f2(a865)),x69452))+P101(f323(f323(f237(a865),f42(a865,x69451,x69452)),x69452))
% 188.07/187.96 [6946]~P101(f323(f323(f237(a1),f2(a1)),x69461))+P101(f323(f323(f237(a1),f42(a1,x69461,x69462)),x69461))
% 188.07/187.96 [6947]~P101(f323(f323(f238(a865),f2(a865)),x69472))+P101(f323(f323(f238(a865),f42(a865,x69471,x69472)),x69472))
% 188.07/187.96 [6949]~P101(f323(f323(f238(a1),f2(a1)),x69492))+P101(f323(f323(f238(a1),f42(a1,x69491,x69492)),x69492))
% 188.07/187.96 [7025]~P105(x70251)+E(f323(f323(f22(f872(x70251,a860)),f323(f323(f301(x70251),x70252),f188(f872(x70251,a860)))),f323(f244(x70251),x70252)),f323(f323(f301(x70251),x70252),f188(f872(x70251,a860))))
% 188.07/187.96 [7098]~P49(x70981,x70982)+P40(x70981,f246(f872(x70981,a860)),f323(f243(f871(x70981,x70981)),f323(f262(x70981,x70981,a860),x70982)))
% 188.07/187.96 [7099]P101(f323(x70991,x70992))+P101(f323(f323(f325(f872(f871(a865,a865),a860)),f683(x70992,x70991)),a98))
% 188.07/187.96 [7144]E(f323(f323(f121(a865),f132(a865,f323(f293(a865,x71441),x71442))),f323(f323(f144(a865),x71442),f113(a865))),f132(a865,f323(f293(a865,x71441),f323(a112,x71442))))+~P101(f323(f323(f237(a865),x71441),x71442))
% 188.07/187.96 [7285]E(x72851,f2(a865))+~E(f323(f135(a865,a865,f78(a865),x72851),x72852),f2(a865))
% 188.07/187.96 [7310]~P101(f323(f323(f238(a1),f323(f323(f22(a1),x73101),x73102)),f2(a1)))+P101(f323(f323(f238(a1),x73101),x73102))
% 188.07/187.96 [7339]P38(x73391,x73392)+~P38(x73391,f323(f323(f280(x73391,x73391,x73391),x73392),x73392))
% 188.07/187.96 [7368]~P101(f323(f323(f237(a865),f323(a112,x73681)),x73682))+P101(f185(a860,a241,f323(f237(a865),x73681),x73682))
% 188.07/187.96 [7524]P27(a865,a865,f323(f323(f7(a865,a865,a865),f22(a865)),x75241),x75242)+P101(f323(f323(f325(a865),f337(x75241,x75242)),x75242))
% 188.07/187.96 [7580]E(f323(f323(f323(f63(a865,x75801,f78(a865)),f323(f16(a865,x75801),f76(a865))),f2(a865)),x75802),f323(f35(x75801),x75802))+~P101(f323(f59(x75801),x75802))
% 188.07/187.96 [7622]P27(a865,a865,f323(f323(f7(a865,a865,a865),f22(a865)),x76221),x76222)+~P101(f323(f323(f237(a865),x76221),f337(x76221,x76222)))
% 188.07/187.96 [7680]P38(x76801,x76802)+P101(f323(f323(f237(f872(x76801,a860)),f689(x76802,x76801)),f323(f277(x76801,x76801,x76802),f689(x76802,x76801))))
% 188.07/187.96 [7685]P56(x76851,x76852)+~P38(x76851,f323(f243(f871(x76851,x76851)),f323(f262(x76851,x76851,a860),x76852)))
% 188.07/187.96 [7753]P101(f323(f323(f237(a865),f323(a112,x77531)),x77532))+~P101(f185(a860,a241,f323(f237(a865),x77531),x77532))
% 188.07/187.96 [7808]P101(f323(f323(f325(f871(a865,a865)),f323(f323(f258(a865,a865),x78081),x78082)),f299(a865,a313)))+~P101(f323(f323(f237(a865),x78081),x78082))
% 188.07/187.96 [7909]P49(x79091,x79092)+~P40(x79091,f246(f872(x79091,a860)),f323(f243(f871(x79091,x79091)),f323(f262(x79091,x79091,a860),x79092)))
% 188.07/187.96 [7963]~P101(f323(f130(x79631),x79632))+P101(f323(f130(f872(x79631,a860)),f323(f323(f147(f866(x79631),f872(x79631,a860)),f166(x79631)),f51(x79631,x79632))))
% 188.07/187.96 [8162]~P38(x81621,f323(f278(x81621,x81621),x81622))+P38(x81621,f323(f278(x81621,x81621),f323(f323(f280(x81621,x81621,x81621),x81622),f299(x81621,x81622))))
% 188.07/187.96 [8260]P28(x82601,a865,f467(x82602,x82601),x82602,f323(f293(a865,f2(a865)),f323(f35(x82601),x82602)))+~P101(f323(f59(x82601),x82602))
% 188.07/187.96 [8261]P28(a865,x82611,f468(x82612,x82611),f323(f293(a865,f2(a865)),f323(f35(x82611),x82612)),x82612)+~P101(f323(f59(x82611),x82612))
% 188.07/187.96 [8278]P28(a865,x82781,f456(x82782,x82781),f294(a865,f76(a865),f323(f35(x82781),x82782)),x82782)+~P101(f323(f59(x82781),x82782))
% 188.07/187.96 [8287]P101(f323(f59(f871(x82871,x82871)),f323(f323(f280(x82871,x82871,x82871),x82872),f299(x82871,x82872))))+~P101(f323(f59(f871(x82871,x82871)),x82872))
% 188.07/187.96 [8318]E(x83181,f2(a1))+P101(f323(f46(x83182,x83181),f323(f323(f258(a1,a1),f323(f323(f36(a1),x83182),x83181)),f42(a1,x83182,x83181))))
% 188.07/187.96 [8332]~P101(f323(f323(f325(f871(a865,a865)),f323(f323(f258(a865,a865),x83321),x83322)),f299(a865,a313)))+P101(f323(f323(f237(a865),x83321),x83322))
% 188.07/187.96 [8347]~P78(x83471)+E(f323(f135(x83471,x83471,f323(f7(x83471,x83471,x83471),f78(x83471)),f2(x83471)),f323(f162(x83471),x83472)),f323(f135(x83471,x83471,f78(x83471),f2(x83471)),x83472))
% 188.07/187.96 [8514]~P103(x85141)+E(f323(f135(f866(x85141),x85141,f323(f7(x85141,f866(x85141),f866(x85141)),f141(x85141,x85141,f5(x85141))),f113(x85141)),x85142),f143(x85141,x85141,f5(x85141),x85142))
% 188.07/187.96 [8629]~P54(x86291,f323(f243(f871(x86291,x86291)),f323(f262(x86291,x86291,a860),x86292)))+P54(x86291,f323(f243(f871(x86291,x86291)),f323(f262(x86291,x86291,a860),f247(x86291,x86291,x86292))))
% 188.07/187.96 [8643]P101(f323(f323(f325(f871(a865,a865)),f323(f323(f258(a865,a865),x86431),x86432)),f323(f323(f280(a865,a865,a865),a313),f299(a865,a313))))+~P101(f323(f323(f238(a865),x86431),x86432))
% 188.07/187.96 [8689]~P101(f323(f59(f871(x86891,x86891)),f323(f323(f280(x86891,x86891,x86891),x86892),f299(x86891,x86892))))+P101(f323(f59(f871(x86891,x86891)),x86892))
% 188.07/187.96 [8748]~P54(x87481,f323(f243(f871(x87481,x87481)),f323(f262(x87481,x87481,a860),f247(x87481,x87481,x87482))))+P54(x87481,f323(f243(f871(x87481,x87481)),f323(f262(x87481,x87481,a860),x87482)))
% 188.07/187.96 [8943]P54(x89431,x89432)+P101(f323(f323(f325(f871(x89431,x89431)),f323(f323(f258(x89431,x89431),f726(x89432,x89431)),f726(x89432,x89431))),f323(f323(f280(x89431,x89431,x89431),x89432),f299(x89431,x89432))))
% 188.07/187.96 [8944]P54(x89441,x89442)+P101(f323(f323(f325(f871(x89441,x89441)),f323(f323(f258(x89441,x89441),f740(x89442,x89441)),f740(x89442,x89441))),f323(f323(f280(x89441,x89441,x89441),x89442),f299(x89441,x89442))))
% 188.07/187.96 [9064]~P101(f323(f323(f325(f871(a865,a865)),f323(f323(f258(a865,a865),x90641),x90642)),f323(f323(f280(a865,a865,a865),a313),f299(a865,a313))))+P101(f323(f323(f238(a865),x90641),x90642))
% 188.07/187.96 [5067]~P90(x50671)+E(f323(f323(f78(x50671),f323(f103(x50671),a81)),x50672),x50672)
% 188.07/187.96 [5096]~P87(x50961)+E(f323(f323(f110(x50961),f323(f77(x50961),x50962)),x50962),f246(x50961))
% 188.07/187.96 [5097]~P87(x50971)+E(f323(f323(f101(x50971),f323(f77(x50971),x50972)),x50972),f188(x50971))
% 188.07/187.96 [5098]~P59(x50981)+E(f323(f323(f78(x50981),f323(f77(x50981),x50982)),x50982),f2(x50981))
% 188.07/187.96 [5099]~P60(x50991)+E(f323(f323(f78(x50991),f323(f77(x50991),x50992)),x50992),f2(x50991))
% 188.07/187.96 [5131]~P90(x51311)+E(f323(f323(f79(x51311),f323(f103(x51311),a97)),x51312),f323(f77(x51311),x51312))
% 188.07/187.96 [5289]~P109(x52891)+E(f323(f323(f79(x52891),f323(f77(x52891),f76(x52891))),x52892),f323(f77(x52891),x52892))
% 188.07/187.96 [5332]E(f323(f73(a1),x53321),f76(a1))+~E(f323(f73(a1),f323(f323(f79(a1),x53321),x53322)),f76(a1))
% 188.07/187.96 [5424]~P90(x54241)+E(f323(f323(f78(x54241),f76(x54241)),f323(f103(x54241),x54242)),f323(f103(x54241),f323(f323(f22(a1),x54242),a97)))
% 188.07/187.96 [5477]~P2(x54771)+E(f11(x54771,f323(f323(f301(x54771),x54772),f188(f872(x54771,a860)))),x54772)
% 188.07/187.96 [5478]~P2(x54781)+E(f10(x54781,f323(f323(f301(x54781),x54782),f188(f872(x54781,a860)))),x54782)
% 188.07/187.97 [5479]~P103(x54791)+E(f14(x54791,f323(f323(f301(x54791),x54792),f188(f872(x54791,a860)))),x54792)
% 188.07/187.97 [5480]~P103(x54801)+E(f15(x54801,f323(f323(f301(x54801),x54802),f188(f872(x54801,a860)))),x54802)
% 188.07/187.97 [5481]~P6(x54811)+E(f37(x54811,f323(f323(f301(x54811),x54812),f188(f872(x54811,a860)))),x54812)
% 188.07/187.97 [5482]~P6(x54821)+E(f38(x54821,f323(f323(f301(x54821),x54822),f188(f872(x54821,a860)))),x54822)
% 188.07/187.97 [5504]E(f323(f323(f78(a865),x55041),f323(f323(f22(a865),x55042),x55041)),x55042)+P101(f323(f323(f238(a865),x55042),x55041))
% 188.07/187.97 [5534]E(x55341,f113(x55342))+P101(f323(f323(f238(a865),f2(a865)),f323(f189(f866(x55342)),x55341)))
% 188.07/187.97 [5659]~P103(x56591)+E(f12(x56591,f235(x56591),f323(f323(f301(x56591),x56592),f188(f872(x56591,a860)))),x56592)
% 188.07/187.97 [5660]~P103(x56601)+E(f13(x56601,f236(x56601),f323(f323(f301(x56601),x56602),f188(f872(x56601,a860)))),x56602)
% 188.07/187.97 [5721]E(f323(f323(f22(a865),x57211),f323(f323(f22(a865),x57211),x57212)),x57212)+~P101(f323(f323(f237(a865),x57212),x57211))
% 188.07/187.97 [5722]E(f323(f323(f78(a865),x57221),f323(f323(f22(a865),x57222),x57221)),x57222)+~P101(f323(f323(f237(a865),x57221),x57222))
% 188.07/187.97 [5743]E(f42(a865,f323(f323(f22(a865),x57431),x57432),x57432),f42(a865,x57431,x57432))+P101(f323(f323(f238(a865),x57431),x57432))
% 188.07/187.97 [5754]E(f323(f77(a1),f323(f323(f36(a1),x57541),f323(f77(a1),x57542))),f283(x57541,x57542))+P101(f323(f323(f237(a1),f2(a1)),x57542))
% 188.07/187.97 [5756]~E(x57562,f2(a865))+P101(f323(f323(f238(a865),f2(a865)),f323(f323(f248(a865),x57561),x57562)))
% 188.07/187.97 [5807]~P90(x58071)+E(f323(f323(f78(x58071),f323(f77(x58071),f76(x58071))),f323(f103(x58071),x58072)),f323(f103(x58071),f323(f323(f78(a1),x58072),a97)))
% 188.07/187.97 [5808]E(f323(f323(f248(a865),f323(f103(a865),x58081)),x58082),f323(f323(f248(a865),f2(a865)),x58082))+~P101(f323(a193,f323(f103(a1),x58081)))
% 188.07/187.97 [5903]E(f323(f134(a865),f132(a865,f323(f293(a865,x59031),x59032))),x59031)+~P101(f323(f323(f238(a865),x59031),x59032))
% 188.07/187.97 [5922]E(f323(f323(f79(a865),f323(f103(a865),x59221)),f323(f103(a865),x59222)),f323(f103(a865),f323(f323(f79(a1),x59221),x59222)))+P101(f323(f323(f238(a1),x59221),a81))
% 188.07/187.97 [5928]~P121(x59281)+P101(f323(f323(f237(x59281),f2(x59281)),f323(f323(f79(x59281),x59282),x59282)))
% 188.07/187.97 [5940]E(f323(f323(f22(a865),f323(a112,x59401)),x59402),f323(a112,f323(f323(f22(a865),x59401),x59402)))+~P101(f323(f323(f237(a865),x59402),x59401))
% 188.07/187.97 [5943]E(f42(a865,f323(f323(f22(a865),x59431),x59432),x59432),f42(a865,x59431,x59432))+~P101(f323(f323(f237(a865),x59432),x59431))
% 188.07/187.97 [5991]E(f323(f323(f248(a865),f323(a104,x59911)),x59912),f323(a104,f323(f323(f248(a1),x59911),x59912)))+~P101(f323(f323(f237(a1),f2(a1)),x59911))
% 188.07/187.97 [6007]P101(f323(f130(x60071),x60072))+P101(f323(f323(f238(a865),f532(x60072,x60071)),f323(f189(f866(x60071)),x60072)))
% 188.07/187.97 [6008]P101(f323(f130(x60081),x60082))+P101(f323(f323(f238(a865),f540(x60082,x60081)),f323(f189(f866(x60081)),x60082)))
% 188.07/187.97 [6023]~E(x60231,f113(x60232))+~P101(f323(f323(f238(a865),f2(a865)),f323(f189(f866(x60232)),x60231)))
% 188.07/187.97 [6037]E(f137(a865,f132(a865,f323(f293(a865,x60371),x60372))),f323(f323(f22(a865),x60372),f76(a865)))+~P101(f323(f323(f238(a865),x60371),x60372))
% 188.07/187.97 [6040]E(f323(f323(f78(a1),x60401),f323(f100(a1),f323(a112,f360(x60402,x60401)))),x60402)+~P101(f323(f323(f238(a1),x60401),x60402))
% 188.07/187.97 [6047]E(x60471,f2(a865))+E(f323(f323(f79(a865),x60472),f323(f323(f248(a865),x60472),f323(f323(f22(a865),x60471),f76(a865)))),f323(f323(f248(a865),x60472),x60471))
% 188.07/187.97 [6073]E(f323(f323(f79(a865),f323(a104,x60731)),f323(a104,x60732)),f323(a104,f323(f323(f79(a1),x60731),x60732)))+~P101(f323(f323(f237(a1),f2(a1)),x60731))
% 188.07/187.97 [6074]E(f323(f323(f36(a865),f323(a104,x60741)),f323(a104,x60742)),f323(a104,f323(f323(f36(a1),x60741),x60742)))+~P101(f323(f323(f237(a1),f2(a1)),x60741))
% 188.07/187.97 [6088]~P112(x60881)+E(f323(f323(f78(x60881),x60882),x60882),f323(f323(f79(x60881),f323(f323(f78(x60881),f76(x60881)),f76(x60881))),x60882))
% 188.07/187.97 [6105]E(f323(f323(f22(a1),f323(f100(a1),x61051)),f323(f100(a1),x61052)),f323(f100(a1),f323(f323(f22(a865),x61051),x61052)))+~P101(f323(f323(f237(a865),x61052),x61051))
% 188.07/187.97 [6107]E(f323(f323(f258(a1,a1),f323(f103(a1),a97)),f323(f323(f78(a1),x61071),x61072)),f47(x61071,x61072))+~P101(f323(f323(f237(a1),x61072),f2(a1)))
% 188.07/187.97 [6141]E(f173(x61411,x61412),f113(f866(x61411)))+P101(f323(f323(f325(f866(x61411)),f545(x61412,x61411)),f323(f166(f866(x61411)),x61412)))
% 188.07/187.97 [6225]E(f323(f323(f144(a1),x62251),f172(f323(f323(f78(a1),x62251),f76(a1)),x62252)),f172(x62251,x62252))+~P101(f323(f323(f237(a1),x62251),x62252))
% 188.07/187.97 [6261]~P101(f323(f323(f238(a865),x62612),x62611))+P101(f323(f323(f238(a865),f2(a865)),f323(f323(f22(a865),x62611),x62612)))
% 188.07/187.97 [6292]~P101(f323(f323(f238(a865),x62921),f323(a104,x62922)))+P101(f323(f323(f238(a1),f323(f100(a1),x62921)),x62922))
% 188.07/187.97 [6321]~P103(x63211)+E(f323(f323(f110(f872(x63211,a860)),f323(f244(x63211),x63212)),f323(f323(f301(x63211),x63212),f188(f872(x63211,a860)))),f323(f292(x63211),x63212))
% 188.07/187.97 [6322]~P101(f323(f323(f237(a1),f2(a1)),x63221))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f248(a1),x63221),x63222)))
% 188.07/187.97 [6325]~P101(f323(f323(f238(a865),f2(a865)),x63251))+P101(f323(f323(f238(a865),f2(a865)),f323(f323(f248(a865),x63251),x63252)))
% 188.07/187.97 [6352]~E(f323(x63521,f2(a865)),f2(a865))+E(f323(f323(f6(a865,a865),x63521),f294(a865,f323(a112,f2(a865)),x63522)),f323(f323(f6(a865,a865),x63521),f294(a865,f2(a865),x63522)))
% 188.07/187.97 [6415]~P90(x64151)+E(f323(f323(f79(x64151),f323(f323(f78(x64151),f76(x64151)),f76(x64151))),f323(f103(x64151),x64152)),f323(f103(x64151),f323(f323(f78(a1),x64152),x64152)))
% 188.07/187.97 [6430]E(f323(f323(f301(a1),x64301),f294(a1,f323(f323(f78(a1),x64301),f76(a1)),x64302)),f294(a1,x64301,x64302))+P101(f323(f323(f238(a1),x64302),x64301))
% 188.07/187.97 [6431]P101(f323(f323(f238(a865),x64311),f323(a104,x64312)))+~P101(f323(f323(f238(a1),f323(f100(a1),x64311)),x64312))
% 188.07/187.97 [6532]E(f323(a104,f323(f323(f36(a1),f323(f103(a1),x65321)),f323(f103(a1),x65322))),f323(f323(f36(a865),f323(f103(a865),x65321)),f323(f103(a865),x65322)))+P101(f323(a193,f323(f103(a1),x65321)))
% 188.07/187.97 [6589]P101(f323(f323(f238(a865),x65891),x65892))+~P101(f323(f323(f238(a865),f2(a865)),f323(f323(f22(a865),x65892),x65891)))
% 188.07/187.97 [6633]P101(f323(f323(f238(a865),f2(a865)),x66331))+~P101(f323(f323(f238(a865),f2(a865)),f323(f323(f79(a865),x66332),x66331)))
% 188.07/187.97 [6634]P101(f323(f323(f238(a865),f2(a865)),x66341))+~P101(f323(f323(f238(a865),f2(a865)),f323(f323(f79(a865),x66341),x66342)))
% 188.07/187.97 [6651]~P101(f323(f323(f237(a1),x66511),f2(a1)))+E(f323(f323(f79(a865),f323(a104,f323(f77(a1),x66511))),f323(a104,f323(f77(a1),x66512))),f323(a104,f323(f323(f79(a1),x66511),x66512)))
% 188.07/187.97 [6708]~E(x67082,f188(f872(x67081,a860)))+P101(f323(f323(f237(f872(x67081,a860)),x67082),f323(f77(f872(x67081,a860)),x67082)))
% 188.07/187.97 [6771]~P90(x67711)+E(f323(f323(f78(x67711),f323(f323(f78(x67711),f2(x67711)),f323(f103(x67711),x67712))),f323(f103(x67711),x67712)),f323(f103(x67711),f323(f323(f78(a1),x67712),x67712)))
% 188.07/187.97 [6828]~P101(f323(f323(f238(a1),x68281),x68282))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x68281),f76(a1))),x68282))
% 188.07/187.97 [6892]E(x68921,f2(a865))+~P101(f323(f323(f237(a1),f323(f100(a1),x68922)),f323(f77(a1),f323(f100(a1),x68921))))
% 188.07/187.97 [6893]E(x68931,f2(a865))+~P101(f323(f323(f237(a1),f323(f100(a1),x68931)),f323(f77(a1),f323(f100(a1),x68932))))
% 188.07/187.97 [6996]E(f323(f323(f258(a1,a1),f323(f103(a1),a97)),f323(f323(f78(a1),x69961),x69962)),f47(x69961,x69962))+~P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),x69961),x69962)))
% 188.07/187.97 [7038]~P29(x70381,x70382)+P38(x70381,f323(f257(f872(f871(x70381,x70381),a860),f872(f871(x70381,x70381),a860)),x70382))
% 188.07/187.97 [7056]~P101(f323(f323(f237(a865),f323(a112,f2(a865))),x70561))+P101(f323(f323(f237(a865),f323(a112,f2(a865))),f323(f323(f248(a865),x70561),x70562)))
% 188.07/187.97 [7226]~P101(f323(f323(f237(a1),x72261),x72262))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x72261),x72261)),f323(f323(f78(a1),x72262),x72262)))
% 188.07/187.97 [7231]~P101(f323(f323(f238(a1),x72311),x72312))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x72311),x72311)),f323(f323(f78(a1),x72312),x72312)))
% 188.07/187.97 [7232]~P101(f323(f323(f89(a1),x72321),x72322))+P101(f323(f323(f89(a1),f323(f323(f78(a1),x72321),x72321)),f323(f323(f78(a1),x72322),x72322)))
% 188.07/187.97 [7287]~P101(f323(f323(f238(a865),f2(a865)),x72871))+P101(f323(f323(f238(a865),f323(f323(f22(a865),x72871),f323(a112,x72872))),x72871))
% 188.07/187.97 [7321]P101(f323(f323(f237(a865),f323(a112,f2(a865))),x73211))+~P101(f323(f323(f237(a865),f323(a112,f2(a865))),f323(f323(f79(a865),x73212),x73211)))
% 188.07/187.97 [7322]P101(f323(f323(f237(a865),f323(a112,f2(a865))),x73221))+~P101(f323(f323(f237(a865),f323(a112,f2(a865))),f323(f323(f79(a865),x73221),x73222)))
% 188.07/187.97 [7326]P101(f323(f323(f237(a865),f323(f323(f158(a865),x73261),x73262)),f323(f159(a865),x73261)))+~P101(f323(f323(f238(a865),x73262),f323(f189(f866(a865)),x73261)))
% 188.07/187.97 [7367]P101(f323(f323(f238(a1),x73671),x73672))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),x73671),f76(a1))),x73672))
% 188.07/187.97 [7411]P101(f323(f59(x74111),f246(f872(x74111,a860))))+~P101(f323(f59(f872(x74112,x74111)),f246(f872(f872(x74112,x74111),a860))))
% 188.07/187.97 [7412]P101(f323(f59(x74121),f246(f872(x74121,a860))))+~P101(f323(f59(f870(x74122,x74121)),f246(f872(f870(x74122,x74121),a860))))
% 188.07/187.97 [7413]P101(f323(f59(x74131),f246(f872(x74131,a860))))+~P101(f323(f59(f870(x74131,x74132)),f246(f872(f870(x74131,x74132),a860))))
% 188.07/187.97 [7454]E(x74541,f188(f872(x74542,a860)))+~P101(f323(f323(f237(f872(x74542,a860)),x74541),f323(f77(f872(x74542,a860)),x74541)))
% 188.07/187.97 [7590]E(f323(f135(f866(x75901),f866(x75901),f121(x75901),f113(x75901)),x75902),f113(x75901))+P101(f323(f323(f325(f866(x75901)),f581(x75902,x75901)),f323(f166(f866(x75901)),x75902)))
% 188.07/187.97 [7591]E(f323(f135(f866(x75911),f866(x75911),f121(x75911),f113(x75911)),x75912),f113(x75911))+P101(f323(f323(f325(f866(x75911)),f582(x75912,x75911)),f323(f166(f866(x75911)),x75912)))
% 188.07/187.97 [7827]P101(f323(f323(f237(a1),x78271),x78272))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),x78271),x78271)),f323(f323(f78(a1),x78272),x78272)))
% 188.07/187.97 [7832]P101(f323(f323(f238(a1),x78321),x78322))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),x78321),x78321)),f323(f323(f78(a1),x78322),x78322)))
% 188.07/187.97 [7833]P101(f323(f323(f89(a1),x78331),x78332))+~P101(f323(f323(f89(a1),f323(f323(f78(a1),x78331),x78331)),f323(f323(f78(a1),x78332),x78332)))
% 188.07/187.97 [7929]~P112(x79291)+E(f323(f323(f79(x79291),f323(f323(f78(x79291),f76(x79291)),f76(x79291))),f323(f323(f6(a865,x79291),f100(x79291)),f294(a865,f76(a865),x79292))),f323(f323(f79(x79291),f323(f100(x79291),x79292)),f323(f323(f78(x79291),f323(f100(x79291),x79292)),f76(x79291))))
% 188.07/187.97 [7977]P101(f323(f323(f325(a865),x79771),x79772))+~P101(f323(f323(f325(a1),f323(f100(a1),x79771)),f323(f302(a865,a1,f100(a1)),x79772)))
% 188.07/187.97 [8134]~P101(f323(f59(x81341),x81342))+E(f323(f302(a865,x81341,f833(x81342,x81341)),f323(f243(a865),f323(f323(f7(a865,a865,a860),f238(a865)),f834(x81342,x81341)))),x81342)
% 188.07/187.97 [8418]P42(x84181,x84182)+P101(f323(f323(f325(f871(x84181,x84181)),f323(f323(f258(x84181,x84181),f518(x84182,x84181)),f518(x84182,x84181))),x84182))
% 188.07/187.97 [8558]~P90(x85581)+E(f323(f323(f22(x85581),f76(x85581)),f323(f103(x85581),x85582)),f323(f103(x85581),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f77(a1),x85582))))
% 188.07/187.97 [8560]~P26(a859,a874,f323(f323(f301(f864(a859)),f323(f323(f323(f90(a859),x85601),a875),x85602)),f188(f872(f864(a859),a860))))+~P101(f323(f323(a876,a687),f801(x85601,x85602)))
% 188.07/187.97 [8686]~P101(f323(f323(f238(f872(a865,a860)),x86861),x86862))+P101(f323(f323(f238(f872(a1,a860)),f323(f302(a865,a1,f100(a1)),x86861)),f323(f302(a865,a1,f100(a1)),x86862)))
% 188.07/187.97 [8720]~P101(f323(f323(f238(a1),x87201),x87202))+P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x87201),x87201)),a97)),f323(f323(f78(a1),x87202),x87202)))
% 188.07/187.97 [8722]~P101(f323(f323(f238(a1),x87221),x87222))+P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x87221),x87221)),a97)),f323(f323(f78(a1),x87222),x87222)))
% 188.07/187.97 [8796]~P101(f323(f323(f325(a865),x87961),f323(f166(a865),x87962)))+P101(f323(f323(f237(a865),x87961),f323(f135(a865,a865,f78(a865),f2(a865)),x87962)))
% 188.07/187.97 [8888]P46(x88881,x88882)+~P101(f323(f323(f325(f871(x88881,x88881)),f323(f323(f258(x88881,x88881),f506(x88882,x88881)),f506(x88882,x88881))),x88882))
% 188.07/187.97 [9025]~P101(f323(f323(f237(f872(a1,a860)),f323(f302(a865,a1,f100(a1)),x90251)),f323(f302(a865,a1,f100(a1)),x90252)))+P101(f323(f323(f237(f872(a865,a860)),x90251),x90252))
% 188.07/187.97 [9026]~P101(f323(f323(f238(f872(a1,a860)),f323(f302(a865,a1,f100(a1)),x90261)),f323(f302(a865,a1,f100(a1)),x90262)))+P101(f323(f323(f238(f872(a865,a860)),x90261),x90262))
% 188.07/187.97 [9110]P101(f323(f323(f238(a1),x91101),x91102))+~P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x91101),x91101)),a97)),f323(f323(f78(a1),x91102),x91102)))
% 188.07/187.97 [9112]P101(f323(f323(f238(a1),x91121),x91122))+~P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x91121),x91121)),a97)),f323(f323(f78(a1),x91122),x91122)))
% 188.07/187.97 [10016]~P101(f323(f59(x100161),x100162))+E(f323(f189(f866(x100161)),f88(f866(x100161),f323(f323(f18(f866(x100161),a860,a860),f323(f323(f8(a860,f872(a860,a860),f866(x100161)),a322),f323(f323(f7(f866(x100161),f872(x100161,a860),a860),f323(f323(f8(f872(x100161,a860),f872(f872(x100161,a860),a860),f866(x100161)),a320),f166(x100161))),x100162))),f130(x100161)))),f216(x100161,x100162))
% 188.07/187.97 [6036]E(f323(f323(f78(a865),f323(f323(f22(a865),x60361),x60362)),x60362),x60361)+~P101(f323(f323(f237(a865),x60362),x60361))
% 188.07/187.97 [6101]E(f323(f323(f36(a865),f323(f323(f79(a865),x61011),x61012)),x61012),x61011)+~P101(f323(f323(f238(a865),f2(a865)),x61012))
% 188.07/187.97 [6102]E(f323(f323(f36(a865),f323(f323(f79(a865),x61021),x61022)),x61021),x61022)+~P101(f323(f323(f238(a865),f2(a865)),x61021))
% 188.07/187.97 [6106]~P72(x61061)+E(f323(f323(f6(a865,x61061),f323(f158(x61061),x61062)),f323(f293(a865,f2(a865)),f323(f189(f866(x61061)),x61062))),f323(f159(x61061),x61062))
% 188.07/187.97 [6217]E(f42(a865,f323(a112,f323(f323(f79(a865),x62171),x62172)),x62171),f76(a865))+~P101(f323(f323(f238(a865),f76(a865)),x62171))
% 188.07/187.97 [6223]E(f323(a112,f323(f323(f78(a865),f323(f103(a865),x62231)),x62232)),f323(f323(f78(a865),f76(a865)),x62232))+~P101(f323(a193,f323(f103(a1),x62231)))
% 188.07/187.97 [6250]E(f323(a104,f323(f323(f248(a1),f323(f103(a1),x62501)),x62502)),f323(f323(f248(a865),f323(f103(a865),x62501)),x62502))+P101(f323(a193,f323(f103(a1),x62501)))
% 188.07/187.97 [6484]E(f323(f323(f22(a865),x64841),f323(f103(a865),f323(f323(f78(a1),x64842),a97))),f323(f323(f22(a865),f323(a112,x64841)),f323(f103(a865),x64842)))+~P101(f323(f323(f238(a1),a81),x64842))
% 188.07/187.97 [6563]E(x65631,f2(a865))+E(f323(a112,f323(f323(f78(a865),f323(f323(f22(a865),x65631),f76(a865))),x65632)),f323(f323(f78(a865),x65631),x65632))
% 188.07/187.97 [6603]E(x66031,f2(a1))+P101(f323(f323(f238(a1),f2(a1)),f323(f323(f248(a1),f323(f73(a1),x66031)),x66032)))
% 188.07/187.97 [6618]~E(x66182,f2(a865))+P101(f323(f323(f238(a1),f2(a1)),f323(f323(f248(a1),f323(f73(a1),x66181)),x66182)))
% 188.07/187.97 [6655]E(x66551,f2(a865))+E(f323(f323(f78(a865),x66552),f323(f323(f79(a865),f323(f323(f22(a865),x66551),f76(a865))),x66552)),f323(f323(f79(a865),x66551),x66552))
% 188.07/187.97 [6702]~P101(f323(f323(f237(a1),x67021),x67022))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x67021),a97)),x67022))
% 188.07/187.97 [6831]E(f323(f323(f144(a865),x68311),f132(a865,f323(f293(a865,f323(a112,x68311)),x68312))),f132(a865,f323(f293(a865,x68311),x68312)))+~P101(f323(f323(f238(a865),x68311),x68312))
% 188.07/187.97 [7029]E(x70291,x70292)+~E(f323(f323(f22(a1),f323(f323(f78(a1),x70291),x70291)),a97),f323(f323(f22(a1),f323(f323(f78(a1),x70292),x70292)),a97))
% 188.07/187.97 [7032]E(x70321,f113(x70322))+E(f267(x70322,f323(f323(f147(x70322,f871(a99,x70322)),f323(f258(a99,x70322),f76(a99))),x70321)),f274(x70322,x70321))
% 188.07/187.97 [7256]P101(f323(f323(f237(a1),x72561),x72562))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),x72561),a97)),x72562))
% 188.07/187.97 [7733]~P101(f323(f323(f238(a865),x77331),x77332))+P101(f323(f323(f325(f871(a865,a865)),f323(f323(f258(a865,a865),x77331),x77332)),a242))
% 188.07/187.97 [7954]~P101(f323(f323(f238(a99),f2(a99)),x79541))+P101(f323(f323(f238(a99),f323(f257(a99,f871(a99,a99)),f323(f268(x79541),x79542))),x79541))
% 188.07/187.97 [8264]~P82(x82641)+P101(f323(f323(f237(x82641),f323(f73(x82641),f323(f159(x82641),x82642))),f323(f159(x82641),f323(f323(f147(x82641,x82641),f73(x82641)),x82642))))
% 188.07/187.97 [8289]P101(f323(f323(f238(a865),x82891),x82892))+~P101(f323(f323(f325(f871(a865,a865)),f323(f323(f258(a865,a865),x82891),x82892)),a242))
% 188.07/187.97 [8438]E(f323(f323(f258(x84381,x84381),f738(x84382,x84381)),f738(x84382,x84381)),x84382)+~P101(f323(f323(f325(f871(x84381,x84381)),x84382),f299(x84381,f188(f872(f871(x84381,x84381),a860)))))
% 188.07/187.97 [8480]E(f323(f293(a865,x84801),f323(f323(f78(a865),x84801),f323(f35(a865),x84802))),x84802)+~P101(f323(f323(f237(f872(a865,a860)),x84802),f323(f293(a865,x84801),f323(f323(f78(a865),x84801),f323(f35(a865),x84802)))))
% 188.07/187.97 [8834]E(f323(f323(f36(a1),f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),x88341),x88341)),a97))),f323(f103(a1),f323(f323(f78(a1),x88342),x88342))),f323(f323(f36(a1),f323(f103(a1),x88341)),f323(f103(a1),x88342)))+~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x88342)))
% 188.07/187.97 [8954]E(f171(f866(x89541),f323(f323(f8(a860,a860,f866(x89541)),a318),f323(f323(f7(f866(x89541),f866(x89541),a860),a320),f113(x89541))),x89542),f173(x89541,f173(x89541,x89542)))+~P16(a865,f323(f162(a865),f323(f323(f147(f866(x89541),a865),f189(f866(x89541))),x89542)))
% 188.07/187.97 [8957]E(f323(f323(f36(a1),f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),x89571),x89571)),a97))),f323(f103(a1),f323(f323(f78(a1),x89572),x89572))),f323(f323(f36(a1),f323(f323(f78(a1),f323(f103(a1),x89571)),f76(a1))),f323(f103(a1),x89572)))+P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x89572)))
% 188.07/187.97 [9795]P101(f323(a193,x97952))+E(f323(f323(f84(a1,a865),f323(f323(f22(a1),x97951),x97952)),f323(f323(f18(a1,a865,a865),f323(f323(f7(a1,a865,f872(a865,a865)),f323(f323(f8(a860,f872(a865,f872(a865,a865)),a1),f96(a865)),a193)),f2(a865))),a104)),f323(f323(f22(a865),f323(a104,x97951)),f323(a104,x97952)))
% 188.07/187.97 [9804]E(f323(f323(f84(a1,a865),f323(f103(a1),f323(f323(f78(a1),x98041),f323(f77(a1),x98042)))),f323(f323(f18(a1,a865,a865),f323(f323(f7(a1,a865,f872(a865,a865)),f323(f323(f8(a860,f872(a865,f872(a865,a865)),a1),f96(a865)),a193)),f2(a865))),a104)),f323(f323(f22(a865),f323(f103(a865),x98041)),f323(f103(a865),x98042)))+P101(f323(f323(f238(a1),x98042),a81))
% 188.07/187.97 [9805]~P29(x98051,x98052)+P101(f323(f323(f237(f872(f871(x98051,x98051),a860)),f323(f323(f280(x98051,x98051,x98051),f323(f257(f872(f871(x98051,x98051),a860),f872(f871(x98051,x98051),a860)),x98052)),f323(f261(f872(f871(x98051,x98051),a860),f872(f871(x98051,x98051),a860)),x98052))),f323(f257(f872(f871(x98051,x98051),a860),f872(f871(x98051,x98051),a860)),x98052)))
% 188.07/187.97 [9868]~E(f323(f35(a865),f323(f243(a865),f323(f323(f18(a865,a860,a860),f323(f323(f8(a860,f872(a860,a860),a865),a322),f323(f323(f7(a865,f872(a865,a860),a860),f325(a865)),x98681))),f323(f323(f7(a865,a865,a860),f238(a865)),f323(a112,x98682))))),f2(a865))+~P101(f323(f323(f325(a865),f2(a865)),x98681))
% 188.07/187.97 [9924]E(f42(a1,f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),x99241),x99241)),a97)),f323(f103(a1),f323(f323(f78(a1),x99242),x99242))),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),x99241),f323(f103(a1),x99242)))),f76(a1)))+~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x99242)))
% 188.07/187.97 [9933]E(f42(a1,f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),x99331),x99331)),a97)),f323(f103(a1),f323(f323(f78(a1),x99332),x99332))),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),x99331)),f76(a1)),f323(f103(a1),x99332)))),f76(a1)))+P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x99332)))
% 188.07/187.97 [9985]~P6(x99851)+E(f37(x99851,f323(f243(x99851),f323(f323(f8(f872(x99851,a860),a860,x99851),f86(x99851)),f323(f323(f8(f872(x99851,a860),f872(x99851,a860),x99851),f323(f18(x99851,a860,a860),f323(f323(f8(a860,f872(a860,a860),x99851),a326),f323(f323(f7(x99851,f872(x99851,a860),a860),f325(x99851)),x99852)))),f237(x99851))))),f38(x99851,x99852))
% 188.07/187.97 [10009]~P38(x100091,x100092)+P56(x100091,f323(f323(f7(x100091,f872(f871(x100091,x100091),a860),f872(x100091,a860)),f323(f323(f8(f872(x100091,f872(f872(f871(x100091,x100091),a860),a860)),f872(f872(f871(x100091,x100091),a860),f872(x100091,a860)),x100091),f7(x100091,f872(f871(x100091,x100091),a860),a860)),f323(f323(f8(f872(x100091,f871(x100091,x100091)),f872(x100091,f872(f872(f871(x100091,x100091),a860),a860)),x100091),f323(f8(f871(x100091,x100091),f872(f872(f871(x100091,x100091),a860),a860),x100091),f325(f871(x100091,x100091)))),f258(x100091,x100091)))),x100092))
% 188.07/187.97 [10010]~P9(x100101,f246(f872(x100101,a860)),x100102)+P8(x100101,f323(f323(f7(x100101,f872(f871(x100101,x100101),a860),f872(x100101,a860)),f323(f323(f8(f872(x100101,f872(f872(f871(x100101,x100101),a860),a860)),f872(f872(f871(x100101,x100101),a860),f872(x100101,a860)),x100101),f7(x100101,f872(f871(x100101,x100101),a860),a860)),f323(f323(f8(f872(x100101,f871(x100101,x100101)),f872(x100101,f872(f872(f871(x100101,x100101),a860),a860)),x100101),f323(f8(f871(x100101,x100101),f872(f872(f871(x100101,x100101),a860),a860),x100101),f325(f871(x100101,x100101)))),f258(x100101,x100101)))),x100102))
% 188.07/187.97 [10047]P38(x100471,x100472)+~P56(x100471,f323(f323(f7(x100471,f872(f871(x100471,x100471),a860),f872(x100471,a860)),f323(f323(f8(f872(x100471,f872(f872(f871(x100471,x100471),a860),a860)),f872(f872(f871(x100471,x100471),a860),f872(x100471,a860)),x100471),f7(x100471,f872(f871(x100471,x100471),a860),a860)),f323(f323(f8(f872(x100471,f871(x100471,x100471)),f872(x100471,f872(f872(f871(x100471,x100471),a860),a860)),x100471),f323(f8(f871(x100471,x100471),f872(f872(f871(x100471,x100471),a860),a860),x100471),f325(f871(x100471,x100471)))),f258(x100471,x100471)))),x100472))
% 188.07/187.97 [10048]P9(x100481,f246(f872(x100481,a860)),x100482)+~P8(x100481,f323(f323(f7(x100481,f872(f871(x100481,x100481),a860),f872(x100481,a860)),f323(f323(f8(f872(x100481,f872(f872(f871(x100481,x100481),a860),a860)),f872(f872(f871(x100481,x100481),a860),f872(x100481,a860)),x100481),f7(x100481,f872(f871(x100481,x100481),a860),a860)),f323(f323(f8(f872(x100481,f871(x100481,x100481)),f872(x100481,f872(f872(f871(x100481,x100481),a860),a860)),x100481),f323(f8(f871(x100481,x100481),f872(f872(f871(x100481,x100481),a860),a860),x100481),f325(f871(x100481,x100481)))),f258(x100481,x100481)))),x100482))
% 188.07/187.97 [7207]E(f323(f323(f78(a865),f323(f103(a865),f323(f323(f22(a1),x72071),a97))),x72072),f323(a112,f323(f323(f78(a865),f323(f103(a865),x72071)),x72072)))+P101(f323(a193,f323(f103(a1),x72071)))
% 188.07/187.97 [7649]~P90(x76491)+E(f323(f323(f78(x76491),f323(f323(f78(x76491),f76(x76491)),f323(f103(x76491),x76492))),f323(f103(x76491),x76492)),f323(f103(x76491),f323(f323(f22(a1),f323(f323(f78(a1),x76492),x76492)),a97)))
% 188.07/187.97 [8291]~P101(f323(f323(f237(a1),x82911),x82912))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x82911),x82911)),f323(f323(f22(a1),f323(f323(f78(a1),x82912),x82912)),a97)))
% 188.07/187.97 [8293]~P101(f323(f323(f237(a1),x82931),x82932))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x82931),x82931)),f323(f323(f22(a1),f323(f323(f78(a1),x82932),x82932)),a97)))
% 188.07/187.97 [8724]P101(f323(f323(f237(a1),x87241),x87242))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),x87241),x87241)),f323(f323(f22(a1),f323(f323(f78(a1),x87242),x87242)),a97)))
% 188.07/187.97 [8726]P101(f323(f323(f237(a1),x87261),x87262))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),x87261),x87261)),f323(f323(f22(a1),f323(f323(f78(a1),x87262),x87262)),a97)))
% 188.07/187.97 [9013]~P101(f323(f323(f237(a1),x90131),x90132))+P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90131),x90131)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x90132),x90132)),a97)))
% 188.07/187.97 [9015]~P101(f323(f323(f238(a1),x90151),x90152))+P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90151),x90151)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x90152),x90152)),a97)))
% 188.07/187.97 [9016]~P101(f323(f323(f89(a1),x90161),x90162))+P101(f323(f323(f89(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90161),x90161)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x90162),x90162)),a97)))
% 188.07/187.97 [9280]P101(f323(f323(f237(a1),x92801),x92802))+~P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x92801),x92801)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x92802),x92802)),a97)))
% 188.07/187.97 [9282]P101(f323(f323(f238(a1),x92821),x92822))+~P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x92821),x92821)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x92822),x92822)),a97)))
% 188.07/187.97 [9283]P101(f323(f323(f89(a1),x92831),x92832))+~P101(f323(f323(f89(a1),f323(f323(f22(a1),f323(f323(f78(a1),x92831),x92831)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x92832),x92832)),a97)))
% 188.07/187.97 [9316]~P101(f323(f59(x93161),x93162))+P101(f323(f59(f872(x93161,a860)),f323(f243(f872(x93161,a860)),f323(f323(f7(f872(x93161,a860),f872(x93161,a860),a860),f237(f872(x93161,a860))),x93162))))
% 188.07/187.97 [9363]~E(f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),x93631),f188(f872(f871(a865,a865),a860)))),f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),x93632),f188(f872(f871(a865,a865),a860)))))+P101(f323(f323(f325(f871(f871(a865,a865),f871(a865,a865))),f323(f323(f258(f871(a865,a865),f871(a865,a865)),x93631),x93632)),a108))
% 188.07/187.97 [9449]E(f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),x94491),f188(f872(f871(a865,a865),a860)))),f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),x94492),f188(f872(f871(a865,a865),a860)))))+~P101(f323(f323(f325(f871(f871(a865,a865),f871(a865,a865))),f323(f323(f258(f871(a865,a865),f871(a865,a865)),x94491),x94492)),a108))
% 188.07/187.97 [9485]P101(f323(f323(f237(a1),f2(a1)),f775(x94851,x94852)))+E(f323(f243(a1),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f237(a1),f2(a1)))),x94851)),f323(f243(a1),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f237(a1),f2(a1)))),x94852)))
% 188.07/187.97 [9995]~P6(x99951)+E(f38(x99951,f323(f243(x99951),f323(f323(f8(f872(x99951,a860),a860,x99951),f86(x99951)),f323(f323(f8(f872(x99951,a860),f872(x99951,a860),x99951),f323(f18(x99951,a860,a860),f323(f323(f8(a860,f872(a860,a860),x99951),a326),f323(f323(f7(x99951,f872(x99951,a860),a860),f325(x99951)),x99952)))),f323(f7(x99951,x99951,a860),f237(x99951)))))),f37(x99951,x99952))
% 188.07/187.97 [10015]P101(f323(f323(f325(a865),f2(a865)),x100151))+E(f323(f35(a865),f323(f243(a865),f323(f323(f18(a865,a860,a860),f323(f323(f8(a860,f872(a860,a860),a865),a322),f323(f323(f7(a865,f872(a865,a860),a860),f323(f323(f8(a865,f872(f872(a865,a860),a860),a865),f325(a865)),a112)),x100151))),f323(f323(f7(a865,a865,a860),f238(a865)),x100152)))),f323(f35(a865),f323(f243(a865),f323(f323(f18(a865,a860,a860),f323(f323(f8(a860,f872(a860,a860),a865),a322),f323(f323(f7(a865,f872(a865,a860),a860),f325(a865)),x100151))),f323(f323(f7(a865,a865,a860),f238(a865)),f323(a112,x100152))))))
% 188.07/187.97 [7518]~P90(x75181)+E(f323(f323(f79(x75181),x75182),f323(f103(x75181),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),x75182)
% 188.07/187.97 [7778]~P90(x77781)+E(f323(f323(f78(x77781),f323(f103(x77781),x77782)),f76(x77781)),f323(f103(x77781),f323(f323(f78(a1),x77782),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))
% 188.07/187.97 [7927]P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x79272)))+E(f323(f323(f248(a1),x79271),f323(f103(a865),f323(f323(f22(a1),f323(f323(f78(a1),x79272),x79272)),a97))),f76(a1))
% 188.07/187.97 [9341]~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x93412)))+E(f323(f323(f248(a1),x93411),f323(f103(a865),f323(f323(f22(a1),f323(f323(f78(a1),x93412),x93412)),a97))),f323(f323(f84(a1,a1),f323(f323(f248(a1),x93411),f323(f103(a865),x93412))),f323(f323(f18(a1,a1,a1),f323(f323(f8(a1,f872(a1,a1),a1),f79(a1)),f323(f79(a1),x93411))),f5(a1))))
% 188.07/187.97 [9709]~P101(f323(f323(f237(a865),f792(x97092,x97091)),f323(x97091,f792(x97092,x97091))))+P101(f323(f59(a865),f323(f243(a865),f323(f323(f7(a865,a865,a860),f323(f323(f8(a865,f872(a865,a860),a865),f237(a865)),x97091)),x97092))))
% 188.07/187.97 [9858]~P101(f323(f323(f237(a865),f323(f103(a865),x98581)),f323(a112,x98582)))+P101(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x98581),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a326),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f7(a1,a865,a860),f323(f323(f8(a865,f872(a865,a860),a1),f237(a865)),a104)),x98582))))
% 188.07/187.97 [9859]~P101(f323(f323(f238(a865),f323(f103(a865),x98591)),f323(a112,x98592)))+P101(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x98591),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a326),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f7(a1,a865,a860),f323(f323(f8(a865,f872(a865,a860),a1),f238(a865)),a104)),x98592))))
% 188.07/187.97 [9908]P101(f323(f323(f237(a865),f323(f103(a865),x99081)),f323(a112,x99082)))+~P101(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x99081),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a326),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f7(a1,a865,a860),f323(f323(f8(a865,f872(a865,a860),a1),f237(a865)),a104)),x99082))))
% 188.07/187.97 [9909]P101(f323(f323(f238(a865),f323(f103(a865),x99091)),f323(a112,x99092)))+~P101(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x99091),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a326),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f7(a1,a865,a860),f323(f323(f8(a865,f872(a865,a860),a1),f238(a865)),a104)),x99092))))
% 188.07/187.97 [9939]~P101(f323(f323(f237(a865),f323(a112,x99392)),f323(f103(a865),x99391)))+P101(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x99391),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a326),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f8(a865,a860,a1),f323(f237(a865),x99392)),a104)))))
% 188.07/187.97 [9940]~P101(f323(f323(f238(a865),f323(a112,x99402)),f323(f103(a865),x99401)))+P101(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x99401),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a326),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f8(a865,a860,a1),f323(f238(a865),x99402)),a104)))))
% 188.07/187.97 [9983]P101(f323(f323(f237(a865),f323(a112,x99831)),f323(f103(a865),x99832)))+~P101(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x99832),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a326),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f8(a865,a860,a1),f323(f237(a865),x99831)),a104)))))
% 188.07/187.97 [9984]P101(f323(f323(f238(a865),f323(a112,x99841)),f323(f103(a865),x99842)))+~P101(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x99842),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a326),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f8(a865,a860,a1),f323(f238(a865),x99841)),a104)))))
% 188.07/187.97 [10054]~P101(f323(f323(f325(a865),f2(a865)),x100541))+E(f323(a112,f323(f35(a865),f323(f243(a865),f323(f323(f18(a865,a860,a860),f323(f323(f8(a860,f872(a860,a860),a865),a322),f323(f323(f7(a865,f872(a865,a860),a860),f323(f323(f8(a865,f872(f872(a865,a860),a860),a865),f325(a865)),a112)),x100541))),f323(f323(f7(a865,a865,a860),f238(a865)),x100542))))),f323(f35(a865),f323(f243(a865),f323(f323(f18(a865,a860,a860),f323(f323(f8(a860,f872(a860,a860),a865),a322),f323(f323(f7(a865,f872(a865,a860),a860),f325(a865)),x100541))),f323(f323(f7(a865,a865,a860),f238(a865)),f323(a112,x100542))))))
% 188.07/187.97 [8463]~P90(x84631)+E(f323(f323(f79(x84631),f323(f103(x84631),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),x84632),x84632)
% 188.07/187.97 [8523]~P90(x85231)+E(f323(f323(f78(x85231),f76(x85231)),f323(f103(x85231),x85232)),f323(f103(x85231),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),x85232)))
% 188.07/187.97 [8587]~P90(x85871)+E(f323(f323(f22(x85871),f323(f103(x85871),x85872)),f76(x85871)),f323(f103(x85871),f323(f323(f78(a1),x85872),f323(f77(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 188.07/187.97 [8744]~P101(f323(f323(f238(a865),f323(f103(a865),a81)),x87442))+E(f323(f323(f22(a865),x87441),f323(f323(f22(a865),x87442),f323(f103(a865),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(f323(f22(a865),f323(a112,x87441)),x87442))
% 188.07/187.97 [9379]~P112(x93791)+E(f323(f323(f79(x93791),x93792),x93792),f323(f323(f248(x93791),x93792),f323(f103(a865),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)))))
% 188.07/187.97 [9380]~P77(x93801)+E(f323(f323(f248(x93801),x93802),f323(f103(a865),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(x93801),x93802),x93802))
% 188.07/187.97 [9382]~P90(x93821)+E(f323(f323(f79(x93821),x93822),f323(f103(x93821),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(x93821),x93822),x93822))
% 188.07/187.97 [9626]~P134(x96261)+E(f323(f323(f248(x96261),f323(f77(x96261),x96262)),f323(f103(a865),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(x96261),x96262),f323(f103(a865),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)))))
% 188.07/187.97 [9627]~P116(x96271)+E(f323(f323(f248(x96271),f323(f73(x96271),x96272)),f323(f103(a865),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(x96271),x96272),f323(f103(a865),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)))))
% 188.07/187.97 [9623]~P90(x96231)+E(f323(f323(f79(x96231),f323(f103(x96231),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)))),x96232),f323(f323(f78(x96231),x96232),x96232))
% 188.07/187.97 [9749]~P116(x97491)+E(f323(f73(x97491),f323(f323(f248(x97491),x97492),f323(f103(a865),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(x97491),x97492),f323(f103(a865),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)))))
% 188.07/187.97 [9812]~P116(x98121)+P101(f323(f323(f237(x98121),f2(x98121)),f323(f323(f248(x98121),x98122),f323(f103(a865),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))))))
% 188.07/187.97 [9974]~E(f323(a112,x99742),f323(f103(a865),x99741))+P101(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x99741),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a326),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f7(a1,a865,a860),f323(f323(f8(a865,f872(a865,a860),a1),a320),a104)),x99742)))))
% 188.07/187.97 [9975]~E(f323(f103(a865),x99751),f323(a112,x99752))+P101(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x99751),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a326),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f7(a1,a865,a860),f323(f323(f8(a865,f872(a865,a860),a1),a320),a104)),x99752)))))
% 188.07/187.97 [10018]E(f323(a112,x100181),f323(f103(a865),x100182))+~P101(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x100182),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a326),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f7(a1,a865,a860),f323(f323(f8(a865,f872(a865,a860),a1),a320),a104)),x100181)))))
% 188.07/187.97 [10019]E(f323(f103(a865),x100191),f323(a112,x100192))+~P101(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x100191),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a326),f323(f323(f8(a860,a860,a1),a318),a193))),f323(f323(f7(a1,a865,a860),f323(f323(f8(a865,f872(a865,a860),a1),a320),a104)),x100192)))))
% 188.07/187.97 [9810]~P90(x98101)+E(f323(f323(f248(x98101),f323(f103(x98101),a97)),f323(f323(f79(a865),f323(f103(a865),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)))),x98102)),f76(x98101))
% 188.07/187.97 [9811]~P134(x98111)+E(f323(f323(f248(x98111),f323(f77(x98111),f76(x98111))),f323(f323(f79(a865),f323(f103(a865),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)))),x98112)),f76(x98111))
% 188.07/187.97 [9814]~P77(x98141)+E(f323(f323(f248(x98141),x98142),f323(f103(a865),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(x98141),f323(f323(f79(x98141),x98142),x98142)),x98142))
% 188.07/187.97 [9998]~P101(f323(f323(f237(a1),f2(a1)),x99982))+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)))),x99981)),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)))),x99982)),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,x99981,x99982))))
% 188.07/187.97 [10021]~P101(f323(f323(f237(a1),f2(a1)),x100212))+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)))),x100211))),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)))),x100212)),f323(f323(f36(a1),x100211),x100212))
% 188.07/187.97 [10023]~P101(f323(f323(f237(a1),x100232),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)))),x100231))),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)))),x100232)),f323(f323(f36(a1),f323(f323(f78(a1),x100231),f76(a1))),x100232))
% 188.07/187.97 [10024]~P101(f323(f323(f237(a1),x100242),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)))),x100241)),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)))),x100242)),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),x100241),f76(a1)),x100242))),f76(a1)))
% 188.07/187.97 [9899]~P90(x98991)+E(f323(f323(f248(x98991),f323(f103(x98991),a97)),f323(a112,f323(f323(f79(a865),f323(f103(a865),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)))),x98992))),f323(f103(x98991),a97))
% 188.07/187.97 [9901]~P134(x99011)+E(f323(f323(f248(x99011),f323(f77(x99011),f76(x99011))),f323(a112,f323(f323(f79(a865),f323(f103(a865),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)))),x99012))),f323(f77(x99011),f76(x99011)))
% 188.07/187.97 [5104]~P26(x51041,x51042,x51043)+P31(x51041,x51042,x51043)
% 188.07/187.97 [7992]~E(x79922,x79923)+P35(x79921,x79921,a320,x79922,x79923)
% 188.07/187.97 [8537]E(x85371,x85372)+~P35(x85373,x85373,a320,x85371,x85372)
% 188.07/187.97 [4752]E(f163(x47521,x47522,x47523),f113(x47521))+~E(x47522,f2(a865))
% 188.07/187.97 [4916]~E(f163(x49162,x49161,x49163),f113(x49162))+E(x49161,f2(a865))
% 188.07/187.97 [5109]~P38(x51091,x51093)+P38(x51091,f317(x51091,x51092,x51093))
% 188.07/187.97 [5356]~P9(x53561,x53562,x53563)+P9(f866(x53561),f154(x53561,x53562),f151(x53561,x53563))
% 188.07/187.97 [5357]~P40(x53571,x53572,x53573)+P40(f866(x53571),f154(x53571,x53572),f151(x53571,x53573))
% 188.07/187.97 [5469]P51(x54691,x54692,x54693)+~E(f707(x54693,x54692,x54691),f708(x54693,x54692,x54691))
% 188.07/187.97 [5470]P52(x54701,x54702,x54703)+~E(f732(x54703,x54702,x54701),f733(x54703,x54702,x54701))
% 188.07/187.97 [7998]~E(x79982,x79983)+P28(x79981,x79981,f32(x79981),x79982,x79983)
% 188.07/187.97 [8545]E(x85451,x85452)+~P28(x85453,x85453,f32(x85453),x85451,x85452)
% 188.07/187.97 [4657]~E(x46571,f200(x46572))+~E(x46571,f323(f230(x46572),x46573))
% 188.07/187.97 [4708]~E(f323(f162(x47082),x47081),x47083)+E(x47081,f323(f162(x47082),x47083))
% 188.07/187.97 [4709]~E(x47092,f323(f162(x47091),x47093))+E(f323(f162(x47091),x47092),x47093)
% 188.07/187.97 [4758]E(x47581,x47582)+~E(f323(f230(x47583),x47581),f323(f230(x47583),x47582))
% 188.07/187.97 [4759]E(x47591,x47592)+~E(f323(f162(x47593),x47591),f323(f162(x47593),x47592))
% 188.07/187.97 [4963]~P8(x49633,x49631)+P101(f323(f323(x49631,x49632),x49632))
% 188.07/187.97 [4964]~P49(x49643,x49641)+P101(f323(f323(x49641,x49642),x49642))
% 188.07/187.97 [4966]~P56(x49661,x49662)+P101(f323(f311(x49661,x49662),x49663))
% 188.07/187.97 [5028]~P38(x50281,x50282)+P38(f866(x50281),f323(f136(x50281,x50282),x50283))
% 188.07/187.97 [5033]~P101(f323(x50332,x50333))+~E(f323(f243(x50331),x50332),f188(f872(x50331,a860)))
% 188.07/187.97 [5034]~P101(f323(x50342,x50343))+~E(f188(f872(x50341,a860)),f323(f243(x50341),x50342))
% 188.07/187.97 [5046]E(x50461,f2(a865))+E(f137(x50462,f163(x50462,x50461,x50463)),x50463)
% 188.07/187.97 [5064]~P101(f323(x50641,x50643))+P101(f323(x50641,f88(x50642,x50641)))
% 188.07/187.97 [5076]E(x50761,f2(a865))+E(f323(f134(x50762),f163(x50762,x50761,x50763)),x50763)
% 188.07/187.97 [5181]~E(x51812,x51813)+P101(f323(f323(f325(x51811),x51812),f323(a320,x51813)))
% 188.07/187.97 [5236]E(f323(f162(x52361),x52362),f323(f323(f144(x52361),x52363),f113(x52361)))+~E(x52362,f323(f323(f144(x52361),x52363),f113(x52361)))
% 188.07/187.97 [5237]~E(x52373,f323(f323(f144(x52371),x52372),f113(x52371)))+E(f323(f323(f144(x52371),x52372),f113(x52371)),f323(f162(x52371),x52373))
% 188.07/187.97 [5263]~E(x52633,f323(f16(f869(x52632),x52631),f200(x52632)))+E(f177(x52631,x52632,x52633),f188(f872(x52631,a860)))
% 188.07/187.97 [5284]~P34(x52841,x52842,x52843)+P34(x52841,x52842,f323(f162(x52841),x52843))
% 188.07/187.97 [5285]~P32(x52851,x52852,x52853)+P32(x52851,x52852,f323(f162(x52851),x52853))
% 188.07/187.97 [5288]E(f323(f35(x52881),f803(x52882,x52883,x52881)),x52882)+~E(f323(f35(x52881),x52883),f323(a112,x52882))
% 188.07/187.97 [5294]~P38(x52941,x52943)+P101(f323(f323(f325(x52941),x52942),f312(x52941,x52943)))
% 188.07/187.97 [5298]~E(f323(f162(x52982),x52981),f323(f323(f144(x52982),x52983),f113(x52982)))+E(x52981,f323(f323(f144(x52982),x52983),f113(x52982)))
% 188.07/187.97 [5299]~E(f323(f323(f144(x52992),x52993),f113(x52992)),f323(f162(x52992),x52991))+E(x52991,f323(f323(f144(x52992),x52993),f113(x52992)))
% 188.07/187.97 [5314]E(x53141,f323(f16(f869(x53142),x53143),f200(x53142)))+~E(f177(x53143,x53142,x53141),f188(f872(x53143,a860)))
% 188.07/187.97 [5320]E(f83(f871(a865,a865),f45(x53201,x53202)),x53203)+~P101(f323(f45(x53201,x53202),x53203))
% 188.07/187.97 [5328]~E(x53283,f323(f230(x53281),x53282))+P101(f323(f323(f325(x53281),x53282),f229(x53281,x53283)))
% 188.07/187.97 [5360]P34(x53601,x53602,x53603)+~P34(x53601,x53602,f323(f162(x53601),x53603))
% 188.07/187.97 [5361]P32(x53611,x53612,x53613)+~P32(x53611,x53612,f323(f162(x53611),x53613))
% 188.07/187.97 [5423]~E(x54232,f113(x54231))+P101(f323(f323(f325(f866(x54231)),x54232),f154(x54231,x54233)))
% 188.07/187.97 [5430]~P40(x54301,x54302,x54303)+P40(x54301,x54302,f323(f278(x54301,x54301),x54303))
% 188.07/187.97 [5431]~P52(x54311,x54312,x54313)+P52(x54311,x54312,f323(f278(x54311,x54311),x54313))
% 188.07/187.97 [5450]~P57(x54501)+E(f42(x54501,f42(x54501,x54502,x54503),x54503),f42(x54501,x54502,x54503))
% 188.07/187.97 [5545]E(x55451,x55452)+~P101(f323(f323(f325(x55453),x55451),f323(a320,x55452)))
% 188.07/187.97 [5591]~P140(x55911)+E(f190(x55911,x55912,f2(a865),x55913),x55913)
% 188.07/187.97 [5611]P40(x56111,x56112,x56113)+~P40(x56111,x56112,f323(f278(x56111,x56111),x56113))
% 188.07/187.97 [5612]P52(x56121,x56122,x56123)+~P52(x56121,x56122,f323(f278(x56121,x56121),x56123))
% 188.07/187.97 [5616]~P103(x56162)+E(f143(x56161,x56162,x56163,f113(x56161)),f113(x56161))
% 188.07/187.97 [5629]E(f164(x56291,x56292,f145(x56291,x56293)),f145(x56291,f164(x56291,x56292,x56293)))+~P101(f323(f130(x56291),x56293))
% 188.07/187.97 [5635]E(x56351,f323(f230(x56352),x56353))+~P101(f323(f323(f325(x56352),x56353),f229(x56352,x56351)))
% 188.07/187.97 [5730]E(f323(f129(x57301,x57302),x57303),f113(x57301))+P101(f323(x57302,f565(x57303,x57302,x57301)))
% 188.07/187.97 [5873]~P101(f323(f130(x58731),x58733))+P101(f323(f130(x58731),f164(x58731,x58732,x58733)))
% 188.07/187.97 [5874]~P101(f323(f130(x58741),x58742))+P101(f323(f130(x58741),f170(x58741,x58742,x58743)))
% 188.07/187.97 [5875]~P101(f323(f130(x58751),x58753))+P101(f323(f130(x58751),f171(x58751,x58752,x58753)))
% 188.07/187.97 [5876]~P101(f323(f130(x58761),x58763))+P101(f323(f130(x58761),f133(x58761,x58762,x58763)))
% 188.07/187.97 [5877]~P142(x58771,x58772,x58773)+P101(f323(x58771,f42(a1,x58772,x58773)))
% 188.07/187.97 [5894]~P34(x58943,x58941,x58942)+P101(f323(x58941,f709(x58942,x58941,x58943)))
% 188.07/187.97 [5895]~P36(x58953,x58951,x58952)+P101(f323(x58951,f788(x58952,x58951,x58953)))
% 188.07/187.97 [5916]E(f323(f129(x59161,x59162),x59163),f171(x59161,x59162,x59163))+P101(f323(x59162,f613(x59163,x59162,x59161)))
% 188.07/187.97 [5955]~P101(f323(f130(x59551),x59553))+P101(f323(f130(f866(x59551)),f52(x59551,x59552,x59553)))
% 188.07/187.97 [5986]~P105(x59861)+E(f323(f323(f101(f872(x59861,a860)),f323(f244(x59861),x59862)),f294(x59861,x59862,x59863)),f188(f872(x59861,a860)))
% 188.07/187.97 [5987]~P105(x59871)+E(f323(f323(f101(f872(x59871,a860)),f323(f292(x59871),x59872)),f297(x59871,x59872,x59873)),f188(f872(x59871,a860)))
% 188.07/187.97 [5988]~P105(x59881)+E(f323(f323(f101(f872(x59881,a860)),f323(f292(x59881),x59882)),f296(x59881,x59882,x59883)),f188(f872(x59881,a860)))
% 188.07/187.97 [6213]E(f323(f129(x62131,x62132),x62133),x62133)+~P101(f323(x62132,f556(x62133,x62132,x62131)))
% 188.07/187.97 [6215]E(f323(f323(f301(x62151),f856(x62152,x62153,x62151)),f803(x62152,x62153,x62151)),x62153)+~E(f323(f35(x62151),x62153),f323(a112,x62152))
% 188.07/187.97 [6230]P142(x62301,x62302,x62303)+~P101(f323(x62301,f42(a1,x62302,x62303)))
% 188.07/187.97 [6277]P32(x62771,x62772,x62773)+~P101(f323(x62772,f771(x62772,x62773,x62771)))
% 188.07/187.97 [6278]P32(x62781,x62782,x62783)+~P101(f323(x62782,f784(x62783,x62782,x62781)))
% 188.07/187.97 [6279]P32(x62791,x62792,x62793)+~P101(f323(x62792,f786(x62793,x62792,x62791)))
% 188.07/187.97 [6281]E(f171(x62811,x62812,x62813),x62813)+~P101(f323(x62812,f604(x62813,x62812,x62811)))
% 188.07/187.97 [6359]~P101(f323(x63592,f574(x63593,x63592,x63591)))+P101(f323(f251(x63591,x63592),x63593))
% 188.07/187.97 [6360]~P101(f323(x63602,f624(x63603,x63602,x63601)))+P101(f323(f153(x63601,x63602),x63603))
% 188.07/187.97 [6604]~P101(f323(f311(x66041,x66042),f498(x66043,x66042,x66041)))+P101(f323(f311(x66041,x66042),x66043))
% 188.07/187.97 [6605]~P101(f323(f311(x66051,x66052),f512(x66053,x66052,x66051)))+P101(f323(f311(x66051,x66052),x66053))
% 188.07/187.97 [7208]~P57(x72081)+E(f323(f323(f78(x72081),f323(f323(f79(x72081),x72082),f323(f323(f36(x72081),x72083),x72082))),f42(x72081,x72083,x72082)),x72083)
% 188.07/187.97 [7672]E(f323(f323(f258(x76721,x76721),f527(x76722,x76723,x76721)),f527(x76722,x76723,x76721)),x76723)+~P101(f323(f323(f325(f871(x76721,x76721)),x76723),f255(x76721,x76722)))
% 188.07/187.97 [7786]~P101(f323(f323(f325(x77861),f661(x77863,x77862,x77861)),f312(x77861,x77863)))+P101(f323(f323(f325(x77861),x77862),f312(x77861,x77863)))
% 188.07/187.97 [7787]~P101(f323(f323(f325(x77871),f711(x77873,x77872,x77871)),f312(x77871,x77873)))+P101(f323(f323(f325(x77871),x77872),f312(x77871,x77873)))
% 188.07/187.97 [7788]~P101(f323(f323(f325(x77881),f718(x77883,x77882,x77881)),f312(x77881,x77883)))+P101(f323(f323(f325(x77881),x77882),f312(x77881,x77883)))
% 188.07/187.97 [7973]~P57(x79731)+E(f323(f323(f78(x79731),f323(f323(f79(x79731),f323(f323(f36(x79731),x79732),x79733)),x79733)),f42(x79731,x79732,x79733)),x79732)
% 188.07/187.97 [8019]~E(f323(f35(x80191),x80192),f323(a112,x80193))+~P101(f323(f323(f325(x80191),f856(x80193,x80192,x80191)),f803(x80193,x80192,x80191)))
% 188.07/187.97 [8645]P101(f323(f323(f237(f872(f871(x86451,x86451),a860)),f299(x86451,x86452)),f299(x86451,x86453)))+~P101(f323(f323(f237(f872(f871(x86451,x86451),a860)),x86452),f299(x86451,x86453)))
% 188.07/187.97 [8924]E(x89241,f113(x89242))+~P101(f323(f323(f325(f871(f866(x89242),f866(x89242))),f323(f323(f258(f866(x89242),f866(x89242)),x89241),f113(x89242))),f151(x89242,x89243)))
% 188.07/187.97 [8948]E(x89481,f113(x89482))+~P101(f323(f323(f325(f871(f866(x89482),f866(x89482))),f323(f323(f258(f866(x89482),f866(x89482)),f113(x89482)),x89481)),f151(x89482,x89483)))
% 188.07/187.97 [9075]E(f323(f323(f144(x90751),f622(x90752,x90753,x90751)),f623(x90752,x90753,x90751)),x90753)+~P101(f323(f323(f325(f871(f866(x90751),f866(x90751))),f323(f323(f258(f866(x90751),f866(x90751)),f113(x90751)),x90753)),f140(x90751,x90752)))
% 188.07/187.97 [9309]~P121(x93091)+~P101(f323(f323(f238(x93091),f323(f323(f78(x93091),f323(f323(f79(x93091),x93092),x93092)),f323(f323(f79(x93091),x93093),x93093))),f2(x93091)))
% 188.07/187.97 [9358]P101(f323(f59(x93581),x93582))+~P101(f323(f323(f325(f871(f872(x93581,a860),f872(x93581,a860))),f323(f323(f258(f872(x93581,a860),f872(x93581,a860)),x93583),x93582)),f298(x93581)))
% 188.07/187.97 [9649]~P47(x96491,x96492,x96493)+P101(f323(f323(f237(a1),f323(f323(f71(f871(a1,a1),a1,x96491,f257(a1,a1)),f214(x96491)),f225(x96491,x96492,f222(x96491,x96493)))),f2(a1)))
% 188.07/187.97 [9650]~P48(x96501,x96502,x96503)+P101(f323(f323(f238(a1),f323(f323(f71(f871(a1,a1),a1,x96501,f257(a1,a1)),f214(x96501)),f225(x96501,x96502,f222(x96501,x96503)))),f2(a1)))
% 188.07/187.97 [9778]P48(x97781,x97782,x97783)+~P101(f323(f323(f238(a1),f323(f323(f71(f871(a1,a1),a1,x97781,f257(a1,a1)),f214(x97781)),f225(x97781,x97782,f222(x97781,x97783)))),f2(a1)))
% 188.07/187.97 [9779]P47(x97791,x97792,x97793)+~P101(f323(f323(f237(a1),f323(f323(f71(f871(a1,a1),a1,x97791,f257(a1,a1)),f214(x97791)),f225(x97791,x97792,f222(x97791,x97793)))),f2(a1)))
% 188.07/187.97 [10099]~P116(x100991)+~P101(f323(f323(f238(x100991),f323(f323(f78(x100991),f323(f323(f248(x100991),x100992),f323(f103(a865),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(x100991),x100993),f323(f103(a865),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(x100991)))
% 188.07/187.97 [4739]~E(x47393,f113(x47391))+E(f323(f323(f121(x47391),x47392),x47393),x47392)
% 188.07/187.97 [4740]~E(x47402,f113(x47401))+E(f323(f323(f121(x47401),x47402),x47403),x47403)
% 188.07/187.97 [4747]~E(x47472,f2(a865))+E(f323(f323(f169(x47471),x47472),x47473),f113(x47471))
% 188.07/187.97 [4753]~E(x47533,f113(x47531))+E(f323(f323(f169(x47531),x47532),x47533),f113(x47531))
% 188.07/187.97 [4793]~E(x47931,x47933)+E(x47931,f323(f323(f121(x47932),f113(x47932)),x47933))
% 188.07/187.97 [4879]~P1(x48792)+E(f323(f188(f872(x48791,x48792)),x48793),f188(x48792))
% 188.07/187.97 [4880]~P106(x48802)+E(f323(f246(f872(x48801,x48802)),x48803),f246(x48802))
% 188.07/187.97 [4898]E(x48981,f113(x48982))+~E(f323(f323(f121(x48982),x48983),x48981),x48983)
% 188.07/187.97 [4899]E(x48991,f113(x48992))+~E(f323(f323(f121(x48992),x48991),x48993),x48993)
% 188.07/187.97 [4907]E(x49071,f113(x49072))+~E(f323(f323(f121(x49072),x49073),x49071),f113(x49072))
% 188.07/187.97 [4908]E(x49081,f113(x49082))+~E(f323(f323(f121(x49082),x49081),x49083),f113(x49082))
% 188.07/187.97 [4933]~E(x49332,f2(a865))+E(f323(f323(f79(a865),x49331),x49332),f323(f323(f79(a865),x49333),x49332))
% 188.07/187.97 [4935]~E(x49351,f2(a865))+E(f323(f323(f79(a865),x49351),x49352),f323(f323(f79(a865),x49351),x49353))
% 188.07/187.97 [4988]~P2(x49881)+E(f323(f323(f110(x49881),x49882),x49883),f323(f323(f110(x49881),x49883),x49882))
% 188.07/187.97 [4990]~P97(x49901)+E(f323(f323(f110(x49901),x49902),x49903),f323(f323(f110(x49901),x49903),x49902))
% 188.07/187.97 [4991]~P2(x49911)+E(f323(f323(f101(x49911),x49912),x49913),f323(f323(f101(x49911),x49913),x49912))
% 188.07/187.97 [4993]~P98(x49931)+E(f323(f323(f101(x49931),x49932),x49933),f323(f323(f101(x49931),x49933),x49932))
% 188.07/187.97 [4994]~P112(x49941)+E(f323(f323(f79(x49941),x49942),x49943),f323(f323(f79(x49941),x49943),x49942))
% 188.07/187.97 [4995]~P112(x49951)+E(f323(f323(f78(x49951),x49952),x49953),f323(f323(f78(x49951),x49953),x49952))
% 188.07/187.97 [4997]~P103(x49971)+E(f323(f323(f235(x49971),x49972),x49973),f323(f323(f235(x49971),x49973),x49972))
% 188.07/187.97 [4999]~P103(x49991)+E(f323(f323(f236(x49991),x49992),x49993),f323(f323(f236(x49991),x49993),x49992))
% 188.07/187.97 [5059]E(f42(a865,x50591,x50592),f2(a865))+~E(x50591,f323(f323(f79(a865),x50592),x50593))
% 188.07/187.97 [5060]E(f42(a1,x50601,x50602),f2(a1))+~E(x50601,f323(f323(f79(a1),x50602),x50603))
% 188.07/187.97 [5121]E(x51211,x51212)+~E(f323(f323(f78(a865),x51213),x51211),f323(f323(f78(a865),x51213),x51212))
% 188.07/187.97 [5122]E(x51221,x51222)+~E(f323(f323(f78(a865),x51221),x51223),f323(f323(f78(a865),x51222),x51223))
% 188.07/187.97 [5132]~P87(x51321)+E(f323(f323(f101(x51321),x51322),f323(f77(x51321),x51323)),f323(f323(f22(x51321),x51322),x51323))
% 188.07/187.97 [5133]~P59(x51331)+E(f323(f323(f78(x51331),x51332),f323(f77(x51331),x51333)),f323(f323(f22(x51331),x51332),x51333))
% 188.07/187.97 [5134]~P60(x51341)+E(f323(f323(f78(x51341),x51342),f323(f77(x51341),x51343)),f323(f323(f22(x51341),x51342),x51343))
% 188.07/187.97 [5135]~P109(x51351)+E(f323(f323(f78(x51351),x51352),f323(f77(x51351),x51353)),f323(f323(f22(x51351),x51352),x51353))
% 188.07/187.97 [5136]~P59(x51361)+E(f323(f323(f22(x51361),x51362),f323(f77(x51361),x51363)),f323(f323(f78(x51361),x51362),x51363))
% 188.07/187.97 [5174]~P101(f323(x51743,x51742))+P101(f323(f323(f325(x51741),x51742),x51743))
% 188.07/187.97 [5176]~P72(x51762)+E(f323(f323(f6(x51761,x51762),x51763),f188(f872(x51761,a860))),f2(x51762))
% 188.07/187.97 [5178]~P68(x51782)+E(f323(f323(f9(x51781,x51782),x51783),f188(f872(x51781,a860))),f76(x51782))
% 188.07/187.97 [5224]~E(x52242,f323(f323(f78(a865),x52241),x52243))+P101(f323(f323(f237(a865),x52241),x52242))
% 188.07/187.97 [5227]~E(x52272,f188(f872(x52271,a860)))+E(f323(f323(f58(x52271),x52272),x52273),f188(f872(f872(x52271,a860),a860)))
% 188.07/187.97 [5228]~E(x52282,f188(f872(x52281,a860)))+E(f188(f872(f872(x52281,a860),a860)),f323(f323(f58(x52281),x52282),x52283))
% 188.07/187.97 [5303]~E(f323(f254(x53032,x53033),x53031),f188(f872(x53033,a860)))+E(x53031,f188(f872(f871(x53032,x53033),a860)))
% 188.07/187.97 [5304]~E(f323(f256(x53042,x53043),x53041),f188(f872(x53042,a860)))+E(x53041,f188(f872(f871(x53042,x53043),a860)))
% 188.07/187.97 [5334]E(f323(f254(x53341,x53342),x53343),f188(f872(x53342,a860)))+~E(x53343,f188(f872(f871(x53341,x53342),a860)))
% 188.07/187.97 [5335]E(f323(f256(x53351,x53352),x53353),f188(f872(x53351,a860)))+~E(x53353,f188(f872(f871(x53351,x53352),a860)))
% 188.07/187.97 [5338]E(f273(x53381,x53382,x53383),f323(f323(f22(a99),x53382),x53383))+P101(f323(f323(f238(a99),x53382),x53383))
% 188.07/187.97 [5354]P101(f323(x53541,x53542))+~P101(f323(f323(f325(x53543),x53542),x53541))
% 188.07/187.97 [5393]E(x53931,x53932)+~E(f323(f77(f872(x53933,a860)),x53931),f323(f77(f872(x53933,a860)),x53932))
% 188.07/187.97 [5398]E(f305(x53981,x53982,x53983),f200(f866(a319)))+~P101(f323(f323(f238(a1),x53982),x53983))
% 188.07/187.97 [5403]~E(x54031,f188(f872(x54032,a860)))+~P101(f323(f323(f325(x54032),x54033),x54031))
% 188.07/187.97 [5432]~E(x54322,f323(f323(f78(a1),x54321),f323(f100(a1),x54323)))+P101(f323(f323(f237(a1),x54321),x54322))
% 188.07/187.97 [5448]E(f323(f323(f301(x54481),x54482),x54483),x54483)+~P101(f323(f323(f325(x54481),x54482),x54483))
% 188.07/187.97 [5459]E(x54591,f188(f872(x54592,a860)))+~E(f323(f323(f58(x54592),x54591),x54593),f188(f872(f872(x54592,a860),a860)))
% 188.07/187.97 [5460]E(x54601,f188(f872(x54602,a860)))+~E(f188(f872(f872(x54602,a860),a860)),f323(f323(f58(x54602),x54601),x54603))
% 188.07/187.97 [5466]~P107(x54661)+E(f323(f323(f79(x54661),f323(f77(x54661),x54662)),f323(f77(x54661),x54663)),f323(f323(f79(x54661),x54662),x54663))
% 188.07/187.97 [5468]~P62(x54681)+E(f323(f323(f281(x54681),f323(f77(x54681),x54682)),f323(f77(x54681),x54683)),f323(f323(f281(x54681),x54682),x54683))
% 188.07/187.97 [5500]~P101(f323(x55003,x55002))+P101(f323(f323(f325(x55001),x55002),f323(f243(x55001),x55003)))
% 188.07/187.97 [5538]E(f164(x55381,x55382,x55383),x55383)+P101(f323(f323(f325(x55381),x55382),f323(f166(x55381),x55383)))
% 188.07/187.97 [5620]~P101(f323(f130(x56201),x56203))+P101(f323(f130(x56201),f323(f129(x56201,x56202),x56203)))
% 188.07/187.97 [5665]~P57(x56651)+E(f323(f323(f36(x56651),f42(x56651,x56652,x56653)),x56653),f2(x56651))
% 188.07/187.97 [5684]E(f170(x56841,f323(f323(f144(x56841),x56842),f113(x56841)),x56843),f113(x56841))+P101(f323(f323(f325(a865),f2(a865)),x56843))
% 188.07/187.97 [5690]E(x56901,f2(a865))+E(f323(f165(x56902),f163(x56902,x56901,x56903)),f163(x56902,f323(f323(f22(a865),x56901),f76(a865)),x56903))
% 188.07/187.97 [5740]E(f323(f323(f144(x57401),x57402),x57403),f133(x57401,x57402,x57403))+P101(f323(f323(f325(x57401),x57402),f323(f166(x57401),x57403)))
% 188.07/187.97 [5749]E(x57491,x57492)+~E(f323(f323(f79(a865),f323(a112,x57493)),x57491),f323(f323(f79(a865),f323(a112,x57493)),x57492))
% 188.07/187.97 [5750]~E(x57502,f323(f323(f78(a1),x57501),f323(f100(a1),f323(a112,x57503))))+P101(f323(f323(f238(a1),x57501),x57502))
% 188.07/187.97 [5855]~E(x58553,f113(x58551))+E(f323(f323(f323(f183(f866(x58551),f866(x58551)),x58552),f161(x58551)),x58553),f113(x58551))
% 188.07/187.97 [5859]P101(f323(x58591,x58592))+~P101(f323(f323(f325(x58593),x58592),f323(f243(x58593),x58591)))
% 188.07/187.97 [5889]E(x58891,x58892)+~E(f323(f323(f301(x58893),x58891),f188(f872(x58893,a860))),f323(f323(f301(x58893),x58892),f188(f872(x58893,a860))))
% 188.07/187.97 [5900]~P105(x59001)+E(f323(f323(f101(f872(x59001,a860)),f323(f244(x59001),x59002)),f323(f293(x59001,x59002),x59003)),f188(f872(x59001,a860)))
% 188.07/187.97 [5942]E(f133(x59421,x59422,x59423),x59423)+~P101(f323(f323(f325(x59421),x59422),f323(f166(x59421),x59423)))
% 188.07/187.97 [5962]~P75(x59621)+E(f323(f302(x59621,x59621,f77(x59621)),f323(f293(x59621,x59622),x59623)),f296(x59621,f323(f77(x59621),x59623),f323(f77(x59621),x59622)))
% 188.07/187.97 [5970]E(f323(f189(f866(x59701)),f164(x59701,x59702,x59703)),f323(f189(f866(x59701)),x59703))+P101(f323(f323(f325(x59701),x59702),f323(f166(x59701),x59703)))
% 188.07/187.97 [6022]~P105(x60221)+E(f323(f323(f101(f872(x60221,a860)),f323(f293(x60221,x60222),x60223)),f323(f245(x60221),x60223)),f188(f872(x60221,a860)))
% 188.07/187.97 [6045]~P75(x60451)+E(f323(f302(x60451,x60451,f77(x60451)),f294(x60451,x60452,x60453)),f294(x60451,f323(f77(x60451),x60453),f323(f77(x60451),x60452)))
% 188.07/187.97 [6046]~P75(x60461)+E(f323(f302(x60461,x60461,f77(x60461)),f297(x60461,x60462,x60463)),f297(x60461,f323(f77(x60461),x60463),f323(f77(x60461),x60462)))
% 188.07/187.97 [6103]E(f170(x61031,f323(f323(f144(x61031),x61032),f113(x61031)),x61033),f323(f323(f144(x61031),x61032),f113(x61031)))+~P101(f323(f323(f325(a865),f2(a865)),x61033))
% 188.07/187.97 [6110]~P75(x61101)+E(f323(f302(x61101,x61101,f77(x61101)),f296(x61101,x61102,x61103)),f323(f293(x61101,f323(f77(x61101),x61103)),f323(f77(x61101),x61102)))
% 188.07/187.97 [6130]~P58(x61301)+E(f42(x61301,f323(f77(x61301),f42(x61301,x61302,x61303)),x61303),f42(x61301,f323(f77(x61301),x61302),x61303))
% 188.07/187.97 [6228]~P101(f323(f59(f871(x62282,x62281)),x62283))+P101(f323(f59(x62281),f323(f254(x62282,x62281),x62283)))
% 188.07/187.97 [6229]~P101(f323(f59(f871(x62291,x62292)),x62293))+P101(f323(f59(x62291),f323(f256(x62291,x62292),x62293)))
% 188.07/187.97 [6234]~P105(x62341)+E(f323(f323(f101(f872(x62341,a860)),f294(x62341,x62342,x62343)),f323(f295(x62341),x62343)),f188(f872(x62341,a860)))
% 188.07/187.97 [6235]~P105(x62351)+E(f323(f323(f101(f872(x62351,a860)),f297(x62351,x62352,x62353)),f323(f245(x62351),x62353)),f188(f872(x62351,a860)))
% 188.07/187.97 [6236]~P105(x62361)+E(f323(f323(f101(f872(x62361,a860)),f296(x62361,x62362,x62363)),f323(f295(x62361),x62363)),f188(f872(x62361,a860)))
% 188.07/187.97 [6302]E(f323(f323(f158(x63021),x63022),f543(x63022,x63023,x63021)),x63023)+~P101(f323(f323(f325(x63021),x63023),f323(f166(x63021),x63022)))
% 188.07/187.97 [6440]E(x64401,f113(x64402))+~E(f323(f323(f323(f183(f866(x64402),f866(x64402)),x64403),f161(x64402)),x64401),f113(x64402))
% 188.07/187.97 [6542]~P101(f323(f59(f871(x65422,x65421)),x65423))+P101(f323(f59(f871(x65421,x65422)),f323(f278(x65422,x65421),x65423)))
% 188.07/187.97 [6692]P52(x66921,x66922,x66923)+P101(f323(f323(f325(x66921),f733(x66923,x66922,x66921)),x66922))
% 188.07/187.97 [6693]P52(x66931,x66932,x66933)+P101(f323(f323(f325(x66931),f732(x66933,x66932,x66931)),x66932))
% 188.07/187.97 [6704]P101(f323(f311(x67041,x67042),x67043))+P101(f323(f323(x67042,f498(x67043,x67042,x67041)),x67043))
% 188.07/187.97 [6705]P101(f323(f311(x67051,x67052),x67053))+P101(f323(f323(x67052,f512(x67053,x67052,x67051)),x67053))
% 188.07/187.97 [6736]E(f323(f189(f866(x67361)),f164(x67361,x67362,x67363)),f323(f323(f22(a865),f323(f189(f866(x67361)),x67363)),f76(a865)))+~P101(f323(f323(f325(x67361),x67362),f323(f166(x67361),x67363)))
% 188.07/187.97 [6776]P101(f323(f251(x67761,x67762),x67763))+P101(f323(f323(f325(x67761),f574(x67763,x67762,x67761)),x67763))
% 188.07/187.97 [6787]~P101(f323(f59(f871(x67872,x67871)),f323(f278(x67871,x67872),x67873)))+P101(f323(f59(f871(x67871,x67872)),x67873))
% 188.07/187.97 [6843]~P101(f323(f323(f325(x68431),x68432),f323(f166(x68431),f114(x68431,x68433))))+P101(f323(f323(f325(x68431),x68432),f323(f166(x68431),x68433)))
% 188.07/187.97 [6875]E(f323(f129(x68751,x68752),x68753),x68753)+P101(f323(f323(f325(x68751),f556(x68753,x68752,x68751)),f323(f166(x68751),x68753)))
% 188.07/187.97 [6890]E(f323(f129(x68901,x68902),x68903),f113(x68901))+P101(f323(f323(f325(x68901),f565(x68903,x68902,x68901)),f323(f166(x68901),x68903)))
% 188.07/187.97 [6913]P32(x69131,x69132,x69133)+P101(f323(f323(f325(x69131),f784(x69133,x69132,x69131)),f323(f166(x69131),x69133)))
% 188.07/187.97 [6914]P32(x69141,x69142,x69143)+P101(f323(f323(f325(x69141),f786(x69143,x69142,x69141)),f323(f166(x69141),x69143)))
% 188.07/187.97 [6915]P32(x69151,x69152,x69153)+P101(f323(f323(f325(x69151),f771(x69152,x69153,x69151)),f323(f166(x69151),x69153)))
% 188.07/187.97 [6918]E(f171(x69181,x69182,x69183),x69183)+P101(f323(f323(f325(x69181),f604(x69183,x69182,x69181)),f323(f166(x69181),x69183)))
% 188.07/187.97 [6997]P101(f323(f153(x69971,x69972),x69973))+P101(f323(f323(f325(x69971),f624(x69973,x69972,x69971)),f323(f166(x69971),x69973)))
% 188.07/187.97 [7006]~P34(x70061,x70063,x70062)+P101(f323(f323(f325(x70061),f709(x70062,x70063,x70061)),f323(f166(x70061),x70062)))
% 188.07/187.97 [7007]~P36(x70071,x70073,x70072)+P101(f323(f323(f325(x70071),f788(x70072,x70073,x70071)),f323(f166(x70071),x70072)))
% 188.07/187.97 [7042]P101(f323(f323(f325(x70421),x70422),f773(x70423,x70422,x70421)))+~P101(f323(f323(f325(x70421),x70422),f37(f872(x70421,a860),x70423)))
% 188.07/187.97 [7043]~P72(x70431)+E(f323(f323(f78(x70431),f323(f323(f6(a865,x70431),x70432),f323(f244(a865),x70433))),f323(x70432,x70433)),f323(f323(f6(a865,x70431),x70432),f323(f244(a865),f323(a112,x70433))))
% 188.07/187.97 [7132]~P34(x71322,x71321,x71323)+P101(f323(x71321,f323(f323(f158(x71322),x71323),f723(x71323,x71321,x71322))))
% 188.07/187.97 [7145]~P101(f323(f323(f325(x71451),x71452),f724(x71452,x71453,x71451)))+P101(f323(f323(f325(x71451),x71452),f38(f872(x71451,a860),x71453)))
% 188.07/187.97 [7175]~P72(x71751)+E(f323(f323(f78(x71751),f323(f323(f6(a865,x71751),x71752),f323(f292(a865),x71753))),f323(x71752,f323(a112,x71753))),f323(f323(f6(a865,x71751),x71752),f323(f292(a865),f323(a112,x71753))))
% 188.07/187.97 [7308]P101(f323(f323(f325(f866(x73081)),x73082),f154(x73081,x73083)))+P101(f323(f323(f325(x73081),f614(x73083,x73082,x73081)),f323(f166(x73081),x73082)))
% 188.07/187.97 [7324]~P101(f323(f323(f325(f866(x73241)),x73242),f154(x73241,f312(x73241,x73243))))+P101(f323(f323(f325(f866(x73241)),x73242),f312(f866(x73241),f150(x73241,x73243))))
% 188.07/187.97 [7349]~P101(f323(f323(f325(f866(x73491)),x73492),f312(f866(x73491),f150(x73491,x73493))))+P101(f323(f323(f325(f866(x73491)),x73492),f154(x73491,f312(x73491,x73493))))
% 188.07/187.97 [7385]E(f323(f323(f323(f183(f866(x73851),f866(x73851)),x73852),f161(x73851)),x73853),x73853)+~P101(f323(f323(f237(a865),f323(f189(f866(x73851)),x73853)),f76(a865)))
% 188.07/187.97 [7420]E(f323(f323(f121(x74201),f737(x74202,x74203,x74201)),f323(f323(f144(x74201),x74203),f759(x74202,x74203,x74201))),x74202)+~P101(f323(f323(f325(x74201),x74203),f323(f166(x74201),x74202)))
% 188.07/187.97 [7421]E(f323(f323(f121(x74211),f760(x74212,x74213,x74211)),f323(f323(f144(x74211),x74213),f761(x74212,x74213,x74211))),x74212)+~P101(f323(f323(f325(x74211),x74213),f323(f166(x74211),x74212)))
% 188.07/187.97 [7422]E(f323(f323(f121(x74221),f762(x74222,x74223,x74221)),f323(f323(f144(x74221),x74223),f763(x74222,x74223,x74221))),x74222)+~P101(f323(f323(f325(x74221),x74223),f323(f166(x74221),x74222)))
% 188.07/187.97 [7445]~P27(x74451,x74452,x74453,f246(f872(x74451,a860)))+P27(f866(x74451),f866(x74452),f323(f147(x74451,x74452),x74453),f246(f872(f866(x74451),a860)))
% 188.07/187.97 [7593]E(x75931,f323(f323(f78(a865),f323(f323(f79(a865),f323(f257(a865,a865),x75932)),x75933)),f323(f261(a865,a865),x75932)))+~P101(f323(f45(x75931,x75933),x75932))
% 188.07/187.97 [7601]P27(x76011,x76012,x76013,f246(f872(x76011,a860)))+~P27(f866(x76011),f866(x76012),f323(f147(x76011,x76012),x76013),f246(f872(f866(x76011),a860)))
% 188.07/187.97 [7644]P101(f323(f323(f325(f872(x76441,a860)),f724(x76442,x76443,x76441)),x76443))+P101(f323(f323(f325(x76441),x76442),f38(f872(x76441,a860),x76443)))
% 188.07/187.97 [7736]P101(f323(f323(f325(f866(x77361)),x77362),f154(x77361,x77363)))+~P101(f323(f323(f325(x77361),f614(x77363,x77362,x77361)),x77363))
% 188.07/187.97 [7837]P32(x78371,x78372,x78373)+~P101(f323(x78372,f323(f323(f158(x78371),x78373),f772(x78373,x78372,x78371))))
% 188.07/187.97 [7861]E(x78611,x78612)+~E(f323(f323(f7(x78613,f872(x78613,a860),a860),f325(x78613)),x78611),f323(f323(f7(x78613,f872(x78613,a860),a860),f325(x78613)),x78612))
% 188.07/187.97 [7869]~P101(f323(f323(f325(f871(x78691,x78691)),x78693),f255(x78691,x78692)))+P101(f323(f323(f325(x78691),f527(x78692,x78693,x78691)),x78692))
% 188.07/187.97 [7871]~P101(f323(f323(f325(x78711),x78713),f37(f872(x78711,a860),x78712)))+P101(f323(f323(f325(f872(x78711,a860)),f773(x78712,x78713,x78711)),x78712))
% 188.07/187.97 [7993]P27(x79931,x79932,f91(x79932,x79931,f246(f872(x79932,a860)),x79933),f246(f872(x79931,a860)))+~E(f323(f302(x79932,x79931,x79933),f246(f872(x79932,a860))),f246(f872(x79931,a860)))
% 188.07/187.97 [8045]~P101(f323(f323(f325(x80451),x80452),f323(f166(x80451),f760(x80453,x80452,x80451))))+~P101(f323(f323(f325(x80451),x80452),f323(f166(x80451),x80453)))
% 188.07/187.97 [8046]~P101(f323(f323(f325(x80461),x80462),f323(f166(x80461),f763(x80463,x80462,x80461))))+~P101(f323(f323(f325(x80461),x80462),f323(f166(x80461),x80463)))
% 188.07/187.97 [8133]E(f323(f232(f869(f866(a319)),f866(a319),f305(x81331,x81332,f323(f323(f78(a1),x81333),f76(a1))),f230(f866(a319))),f323(x81331,x81333)),f305(x81331,x81332,x81333))+P101(f323(f323(f238(a1),x81332),x81333))
% 188.07/187.97 [8235]E(x82351,f113(x82352))+P101(f323(f323(f325(x82352),f323(f257(x82352,f871(a99,a99)),f323(f274(x82352,x82351),x82353))),f323(f166(x82352),x82351)))
% 188.07/187.97 [8337]~P67(x83371)+E(f323(f135(x83371,x83371,f323(f7(x83371,x83371,x83371),f78(x83371)),x83372),f323(f162(x83371),x83373)),f323(f135(x83371,x83371,f78(x83371),x83372),x83373))
% 188.07/187.97 [8524]~P27(x85242,x85241,x85243,f246(f872(x85242,a860)))+E(f323(f302(x85241,x85242,f91(x85242,x85241,f246(f872(x85242,a860)),x85243)),f246(f872(x85241,a860))),f246(f872(x85242,a860)))
% 188.07/187.97 [8840]~P103(x88401)+E(f323(f166(x88401),f142(x88401,x88401,f5(x88401),x88402,x88403)),f323(f323(f301(x88401),x88402),f323(f166(x88401),x88403)))
% 188.07/187.97 [8850]~E(f323(x88503,f323(f91(x88501,x88502,f246(f872(x88501,a860)),x88503),f720(x88503,x88502,x88501))),f720(x88503,x88502,x88501))+E(f323(f302(x88501,x88502,x88503),f246(f872(x88501,a860))),f246(f872(x88502,a860)))
% 188.07/187.97 [8852]P101(f323(f323(f238(a865),f2(a865)),f741(x88521,x88522,x88523)))+~P101(f323(f323(f325(f871(x88523,x88523)),x88522),f323(f323(f280(x88523,x88523,x88523),x88521),f299(x88523,x88521))))
% 188.07/187.97 [9132]~P54(x91321,x91322)+~P101(f323(f323(f325(f871(x91321,x91321)),f323(f323(f258(x91321,x91321),x91323),x91323)),f323(f323(f280(x91321,x91321,x91321),x91322),f299(x91321,x91322))))
% 188.07/187.97 [9263]~E(f323(f323(f101(f872(f871(x92631,x92631),a860)),f323(f278(x92631,x92631),x92632)),f299(x92631,x92632)),f188(f872(f871(x92631,x92631),a860)))+~P101(f323(f323(f325(f871(x92631,x92631)),f323(f323(f258(x92631,x92631),x92633),x92633)),f323(f323(f280(x92631,x92631,x92631),x92632),f299(x92631,x92632))))
% 188.07/187.97 [9442]~P101(f323(f59(x94421),x94422))+P101(f323(f323(f237(a865),f323(f35(x94421),f323(f323(f22(f872(x94421,a860)),x94422),f323(f323(f301(x94421),x94423),f188(f872(x94421,a860)))))),f323(f35(x94421),x94422)))
% 188.07/187.97 [5048]~E(x50483,f113(x50481))+E(f137(x50481,f323(f323(f144(x50481),x50482),x50483)),x50482)
% 188.07/187.97 [5056]~E(x50563,f113(x50561))+E(f114(x50561,f323(f323(f144(x50561),x50562),x50563)),f113(x50561))
% 188.07/187.97 [5085]E(x50851,f113(x50852))+E(f137(x50852,f323(f323(f144(x50852),x50853),x50851)),f137(x50852,x50851))
% 188.07/187.97 [5087]E(x50871,f113(x50872))+E(f137(x50872,f323(f323(f121(x50872),x50873),x50871)),f137(x50872,x50871))
% 188.07/187.97 [5093]~E(x50933,f113(x50931))+E(f137(x50931,f323(f323(f121(x50931),x50932),x50933)),f137(x50931,x50932))
% 188.07/187.97 [5094]~E(x50943,f113(x50941))+E(f114(x50941,f323(f323(f121(x50941),x50942),x50943)),f114(x50941,x50942))
% 188.07/187.97 [5126]E(x51261,f113(x51262))+E(f323(f134(x51262),f323(f323(f121(x51262),x51261),x51263)),f323(f134(x51262),x51261))
% 188.07/187.97 [5154]~E(x51542,f113(x51541))+E(f323(f134(x51541),f323(f323(f121(x51541),x51542),x51543)),f323(f134(x51541),x51543))
% 188.07/187.97 [5202]~P2(x52021)+E(f323(f323(f110(x52021),x52022),f323(f323(f101(x52021),x52022),x52023)),x52022)
% 188.07/187.97 [5203]~P2(x52031)+E(f323(f323(f101(x52031),x52032),f323(f323(f110(x52031),x52032),x52033)),x52032)
% 188.07/187.97 [5204]~P103(x52041)+E(f323(f323(f235(x52041),x52042),f323(f323(f236(x52041),x52042),x52043)),x52042)
% 188.07/187.97 [5205]~P103(x52051)+E(f323(f323(f236(x52051),x52052),f323(f323(f235(x52051),x52052),x52053)),x52052)
% 188.07/187.97 [5222]~P57(x52221)+E(f42(x52221,f323(f323(f79(x52221),x52222),x52223),x52223),f2(x52221))
% 188.07/187.97 [5223]~P57(x52231)+E(f42(x52231,f323(f323(f79(x52231),x52232),x52233),x52232),f2(x52231))
% 188.07/187.97 [5297]~P60(x52971)+E(f323(f77(x52971),f323(f323(f22(x52971),x52972),x52973)),f323(f323(f22(x52971),x52973),x52972))
% 188.07/187.97 [5358]E(x53581,f113(x53582))+E(f114(x53582,f323(f323(f144(x53582),x53583),x53581)),f323(f323(f144(x53582),x53583),f114(x53582,x53581)))
% 188.07/187.97 [5359]E(x53591,f113(x53592))+E(f114(x53592,f323(f323(f121(x53592),x53593),x53591)),f323(f323(f121(x53592),x53593),f114(x53592,x53591)))
% 188.07/187.97 [5362]~P6(x53621)+E(f37(x53621,f323(f323(f301(x53621),x53622),x53623)),f323(f323(f110(x53621),x53622),f37(x53621,x53623)))
% 188.07/187.97 [5363]~P6(x53631)+E(f38(x53631,f323(f323(f301(x53631),x53632),x53633)),f323(f323(f101(x53631),x53632),f38(x53631,x53633)))
% 188.07/187.97 [5408]~P2(x54081)+E(f323(f323(f110(x54081),x54082),f323(f323(f110(x54081),x54082),x54083)),f323(f323(f110(x54081),x54082),x54083))
% 188.07/187.97 [5410]~P97(x54101)+E(f323(f323(f110(x54101),x54102),f323(f323(f110(x54101),x54102),x54103)),f323(f323(f110(x54101),x54102),x54103))
% 188.07/187.97 [5411]~P2(x54111)+E(f323(f323(f101(x54111),x54112),f323(f323(f101(x54111),x54112),x54113)),f323(f323(f101(x54111),x54112),x54113))
% 188.07/187.97 [5413]~P98(x54131)+E(f323(f323(f101(x54131),x54132),f323(f323(f101(x54131),x54132),x54133)),f323(f323(f101(x54131),x54132),x54133))
% 188.07/187.97 [5414]~P93(x54141)+E(f323(f323(f79(x54141),x54142),f323(f323(f79(x54141),x54142),x54143)),f323(f323(f79(x54141),x54142),x54143))
% 188.07/187.97 [5416]~P103(x54161)+E(f323(f323(f235(x54161),x54162),f323(f323(f235(x54161),x54162),x54163)),f323(f323(f235(x54161),x54162),x54163))
% 188.07/187.97 [5418]~P103(x54181)+E(f323(f323(f236(x54181),x54182),f323(f323(f236(x54181),x54182),x54183)),f323(f323(f236(x54181),x54182),x54183))
% 188.07/187.97 [5426]~P57(x54261)+E(f42(x54261,f323(f323(f78(x54261),x54262),x54263),x54263),f42(x54261,x54262,x54263))
% 188.07/187.97 [5427]~P57(x54271)+E(f42(x54271,f323(f323(f78(x54271),x54272),x54273),x54272),f42(x54271,x54273,x54272))
% 188.07/187.97 [5433]~P107(x54331)+E(f323(f323(f79(x54331),x54332),f323(f77(x54331),x54333)),f323(f77(x54331),f323(f323(f79(x54331),x54332),x54333)))
% 188.07/187.97 [5434]~P62(x54341)+E(f323(f323(f281(x54341),x54342),f323(f77(x54341),x54343)),f323(f77(x54341),f323(f323(f281(x54341),x54342),x54343)))
% 188.07/187.97 [5435]~P78(x54351)+E(f323(f323(f78(x54351),x54352),f323(f159(x54351),x54353)),f323(f159(x54351),f323(f323(f144(x54351),x54352),x54353)))
% 188.07/187.97 [5465]~P107(x54651)+E(f323(f323(f79(x54651),f323(f77(x54651),x54652)),x54653),f323(f323(f79(x54651),x54652),f323(f77(x54651),x54653)))
% 188.07/187.97 [5471]~P9(x54711,x54712,x54713)+E(f37(f872(x54711,a860),f323(f323(f58(x54711),x54712),x54713)),x54712)
% 188.07/187.97 [5530]~P110(x55301)+E(f323(f323(f79(x55301),x55302),f323(f323(f248(x55301),x55302),x55303)),f323(f323(f248(x55301),x55302),f323(a112,x55303)))
% 188.07/187.97 [5531]~P112(x55311)+E(f323(f323(f79(x55311),x55312),f323(f323(f248(x55311),x55312),x55313)),f323(f323(f248(x55311),x55312),f323(a112,x55313)))
% 188.07/187.97 [5541]~P59(x55411)+E(f323(f323(f78(x55411),f323(f77(x55411),x55412)),f323(f323(f78(x55411),x55412),x55413)),x55413)
% 188.07/187.97 [5564]~P140(x55641)+E(f323(f323(f248(x55641),f323(f100(x55641),x55642)),x55643),f323(f100(x55641),f323(f323(f248(a865),x55642),x55643)))
% 188.07/187.97 [5565]~P134(x55651)+E(f323(f323(f248(x55651),f323(f102(x55651),x55652)),x55653),f323(f102(x55651),f323(f323(f248(a1),x55652),x55653)))
% 188.07/187.97 [5571]~P82(x55711)+E(f323(f73(x55711),f323(f323(f22(x55711),x55712),x55713)),f323(f73(x55711),f323(f323(f22(x55711),x55713),x55712)))
% 188.07/187.97 [5573]~P116(x55731)+E(f323(f323(f79(x55731),f80(x55731,x55732)),f80(x55731,x55733)),f80(x55731,f323(f323(f79(x55731),x55732),x55733)))
% 188.07/187.97 [5577]E(x55771,f113(x55772))+E(f323(f323(f121(x55772),f323(f165(x55772),x55771)),x55773),f323(f165(x55772),f323(f323(f121(x55772),x55771),x55773)))
% 188.07/187.97 [5582]~E(x55822,f323(a112,f323(f323(f78(a865),x55821),x55823)))+P101(f323(f323(f238(a865),x55821),x55822))
% 188.07/187.97 [5583]~P107(x55831)+E(f323(f323(f79(x55831),f323(f77(x55831),x55832)),x55833),f323(f77(x55831),f323(f323(f79(x55831),x55832),x55833)))
% 188.07/187.97 [5584]~P114(x55841)+E(f323(f323(f281(x55841),f323(f77(x55841),x55842)),x55843),f323(f77(x55841),f323(f323(f281(x55841),x55842),x55843)))
% 188.07/187.97 [5585]~P116(x55851)+E(f323(f323(f248(x55851),f323(f73(x55851),x55852)),x55853),f323(f73(x55851),f323(f323(f248(x55851),x55852),x55853)))
% 188.07/187.97 [5683]E(f555(x56831,x56832,x56833),f564(x56831,x56832,x56833))+E(f323(f323(f101(f872(x56833,a860)),x56832),x56831),f188(f872(x56833,a860)))
% 188.07/187.97 [5698]~P72(x56982)+E(f323(f323(f6(x56981,x56982),f323(f16(x56982,x56981),f2(x56982))),x56983),f2(x56982))
% 188.07/187.97 [5699]~P68(x56992)+E(f323(f323(f9(x56991,x56992),f323(f16(x56992,x56991),f76(x56992))),x56993),f76(x56992))
% 188.07/187.97 [5701]~P140(x57011)+E(f323(f323(f79(x57011),f323(f100(x57011),x57012)),f323(f100(x57011),x57013)),f323(f100(x57011),f323(f323(f79(a865),x57012),x57013)))
% 188.07/187.97 [5702]~P140(x57021)+E(f323(f323(f78(x57021),f323(f100(x57021),x57022)),f323(f100(x57021),x57023)),f323(f100(x57021),f323(f323(f78(a865),x57022),x57023)))
% 188.07/187.97 [5703]~P134(x57031)+E(f323(f323(f22(x57031),f323(f102(x57031),x57032)),f323(f102(x57031),x57033)),f323(f102(x57031),f323(f323(f22(a1),x57032),x57033)))
% 188.07/187.97 [5704]~P134(x57041)+E(f323(f323(f79(x57041),f323(f102(x57041),x57042)),f323(f102(x57041),x57043)),f323(f102(x57041),f323(f323(f79(a1),x57042),x57043)))
% 188.07/187.97 [5705]~P134(x57051)+E(f323(f323(f78(x57051),f323(f102(x57051),x57052)),f323(f102(x57051),x57053)),f323(f102(x57051),f323(f323(f78(a1),x57052),x57053)))
% 188.07/187.97 [5706]~P90(x57061)+E(f323(f323(f22(x57061),f323(f103(x57061),x57062)),f323(f103(x57061),x57063)),f323(f103(x57061),f323(f323(f22(a1),x57062),x57063)))
% 188.07/187.97 [5709]~P90(x57091)+E(f323(f323(f79(x57091),f323(f103(x57091),x57092)),f323(f103(x57091),x57093)),f323(f103(x57091),f323(f323(f79(a1),x57092),x57093)))
% 188.07/187.97 [5710]~P90(x57101)+E(f323(f323(f78(x57101),f323(f103(x57101),x57102)),f323(f103(x57101),x57103)),f323(f103(x57101),f323(f323(f78(a1),x57102),x57103)))
% 188.07/187.97 [5757]~E(x57573,x57572)+P101(f323(f323(f237(f872(x57571,a860)),x57572),x57573))
% 188.07/187.97 [5763]~E(x57632,x57633)+P101(f323(f323(f237(f872(x57631,a860)),x57632),x57633))
% 188.07/187.97 [5768]~P87(x57681)+E(f323(f323(f101(x57681),f323(f77(x57681),x57682)),f323(f77(x57681),x57683)),f323(f77(x57681),f323(f323(f110(x57681),x57682),x57683)))
% 188.07/187.97 [5769]~P87(x57691)+E(f323(f323(f110(x57691),f323(f77(x57691),x57692)),f323(f77(x57691),x57693)),f323(f77(x57691),f323(f323(f101(x57691),x57692),x57693)))
% 188.07/187.97 [5770]~P59(x57701)+E(f323(f323(f78(x57701),f323(f77(x57701),x57702)),f323(f77(x57701),x57703)),f323(f77(x57701),f323(f323(f78(x57701),x57703),x57702)))
% 188.07/187.97 [5771]~P60(x57711)+E(f323(f323(f78(x57711),f323(f77(x57711),x57712)),f323(f77(x57711),x57713)),f323(f77(x57711),f323(f323(f78(x57711),x57712),x57713)))
% 188.07/187.97 [5772]~P74(x57721)+E(f323(f323(f236(x57721),f323(f77(x57721),x57722)),f323(f77(x57721),x57723)),f323(f77(x57721),f323(f323(f235(x57721),x57722),x57723)))
% 188.07/187.97 [5773]~P74(x57731)+E(f323(f323(f235(x57731),f323(f77(x57731),x57732)),f323(f77(x57731),x57733)),f323(f77(x57731),f323(f323(f236(x57731),x57732),x57733)))
% 188.07/187.97 [5774]~P116(x57741)+E(f323(f323(f79(x57741),f323(f73(x57741),x57742)),f323(f73(x57741),x57743)),f323(f73(x57741),f323(f323(f79(x57741),x57742),x57743)))
% 188.07/187.97 [5775]~P64(x57751)+E(f323(f323(f281(x57751),f323(f73(x57751),x57752)),f323(f73(x57751),x57753)),f323(f73(x57751),f323(f323(f281(x57751),x57752),x57753)))
% 188.07/187.97 [5776]~P78(x57761)+E(f323(f323(f78(x57761),f323(f159(x57761),x57762)),f323(f159(x57761),x57763)),f323(f159(x57761),f323(f323(f121(x57761),x57762),x57763)))
% 188.07/187.97 [5777]E(x57771,f188(f872(x57772,a860)))+~E(f323(f323(f110(f872(x57772,a860)),x57773),x57771),f188(f872(x57772,a860)))
% 188.07/187.97 [5778]E(x57781,f188(f872(x57782,a860)))+~E(f323(f323(f110(f872(x57782,a860)),x57781),x57783),f188(f872(x57782,a860)))
% 188.07/187.97 [5779]~P143(x57791,x57792,x57793)+P101(f323(x57791,f323(f323(f36(a1),x57792),x57793)))
% 188.07/187.97 [5829]~P101(f323(f59(x58291),x58293))+P101(f323(f59(x58291),f323(f323(f301(x58291),x58292),x58293)))
% 188.07/187.97 [5830]~P101(f323(f130(x58301),x58303))+P101(f323(f130(x58301),f323(f323(f169(x58301),x58302),x58303)))
% 188.07/187.97 [5831]~P101(f323(f130(x58311),x58313))+P101(f323(f130(x58311),f323(f323(f131(x58311),x58312),x58313)))
% 188.07/187.97 [5860]~P2(x58601)+P101(f323(f323(f237(x58601),x58602),f323(f323(f110(x58601),x58603),x58602)))
% 188.07/187.97 [5861]~P97(x58611)+P101(f323(f323(f237(x58611),x58612),f323(f323(f110(x58611),x58613),x58612)))
% 188.07/187.97 [5862]~P2(x58621)+P101(f323(f323(f237(x58621),x58622),f323(f323(f110(x58621),x58622),x58623)))
% 188.07/187.97 [5863]~P97(x58631)+P101(f323(f323(f237(x58631),x58632),f323(f323(f110(x58631),x58632),x58633)))
% 188.07/187.97 [5864]~P103(x58641)+P101(f323(f323(f237(x58641),x58642),f323(f323(f236(x58641),x58643),x58642)))
% 188.07/187.97 [5865]~P103(x58651)+P101(f323(f323(f237(x58651),x58652),f323(f323(f236(x58651),x58652),x58653)))
% 188.07/187.97 [5879]~E(x58791,f2(a865))+E(f323(f323(f36(a865),f323(f323(f79(a865),x58791),x58792)),f323(f323(f79(a865),x58791),x58793)),f2(a865))
% 188.07/187.97 [5957]~P90(x59571)+E(f323(f323(f22(x59571),f323(f103(x59571),x59572)),f323(f103(x59571),x59573)),f323(f103(x59571),f323(f323(f78(a1),x59572),f323(f77(a1),x59573))))
% 188.07/187.97 [6009]E(x60091,f2(a865))+E(f323(f323(f36(a865),f323(f323(f79(a865),x60091),x60092)),f323(f323(f79(a865),x60091),x60093)),f323(f323(f36(a865),x60092),x60093))
% 188.07/187.97 [6043]E(f145(x60431,f323(f323(f144(x60431),x60432),x60433)),f323(f323(f144(x60431),x60432),f145(x60431,x60433)))+P101(f323(f323(f325(x60431),x60432),f323(f166(x60431),x60433)))
% 188.07/187.97 [6077]P143(x60771,x60772,x60773)+~P101(f323(x60771,f323(f323(f36(a1),x60772),x60773)))
% 188.07/187.97 [6146]E(x61461,f113(x61462))+E(f323(f323(f144(x61462),f323(f134(x61462),x61461)),f323(f323(f169(x61462),x61463),f323(f165(x61462),x61461))),f323(f323(f169(x61462),f323(a112,x61463)),x61461))
% 188.07/187.97 [6152]E(f323(f323(f22(f872(x61521,a860)),x61522),x61523),x61522)+~E(f323(f323(f101(f872(x61521,a860)),x61522),x61523),f188(f872(x61521,a860)))
% 188.07/187.97 [6166]E(f145(x61661,f323(f323(f144(x61661),x61662),x61663)),f145(x61661,x61663))+~P101(f323(f323(f325(x61661),x61662),f323(f166(x61661),x61663)))
% 188.07/187.97 [6198]~P101(f323(f323(f237(a865),x61981),x61983))+P101(f323(f323(f237(a865),x61981),f323(f323(f78(a865),x61982),x61983)))
% 188.07/187.97 [6200]~P101(f323(f323(f237(a865),x62001),x62002))+P101(f323(f323(f237(a865),x62001),f323(f323(f78(a865),x62002),x62003)))
% 188.07/187.97 [6202]~P101(f323(f323(f238(a865),x62021),x62023))+P101(f323(f323(f238(a865),x62021),f323(f323(f78(a865),x62022),x62023)))
% 188.07/187.97 [6204]~P101(f323(f323(f238(a865),x62041),x62042))+P101(f323(f323(f238(a865),x62041),f323(f323(f78(a865),x62042),x62043)))
% 188.07/187.97 [6242]P101(f323(f59(x62421),x62422))+~P101(f323(f59(x62421),f323(f323(f301(x62421),x62423),x62422)))
% 188.07/187.97 [6243]P101(f323(f130(x62431),x62432))+~P101(f323(f130(x62431),f323(f323(f144(x62431),x62433),x62432)))
% 188.07/187.97 [6244]P101(f323(f130(x62441),x62442))+~P101(f323(f130(x62441),f323(f323(f121(x62441),x62443),x62442)))
% 188.07/187.97 [6245]P101(f323(f130(x62451),x62452))+~P101(f323(f130(x62451),f323(f323(f121(x62451),x62452),x62453)))
% 188.07/187.97 [6291]~P112(x62911)+E(f323(f323(f78(x62911),x62912),f323(f323(f79(x62911),x62913),x62912)),f323(f323(f79(x62911),f323(f323(f78(x62911),x62913),f76(x62911))),x62912))
% 188.07/187.97 [6337]~E(x63371,x63372)+~P101(f323(f323(f238(f872(x63373,a860)),x63371),x63372))
% 188.07/187.97 [6382]P101(f323(f323(f325(x63821),x63822),x63823))+P101(f323(f323(f325(x63821),x63822),f323(f77(f872(x63821,a860)),x63823)))
% 188.07/187.97 [6388]E(f137(x63881,f323(f323(f131(x63881),x63882),x63883)),f137(x63881,x63883))+~P101(f323(f323(f238(a865),x63882),f323(f189(f866(x63881)),x63883)))
% 188.07/187.97 [6389]E(f323(f323(f169(x63891),x63892),f114(x63891,x63893)),f323(f323(f169(x63891),x63892),x63893))+~P101(f323(f323(f238(a865),x63892),f323(f189(f866(x63891)),x63893)))
% 188.07/187.97 [6442]E(f323(f323(f323(f183(f866(x64421),f866(x64421)),x64422),f161(x64421)),x64423),x64423)+~E(f42(a865,x64422,f323(f189(f866(x64421)),x64423)),f2(a865))
% 188.07/187.97 [6449]~P9(x64491,x64493,x64492)+E(f323(f323(f280(x64491,x64491,x64491),f323(f278(x64491,x64491),x64492)),x64492),x64492)
% 188.07/187.97 [6491]~E(f323(f323(f110(f872(x64911,a860)),x64912),x64913),x64913)+P101(f323(f323(f237(f872(x64911,a860)),x64912),x64913))
% 188.07/187.97 [6496]~P51(x64961,x64961,x64963)+P51(x64961,x64961,f323(f323(f183(f871(x64961,x64961),a860),x64962),x64963))
% 188.07/187.97 [6499]~P101(f323(f323(f325(x64991),x64993),f323(f166(x64991),x64992)))+P101(f323(f323(f238(a865),f2(a865)),f323(f189(f866(x64991)),x64992)))
% 188.07/187.97 [6525]~P82(x65251)+E(f323(f73(x65251),f323(f323(f78(x65251),f323(f73(x65251),x65252)),f323(f73(x65251),x65253))),f323(f323(f78(x65251),f323(f73(x65251),x65252)),f323(f73(x65251),x65253)))
% 188.07/187.97 [6535]E(f323(f323(f36(a865),f323(f323(f79(a865),x65351),x65352)),f323(f323(f79(a865),x65351),x65353)),f323(f323(f36(a865),x65352),x65353))+~P101(f323(f323(f238(a865),f2(a865)),x65351))
% 188.07/187.97 [6671]~P101(f323(f59(x66711),x66713))+E(f323(f323(f62(x66711,f872(x66711,a860),f301(x66711)),x66712),x66713),f323(f323(f110(f872(x66711,a860)),x66713),x66712))
% 188.07/187.97 [6729]E(f323(f323(f110(f872(x67291,a860)),x67292),x67293),x67292)+~P101(f323(f323(f237(f872(x67291,a860)),x67293),x67292))
% 188.07/187.97 [6731]E(f323(f323(f110(f872(x67311,a860)),x67312),x67313),x67313)+~P101(f323(f323(f237(f872(x67311,a860)),x67312),x67313))
% 188.07/187.97 [6732]E(f323(f323(f101(f872(x67321,a860)),x67322),x67323),x67323)+~P101(f323(f323(f237(f872(x67321,a860)),x67323),x67322))
% 188.07/187.97 [6733]E(f323(f323(f101(f872(x67331,a860)),x67332),x67333),x67332)+~P101(f323(f323(f237(f872(x67331,a860)),x67332),x67333))
% 188.07/187.97 [6785]~P101(f323(f130(x67851),x67852))+E(f323(f323(f22(f872(x67851,a860)),f323(f166(x67851),x67852)),f323(f323(f301(x67851),x67853),f188(f872(x67851,a860)))),f323(f166(x67851),f164(x67851,x67853,x67852)))
% 188.07/187.97 [6838]P38(x68381,x68382)+~P38(x68381,f323(f323(f183(f871(x68381,x68381),a860),x68383),x68382))
% 188.07/187.97 [6901]P101(f323(f46(x69011,x69012),f323(a48,x69013)))+~P101(f323(f46(f323(f77(a1),x69011),f323(f77(a1),x69012)),x69013))
% 188.07/187.97 [6906]E(f323(f323(f22(f872(x69061,a860)),f323(f323(f301(x69061),x69062),x69063)),f323(f323(f301(x69061),x69062),f188(f872(x69061,a860)))),x69063)+P101(f323(f323(f325(x69061),x69062),x69063))
% 188.07/187.97 [6927]E(f323(f323(f101(f872(x69271,a860)),f323(f166(x69271),x69272)),f323(f166(x69271),x69273)),f188(f872(x69271,a860)))+~P101(f323(f130(x69271),f323(f323(f121(x69271),x69272),x69273)))
% 188.07/187.97 [6943]~P101(f323(f323(f325(x69431),x69432),f323(f166(x69431),x69433)))+~P101(f323(f130(x69431),f323(f323(f144(x69431),x69432),x69433)))
% 188.07/187.97 [7013]P32(x70131,x70132,x70133)+P101(f323(f323(f238(a865),f772(x70133,x70132,x70131)),f323(f189(f866(x70131)),x70133)))
% 188.07/187.97 [7023]E(f323(f323(f101(f872(x70231,a860)),x70232),x70233),f188(f872(x70231,a860)))+P101(f323(f323(f325(x70231),f555(x70233,x70232,x70231)),x70232))
% 188.07/187.97 [7024]E(f323(f323(f101(f872(x70241,a860)),x70242),x70243),f188(f872(x70241,a860)))+P101(f323(f323(f325(x70241),f564(x70243,x70242,x70241)),x70243))
% 188.07/187.97 [7028]E(f114(x70281,f323(f323(f169(x70281),x70282),x70283)),f323(f323(f169(x70281),f323(f323(f22(a865),x70282),f76(a865))),x70283))+~P101(f323(f323(f237(a865),x70282),f323(f189(f866(x70281)),x70283)))
% 188.07/187.97 [7087]~P34(x70873,x70872,x70871)+P101(f323(f323(f238(a865),f723(x70871,x70872,x70873)),f323(f189(f866(x70873)),x70871)))
% 188.07/187.97 [7105]P101(f323(f323(f238(a865),f2(a865)),x71051))+P101(f323(f323(f237(a865),f323(f323(f79(a865),x71052),x71051)),f323(f323(f79(a865),x71053),x71051)))
% 188.07/187.97 [7106]P101(f323(f323(f238(a865),f2(a865)),x71061))+P101(f323(f323(f237(a865),f323(f323(f79(a865),x71061),x71062)),f323(f323(f79(a865),x71061),x71063)))
% 188.07/187.97 [7109]~P101(f323(f323(f325(x71091),x71092),x71093))+~P101(f323(f323(f325(x71091),x71092),f323(f77(f872(x71091,a860)),x71093)))
% 188.07/187.97 [7116]~P101(f323(f323(f238(f872(x71161,a860)),x71162),x71163))+P101(f323(f323(f237(f872(x71161,a860)),x71162),x71163))
% 188.07/187.97 [7215]~P101(f323(f323(f237(a865),x72153),x72152))+P101(f323(f323(f237(a865),f323(f323(f22(a865),x72151),x72152)),f323(f323(f22(a865),x72151),x72153)))
% 188.07/187.97 [7216]~P101(f323(f323(f237(a865),x72161),x72163))+P101(f323(f323(f237(a865),f323(f323(f22(a865),x72161),x72162)),f323(f323(f22(a865),x72163),x72162)))
% 188.07/187.97 [7218]~P101(f323(f323(f237(a865),x72182),x72183))+P101(f323(f323(f237(a865),f323(f323(f79(a865),x72181),x72182)),f323(f323(f79(a865),x72181),x72183)))
% 188.07/187.97 [7220]~P101(f323(f323(f237(a865),x72201),x72203))+P101(f323(f323(f237(a865),f323(f323(f79(a865),x72201),x72202)),f323(f323(f79(a865),x72203),x72202)))
% 188.07/187.97 [7221]~P101(f323(f323(f237(a865),x72212),x72213))+P101(f323(f323(f237(a865),f323(f323(f78(a865),x72211),x72212)),f323(f323(f78(a865),x72211),x72213)))
% 188.07/187.97 [7222]~P101(f323(f323(f237(a865),x72221),x72223))+P101(f323(f323(f237(a865),f323(f323(f78(a865),x72221),x72222)),f323(f323(f78(a865),x72223),x72222)))
% 188.07/187.97 [7223]~P101(f323(f323(f237(a865),x72231),x72233))+P101(f323(f323(f237(a865),f323(f323(f36(a865),x72231),x72232)),f323(f323(f36(a865),x72233),x72232)))
% 188.07/187.97 [7224]~P101(f323(f323(f237(a1),x72242),x72243))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x72241),x72242)),f323(f323(f78(a1),x72241),x72243)))
% 188.07/187.97 [7227]~P101(f323(f323(f238(a865),x72272),x72273))+P101(f323(f323(f238(a865),f323(f323(f78(a865),x72271),x72272)),f323(f323(f78(a865),x72271),x72273)))
% 188.07/187.97 [7228]~P101(f323(f323(f238(a865),x72281),x72283))+P101(f323(f323(f238(a865),f323(f323(f78(a865),x72281),x72282)),f323(f323(f78(a865),x72283),x72282)))
% 188.07/187.97 [7229]~P101(f323(f323(f238(a1),x72291),x72293))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x72291),x72292)),f323(f323(f78(a1),x72293),x72292)))
% 188.07/187.97 [7307]E(x73071,x73072)+~P101(f323(f323(f325(x73073),x73071),f323(f323(f301(x73073),x73072),f188(f872(x73073,a860)))))
% 188.07/187.97 [7309]~E(f323(f323(f101(f872(x73091,a860)),x73092),x73093),f188(f872(x73091,a860)))+P101(f323(f323(f237(f872(x73091,a860)),x73092),f323(f77(f872(x73091,a860)),x73093)))
% 188.07/187.97 [7316]P101(f323(f323(f325(f872(x73161,a860)),x73162),f323(f300(x73161),x73163)))+~P101(f323(f323(f237(f872(x73161,a860)),x73162),x73163))
% 188.07/187.97 [7369]E(f323(f323(f144(x73691),f323(f323(f158(x73691),x73692),x73693)),f323(f323(f131(x73691),f323(a112,x73693)),x73692)),f323(f323(f131(x73691),x73693),x73692))+~P101(f323(f323(f238(a865),x73693),f323(f189(f866(x73691)),x73692)))
% 188.07/187.97 [7396]P101(f323(f323(f325(f871(x73961,x73961)),x73962),f299(x73961,x73963)))+~P101(f323(f323(f325(f871(x73961,x73961)),x73962),x73963))
% 188.07/187.97 [7406]~P101(f323(f323(f325(f872(x74061,a860)),x74062),f323(f300(x74061),x74063)))+P101(f323(f323(f237(f872(x74061,a860)),x74062),x74063))
% 188.07/187.97 [7451]P101(f323(f323(f237(f872(x74511,a860)),x74512),f37(f872(x74511,a860),x74513)))+~P101(f323(f323(f325(f872(x74511,a860)),x74512),x74513))
% 188.07/187.97 [7476]~P134(x74761)+E(f323(f323(f79(x74761),f323(f323(f248(x74761),f323(f77(x74761),f76(x74761))),x74762)),f323(f323(f248(x74761),x74763),x74762)),f323(f323(f248(x74761),f323(f77(x74761),x74763)),x74762))
% 188.07/187.97 [7497]E(f323(f323(f158(x74971),x74972),f323(f323(f22(a865),f323(f189(f866(x74971)),x74972)),f323(a112,x74973))),f323(f323(f158(x74971),f323(f162(x74971),x74972)),x74973))+~P101(f323(f323(f238(a865),x74973),f323(f189(f866(x74971)),x74972)))
% 188.07/187.97 [7514]~E(f323(f323(f101(f872(x75141,a860)),f550(x75143,x75142,x75141)),x75143),f188(f872(x75141,a860)))+E(f323(f323(f101(f872(x75141,a860)),f37(f872(x75141,a860),x75142)),x75143),f188(f872(x75141,a860)))
% 188.07/187.97 [7575]~P101(f323(f323(f325(x75753),x75752),f323(f166(x75753),x75751)))+P101(f323(f323(f238(a865),f543(x75751,x75752,x75753)),f323(f189(f866(x75753)),x75751)))
% 188.07/187.97 [7583]P101(f323(f323(f325(x75831),f323(f323(f158(x75831),x75832),x75833)),f323(f166(x75831),x75832)))+~P101(f323(f323(f238(a865),x75833),f323(f189(f866(x75831)),x75832)))
% 188.07/187.97 [7683]~P101(f323(x76832,f606(x76833,x76832,x76831)))+E(f323(f323(f131(x76831),f323(f189(f866(x76831)),f171(x76831,x76832,x76833))),x76833),f113(x76831))
% 188.07/187.97 [7694]P101(f323(f323(f237(f872(f866(x76941),a860)),f154(x76941,x76942)),f154(x76941,x76943)))+~P101(f323(f323(f237(f872(x76941,a860)),x76942),x76943))
% 188.07/187.97 [7695]P101(f323(f323(f237(f872(f866(x76951),a860)),f153(x76951,x76952)),f153(x76951,x76953)))+~P101(f323(f323(f237(f872(x76951,a860)),x76952),x76953))
% 188.07/187.97 [7722]E(f323(f323(f101(f872(x77221,a860)),f37(f872(x77221,a860),x77222)),x77223),f188(f872(x77221,a860)))+P101(f323(f323(f325(f872(x77221,a860)),f550(x77223,x77222,x77221)),x77222))
% 188.07/187.97 [7725]~P101(f323(f323(f325(f872(x77251,a860)),x77253),x77252))+P101(f323(f323(f237(f872(x77251,a860)),f38(f872(x77251,a860),x77252)),x77253))
% 188.07/187.97 [7727]E(f323(f323(f101(f872(x77271,a860)),x77272),x77273),f188(f872(x77271,a860)))+~P101(f323(f323(f237(f872(x77271,a860)),x77272),f323(f77(f872(x77271,a860)),x77273)))
% 188.07/187.97 [7773]E(f323(f323(f22(a865),f323(f323(f78(a865),f323(f159(a865),x77731)),x77732)),f323(f323(f158(a865),x77731),x77733)),f323(f159(a865),f323(f323(f152(a865,x77731),x77733),x77732)))+~P101(f323(f323(f238(a865),x77733),f323(f189(f866(a865)),x77731)))
% 188.07/187.97 [7825]P101(f323(f323(f237(a865),x78251),x78252))+~P101(f323(f323(f237(a865),f323(f323(f78(a865),x78253),x78251)),f323(f323(f78(a865),x78253),x78252)))
% 188.07/187.97 [7828]P101(f323(f323(f238(a865),x78281),x78282))+~P101(f323(f323(f238(a865),f323(f323(f78(a865),x78283),x78281)),f323(f323(f78(a865),x78283),x78282)))
% 188.07/187.97 [7829]P101(f323(f323(f238(a865),x78291),x78292))+~P101(f323(f323(f238(a865),f323(f323(f79(a865),x78293),x78291)),f323(f323(f79(a865),x78293),x78292)))
% 188.07/187.97 [7830]P101(f323(f323(f238(a865),x78301),x78302))+~P101(f323(f323(f238(a865),f323(f323(f79(a865),x78301),x78303)),f323(f323(f79(a865),x78302),x78303)))
% 188.07/187.97 [7859]P101(f323(f323(f238(a865),f2(a865)),x78591))+~P101(f323(f323(f238(a865),f323(f323(f79(a865),x78592),x78591)),f323(f323(f79(a865),x78593),x78591)))
% 188.07/187.97 [7860]P101(f323(f323(f238(a865),f2(a865)),x78601))+~P101(f323(f323(f238(a865),f323(f323(f79(a865),x78601),x78602)),f323(f323(f79(a865),x78601),x78603)))
% 188.07/187.97 [7936]E(f250(x79361,x79362,x79363),x79362)+~P101(f323(f323(f237(f872(x79361,a860)),x79363),f323(f323(f301(x79361),x79362),f188(f872(x79361,a860)))))
% 188.07/187.97 [7986]~P101(f323(f130(x79861),x79863))+E(f323(f129(x79861,f323(f323(f8(a860,a860,x79861),a318),f323(a320,x79862))),x79863),f164(x79861,x79862,x79863))
% 188.07/187.97 [8011]E(f323(f323(f131(x80111),f323(f189(f866(x80111)),f171(x80111,x80112,x80113))),x80113),f113(x80111))+P101(f323(f323(f325(x80111),f606(x80113,x80112,x80111)),f323(f166(x80111),x80113)))
% 188.07/187.97 [8015]E(f323(f323(f121(x80151),f323(f323(f169(x80151),x80152),x80153)),f323(f323(f144(x80151),f323(f323(f158(x80151),x80153),x80152)),f113(x80151))),f323(f323(f169(x80151),f323(a112,x80152)),x80153))+~P101(f323(f323(f238(a865),x80152),f323(f189(f866(x80151)),x80153)))
% 188.07/187.97 [8074]E(f323(f129(x80741,f323(f323(f8(a860,a860,x80741),a318),f323(a320,x80742))),x80743),x80743)+P101(f323(f323(f325(x80741),x80742),f323(f166(x80741),x80743)))
% 188.07/187.97 [8081]P101(f323(f323(f237(f872(f872(x80811,a860),a860)),f251(x80811,x80812)),f251(x80811,x80813)))+~P101(f323(f323(f237(f872(x80811,a860)),x80812),x80813))
% 188.07/187.97 [8124]~P101(f323(f130(x81241),x81243))+P101(f323(f130(x81241),f323(f323(f323(f183(f866(x81241),f866(x81241)),x81242),f161(x81241)),x81243)))
% 188.07/187.97 [8130]~P101(f323(f323(f238(a865),x81302),x81303))+P101(f323(f323(f238(a865),f323(f323(f79(a865),f323(a112,x81301)),x81302)),f323(f323(f79(a865),f323(a112,x81301)),x81303)))
% 188.07/187.97 [8151]P101(f323(f323(f237(f872(f872(x81511,a860),a860)),f323(f300(x81511),x81512)),f323(f300(x81511),x81513)))+~P101(f323(f323(f237(f872(x81511,a860)),x81512),x81513))
% 188.07/187.97 [8220]~E(f323(f302(x82201,x82202,x82203),f246(f872(x82201,a860))),f246(f872(x82202,a860)))+E(f323(f71(x82201,x82202,x82202,x82203),f91(x82201,x82202,f246(f872(x82201,a860)),x82203)),f32(x82202))
% 188.07/187.97 [8317]~P101(f323(f323(f237(f872(x83171,a860)),x83173),x83172))+P101(f323(f323(f237(f872(x83171,a860)),f323(f77(f872(x83171,a860)),x83172)),f323(f77(f872(x83171,a860)),x83173)))
% 188.07/187.97 [8350]E(f323(f302(a865,a865,f323(f323(f7(a865,a865,a865),f22(a865)),x83501)),f323(f293(a865,x83502),x83503)),f323(f293(a865,f323(f323(f22(a865),x83502),x83501)),f323(f323(f22(a865),x83503),x83501)))+~P101(f323(f323(f238(a865),x83501),x83503))
% 188.07/187.97 [8378]~P78(x83781)+E(f323(f323(f78(x83781),x83782),f323(f135(x83781,x83781,f78(x83781),f2(x83781)),x83783)),f323(f135(x83781,x83781,f78(x83781),x83782),x83783))
% 188.07/187.97 [8450]~P82(x84501)+P101(f323(f323(f237(x84501),f323(f73(x84501),f323(f323(f22(x84501),x84502),x84503))),f323(f323(f78(x84501),f323(f73(x84501),x84502)),f323(f73(x84501),x84503))))
% 188.07/187.97 [8451]~P82(x84511)+P101(f323(f323(f237(x84511),f323(f73(x84511),f323(f323(f78(x84511),x84512),x84513))),f323(f323(f78(x84511),f323(f73(x84511),x84512)),f323(f73(x84511),x84513))))
% 188.07/187.97 [8461]E(f323(f323(f78(a1),f323(f323(f79(a1),x84611),f42(a1,f323(f323(f36(a1),x84612),x84611),x84613))),f42(a1,x84612,x84611)),f42(a1,x84612,f323(f323(f79(a1),x84611),x84613)))+~P101(f323(f323(f238(a1),f2(a1)),x84613))
% 188.07/187.97 [8467]E(f323(f323(f121(x84671),f323(f323(f169(x84671),x84672),x84673)),f323(f323(f144(x84671),f323(f134(x84671),f323(f323(f131(x84671),x84672),x84673))),f113(x84671))),f323(f323(f169(x84671),f323(a112,x84672)),x84673))+~P101(f323(f323(f238(a865),x84672),f323(f189(f866(x84671)),x84673)))
% 188.07/187.97 [8487]E(f323(f269(x84871,f323(f323(f147(x84871,f871(a99,x84871)),f323(f258(a99,x84871),f76(a99))),x84872)),f323(a3,x84873)),f323(f323(f158(x84871),x84872),x84873))+~P101(f323(f323(f238(a865),x84873),f323(f189(f866(x84871)),x84872)))
% 188.07/187.97 [8555]P101(f323(f323(f325(f871(x85551,x85551)),x85552),f323(f323(f280(x85551,x85551,x85551),x85553),f299(x85551,x85553))))+~P101(f323(f323(f325(f871(x85551,x85551)),x85552),x85553))
% 188.07/187.97 [8567]E(f323(f302(x85671,x85672,x85673),f246(f872(x85671,a860))),f246(f872(x85672,a860)))+~E(f323(f71(x85671,x85672,x85672,x85673),f91(x85671,x85672,f246(f872(x85671,a860)),x85673)),f32(x85672))
% 188.07/187.97 [8577]P101(f323(f323(f237(a865),x85771),x85772))+~P101(f323(f323(f237(a865),f323(f323(f79(a865),f323(a112,x85773)),x85771)),f323(f323(f79(a865),f323(a112,x85773)),x85772)))
% 188.07/187.97 [8592]P101(f323(f323(f237(f872(x85921,a860)),x85922),x85923))+~P101(f323(f323(f237(f872(x85921,a860)),f323(f77(f872(x85921,a860)),x85923)),f323(f77(f872(x85921,a860)),x85922)))
% 188.07/187.97 [8616]P101(f323(f130(x86161),x86162))+~P101(f323(f130(x86161),f323(f323(f323(f183(f866(x86161),f866(x86161)),x86163),f161(x86161)),x86162)))
% 188.07/187.97 [8681]E(f323(f302(f871(x86811,x86812),x86812,f261(x86811,x86812)),f323(f166(f871(x86811,x86812)),x86813)),f178(x86811,x86812,f323(f179(x86811,x86812),x86813)))+~P101(f323(f130(x86811),f323(f323(f147(f871(x86811,x86812),x86811),f257(x86811,x86812)),x86813)))
% 188.07/187.97 [8690]E(f323(f277(x86901,x86901,f299(x86901,x86902)),x86903),x86903)+~P101(f323(f323(f237(f872(x86901,a860)),f323(f277(x86901,x86901,x86902),x86903)),x86903))
% 188.07/187.97 [8738]~P103(x87381)+P16(x87381,f323(f129(x87381,f323(f323(f7(x87381,x87381,a860),a320),f323(x87382,x87383))),x87383))
% 188.07/187.97 [8746]~P101(f323(f323(f237(a865),x87461),x87462))+P101(f323(f323(f237(a865),x87461),f323(f135(a865,a865,f78(a865),x87462),x87463)))
% 188.07/187.97 [8825]~P101(f323(f323(f325(f871(x88251,x88251)),x88252),f299(x88251,x88253)))+P101(f323(f323(f325(f871(x88251,x88251)),x88252),f323(f323(f183(f871(x88251,x88251),a860),f739(x88253,x88252,x88251)),x88253)))
% 188.07/187.97 [8913]~P78(x89131)+E(f323(f323(f78(x89131),x89132),f323(f135(x89131,x89131,f323(f7(x89131,x89131,x89131),f78(x89131)),f2(x89131)),f323(f162(x89131),x89133))),f323(f135(x89131,x89131,f78(x89131),x89132),x89133))
% 188.07/187.97 [9029]~P28(x90292,x90291,x90293,f246(f872(x90292,a860)),f246(f872(x90291,a860)))+E(f91(x90291,x90292,f246(f872(x90291,a860)),f91(x90292,x90291,f246(f872(x90292,a860)),x90293)),x90293)
% 188.07/187.97 [9183]P51(x91831,x91832,x91833)+P101(f323(f323(f325(f871(x91831,x91832)),f323(f323(f258(x91831,x91832),f729(x91833,x91832,x91831)),f708(x91833,x91832,x91831))),x91833))
% 188.07/187.97 [9184]P51(x91841,x91842,x91843)+P101(f323(f323(f325(f871(x91841,x91842)),f323(f323(f258(x91841,x91842),f729(x91843,x91842,x91841)),f707(x91843,x91842,x91841))),x91843))
% 188.07/187.97 [9249]~P101(f323(f323(f325(f871(x92491,x92491)),x92492),f323(f323(f280(x92491,x92491,x92491),x92493),f299(x92491,x92493))))+P101(f323(f323(f325(f871(x92491,x92491)),x92492),f323(f323(f183(f871(x92491,x92491),a860),f741(x92493,x92492,x92491)),x92493)))
% 188.07/187.97 [9250]~P101(f323(x92501,f323(f323(f158(x92502),x92503),f323(f189(f866(x92502)),f171(x92502,x92501,x92503)))))+~P101(f323(f323(f238(a865),f323(f189(f866(x92502)),f171(x92502,x92501,x92503))),f323(f189(f866(x92502)),x92503)))
% 188.07/187.97 [9339]~P101(f323(f323(f237(f872(x93391,a860)),x93392),x93393))+P101(f323(f323(f237(f872(x93391,a860)),f323(f323(f7(x93391,f872(x93391,a860),a860),f325(x93391)),x93392)),f323(f323(f7(x93391,f872(x93391,a860),a860),f325(x93391)),x93393)))
% 188.07/187.97 [9392]~P101(f323(f323(f325(f871(f872(x93921,a860),f872(x93921,a860))),f323(f323(f258(f872(x93921,a860),f872(x93921,a860)),x93922),x93923)),f298(x93921)))+P101(f323(f323(f238(f872(x93921,a860)),x93922),x93923))
% 188.07/187.97 [9415]P52(x94151,x94152,x94153)+~P101(f323(f323(f325(f871(x94151,x94151)),f323(f323(f258(x94151,x94151),f733(x94153,x94152,x94151)),f732(x94153,x94152,x94151))),x94153))
% 188.07/187.97 [9416]P52(x94161,x94162,x94163)+~P101(f323(f323(f325(f871(x94161,x94161)),f323(f323(f258(x94161,x94161),f732(x94163,x94162,x94161)),f733(x94163,x94162,x94161))),x94163))
% 188.07/187.97 [9456]~P101(f323(f323(f325(f871(f866(x94561),f866(x94561))),f323(f323(f258(f866(x94561),f866(x94561)),x94562),x94562)),f140(x94561,x94563)))+P101(f323(f323(f325(f871(x94561,x94561)),f323(f323(f258(x94561,x94561),f627(x94562,x94563,x94561)),f627(x94562,x94563,x94561))),x94563))
% 188.07/187.97 [9506]P101(f323(f323(f237(f872(x95061,a860)),x95062),x95063))+~P101(f323(f323(f237(f872(x95061,a860)),f323(f323(f7(x95061,f872(x95061,a860),a860),f325(x95061)),x95062)),f323(f323(f7(x95061,f872(x95061,a860),a860),f325(x95061)),x95063)))
% 188.07/187.97 [9589]E(f323(f323(f22(a865),f323(f323(f6(a865,a865),x95891),f323(f244(a865),x95892))),f323(f323(f6(a865,a865),x95893),f323(f244(a865),x95892))),f323(f323(f6(a865,a865),f323(f323(f18(a865,a865,a865),f323(f323(f8(a865,f872(a865,a865),a865),f22(a865)),x95891)),x95893)),f323(f244(a865),x95892)))+~P101(f323(f323(f237(a865),f323(x95893,f366(x95892,x95891,x95893))),f323(x95891,f366(x95892,x95891,x95893))))
% 188.07/187.97 [9893]E(f323(f243(f871(x98931,x98932)),f323(f262(x98931,x98932,a860),f323(f323(f7(x98931,f872(x98932,f869(x98932)),f872(x98932,a860)),f323(f323(f8(f872(f869(x98932),a860),f872(f872(x98932,f869(x98932)),f872(x98932,a860)),x98931),f8(f869(x98932),a860,x98932)),f323(f323(f8(f869(x98932),f872(f869(x98932),a860),x98931),a320),f323(f179(x98931,x98932),x98933)))),f230(x98932)))),f323(f166(f871(x98931,x98932)),x98933))+~P101(f323(f130(x98931),f323(f323(f147(f871(x98931,x98932),x98931),f257(x98931,x98932)),x98933)))
% 188.07/187.97 [5617]~P59(x56171)+E(f323(f323(f22(x56171),f323(f323(f78(x56171),x56172),x56173)),x56173),x56172)
% 188.07/187.97 [5618]~P59(x56181)+E(f323(f323(f78(x56181),f323(f323(f22(x56181),x56182),x56183)),x56183),x56182)
% 188.07/187.97 [5837]~P59(x58371)+E(f323(f323(f78(x58371),x58372),f323(f323(f78(x58371),f323(f77(x58371),x58372)),x58373)),x58373)
% 188.07/187.97 [5919]~P77(x59191)+E(f323(f323(f79(x59191),f323(f323(f248(x59191),x59192),x59193)),x59192),f323(f323(f248(x59191),x59192),f323(a112,x59193)))
% 188.07/187.97 [5920]~P112(x59201)+E(f323(f323(f79(x59201),f323(f323(f248(x59201),x59202),x59203)),x59202),f323(f323(f248(x59201),x59202),f323(a112,x59203)))
% 188.07/187.97 [6127]~P116(x61271)+E(f323(f73(x61271),f323(f323(f248(x61271),f323(f77(x61271),x61272)),x61273)),f323(f73(x61271),f323(f323(f248(x61271),x61272),x61273)))
% 188.07/187.97 [6178]~P77(x61781)+E(f323(f323(f79(x61781),f323(f323(f248(x61781),x61782),x61783)),x61782),f323(f323(f79(x61781),x61782),f323(f323(f248(x61781),x61782),x61783)))
% 188.07/187.97 [6233]E(f323(f323(f22(a99),f323(f323(f78(a99),x62331),x62332)),x62333),f273(x62331,x62332,x62333))+~P101(f323(f323(f238(a99),x62332),x62333))
% 188.07/187.97 [6254]~E(f323(f323(f131(x62541),x62543),x62542),f113(x62541))+P101(f323(f323(f237(a865),f323(f189(f866(x62541)),x62542)),x62543))
% 188.07/187.97 [6387]E(f323(f323(f79(a865),f323(f103(a865),x63871)),f323(f323(f79(a865),f323(f103(a865),x63872)),x63873)),f2(a865))+~P101(f323(f323(f238(a1),x63871),a81))
% 188.07/187.97 [6402]~P62(x64021)+E(f323(f323(f248(x64021),f323(f323(f281(x64021),f76(x64021)),x64022)),x64023),f323(f323(f281(x64021),f76(x64021)),f323(f323(f248(x64021),x64022),x64023)))
% 188.07/187.97 [6478]E(f323(f323(f22(a865),f323(f323(f78(a865),x64781),x64782)),x64783),f323(f323(f22(a865),x64781),f323(f323(f22(a865),x64783),x64782)))+~P101(f323(f323(f237(a865),x64782),x64783))
% 188.07/187.97 [6480]E(f323(f323(f22(a865),f323(f323(f78(a865),x64801),x64802)),x64803),f323(f323(f78(a865),x64801),f323(f323(f22(a865),x64802),x64803)))+~P101(f323(f323(f237(a865),x64803),x64802))
% 188.07/187.97 [6516]~P2(x65161)+P101(f323(f323(f237(x65161),f323(f323(f101(x65161),x65162),x65163)),x65163))
% 188.07/187.97 [6517]~P98(x65171)+P101(f323(f323(f237(x65171),f323(f323(f101(x65171),x65172),x65173)),x65173))
% 188.07/187.97 [6518]~P2(x65181)+P101(f323(f323(f237(x65181),f323(f323(f101(x65181),x65182),x65183)),x65182))
% 188.07/187.97 [6519]~P98(x65191)+P101(f323(f323(f237(x65191),f323(f323(f101(x65191),x65192),x65193)),x65192))
% 188.07/187.97 [6520]~P103(x65201)+P101(f323(f323(f237(x65201),f323(f323(f235(x65201),x65202),x65203)),x65203))
% 188.07/187.97 [6521]~P103(x65211)+P101(f323(f323(f237(x65211),f323(f323(f235(x65211),x65212),x65213)),x65212))
% 188.07/187.97 [6534]E(f323(f323(f36(a1),f323(f323(f36(a1),x65341),x65342)),x65343),f323(f323(f36(a1),x65341),f323(f323(f79(a1),x65342),x65343)))+~P101(f323(f323(f238(a1),f2(a1)),x65343))
% 188.07/187.97 [6585]~P112(x65851)+E(f323(f323(f78(x65851),f323(f323(f79(x65851),x65852),x65853)),x65853),f323(f323(f79(x65851),f323(f323(f78(x65851),x65852),f76(x65851))),x65853))
% 188.07/187.97 [6586]~P90(x65861)+E(f323(f323(f79(x65861),f323(f77(x65861),f323(f103(x65861),x65862))),x65863),f323(f323(f79(x65861),f323(f103(x65861),f323(f77(a1),x65862))),x65863))
% 188.07/187.97 [6658]~P78(x66581)+E(f323(f159(x66581),f323(f323(f147(x66582,x66581),f323(f16(x66581,x66582),f2(x66581))),x66583)),f2(x66581))
% 188.07/187.97 [6674]E(f323(f323(f78(a865),f323(f103(a865),x66741)),f323(f323(f78(a865),f323(f103(a865),x66742)),x66743)),f323(f323(f78(a865),f323(f103(a865),x66742)),x66743))+~P101(f323(a193,f323(f103(a1),x66741)))
% 188.07/187.97 [6688]~P6(x66881)+E(f37(x66881,f323(f323(f301(x66881),x66882),f323(f323(f301(x66881),x66883),f188(f872(x66881,a860))))),f323(f323(f110(x66881),x66882),x66883))
% 188.07/187.97 [6689]~P6(x66891)+E(f38(x66891,f323(f323(f301(x66891),x66892),f323(f323(f301(x66891),x66893),f188(f872(x66891,a860))))),f323(f323(f101(x66891),x66892),x66893))
% 188.07/187.97 [6711]E(f323(f323(f169(x67111),x67112),x67113),x67113)+~P101(f323(f323(f237(a865),f323(f189(f866(x67111)),x67113)),x67112))
% 188.07/187.97 [6724]E(f323(f323(f131(x67241),x67242),x67243),f113(x67241))+~P101(f323(f323(f237(a865),f323(f189(f866(x67241)),x67243)),x67242))
% 188.07/187.97 [6735]E(f323(f323(f78(a865),f323(f323(f22(a865),x67351),x67352)),x67353),f323(f323(f22(a865),f323(f323(f78(a865),x67351),x67353)),x67352))+~P101(f323(f323(f237(a865),x67352),x67351))
% 188.07/187.97 [6749]~P101(f323(f323(f238(a865),x67491),x67493))+P101(f323(f323(f238(a865),f323(f323(f22(a865),x67491),x67492)),x67493))
% 188.07/187.97 [6777]~P103(x67771)+E(f164(x67771,x67772,f323(f323(f141(x67771,x67771,f5(x67771)),x67772),x67773)),x67773)
% 188.07/187.97 [6865]E(f323(f323(f22(a865),f323(f323(f78(a865),x68651),x68652)),f323(a112,x68653)),f323(f323(f22(a865),x68651),f323(a112,f323(f323(f22(a865),x68653),x68652))))+~P101(f323(f323(f237(a865),x68652),x68653))
% 188.07/187.97 [6866]~P116(x68661)+P101(f323(f323(f237(x68661),f2(x68661)),f323(f323(f248(x68661),f323(f73(x68661),x68662)),x68663)))
% 188.07/187.97 [6911]P26(x69111,x69112,x69113)+~P101(f323(f323(f237(f872(f864(x69111),a860)),x69113),x69112))
% 188.07/187.97 [6954]~P101(f323(f59(x69541),x69542))+P101(f323(f59(x69541),f323(f323(f22(f872(x69541,a860)),x69542),x69543)))
% 188.07/187.97 [6955]~P101(f323(f59(x69551),x69553))+P101(f323(f59(x69551),f323(f323(f101(f872(x69551,a860)),x69552),x69553)))
% 188.07/187.97 [6956]~P101(f323(f59(x69561),x69562))+P101(f323(f59(x69561),f323(f323(f101(f872(x69561,a860)),x69562),x69563)))
% 188.07/187.97 [7095]~P38(x70951,x70953)+P38(x70951,f323(f323(f101(f872(f871(x70951,x70951),a860)),x70952),x70953))
% 188.07/187.97 [7096]~P38(x70961,x70962)+P38(x70961,f323(f323(f101(f872(f871(x70961,x70961),a860)),x70962),x70963))
% 188.07/187.97 [7211]~P2(x72111)+E(f11(x72111,f323(f166(x72111),f323(f323(f144(x72111),x72112),x72113))),f323(f135(x72111,x72111,f101(x72111),x72112),x72113))
% 188.07/187.97 [7212]~P2(x72121)+E(f10(x72121,f323(f166(x72121),f323(f323(f144(x72121),x72122),x72123))),f323(f135(x72121,x72121,f110(x72121),x72122),x72123))
% 188.07/187.97 [7213]~P103(x72131)+E(f14(x72131,f323(f166(x72131),f323(f323(f144(x72131),x72132),x72133))),f323(f135(x72131,x72131,f236(x72131),x72132),x72133))
% 188.07/187.97 [7214]~P103(x72141)+E(f15(x72141,f323(f166(x72141),f323(f323(f144(x72141),x72142),x72143))),f323(f135(x72141,x72141,f235(x72141),x72142),x72143))
% 188.07/187.97 [7274]~P101(f323(f59(x72741),x72742))+P101(f323(f323(f237(a865),f323(f35(x72741),x72742)),f323(f35(x72741),f323(f323(f301(x72741),x72743),x72742))))
% 188.07/187.97 [7282]E(f323(f323(f110(f872(a865,a860)),f323(f293(a865,x72821),x72822)),f323(f293(a865,x72822),f323(f323(f78(a865),x72822),x72823))),f323(f293(a865,x72821),f323(f323(f78(a865),x72822),x72823)))+~P101(f323(f323(f237(a865),x72821),x72822))
% 188.07/187.97 [7292]P101(f323(f323(f237(a865),x72921),x72922))+~P101(f323(f323(f237(a865),f323(f323(f78(a865),x72923),x72921)),x72922))
% 188.07/187.97 [7293]P101(f323(f323(f237(a865),x72931),x72932))+~P101(f323(f323(f237(a865),f323(f323(f78(a865),x72931),x72933)),x72932))
% 188.07/187.97 [7294]P101(f323(f323(f238(a865),x72941),x72942))+~P101(f323(f323(f238(a865),f323(f323(f78(a865),x72941),x72943)),x72942))
% 188.07/187.97 [7333]~P103(x73331)+E(f12(x73331,f235(x73331),f323(f166(x73331),f323(f323(f144(x73331),x73332),x73333))),f323(f135(x73331,x73331,f235(x73331),x73332),x73333))
% 188.07/187.97 [7334]~P103(x73341)+E(f13(x73341,f236(x73341),f323(f166(x73341),f323(f323(f144(x73341),x73342),x73343))),f323(f135(x73341,x73341,f236(x73341),x73342),x73343))
% 188.07/187.97 [7338]~E(x73382,f188(f872(f871(x73381,x73381),a860)))+P101(f323(f323(f237(f872(f871(x73381,x73381),a860)),x73382),x73383))
% 188.07/187.97 [7446]E(f323(f323(f110(f872(x74461,a860)),x74462),f323(f323(f22(f872(x74461,a860)),x74463),x74462)),x74463)+~P101(f323(f323(f237(f872(x74461,a860)),x74462),x74463))
% 188.07/187.97 [7447]~P101(f323(f323(f237(a865),x74471),f323(f323(f78(a865),x74473),x74472)))+P101(f323(f323(f237(a865),f323(f323(f22(a865),x74471),x74472)),x74473))
% 188.07/187.97 [7448]~P101(f323(f323(f238(a865),x74481),f323(f323(f22(a865),x74483),x74482)))+P101(f323(f323(f238(a865),f323(f323(f78(a865),x74481),x74482)),x74483))
% 188.07/187.97 [7504]E(x75041,f113(x75042))+E(f323(f134(x75042),f323(f323(f323(f183(f866(x75042),f866(x75042)),x75043),f161(x75042)),x75041)),f323(f323(f158(x75042),x75041),f42(a865,x75043,f323(f189(f866(x75042)),x75041))))
% 188.07/187.97 [7513]E(f323(f323(f301(x75131),x75132),f323(f323(f22(f872(x75131,a860)),x75133),f323(f323(f301(x75131),x75132),f188(f872(x75131,a860))))),x75133)+~P101(f323(f323(f325(x75131),x75132),x75133))
% 188.07/187.97 [7674]P101(f323(f323(f237(a865),x76741),f323(f323(f78(a865),x76742),x76743)))+~P101(f323(f323(f237(a865),f323(f323(f22(a865),x76741),x76743)),x76742))
% 188.07/187.97 [7675]P101(f323(f323(f238(a865),x76751),f323(f323(f22(a865),x76752),x76753)))+~P101(f323(f323(f238(a865),f323(f323(f78(a865),x76751),x76753)),x76752))
% 188.07/187.97 [7698]P101(f323(f59(x76981),x76982))+~P101(f323(f59(x76981),f323(f323(f110(f872(x76981,a860)),x76983),x76982)))
% 188.07/187.97 [7699]P101(f323(f59(x76991),x76992))+~P101(f323(f59(x76991),f323(f323(f110(f872(x76991,a860)),x76992),x76993)))
% 188.07/187.97 [7772]~P46(x77721,x77723)+P101(f323(f323(f325(f871(x77721,x77721)),f323(f323(f258(x77721,x77721),x77722),x77722)),x77723))
% 188.07/187.97 [7910]E(f323(f323(f158(a865),f132(a865,f323(f293(a865,x79101),x79102))),x79103),f323(f323(f78(a865),x79101),x79103))+~P101(f323(f323(f238(a865),f323(f323(f78(a865),x79101),x79103)),x79102))
% 188.07/187.97 [7975]E(f323(f323(f169(a865),x79751),f132(a865,f323(f293(a865,x79752),x79753))),f132(a865,f323(f293(a865,x79752),f323(f323(f78(a865),x79752),x79751))))+~P101(f323(f323(f237(a865),f323(f323(f78(a865),x79752),x79751)),x79753))
% 188.07/187.97 [8029]~P90(x80291)+E(f323(f323(f248(x80291),x80292),f323(f103(a865),f323(f323(f78(a1),x80293),x80293))),f323(f323(f84(x80291,x80291),f323(f323(f248(x80291),x80292),f323(f103(a865),x80293))),f323(f323(f18(x80291,x80291,x80291),f79(x80291)),f5(x80291))))
% 188.07/187.97 [8297]E(f323(f323(f121(x82971),f323(f323(f169(x82971),x82972),x82973)),f323(f323(f144(x82971),f323(f323(f158(x82971),x82973),x82972)),f323(f323(f131(x82971),f323(a112,x82972)),x82973))),x82973)+~P101(f323(f323(f238(a865),x82972),f323(f189(f866(x82971)),x82973)))
% 188.07/187.97 [8304]P101(f323(f323(f237(f872(x83041,a860)),f311(x83041,x83042)),f311(x83041,x83043)))+~P101(f323(f323(f237(f872(x83041,f872(x83041,a860))),x83043),x83042))
% 188.07/187.97 [8306]~P52(x83061,x83062,x83063)+P52(x83061,x83062,f323(f323(f22(f872(f871(x83061,x83061),a860)),x83063),f299(x83061,f188(f872(f871(x83061,x83061),a860)))))
% 188.07/187.97 [8325]P101(f323(f323(f237(f872(x83251,a860)),f312(x83251,x83252)),f312(x83251,x83253)))+~P101(f323(f323(f237(f872(f871(x83251,x83251),a860)),x83253),x83252))
% 188.07/187.97 [8331]~P101(f323(f323(f238(f872(x83311,a860)),x83313),x83312))+P101(f323(f323(f325(x83311),f682(x83312,x83313,x83311)),f323(f323(f22(f872(x83311,a860)),x83312),x83313)))
% 188.07/187.97 [8333]~P121(x83331)+P101(f323(f323(f237(x83331),f2(x83331)),f323(f323(f78(x83331),f323(f323(f79(x83331),x83332),x83332)),f323(f323(f79(x83331),x83333),x83333))))
% 188.07/187.97 [8366]P101(f323(f323(f237(f872(x83661,a860)),f323(f276(x83661),x83662)),f323(f276(x83661),x83663)))+~P101(f323(f323(f237(f872(f871(x83661,x83661),a860)),x83662),x83663))
% 188.07/187.97 [8396]~P42(x83961,x83962)+~P101(f323(f323(f325(f871(x83961,x83961)),f323(f323(f258(x83961,x83961),x83963),x83963)),x83962))
% 188.07/187.97 [8398]~P38(x83981,x83982)+~P101(f323(f323(f325(f871(x83981,x83981)),f323(f323(f258(x83981,x83981),x83983),x83983)),x83982))
% 188.07/187.97 [8452]P101(f323(f323(f237(f872(x84521,a860)),f37(f872(x84521,a860),x84522)),f37(f872(x84521,a860),x84523)))+~P101(f323(f323(f237(f872(f872(x84521,a860),a860)),x84522),x84523))
% 188.07/187.97 [8453]P101(f323(f323(f237(f872(x84531,a860)),f38(f872(x84531,a860),x84532)),f38(f872(x84531,a860),x84533)))+~P101(f323(f323(f237(f872(f872(x84531,a860),a860)),x84533),x84532))
% 188.07/187.97 [8506]~P9(x85061,x85063,x85062)+P101(f323(f323(f237(f872(f871(x85061,x85061),a860)),x85062),f323(f323(f260(x85061,x85061),x85063),f323(f16(f872(x85061,a860),x85061),x85063))))
% 188.07/187.97 [8507]~P40(x85071,x85073,x85072)+P101(f323(f323(f237(f872(f871(x85071,x85071),a860)),x85072),f323(f323(f260(x85071,x85071),x85073),f323(f16(f872(x85071,a860),x85071),x85073))))
% 188.07/187.97 [8556]~P82(x85561)+P101(f323(f323(f237(x85561),f323(f323(f22(x85561),f323(f73(x85561),x85562)),f323(f73(x85561),x85563))),f323(f73(x85561),f323(f323(f22(x85561),x85563),x85562))))
% 188.07/187.97 [8557]~P82(x85571)+P101(f323(f323(f237(x85571),f323(f323(f22(x85571),f323(f73(x85571),x85572)),f323(f73(x85571),x85573))),f323(f73(x85571),f323(f323(f22(x85571),x85572),x85573))))
% 188.07/187.97 [8590]P101(f323(f323(f237(f872(f871(x85901,x85901),a860)),f299(x85901,x85902)),f299(x85901,x85903)))+~P101(f323(f323(f237(f872(f871(x85901,x85901),a860)),x85902),x85903))
% 188.07/187.97 [8703]~P27(x87032,x87031,x87033,f246(f872(x87032,a860)))+E(f323(f71(x87031,x87032,x87032,f91(x87032,x87031,f246(f872(x87032,a860)),x87033)),x87033),f32(x87032))
% 188.07/187.97 [8764]P52(x87641,x87642,x87643)+~P52(x87641,x87642,f323(f323(f22(f872(f871(x87641,x87641),a860)),x87643),f299(x87641,f188(f872(f871(x87641,x87641),a860)))))
% 188.07/187.97 [8784]P101(f323(f323(f237(f872(f871(f866(x87841),f866(x87841)),a860)),f151(x87841,x87842)),f151(x87841,x87843)))+~P101(f323(f323(f237(f872(f871(x87841,x87841),a860)),x87842),x87843))
% 188.07/187.97 [8785]P101(f323(f323(f237(f872(f871(f866(x87851),f866(x87851)),a860)),f150(x87851,x87852)),f150(x87851,x87853)))+~P101(f323(f323(f237(f872(f871(x87851,x87851),a860)),x87852),x87853))
% 188.07/187.97 [8804]~P40(x88041,x88043,x88042)+P101(f323(f323(f237(f872(f871(x88041,x88041),a860)),x88042),f323(f323(f280(x88041,x88041,x88041),f323(f278(x88041,x88041),x88042)),x88042)))
% 188.07/187.97 [8853]~P101(f323(f130(x88531),x88532))+E(f323(f129(x88531,f323(f323(f7(x88531,f872(x88531,a860),a860),f325(x88531)),f323(f166(x88531),f170(x88531,x88532,x88533)))),x88532),f170(x88531,x88532,x88533))
% 188.07/187.97 [8911]E(x89111,x89112)+~P101(f323(f323(f325(f871(x89113,x89113)),f323(f323(f258(x89113,x89113),x89111),x89112)),f299(x89113,f188(f872(f871(x89113,x89113),a860)))))
% 188.07/187.97 [8991]P101(f323(f323(f325(x89911),x89912),f312(x89911,x89913)))+P101(f323(f323(f325(f871(x89911,x89911)),f323(f323(f258(x89911,x89911),f661(x89913,x89912,x89911)),x89912)),x89913))
% 188.07/187.97 [8992]P101(f323(f323(f325(x89921),x89922),f312(x89921,x89923)))+P101(f323(f323(f325(f871(x89921,x89921)),f323(f323(f258(x89921,x89921),f711(x89923,x89922,x89921)),x89922)),x89923))
% 188.07/187.97 [8993]P101(f323(f323(f325(x89931),x89932),f312(x89931,x89933)))+P101(f323(f323(f325(f871(x89931,x89931)),f323(f323(f258(x89931,x89931),f718(x89933,x89932,x89931)),x89932)),x89933))
% 188.07/187.97 [9030]P27(x90301,x90302,x90303,f246(f872(x90301,a860)))+~E(f323(f71(x90302,x90301,x90301,f91(x90301,x90302,f246(f872(x90301,a860)),x90303)),x90303),f32(x90301))
% 188.07/187.97 [9084]~P101(f323(f323(f325(f866(x90841)),x90843),f154(x90841,x90842)))+P101(f323(f153(x90841,f323(f323(f7(x90841,f872(x90841,a860),a860),f325(x90841)),x90842)),x90843))
% 188.07/187.97 [9105]P101(f323(x91053,x91052))+E(f323(f243(x91051),f323(f323(f18(x91051,a860,a860),f323(f323(f8(a860,f872(a860,a860),x91051),a322),f323(a320,x91052))),x91053)),f188(f872(x91051,a860)))
% 188.07/187.97 [9123]~P82(x91231)+P101(f323(f323(f237(x91231),f323(f73(x91231),f323(f323(f22(x91231),f323(f73(x91231),x91232)),f323(f73(x91231),x91233)))),f323(f73(x91231),f323(f323(f22(x91231),x91232),x91233))))
% 188.07/187.97 [9137]~P101(f323(x91373,x91372))+E(f323(f243(x91371),f323(f323(f18(x91371,a860,a860),f323(f323(f8(a860,f872(a860,a860),x91371),a322),f323(a320,x91372))),x91373)),f323(f323(f301(x91371),x91372),f188(f872(x91371,a860))))
% 188.07/187.97 [9145]~P101(f323(f323(f325(f872(x91451,a860)),x91453),f323(f300(x91451),x91452)))+P101(f323(f251(x91451,f323(f323(f7(x91451,f872(x91451,a860),a860),f325(x91451)),x91452)),x91453))
% 188.07/187.97 [9182]P38(x91821,x91822)+P101(f323(f323(f325(f871(x91821,x91821)),f323(f323(f258(x91821,x91821),f323(f665(x91822,x91821),f323(a112,x91823))),f323(f665(x91822,x91821),x91823))),x91822))
% 188.07/187.97 [9318]P101(f323(f323(f325(f866(x93181)),x93182),f154(x93181,x93183)))+~P101(f323(f153(x93181,f323(f323(f7(x93181,f872(x93181,a860),a860),f325(x93181)),x93183)),x93182))
% 188.07/187.97 [9331]P101(f323(f323(f325(f872(x93311,a860)),x93312),f323(f300(x93311),x93313)))+~P101(f323(f251(x93311,f323(f323(f7(x93311,f872(x93311,a860),a860),f325(x93311)),x93313)),x93312))
% 188.07/187.97 [9387]P101(f323(f323(f325(x93871),f323(f269(x93871,x93872),x93873)),f323(f166(x93871),f323(f323(f147(f871(a99,x93871),x93871),f261(a99,x93871)),x93872))))+~P101(f323(f323(f238(a99),x93873),f323(f159(a99),f323(f323(f147(f871(a99,x93871),a99),f257(a99,x93871)),x93872))))
% 188.07/187.97 [9435]P101(f323(f323(f237(f872(f871(f866(x94351),f866(x94351)),a860)),f151(x94351,x94352)),f323(f323(f260(f866(x94351),f866(x94351)),f154(x94351,x94353)),f323(f16(f872(f866(x94351),a860),f866(x94351)),f154(x94351,x94353)))))+~P101(f323(f323(f237(f872(f871(x94351,x94351),a860)),x94352),f323(f323(f260(x94351,x94351),x94353),f323(f16(f872(x94351,a860),x94351),x94353))))
% 188.07/187.97 [9459]P101(f323(f323(f325(x94591),f323(f257(x94591,f871(a99,a99)),f323(f267(x94591,x94592),x94593))),f323(f166(x94591),f323(f323(f147(f871(a99,x94591),x94591),f261(a99,x94591)),x94592))))+~P101(f323(f323(f238(a99),f2(a99)),f323(f159(a99),f323(f323(f147(f871(a99,x94591),a99),f257(a99,x94591)),x94592))))
% 188.07/187.97 [9475]~P101(f323(f323(f237(f872(f871(x94751,x94751),a860)),x94752),f323(f323(f260(x94751,x94751),x94753),f323(f16(f872(x94751,a860),x94751),x94753))))+P101(f323(f323(f237(f872(f871(x94751,x94751),a860)),f323(f323(f280(x94751,x94751,x94751),x94752),f299(x94751,x94752))),f323(f323(f260(x94751,x94751),x94753),f323(f16(f872(x94751,a860),x94751),x94753))))
% 188.07/187.97 [9781]~P38(x97811,x97812)+~P101(f323(f323(f325(f871(x97811,x97811)),f323(f323(f258(x97811,x97811),f323(x97813,f323(a112,f667(x97812,x97811,x97813)))),f323(x97813,f667(x97812,x97811,x97813)))),x97812))
% 188.07/187.97 [9782]~P38(x97821,x97822)+~P101(f323(f323(f325(f871(x97821,x97821)),f323(f323(f258(x97821,x97821),f323(x97823,f323(a112,f725(x97823,x97822,x97821)))),f323(x97823,f725(x97823,x97822,x97821)))),x97822))
% 188.07/187.97 [10032]P101(f323(f323(f237(f872(f871(f872(x100321,a860),f872(x100321,a860)),a860)),f323(f323(f280(f872(x100321,a860),f872(x100321,a860),f872(x100321,a860)),f316(x100321,x100322)),f323(f323(f110(f872(f871(f872(x100321,a860),f872(x100321,a860)),a860)),f316(x100321,x100323)),f323(f323(f301(f871(f872(x100321,a860),f872(x100321,a860))),f323(f323(f258(f872(x100321,a860),f872(x100321,a860)),f188(f872(x100321,a860))),f188(f872(x100321,a860)))),f188(f872(f871(f872(x100321,a860),f872(x100321,a860)),a860)))))),f316(x100321,x100322)))+~P101(f323(f323(f237(f872(f871(x100321,x100321),a860)),f323(f323(f280(x100321,x100321,x100321),x100322),x100323)),x100322))
% 188.07/187.97 [10033]P101(f323(f323(f237(f872(f871(f872(x100331,a860),f872(x100331,a860)),a860)),f323(f323(f280(f872(x100331,a860),f872(x100331,a860),f872(x100331,a860)),f314(x100331,x100332)),f323(f323(f110(f872(f871(f872(x100331,a860),f872(x100331,a860)),a860)),f314(x100331,x100333)),f323(f323(f301(f871(f872(x100331,a860),f872(x100331,a860))),f323(f323(f258(f872(x100331,a860),f872(x100331,a860)),f188(f872(x100331,a860))),f188(f872(x100331,a860)))),f188(f872(f871(f872(x100331,a860),f872(x100331,a860)),a860)))))),f314(x100331,x100332)))+~P101(f323(f323(f237(f872(f871(x100331,x100331),a860)),f323(f323(f280(x100331,x100331,x100331),x100332),x100333)),x100332))
% 188.07/187.97 [7210]~P101(f323(f323(f237(a865),x72102),x72101))+E(f323(f323(f22(a865),f323(a112,f323(f323(f22(a865),x72101),x72102))),x72103),f323(f323(f22(a865),f323(a112,x72101)),f323(f323(f78(a865),x72102),x72103)))
% 188.07/187.97 [7249]~P57(x72491)+E(f323(f323(f78(x72491),f42(x72491,x72492,x72493)),f323(f323(f79(x72491),f323(f323(f36(x72491),x72492),x72493)),x72493)),x72492)
% 188.07/187.97 [7452]E(f323(f323(f79(a865),f323(f103(a865),x74521)),f323(f323(f79(a865),f323(f103(a865),x74522)),x74523)),f323(f323(f79(a865),f323(f103(a865),f323(f323(f79(a1),x74521),x74522))),x74523))+P101(f323(f323(f238(a1),x74521),a81))
% 188.07/187.97 [7919]~P101(f323(f323(f237(a865),x79193),x79192))+P101(f323(f323(f237(a865),x79191),f323(f323(f22(a865),f323(f323(f78(a865),x79192),x79191)),x79193)))
% 188.07/187.97 [8114]~P101(f323(f323(f237(a865),x81141),x81142))+E(f323(f323(f121(a865),f132(a865,f323(f293(a865,x81141),x81142))),f132(a865,f323(f293(a865,x81142),f323(f323(f78(a865),x81142),x81143)))),f132(a865,f323(f293(a865,x81141),f323(f323(f78(a865),x81142),x81143))))
% 188.07/187.97 [8375]~P101(f323(f59(x83751),x83752))+E(f323(a112,f323(f35(x83751),f323(f323(f22(f872(x83751,a860)),x83752),f323(f323(f301(x83751),x83753),f188(f872(x83751,a860)))))),f323(f35(x83751),f323(f323(f301(x83751),x83753),x83752)))
% 188.07/187.97 [8415]~P101(f323(f59(x84151),x84152))+E(f323(f323(f78(a865),f76(a865)),f323(f35(x84151),f323(f323(f22(f872(x84151,a860)),x84152),f323(f323(f301(x84151),x84153),f188(f872(x84151,a860)))))),f323(f35(x84151),f323(f323(f301(x84151),x84153),x84152)))
% 188.07/187.97 [8600]E(f323(f323(f22(a865),f323(f35(x86001),x86002)),f323(f35(x86001),f323(f323(f101(f872(x86001,a860)),x86002),x86003))),f323(f35(x86001),f323(f323(f22(f872(x86001,a860)),x86002),x86003)))+~P101(f323(f59(x86001),f323(f323(f101(f872(x86001,a860)),x86002),x86003)))
% 188.07/187.97 [8848]~P7(f323(x88482,f429(x88482,x88483,x88481)))+E(f323(f100(a1),f323(f323(f6(x88481,a865),f323(f323(f8(a1,a865,x88481),a104),x88482)),x88483)),f323(f323(f6(x88481,a1),x88482),x88483))
% 188.07/187.97 [8849]~P7(f323(x88492,f471(x88492,x88493,x88491)))+E(f323(f100(a1),f323(f323(f9(x88491,a865),f323(f323(f8(a1,a865,x88491),a104),x88492)),x88493)),f323(f323(f9(x88491,a1),x88492),x88493))
% 188.07/187.97 [8896]~P101(f323(f59(x88961),x88963))+P101(f323(f323(f237(a865),f323(f323(f22(a865),f323(f35(x88961),x88962)),f323(f35(x88961),x88963))),f323(f35(x88961),f323(f323(f22(f872(x88961,a860)),x88962),x88963))))
% 188.07/187.97 [8919]P101(f323(f323(f325(x89191),f429(x89192,x89193,x89191)),x89193))+E(f323(f100(a1),f323(f323(f6(x89191,a865),f323(f323(f8(a1,a865,x89191),a104),x89192)),x89193)),f323(f323(f6(x89191,a1),x89192),x89193))
% 188.07/187.97 [8920]P101(f323(f323(f325(x89201),f471(x89202,x89203,x89201)),x89203))+E(f323(f100(a1),f323(f323(f9(x89201,a865),f323(f323(f8(a1,a865,x89201),a104),x89202)),x89203)),f323(f323(f9(x89201,a1),x89202),x89203))
% 188.07/187.97 [8983]E(f83(x89831,f323(f323(f7(x89831,f872(x89831,a860),a860),f325(x89831)),f323(f323(f22(f872(x89831,a860)),x89832),f323(f323(f301(x89831),x89833),f188(f872(x89831,a860)))))),f250(x89831,x89833,x89832))+P101(f323(f323(f237(f872(x89831,a860)),x89832),f323(f323(f301(x89831),x89833),f188(f872(x89831,a860)))))
% 188.07/187.97 [9332]E(f323(f323(f147(f866(x93321),x93321),f323(f323(f7(f866(x93321),a865,x93321),f158(x93321)),x93322)),f323(f129(f866(x93321),f323(f323(f8(a865,a860,f866(x93321)),f323(f238(a865),x93322)),f189(f866(x93321)))),x93323)),f323(f323(f158(f866(x93321)),f173(x93321,x93323)),x93322))+~P101(f323(f323(f238(a865),x93322),f323(f189(f866(f866(x93321))),f173(x93321,x93323))))
% 188.07/187.97 [9405]E(f323(f129(x94051,x94052),x94053),f171(x94051,x94052,x94053))+P101(f323(f323(f325(x94051),f613(x94053,x94052,x94051)),f323(f166(x94051),f323(f323(f131(x94051),f323(f189(f866(x94051)),f171(x94051,x94052,x94053))),x94053))))
% 188.07/187.97 [9547]E(f323(f323(f131(x95471),f323(f189(f866(x95471)),f171(x95471,x95472,x95473))),x95473),f113(x95471))+~P101(f323(x95472,f323(f134(x95471),f323(f323(f131(x95471),f323(f189(f866(x95471)),f171(x95471,x95472,x95473))),x95473))))
% 188.07/187.97 [9641]~P101(f323(f323(f325(f871(x96411,x96411)),x96412),f299(x96411,x96413)))+P101(f323(f323(f325(f871(x96411,x96411)),x96412),f323(f323(f39(a865,f872(f871(x96411,x96411),a860)),f246(f872(a865,a860))),f323(f323(f7(a865,f872(f871(x96411,x96411),a860),f872(f871(x96411,x96411),a860)),f183(f871(x96411,x96411),a860)),x96413))))
% 188.07/187.97 [9699]~P101(f323(f323(f237(f872(x96991,a860)),f323(f323(f39(a865,f872(x96991,a860)),f323(f293(a865,f2(a865)),f459(x96993,x96992,x96991))),x96992)),x96993))+P101(f323(f323(f237(f872(x96991,a860)),f323(f323(f39(a865,f872(x96991,a860)),f246(f872(a865,a860))),x96992)),x96993))
% 188.07/187.97 [9757]~P101(f323(f323(f238(a1),f2(a1)),x97573))+P101(f323(f323(f238(a1),x97571),f323(f323(f78(a1),x97572),f323(f323(f79(a1),f323(f323(f78(a1),f323(f73(a1),f323(f323(f22(a1),x97572),x97571))),f76(a1))),x97573))))
% 188.07/187.97 [9768]~P38(x97681,f323(f323(f110(f872(f871(x97681,x97681),a860)),x97682),x97683))+P38(x97681,f323(f323(f110(f872(f871(x97681,x97681),a860)),f323(f323(f110(f872(f871(x97681,x97681),a860)),f323(f323(f280(x97681,x97681,x97681),x97682),x97682)),f323(f323(f280(x97681,x97681,x97681),x97683),x97682))),x97683))
% 188.07/187.97 [9849]P38(x98491,f323(f323(f110(f872(f871(x98491,x98491),a860)),x98492),x98493))+~P38(x98491,f323(f323(f110(f872(f871(x98491,x98491),a860)),f323(f323(f110(f872(f871(x98491,x98491),a860)),f323(f323(f280(x98491,x98491,x98491),x98492),x98492)),f323(f323(f280(x98491,x98491,x98491),x98493),x98492))),x98493))
% 188.07/187.97 [9408]~P134(x94081)+E(f323(f102(x94081),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x94082),x94083)),f188(f872(f871(a865,a865),a860)))))),f323(f323(f22(x94081),f323(f100(x94081),x94082)),f323(f100(x94081),x94083)))
% 188.07/187.97 [9493]P101(f323(x94933,x94932))+E(f323(f243(x94931),f323(f323(f18(x94931,a860,a860),f323(f323(f8(a860,f872(a860,a860),x94931),a322),f323(f323(f7(x94931,x94931,a860),a320),x94932))),x94933)),f188(f872(x94931,a860)))
% 188.07/187.97 [9495]~P101(f323(x94953,x94952))+E(f323(f243(x94951),f323(f323(f18(x94951,a860,a860),f323(f323(f8(a860,f872(a860,a860),x94951),a322),f323(f323(f7(x94951,x94951,a860),a320),x94952))),x94953)),f323(f323(f301(x94951),x94952),f188(f872(x94951,a860))))
% 188.07/187.97 [9735]E(x97351,x97352)+P101(f323(f323(f247(x97353,x97353,f323(f323(f8(f872(x97353,a860),f872(x97353,a860),x97353),f323(f8(a860,a860,x97353),a318)),a320)),x97351),x97352))
% 188.07/187.97 [9827]~E(x98271,x98272)+~P101(f323(f323(f247(x98273,x98273,f323(f323(f8(f872(x98273,a860),f872(x98273,a860),x98273),f323(f8(a860,a860,x98273),a318)),a320)),x98271),x98272))
% 188.07/187.97 [9841]~P101(f323(f59(x98411),x98413))+E(f323(f323(f62(x98411,f872(x98411,a860),f323(f323(f8(f872(x98411,a860),f872(f872(x98411,a860),f872(x98411,a860)),x98411),f323(f7(f872(x98411,a860),f872(x98411,a860),f872(x98411,a860)),f22(f872(x98411,a860)))),f323(f323(f7(x98411,f872(x98411,a860),f872(x98411,a860)),f301(x98411)),f188(f872(x98411,a860))))),x98412),x98413),f323(f323(f22(f872(x98411,a860)),x98412),x98413))
% 188.07/187.97 [9873]~P101(f323(f323(f238(a1),f2(a1)),x98733))+P101(f323(f323(f238(a1),f323(f323(f22(a1),x98731),f323(f323(f79(a1),f323(f323(f78(a1),f323(f73(a1),f323(f323(f22(a1),x98731),x98732))),f76(a1))),x98733))),x98732))
% 188.07/187.97 [10095]~P101(f323(f323(f325(x100951),x100953),f312(x100951,x100952)))+P101(f323(f311(x100951,f323(f323(f7(x100951,f872(f871(x100951,x100951),a860),f872(x100951,a860)),f323(f323(f8(f872(x100951,f872(f872(f871(x100951,x100951),a860),a860)),f872(f872(f871(x100951,x100951),a860),f872(x100951,a860)),x100951),f7(x100951,f872(f871(x100951,x100951),a860),a860)),f323(f323(f8(f872(x100951,f871(x100951,x100951)),f872(x100951,f872(f872(f871(x100951,x100951),a860),a860)),x100951),f323(f8(f871(x100951,x100951),f872(f872(f871(x100951,x100951),a860),a860),x100951),f325(f871(x100951,x100951)))),f258(x100951,x100951)))),x100952)),x100953))
% 188.07/187.97 [10108]P101(f323(f323(f325(x101081),x101082),f312(x101081,x101083)))+~P101(f323(f311(x101081,f323(f323(f7(x101081,f872(f871(x101081,x101081),a860),f872(x101081,a860)),f323(f323(f8(f872(x101081,f872(f872(f871(x101081,x101081),a860),a860)),f872(f872(f871(x101081,x101081),a860),f872(x101081,a860)),x101081),f7(x101081,f872(f871(x101081,x101081),a860),a860)),f323(f323(f8(f872(x101081,f871(x101081,x101081)),f872(x101081,f872(f872(f871(x101081,x101081),a860),a860)),x101081),f323(f8(f871(x101081,x101081),f872(f872(f871(x101081,x101081),a860),a860),x101081),f325(f871(x101081,x101081)))),f258(x101081,x101081)))),x101083)),x101082))
% 188.07/187.97 [9697]~P101(f323(f59(x96971),f323(f243(x96971),x96973)))+P101(f323(f59(x96971),f323(f243(x96971),f323(f323(f18(x96971,a860,a860),f323(f323(f8(a860,f872(a860,a860),x96971),a322),x96972)),x96973))))
% 188.07/187.97 [9698]~P101(f323(f59(x96981),f323(f243(x96981),x96982)))+P101(f323(f59(x96981),f323(f243(x96981),f323(f323(f18(x96981,a860,a860),f323(f323(f8(a860,f872(a860,a860),x96981),a322),x96982)),x96983))))
% 188.07/187.97 [9802]P101(f323(f59(x98021),f323(f243(x98021),x98022)))+~P101(f323(f59(x98021),f323(f243(x98021),f323(f323(f18(x98021,a860,a860),f323(f323(f8(a860,f872(a860,a860),x98021),a321),x98023)),x98022))))
% 188.07/187.97 [9803]P101(f323(f59(x98031),f323(f243(x98031),x98032)))+~P101(f323(f59(x98031),f323(f243(x98031),f323(f323(f18(x98031,a860,a860),f323(f323(f8(a860,f872(a860,a860),x98031),a321),x98032)),x98033))))
% 188.07/187.97 [10080]~P101(f323(f59(x100801),x100802))+P101(f323(f59(f866(x100801)),f323(f243(f866(x100801)),f323(f323(f18(f866(x100801),a860,a860),f323(f323(f8(a860,f872(a860,a860),f866(x100801)),a322),f323(f323(f7(f866(x100801),f872(x100801,a860),a860),f323(f323(f8(f872(x100801,a860),f872(f872(x100801,a860),a860),f866(x100801)),f237(f872(x100801,a860))),f166(x100801))),x100802))),f323(f323(f7(f866(x100801),a865,a860),f323(f323(f8(a865,f872(a865,a860),f866(x100801)),a320),f189(f866(x100801)))),x100803)))))
% 188.07/187.97 [10081]~P101(f323(f59(x100811),x100812))+P101(f323(f59(f866(x100811)),f323(f243(f866(x100811)),f323(f323(f18(f866(x100811),a860,a860),f323(f323(f8(a860,f872(a860,a860),f866(x100811)),a322),f323(f323(f7(f866(x100811),f872(x100811,a860),a860),f323(f323(f8(f872(x100811,a860),f872(f872(x100811,a860),a860),f866(x100811)),f237(f872(x100811,a860))),f166(x100811))),x100812))),f323(f323(f7(f866(x100811),a865,a860),f323(f323(f8(a865,f872(a865,a860),f866(x100811)),f237(a865)),f189(f866(x100811)))),x100813)))))
% 188.07/187.97 [9816]~P112(x98161)+E(f323(f323(f248(x98161),x98162),f323(f323(f79(a865),f323(f103(a865),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)))),x98163)),f323(f323(f79(x98161),f323(f323(f248(x98161),x98162),x98163)),f323(f323(f248(x98161),x98162),x98163)))
% 188.07/187.97 [9854]~P77(x98541)+E(f323(f323(f248(x98541),f323(f323(f248(x98541),x98542),x98543)),f323(f103(a865),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(x98541),x98542),f323(f323(f79(a865),f323(f103(a865),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)))),x98543)))
% 188.07/187.97 [9900]~P134(x99001)+E(f323(f323(f248(x99001),f323(f77(x99001),x99002)),f323(f323(f79(a865),f323(f103(a865),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)))),x99003)),f323(f323(f248(x99001),x99002),f323(f323(f79(a865),f323(f103(a865),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)))),x99003)))
% 188.07/187.97 [10039]~P116(x100391)+P101(f323(f323(f237(x100391),f2(x100391)),f323(f323(f78(x100391),f323(f323(f248(x100391),x100392),f323(f103(a865),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(x100391),x100393),f323(f103(a865),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)))))))
% 188.07/187.97 [9910]~P112(x99101)+E(f323(f323(f248(x99101),x99102),f323(a112,f323(f323(f79(a865),f323(f103(a865),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)))),x99103))),f323(f323(f79(x99101),x99102),f323(f323(f79(x99101),f323(f323(f248(x99101),x99102),x99103)),f323(f323(f248(x99101),x99102),x99103))))
% 188.07/187.97 [9959]~P77(x99591)+E(f323(f323(f79(x99591),x99592),f323(f323(f248(x99591),f323(f323(f248(x99591),x99592),x99593)),f323(f103(a865),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(x99591),x99592),f323(a112,f323(f323(f79(a865),f323(f103(a865),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)))),x99593))))
% 188.07/187.97 [9997]~P116(x99971)+P101(f323(f323(f237(x99971),f2(x99971)),f323(f323(f248(x99971),x99972),f323(f323(f79(a865),f323(f103(a865),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)))),x99973))))
% 188.07/187.97 [10061]~P90(x100611)+E(f323(f323(f22(x100611),f323(f323(f78(x100611),f323(f323(f248(x100611),x100612),f323(f103(a865),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(x100611),x100613),f323(f103(a865),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(x100611),f323(f323(f79(x100611),f323(f103(x100611),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)))),x100612)),x100613)),f323(f323(f248(x100611),f323(f323(f22(x100611),x100612),x100613)),f323(f103(a865),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)))))
% 188.07/187.97 [10062]~P90(x100621)+E(f323(f323(f78(x100621),f323(f323(f78(x100621),f323(f323(f248(x100621),x100622),f323(f103(a865),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(x100621),x100623),f323(f103(a865),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(x100621),f323(f323(f79(x100621),f323(f103(x100621),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)))),x100622)),x100623)),f323(f323(f248(x100621),f323(f323(f78(x100621),x100622),x100623)),f323(f103(a865),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)))))
% 188.07/187.97 [4676]E(x46761,x46762)+~E(f30(x46763,x46761),f30(x46764,x46762))
% 188.07/187.97 [4677]E(x46771,x46772)+~E(f30(x46771,x46773),f30(x46772,x46774))
% 188.07/187.97 [4678]E(x46781,x46782)+~E(f29(x46783,x46781),f29(x46784,x46782))
% 188.07/187.97 [4679]E(x46791,x46792)+~E(f29(x46791,x46793),f29(x46792,x46794))
% 188.07/187.97 [4680]E(x46801,x46802)+~E(f25(x46803,x46801),f25(x46804,x46802))
% 188.07/187.97 [4681]E(x46811,x46812)+~E(f25(x46811,x46813),f25(x46812,x46814))
% 188.07/187.97 [7716]P27(x77161,x77162,x77163,x77164)+~E(f513(x77164,x77163,x77162,x77161),f528(x77164,x77163,x77162,x77161))
% 188.07/187.97 [8009]P35(x80091,x80092,x80093,x80094,f113(x80092))+~E(x80094,f113(x80091))
% 188.07/187.97 [8010]P35(x80101,x80102,x80103,f113(x80101),x80104)+~E(x80104,f113(x80102))
% 188.07/187.97 [8219]~P27(x82191,f869(x82192),x82194,f177(x82191,x82192,x82194))+P27(x82191,f869(x82192),f180(x82191,x82192,x82193,x82194),f177(x82191,x82192,x82194))
% 188.07/187.97 [8429]~P27(x84291,f869(x84292),f180(x84291,x84292,x84294,x84293),f177(x84291,x84292,x84293))+P27(x84291,f869(x84292),x84293,f177(x84291,x84292,x84293))
% 188.07/187.97 [8546]~P35(x85462,x85463,x85464,x85461,f113(x85463))+E(x85461,f113(x85462))
% 188.07/187.97 [8547]~P35(x85473,x85472,x85474,f113(x85473),x85471)+E(x85471,f113(x85472))
% 188.07/187.97 [5052]~P19(x50523,x50521,x50524)+E(f323(f323(x50521,x50522),x50522),x50522)
% 188.07/187.97 [5295]P101(f323(x52952,x52954))+E(f323(f129(x52951,x52952),f163(x52951,x52953,x52954)),f113(x52951))
% 188.07/187.97 [5331]~E(x53314,f188(f872(x53311,a860)))+E(f323(f302(x53311,x53312,x53313),x53314),f188(f872(x53312,a860)))
% 188.07/187.97 [5569]~P101(f323(x55692,x55694))+E(f323(f129(x55691,x55692),f163(x55691,x55693,x55694)),f163(x55691,x55693,x55694))
% 188.07/187.97 [5598]~E(f323(f302(x55982,x55983,x55984),x55981),f188(f872(x55983,a860)))+E(x55981,f188(f872(x55982,a860)))
% 188.07/187.97 [5880]~P103(x58802)+E(f323(f323(f141(x58801,x58802,x58803),x58804),f113(x58801)),f323(f323(f144(x58801),x58804),f113(x58801)))
% 188.07/187.97 [5915]E(f323(x59151,x59152),f200(x59153))+P101(f323(f323(f325(x59154),x59152),f177(x59154,x59153,x59151)))
% 188.07/187.97 [6227]~E(x62271,f188(f872(x62272,a860)))+~P101(f323(f60(x62272,x62273,x62271),x62274))
% 188.07/187.97 [6248]~P55(x62481,x62483,x62484,x62482)+P101(f323(f59(x62481),x62482))
% 188.07/187.97 [6249]~P55(x62491,x62493,x62492,x62494)+P101(f323(f59(x62491),x62492))
% 188.07/187.97 [6255]~P55(x62552,x62553,x62554,x62551)+~E(x62551,f188(f872(x62552,a860)))
% 188.07/187.97 [6286]~P105(x62861)+E(f323(f323(f101(f872(x62861,a860)),f323(f293(x62861,x62862),x62863)),f294(x62861,x62863,x62864)),f188(f872(x62861,a860)))
% 188.07/187.97 [6313]~P101(f323(f323(x63133,x63134),x63132))+P101(f323(f323(f325(x63131),x63132),f284(x63131,x63133,x63134)))
% 188.07/187.97 [6314]~P101(f323(f323(x63143,x63144),x63142))+P101(f323(f323(f325(x63141),x63142),f285(x63141,x63143,x63144)))
% 188.07/187.97 [6315]~P101(f323(f323(x63153,x63152),x63154))+P101(f323(f323(f325(x63151),x63152),f289(x63151,x63153,x63154)))
% 188.07/187.97 [6316]~P101(f323(f323(x63163,x63162),x63164))+P101(f323(f323(f325(x63161),x63162),f286(x63161,x63163,x63164)))
% 188.07/187.97 [6378]~P50(x63784,x63781,x63782,x63783)+P101(f323(f323(x63781,x63782),x63783))
% 188.07/187.97 [6453]~P105(x64531)+E(f323(f323(f101(f872(x64531,a860)),f294(x64531,x64532,x64533)),f297(x64531,x64533,x64534)),f188(f872(x64531,a860)))
% 188.07/187.97 [6454]~P105(x64541)+E(f323(f323(f101(f872(x64541,a860)),f294(x64541,x64542,x64543)),f296(x64541,x64543,x64544)),f188(f872(x64541,a860)))
% 188.07/187.97 [6455]~P105(x64551)+E(f323(f323(f101(f872(x64551,a860)),f297(x64551,x64552,x64553)),f294(x64551,x64553,x64554)),f188(f872(x64551,a860)))
% 188.07/187.97 [6456]~P105(x64561)+E(f323(f323(f101(f872(x64561,a860)),f296(x64561,x64562,x64563)),f297(x64561,x64563,x64564)),f188(f872(x64561,a860)))
% 188.07/187.97 [6457]~P105(x64571)+E(f323(f323(f101(f872(x64571,a860)),f296(x64571,x64572,x64573)),f296(x64571,x64573,x64574)),f188(f872(x64571,a860)))
% 188.07/187.97 [6494]P101(f323(f323(x64941,x64942),f672(x64942,x64941)))+~P101(f323(f252(x64943,x64944,x64941),x64942))
% 188.07/187.97 [6498]~P50(x64981,x64982,x64983,x64984)+~P101(f323(f323(x64982,x64984),x64983))
% 188.07/187.97 [6543]~E(f323(x65431,x65432),f200(x65433))+~P101(f323(f323(f325(x65434),x65432),f177(x65434,x65433,x65431)))
% 188.07/187.97 [6572]~P103(x65722)+E(f323(f166(x65721),f143(x65721,x65722,x65723,x65724)),f323(f166(x65721),x65724))
% 188.07/187.97 [6623]~P140(x66231)+E(f190(x66231,x66232,f323(a112,x66233),x66234),f190(x66231,x66232,x66233,f323(x66232,x66234)))
% 188.07/187.97 [6683]~P101(f323(f323(f325(x66834),x66833),f284(x66834,x66831,x66832)))+P101(f323(f323(x66831,x66832),x66833))
% 188.07/187.97 [6684]~P101(f323(f323(f325(x66844),x66843),f285(x66844,x66841,x66842)))+P101(f323(f323(x66841,x66842),x66843))
% 188.07/187.97 [6685]~P101(f323(f323(f325(x66854),x66852),f289(x66854,x66851,x66853)))+P101(f323(f323(x66851,x66852),x66853))
% 188.07/187.97 [6686]~P101(f323(f323(f325(x66864),x66862),f286(x66864,x66861,x66863)))+P101(f323(f323(x66861,x66862),x66863))
% 188.07/187.97 [6762]E(f323(f35(f870(x67621,x67622)),f310(x67621,x67622,x67623,x67624)),f2(a865))+P101(f323(f59(x67622),x67624))
% 188.07/187.97 [6763]E(f323(f35(f870(x67631,x67632)),f310(x67631,x67632,x67633,x67634)),f2(a865))+P101(f323(f59(x67631),x67633))
% 188.07/187.97 [6963]~P17(x69634,x69631,x69632)+E(f323(f71(x69631,x69631,x69631,f323(x69632,x69633)),f323(x69632,x69633)),f323(x69632,x69633))
% 188.07/187.97 [7838]~E(x78382,x78383)+P101(f323(f323(f325(f871(x78381,x78381)),f323(f323(f258(x78381,x78381),x78382),x78383)),f299(x78381,x78384)))
% 188.07/187.97 [7867]~P27(x78671,x78672,x78673,f246(f872(x78671,a860)))+E(f323(f75(x78671,x78672,f246(f872(x78671,a860)),x78673),f323(x78673,x78674)),x78674)
% 188.07/187.97 [7868]~P27(x78681,x78682,x78683,f246(f872(x78681,a860)))+E(f323(f91(x78681,x78682,f246(f872(x78681,a860)),x78683),f323(x78683,x78684)),x78684)
% 188.07/187.97 [7958]~P101(f323(f323(f325(f866(x79581)),f323(f323(f144(x79581),x79584),x79582)),f154(x79581,x79583)))+P101(f323(f323(f325(f866(x79581)),x79582),f154(x79581,x79583)))
% 188.07/187.97 [7959]~P101(f323(f323(f325(f866(x79591)),f323(f323(f121(x79591),x79594),x79592)),f154(x79591,x79593)))+P101(f323(f323(f325(f866(x79591)),x79592),f154(x79591,x79593)))
% 188.07/187.97 [7960]~P101(f323(f323(f325(f866(x79601)),f323(f323(f121(x79601),x79602),x79604)),f154(x79601,x79603)))+P101(f323(f323(f325(f866(x79601)),x79602),f154(x79601,x79603)))
% 188.07/187.97 [7971]~P103(x79711)+P16(x79711,f323(f323(f147(x79712,x79711),x79713),f143(x79712,x79711,x79713,x79714)))
% 188.07/187.97 [8068]P27(x80684,x80683,x80681,x80682)+E(f323(x80681,f513(x80682,x80681,x80683,x80684)),f323(x80681,f528(x80682,x80681,x80683,x80684)))
% 188.07/187.97 [8080]E(f180(x80801,x80802,x80803,x80804),f180(x80801,x80802,x80804,x80803))+~E(f323(f323(f101(f872(x80801,a860)),f177(x80801,x80802,x80803)),f177(x80801,x80802,x80804)),f188(f872(x80801,a860)))
% 188.07/187.97 [8182]~P27(x81822,x81821,x81824,x81823)+P27(x81821,x81822,f75(x81822,x81821,x81823,x81824),f323(f302(x81822,x81821,x81824),x81823))
% 188.07/187.97 [8323]P38(f871(x83232,x83234),f275(x83232,x83234,x83231,x83233))+P101(f323(x83231,f663(x83232,x83233,x83234,x83231)))
% 188.07/187.97 [8436]E(x84361,x84362)+~P101(f323(f323(f325(f871(x84363,x84363)),f323(f323(f258(x84363,x84363),x84361),x84362)),f255(x84363,x84364)))
% 188.07/187.97 [8498]~P101(f323(f59(f870(x84983,x84981)),f310(x84983,x84981,x84984,x84982)))+P101(f323(f59(x84981),x84982))
% 188.07/187.97 [8499]~P101(f323(f59(f870(x84991,x84993)),f310(x84991,x84993,x84992,x84994)))+P101(f323(f59(x84991),x84992))
% 188.07/187.97 [8508]~P27(x85081,x85082,x85083,x85084)+P28(x85081,x85082,x85083,x85084,f323(f302(x85081,x85082,x85083),x85084))
% 188.07/187.97 [8601]~P28(x86012,x86013,x86014,x86011,f188(f872(x86013,a860)))+E(x86011,f188(f872(x86012,a860)))
% 188.07/187.97 [8602]~P28(x86023,x86022,x86024,f188(f872(x86023,a860)),x86021)+E(x86021,f188(f872(x86022,a860)))
% 188.07/187.97 [8695]P38(f871(x86951,x86952),f275(x86951,x86952,x86953,x86954))+~P38(x86952,f323(x86954,f663(x86951,x86954,x86952,x86953)))
% 188.07/187.97 [9254]E(f323(f323(f152(x92541,x92542),f589(x92543,x92544,x92542,x92541)),f590(x92543,x92544,x92542,x92541)),x92544)+~P101(f323(f323(f325(f871(f866(x92541),f866(x92541))),f323(f323(f258(f866(x92541),f866(x92541)),x92542),x92544)),f150(x92541,x92543)))
% 188.07/187.97 [9260]~P101(f323(f323(f325(f871(f866(x92601),f866(x92601))),f323(f323(f258(f866(x92601),f866(x92601)),x92602),x92603)),f138(x92601,x92604)))+P101(f323(f323(f325(f871(f866(x92601),f866(x92601))),f323(f323(f258(f866(x92601),f866(x92601)),x92602),x92603)),f140(x92601,x92604)))
% 188.07/187.97 [9366]P101(f323(f59(x93661),x93662))+~P101(f323(f323(f325(f871(f872(x93661,a860),f872(x93661,a860))),f323(f323(f258(f872(x93661,a860),f872(x93661,a860)),x93663),x93662)),f314(x93661,x93664)))
% 188.07/187.97 [9367]P101(f323(f59(x93671),x93672))+~P101(f323(f323(f325(f871(f872(x93671,a860),f872(x93671,a860))),f323(f323(f258(f872(x93671,a860),f872(x93671,a860)),x93672),x93673)),f314(x93671,x93674)))
% 188.07/187.97 [9370]~E(x93701,f188(f872(x93702,a860)))+~P101(f323(f323(f325(f871(f872(x93702,a860),f872(x93702,a860))),f323(f323(f258(f872(x93702,a860),f872(x93702,a860)),x93703),x93701)),f314(x93702,x93704)))
% 188.07/187.97 [10008]P14(x100081,x100082,x100083,x100084)+~P101(f323(f323(f262(x100081,x100081,a860),f323(f323(f7(x100081,f872(x100081,x100082),f872(x100081,a860)),f323(f323(f8(f872(x100082,a860),f872(f872(x100081,x100082),f872(x100081,a860)),x100081),f8(x100082,a860,x100081)),f323(f323(f8(x100082,f872(x100082,a860),x100081),a320),x100084))),x100084)),f584(x100084,x100083,x100082,x100081)))
% 188.07/187.97 [4954]~E(x49544,f200(x49541))+E(f323(f323(f201(x49541,x49542),x49543),x49544),f200(x49542))
% 188.07/187.97 [4955]~E(x49554,f113(x49551))+E(f323(f323(f147(x49551,x49552),x49553),x49554),f113(x49552))
% 188.07/187.97 [4956]~E(x49562,f113(x49561))+E(f323(f323(f152(x49561,x49562),x49563),x49564),f113(x49561))
% 188.07/187.97 [5183]E(x51831,f200(x51832))+~E(f323(f323(f201(x51832,x51833),x51834),x51831),f200(x51833))
% 188.07/187.97 [5184]E(x51841,f113(x51842))+~E(f323(f323(f147(x51842,x51843),x51844),x51841),f113(x51843))
% 188.07/187.97 [5185]E(x51851,f113(x51852))+~E(f323(f323(f152(x51852,x51851),x51853),x51854),f113(x51852))
% 188.07/187.97 [5214]E(x52141,x52142)+~E(f323(f323(f121(x52143),x52144),x52141),f323(f323(f121(x52143),x52144),x52142))
% 188.07/187.97 [5215]E(x52151,x52152)+~E(f323(f323(f121(x52153),x52151),x52154),f323(f323(f121(x52153),x52152),x52154))
% 188.07/187.97 [5368]P101(f323(x53683,x53682))+E(f164(x53681,x53682,f323(f129(x53681,x53683),x53684)),f323(f129(x53681,x53683),x53684))
% 188.07/187.97 [5371]~P101(f323(x53712,x53713))+P34(x53711,x53712,f323(f323(f144(x53711),x53713),x53714))
% 188.07/187.97 [5380]E(x53801,x53802)+~E(f132(a865,f323(f293(a865,x53801),x53803)),f323(f323(f144(a865),x53802),x53804))
% 188.07/187.97 [5428]~P29(x54282,x54283)+P29(x54281,f323(f323(f72(x54282,x54281),x54283),x54284))
% 188.07/187.97 [5429]~P38(x54292,x54293)+P38(x54291,f323(f323(f279(x54292,x54291),x54293),x54294))
% 188.07/187.97 [5553]~P34(x55531,x55532,x55534)+P34(x55531,x55532,f323(f323(f144(x55531),x55533),x55534))
% 188.07/187.97 [5554]~P34(x55541,x55542,x55544)+P34(x55541,x55542,f323(f323(f121(x55541),x55543),x55544))
% 188.07/187.97 [5555]~P34(x55551,x55552,x55553)+P34(x55551,x55552,f323(f323(f121(x55551),x55553),x55554))
% 188.07/187.97 [5641]~E(x56411,f113(x56412))+~E(f323(f323(f121(x56412),x56413),f323(f323(f144(x56412),x56414),f113(x56412))),x56411)
% 188.07/187.97 [5666]~P32(x56663,x56661,f323(f323(f144(x56663),x56662),x56664))+P101(f323(x56661,x56662))
% 188.07/187.97 [5676]E(f137(x56761,x56762),x56763)+~E(f323(f323(f121(x56761),x56764),f323(f323(f144(x56761),x56763),f113(x56761))),x56762)
% 188.07/187.97 [5677]E(f114(x56771,x56772),x56773)+~E(f323(f323(f121(x56771),x56773),f323(f323(f144(x56771),x56774),f113(x56771))),x56772)
% 188.07/187.97 [5785]~E(f132(a865,f323(f293(a865,x57851),x57852)),f323(f323(f144(a865),x57853),x57854))+P101(f323(f323(f238(a865),x57851),x57852))
% 188.07/187.97 [5793]P32(x57931,x57932,x57933)+~P32(x57931,x57932,f323(f323(f144(x57931),x57934),x57933))
% 188.07/187.97 [5794]P32(x57941,x57942,x57943)+~P32(x57941,x57942,f323(f323(f121(x57941),x57944),x57943))
% 188.07/187.97 [5795]P32(x57951,x57952,x57953)+~P32(x57951,x57952,f323(f323(f121(x57951),x57953),x57954))
% 188.07/187.97 [5977]E(x59771,f323(f323(f121(x59772),f323(f162(x59772),x59773)),f323(f323(f144(x59772),x59774),f113(x59772))))+~E(f323(f162(x59772),x59771),f323(f323(f144(x59772),x59774),x59773))
% 188.07/187.97 [6148]~P105(x61481)+E(f323(f323(f101(f872(x61481,a860)),f323(f293(x61481,x61482),x61483)),f323(f293(x61481,x61483),x61484)),f188(f872(x61481,a860)))
% 188.07/187.97 [6158]E(f323(f323(f158(x61581),f163(x61581,x61582,x61583)),x61584),x61583)+~P101(f323(f323(f238(a865),x61584),x61582))
% 188.07/187.97 [6185]~P72(x61851)+E(f323(f159(x61851),f323(f323(f147(a1,x61851),x61852),f172(x61853,x61854))),f323(f323(f6(a1,x61851),x61852),f323(f166(a1),f172(x61853,x61854))))
% 188.07/187.97 [6186]~P72(x61861)+E(f323(f323(f6(a1,x61861),x61862),f323(f166(a1),f172(x61863,x61864))),f323(f159(x61861),f323(f323(f147(a1,x61861),x61862),f172(x61863,x61864))))
% 188.07/187.97 [6326]~E(x63262,f323(f323(f121(x63261),f323(f162(x63261),x63264)),f323(f323(f144(x63261),x63263),f113(x63261))))+E(f323(f162(x63261),x63262),f323(f323(f144(x63261),x63263),x63264))
% 188.07/187.97 [6341]~P21(x63412,x63413,x63414,x63411)+E(f323(x63411,f188(f872(x63412,a860))),f32(x63413))
% 188.07/187.97 [6367]~P105(x63671)+E(f323(f323(f101(f872(x63671,a860)),f297(x63671,x63672,x63673)),f323(f293(x63671,x63673),x63674)),f188(f872(x63671,a860)))
% 188.07/187.97 [6573]E(x65731,f188(f872(x65732,a860)))+~E(f310(x65733,x65732,x65734,x65731),f188(f872(f870(x65733,x65732),a860)))
% 188.07/187.97 [6574]E(x65741,f188(f872(x65742,a860)))+~E(f310(x65742,x65743,x65741,x65744),f188(f872(f870(x65742,x65743),a860)))
% 188.07/187.97 [6642]~P103(x66422)+E(f323(f189(f866(x66421)),f143(x66421,x66422,x66423,x66424)),f323(f189(f866(x66421)),x66424))
% 188.07/187.97 [6654]~P101(f323(f253(x66543,x66544,x66541),x66542))+P101(f323(f323(x66541,f673(x66542,x66541)),x66542))
% 188.07/187.97 [6694]~P101(f323(f59(x66942),x66944))+P101(f323(f59(x66941),f323(f302(x66942,x66941,x66943),x66944)))
% 188.07/187.97 [6923]~P27(x69232,x69231,x69233,x69234)+E(f323(f35(x69231),f323(f302(x69232,x69231,x69233),x69234)),f323(f35(x69232),x69234))
% 188.07/187.97 [6942]E(f323(f302(x69421,x69422,x69423),f323(f303(x69421,x69422,x69423),x69424)),x69424)+~E(f323(f302(x69421,x69422,x69423),f246(f872(x69421,a860))),f246(f872(x69422,a860)))
% 188.07/187.97 [7347]~P27(x73471,x73472,x73473,f246(f872(x73471,a860)))+E(f323(f303(x73471,x73472,x73473),f323(f302(x73471,x73472,x73473),x73474)),x73474)
% 188.07/187.97 [7632]E(x76321,x76322)+~P101(f323(f323(f325(x76323),x76321),f323(f166(x76323),f163(x76323,x76324,x76322))))
% 188.07/187.97 [7641]~E(x76411,f2(a865))+~P101(f323(f323(f325(x76412),x76413),f323(f166(x76412),f163(x76412,x76411,x76414))))
% 188.07/187.97 [7677]P101(f323(x76771,x76772))+~P101(f323(f323(f325(x76773),x76772),f323(f166(x76773),f171(x76773,x76771,x76774))))
% 188.07/187.97 [7783]~P101(f323(f323(f325(f866(x77831)),f323(f323(f144(x77831),x77832),x77834)),f154(x77831,x77833)))+P101(f323(f323(f325(x77831),x77832),x77833))
% 188.07/187.97 [7915]~P101(f323(f323(f325(x79151),x79152),f323(f166(x79151),f164(x79151,x79154,x79153))))+P101(f323(f323(f325(x79151),x79152),f323(f166(x79151),x79153)))
% 188.07/187.97 [7917]~P101(f323(f323(f325(x79171),x79172),f323(f166(x79171),f170(x79171,x79173,x79174))))+P101(f323(f323(f325(x79171),x79172),f323(f166(x79171),x79173)))
% 188.07/187.97 [7918]~P101(f323(f323(f325(x79181),x79182),f323(f166(x79181),f171(x79181,x79184,x79183))))+P101(f323(f323(f325(x79181),x79182),f323(f166(x79181),x79183)))
% 188.07/187.97 [7928]E(f323(f189(f866(x79281)),x79282),x79283)+~P101(f323(f323(f325(f866(x79281)),x79282),f323(f166(f866(x79281)),f52(x79281,x79283,x79284))))
% 188.07/187.97 [8020]P101(f323(x80203,x80202))+E(f323(f129(x80201,f323(f323(f8(a860,a860,x80201),a318),f323(a320,x80202))),f323(f129(x80201,x80203),x80204)),f323(f129(x80201,x80203),x80204))
% 188.07/187.97 [8131]E(f323(f323(f158(x81311),f171(x81311,x81312,x81313)),x81314),f323(f323(f158(x81311),x81313),x81314))+~P101(f323(f323(f238(a865),x81314),f323(f189(f866(x81311)),f171(x81311,x81312,x81313))))
% 188.07/187.97 [8217]~P72(x82171)+E(f323(f323(f6(a865,x82171),f323(f323(f8(a865,x82171,a865),x82172),a112)),f323(f293(a865,x82173),x82174)),f323(f323(f6(a865,x82171),x82172),f323(f293(a865,f323(a112,x82173)),f323(a112,x82174))))
% 188.07/187.97 [8228]~P72(x82281)+E(f323(f323(f6(a865,x82281),f323(f323(f8(a865,x82281,a865),x82282),a112)),f294(a865,x82283,x82284)),f323(f323(f6(a865,x82281),x82282),f294(a865,f323(a112,x82283),f323(a112,x82284))))
% 188.07/187.97 [8359]~P27(x83591,x83593,x83594,f246(f872(x83591,a860)))+P27(x83591,f872(x83592,x83593),f323(f323(f8(x83593,f872(x83592,x83593),x83591),f16(x83593,x83592)),x83594),f246(f872(x83591,a860)))
% 188.07/187.97 [8441]~P27(x84412,x84411,x84414,x84413)+E(f323(f302(x84411,x84412,f75(x84412,x84411,x84413,x84414)),f323(f302(x84412,x84411,x84414),x84413)),x84413)
% 188.07/187.97 [8500]~P101(f323(f323(f325(f871(x85001,x85001)),f323(f323(f258(x85001,x85001),x85002),x85004)),f255(x85001,x85003)))+P101(f323(f323(f325(x85001),x85002),x85003))
% 188.07/187.97 [8595]E(f323(f323(f323(f70(x85951,f869(x85952)),f323(f16(f869(x85952),x85951),f200(x85952))),x85953),f323(f230(x85952),f785(x85953,x85954,x85952,x85951))),x85954)+~E(f177(x85951,x85952,x85954),f323(f323(f301(x85951),x85953),f188(f872(x85951,a860))))
% 188.07/187.97 [8626]~P27(x86262,x86261,x86263,f246(f872(x86262,a860)))+E(f323(f302(x86261,x86262,f91(x86262,x86261,f246(f872(x86262,a860)),x86263)),f323(f302(x86262,x86261,x86263),x86264)),x86264)
% 188.07/187.97 [8701]~P28(x87011,x87012,x87013,x87014,f246(f872(x87012,a860)))+E(f323(f302(x87011,x87012,x87013),f246(f872(x87011,a860))),f246(f872(x87012,a860)))
% 188.07/187.97 [8734]~E(f323(f323(f6(x87341,a865),x87344),x87343),f323(a112,x87342))+P101(f323(f323(f325(x87341),f462(x87342,x87343,x87344,x87341)),x87343))
% 188.07/187.97 [8756]~E(f323(f323(f6(x87564,a865),x87561),x87563),f323(a112,x87562))+P101(f323(f323(f238(a865),f2(a865)),f323(x87561,f462(x87562,x87563,x87561,x87564))))
% 188.07/187.97 [8767]~P101(f323(f59(x87672),x87674))+P101(f323(f323(f237(a865),f323(f35(x87671),f323(f302(x87672,x87671,x87673),x87674))),f323(f35(x87672),x87674)))
% 188.07/187.97 [8768]E(f323(f323(f258(x87681,x87682),f778(x87683,x87684,x87682,x87681)),f779(x87683,x87684,x87682,x87681)),x87684)+~P101(f323(f323(f325(f871(x87681,x87682)),x87684),f323(f278(x87682,x87681),x87683)))
% 188.07/187.97 [8776]P27(x87761,x87762,x87763,x87764)+P101(f323(f323(f325(x87761),f513(x87764,x87763,x87762,x87761)),x87764))
% 188.07/187.97 [8777]P27(x87771,x87772,x87773,x87774)+P101(f323(f323(f325(x87771),f528(x87774,x87773,x87772,x87771)),x87774))
% 188.07/187.97 [8839]P14(x88391,x88392,x88393,x88394)+P101(f323(f323(f325(f871(x88391,x88391)),f584(x88394,x88393,x88392,x88391)),x88393))
% 188.07/187.97 [8900]P101(f323(x89001,x89002))+~P101(f323(x89001,f323(f323(f258(x89003,x89004),f507(x89004,x89003,x89001)),f508(x89004,x89003,x89001))))
% 188.07/187.97 [8916]E(f323(f189(f866(x89161)),x89162),f323(f189(f866(x89161)),x89163))+~P101(f323(f323(f325(f871(f866(x89161),f866(x89161))),f323(f323(f258(f866(x89161),f866(x89161)),x89162),x89163)),f151(x89161,x89164)))
% 188.07/187.97 [8917]E(f323(f189(f866(x89171)),x89172),f323(f189(f866(x89171)),x89173))+~P101(f323(f323(f325(f871(f866(x89171),f866(x89171))),f323(f323(f258(f866(x89171),f866(x89171)),x89172),x89173)),f138(x89171,x89174)))
% 188.07/187.97 [8918]E(f323(f189(f866(x89181)),x89182),f323(f189(f866(x89181)),x89183))+~P101(f323(f323(f325(f871(f866(x89181),f866(x89181))),f323(f323(f258(f866(x89181),f866(x89181)),x89182),x89183)),f150(x89181,x89184)))
% 188.07/187.97 [8987]P101(f323(f323(f237(a865),f148(x89871,x89872,x89873)),f148(x89871,x89874,x89873)))+P101(f323(f323(f325(x89871),f633(x89874,x89872,x89873,x89871)),f323(f166(x89871),x89873)))
% 188.07/187.97 [8990]E(f323(f189(f866(x89901)),x89902),f323(f189(f866(x89901)),x89903))+~P101(f323(f323(f325(f871(f866(x89901),f866(x89901))),f323(f323(f258(f866(x89901),f866(x89901)),x89902),x89903)),f299(f866(x89901),f150(x89901,x89904))))
% 188.07/187.97 [9226]~P27(x92261,x92262,x92263,x92264)+~P101(f323(f323(f238(a865),f323(f35(x92262),f323(f302(x92261,x92262,x92263),x92264))),f323(f35(x92261),x92264)))
% 188.07/187.97 [9271]~P101(f323(f323(f325(f871(f866(x92711),f866(x92711))),f323(f323(f258(f866(x92711),f866(x92711)),x92712),x92713)),f150(x92711,x92714)))+P101(f323(f323(f325(f871(f866(x92711),f866(x92711))),f323(f323(f258(f866(x92711),f866(x92711)),x92712),x92713)),f151(x92711,f299(x92711,x92714))))
% 188.07/187.97 [9275]~P101(f323(f323(f325(f871(f866(x92751),f866(x92751))),f323(f323(f258(f866(x92751),f866(x92751)),x92752),x92753)),f151(x92751,x92754)))+P101(f323(f323(f325(f871(f866(x92751),f866(x92751))),f323(f323(f258(f866(x92751),f866(x92751)),x92752),x92753)),f299(f866(x92751),f150(x92751,x92754))))
% 188.07/187.97 [9292]P101(f323(f323(f325(f871(x92921,x92921)),f323(f323(f258(x92921,x92921),x92922),x92923)),f299(x92921,x92924)))+~P101(f323(f323(f325(f871(x92921,x92921)),f323(f323(f258(x92921,x92921),x92922),x92923)),f323(f323(f280(x92921,x92921,x92921),x92924),f299(x92921,x92924))))
% 188.07/187.97 [9476]E(f323(f323(f121(x94761),f591(x94762,x94763,x94764,x94761)),f323(f323(f144(x94761),f592(x94762,x94763,x94764,x94761)),f594(x94762,x94763,x94764,x94761))),x94764)+~P101(f323(f323(f325(f871(f866(x94761),f866(x94761))),f323(f323(f258(f866(x94761),f866(x94761)),x94764),x94763)),f150(x94761,x94762)))
% 188.07/187.97 [9477]E(f323(f323(f121(x94771),f591(x94772,x94773,x94774,x94771)),f323(f323(f144(x94771),f593(x94772,x94773,x94774,x94771)),f594(x94772,x94773,x94774,x94771))),x94773)+~P101(f323(f323(f325(f871(f866(x94771),f866(x94771))),f323(f323(f258(f866(x94771),f866(x94771)),x94774),x94773)),f150(x94771,x94772)))
% 188.07/187.97 [9554]P101(f323(f323(f325(f871(x95541,x95541)),f323(f323(f258(x95541,x95541),x95542),f748(x95543,x95544,x95542,x95541))),f299(x95541,x95543)))+~P101(f323(f323(f325(f871(x95541,x95541)),f323(f323(f258(x95541,x95541),x95542),x95544)),f323(f323(f280(x95541,x95541,x95541),x95543),f299(x95541,x95543))))
% 188.07/187.97 [9624]P101(f323(f323(f237(a865),f148(x96241,x96242,x96243)),f148(x96241,x96244,x96243)))+~P101(f323(f323(f238(a865),f323(x96242,f633(x96244,x96242,x96243,x96241))),f323(x96244,f633(x96244,x96242,x96243,x96241))))
% 188.07/187.97 [9693]P101(f323(f323(f325(f871(x96931,x96931)),f323(f323(f258(x96931,x96931),f756(x96932,x96933,x96934,x96931)),x96933)),f299(x96931,x96932)))+~P101(f323(f323(f325(f871(x96931,x96931)),f323(f323(f258(x96931,x96931),x96934),x96933)),f323(f323(f280(x96931,x96931,x96931),x96932),f299(x96931,x96932))))
% 188.07/187.97 [5198]~E(x51982,x51983)+E(f164(x51981,x51982,f323(f323(f144(x51981),x51983),x51984)),x51984)
% 188.07/187.97 [5323]P101(f323(x53232,x53233))+E(f171(x53231,x53232,f323(f323(f144(x53231),x53233),x53234)),f113(x53231))
% 188.07/187.97 [5392]~P79(x53922)+E(f323(f323(f77(f872(x53921,x53922)),x53923),x53924),f323(f77(x53922),f323(x53923,x53924)))
% 188.07/187.97 [5404]~E(x54042,f2(a865))+E(f323(f323(f131(x54041),x54042),f323(f323(f144(x54041),x54043),x54044)),f323(f323(f144(x54041),x54043),x54044))
% 188.07/187.97 [5405]P101(f323(x54052,x54053))+E(f323(f129(x54051,x54052),f323(f323(f144(x54051),x54053),x54054)),f323(f129(x54051,x54052),x54054))
% 188.07/187.97 [5536]~E(x55362,x55364)+P101(f323(f323(f323(f301(x55361),x55362),x55363),x55364))
% 188.07/187.97 [5544]E(x55441,f113(x55442))+E(f137(x55443,f323(f323(f147(x55442,x55443),x55444),x55441)),f323(x55444,f137(x55442,x55441)))
% 188.07/187.97 [5558]~E(x55581,f61(x55582,x55584))+E(f323(x55581,f323(f323(f301(x55582),x55583),f188(f872(x55582,a860)))),x55583)
% 188.07/187.97 [5593]E(x55931,f113(x55932))+E(f323(f134(x55933),f323(f323(f147(x55932,x55933),x55934),x55931)),f323(x55934,f323(f134(x55932),x55931)))
% 188.07/187.97 [5696]~P101(f323(x56963,x56964))+P101(f323(f323(f323(f301(x56961),x56962),x56963),x56964))
% 188.07/187.97 [5810]~P20(x58102,x58104,x58101)+E(f323(x58101,f323(f323(f301(x58102),x58103),f188(f872(x58102,a860)))),x58103)
% 188.07/187.97 [5834]~E(x58342,x58343)+P101(f323(f323(f325(x58341),x58342),f323(f323(f301(x58341),x58343),x58344)))
% 188.07/187.97 [5838]~P2(x58381)+E(f323(f323(f110(x58381),x58382),f323(f323(f110(x58381),x58383),x58384)),f323(f323(f110(x58381),x58383),f323(f323(f110(x58381),x58382),x58384)))
% 188.07/187.97 [5840]~P97(x58401)+E(f323(f323(f110(x58401),x58402),f323(f323(f110(x58401),x58403),x58404)),f323(f323(f110(x58401),x58403),f323(f323(f110(x58401),x58402),x58404)))
% 188.07/187.97 [5841]~P2(x58411)+E(f323(f323(f101(x58411),x58412),f323(f323(f101(x58411),x58413),x58414)),f323(f323(f101(x58411),x58413),f323(f323(f101(x58411),x58412),x58414)))
% 188.07/187.97 [5843]~P98(x58431)+E(f323(f323(f101(x58431),x58432),f323(f323(f101(x58431),x58433),x58434)),f323(f323(f101(x58431),x58433),f323(f323(f101(x58431),x58432),x58434)))
% 188.07/187.97 [5844]~P112(x58441)+E(f323(f323(f79(x58441),x58442),f323(f323(f79(x58441),x58443),x58444)),f323(f323(f79(x58441),x58443),f323(f323(f79(x58441),x58442),x58444)))
% 188.07/187.97 [5845]~P112(x58451)+E(f323(f323(f78(x58451),x58452),f323(f323(f78(x58451),x58453),x58454)),f323(f323(f78(x58451),x58453),f323(f323(f78(x58451),x58452),x58454)))
% 188.07/187.97 [5847]~P103(x58471)+E(f323(f323(f235(x58471),x58472),f323(f323(f235(x58471),x58473),x58474)),f323(f323(f235(x58471),x58473),f323(f323(f235(x58471),x58472),x58474)))
% 188.07/187.97 [5849]~P103(x58491)+E(f323(f323(f236(x58491),x58492),f323(f323(f236(x58491),x58493),x58494)),f323(f323(f236(x58491),x58493),f323(f323(f236(x58491),x58492),x58494)))
% 188.07/187.97 [5854]E(x58541,x58542)+E(f164(x58543,x58541,f323(f323(f144(x58543),x58542),x58544)),f323(f323(f144(x58543),x58542),f164(x58543,x58541,x58544)))
% 188.07/187.97 [5867]~P101(f323(x58672,x58673))+E(f323(f129(x58671,x58672),f323(f323(f144(x58671),x58673),x58674)),f323(f323(f144(x58671),x58673),f323(f129(x58671,x58672),x58674)))
% 188.07/187.97 [5997]~P101(f323(x59972,x59973))+E(f171(x59971,x59972,f323(f323(f144(x59971),x59973),x59974)),f323(f323(f144(x59971),x59973),f171(x59971,x59972,x59974)))
% 188.07/187.97 [6048]P26(x60481,x60482,x60483)+~P26(x60481,x60482,f323(f323(f301(f864(x60481)),x60484),x60483))
% 188.07/187.97 [6061]E(x60611,f188(f872(x60612,a860)))+E(f323(f323(f39(x60612,f872(x60613,a860)),x60611),f323(f16(f872(x60613,a860),x60612),x60614)),x60614)
% 188.07/187.97 [6062]E(x60621,f188(f872(x60622,a860)))+E(f323(f323(f40(x60622,f872(x60623,a860)),x60621),f323(f16(f872(x60623,a860),x60622),x60624)),x60624)
% 188.07/187.97 [6071]~E(x60714,f188(f872(x60712,a860)))+E(f323(f323(f260(x60711,x60712),x60713),f323(f16(f872(x60712,a860),x60711),x60714)),f188(f872(f871(x60711,x60712),a860)))
% 188.07/187.97 [6072]~E(x60723,f188(f872(x60721,a860)))+E(f323(f323(f260(x60721,x60722),x60723),f323(f16(f872(x60722,a860),x60721),x60724)),f188(f872(f871(x60721,x60722),a860)))
% 188.07/187.97 [6118]E(x61181,f2(a865))+E(f323(f323(f131(x61182),x61181),f323(f323(f144(x61182),x61183),x61184)),f323(f323(f131(x61182),f323(f323(f22(a865),x61181),f76(a865))),x61184))
% 188.07/187.97 [6142]E(x61421,f188(f872(x61422,a860)))+E(f323(f302(x61422,x61423,f323(f16(x61423,x61422),x61424)),x61421),f323(f323(f301(x61423),x61424),f188(f872(x61423,a860))))
% 188.07/187.97 [6145]E(f323(f303(x61451,x61452,f323(f16(x61452,x61451),x61453)),x61454),f188(f872(x61451,a860)))+P101(f323(f323(f325(x61452),x61453),x61454))
% 188.07/187.97 [6211]~E(x62113,f188(f872(x62111,a860)))+E(f323(f323(f39(x62111,f872(x62112,a860)),x62113),f323(f16(f872(x62112,a860),x62111),x62114)),f188(f872(x62112,a860)))
% 188.07/187.97 [6212]~E(x62123,f188(f872(x62121,a860)))+E(f323(f323(f40(x62121,f872(x62122,a860)),x62123),f323(f16(f872(x62122,a860),x62121),x62124)),f246(f872(x62122,a860)))
% 188.07/187.97 [6214]~P57(x62141)+E(f42(x62141,f323(f323(f79(x62141),x62142),x62143),f323(f323(f79(x62141),x62142),x62144)),f323(f323(f79(x62141),x62142),f42(x62141,x62143,x62144)))
% 188.07/187.97 [6377]E(f323(f303(x63771,x63772,f323(f16(x63772,x63771),x63773)),x63774),f246(f872(x63771,a860)))+~P101(f323(f323(f325(x63772),x63773),x63774))
% 188.07/187.97 [6400]~P101(f323(f323(f325(x64001),x64002),x64004))+P101(f323(f323(f325(x64001),x64002),f323(f323(f301(x64001),x64003),x64004)))
% 188.07/187.97 [6405]P101(f323(x64051,x64052))+~P101(f323(f153(x64053,x64051),f323(f323(f144(x64053),x64052),x64054)))
% 188.07/187.97 [6414]~E(x64143,f323(f323(f22(a865),f323(f189(f866(x64141)),x64142)),f76(a865)))+E(f114(x64141,f323(f323(f152(x64141,x64142),x64143),x64144)),f114(x64141,x64142))
% 188.07/187.97 [6432]~P103(x64321)+E(f323(f323(f101(f872(x64321,a860)),f323(f292(x64321),x64322)),f294(x64321,x64323,x64324)),f294(x64321,x64323,f323(f323(f235(x64321),x64322),x64324)))
% 188.07/187.97 [6433]~P103(x64331)+E(f323(f323(f101(f872(x64331,a860)),f323(f245(x64331),x64332)),f294(x64331,x64333,x64334)),f294(x64331,f323(f323(f236(x64331),x64332),x64333),x64334))
% 188.07/187.97 [6448]E(f323(f323(f101(f872(x64481,a860)),x64482),f323(f323(f301(x64481),x64483),x64484)),f323(f323(f101(f872(x64481,a860)),x64482),x64484))+P101(f323(f323(f325(x64481),x64483),x64482))
% 188.07/187.97 [6460]E(f164(x64601,x64602,f323(f323(f121(x64601),x64603),x64604)),f323(f323(f121(x64601),x64603),f164(x64601,x64602,x64604)))+P101(f323(f323(f325(x64601),x64602),f323(f166(x64601),x64603)))
% 188.07/187.97 [6464]~P77(x64641)+E(f323(f323(f79(x64641),f323(f323(f248(x64641),x64642),x64643)),f323(f323(f248(x64641),x64642),x64644)),f323(f323(f248(x64641),x64642),f323(f323(f78(a865),x64643),x64644)))
% 188.07/187.97 [6465]~P112(x64651)+E(f323(f323(f79(x64651),f323(f323(f248(x64651),x64652),x64653)),f323(f323(f248(x64651),x64652),x64654)),f323(f323(f248(x64651),x64652),f323(f323(f78(a865),x64653),x64654)))
% 188.07/187.97 [6502]~P96(x65021)+E(f323(f323(f101(x65021),f323(f323(f110(x65021),x65022),x65023)),f323(f323(f110(x65021),x65022),x65024)),f323(f323(f110(x65021),x65022),f323(f323(f101(x65021),x65023),x65024)))
% 188.07/187.97 [6503]~P96(x65031)+E(f323(f323(f110(x65031),f323(f323(f101(x65031),x65032),x65033)),f323(f323(f101(x65031),x65032),x65034)),f323(f323(f101(x65031),x65032),f323(f323(f110(x65031),x65033),x65034)))
% 188.07/187.97 [6504]~P112(x65041)+E(f323(f323(f78(x65041),f323(f323(f79(x65041),x65042),x65043)),f323(f323(f79(x65041),x65042),x65044)),f323(f323(f79(x65041),x65042),f323(f323(f78(x65041),x65043),x65044)))
% 188.07/187.97 [6505]~P103(x65051)+E(f323(f323(f236(x65051),f323(f323(f235(x65051),x65052),x65053)),f323(f323(f235(x65051),x65052),x65054)),f323(f323(f235(x65051),x65052),f323(f323(f236(x65051),x65053),x65054)))
% 188.07/187.97 [6506]~P103(x65061)+E(f323(f323(f235(x65061),f323(f323(f236(x65061),x65062),x65063)),f323(f323(f236(x65061),x65062),x65064)),f323(f323(f236(x65061),x65062),f323(f323(f235(x65061),x65063),x65064)))
% 188.07/187.97 [6537]~P57(x65371)+E(f42(x65371,f323(f323(f79(x65371),x65372),x65373),f323(f323(f79(x65371),x65374),x65373)),f323(f323(f79(x65371),f42(x65371,x65372,x65374)),x65373))
% 188.07/187.97 [6540]~E(f323(f189(f866(x65401)),x65403),f323(f189(f866(x65402)),x65404))+E(f323(f323(f147(f871(x65401,x65402),x65402),f261(x65401,x65402)),f323(f323(f175(x65401,x65402),x65403),x65404)),x65404)
% 188.07/187.97 [6541]~E(f323(f189(f866(x65411)),x65413),f323(f189(f866(x65412)),x65414))+E(f323(f323(f147(f871(x65411,x65412),x65411),f257(x65411,x65412)),f323(f323(f175(x65411,x65412),x65413),x65414)),x65413)
% 188.07/187.97 [6547]P101(f323(f153(x65471,x65472),x65473))+~P101(f323(f153(x65471,x65472),f323(f323(f144(x65471),x65474),x65473)))
% 188.07/187.97 [6548]P101(f323(f153(x65481,x65482),x65483))+~P101(f323(f153(x65481,x65482),f323(f323(f121(x65481),x65484),x65483)))
% 188.07/187.97 [6549]P101(f323(f153(x65491,x65492),x65493))+~P101(f323(f153(x65491,x65492),f323(f323(f121(x65491),x65493),x65494)))
% 188.07/187.97 [6554]~P58(x65541)+E(f42(x65541,f323(f323(f22(x65541),x65542),f42(x65541,x65543,x65544)),x65544),f42(x65541,f323(f323(f22(x65541),x65542),x65543),x65544))
% 188.07/187.97 [6555]~P57(x65551)+E(f42(x65551,f323(f323(f79(x65551),x65552),f42(x65551,x65553,x65554)),x65554),f42(x65551,f323(f323(f79(x65551),x65552),x65553),x65554))
% 188.07/187.97 [6557]~P57(x65571)+E(f42(x65571,f323(f323(f78(x65571),x65572),f42(x65571,x65573,x65574)),x65574),f42(x65571,f323(f323(f78(x65571),x65572),x65573),x65574))
% 188.07/187.97 [6636]~P103(x66361)+E(f323(f323(f101(f872(x66361,a860)),f294(x66361,x66362,x66363)),f323(f292(x66361),x66364)),f294(x66361,x66362,f323(f323(f235(x66361),x66363),x66364)))
% 188.07/187.97 [6637]~P103(x66371)+E(f323(f323(f101(f872(x66371,a860)),f294(x66371,x66372,x66373)),f323(f245(x66371),x66374)),f294(x66371,f323(f323(f236(x66371),x66372),x66374),x66373))
% 188.07/187.97 [6640]~E(f323(f189(f866(x66401)),x66403),f323(f189(f866(x66402)),x66404))+E(f323(f323(f175(x66401,x66402),f323(f162(x66401),x66403)),f323(f162(x66402),x66404)),f323(f162(f871(x66401,x66402)),f323(f323(f175(x66401,x66402),x66403),x66404)))
% 188.07/187.97 [6650]E(x66501,f323(f323(f22(a865),f323(f189(f866(x66502)),x66503)),f76(a865)))+E(f114(x66502,f323(f323(f152(x66502,x66503),x66501),x66504)),f323(f323(f152(x66502,f114(x66502,x66503)),x66501),x66504))
% 188.07/187.97 [6665]~P101(f323(f130(x66652),x66654))+P101(f323(f130(f871(x66651,x66652)),f323(f323(f175(x66651,x66652),x66653),x66654)))
% 188.07/187.97 [6666]~P101(f323(f130(x66661),x66663))+P101(f323(f130(f871(x66661,x66662)),f323(f323(f175(x66661,x66662),x66663),x66664)))
% 188.07/187.97 [6926]E(f323(f323(f36(a865),x69261),x69262),x69263)+~P101(f323(f45(x69261,x69262),f323(f323(f258(a865,a865),x69263),x69264)))
% 188.07/187.97 [6950]E(f42(a865,x69501,x69502),x69503)+~P101(f323(f45(x69501,x69502),f323(f323(f258(a865,a865),x69504),x69503)))
% 188.07/187.97 [6953]P101(f323(f130(x69531),x69532))+~P101(f323(f130(x69533),f323(f323(f147(x69531,x69533),x69534),x69532)))
% 188.07/187.97 [6961]~P26(x69611,x69612,f323(f323(f301(f864(x69611)),x69613),x69614))+P26(x69611,x69612,f323(f323(f301(f864(x69611)),x69613),f188(f872(f864(x69611),a860))))
% 188.07/187.97 [7037]E(f164(x70371,x70372,f323(f323(f121(x70371),x70373),x70374)),f323(f323(f121(x70371),f164(x70371,x70372,x70373)),x70374))+~P101(f323(f323(f325(x70371),x70372),f323(f166(x70371),x70373)))
% 188.07/187.97 [7127]~P58(x71271)+E(f42(x71271,f323(f323(f22(x71271),f42(x71271,x71272,x71273)),x71274),x71273),f42(x71271,f323(f323(f22(x71271),x71272),x71274),x71273))
% 188.07/187.97 [7130]~P57(x71301)+E(f42(x71301,f323(f323(f79(x71301),f42(x71301,x71302,x71303)),x71304),x71303),f42(x71301,f323(f323(f79(x71301),x71302),x71304),x71303))
% 188.07/187.97 [7131]~P57(x71311)+E(f42(x71311,f323(f323(f78(x71311),f42(x71311,x71312,x71313)),x71314),x71313),f42(x71311,f323(f323(f78(x71311),x71312),x71314),x71313))
% 188.07/187.97 [7318]~E(x73181,f323(f323(f144(x73182),x73183),x73184))+~P101(f323(f323(f237(a865),f323(f189(f866(x73182)),x73181)),f323(f189(f866(x73182)),x73184)))
% 188.07/187.97 [7393]~E(f323(f179(x73931,x73932),x73933),f323(f179(x73931,x73932),x73934))+E(f323(f302(f871(x73931,x73932),x73931,f257(x73931,x73932)),f323(f166(f871(x73931,x73932)),x73933)),f323(f302(f871(x73931,x73932),x73931,f257(x73931,x73932)),f323(f166(f871(x73931,x73932)),x73934)))
% 188.07/187.97 [7525]P27(x75251,x75252,x75253,f323(f166(x75251),x75254))+~P101(f323(f130(x75252),f323(f323(f147(x75251,x75252),x75253),x75254)))
% 188.07/187.97 [7599]~P101(f323(f323(f237(f872(x75991,a860)),x75992),x75994))+P101(f323(f323(f237(f872(x75991,a860)),x75992),f323(f323(f301(x75991),x75993),x75994)))
% 188.07/187.97 [7633]~P58(x76331)+E(f42(x76331,f323(f323(f22(x76331),f42(x76331,x76332,x76333)),f42(x76331,x76334,x76333)),x76333),f42(x76331,f323(f323(f22(x76331),x76332),x76334),x76333))
% 188.07/187.97 [7634]~P57(x76341)+E(f42(x76341,f323(f323(f79(x76341),f42(x76341,x76342,x76343)),f42(x76341,x76344,x76343)),x76343),f42(x76341,f323(f323(f79(x76341),x76342),x76344),x76343))
% 188.07/187.97 [7635]~P57(x76351)+E(f42(x76351,f323(f323(f78(x76351),f42(x76351,x76352,x76353)),f42(x76351,x76354,x76353)),x76353),f42(x76351,f323(f323(f78(x76351),x76352),x76354),x76353))
% 188.07/187.97 [7740]~E(f323(x77404,f444(x77404,x77403,x77401,x77402)),f188(f872(x77402,a860)))+E(f323(f323(f39(x77401,f872(x77402,a860)),x77403),x77404),f188(f872(x77402,a860)))
% 188.07/187.97 [7741]~E(f323(x77414,f631(x77414,x77413,x77411,x77412)),f246(f872(x77412,a860)))+E(f323(f323(f40(x77411,f872(x77412,a860)),x77413),x77414),f246(f872(x77412,a860)))
% 188.07/187.97 [7742]~E(f323(x77424,f454(x77424,x77423,x77422,x77421)),f188(f872(x77422,a860)))+E(f323(f323(f39(x77421,f872(x77422,a860)),x77423),x77424),f188(f872(x77422,a860)))
% 188.07/187.97 [7743]~E(f323(x77434,f636(x77434,x77433,x77432,x77431)),f246(f872(x77432,a860)))+E(f323(f323(f40(x77431,f872(x77432,a860)),x77433),x77434),f246(f872(x77432,a860)))
% 188.07/187.97 [8132]P101(f323(x81321,x81322))+~P101(f323(f323(f325(x81323),x81322),f323(f323(f101(f872(x81323,a860)),x81324),f323(f243(x81323),x81321))))
% 188.07/187.97 [8170]~P101(f323(f323(f237(f872(x81701,a860)),x81703),x81704))+P101(f323(f323(f237(f872(x81701,a860)),f323(f323(f301(x81701),x81702),x81703)),f323(f323(f301(x81701),x81702),x81704)))
% 188.07/187.97 [8181]E(f323(x81811,f647(x81811,x81812,x81813)),x81813)+~P101(f323(f323(f325(x81814),x81813),f323(f302(x81812,x81814,x81811),f246(f872(x81812,a860)))))
% 188.07/187.97 [8351]P101(f323(x83512,x83513))+E(f323(f323(f131(x83511),f323(f189(f866(x83511)),f171(x83511,x83512,f323(f323(f144(x83511),x83513),x83514)))),f323(f323(f144(x83511),x83513),x83514)),f323(f323(f144(x83511),x83513),x83514))
% 188.07/187.97 [8455]~P101(f323(f323(f238(a865),f323(x84554,x84552)),f323(x84554,x84553)))+P101(f323(f323(f325(f871(x84551,x84551)),f323(f323(f258(x84551,x84551),x84552),x84553)),f323(f323(f279(a865,x84551),a242),x84554)))
% 188.07/187.97 [8549]~P101(f323(x85492,f701(x85494,x85492,x85493,x85491)))+E(f171(x85491,x85492,f323(f323(f121(x85491),x85493),x85494)),f323(f323(f121(x85491),x85493),f171(x85491,x85492,x85494)))
% 188.07/187.97 [8630]P27(f866(x86301),f866(x86302),f323(f147(x86301,x86302),x86303),x86304)+~P27(x86301,x86302,x86303,f37(f872(x86301,a860),f323(f302(f866(x86301),f872(x86301,a860),f166(x86301)),x86304)))
% 188.07/187.97 [8705]~P101(f323(x87052,x87053))+E(f323(f323(f131(x87051),f323(f189(f866(x87051)),f171(x87051,x87052,f323(f323(f144(x87051),x87053),x87054)))),f323(f323(f144(x87051),x87053),x87054)),f323(f323(f131(x87051),f323(f189(f866(x87051)),f171(x87051,x87052,x87054))),x87054))
% 188.07/187.97 [8747]~E(x87472,x87473)+E(f323(f129(x87471,f323(f323(f8(a860,a860,x87471),a318),f323(a320,x87472))),f323(f323(f144(x87471),x87473),x87474)),f323(f129(x87471,f323(f323(f8(a860,a860,x87471),a318),f323(a320,x87472))),x87474))
% 188.07/187.97 [8757]E(f323(f323(f39(x87571,f872(x87572,a860)),x87573),x87574),f188(f872(x87572,a860)))+P101(f323(f323(f325(x87571),f444(x87574,x87573,x87571,x87572)),x87573))
% 188.07/187.97 [8758]E(f323(f323(f40(x87581,f872(x87582,a860)),x87583),x87584),f246(f872(x87582,a860)))+P101(f323(f323(f325(x87581),f631(x87584,x87583,x87581,x87582)),x87583))
% 188.07/187.97 [8759]E(f323(f323(f39(x87591,f872(x87592,a860)),x87593),x87594),f188(f872(x87592,a860)))+P101(f323(f323(f325(x87591),f454(x87594,x87593,x87592,x87591)),x87593))
% 188.07/187.97 [8760]E(f323(f323(f40(x87601,f872(x87602,a860)),x87603),x87604),f246(f872(x87602,a860)))+P101(f323(f323(f325(x87601),f636(x87604,x87603,x87602,x87601)),x87603))
% 188.07/187.97 [8798]P101(f323(f323(f238(a865),f323(x87981,x87982)),f323(x87981,x87983)))+~P101(f323(f323(f325(f871(x87984,x87984)),f323(f323(f258(x87984,x87984),x87982),x87983)),f323(f323(f279(a865,x87984),a242),x87981)))
% 188.07/187.97 [8819]E(f171(x88191,x88192,f323(f323(f121(x88191),x88193),x88194)),f323(f323(f121(x88191),x88193),f171(x88191,x88192,x88194)))+P101(f323(f323(f325(x88191),f701(x88194,x88192,x88193,x88191)),f323(f166(x88191),x88193)))
% 188.07/187.97 [8874]~P28(x88741,x88742,x88743,f246(f872(x88741,a860)),f246(f872(x88742,a860)))+E(f323(f302(x88741,x88742,x88743),f323(f77(f872(x88741,a860)),x88744)),f323(f77(f872(x88742,a860)),f323(f302(x88741,x88742,x88743),x88744)))
% 188.07/187.97 [8976]P101(f323(f323(f325(x89761),f496(x89762,x89763,x89764,x89761)),x89763))+~P101(f323(f323(f325(f872(x89761,a860)),x89764),f323(f323(f58(x89761),x89763),x89762)))
% 188.07/187.97 [8979]E(x89791,x89792)+~P101(f323(f323(f325(f871(x89793,x89793)),f323(f323(f258(x89793,x89793),x89791),x89792)),f323(f323(f183(f871(x89793,x89793),a860),f2(a865)),x89794)))
% 188.07/187.97 [9063]E(f323(f277(x90631,x90631,x90632),f323(f323(f301(x90631),f496(x90632,x90633,x90634,x90631)),f188(f872(x90631,a860)))),x90634)+~P101(f323(f323(f325(f872(x90631,a860)),x90634),f323(f323(f58(x90631),x90633),x90632)))
% 188.07/187.97 [9068]~P101(f323(f323(f325(f871(x90681,x90681)),f323(f323(f258(x90681,x90681),x90683),x90682)),f299(x90681,x90684)))+P101(f323(f323(f325(f871(x90681,x90681)),f323(f323(f258(x90681,x90681),x90682),x90683)),f299(x90681,f323(f278(x90681,x90681),x90684))))
% 188.07/187.97 [9080]~P57(x90801)+E(f323(f323(f78(x90801),f323(f323(f78(x90801),f323(f323(f79(x90801),x90802),f323(f323(f36(x90801),x90803),x90802))),f42(x90801,x90803,x90802))),x90804),f323(f323(f78(x90801),x90803),x90804))
% 188.07/187.97 [9090]~P101(f323(f323(f325(x90901),x90903),x90904))+P101(f323(f323(f325(f872(x90901,a860)),f323(f277(x90901,x90901,x90902),f323(f323(f301(x90901),x90903),f188(f872(x90901,a860))))),f323(f323(f58(x90901),x90904),x90902)))
% 188.07/187.97 [9101]P101(f323(f323(f325(f871(x91011,x91011)),f323(f323(f258(x91011,x91011),x91012),x91013)),f299(x91011,x91014)))+~P101(f323(f323(f325(f871(x91011,x91011)),f323(f323(f258(x91011,x91011),x91013),x91012)),f299(x91011,f323(f278(x91011,x91011),x91014))))
% 188.07/187.97 [9189]E(f323(f323(f152(x91891,f323(f162(x91891),x91892)),f323(f323(f22(a865),f323(f323(f22(a865),f323(f189(f866(x91891)),x91892)),x91893)),f76(a865))),x91894),f323(f162(x91891),f323(f323(f152(x91891,x91892),x91893),x91894)))+~P101(f323(f323(f238(a865),x91893),f323(f189(f866(x91891)),x91892)))
% 188.07/187.97 [9192]~P101(f323(x91922,f695(x91924,x91922,x91923,x91921)))+E(f323(f323(f131(x91921),f323(f189(f866(x91921)),f171(x91921,x91922,f323(f323(f121(x91921),x91923),x91924)))),f323(f323(f121(x91921),x91923),x91924)),f323(f323(f131(x91921),f323(f189(f866(x91921)),f171(x91921,x91922,x91924))),x91924))
% 188.07/187.97 [9234]~P27(x92342,x92341,x92343,f246(f872(x92342,a860)))+P101(f323(f323(f237(f872(x92341,a860)),f323(f302(x92342,x92341,x92343),f323(f77(f872(x92342,a860)),x92344))),f323(f77(f872(x92341,a860)),f323(f302(x92342,x92341,x92343),x92344))))
% 188.07/187.97 [9245]~P6(x92451)+E(f323(f135(x92451,x92452,f323(f7(x92452,x92451,x92451),f323(f323(f8(x92451,f872(x92451,x92451),x92452),f110(x92451)),x92453)),f188(x92451)),x92454),f323(f323(f39(x92452,x92451),f323(f166(x92452),x92454)),x92453))
% 188.07/187.97 [9246]~P6(x92461)+E(f323(f135(x92461,x92462,f323(f7(x92462,x92461,x92461),f323(f323(f8(x92461,f872(x92461,x92461),x92462),f101(x92461)),x92463)),f246(x92461)),x92464),f323(f323(f40(x92462,x92461),f323(f166(x92462),x92464)),x92463))
% 188.07/187.97 [9256]E(f323(f323(f131(x92561),f323(f189(f866(x92561)),f171(x92561,x92562,f323(f323(f121(x92561),x92563),x92564)))),f323(f323(f121(x92561),x92563),x92564)),f323(f323(f131(x92561),f323(f189(f866(x92561)),f171(x92561,x92562,x92564))),x92564))+P101(f323(f323(f325(x92561),f695(x92564,x92562,x92563,x92561)),f323(f166(x92561),x92563)))
% 188.07/187.97 [9258]P26(x92583,x92582,f323(f323(f301(f864(x92583)),f323(f323(f323(f90(x92583),x92581),a24),x92584)),f188(f872(f864(x92583),a860))))+P101(f323(f323(x92581,f831(x92582,x92583,x92584,x92581)),f843(x92582,x92583,x92584,x92581)))
% 188.07/187.97 [9326]~P101(f323(f323(f325(f871(f866(x93264),f866(x93264))),f323(f323(f258(f866(x93264),f866(x93264)),x93263),x93262)),f150(x93264,x93261)))+P101(f323(f323(f238(a865),f589(x93261,x93262,x93263,x93264)),f323(f189(f866(x93264)),x93263)))
% 188.07/187.97 [9327]~P57(x93271)+E(f323(f323(f78(x93271),f323(f323(f78(x93271),f323(f323(f79(x93271),f323(f323(f36(x93271),x93272),x93273)),x93273)),f42(x93271,x93272,x93273))),x93274),f323(f323(f78(x93271),x93272),x93274))
% 188.07/187.97 [9354]~P101(f323(f323(f325(f871(f866(x93541),f866(x93541))),f323(f323(f258(f866(x93541),f866(x93541)),x93542),x93543)),f323(f278(f866(x93541),f866(x93541)),f150(x93541,x93544))))+P101(f323(f323(f325(f871(f866(x93541),f866(x93541))),f323(f323(f258(f866(x93541),f866(x93541)),x93542),x93543)),f150(x93541,f323(f278(x93541,x93541),x93544))))
% 188.07/187.97 [9355]P101(f323(f323(f325(f871(f866(x93551),f866(x93551))),f323(f323(f258(f866(x93551),f866(x93551)),x93552),x93553)),f323(f278(f866(x93551),f866(x93551)),f150(x93551,x93554))))+~P101(f323(f323(f325(f871(f866(x93551),f866(x93551))),f323(f323(f258(f866(x93551),f866(x93551)),x93552),x93553)),f150(x93551,f323(f278(x93551,x93551),x93554))))
% 188.07/187.97 [9390]~P101(f323(f323(f325(x93901),x93903),f323(f256(x93901,x93902),x93904)))+P101(f323(f323(f325(f871(x93901,x93902)),f323(f323(f258(x93901,x93902),x93903),f678(x93904,x93902,x93903,x93901))),x93904))
% 188.07/187.97 [9391]~P101(f323(f323(f325(x93911),x93913),f323(f256(x93911,x93912),x93914)))+P101(f323(f323(f325(f871(x93911,x93912)),f323(f323(f258(x93911,x93912),x93913),f680(x93914,x93912,x93913,x93911))),x93914))
% 188.07/187.97 [9447]P26(x94471,x94472,f323(f323(f301(f864(x94471)),f323(f323(f323(f90(x94471),x94473),a24),x94474)),f188(f872(f864(x94471),a860))))+~P101(f323(f323(x94474,f831(x94472,x94471,x94474,x94473)),f843(x94472,x94471,x94474,x94473)))
% 188.07/187.97 [9501]~P101(f323(f59(f869(x95011)),f323(f302(x95012,f869(x95011),x95013),f246(f872(x95012,a860)))))+P101(f323(f59(f869(x95011)),f323(f302(x95012,f869(x95011),f180(x95012,x95011,x95013,f323(f179(x95012,x95011),x95014))),f246(f872(x95012,a860)))))
% 188.07/187.97 [9549]~P101(f323(f323(f325(f871(x95491,x95491)),f323(f323(f258(x95491,x95491),x95492),x95494)),f323(f323(f280(x95491,x95491,x95491),x95493),f299(x95491,x95493))))+P101(f323(f323(f325(f871(x95491,x95491)),f323(f323(f258(x95491,x95491),x95492),f756(x95493,x95494,x95492,x95491))),x95493))
% 188.07/187.97 [9720]~P101(f323(f323(f325(f871(x97202,x97201)),x97204),f323(f278(x97201,x97202),x97203)))+P101(f323(f323(f325(f871(x97201,x97202)),f323(f323(f258(x97201,x97202),f779(x97203,x97204,x97201,x97202)),f778(x97203,x97204,x97201,x97202))),x97203))
% 188.07/187.97 [9748]~P101(f323(f323(f325(f871(f866(x97481),f866(x97481))),f323(f323(f258(f866(x97481),f866(x97481)),x97484),x97483)),f150(x97481,x97482)))+P101(f323(f323(f325(f871(x97481,x97481)),f323(f323(f258(x97481,x97481),f592(x97482,x97483,x97484,x97481)),f593(x97482,x97483,x97484,x97481))),x97482))
% 188.07/187.97 [9843]~P101(f323(f323(f325(f871(f866(x98431),f866(x98431))),f323(f323(f258(f866(x98431),f866(x98431)),x98432),x98434)),f150(x98431,x98433)))+P101(f323(f323(f325(f871(x98431,x98431)),f323(f323(f258(x98431,x98431),f323(f323(f158(x98431),x98432),f589(x98433,x98434,x98432,x98431))),f590(x98433,x98434,x98432,x98431))),x98433))
% 188.07/187.97 [9865]~P101(f323(f59(x98652),x98654))+E(f323(f323(f323(f63(f872(x98651,a860),x98652,f110(f872(x98651,a860))),f323(f323(f7(x98652,f872(x98651,a860),f872(x98651,a860)),f323(f323(f8(x98651,f872(f872(x98651,a860),f872(x98651,a860)),x98652),f301(x98651)),x98653)),f188(f872(x98651,a860)))),f188(f872(x98651,a860))),x98654),f323(f302(x98652,x98651,x98653),x98654))
% 188.07/187.97 [9960]~P27(x99601,x99602,x99603,f246(f872(x99601,a860)))+P101(f323(f323(f237(f872(x99601,a860)),f323(f303(x99601,x99602,x99603),f323(f323(f301(x99602),x99604),f188(f872(x99602,a860))))),f323(f323(f301(x99601),f83(x99601,f323(f323(f7(x99601,x99602,a860),f323(f323(f8(x99602,f872(x99602,a860),x99601),a320),x99603)),x99604))),f188(f872(x99601,a860)))))
% 188.07/187.97 [5602]~E(f323(f323(f121(x56021),x56022),x56024),x56023)+E(f323(f323(f169(x56021),f323(f189(f866(x56021)),x56022)),x56023),x56022)
% 188.07/187.97 [5603]~E(f323(f323(f121(x56032),x56033),x56031),x56034)+E(x56031,f323(f323(f131(x56032),f323(f189(f866(x56032)),x56033)),x56034))
% 188.07/187.97 [5614]~E(x56144,f2(a865))+E(f323(f323(f158(x56141),f323(f323(f144(x56141),x56142),x56143)),x56144),x56142)
% 188.07/187.97 [6131]~P112(x61311)+E(f323(f323(f248(x61311),f323(f323(f248(x61311),x61312),x61313)),x61314),f323(f323(f248(x61311),x61312),f323(f323(f79(a865),x61313),x61314)))
% 188.07/187.97 [6132]~P77(x61321)+E(f323(f323(f248(x61321),f323(f323(f248(x61321),x61322),x61323)),x61324),f323(f323(f248(x61321),x61322),f323(f323(f79(a865),x61323),x61324)))
% 188.07/187.97 [6143]E(x61431,f2(a865))+E(f323(f323(f158(x61432),f323(f323(f144(x61432),x61433),x61434)),x61431),f323(f323(f158(x61432),x61434),f323(f323(f22(a865),x61431),f76(a865))))
% 188.07/187.97 [6168]~P114(x61681)+E(f323(f323(f281(x61681),f323(f323(f79(x61681),x61682),x61683)),x61684),f323(f323(f79(x61681),x61682),f323(f323(f281(x61681),x61683),x61684)))
% 188.07/187.97 [6170]~P2(x61701)+E(f323(f323(f110(x61701),f323(f323(f110(x61701),x61702),x61703)),x61704),f323(f323(f110(x61701),x61702),f323(f323(f110(x61701),x61703),x61704)))
% 188.07/187.97 [6172]~P97(x61721)+E(f323(f323(f110(x61721),f323(f323(f110(x61721),x61722),x61723)),x61724),f323(f323(f110(x61721),x61722),f323(f323(f110(x61721),x61723),x61724)))
% 188.07/187.97 [6173]~P2(x61731)+E(f323(f323(f101(x61731),f323(f323(f101(x61731),x61732),x61733)),x61734),f323(f323(f101(x61731),x61732),f323(f323(f101(x61731),x61733),x61734)))
% 188.07/187.97 [6175]~P98(x61751)+E(f323(f323(f101(x61751),f323(f323(f101(x61751),x61752),x61753)),x61754),f323(f323(f101(x61751),x61752),f323(f323(f101(x61751),x61753),x61754)))
% 188.07/187.97 [6176]~P66(x61761)+E(f323(f323(f79(x61761),f323(f323(f79(x61761),x61762),x61763)),x61764),f323(f323(f79(x61761),x61762),f323(f323(f79(x61761),x61763),x61764)))
% 188.07/187.97 [6177]~P112(x61771)+E(f323(f323(f79(x61771),f323(f323(f79(x61771),x61772),x61773)),x61774),f323(f323(f79(x61771),x61772),f323(f323(f79(x61771),x61773),x61774)))
% 188.07/187.97 [6179]~P112(x61791)+E(f323(f323(f78(x61791),f323(f323(f78(x61791),x61792),x61793)),x61794),f323(f323(f78(x61791),x61792),f323(f323(f78(x61791),x61793),x61794)))
% 188.07/187.97 [6180]~P67(x61801)+E(f323(f323(f78(x61801),f323(f323(f78(x61801),x61802),x61803)),x61804),f323(f323(f78(x61801),x61802),f323(f323(f78(x61801),x61803),x61804)))
% 188.07/187.97 [6182]~P103(x61821)+E(f323(f323(f235(x61821),f323(f323(f235(x61821),x61822),x61823)),x61824),f323(f323(f235(x61821),x61822),f323(f323(f235(x61821),x61823),x61824)))
% 188.07/187.97 [6184]~P103(x61841)+E(f323(f323(f236(x61841),f323(f323(f236(x61841),x61842),x61843)),x61844),f323(f323(f236(x61841),x61842),f323(f323(f236(x61841),x61843),x61844)))
% 188.07/187.97 [6195]~P57(x61951)+E(f42(x61951,f323(f323(f78(x61951),x61952),f323(f323(f79(x61951),x61953),x61954)),x61954),f42(x61951,x61952,x61954))
% 188.07/187.97 [6196]~P57(x61961)+E(f42(x61961,f323(f323(f78(x61961),x61962),f323(f323(f79(x61961),x61963),x61964)),x61963),f42(x61961,x61962,x61963))
% 188.07/187.97 [6327]E(f323(f323(f158(x63271),f323(f323(f169(x63271),x63272),x63273)),x63274),f323(f323(f158(x63271),x63273),x63274))+~P101(f323(f323(f238(a865),x63274),x63272))
% 188.07/187.97 [6500]~P112(x65001)+E(f323(f323(f79(x65001),f323(f323(f79(x65001),x65002),x65003)),x65004),f323(f323(f79(x65001),f323(f323(f79(x65001),x65002),x65004)),x65003))
% 188.07/187.97 [6501]~P112(x65011)+E(f323(f323(f78(x65011),f323(f323(f78(x65011),x65012),x65013)),x65014),f323(f323(f78(x65011),f323(f323(f78(x65011),x65012),x65014)),x65013))
% 188.07/187.97 [6560]~P140(x65602)+E(f323(f323(f6(x65601,x65602),f323(f16(x65602,x65601),x65603)),x65604),f323(f323(f79(x65602),f323(f100(x65602),f323(f35(x65601),x65604))),x65603))
% 188.07/187.97 [6727]E(f323(f323(f101(f872(x67271,a860)),f323(f323(f301(x67271),x67272),x67273)),x67274),f323(f323(f101(f872(x67271,a860)),x67273),x67274))+P101(f323(f323(f325(x67271),x67272),x67274))
% 188.07/187.97 [6797]~P96(x67971)+E(f323(f323(f101(x67971),f323(f323(f110(x67971),x67972),x67973)),f323(f323(f110(x67971),x67974),x67973)),f323(f323(f110(x67971),f323(f323(f101(x67971),x67972),x67974)),x67973))
% 188.07/187.97 [6798]~P75(x67981)+E(f323(f323(f235(x67981),f323(f323(f22(x67981),x67982),x67983)),f323(f323(f22(x67981),x67984),x67983)),f323(f323(f22(x67981),f323(f323(f235(x67981),x67982),x67984)),x67983))
% 188.07/187.97 [6799]~P75(x67991)+E(f323(f323(f236(x67991),f323(f323(f22(x67991),x67992),x67993)),f323(f323(f22(x67991),x67994),x67993)),f323(f323(f22(x67991),f323(f323(f236(x67991),x67992),x67994)),x67993))
% 188.07/187.97 [6800]~P96(x68001)+E(f323(f323(f110(x68001),f323(f323(f101(x68001),x68002),x68003)),f323(f323(f101(x68001),x68004),x68003)),f323(f323(f101(x68001),f323(f323(f110(x68001),x68002),x68004)),x68003))
% 188.07/187.97 [6802]~P113(x68021)+E(f323(f323(f78(x68021),f323(f323(f79(x68021),x68022),x68023)),f323(f323(f79(x68021),x68024),x68023)),f323(f323(f79(x68021),f323(f323(f78(x68021),x68022),x68024)),x68023))
% 188.07/187.97 [6803]~P80(x68031)+E(f323(f323(f235(x68031),f323(f323(f78(x68031),x68032),x68033)),f323(f323(f78(x68031),x68034),x68033)),f323(f323(f78(x68031),f323(f323(f235(x68031),x68032),x68034)),x68033))
% 188.07/187.97 [6804]~P80(x68041)+E(f323(f323(f236(x68041),f323(f323(f78(x68041),x68042),x68043)),f323(f323(f78(x68041),x68044),x68043)),f323(f323(f78(x68041),f323(f323(f236(x68041),x68042),x68044)),x68043))
% 188.07/187.97 [6805]~P103(x68051)+E(f323(f323(f236(x68051),f323(f323(f235(x68051),x68052),x68053)),f323(f323(f235(x68051),x68054),x68053)),f323(f323(f235(x68051),f323(f323(f236(x68051),x68052),x68054)),x68053))
% 188.07/187.97 [6806]~P103(x68061)+E(f323(f323(f235(x68061),f323(f323(f236(x68061),x68062),x68063)),f323(f323(f236(x68061),x68064),x68063)),f323(f323(f236(x68061),f323(f323(f235(x68061),x68062),x68064)),x68063))
% 188.07/187.97 [6807]~P68(x68071)+E(f323(f323(f79(x68071),f323(f323(f248(x68071),x68072),x68073)),f323(f323(f248(x68071),x68074),x68073)),f323(f323(f248(x68071),f323(f323(f79(x68071),x68072),x68074)),x68073))
% 188.07/187.97 [6808]~P112(x68081)+E(f323(f323(f79(x68081),f323(f323(f248(x68081),x68082),x68083)),f323(f323(f248(x68081),x68084),x68083)),f323(f323(f248(x68081),f323(f323(f79(x68081),x68082),x68084)),x68083))
% 188.07/187.97 [6809]~P62(x68091)+E(f323(f323(f281(x68091),f323(f323(f248(x68091),x68092),x68093)),f323(f323(f248(x68091),x68094),x68093)),f323(f323(f248(x68091),f323(f323(f281(x68091),x68092),x68094)),x68093))
% 188.07/187.97 [6810]~P114(x68101)+E(f323(f323(f22(x68101),f323(f323(f281(x68101),x68102),x68103)),f323(f323(f281(x68101),x68104),x68103)),f323(f323(f281(x68101),f323(f323(f22(x68101),x68102),x68104)),x68103))
% 188.07/187.97 [6811]~P114(x68111)+E(f323(f323(f78(x68111),f323(f323(f281(x68111),x68112),x68113)),f323(f323(f281(x68111),x68114),x68113)),f323(f323(f281(x68111),f323(f323(f78(x68111),x68112),x68114)),x68113))
% 188.07/187.97 [6812]~P112(x68121)+E(f323(f323(f78(x68121),f323(f323(f79(x68121),x68122),x68123)),f323(f323(f79(x68121),x68124),x68123)),f323(f323(f79(x68121),f323(f323(f78(x68121),x68122),x68124)),x68123))
% 188.07/187.97 [6844]E(f323(f323(f152(x68441,x68442),x68443),x68444),x68442)+~P101(f323(f323(f237(a865),f323(f189(f866(x68441)),x68442)),x68443))
% 188.07/187.97 [6868]~P101(f323(x68683,x68684))+P101(f323(f323(f323(f110(f872(x68681,a860)),x68682),x68683),x68684))
% 188.07/187.97 [6870]~P101(f323(x68702,x68704))+P101(f323(f323(f323(f110(f872(x68701,a860)),x68702),x68703),x68704))
% 188.07/187.97 [6889]E(f323(f323(f158(x68891),f323(f323(f121(x68891),x68892),x68893)),x68894),f323(f323(f158(x68891),x68892),x68894))+~P101(f323(f323(f238(a865),x68894),f323(f189(f866(x68891)),x68892)))
% 188.07/187.97 [6899]E(f323(f323(f22(f872(x68991,a860)),f323(f323(f301(x68991),x68992),x68993)),x68994),f323(f323(f22(f872(x68991,a860)),x68993),x68994))+~P101(f323(f323(f325(x68991),x68992),x68994))
% 188.07/187.97 [6940]~E(f132(a865,f323(f293(a865,x69401),x69402)),f323(f323(f144(a865),x69404),x69403))+E(f132(a865,f323(f293(a865,f323(f323(f78(a865),x69401),f76(a865))),x69402)),x69403)
% 188.07/187.97 [7011]E(x70111,f2(a865))+E(f323(f323(f144(x70112),x70113),f323(f323(f169(x70112),f323(f323(f22(a865),x70111),f76(a865))),x70114)),f323(f323(f169(x70112),x70111),f323(f323(f144(x70112),x70113),x70114)))
% 188.07/187.97 [7111]E(f323(f323(f158(x71111),x71112),f323(f323(f22(a865),x71113),f323(f189(f866(x71111)),x71114))),f323(f323(f158(x71111),f323(f323(f121(x71111),x71114),x71112)),x71113))+P101(f323(f323(f238(a865),x71113),f323(f189(f866(x71111)),x71114)))
% 188.07/187.97 [7141]E(f323(f323(f101(f872(x71411,a860)),x71412),f323(f323(f301(x71411),x71413),x71414)),f323(f323(f301(x71411),x71413),f323(f323(f101(f872(x71411,a860)),x71412),x71414)))+~P101(f323(f323(f325(x71411),x71413),x71412))
% 188.07/187.97 [7176]E(f323(f323(f158(x71761),f323(f323(f152(x71761,x71762),x71763),x71764)),x71763),x71764)+~P101(f323(f323(f238(a865),x71763),f323(f189(f866(x71761)),x71762)))
% 188.07/187.97 [7197]E(x71971,f188(f872(x71972,a860)))+E(f323(f302(f871(x71973,x71972),x71973,f257(x71973,x71972)),f323(f323(f260(x71973,x71972),x71974),f323(f16(f872(x71972,a860),x71973),x71971))),x71974)
% 188.07/187.97 [7198]E(x71981,f188(f872(x71982,a860)))+E(f323(f302(f871(x71982,x71983),x71983,f261(x71982,x71983)),f323(f323(f260(x71982,x71983),x71981),f323(f16(f872(x71983,a860),x71982),x71984))),x71984)
% 188.07/187.97 [7265]E(f323(f323(f22(f872(x72651,a860)),f323(f323(f301(x72651),x72652),x72653)),x72654),f323(f323(f301(x72651),x72652),f323(f323(f22(f872(x72651,a860)),x72653),x72654)))+P101(f323(f323(f325(x72651),x72652),x72654))
% 188.07/187.97 [7302]~E(x73024,f188(f872(x73022,a860)))+E(f323(f302(f871(x73021,x73022),x73021,f257(x73021,x73022)),f323(f323(f260(x73021,x73022),x73023),f323(f16(f872(x73022,a860),x73021),x73024))),f188(f872(x73021,a860)))
% 188.07/187.97 [7303]~E(x73033,f188(f872(x73031,a860)))+E(f323(f302(f871(x73031,x73032),x73032,f261(x73031,x73032)),f323(f323(f260(x73031,x73032),x73033),f323(f16(f872(x73032,a860),x73031),x73034))),f188(f872(x73032,a860)))
% 188.07/187.97 [7358]~P101(f323(f323(f325(x73581),x73582),x73584))+P101(f323(f323(f325(x73581),x73582),f323(f323(f110(f872(x73581,a860)),x73583),x73584)))
% 188.07/187.97 [7361]~P101(f323(f323(f325(x73611),x73612),x73613))+P101(f323(f323(f325(x73611),x73612),f323(f323(f110(f872(x73611,a860)),x73613),x73614)))
% 188.07/187.97 [7380]E(f323(f323(f101(f872(x73801,a860)),f323(f323(f301(x73801),x73802),x73803)),x73804),f323(f323(f301(x73801),x73802),f323(f323(f101(f872(x73801,a860)),x73803),x73804)))+~P101(f323(f323(f325(x73801),x73802),x73804))
% 188.07/187.97 [7656]P101(f323(x76561,x76562))+~P101(f323(f323(f323(f101(f872(x76563,a860)),x76564),x76561),x76562))
% 188.07/187.97 [7657]P101(f323(x76571,x76572))+~P101(f323(f323(f323(f101(f872(x76573,a860)),x76571),x76574),x76572))
% 188.07/187.97 [7660]E(f323(f323(f6(x76601,a865),x76602),f323(f323(f22(f872(x76601,a860)),x76603),f323(f323(f301(x76601),x76604),f188(f872(x76601,a860))))),f323(f323(f6(x76601,a865),x76602),x76603))+P101(f323(f323(f325(x76601),x76604),x76603))
% 188.07/187.97 [7665]~P72(x76651)+E(f323(f159(x76651),f323(f323(f147(a865,x76651),x76652),f132(a865,f323(f293(a865,x76653),x76654)))),f323(f323(f6(a865,x76651),x76652),f323(f166(a865),f132(a865,f323(f293(a865,x76653),x76654)))))
% 188.07/187.97 [7666]~P72(x76661)+E(f323(f323(f6(a865,x76661),x76662),f323(f166(a865),f132(a865,f323(f293(a865,x76663),x76664)))),f323(f159(x76661),f323(f323(f147(a865,x76661),x76662),f132(a865,f323(f293(a865,x76663),x76664)))))
% 188.07/187.97 [7776]~E(x77763,x77764)+P101(f323(f60(x77761,x77762,f323(f323(f301(x77761),x77763),f188(f872(x77761,a860)))),x77764))
% 188.07/187.97 [7876]P101(f323(f323(f325(x78761),x78762),f323(f166(x78761),x78763)))+~P101(f323(f323(f325(x78761),x78762),f323(f166(x78761),f323(f323(f169(x78761),x78764),x78763))))
% 188.07/187.97 [7877]P101(f323(f323(f325(x78771),x78772),f323(f166(x78771),x78773)))+~P101(f323(f323(f325(x78771),x78772),f323(f166(x78771),f323(f323(f131(x78771),x78774),x78773))))
% 188.07/187.97 [7948]P101(f323(f323(f325(x79481),x79482),x79483))+~P101(f323(f323(f325(x79481),x79482),f323(f323(f22(f872(x79481,a860)),x79483),x79484)))
% 188.07/187.97 [7950]P101(f323(f323(f325(x79501),x79502),x79503))+~P101(f323(f323(f325(x79501),x79502),f323(f323(f101(f872(x79501,a860)),x79504),x79503)))
% 188.07/187.97 [7953]P101(f323(f323(f325(x79531),x79532),x79533))+~P101(f323(f323(f325(x79531),x79532),f323(f323(f101(f872(x79531,a860)),x79533),x79534)))
% 188.07/187.97 [7968]E(f323(f323(f121(x79681),f323(f323(f169(x79681),x79682),x79683)),f323(f323(f144(x79681),x79684),f323(f323(f131(x79681),f323(a112,x79682)),x79683))),f323(f323(f152(x79681,x79683),x79682),x79684))+~P101(f323(f323(f238(a865),x79682),f323(f189(f866(x79681)),x79683)))
% 188.07/187.97 [7991]P101(f323(f323(f325(x79911),x79912),x79913))+~P101(f323(f323(f237(f872(x79911,a860)),f323(f323(f301(x79911),x79912),x79914)),x79913))
% 188.07/187.97 [8025]~P101(f323(f323(f325(x80251),x80252),x80253))+~P101(f323(f323(f325(x80251),x80252),f323(f323(f22(f872(x80251,a860)),x80254),x80253)))
% 188.07/187.97 [8056]~P101(f323(f323(f238(a865),x80564),f323(f189(f866(x80561)),x80563)))+P101(f323(f323(f325(x80561),x80562),f323(f166(x80561),f323(f323(f152(x80561,x80563),x80564),x80562))))
% 188.07/187.97 [8109]E(f323(f323(f158(x81091),f323(f323(f131(x81091),x81092),x81093)),x81094),f323(f323(f158(x81091),x81093),f323(f323(f78(a865),x81092),x81094)))+~P101(f323(f323(f237(a865),f323(f323(f78(a865),x81092),x81094)),f323(f189(f866(x81091)),x81093)))
% 188.07/187.97 [8119]~P140(x81192)+E(f323(f323(f6(x81191,x81192),f323(f323(f8(a865,x81192,x81191),f100(x81192)),x81193)),x81194),f323(f100(x81192),f323(f323(f6(x81191,a865),x81193),x81194)))
% 188.07/187.97 [8120]~P134(x81202)+E(f323(f323(f6(x81201,x81202),f323(f323(f8(a1,x81202,x81201),f102(x81202)),x81203)),x81204),f323(f102(x81202),f323(f323(f6(x81201,a1),x81203),x81204)))
% 188.07/187.97 [8172]~P65(x81722)+E(f323(f323(f9(x81721,x81722),f323(f323(f8(x81722,x81722,x81721),f73(x81722)),x81723)),x81724),f323(f73(x81722),f323(f323(f9(x81721,x81722),x81723),x81724)))
% 188.07/187.97 [8173]~P60(x81732)+E(f323(f323(f6(x81731,x81732),f323(f323(f8(x81732,x81732,x81731),f77(x81732)),x81733)),x81734),f323(f77(x81732),f323(f323(f6(x81731,x81732),x81733),x81734)))
% 188.07/187.97 [8175]E(f323(f323(f6(x81751,a865),x81752),f323(f323(f22(f872(x81751,a860)),x81753),f323(f323(f301(x81751),x81754),f188(f872(x81751,a860))))),f323(f323(f22(a865),f323(f323(f6(x81751,a865),x81752),x81753)),f323(x81752,x81754)))+~P101(f323(f323(f325(x81751),x81754),x81753))
% 188.07/187.97 [8196]P101(f323(f323(f237(f872(x81961,a860)),x81962),x81963))+~P101(f323(f323(f237(f872(x81961,a860)),f323(f323(f301(x81961),x81964),x81962)),x81963))
% 188.07/187.97 [8321]~E(f323(f302(x83212,x83213,x83211),f246(f872(x83212,a860))),f246(f872(x83213,a860)))+E(f323(x83211,f323(f91(x83212,x83213,f246(f872(x83212,a860)),x83211),x83214)),x83214)
% 188.07/187.97 [8405]E(f323(f323(f179(x84051,x84052),x84053),x84054),f200(x84052))+P101(f323(f323(f325(x84051),x84054),f323(f302(f871(x84051,x84052),x84051,f257(x84051,x84052)),f323(f166(f871(x84051,x84052)),x84053))))
% 188.07/187.97 [8406]P38(x84061,x84062)+~P38(x84061,f323(f323(f301(f871(x84061,x84061)),f323(f323(f258(x84061,x84061),x84063),x84064)),x84062))
% 188.07/187.97 [8407]P54(x84071,x84072)+~P54(x84071,f323(f323(f301(f871(x84071,x84071)),f323(f323(f258(x84071,x84071),x84073),x84074)),x84072))
% 188.07/187.97 [8412]~P103(x84121)+E(f323(f323(f141(x84121,x84121,f5(x84121)),x84122),f323(f323(f141(x84121,x84121,f5(x84121)),x84123),x84124)),f323(f323(f141(x84121,x84121,f5(x84121)),x84123),f323(f323(f141(x84121,x84121,f5(x84121)),x84122),x84124)))
% 188.07/187.97 [8422]E(x84221,x84222)+~P101(f323(f60(x84223,x84224,f323(f323(f301(x84223),x84221),f188(f872(x84223,a860)))),x84222))
% 188.07/187.97 [8432]E(f323(f323(f121(x84321),f323(f323(f169(x84321),x84322),x84323)),f323(f323(f169(x84321),x84324),f323(f323(f131(x84321),x84322),x84323))),f323(f323(f169(x84321),f323(f323(f78(a865),x84322),x84324)),x84323))+~P101(f323(f323(f237(a865),f323(f323(f78(a865),x84322),x84324)),f323(f189(f866(x84321)),x84323)))
% 188.07/187.97 [8470]P101(f323(f59(x84701),x84702))+~E(x84702,f323(f302(a865,x84701,x84703),f323(f243(a865),f323(f323(f7(a865,a865,a860),f238(a865)),x84704))))
% 188.07/187.97 [8490]~P86(x84901)+E(f323(f135(x84901,x84901,f78(x84901),f323(f323(f78(x84901),x84902),x84903)),x84904),f323(f323(f78(x84901),x84902),f323(f135(x84901,x84901,f78(x84901),x84903),x84904)))
% 188.07/187.97 [8525]P101(f323(f323(f237(f872(x85251,a860)),f323(f256(x85251,x85252),x85253)),f323(f256(x85251,x85252),x85254)))+~P101(f323(f323(f237(f872(f871(x85251,x85252),a860)),x85253),x85254))
% 188.07/187.97 [8538]~P101(f323(f323(f237(a865),x85382),x85384))+P101(f323(f323(f237(f872(x85381,a860)),f323(f166(x85381),f323(f323(f169(x85381),x85382),x85383))),f323(f166(x85381),f323(f323(f169(x85381),x85384),x85383))))
% 188.07/187.97 [8539]~P101(f323(f323(f237(a865),x85394),x85392))+P101(f323(f323(f237(f872(x85391,a860)),f323(f166(x85391),f323(f323(f131(x85391),x85392),x85393))),f323(f166(x85391),f323(f323(f131(x85391),x85394),x85393))))
% 188.07/187.97 [8597]~P101(f323(f59(x85971),f323(f323(f22(f872(x85971,a860)),x85972),x85974)))+P101(f323(f59(x85971),f323(f323(f22(f872(x85971,a860)),x85972),f323(f323(f301(x85971),x85973),x85974))))
% 188.07/187.97 [8641]P101(f323(f323(f325(f871(x86411,x86411)),x86412),f299(x86411,x86413)))+~P101(f323(f323(f325(f871(x86411,x86411)),x86412),f323(f323(f183(f871(x86411,x86411),a860),x86414),x86413)))
% 188.07/187.97 [8727]~P101(f323(f59(x87271),f323(f323(f22(f872(x87271,a860)),x87272),f323(f323(f301(x87271),x87274),x87273))))+P101(f323(f59(x87271),f323(f323(f22(f872(x87271,a860)),x87272),x87273)))
% 188.07/187.97 [8877]~E(f323(f323(f179(x88771,x88772),x88773),x88774),f200(x88772))+~P101(f323(f323(f325(x88771),x88774),f323(f302(f871(x88771,x88772),x88771,f257(x88771,x88772)),f323(f166(f871(x88771,x88772)),x88773))))
% 188.07/187.97 [8937]~P2(x89371)+P101(f323(f323(f237(x89371),f323(f323(f110(x89371),x89372),f323(f323(f101(x89371),x89373),x89374))),f323(f323(f101(x89371),f323(f323(f110(x89371),x89372),x89373)),f323(f323(f110(x89371),x89372),x89374))))
% 188.07/187.97 [8938]~P103(x89381)+P101(f323(f323(f237(x89381),f323(f323(f236(x89381),x89382),f323(f323(f235(x89381),x89383),x89384))),f323(f323(f235(x89381),f323(f323(f236(x89381),x89382),x89383)),f323(f323(f236(x89381),x89382),x89384))))
% 188.07/187.97 [9086]E(x90861,x90862)+~P101(f323(f323(f325(f871(x90863,x90863)),f323(f323(f258(x90863,x90863),x90861),x90862)),f323(f166(f871(x90863,x90863)),f323(f323(f175(x90863,x90863),x90864),x90864))))
% 188.07/187.97 [9116]~P101(f323(f323(f325(f871(x91161,x91161)),f323(f323(f258(x91161,x91161),x91163),x91162)),f299(x91161,x91164)))+~P38(x91161,f323(f323(f301(f871(x91161,x91161)),f323(f323(f258(x91161,x91161),x91162),x91163)),x91164))
% 188.07/187.97 [9117]~P101(f323(f323(f325(f871(x91171,x91171)),f323(f323(f258(x91171,x91171),x91173),x91172)),f299(x91171,x91174)))+~P54(x91171,f323(f323(f301(f871(x91171,x91171)),f323(f323(f258(x91171,x91171),x91172),x91173)),x91174))
% 188.07/187.97 [9122]E(x91221,x91222)+E(f323(f129(x91223,f323(f323(f8(a860,a860,x91223),a318),f323(a320,x91221))),f323(f323(f144(x91223),x91222),x91224)),f323(f323(f144(x91223),x91222),f323(f129(x91223,f323(f323(f8(a860,a860,x91223),a318),f323(a320,x91221))),x91224)))
% 188.07/187.97 [9152]~P28(x91522,x91521,x91523,f246(f872(x91522,a860)),f246(f872(x91521,a860)))+E(f323(f302(x91521,x91522,f91(x91522,x91521,f246(f872(x91522,a860)),x91523)),x91524),f323(f303(x91522,x91521,x91523),x91524))
% 188.07/187.97 [9171]~P2(x91711)+P101(f323(f323(f237(x91711),f323(f323(f110(x91711),f323(f323(f101(x91711),x91712),x91713)),f323(f323(f101(x91711),x91712),x91714))),f323(f323(f101(x91711),x91712),f323(f323(f110(x91711),x91713),x91714))))
% 188.07/187.97 [9172]~P103(x91721)+P101(f323(f323(f237(x91721),f323(f323(f236(x91721),f323(f323(f235(x91721),x91722),x91723)),f323(f323(f235(x91721),x91722),x91724))),f323(f323(f235(x91721),x91722),f323(f323(f236(x91721),x91723),x91724))))
% 188.07/187.97 [9228]~P28(x92282,x92281,x92284,f246(f872(x92282,a860)),f246(f872(x92281,a860)))+E(f323(f243(x92281),f323(f323(f8(x92282,a860,x92281),x92283),f91(x92282,x92281,f246(f872(x92282,a860)),x92284))),f323(f302(x92282,x92281,x92284),f323(f243(x92282),x92283)))
% 188.07/187.97 [9241]~E(f323(f302(x92412,x92411,x92413),f246(f872(x92412,a860))),f246(f872(x92411,a860)))+P101(f323(f323(f237(f872(x92411,a860)),f323(f77(f872(x92411,a860)),f323(f302(x92412,x92411,x92413),x92414))),f323(f302(x92412,x92411,x92413),f323(f77(f872(x92412,a860)),x92414))))
% 188.07/187.97 [9564]P101(f323(f323(f325(f871(x95641,x95641)),f323(f323(f258(x95641,x95641),x95642),x95643)),f323(f278(x95641,x95641),f323(f323(f280(x95641,x95641,x95641),x95644),f299(x95641,x95644)))))+~P101(f323(f323(f325(f871(x95641,x95641)),f323(f323(f258(x95641,x95641),x95642),x95643)),f323(f323(f280(x95641,x95641,x95641),f323(f278(x95641,x95641),x95644)),f299(x95641,f323(f278(x95641,x95641),x95644)))))
% 188.07/187.97 [9565]~P101(f323(f323(f325(f871(x95651,x95651)),f323(f323(f258(x95651,x95651),x95652),x95653)),f323(f278(x95651,x95651),f323(f323(f280(x95651,x95651,x95651),x95654),f299(x95651,x95654)))))+P101(f323(f323(f325(f871(x95651,x95651)),f323(f323(f258(x95651,x95651),x95652),x95653)),f323(f323(f280(x95651,x95651,x95651),f323(f278(x95651,x95651),x95654)),f299(x95651,f323(f278(x95651,x95651),x95654)))))
% 188.07/187.97 [9586]~P101(f323(f323(f325(x95862),x95864),f323(f254(x95861,x95862),x95863)))+P101(f323(f323(f325(f871(x95861,x95862)),f323(f323(f258(x95861,x95862),f676(x95863,x95861,x95864,x95862)),x95864)),x95863))
% 188.07/187.97 [9587]~P101(f323(f323(f325(x95872),x95874),f323(f254(x95871,x95872),x95873)))+P101(f323(f323(f325(f871(x95871,x95872)),f323(f323(f258(x95871,x95872),f677(x95873,x95871,x95874,x95872)),x95874)),x95873))
% 188.07/187.97 [9612]~P101(f323(f323(f325(x96121),x96124),f323(f323(f110(f872(x96121,a860)),x96122),x96123)))+P101(f323(f323(f323(f110(f872(x96121,a860)),f323(f323(f7(x96121,f872(x96121,a860),a860),f325(x96121)),x96122)),f323(f323(f7(x96121,f872(x96121,a860),a860),f325(x96121)),x96123)),x96124))
% 188.07/187.97 [9613]~P101(f323(f323(f325(x96131),x96134),f323(f323(f101(f872(x96131,a860)),x96132),x96133)))+P101(f323(f323(f323(f101(f872(x96131,a860)),f323(f323(f7(x96131,f872(x96131,a860),a860),f325(x96131)),x96132)),f323(f323(f7(x96131,f872(x96131,a860),a860),f325(x96131)),x96133)),x96134))
% 188.07/187.97 [9691]~P101(f323(f323(f325(f871(x96911,x96911)),f323(f323(f258(x96911,x96911),x96914),x96913)),f323(f323(f280(x96911,x96911,x96911),x96912),f299(x96911,x96912))))+P101(f323(f323(f325(f871(x96911,x96911)),f323(f323(f258(x96911,x96911),f748(x96912,x96913,x96914,x96911)),x96913)),x96912))
% 188.07/187.97 [9736]P101(f323(f323(f325(x97361),x97362),f323(f323(f110(f872(x97361,a860)),x97363),x97364)))+~P101(f323(f323(f323(f110(f872(x97361,a860)),f323(f323(f7(x97361,f872(x97361,a860),a860),f325(x97361)),x97363)),f323(f323(f7(x97361,f872(x97361,a860),a860),f325(x97361)),x97364)),x97362))
% 188.07/187.97 [9737]P101(f323(f323(f325(x97371),x97372),f323(f323(f101(f872(x97371,a860)),x97373),x97374)))+~P101(f323(f323(f323(f101(f872(x97371,a860)),f323(f323(f7(x97371,f872(x97371,a860),a860),f325(x97371)),x97373)),f323(f323(f7(x97371,f872(x97371,a860),a860),f325(x97371)),x97374)),x97372))
% 188.07/187.97 [10013]P33(x100131,f323(f323(f7(x100131,f872(f871(x100131,x100131),a860),f872(x100131,a860)),f323(f323(f8(f872(x100131,f872(f872(f871(x100131,x100131),a860),a860)),f872(f872(f871(x100131,x100131),a860),f872(x100131,a860)),x100131),f7(x100131,f872(f871(x100131,x100131),a860),a860)),f323(f323(f8(f872(x100131,f871(x100131,x100131)),f872(x100131,f872(f872(f871(x100131,x100131),a860),a860)),x100131),f323(f8(f871(x100131,x100131),f872(f872(f871(x100131,x100131),a860),a860),x100131),f325(f871(x100131,x100131)))),f258(x100131,x100131)))),x100132),x100133,x100134)+~P101(f323(f323(f325(f871(f866(x100131),f866(x100131))),f323(f323(f258(f866(x100131),f866(x100131)),x100133),x100134)),f151(x100131,x100132)))
% 188.07/187.97 [10017]P55(x100171,f323(f323(f7(x100171,f872(f871(x100171,x100171),a860),f872(x100171,a860)),f323(f323(f8(f872(x100171,f872(f872(f871(x100171,x100171),a860),a860)),f872(f872(f871(x100171,x100171),a860),f872(x100171,a860)),x100171),f7(x100171,f872(f871(x100171,x100171),a860),a860)),f323(f323(f8(f872(x100171,f871(x100171,x100171)),f872(x100171,f872(f872(f871(x100171,x100171),a860),a860)),x100171),f323(f8(f871(x100171,x100171),f872(f872(f871(x100171,x100171),a860),a860),x100171),f325(f871(x100171,x100171)))),f258(x100171,x100171)))),x100172),x100173,x100174)+~P101(f323(f323(f325(f871(f872(x100171,a860),f872(x100171,a860))),f323(f323(f258(f872(x100171,a860),f872(x100171,a860)),x100173),x100174)),f314(x100171,x100172)))
% 188.07/187.97 [10046]E(x100461,x100462)+~E(f323(f323(f7(x100463,f872(f871(x100463,x100464),a860),f872(x100464,a860)),f323(f323(f8(f872(x100464,f872(f872(f871(x100463,x100464),a860),a860)),f872(f872(f871(x100463,x100464),a860),f872(x100464,a860)),x100463),f7(x100464,f872(f871(x100463,x100464),a860),a860)),f323(f323(f8(f872(x100464,f871(x100463,x100464)),f872(x100464,f872(f872(f871(x100463,x100464),a860),a860)),x100463),f323(f8(f871(x100463,x100464),f872(f872(f871(x100463,x100464),a860),a860),x100464),f325(f871(x100463,x100464)))),f258(x100463,x100464)))),x100461),f323(f323(f7(x100463,f872(f871(x100463,x100464),a860),f872(x100464,a860)),f323(f323(f8(f872(x100464,f872(f872(f871(x100463,x100464),a860),a860)),f872(f872(f871(x100463,x100464),a860),f872(x100464,a860)),x100463),f7(x100464,f872(f871(x100463,x100464),a860),a860)),f323(f323(f8(f872(x100464,f871(x100463,x100464)),f872(x100464,f872(f872(f871(x100463,x100464),a860),a860)),x100463),f323(f8(f871(x100463,x100464),f872(f872(f871(x100463,x100464),a860),a860),x100464),f325(f871(x100463,x100464)))),f258(x100463,x100464)))),x100462))
% 188.07/187.97 [10049]~P33(x100491,f323(f323(f7(x100491,f872(f871(x100491,x100491),a860),f872(x100491,a860)),f323(f323(f8(f872(x100491,f872(f872(f871(x100491,x100491),a860),a860)),f872(f872(f871(x100491,x100491),a860),f872(x100491,a860)),x100491),f7(x100491,f872(f871(x100491,x100491),a860),a860)),f323(f323(f8(f872(x100491,f871(x100491,x100491)),f872(x100491,f872(f872(f871(x100491,x100491),a860),a860)),x100491),f323(f8(f871(x100491,x100491),f872(f872(f871(x100491,x100491),a860),a860),x100491),f325(f871(x100491,x100491)))),f258(x100491,x100491)))),x100494),x100492,x100493)+P101(f323(f323(f325(f871(f866(x100491),f866(x100491))),f323(f323(f258(f866(x100491),f866(x100491)),x100492),x100493)),f151(x100491,x100494)))
% 188.07/187.97 [10050]~P55(x100501,f323(f323(f7(x100501,f872(f871(x100501,x100501),a860),f872(x100501,a860)),f323(f323(f8(f872(x100501,f872(f872(f871(x100501,x100501),a860),a860)),f872(f872(f871(x100501,x100501),a860),f872(x100501,a860)),x100501),f7(x100501,f872(f871(x100501,x100501),a860),a860)),f323(f323(f8(f872(x100501,f871(x100501,x100501)),f872(x100501,f872(f872(f871(x100501,x100501),a860),a860)),x100501),f323(f8(f871(x100501,x100501),f872(f872(f871(x100501,x100501),a860),a860),x100501),f325(f871(x100501,x100501)))),f258(x100501,x100501)))),x100504),x100502,x100503)+P101(f323(f323(f325(f871(f872(x100501,a860),f872(x100501,a860))),f323(f323(f258(f872(x100501,a860),f872(x100501,a860)),x100502),x100503)),f314(x100501,x100504)))
% 188.07/187.97 [7431]~P90(x74311)+E(f323(f323(f79(x74311),f323(f103(x74311),x74312)),f323(f323(f79(x74311),f323(f103(x74311),x74313)),x74314)),f323(f323(f79(x74311),f323(f103(x74311),f323(f323(f79(a1),x74312),x74313))),x74314))
% 188.07/187.97 [7432]~P90(x74321)+E(f323(f323(f78(x74321),f323(f103(x74321),x74322)),f323(f323(f22(x74321),f323(f103(x74321),x74323)),x74324)),f323(f323(f22(x74321),f323(f103(x74321),f323(f323(f78(a1),x74322),x74323))),x74324))
% 188.07/187.97 [7433]~P90(x74331)+E(f323(f323(f78(x74331),f323(f103(x74331),x74332)),f323(f323(f78(x74331),f323(f103(x74331),x74333)),x74334)),f323(f323(f78(x74331),f323(f103(x74331),f323(f323(f78(a1),x74332),x74333))),x74334))
% 188.07/187.97 [7477]~P140(x74771)+E(f323(f159(x74771),f323(f323(f147(x74772,x74771),f323(f16(x74771,x74772),x74773)),x74774)),f323(f323(f79(x74771),f323(f100(x74771),f323(f189(f866(x74772)),x74774))),x74773))
% 188.07/187.97 [7712]E(f323(f269(x77121,f323(f323(f144(f871(a99,x77121)),x77122),x77123)),x77124),f323(f261(a99,x77121),x77122))+~P101(f323(f323(f238(a99),x77124),f323(f257(a99,x77121),x77122)))
% 188.07/187.97 [7754]~P90(x77541)+E(f323(f323(f78(x77541),f323(f103(x77541),x77542)),f323(f323(f22(x77541),x77543),f323(f103(x77541),x77544))),f323(f323(f78(x77541),f323(f103(x77541),f323(f323(f78(a1),x77542),f323(f77(a1),x77544)))),x77543))
% 188.07/187.97 [7889]E(f323(f269(x78891,x78892),f323(f323(f22(a99),x78893),f323(f257(a99,x78891),x78894))),f323(f269(x78891,f323(f323(f144(f871(a99,x78891)),x78894),x78892)),x78893))+P101(f323(f323(f238(a99),x78893),f323(f257(a99,x78891),x78894)))
% 188.07/187.97 [8327]~P101(f323(f323(f325(x83271),x83272),f323(f166(x83271),f114(x83271,x83274))))+P101(f323(f323(f325(x83271),x83272),f323(f166(x83271),f114(x83271,f323(f323(f121(x83271),x83273),x83274)))))
% 188.07/187.97 [8328]~P101(f323(f323(f325(x83281),x83282),f323(f166(x83281),f114(x83281,x83283))))+P101(f323(f323(f325(x83281),x83282),f323(f166(x83281),f114(x83281,f323(f323(f121(x83281),x83283),x83284)))))
% 188.07/187.97 [8346]E(f323(f323(f110(f872(x83461,a860)),f323(f323(f101(f872(x83461,a860)),x83462),x83463)),x83464),f323(f323(f101(f872(x83461,a860)),x83462),f323(f323(f110(f872(x83461,a860)),x83463),x83464)))+~P101(f323(f323(f237(f872(x83461,a860)),x83464),x83462))
% 188.07/187.97 [8655]~E(f323(f323(f110(f872(x86551,a860)),f323(f323(f101(f872(x86551,a860)),x86553),x86554)),x86552),f323(f323(f101(f872(x86551,a860)),x86553),f323(f323(f110(f872(x86551,a860)),x86554),x86552)))+P101(f323(f323(f237(f872(x86551,a860)),x86552),x86553))
% 188.07/187.97 [8942]~P101(f323(f323(f237(f872(x89421,a860)),x89422),f323(f323(f110(f872(x89421,a860)),x89423),x89424)))+P101(f323(f323(f237(f872(x89421,a860)),f323(f323(f22(f872(x89421,a860)),x89422),x89423)),x89424))
% 188.07/187.97 [9060]~E(f323(f302(x90601,x90602,x90603),f246(f872(x90601,a860))),f246(f872(x90602,a860)))+E(f323(f302(x90601,x90602,x90603),f323(f302(x90602,x90601,f91(x90601,x90602,f246(f872(x90601,a860)),x90603)),x90604)),x90604)
% 188.07/187.97 [9065]P101(f323(f323(f237(f872(x90651,a860)),x90652),f323(f323(f110(f872(x90651,a860)),x90653),x90654)))+~P101(f323(f323(f237(f872(x90651,a860)),f323(f323(f22(f872(x90651,a860)),x90652),x90653)),x90654))
% 188.07/187.97 [9148]~P82(x91481)+E(f323(f73(x91481),f323(f323(f6(x91482,x91481),f323(f323(f8(x91481,x91481,x91482),f73(x91481)),x91483)),x91484)),f323(f323(f6(x91482,x91481),f323(f323(f8(x91481,x91481,x91482),f73(x91481)),x91483)),x91484))
% 188.07/187.97 [9317]~P82(x93171)+P101(f323(f323(f237(x93171),f2(x93171)),f323(f323(f6(x93172,x93171),f323(f323(f8(x93171,x93171,x93172),f73(x93171)),x93173)),x93174)))
% 188.07/187.97 [9321]~P60(x93211)+E(f323(f159(x93211),f323(f323(f147(x93212,x93211),f323(f71(x93211,x93211,x93212,f77(x93211)),x93213)),x93214)),f323(f77(x93211),f323(f159(x93211),f323(f323(f147(x93212,x93211),x93213),x93214))))
% 188.07/187.97 [9458]~P82(x94581)+P101(f323(f323(f237(x94581),f323(f73(x94581),f323(f323(f6(x94582,x94581),x94583),x94584))),f323(f323(f6(x94582,x94581),f323(f323(f8(x94581,x94581,x94582),f73(x94581)),x94583)),x94584)))
% 188.07/187.97 [9487]~E(f323(f323(f78(a865),x94871),x94874),f323(f323(f78(a865),x94873),x94872))+P101(f323(f323(f325(f871(f871(a865,a865),f871(a865,a865))),f323(f323(f258(f871(a865,a865),f871(a865,a865)),f323(f323(f258(a865,a865),x94871),x94872)),f323(f323(f258(a865,a865),x94873),x94874))),a108))
% 188.07/187.97 [9488]~P101(f323(f323(f238(a865),x94881),x94883))+P101(f323(f323(f325(f871(f871(a865,a865),f871(a865,a865))),f323(f323(f258(f871(a865,a865),f871(a865,a865)),f323(f323(f258(a865,a865),x94881),x94882)),f323(f323(f258(a865,a865),x94883),x94884))),a33))
% 188.07/187.97 [9489]~P101(f323(f323(f238(a865),x94891),x94893))+P101(f323(f323(f325(f871(f871(a865,a865),f871(a865,a865))),f323(f323(f258(f871(a865,a865),f871(a865,a865)),f323(f323(f258(a865,a865),x94891),x94892)),f323(f323(f258(a865,a865),x94893),x94894))),a68))
% 188.07/187.97 [9637]E(f323(f323(f78(a865),x96371),x96372),f323(f323(f78(a865),x96373),x96374))+~P101(f323(f323(f325(f871(f871(a865,a865),f871(a865,a865))),f323(f323(f258(f871(a865,a865),f871(a865,a865)),f323(f323(f258(a865,a865),x96371),x96374)),f323(f323(f258(a865,a865),x96373),x96372))),a108))
% 188.07/187.97 [9665]E(f323(f323(f158(x96651),f323(f323(f131(x96651),f323(f189(f866(x96651)),f171(x96651,x96652,x96653))),x96653)),x96654),f323(f323(f158(x96651),x96653),f323(f323(f78(a865),x96654),f323(f189(f866(x96651)),f171(x96651,x96652,x96653)))))+~P101(f323(f323(f238(a865),x96654),f323(f189(f866(x96651)),f323(f323(f131(x96651),f323(f189(f866(x96651)),f171(x96651,x96652,x96653))),x96653))))
% 188.07/187.97 [9682]~P101(f323(f323(f325(x96822),x96824),f323(f323(f39(x96821,f872(x96822,a860)),f246(f872(x96821,a860))),x96823)))+P101(f323(f323(f323(f39(x96821,f872(x96822,a860)),f246(f872(x96821,a860))),f323(f323(f8(f872(x96822,a860),f872(x96822,a860),x96821),f323(f7(x96822,f872(x96822,a860),a860),f325(x96822))),x96823)),x96824))
% 188.07/187.97 [9683]~P101(f323(f323(f325(x96832),x96834),f323(f323(f40(x96831,f872(x96832,a860)),f246(f872(x96831,a860))),x96833)))+P101(f323(f323(f323(f40(x96831,f872(x96832,a860)),f246(f872(x96831,a860))),f323(f323(f8(f872(x96832,a860),f872(x96832,a860),x96831),f323(f7(x96832,f872(x96832,a860),a860),f325(x96832))),x96833)),x96834))
% 188.07/187.97 [9764]~P101(f323(f46(x97641,x97642),f323(f323(f258(a1,a1),x97644),x97643)))+P101(f323(f46(f323(f77(a1),x97641),x97642),f323(f323(f258(a1,a1),f323(f323(f323(f96(a1),f323(f323(a320,x97643),f2(a1))),f323(f77(a1),x97644)),f323(f323(f22(a1),f323(f77(a1),x97644)),f76(a1)))),f323(f323(f323(f96(a1),f323(f323(a320,x97643),f2(a1))),f2(a1)),f323(f323(f22(a1),x97642),x97643)))))
% 188.07/187.97 [9773]P101(f323(f323(f325(x97731),x97732),f323(f323(f39(x97733,f872(x97731,a860)),f246(f872(x97733,a860))),x97734)))+~P101(f323(f323(f323(f39(x97733,f872(x97731,a860)),f246(f872(x97733,a860))),f323(f323(f8(f872(x97731,a860),f872(x97731,a860),x97733),f323(f7(x97731,f872(x97731,a860),a860),f325(x97731))),x97734)),x97732))
% 188.07/187.97 [9774]P101(f323(f323(f325(x97741),x97742),f323(f323(f40(x97743,f872(x97741,a860)),f246(f872(x97743,a860))),x97744)))+~P101(f323(f323(f323(f40(x97743,f872(x97741,a860)),f246(f872(x97743,a860))),f323(f323(f8(f872(x97741,a860),f872(x97741,a860),x97743),f323(f7(x97741,f872(x97741,a860),a860),f325(x97741))),x97744)),x97742))
% 188.07/187.97 [9786]E(f323(f323(f39(a865,f872(x97861,a860)),f246(f872(a865,a860))),x97862),f323(f323(f39(a865,f872(x97861,a860)),f246(f872(a865,a860))),x97863))+~E(f323(f323(f39(a865,f872(x97861,a860)),f323(f293(a865,f2(a865)),f460(x97862,x97864,x97863,x97861))),x97863),f323(f323(f39(a865,f872(x97861,a860)),f323(f293(a865,f2(a865)),f323(f323(f78(a865),f460(x97862,x97864,x97863,x97861)),x97864))),x97862))
% 188.07/187.97 [10106]~P101(f323(f323(f237(f872(f871(x101061,x101062),a860)),x101063),x101064))+P101(f323(f323(f237(f872(x101061,f872(x101062,a860))),f323(f323(f7(x101061,f872(f871(x101061,x101062),a860),f872(x101062,a860)),f323(f323(f8(f872(x101062,f872(f872(f871(x101061,x101062),a860),a860)),f872(f872(f871(x101061,x101062),a860),f872(x101062,a860)),x101061),f7(x101062,f872(f871(x101061,x101062),a860),a860)),f323(f323(f8(f872(x101062,f871(x101061,x101062)),f872(x101062,f872(f872(f871(x101061,x101062),a860),a860)),x101061),f323(f8(f871(x101061,x101062),f872(f872(f871(x101061,x101062),a860),a860),x101062),f325(f871(x101061,x101062)))),f258(x101061,x101062)))),x101063)),f323(f323(f7(x101061,f872(f871(x101061,x101062),a860),f872(x101062,a860)),f323(f323(f8(f872(x101062,f872(f872(f871(x101061,x101062),a860),a860)),f872(f872(f871(x101061,x101062),a860),f872(x101062,a860)),x101061),f7(x101062,f872(f871(x101061,x101062),a860),a860)),f323(f323(f8(f872(x101062,f871(x101061,x101062)),f872(x101062,f872(f872(f871(x101061,x101062),a860),a860)),x101061),f323(f8(f871(x101061,x101062),f872(f872(f871(x101061,x101062),a860),a860),x101062),f325(f871(x101061,x101062)))),f258(x101061,x101062)))),x101064)))
% 188.07/187.97 [10123]P101(f323(f323(f237(f872(f871(x101231,x101232),a860)),x101233),x101234))+~P101(f323(f323(f237(f872(x101231,f872(x101232,a860))),f323(f323(f7(x101231,f872(f871(x101231,x101232),a860),f872(x101232,a860)),f323(f323(f8(f872(x101232,f872(f872(f871(x101231,x101232),a860),a860)),f872(f872(f871(x101231,x101232),a860),f872(x101232,a860)),x101231),f7(x101232,f872(f871(x101231,x101232),a860),a860)),f323(f323(f8(f872(x101232,f871(x101231,x101232)),f872(x101232,f872(f872(f871(x101231,x101232),a860),a860)),x101231),f323(f8(f871(x101231,x101232),f872(f872(f871(x101231,x101232),a860),a860),x101232),f325(f871(x101231,x101232)))),f258(x101231,x101232)))),x101233)),f323(f323(f7(x101231,f872(f871(x101231,x101232),a860),f872(x101232,a860)),f323(f323(f8(f872(x101232,f872(f872(f871(x101231,x101232),a860),a860)),f872(f872(f871(x101231,x101232),a860),f872(x101232,a860)),x101231),f7(x101232,f872(f871(x101231,x101232),a860),a860)),f323(f323(f8(f872(x101232,f871(x101231,x101232)),f872(x101232,f872(f872(f871(x101231,x101232),a860),a860)),x101231),f323(f8(f871(x101231,x101232),f872(f872(f871(x101231,x101232),a860),a860),x101232),f325(f871(x101231,x101232)))),f258(x101231,x101232)))),x101234)))
% 188.07/187.97 [9195]~P101(f323(f323(f325(f871(x91951,x91951)),x91952),f299(x91951,x91954)))+P101(f323(f323(f325(f871(x91951,x91951)),x91952),f299(x91951,f323(f323(f110(f872(f871(x91951,x91951),a860)),x91953),x91954))))
% 188.07/187.97 [9196]~P101(f323(f323(f325(f871(x91961,x91961)),x91962),f299(x91961,x91963)))+P101(f323(f323(f325(f871(x91961,x91961)),x91962),f299(x91961,f323(f323(f110(f872(f871(x91961,x91961),a860)),x91963),x91964))))
% 188.07/187.97 [9555]~E(f323(f166(x95551),x95554),f177(x95551,x95552,x95553))+E(f323(f179(x95551,x95552),f323(f323(f147(x95551,f871(x95551,x95552)),f323(f323(f18(x95551,x95552,f871(x95551,x95552)),f258(x95551,x95552)),f323(f323(f8(f869(x95552),x95552,x95551),f234(x95552)),x95553))),x95554)),x95553)
% 188.07/187.97 [9879]~P101(f323(f323(f237(a865),f323(f323(f78(a865),x98791),x98794)),f323(f323(f78(a865),x98793),x98792)))+P101(f323(f323(f237(a1),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x98791),x98792)),f188(f872(f871(a865,a865),a860)))))),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x98793),x98794)),f188(f872(f871(a865,a865),a860)))))))
% 188.07/187.97 [9880]~P101(f323(f323(f238(a865),f323(f323(f78(a865),x98801),x98804)),f323(f323(f78(a865),x98803),x98802)))+P101(f323(f323(f238(a1),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x98801),x98802)),f188(f872(f871(a865,a865),a860)))))),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x98803),x98804)),f188(f872(f871(a865,a865),a860)))))))
% 188.07/187.97 [9957]P101(f323(f323(f237(a865),f323(f323(f78(a865),x99571),x99572)),f323(f323(f78(a865),x99573),x99574)))+~P101(f323(f323(f237(a1),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x99571),x99574)),f188(f872(f871(a865,a865),a860)))))),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x99573),x99572)),f188(f872(f871(a865,a865),a860)))))))
% 188.07/187.97 [9958]P101(f323(f323(f238(a865),f323(f323(f78(a865),x99581),x99582)),f323(f323(f78(a865),x99583),x99584)))+~P101(f323(f323(f238(a1),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x99581),x99584)),f188(f872(f871(a865,a865),a860)))))),f323(a87,f323(f277(f871(a865,a865),f871(a865,a865),a108),f323(f323(f301(f871(a865,a865)),f323(f323(f258(a865,a865),x99583),x99582)),f188(f872(f871(a865,a865),a860)))))))
% 188.07/187.97 [9999]P101(f323(f323(f237(f872(x99991,a860)),f323(f323(f39(a865,f872(x99991,a860)),f246(f872(a865,a860))),x99992)),f323(f323(f39(a865,f872(x99991,a860)),f246(f872(a865,a860))),x99993)))+~P101(f323(f323(f237(f872(x99991,a860)),f323(f323(f39(a865,f872(x99991,a860)),f323(f293(a865,f2(a865)),f461(x99993,x99994,x99992,x99991))),x99992)),f323(f323(f39(a865,f872(x99991,a860)),f323(f293(a865,f2(a865)),f323(f323(f78(a865),f461(x99993,x99994,x99992,x99991)),x99994))),x99993)))
% 188.07/187.97 [10096]~P101(f323(f323(f325(x100962),x100964),f323(f254(x100961,x100962),x100963)))+P101(f323(f253(x100961,x100962,f323(f323(f7(x100961,f872(f871(x100961,x100962),a860),f872(x100962,a860)),f323(f323(f8(f872(x100962,f872(f872(f871(x100961,x100962),a860),a860)),f872(f872(f871(x100961,x100962),a860),f872(x100962,a860)),x100961),f7(x100962,f872(f871(x100961,x100962),a860),a860)),f323(f323(f8(f872(x100962,f871(x100961,x100962)),f872(x100962,f872(f872(f871(x100961,x100962),a860),a860)),x100961),f323(f8(f871(x100961,x100962),f872(f872(f871(x100961,x100962),a860),a860),x100962),f325(f871(x100961,x100962)))),f258(x100961,x100962)))),x100963)),x100964))
% 188.07/187.97 [10097]~P101(f323(f323(f325(x100971),x100974),f323(f256(x100971,x100972),x100973)))+P101(f323(f252(x100971,x100972,f323(f323(f7(x100971,f872(f871(x100971,x100972),a860),f872(x100972,a860)),f323(f323(f8(f872(x100972,f872(f872(f871(x100971,x100972),a860),a860)),f872(f872(f871(x100971,x100972),a860),f872(x100972,a860)),x100971),f7(x100972,f872(f871(x100971,x100972),a860),a860)),f323(f323(f8(f872(x100972,f871(x100971,x100972)),f872(x100972,f872(f872(f871(x100971,x100972),a860),a860)),x100971),f323(f8(f871(x100971,x100972),f872(f872(f871(x100971,x100972),a860),a860),x100972),f325(f871(x100971,x100972)))),f258(x100971,x100972)))),x100973)),x100974))
% 188.07/187.97 [10109]P101(f323(f323(f325(x101091),x101092),f323(f254(x101093,x101091),x101094)))+~P101(f323(f253(x101093,x101091,f323(f323(f7(x101093,f872(f871(x101093,x101091),a860),f872(x101091,a860)),f323(f323(f8(f872(x101091,f872(f872(f871(x101093,x101091),a860),a860)),f872(f872(f871(x101093,x101091),a860),f872(x101091,a860)),x101093),f7(x101091,f872(f871(x101093,x101091),a860),a860)),f323(f323(f8(f872(x101091,f871(x101093,x101091)),f872(x101091,f872(f872(f871(x101093,x101091),a860),a860)),x101093),f323(f8(f871(x101093,x101091),f872(f872(f871(x101093,x101091),a860),a860),x101091),f325(f871(x101093,x101091)))),f258(x101093,x101091)))),x101094)),x101092))
% 188.07/187.97 [10110]P101(f323(f323(f325(x101101),x101102),f323(f256(x101101,x101103),x101104)))+~P101(f323(f252(x101101,x101103,f323(f323(f7(x101101,f872(f871(x101101,x101103),a860),f872(x101103,a860)),f323(f323(f8(f872(x101103,f872(f872(f871(x101101,x101103),a860),a860)),f872(f872(f871(x101101,x101103),a860),f872(x101103,a860)),x101101),f7(x101103,f872(f871(x101101,x101103),a860),a860)),f323(f323(f8(f872(x101103,f871(x101101,x101103)),f872(x101103,f872(f872(f871(x101101,x101103),a860),a860)),x101101),f323(f8(f871(x101101,x101103),f872(f872(f871(x101101,x101103),a860),a860),x101103),f325(f871(x101101,x101103)))),f258(x101101,x101103)))),x101104)),x101102))
% 188.07/187.97 [9797]P101(f323(f153(x97971,x97972),x97973))+~P101(f323(f153(x97971,f323(f323(f18(x97971,a860,a860),f323(f323(f8(a860,f872(a860,a860),x97971),a322),x97974)),x97972)),x97973))
% 188.07/187.97 [9798]P101(f323(f153(x97981,x97982),x97983))+~P101(f323(f153(x97981,f323(f323(f18(x97981,a860,a860),f323(f323(f8(a860,f872(a860,a860),x97981),a322),x97982)),x97984)),x97983))
% 188.07/187.97 [9881]~P112(x98811)+E(f323(f323(f79(x98811),f323(f323(f78(x98811),f76(x98811)),f76(x98811))),f323(f323(f6(a865,x98811),f323(f323(f8(x98811,x98811,a865),f323(f78(x98811),x98812)),f323(f323(f7(a865,x98811,x98811),f323(f323(f8(x98811,f872(x98811,x98811),a865),f79(x98811)),f100(x98811))),x98813))),f323(f244(a865),x98814))),f323(f323(f79(x98811),f323(f100(x98811),x98814)),f323(f323(f78(x98811),x98812),f323(f323(f78(x98811),x98812),f323(f323(f79(x98811),f323(f100(x98811),f323(f323(f22(a865),x98814),f76(a865)))),x98813)))))
% 188.07/187.97 [10020]P101(f323(x100201,f669(x100202,x100203,x100204,x100201)))+P38(x100202,f323(f243(f871(x100202,x100202)),f323(f262(x100202,x100202,a860),f323(f323(f8(f872(x100202,a860),f872(x100202,a860),x100202),f323(f18(x100202,a860,a860),f323(f323(f8(a860,f872(a860,a860),x100202),a322),x100201))),f323(f323(f7(x100202,f872(x100202,x100202),f872(x100202,a860)),f323(f323(f8(f872(x100202,a860),f872(f872(x100202,x100202),f872(x100202,a860)),x100202),f8(x100202,a860,x100202)),a320)),x100203)))))
% 188.07/187.97 [10034]~P101(f323(f323(f238(a865),f323(x100344,f323(x100343,f669(x100341,x100343,x100344,x100342)))),f323(x100344,f669(x100341,x100343,x100344,x100342))))+P38(x100341,f323(f243(f871(x100341,x100341)),f323(f262(x100341,x100341,a860),f323(f323(f8(f872(x100341,a860),f872(x100341,a860),x100341),f323(f18(x100341,a860,a860),f323(f323(f8(a860,f872(a860,a860),x100341),a322),x100342))),f323(f323(f7(x100341,f872(x100341,x100341),f872(x100341,a860)),f323(f323(f8(f872(x100341,a860),f872(f872(x100341,x100341),f872(x100341,a860)),x100341),f8(x100341,a860,x100341)),a320)),x100343)))))
% 188.07/187.97 [10136]~P101(f323(f323(f325(f871(x101361,x101361)),f323(f323(f258(x101361,x101361),x101363),x101364)),f323(f323(f110(f872(f871(x101361,x101361),a860)),x101362),f299(x101361,f188(f872(f871(x101361,x101361),a860))))))+P101(f323(f323(f323(f323(f110(f872(x101361,f872(x101361,a860))),f323(f323(f7(x101361,f872(f871(x101361,x101361),a860),f872(x101361,a860)),f323(f323(f8(f872(x101361,f872(f872(f871(x101361,x101361),a860),a860)),f872(f872(f871(x101361,x101361),a860),f872(x101361,a860)),x101361),f7(x101361,f872(f871(x101361,x101361),a860),a860)),f323(f323(f8(f872(x101361,f871(x101361,x101361)),f872(x101361,f872(f872(f871(x101361,x101361),a860),a860)),x101361),f323(f8(f871(x101361,x101361),f872(f872(f871(x101361,x101361),a860),a860),x101361),f325(f871(x101361,x101361)))),f258(x101361,x101361)))),x101362)),a320),x101363),x101364))
% 188.07/187.97 [10144]P101(f323(f323(f325(f871(x101441,x101441)),f323(f323(f258(x101441,x101441),x101442),x101443)),f323(f323(f110(f872(f871(x101441,x101441),a860)),x101444),f299(x101441,f188(f872(f871(x101441,x101441),a860))))))+~P101(f323(f323(f323(f323(f110(f872(x101441,f872(x101441,a860))),f323(f323(f7(x101441,f872(f871(x101441,x101441),a860),f872(x101441,a860)),f323(f323(f8(f872(x101441,f872(f872(f871(x101441,x101441),a860),a860)),f872(f872(f871(x101441,x101441),a860),f872(x101441,a860)),x101441),f7(x101441,f872(f871(x101441,x101441),a860),a860)),f323(f323(f8(f872(x101441,f871(x101441,x101441)),f872(x101441,f872(f872(f871(x101441,x101441),a860),a860)),x101441),f323(f8(f871(x101441,x101441),f872(f872(f871(x101441,x101441),a860),a860),x101441),f325(f871(x101441,x101441)))),f258(x101441,x101441)))),x101444)),a320),x101442),x101443))
% 188.07/187.97 [10093]E(f323(f323(f144(f866(x100931)),f323(f323(f144(x100931),x100932),f323(f135(f866(x100931),f866(x100931),f121(x100931),f113(x100931)),f323(f323(f147(f866(x100931),f866(x100931)),f149(f866(x100931),x100931,f113(x100931),f323(f323(f8(f866(x100931),f872(f866(x100931),f866(x100931)),x100931),f16(f866(x100931),f866(x100931))),f323(f323(f7(x100931,f866(x100931),f866(x100931)),f144(x100931)),f113(x100931))))),x100933)))),f173(x100931,f323(f323(f144(f866(x100931)),x100934),f323(f135(f866(f866(x100931)),f866(f866(x100931)),f121(f866(x100931)),f113(f866(x100931))),f323(f323(f147(f866(x100931),f866(f866(x100931))),f149(f866(f866(x100931)),x100931,f113(f866(x100931)),f323(f16(f872(f866(x100931),f866(f866(x100931))),x100931),f323(f323(f7(f866(x100931),f866(f866(x100931)),f866(f866(x100931))),f144(f866(x100931))),f113(f866(x100931)))))),x100933))))),f173(x100931,f323(f323(f144(f866(x100931)),f323(f323(f144(x100931),x100932),x100934)),x100933)))+~P101(f323(f311(f866(f866(x100931)),f174(x100931)),f323(f323(f144(f866(x100931)),f323(f323(f144(x100931),x100932),x100934)),x100933)))
% 188.07/187.97 [10135]~P101(f323(f59(x101352),f323(f243(x101352),x101354)))+P101(f323(f59(x101351),f323(f243(x101351),f323(f323(f8(f872(x101352,a860),a860,x101351),f85(x101352)),f323(f323(f7(x101351,f872(x101352,a860),f872(x101352,a860)),f323(f323(f8(f872(x101352,f872(a860,a860)),f872(f872(x101352,a860),f872(x101352,a860)),x101351),f18(x101352,a860,a860)),f323(f323(f8(f872(x101352,a860),f872(x101352,f872(a860,a860)),x101351),f323(f8(a860,f872(a860,a860),x101352),a322)),f323(f323(f7(x101351,f872(x101352,x101351),f872(x101352,a860)),f323(f323(f8(f872(x101351,a860),f872(f872(x101352,x101351),f872(x101352,a860)),x101351),f8(x101351,a860,x101352)),a320)),x101353)))),x101354)))))
% 188.07/187.97 [8693]P27(x86931,x86932,x86933,x86934)+~P28(x86931,x86932,x86933,x86934,x86935)
% 188.07/187.97 [5250]E(x52501,x52502)+~E(f123(x52503,x52504,x52501),f123(x52503,x52505,x52502))
% 188.07/187.97 [5251]E(x52511,x52512)+~E(f123(x52513,x52511,x52514),f123(x52513,x52512,x52515))
% 188.07/187.97 [5252]E(x52521,x52522)+~E(f163(x52523,x52521,x52524),f163(x52523,x52522,x52525))
% 188.07/187.97 [9169]~P28(x91692,x91691,x91694,x91693,x91695)+P28(x91691,x91692,f75(x91692,x91691,x91693,x91694),x91695,x91693)
% 188.07/187.97 [9170]~P28(x91702,x91701,x91704,x91703,x91705)+P28(x91701,x91702,f91(x91702,x91701,x91703,x91704),x91705,x91703)
% 188.07/187.97 [5627]E(f323(f323(f301(x56271),x56272),f177(x56271,x56273,x56274)),f177(x56271,x56273,x56274))+~E(f323(x56274,x56272),f323(f230(x56273),x56275))
% 188.07/187.97 [6027]P101(f323(f253(x60271,x60272,x60273),x60274))+~P101(f323(f323(x60273,x60275),x60274))
% 188.07/187.97 [6029]P101(f323(f252(x60291,x60292,x60293),x60294))+~P101(f323(f323(x60293,x60294),x60295))
% 188.07/187.97 [6032]~E(f323(x60324,x60322),f323(f230(x60323),x60325))+P101(f323(f323(f325(x60321),x60322),f177(x60321,x60323,x60324)))
% 188.07/187.97 [6033]~E(f323(x60334,x60335),f323(f230(x60331),x60332))+P101(f323(f323(f325(x60331),x60332),f178(x60333,x60331,x60334)))
% 188.07/187.97 [6489]~E(x64895,f2(a99))+E(f323(f197(x64891,x64892,x64893,x64894),x64895),f124(x64892))
% 188.07/187.97 [6490]~E(x64905,f2(a99))+E(f323(f199(x64901,x64902,x64903,x64904),x64905),f115(x64902))
% 188.07/187.97 [6625]~E(x66253,f2(a99))+E(f323(f272(x66251,x66252,x66253,x66254),x66255),f323(f258(x66251,x66252),x66255))
% 188.07/187.97 [6696]~E(f323(x66964,x66965),f200(x66962))+E(f323(f232(f869(x66961),x66962,f200(x66961),x66963),f323(x66964,x66965)),f200(x66961))
% 188.07/187.97 [7313]E(f323(x73131,x73132),f200(x73133))+~E(f323(f180(x73134,x73133,x73135,x73131),x73132),f200(x73133))
% 188.07/187.97 [7314]E(f323(x73141,x73142),f200(x73143))+~E(f323(f180(x73144,x73143,x73141,x73145),x73142),f200(x73143))
% 188.07/187.97 [7350]E(f323(f180(x73501,x73502,x73503,x73504),x73505),f323(x73503,x73505))+P101(f323(f323(f325(x73501),x73505),f177(x73501,x73502,x73504)))
% 188.07/187.97 [7351]E(f323(f180(x73511,x73512,x73513,x73514),x73515),f323(x73514,x73515))+P101(f323(f323(f325(x73511),x73515),f177(x73511,x73512,x73513)))
% 188.07/187.97 [7670]~P22(x76704,x76701,x76702,x76705)+E(f323(f71(x76701,x76701,x76701,f323(x76702,x76703)),f323(x76702,x76703)),f323(x76702,x76703))
% 188.07/187.97 [7714]E(f323(f180(x77141,x77142,x77143,x77144),x77145),f323(x77144,x77145))+~P101(f323(f323(f325(x77141),x77145),f177(x77141,x77142,x77144)))
% 188.07/187.97 [8057]~P18(x80575,x80571,x80572)+E(f323(f71(x80571,x80571,x80571,f323(x80572,x80573)),f323(x80572,x80574)),f323(f71(x80571,x80571,x80571,f323(x80572,x80574)),f323(x80572,x80573)))
% 188.07/187.97 [8388]P101(f323(f323(f325(f871(x83881,x83881)),f323(f323(f258(x83881,x83881),x83882),x83883)),f317(x83881,x83884,x83885)))+~P101(f323(f323(f238(a865),f323(x83884,x83882)),f323(x83884,x83883)))
% 188.07/187.97 [8476]~P101(f323(f323(f325(x84764),x84763),f290(x84764,x84761,x84762,x84765)))+P101(f323(f323(x84761,x84762),x84763))
% 188.07/187.97 [8477]~P101(f323(f323(f325(x84774),x84773),f287(x84774,x84771,x84772,x84775)))+P101(f323(f323(x84771,x84772),x84773))
% 188.07/187.97 [8478]~P101(f323(f323(f325(x84784),x84782),f290(x84784,x84781,x84785,x84783)))+P101(f323(f323(x84781,x84782),x84783))
% 188.07/187.97 [8479]~P101(f323(f323(f325(x84794),x84792),f287(x84794,x84791,x84795,x84793)))+P101(f323(f323(x84791,x84792),x84793))
% 188.07/187.97 [8561]~P28(x85611,x85613,x85615,x85612,x85614)+E(f323(f35(x85611),x85612),f323(f35(x85613),x85614))
% 188.07/187.97 [8610]~P28(x86101,x86102,x86103,x86104,x86105)+E(f323(f302(x86101,x86102,x86103),x86104),x86105)
% 188.07/187.97 [8631]~P53(x86312,x86311,x86315,x86313,x86314)+E(f323(f302(x86311,x86312,x86313),x86314),f246(f872(x86312,a860)))
% 188.07/187.97 [9076]~P35(x90761,x90762,x90763,x90764,x90765)+P35(x90761,x90762,x90763,f323(f162(x90761),x90764),f323(f162(x90762),x90765))
% 188.07/187.97 [9078]~P35(x90781,x90782,x90783,f323(f162(x90781),x90784),x90785)+P35(x90781,x90782,x90783,x90784,f323(f162(x90782),x90785))
% 188.07/187.97 [9079]~P35(x90791,x90792,x90793,x90794,f323(f162(x90792),x90795))+P35(x90791,x90792,x90793,f323(f162(x90791),x90794),x90795)
% 188.07/187.97 [9085]P35(x90851,x90852,x90853,x90854,x90855)+~P35(x90851,x90852,x90853,f323(f162(x90851),x90854),f323(f162(x90852),x90855))
% 188.07/187.97 [9478]P101(f323(f323(f325(f871(f866(x94781),f866(x94781))),f323(f323(f258(f866(x94781),f866(x94781)),f323(f323(f144(x94781),x94782),x94783)),f323(f323(f144(x94781),x94782),x94784))),f150(x94781,x94785)))+~P101(f323(f323(f325(f871(f866(x94781),f866(x94781))),f323(f323(f258(f866(x94781),f866(x94781)),x94783),x94784)),f150(x94781,x94785)))
% 188.07/187.97 [9479]P101(f323(f323(f325(f871(f866(x94791),f866(x94791))),f323(f323(f258(f866(x94791),f866(x94791)),f323(f323(f121(x94791),x94792),x94793)),f323(f323(f121(x94791),x94792),x94794))),f140(x94791,x94795)))+~P101(f323(f323(f325(f871(f866(x94791),f866(x94791))),f323(f323(f258(f866(x94791),f866(x94791)),x94793),x94794)),f140(x94791,x94795)))
% 188.07/187.97 [9672]E(f323(f323(f144(x96721),f577(x96722,x96723,x96724,x96725,x96721)),f578(x96722,x96723,x96724,x96725,x96721)),x96725)+~P101(f323(f323(f325(f871(f866(x96721),f866(x96721))),f323(f323(f258(f866(x96721),f866(x96721)),x96725),f323(f323(f144(x96721),x96724),x96723))),f151(x96721,x96722)))
% 188.07/187.97 [9694]E(f323(f323(f144(x96941),f579(x96942,x96943,x96944,x96945,x96941)),f580(x96942,x96943,x96944,x96945,x96941)),x96943)+~P101(f323(f323(f325(f871(f866(x96941),f866(x96941))),f323(f323(f258(f866(x96941),f866(x96941)),f323(f323(f144(x96941),x96945),x96944)),x96943)),f151(x96941,x96942)))
% 188.07/187.97 [9855]~P101(f323(f323(f325(f871(f866(x98551),f866(x98551))),f323(f323(f258(f866(x98551),f866(x98551)),f323(f323(f144(x98551),x98555),x98552)),x98554)),f151(x98551,x98553)))+P101(f323(f323(f325(f871(f866(x98551),f866(x98551))),f323(f323(f258(f866(x98551),f866(x98551)),x98552),f580(x98553,x98554,x98552,x98555,x98551))),f151(x98551,x98553)))
% 188.07/187.97 [9925]~P101(f323(f323(f325(f871(f866(x99251),f866(x99251))),f323(f323(f258(f866(x99251),f866(x99251)),x99255),f323(f323(f144(x99251),x99254),x99253))),f151(x99251,x99252)))+P101(f323(f323(f325(f871(f866(x99251),f866(x99251))),f323(f323(f258(f866(x99251),f866(x99251)),f578(x99252,x99253,x99254,x99255,x99251)),x99253)),f151(x99251,x99252)))
% 188.07/187.97 [10088]P101(f323(f323(f325(f871(x100881,x100881)),f323(f323(f258(x100881,x100881),f323(x100882,f323(f323(f78(a865),x100883),x100884))),f323(x100882,x100883))),f299(x100881,x100885)))+~P101(f323(f323(f325(f871(x100881,x100881)),f323(f323(f258(x100881,x100881),f323(x100882,f323(a112,f731(x100884,x100883,x100885,x100882,x100881)))),f323(x100882,f731(x100884,x100883,x100885,x100882,x100881)))),f299(x100881,x100885)))
% 188.07/187.97 [5216]E(x52161,x52162)+~E(f323(f323(f144(x52163),x52164),x52161),f323(f323(f144(x52163),x52165),x52162))
% 188.07/187.97 [5217]E(x52171,x52172)+~E(f323(f323(f144(x52173),x52171),x52174),f323(f323(f144(x52173),x52172),x52175))
% 188.07/187.97 [5268]P101(f323(x52681,x52682))+~E(f323(f129(x52683,x52681),x52684),f323(f323(f144(x52683),x52682),x52685))
% 188.07/187.97 [5269]P101(f323(x52691,x52692))+~E(f323(f323(f144(x52693),x52692),x52694),f323(f129(x52693,x52691),x52695))
% 188.07/187.97 [5425]~E(f323(f323(f131(x54251),x54253),x54252),f323(f323(f144(x54251),x54254),x54255))+E(f323(f323(f158(x54251),x54252),x54253),x54254)
% 188.07/187.97 [5557]~P17(x55574,x55575,x55571)+E(f323(f323(x55571,x55572),f323(f323(x55571,x55572),x55573)),f323(f323(x55571,x55572),x55573))
% 188.07/187.97 [6085]~E(x60854,f2(a99))+E(f323(f323(f117(x60851,x60852,x60853),x60854),x60855),f323(f323(f258(f866(x60852),x60851),f113(x60852)),x60855))
% 188.07/187.97 [6151]~P103(x61512)+~E(f323(f323(f141(x61511,x61512,x61513),x61514),x61515),f113(x61511))
% 188.07/187.97 [6527]E(x65271,x65272)+~E(f323(f323(f121(x65273),x65274),f323(f323(f144(x65273),x65271),f113(x65273))),f323(f323(f121(x65273),x65275),f323(f323(f144(x65273),x65272),f113(x65273))))
% 188.07/187.97 [6528]E(x65281,x65282)+~E(f323(f323(f121(x65283),x65281),f323(f323(f144(x65283),x65284),f113(x65283))),f323(f323(f121(x65283),x65282),f323(f323(f144(x65283),x65285),f113(x65283))))
% 188.07/187.97 [6780]E(f323(f182(x67801,x67802,x67803,x67804),x67805),f200(x67802))+P101(f323(f323(f325(x67801),x67805),x67804))
% 188.07/187.97 [6842]E(f323(f323(f301(x68421),f323(x68422,x68423)),f323(f302(x68424,x68421,x68422),x68425)),f323(f302(x68424,x68421,x68422),x68425))+~P101(f323(f323(f325(x68424),x68423),x68425))
% 188.07/187.97 [6848]~P101(f323(x68484,f323(x68483,x68485)))+P101(f323(f323(f303(x68481,x68482,x68483),x68484),x68485))
% 188.07/187.97 [6851]~P101(f323(f323(x68513,x68515),x68514))+P101(f323(f323(f247(x68511,x68512,x68513),x68514),x68515))
% 188.07/187.97 [6944]~E(f323(f302(x69441,x69442,x69443),x69444),x69445)+E(f323(f302(f872(x69441,a860),f872(x69442,a860),f302(x69441,x69442,x69443)),f323(f300(x69441),x69444)),f323(f300(x69442),x69445))
% 188.07/187.97 [6974]E(f323(f182(x69741,x69742,x69743,x69744),x69745),f323(x69743,x69745))+~P101(f323(f323(f325(x69741),x69745),x69744))
% 188.07/187.97 [7273]P27(x72731,x72732,x72733,x72734)+~P27(x72731,x72732,x72733,f323(f323(f301(x72731),x72735),x72734))
% 188.07/187.97 [7340]P101(f323(x73401,x73402))+~P101(f323(f323(f92(x73403,x73404,x73401),x73405),x73402))
% 188.07/187.97 [7384]~P101(f323(f323(f325(x73844),x73843),x73845))+P101(f323(f323(f325(x73841),f323(x73842,x73843)),f323(f302(x73844,x73841,x73842),x73845)))
% 188.07/187.97 [7407]~P103(x74072)+E(f143(x74071,x74072,x74073,f323(f129(x74071,x74074),x74075)),f323(f129(x74071,x74074),f143(x74071,x74072,x74073,x74075)))
% 188.07/187.97 [7439]P101(f323(x74391,f323(x74392,x74393)))+~P101(f323(f323(f303(x74394,x74395,x74392),x74391),x74393))
% 188.07/187.97 [7442]P101(f323(f323(x74421,x74422),x74423))+~P101(f323(f323(f247(x74424,x74425,x74421),x74423),x74422))
% 188.07/187.97 [7443]P101(f323(f323(x74431,x74432),x74433))+~P101(f323(f323(f92(x74434,x74431,x74435),x74432),x74433))
% 188.07/187.97 [7506]~P101(f323(f323(f325(x75063),f323(x75064,x75062)),x75065))+P101(f323(f323(f325(x75061),x75062),f323(f303(x75061,x75063,x75064),x75065)))
% 188.07/187.97 [7904]~P101(f323(f323(f325(x79045),x79043),f323(f303(x79045,x79041,x79042),x79044)))+P101(f323(f323(f325(x79041),f323(x79042,x79043)),x79044))
% 188.07/187.97 [8121]~E(x81213,f323(f323(f323(f70(x81211,f869(x81212)),f323(f16(f869(x81212),x81211),f200(x81212))),x81214),f323(f230(x81212),x81215)))+E(f177(x81211,x81212,x81213),f323(f323(f301(x81211),x81214),f188(f872(x81211,a860))))
% 188.07/187.97 [8201]~P18(x82012,x82011,x82013)+E(f323(f135(x82011,x82012,f323(f7(x82012,x82011,x82011),x82013),x82014),f145(x82012,x82015)),f323(f323(f62(x82012,x82011,x82013),x82014),f323(f166(x82012),x82015)))
% 188.07/187.97 [8221]E(f323(x82211,f486(x82212,x82211,x82213,x82214)),x82214)+~P101(f323(f323(f325(x82215),x82214),f323(f302(x82213,x82215,x82211),x82212)))
% 188.07/187.97 [8222]E(f323(x82221,f495(x82222,x82221,x82223,x82224)),x82224)+~P101(f323(f323(f325(x82225),x82224),f323(f302(x82223,x82225,x82221),x82222)))
% 188.07/187.97 [8522]~E(x85222,f323(f323(f144(x85221),x85224),x85225))+P101(f323(f323(f325(f871(f866(x85221),f866(x85221))),f323(f323(f258(f866(x85221),f866(x85221)),f113(x85221)),x85222)),f140(x85221,x85223)))
% 188.07/187.97 [8570]E(f323(x85701,f323(f91(x85702,x85703,x85704,x85701),x85705)),x85705)+~P101(f323(f323(f325(x85703),x85705),f323(f302(x85702,x85703,x85701),x85704)))
% 188.07/187.97 [8573]P27(x85731,x85732,f91(x85732,x85731,x85733,x85734),x85735)+~P101(f323(f323(f237(f872(x85731,a860)),x85735),f323(f302(x85732,x85731,x85734),x85733)))
% 188.07/187.97 [8581]~P35(x85811,x85813,x85815,x85812,x85814)+E(f323(f189(f866(x85811)),x85812),f323(f189(f866(x85813)),x85814))
% 188.07/187.97 [8591]P101(f323(f323(f237(f872(x85911,a860)),f323(f323(f40(x85912,f872(x85911,a860)),x85913),x85914)),f323(x85914,x85915)))+~P101(f323(f323(f325(x85912),x85915),x85913))
% 188.07/187.97 [8647]~P53(x86471,x86472,x86473,x86475,x86474)+E(f323(f302(x86471,x86472,x86473),f246(f872(x86471,a860))),x86474)
% 188.07/187.97 [8863]E(f323(f323(f323(f70(x88631,f869(x88632)),f182(x88631,x88632,x88633,x88634)),x88635),f200(x88632)),f182(x88631,x88632,x88633,x88634))+P101(f323(f323(f325(x88631),x88635),x88634))
% 188.07/187.97 [8868]E(f323(f129(x88681,x88682),f712(x88683,x88684,x88685,x88682,x88681)),x88683)+~E(f323(f129(x88681,x88682),x88685),f323(f323(f144(x88681),x88684),x88683))
% 188.07/187.97 [8869]E(f323(f129(x88691,x88692),f713(x88693,x88692,x88694,x88695,x88691)),x88694)+~E(f323(f323(f144(x88691),x88695),x88694),f323(f129(x88691,x88692),x88693))
% 188.07/187.97 [8870]E(f323(x88701,f841(x88702,x88703,x88701,x88704,x88705)),x88702)+~E(f323(f323(f201(x88705,x88704),x88701),x88703),f323(f230(x88704),x88702))
% 188.07/187.97 [8873]E(f323(f230(x88731),f841(x88732,x88733,x88734,x88735,x88731)),x88733)+~E(f323(f323(f201(x88731,x88735),x88734),x88733),f323(f230(x88735),x88732))
% 188.07/187.97 [8963]E(f323(f189(f866(x89631)),x89632),x89633)+~P101(f323(f323(f325(f871(f866(x89631),f866(x89631))),f323(f323(f258(f866(x89631),f866(x89631)),x89634),x89632)),f323(f136(x89631,x89635),x89633)))
% 188.07/187.97 [8964]E(f323(f189(f866(x89641)),x89642),x89643)+~P101(f323(f323(f325(f871(f866(x89641),f866(x89641))),f323(f323(f258(f866(x89641),f866(x89641)),x89642),x89644)),f323(f136(x89641,x89645),x89643)))
% 188.07/187.97 [9034]P101(f323(f323(f325(x90341),f486(x90342,x90343,x90341,x90344)),x90342))+~P101(f323(f323(f325(x90345),x90344),f323(f302(x90341,x90345,x90343),x90342)))
% 188.07/187.97 [9035]P101(f323(f323(f325(x90351),f495(x90352,x90353,x90351,x90354)),x90352))+~P101(f323(f323(f325(x90355),x90354),f323(f302(x90351,x90355,x90353),x90352)))
% 188.07/187.97 [9193]E(f323(f302(x91931,x91932,x91933),f587(x91934,x91933,x91931,x91935,x91932)),x91935)+~P101(f323(f323(f237(f872(x91932,a860)),x91935),f323(f302(x91931,x91932,x91933),x91934)))
% 188.07/187.97 [9448]E(f323(x94481,f812(x94482,x94481,x94483,x94484,x94485)),f323(f230(x94485),x94484))+~P101(f323(f323(f325(x94485),x94484),f178(x94483,x94485,f182(x94483,x94485,x94481,x94482))))
% 188.07/187.97 [9494]P101(f323(f323(f325(f871(f866(x94941),f866(x94941))),f323(f323(f258(f866(x94941),f866(x94941)),f323(f323(f144(x94941),x94942),x94943)),f323(f323(f144(x94941),x94942),x94944))),f299(f866(x94941),f150(x94941,x94945))))+~P101(f323(f323(f325(f871(f866(x94941),f866(x94941))),f323(f323(f258(f866(x94941),f866(x94941)),x94943),x94944)),f299(f866(x94941),f150(x94941,x94945))))
% 188.07/187.97 [9526]~E(f323(x95263,f536(x95265,x95264,x95263,x95262,x95261)),f323(x95265,f536(x95265,x95264,x95263,x95262,x95261)))+E(f323(f323(f147(x95261,x95262),x95263),x95264),f323(f323(f147(x95261,x95262),x95265),x95264))
% 188.07/187.97 [9603]~E(f323(f129(x96031,x96035),x96034),f323(f323(f144(x96031),x96033),x96032))+E(f323(f323(f121(x96031),f714(x96032,x96033,x96034,x96035,x96031)),f323(f323(f144(x96031),x96033),f712(x96032,x96033,x96034,x96035,x96031))),x96034)
% 188.07/187.97 [9604]~E(f323(f323(f144(x96041),x96045),x96044),f323(f129(x96041,x96043),x96042))+E(f323(f323(f121(x96041),f704(x96042,x96043,x96044,x96045,x96041)),f323(f323(f144(x96041),x96045),f713(x96042,x96043,x96044,x96045,x96041))),x96042)
% 188.07/187.97 [9608]E(f323(f323(f147(x96081,x96082),x96083),x96084),f323(f323(f147(x96081,x96082),x96085),x96084))+P101(f323(f323(f325(x96081),f536(x96083,x96084,x96085,x96082,x96081)),f323(f166(x96081),x96084)))
% 188.07/187.97 [9638]~P101(f323(f323(f325(x96385),x96384),f323(f277(x96381,x96385,x96383),x96382)))+P101(f323(f323(f325(x96381),f502(x96382,x96383,x96381,x96384,x96385)),x96382))
% 188.07/187.97 [9639]~P101(f323(f323(f325(x96395),x96394),f323(f277(x96391,x96395,x96393),x96392)))+P101(f323(f323(f325(x96391),f529(x96392,x96393,x96391,x96394,x96395)),x96392))
% 188.07/187.97 [9666]~P101(f323(f323(f237(f872(x96665,a860)),x96664),f323(f302(x96661,x96665,x96663),x96662)))+P101(f323(f323(f237(f872(x96661,a860)),f587(x96662,x96663,x96661,x96664,x96665)),x96662))
% 188.07/187.97 [9717]~P101(f323(f323(f325(x97175),x97174),f178(x97171,x97175,f182(x97171,x97175,x97173,x97172))))+P101(f323(f323(f325(x97171),f812(x97172,x97173,x97171,x97174,x97175)),x97172))
% 188.07/187.97 [10112]E(x101121,f2(a99))+E(f323(f232(f871(f866(x101122),x101123),f871(x101122,x101123),f323(f323(f258(f866(x101122),x101123),f113(x101122)),x101124),f323(f262(x101122,x101123,f871(f866(x101122),x101123)),f323(f323(f7(x101122,f872(x101123,f871(f866(x101122),x101123)),f872(x101123,f871(f866(x101122),x101123))),f323(f323(f8(f872(f871(f866(x101122),x101123),f871(f866(x101122),x101123)),f872(f872(x101123,f871(f866(x101122),x101123)),f872(x101123,f871(f866(x101122),x101123))),x101122),f8(f871(f866(x101122),x101123),f871(f866(x101122),x101123),x101123)),f323(f323(f8(f872(f866(x101122),f872(x101123,f871(f866(x101122),x101123))),f872(f871(f866(x101122),x101123),f871(f866(x101122),x101123)),x101122),f262(f866(x101122),x101123,f871(f866(x101122),x101123))),f323(f323(f8(f872(f866(x101122),f866(x101122)),f872(f866(x101122),f872(x101123,f871(f866(x101122),x101123))),x101122),f323(f8(f866(x101122),f872(x101123,f871(f866(x101122),x101123)),f866(x101122)),f258(f866(x101122),x101123))),f144(x101122))))),f323(f117(x101123,x101122,x101125),f323(f323(f22(a99),x101121),f76(a99)))))),f323(x101125,x101124)),f323(f323(f117(x101123,x101122,x101125),x101121),x101124))
% 188.07/187.97 [5438]~E(f323(x54383,x54384),x54385)+E(f323(f323(f323(f70(x54381,x54382),x54383),x54384),x54385),x54383)
% 188.07/187.97 [5878]E(f323(x58781,x58782),x58783)+~E(f323(f323(f323(f70(x58784,x58785),x58781),x58782),x58783),x58781)
% 188.07/187.97 [5967]E(x59671,x59672)+~E(f323(f261(x59673,x59674),f323(f323(f258(x59673,x59674),x59675),x59671)),x59672)
% 188.07/187.97 [5968]E(x59681,x59682)+~E(f323(f257(x59683,x59684),f323(f323(f258(x59683,x59684),x59681),x59685)),x59682)
% 188.07/187.97 [6226]~E(x62263,f323(f323(f121(x62261),x62264),f323(f323(f144(x62261),x62262),x62265)))+P101(f323(f323(f325(x62261),x62262),f323(f166(x62261),x62263)))
% 188.07/187.97 [6612]E(f323(f302(x66121,x66122,f323(f16(x66122,x66121),x66123)),x66124),f323(f323(f301(x66122),x66123),f188(f872(x66122,a860))))+~P101(f323(f323(f325(x66121),x66125),x66124))
% 188.07/187.97 [6682]E(f323(f323(f110(f872(x66821,a860)),f323(f166(x66821),x66822)),f323(f166(x66821),x66823)),f323(f166(x66821),x66824))+~E(f160(x66821,x66825,x66824),f323(f323(f258(f866(x66821),f866(x66821)),x66822),x66823))
% 188.07/187.97 [6784]~P103(x67842)+E(f323(f189(f866(x67841)),f323(f323(f141(x67841,x67842,x67843),x67844),x67845)),f323(a112,f323(f189(f866(x67841)),x67845)))
% 188.07/187.97 [6796]~P103(x67962)+E(f323(f166(x67961),f323(f323(f141(x67961,x67962,x67963),x67964),x67965)),f323(f323(f301(x67961),x67964),f323(f166(x67961),x67965)))
% 188.07/187.97 [7065]~P112(x70651)+E(f323(f323(f79(x70651),f323(f323(f79(x70651),x70652),x70653)),f323(f323(f79(x70651),x70654),x70655)),f323(f323(f79(x70651),f323(f323(f79(x70651),x70652),x70654)),f323(f323(f79(x70651),x70653),x70655)))
% 188.07/187.97 [7066]~P112(x70661)+E(f323(f323(f78(x70661),f323(f323(f78(x70661),x70662),x70663)),f323(f323(f78(x70661),x70664),x70665)),f323(f323(f78(x70661),f323(f323(f78(x70661),x70662),x70664)),f323(f323(f78(x70661),x70663),x70665)))
% 188.07/187.97 [7067]~P62(x70671)+E(f323(f323(f281(x70671),f323(f323(f79(x70671),x70672),x70673)),f323(f323(f79(x70671),x70674),x70675)),f323(f323(f79(x70671),f323(f323(f281(x70671),x70672),x70674)),f323(f323(f281(x70671),x70673),x70675)))
% 188.07/187.97 [7081]~P103(x70811)+E(f294(x70811,f323(f323(f236(x70811),x70812),x70813),f323(f323(f235(x70811),x70814),x70815)),f323(f323(f101(f872(x70811,a860)),f294(x70811,x70812,x70814)),f294(x70811,x70813,x70815)))
% 188.07/187.97 [7082]~P103(x70821)+E(f297(x70821,f323(f323(f236(x70821),x70822),x70823),f323(f323(f235(x70821),x70824),x70825)),f323(f323(f101(f872(x70821,a860)),f297(x70821,x70822,x70824)),f297(x70821,x70823,x70825)))
% 188.07/187.97 [7083]~P103(x70831)+E(f296(x70831,f323(f323(f236(x70831),x70832),x70833),f323(f323(f235(x70831),x70834),x70835)),f323(f323(f101(f872(x70831,a860)),f296(x70831,x70832,x70834)),f296(x70831,x70833,x70835)))
% 188.07/187.97 [7084]~P103(x70841)+E(f323(f323(f101(f872(x70841,a860)),f323(f293(x70841,x70842),x70843)),f323(f293(x70841,x70844),x70845)),f323(f293(x70841,f323(f323(f236(x70841),x70842),x70844)),f323(f323(f235(x70841),x70843),x70845)))
% 188.07/187.97 [7199]~P101(f323(x71991,f501(x71993,x71992,x71991)))+P101(f323(x71991,f323(f323(f258(x71992,x71993),x71994),x71995)))
% 188.07/187.97 [7286]~E(f323(x72863,x72864),f200(x72862))+E(f178(x72861,x72862,f323(f323(f323(f70(x72861,f869(x72862)),x72863),x72864),f323(f230(x72862),x72865))),f323(f323(f301(x72862),x72865),f178(x72861,x72862,x72863)))
% 188.07/187.97 [7305]~E(x73052,f323(x73054,x73055))+P101(f323(f323(f325(x73051),x73052),f323(f302(x73053,x73051,x73054),f246(f872(x73053,a860)))))
% 188.07/187.97 [7362]~E(f323(x73623,x73624),f200(x73622))+E(f323(f323(f22(f872(x73621,a860)),f177(x73621,x73622,x73623)),f323(f323(f301(x73621),x73624),x73625)),f323(f323(f22(f872(x73621,a860)),f177(x73621,x73622,x73623)),x73625))
% 188.07/187.97 [7381]~P17(x73813,x73812,x73814)+P17(x73811,x73812,f323(f323(f8(x73813,f872(x73812,x73812),x73811),x73814),x73815))
% 188.07/187.97 [7382]~P18(x73823,x73822,x73824)+P18(x73821,x73822,f323(f323(f8(x73823,f872(x73822,x73822),x73821),x73824),x73825))
% 188.07/187.97 [7522]~P27(x75221,x75222,x75223,x75224)+P27(x75221,x75222,x75223,f323(f323(f22(f872(x75221,a860)),x75224),x75225))
% 188.07/187.97 [7679]~P101(f323(f323(x76793,x76794),x76795))+P101(f323(f323(f262(x76791,x76792,a860),x76793),f323(f323(f258(x76791,x76792),x76794),x76795)))
% 188.07/187.97 [7789]~P101(f323(x77892,x77894))+~E(f323(f323(f131(x77891),f323(f189(f866(x77891)),f171(x77891,x77892,x77893))),x77893),f323(f323(f144(x77891),x77894),x77895))
% 188.07/187.97 [7809]P27(x78091,x78092,x78093,x78094)+~P27(x78091,x78092,x78093,f323(f323(f110(f872(x78091,a860)),x78095),x78094))
% 188.07/187.97 [7810]P27(x78101,x78102,x78103,x78104)+~P27(x78101,x78102,x78103,f323(f323(f110(f872(x78101,a860)),x78104),x78105))
% 188.07/187.97 [7858]~P103(x78582)+E(f323(f323(f141(x78581,x78582,x78583),x78584),f143(x78581,x78582,x78583,x78585)),f143(x78581,x78582,x78583,f323(f323(f144(x78581),x78584),x78585)))
% 188.07/187.97 [8176]~P17(x81762,x81761,x81763)+E(f323(f135(x81761,x81762,f323(f7(x81762,x81761,x81761),x81763),x81764),x81765),f323(f323(f62(x81762,x81761,x81763),x81764),f323(f166(x81762),x81765)))
% 188.07/187.97 [8206]~E(f323(f323(f131(x82061),f323(f189(f866(x82061)),f171(x82061,x82062,x82063))),x82063),f323(f323(f144(x82061),x82064),x82065))+E(f323(f323(f121(x82061),f171(x82061,x82062,x82063)),f323(f323(f144(x82061),x82064),x82065)),x82063)
% 188.07/187.97 [8232]P101(f323(f323(x82321,x82322),x82323))+~P101(f323(f323(f262(x82324,x82325,a860),x82321),f323(f323(f258(x82324,x82325),x82322),x82323)))
% 188.07/187.97 [8296]~E(f323(f323(f179(x82961,x82962),x82965),x82963),f323(f230(x82962),x82964))+P101(f323(f323(f325(f871(x82961,x82962)),f323(f323(f258(x82961,x82962),x82963),x82964)),f323(f166(f871(x82961,x82962)),x82965)))
% 188.07/187.97 [8710]P101(f323(f323(f237(f872(x87101,a860)),f323(f302(x87102,x87101,x87103),x87104)),f323(f302(x87102,x87101,x87103),x87105)))+~P101(f323(f323(f237(f872(x87102,a860)),x87104),x87105))
% 188.07/187.97 [8711]P101(f323(f323(f237(f872(x87111,a860)),f323(f303(x87111,x87112,x87113),x87114)),f323(f303(x87111,x87112,x87113),x87115)))+~P101(f323(f323(f237(f872(x87112,a860)),x87114),x87115))
% 188.07/187.97 [8791]E(x87911,f2(a99))+E(f323(f323(f264(x87912,x87913,x87912,f871(x87913,x87912)),f323(x87914,x87915)),f272(x87913,x87912,f323(f323(f22(a99),x87911),f76(a99)),x87914)),f323(f272(x87913,x87912,x87911,x87914),x87915))
% 188.07/187.97 [9303]E(f323(f230(x93031),f535(x93032,x93033,x93034,x93031,x93035)),f323(f323(f179(x93035,x93031),x93032),x93034))+~P101(f323(f323(f325(f871(x93035,x93031)),f323(f323(f258(x93035,x93031),x93034),x93033)),f323(f166(f871(x93035,x93031)),x93032)))
% 188.07/187.97 [9349]~P101(f323(f323(f325(x93492),x93495),f323(f302(x93491,x93492,x93494),x93493)))+P101(f323(f323(f325(x93491),f323(f91(x93491,x93492,x93493,x93494),x93495)),x93493))
% 188.07/187.97 [9437]~P101(f323(f59(x94373),f323(f302(x94372,x94373,x94375),f246(f872(x94372,a860)))))+P101(f323(f59(x94371),f323(f302(x94372,x94371,f323(f323(f8(x94373,x94371,x94372),x94374),x94375)),f246(f872(x94372,a860)))))
% 188.07/187.97 [9462]P101(f323(f323(f237(f872(f872(x94621,a860),a860)),f323(f302(f872(x94622,a860),f872(x94621,a860),f302(x94622,x94621,x94623)),f323(f300(x94622),x94624))),f323(f300(x94621),x94625)))+~P101(f323(f323(f237(f872(x94621,a860)),f323(f302(x94622,x94621,x94623),x94624)),x94625))
% 188.07/187.97 [9473]~P101(f323(f59(f869(x94731)),f323(f302(x94732,f869(x94731),x94733),f246(f872(x94732,a860)))))+P101(f323(f59(f869(x94731)),f323(f302(x94732,f869(x94731),f323(f323(f323(f70(x94732,f869(x94731)),x94733),x94734),f323(f230(x94731),x94735))),f246(f872(x94732,a860)))))
% 188.07/187.97 [9534]E(x95341,x95342)+~P101(f323(f64(x95343,x95344,x95345,x95341,f188(f872(x95343,a860))),x95342))
% 188.07/187.97 [9550]E(f323(f323(f258(x95501,x95502),f655(x95503,x95504,x95505,x95502,x95501)),f658(x95503,x95504,x95505,x95502,x95501)),x95505)+~P101(f323(f323(f325(f871(x95501,x95502)),x95505),f323(f323(f260(x95501,x95502),x95504),x95503)))
% 188.07/187.97 [9643]P101(f323(f323(f325(x96431),f655(x96432,x96433,x96434,x96435,x96431)),x96433))+~P101(f323(f323(f325(f871(x96431,x96435)),x96434),f323(f323(f260(x96431,x96435),x96433),x96432)))
% 188.07/187.97 [9753]P26(x97535,x97534,f323(f323(f301(f864(x97535)),f323(f323(f323(f90(x97535),x97531),x97533),x97532)),f188(f872(f864(x97535),a860))))+P101(f323(f323(x97531,f552(x97532,x97533,x97534,x97535,x97531)),f662(x97532,x97533,x97534,x97535,x97531)))
% 188.07/187.97 [9806]P101(f323(f323(f325(x98061),f658(x98062,x98063,x98064,x98061,x98065)),f323(x98062,f655(x98062,x98063,x98064,x98061,x98065))))+~P101(f323(f323(f325(f871(x98065,x98061)),x98064),f323(f323(f260(x98065,x98061),x98063),x98062)))
% 188.07/187.97 [9831]P101(f323(f323(f325(f871(x98311,x98311)),f323(f323(f258(x98311,x98311),x98312),f753(x98313,x98314,x98315,x98312,x98311))),x98313))+~P101(f323(f323(f325(f871(x98311,x98311)),f323(f323(f258(x98311,x98311),x98312),x98315)),f323(f323(f183(f871(x98311,x98311),a860),f323(a112,x98314)),x98313)))
% 188.07/187.97 [9832]P101(f323(f323(f325(f871(x98321,x98321)),f323(f323(f258(x98321,x98321),x98322),f754(x98323,x98324,x98325,x98322,x98321))),x98323))+~P101(f323(f323(f325(f871(x98321,x98321)),f323(f323(f258(x98321,x98321),x98322),x98325)),f323(f323(f183(f871(x98321,x98321),a860),f323(a112,x98324)),x98323)))
% 188.07/187.97 [9850]~P101(f323(f323(f325(f871(f866(x98501),f866(x98501))),f323(f323(f258(f866(x98501),f866(x98501)),f323(f323(f144(x98501),x98502),x98505)),x98504)),f151(x98501,x98503)))+P101(f323(f323(f325(f871(x98501,x98501)),f323(f323(f258(x98501,x98501),x98502),f579(x98503,x98504,x98505,x98502,x98501))),x98503))
% 188.07/187.97 [9852]~P26(x98521,x98522,f323(f323(f301(f864(x98521)),f323(f323(f323(f90(x98521),f92(x98521,x98523,x98524)),x98525),x98523)),f188(f872(f864(x98521),a860))))+P26(x98521,x98522,f323(f323(f301(f864(x98521)),f323(f323(f323(f90(x98521),x98523),f29(x98524,x98525)),f92(x98521,x98523,f323(f71(a860,a860,a861,a318),x98524)))),f188(f872(f864(x98521),a860))))
% 188.07/187.97 [9853]~P31(x98531,x98532,f323(f323(f301(f864(x98531)),f323(f323(f323(f90(x98531),f92(x98531,x98533,x98534)),x98535),x98533)),f188(f872(f864(x98531),a860))))+P31(x98531,x98532,f323(f323(f301(f864(x98531)),f323(f323(f323(f90(x98531),x98533),f29(x98534,x98535)),f92(x98531,x98533,f323(f71(a860,a860,a861,a318),x98534)))),f188(f872(f864(x98531),a860))))
% 188.07/187.97 [10113]P26(x101131,x101132,f323(f323(f301(f864(x101131)),f323(f323(f323(f90(x101131),x101133),x101134),x101135)),f188(f872(f864(x101131),a860))))+~P26(x101131,x101132,f323(f323(f301(f864(x101131)),f323(f323(f323(f90(x101131),f323(f16(f872(a861,a860),x101131),f323(f323(f7(a861,a861,a860),a320),f662(x101135,x101134,x101132,x101131,x101133)))),x101134),f323(f16(f872(a861,a860),x101131),f323(x101135,f552(x101135,x101134,x101132,x101131,x101133))))),f188(f872(f864(x101131),a860))))
% 188.07/187.97 [6299]P101(f323(x62992,x62994))+E(f171(x62991,x62992,f323(f323(f121(x62991),x62993),f323(f323(f144(x62991),x62994),x62995))),f171(x62991,x62992,x62993))
% 188.07/187.97 [6347]~P2(x63472)+E(f323(f323(f323(f110(f872(x63471,x63472)),x63473),x63474),x63475),f323(f323(f110(x63472),f323(x63473,x63475)),f323(x63474,x63475)))
% 188.07/187.97 [6349]~P4(x63492)+E(f323(f323(f323(f22(f872(x63491,x63492)),x63493),x63494),x63495),f323(f323(f22(x63492),f323(x63493,x63495)),f323(x63494,x63495)))
% 188.07/187.97 [6351]~P2(x63512)+E(f323(f323(f323(f101(f872(x63511,x63512)),x63513),x63514),x63515),f323(f323(f101(x63512),f323(x63513,x63515)),f323(x63514,x63515)))
% 188.07/187.97 [6368]E(x63681,x63682)+E(f323(f323(f158(x63683),f323(f323(f152(x63683,x63684),x63681),x63685)),x63682),f323(f323(f158(x63683),x63684),x63682))
% 188.07/187.97 [6630]~E(x66304,f188(f872(x66303,a860)))+E(f323(f323(f110(f872(x66301,a860)),x66302),f323(f323(f39(x66303,f872(x66301,a860)),x66304),x66305)),x66302)
% 188.07/187.97 [6631]~E(x66314,f188(f872(x66313,a860)))+E(f323(f323(f22(f872(x66311,a860)),x66312),f323(f323(f39(x66313,f872(x66311,a860)),x66314),x66315)),x66312)
% 188.07/187.97 [6632]~E(x66324,f188(f872(x66323,a860)))+E(f323(f323(f101(f872(x66321,a860)),x66322),f323(f323(f40(x66323,f872(x66321,a860)),x66324),x66325)),x66322)
% 188.07/187.97 [6646]~E(x66464,f188(f872(x66463,a860)))+E(f323(f323(f301(x66461),x66462),f323(f323(f39(x66463,f872(x66461,a860)),x66464),x66465)),f323(f323(f301(x66461),x66462),f188(f872(x66461,a860))))
% 188.07/187.97 [7429]E(f323(f323(f158(x74291),f323(f323(f147(x74292,x74291),x74293),x74294)),x74295),f323(x74293,f323(f323(f158(x74292),x74294),x74295)))+~P101(f323(f323(f238(a865),x74295),f323(f189(f866(x74292)),x74294)))
% 188.07/187.97 [7494]E(f323(f323(f110(f872(x74941,a860)),f323(x74942,x74943)),f323(f323(f39(x74944,f872(x74941,a860)),x74945),x74942)),f323(f323(f39(x74944,f872(x74941,a860)),x74945),x74942))+~P101(f323(f323(f325(x74944),x74943),x74945))
% 188.07/187.97 [7495]E(f323(f323(f101(f872(x74951,a860)),f323(x74952,x74953)),f323(f323(f40(x74954,f872(x74951,a860)),x74955),x74952)),f323(f323(f40(x74954,f872(x74951,a860)),x74955),x74952))+~P101(f323(f323(f325(x74954),x74953),x74955))
% 188.07/187.97 [8094]~E(x80943,f188(f872(x80941,a860)))+E(f323(f323(f39(x80941,f872(x80942,a860)),x80943),f323(f323(f8(f872(x80942,a860),f872(x80942,a860),x80941),f323(f301(x80942),x80944)),x80945)),f188(f872(x80942,a860)))
% 188.07/187.97 [8099]~P101(f323(f323(f325(x80994),x80993),x80995))+P101(f323(f323(f237(f872(x80991,a860)),f323(x80992,x80993)),f323(f323(f39(x80994,f872(x80991,a860)),x80995),x80992)))
% 188.07/187.97 [8231]~E(f323(x82314,x82312),x82315)+P101(f323(f323(f325(x82311),x82312),f323(f303(x82311,x82313,x82314),f323(f323(f301(x82313),x82315),f188(f872(x82313,a860))))))
% 188.07/187.97 [8277]~P51(x82771,x82772,f323(f278(x82772,x82771),x82773))+E(f323(f323(f101(f872(x82771,a860)),f323(f277(x82772,x82771,x82773),x82774)),f323(f277(x82772,x82771,x82773),x82775)),f323(f277(x82772,x82771,x82773),f323(f323(f101(f872(x82772,a860)),x82774),x82775)))
% 188.07/187.97 [8355]E(x83551,f2(a99))+E(f323(f116(x83552,x83553,f323(x83554,f323(f323(f22(a99),x83551),f76(a99)))),f323(f323(f7(x83552,a99,f867(x83553)),x83555),x83551)),f323(f199(x83552,x83553,x83554,x83555),x83551))
% 188.07/187.97 [8395]E(x83951,f188(f872(x83952,a860)))+E(f323(f323(f39(x83952,f872(x83953,a860)),x83951),f323(f323(f8(f872(x83953,a860),f872(x83953,a860),x83952),f323(f301(x83953),x83954)),x83955)),f323(f323(f301(x83953),x83954),f323(f323(f39(x83952,f872(x83953,a860)),x83951),x83955)))
% 188.07/187.97 [8442]~P27(x84422,x84421,x84423,f246(f872(x84422,a860)))+E(f323(f323(f22(f872(x84421,a860)),f323(f302(x84422,x84421,x84423),x84424)),f323(f302(x84422,x84421,x84423),x84425)),f323(f302(x84422,x84421,x84423),f323(f323(f22(f872(x84422,a860)),x84424),x84425)))
% 188.07/187.97 [8443]~P27(x84432,x84431,x84433,f246(f872(x84432,a860)))+E(f323(f323(f101(f872(x84431,a860)),f323(f302(x84432,x84431,x84433),x84434)),f323(f302(x84432,x84431,x84433),x84435)),f323(f302(x84432,x84431,x84433),f323(f323(f101(f872(x84432,a860)),x84434),x84435)))
% 188.07/187.97 [8509]~P101(f323(f323(f65(x85091,x85092,x85095),x85093),x85094))+P101(f323(f323(f325(f871(x85091,x85092)),f323(f323(f258(x85091,x85092),x85093),x85094)),x85095))
% 188.07/187.97 [8542]P101(f323(f323(f325(x85421),x85422),f323(f254(x85423,x85421),x85424)))+~P101(f323(f323(f325(f871(x85423,x85421)),f323(f323(f258(x85423,x85421),x85425),x85422)),x85424))
% 188.07/187.97 [8544]P101(f323(f323(f325(x85441),x85442),f323(f256(x85441,x85443),x85444)))+~P101(f323(f323(f325(f871(x85441,x85443)),f323(f323(f258(x85441,x85443),x85442),x85445)),x85444))
% 188.07/187.97 [8694]P101(f323(f323(f65(x86941,x86942,x86943),x86944),x86945))+~P101(f323(f323(f325(f871(x86941,x86942)),f323(f323(f258(x86941,x86942),x86944),x86945)),x86943))
% 188.07/187.97 [8733]E(f323(x87331,x87332),x87333)+~P101(f323(f323(f325(x87334),x87332),f323(f303(x87334,x87335,x87331),f323(f323(f301(x87335),x87333),f188(f872(x87335,a860))))))
% 188.07/187.97 [8960]P101(f323(f323(f325(f871(x89601,x89602)),f323(f323(f258(x89601,x89602),x89603),x89604)),f323(f278(x89602,x89601),x89605)))+~P101(f323(f323(f325(f871(x89602,x89601)),f323(f323(f258(x89602,x89601),x89604),x89603)),x89605))
% 188.07/187.97 [8978]~P101(f323(f323(x89781,x89785),x89784))+P101(f323(f323(x89781,f323(f261(x89782,x89783),f323(f323(f258(x89782,x89783),x89784),x89785))),f323(f257(x89782,x89783),f323(f323(f258(x89782,x89783),x89784),x89785))))
% 188.07/187.97 [9008]~P101(f323(f323(f325(f871(x90082,x90081)),f323(f323(f258(x90082,x90081),x90084),x90083)),f323(f278(x90081,x90082),x90085)))+P101(f323(f323(f325(f871(x90081,x90082)),f323(f323(f258(x90081,x90082),x90083),x90084)),x90085))
% 188.07/187.97 [9042]~P101(f323(f323(f325(f871(x90423,x90421)),f323(f323(f258(x90423,x90421),x90425),x90422)),x90424))+P101(f323(f323(f325(x90421),x90422),f323(f277(x90423,x90421,x90424),f323(f323(f301(x90423),x90425),f188(f872(x90423,a860))))))
% 188.07/187.97 [9088]P101(f323(f323(f325(f871(x90881,x90882)),f323(f323(f258(x90881,x90882),x90883),x90884)),x90885))+~P101(f323(f323(f325(x90882),x90884),f323(f277(x90881,x90882,x90885),f323(f323(f301(x90881),x90883),f188(f872(x90881,a860))))))
% 188.07/187.97 [9108]E(f323(f323(f323(f70(x91081,f869(x91082)),f182(x91081,x91082,x91083,x91084)),x91085),f200(x91082)),f182(x91081,x91082,x91083,f323(f323(f22(f872(x91081,a860)),x91084),f323(f323(f301(x91081),x91085),f188(f872(x91081,a860))))))+~P101(f323(f323(f325(x91081),x91085),x91084))
% 188.07/187.97 [9179]~P72(x91791)+E(f323(f323(f6(a865,x91791),x91792),f294(a865,f323(f323(f78(a865),x91793),x91794),f323(f323(f78(a865),x91795),x91794))),f323(f323(f6(a865,x91791),f323(f323(f8(a865,x91791,a865),x91792),f323(f323(f7(a865,a865,a865),f78(a865)),x91794))),f294(a865,x91793,x91795)))
% 188.07/187.97 [9198]~P72(x91981)+E(f323(f323(f6(a865,x91981),x91982),f323(f293(a865,f323(f323(f78(a865),x91983),x91984)),f323(f323(f78(a865),x91985),x91984))),f323(f323(f6(a865,x91981),f323(f323(f8(a865,x91981,a865),x91982),f323(f323(f7(a865,a865,a865),f78(a865)),x91984))),f323(f293(a865,x91983),x91985)))
% 188.07/187.97 [9251]~P27(x92511,x92512,x92513,f246(f872(x92511,a860)))+E(f323(f323(f147(x92511,x92512),x92513),f323(f129(x92511,f323(f323(f8(a860,a860,x92511),a318),f323(a320,x92514))),x92515)),f323(f129(x92512,f323(f323(f8(a860,a860,x92512),a318),f323(a320,f323(x92513,x92514)))),f323(f323(f147(x92511,x92512),x92513),x92515)))
% 188.07/187.97 [9268]~P27(x92681,x92682,x92683,f323(f323(f301(x92681),x92684),f323(f166(x92681),x92685)))+E(f323(f323(f147(x92681,x92682),x92683),f323(f129(x92681,f323(f323(f8(a860,a860,x92681),a318),f323(a320,x92684))),x92685)),f323(f129(x92682,f323(f323(f8(a860,a860,x92682),a318),f323(a320,f323(x92683,x92684)))),f323(f323(f147(x92681,x92682),x92683),x92685)))
% 188.07/187.97 [9423]P101(f323(f323(f325(f871(f866(x94231),f866(x94231))),f323(f323(f258(f866(x94231),f866(x94231)),f323(f323(f144(x94231),x94232),x94233)),f323(f323(f144(x94231),x94234),x94233))),f150(x94231,x94235)))+~P101(f323(f323(f325(f871(x94231,x94231)),f323(f323(f258(x94231,x94231),x94232),x94234)),x94235))
% 188.07/187.97 [9545]E(f323(f323(f301(x95451),f745(x95452,x95453,x95454,x95455,x95451)),f747(x95452,x95453,x95454,x95455,x95451)),f323(f323(f301(x95451),x95454),x95453))+~P101(f323(f60(x95451,x95455,f323(f323(f301(x95451),x95454),x95453)),x95452))
% 188.07/187.97 [9546]E(f323(f323(f301(x95461),f767(x95462,x95463,x95464,x95465,x95461)),f776(x95462,x95463,x95464,x95465,x95461)),f323(f323(f301(x95461),x95464),x95463))+~P101(f323(f60(x95461,x95465,f323(f323(f301(x95461),x95464),x95463)),x95462))
% 188.07/187.97 [9629]P101(f323(f323(f325(x96291),f642(x96292,x96293,x96294,x96295,x96291)),x96294))+P101(f323(f323(f323(f40(x96291,f872(x96295,a860)),x96294),x96293),x96292))
% 188.07/187.97 [9634]P101(f323(f323(f325(x96341),f639(x96342,x96343,x96341,x96344,x96345)),x96343))+P101(f323(f323(f325(x96345),x96344),f323(f323(f40(x96341,f872(x96345,a860)),x96343),x96342)))
% 188.07/187.97 [9642]P101(f323(f323(f325(x96421),f641(x96422,x96423,x96421,x96424,x96425)),x96423))+P101(f323(f323(f237(f872(x96425,a860)),x96424),f323(f323(f40(x96421,f872(x96425,a860)),x96423),x96422)))
% 188.07/187.97 [9644]P101(f323(f323(x96441,f447(x96442,x96441,x96443,x96444,x96445)),x96442))+~P101(f323(f323(f323(f39(x96445,f872(x96444,a860)),x96443),x96441),x96442))
% 188.07/187.97 [9648]P101(f323(f323(f325(x96481),f447(x96482,x96483,x96484,x96485,x96481)),x96484))+~P101(f323(f323(f323(f39(x96481,f872(x96485,a860)),x96484),x96483),x96482))
% 188.07/187.97 [9658]P101(f323(f323(f325(x96581),f453(x96582,x96583,x96581,x96584,x96585)),x96583))+~P101(f323(f323(f325(x96585),x96584),f323(f323(f39(x96581,f872(x96585,a860)),x96583),x96582)))
% 188.07/187.97 [9664]P101(f323(f323(f325(x96641),x96642),f323(x96643,f453(x96643,x96644,x96645,x96642,x96641))))+~P101(f323(f323(f325(x96641),x96642),f323(f323(f39(x96645,f872(x96641,a860)),x96644),x96643)))
% 188.07/187.97 [9758]~P101(f323(f323(x97584,f642(x97585,x97584,x97583,x97582,x97581)),x97585))+P101(f323(f323(f323(f40(x97581,f872(x97582,a860)),x97583),x97584),x97585))
% 188.07/187.97 [9761]~P101(f323(f323(f325(x97611),x97612),f323(x97615,f639(x97615,x97614,x97613,x97612,x97611))))+P101(f323(f323(f325(x97611),x97612),f323(f323(f40(x97613,f872(x97611,a860)),x97614),x97615)))
% 188.07/187.97 [9765]~P101(f323(f323(f237(f872(x97651,a860)),x97652),f323(x97655,f641(x97655,x97654,x97653,x97652,x97651))))+P101(f323(f323(f237(f872(x97651,a860)),x97652),f323(f323(f40(x97653,f872(x97651,a860)),x97654),x97655)))
% 188.07/187.97 [9835]~P101(f323(f323(f325(x98351),f745(x98355,x98354,x98353,x98352,x98351)),f747(x98355,x98354,x98353,x98352,x98351)))+~P101(f323(f60(x98351,x98352,f323(f323(f301(x98351),x98353),x98354)),x98355))
% 188.07/187.97 [9836]~P101(f323(f323(f325(x98361),f767(x98365,x98364,x98363,x98362,x98361)),f776(x98365,x98364,x98363,x98362,x98361)))+~P101(f323(f60(x98361,x98362,f323(f323(f301(x98361),x98363),x98364)),x98365))
% 188.07/187.97 [9837]~P101(f323(f323(f325(f871(x98371,x98371)),f323(f323(f258(x98371,x98371),x98372),x98375)),f323(f323(f183(f871(x98371,x98371),a860),f323(a112,x98374)),x98373)))+P101(f323(f323(f325(f871(x98371,x98371)),f323(f323(f258(x98371,x98371),x98372),f755(x98373,x98374,x98375,x98372,x98371))),f323(f323(f183(f871(x98371,x98371),a860),x98374),x98373)))
% 188.07/187.97 [9844]P101(f323(f64(x98441,x98441,x98442,f745(x98443,x98444,x98445,x98442,x98441),f747(x98443,x98444,x98445,x98442,x98441)),x98443))+~P101(f323(f60(x98441,x98442,f323(f323(f301(x98441),x98445),x98444)),x98443))
% 188.07/187.97 [9845]P101(f323(f64(x98451,x98451,x98452,f767(x98453,x98454,x98455,x98452,x98451),f776(x98453,x98454,x98455,x98452,x98451)),x98453))+~P101(f323(f60(x98451,x98452,f323(f323(f301(x98451),x98455),x98454)),x98453))
% 188.07/187.97 [9857]~P103(x98571)+P16(x98571,f323(f323(f147(x98572,x98571),x98573),f323(f129(x98572,f323(f323(f7(x98572,x98571,a860),f323(f323(f8(x98571,f872(x98571,a860),x98572),a320),x98573)),f323(x98574,x98575))),x98575)))
% 188.07/187.97 [9897]~P101(f323(f323(f325(x98972),x98975),f323(f277(x98971,x98972,x98974),x98973)))+P101(f323(f323(f325(f871(x98971,x98972)),f323(f323(f258(x98971,x98972),f502(x98973,x98974,x98971,x98975,x98972)),x98975)),x98974))
% 188.07/187.97 [9898]~P101(f323(f323(f325(x98982),x98985),f323(f277(x98981,x98982,x98984),x98983)))+P101(f323(f323(f325(f871(x98981,x98982)),f323(f323(f258(x98981,x98982),f529(x98983,x98984,x98981,x98985,x98982)),x98985)),x98984))
% 188.07/187.97 [9918]~P101(f323(f323(f325(f871(x99181,x99181)),f323(f323(f258(x99181,x99181),x99185),x99184)),f323(f323(f183(f871(x99181,x99181),a860),f323(a112,x99183)),x99182)))+P101(f323(f323(f325(f871(x99181,x99181)),f323(f323(f258(x99181,x99181),f755(x99182,x99183,x99184,x99185,x99181)),x99184)),x99182))
% 188.07/187.97 [9921]~P101(f323(f323(f325(f871(x99211,x99211)),f323(f323(f258(x99211,x99211),x99215),x99214)),f323(f323(f183(f871(x99211,x99211),a860),f323(a112,x99213)),x99212)))+P101(f323(f323(f325(f871(x99211,x99211)),f323(f323(f258(x99211,x99211),f753(x99212,x99213,x99214,x99215,x99211)),x99214)),f323(f323(f183(f871(x99211,x99211),a860),x99213),x99212)))
% 188.07/187.97 [9922]~P101(f323(f323(f325(f871(x99221,x99221)),f323(f323(f258(x99221,x99221),x99225),x99224)),f323(f323(f183(f871(x99221,x99221),a860),f323(a112,x99223)),x99222)))+P101(f323(f323(f325(f871(x99221,x99221)),f323(f323(f258(x99221,x99221),f754(x99222,x99223,x99224,x99225,x99221)),x99224)),f323(f323(f183(f871(x99221,x99221),a860),x99223),x99222)))
% 188.07/187.97 [9923]~P101(f323(f323(f325(f871(f866(x99231),f866(x99231))),f323(f323(f258(f866(x99231),f866(x99231)),x99235),f323(f323(f144(x99231),x99234),x99233))),f151(x99231,x99232)))+P101(f323(f323(f325(f871(x99231,x99231)),f323(f323(f258(x99231,x99231),f577(x99232,x99233,x99234,x99235,x99231)),x99234)),x99232))
% 188.07/187.97 [7027]E(x70271,f200(x70272))+E(f177(x70273,x70272,f323(f323(f323(f70(x70273,f869(x70272)),x70274),x70275),x70271)),f323(f323(f301(x70273),x70275),f177(x70273,x70272,x70274)))
% 188.07/187.97 [7515]~E(x75153,f188(f872(x75152,a860)))+E(f323(f323(f110(f872(x75151,a860)),f323(f323(f39(x75152,f872(x75151,a860)),x75153),x75154)),x75155),x75155)
% 188.07/187.97 [7516]~E(x75163,f188(f872(x75162,a860)))+E(f323(f323(f101(f872(x75161,a860)),f323(f323(f40(x75162,f872(x75161,a860)),x75163),x75164)),x75165),x75165)
% 188.07/187.97 [7875]~E(x78755,f200(x78752))+E(f177(x78751,x78752,f323(f323(f323(f70(x78751,f869(x78752)),x78753),x78754),x78755)),f323(f323(f22(f872(x78751,a860)),f177(x78751,x78752,x78753)),f323(f323(f301(x78751),x78754),f188(f872(x78751,a860)))))
% 188.07/187.97 [7942]~E(x79423,f188(f872(x79422,a860)))+E(f323(f323(f22(f872(x79421,a860)),f323(f323(f40(x79422,f872(x79421,a860)),x79423),x79424)),x79425),f323(f323(f22(f872(x79421,a860)),f246(f872(x79421,a860))),x79425))
% 188.07/187.97 [8067]E(f323(f323(f152(x80671,f323(f323(f121(x80671),x80672),x80673)),x80674),x80675),f323(f323(f121(x80671),f323(f323(f152(x80671,x80672),x80674),x80675)),x80673))+~P101(f323(f323(f238(a865),x80674),f323(f189(f866(x80671)),x80672)))
% 188.07/187.97 [8180]P101(f323(f323(f325(x81801),x81805),f323(f166(x81801),x81803)))+E(f323(f323(f179(x81801,x81802),f323(f323(f175(x81801,x81802),x81803),f323(f323(f147(x81801,x81802),x81804),x81803))),x81805),f200(x81802))
% 188.07/187.97 [8305]~P101(f323(f323(f325(x83051),x83055),f323(f166(x83051),x83053)))+E(f323(f323(f179(x83051,x83052),f323(f323(f175(x83051,x83052),x83053),f323(f323(f147(x83051,x83052),x83054),x83053))),x83055),f323(f230(x83052),f323(x83054,x83055)))
% 188.07/187.97 [8345]E(f323(f323(f158(x83451),f323(f323(f147(a865,x83451),x83452),f132(a865,f323(f293(a865,x83453),x83454)))),x83455),f323(x83452,f323(f323(f78(a865),x83453),x83455)))+~P101(f323(f323(f238(a865),x83455),f323(f323(f22(a865),x83454),x83453)))
% 188.07/187.97 [8360]E(x83601,f2(a99))+E(f119(x83602,x83603,f323(x83604,f323(f323(f22(a99),x83601),f76(a99))),f323(f323(f7(x83602,a99,f867(f869(x83603))),x83605),x83601)),f323(f197(x83602,x83603,x83604,x83605),x83601))
% 188.07/187.97 [8385]~E(x83853,f188(f872(x83851,a860)))+E(f323(f323(f39(x83851,f872(x83852,a860)),x83853),f323(f323(f8(f872(x83852,a860),f872(x83852,a860),x83851),f323(f110(f872(x83852,a860)),x83854)),x83855)),f188(f872(x83852,a860)))
% 188.07/187.97 [8386]~E(x83863,f188(f872(x83861,a860)))+E(f323(f323(f40(x83861,f872(x83862,a860)),x83863),f323(f323(f8(f872(x83862,a860),f872(x83862,a860),x83861),f323(f22(f872(x83862,a860)),x83864)),x83865)),f246(f872(x83862,a860)))
% 188.07/187.97 [8387]~E(x83873,f188(f872(x83871,a860)))+E(f323(f323(f40(x83871,f872(x83872,a860)),x83873),f323(f323(f8(f872(x83872,a860),f872(x83872,a860),x83871),f323(f101(f872(x83872,a860)),x83874)),x83875)),f246(f872(x83872,a860)))
% 188.07/187.97 [8389]~P139(x83892)+E(f323(f323(f6(x83891,x83892),f323(f323(f8(x83892,x83892,x83891),f323(f79(x83892),x83893)),x83894)),x83895),f323(f323(f79(x83892),x83893),f323(f323(f6(x83891,x83892),x83894),x83895)))
% 188.07/187.97 [8677]E(x86771,f188(f872(x86772,a860)))+E(f323(f323(f39(x86772,f872(x86773,a860)),x86771),f323(f323(f8(f872(x86773,a860),f872(x86773,a860),x86772),f323(f110(f872(x86773,a860)),x86774)),x86775)),f323(f323(f110(f872(x86773,a860)),x86774),f323(f323(f39(x86772,f872(x86773,a860)),x86771),x86775)))
% 188.07/187.97 [8678]E(x86781,f188(f872(x86782,a860)))+E(f323(f323(f40(x86782,f872(x86783,a860)),x86781),f323(f323(f8(f872(x86783,a860),f872(x86783,a860),x86782),f323(f22(f872(x86783,a860)),x86784)),x86785)),f323(f323(f22(f872(x86783,a860)),x86784),f323(f323(f39(x86782,f872(x86783,a860)),x86781),x86785)))
% 188.07/187.97 [8679]E(x86791,f188(f872(x86792,a860)))+E(f323(f323(f40(x86792,f872(x86793,a860)),x86791),f323(f323(f8(f872(x86793,a860),f872(x86793,a860),x86792),f323(f101(f872(x86793,a860)),x86794)),x86795)),f323(f323(f101(f872(x86793,a860)),x86794),f323(f323(f40(x86792,f872(x86793,a860)),x86791),x86795)))
% 188.07/187.97 [8883]~P101(f323(f323(f238(a865),f323(x88834,x88832)),f323(x88834,x88833)))+P101(f323(f323(f325(f871(x88831,x88831)),f323(f323(f258(x88831,x88831),x88832),x88833)),f146(x88831,f323(f323(f144(f872(x88831,a865)),x88834),x88835))))
% 188.07/187.97 [9142]~P27(x91422,x91421,x91423,f323(f323(f110(f872(x91422,a860)),x91424),x91425))+E(f323(f323(f101(f872(x91421,a860)),f323(f302(x91422,x91421,x91423),f323(f323(f22(f872(x91422,a860)),x91424),x91425))),f323(f302(x91422,x91421,x91423),f323(f323(f22(f872(x91422,a860)),x91425),x91424))),f188(f872(x91421,a860)))
% 188.07/187.97 [9389]~P27(x93893,x93891,x93895,f246(f872(x93893,a860)))+E(f323(f71(x93891,x93892,x93893,f323(f71(x93893,x93892,x93891,x93894),f91(x93893,x93891,f246(f872(x93893,a860)),x93895))),x93895),x93894)
% 188.07/187.97 [9419]~P101(f323(f323(f237(f872(x94193,a860)),f323(f277(x94191,x94193,x94194),x94192)),x94195))+P101(f323(f323(f237(f872(x94191,a860)),x94192),f323(f77(f872(x94191,a860)),f323(f277(x94193,x94191,f323(f278(x94191,x94193),x94194)),f323(f77(f872(x94193,a860)),x94195)))))
% 188.07/187.97 [9446]~P27(x94461,x94462,x94463,f323(f323(f301(x94461),x94464),x94465))+~P101(f323(f323(f325(x94462),f323(x94463,x94464)),f323(f302(x94461,x94462,x94463),f323(f323(f22(f872(x94461,a860)),x94465),f323(f323(f301(x94461),x94464),f188(f872(x94461,a860)))))))
% 188.07/187.97 [9498]P101(f323(f323(f237(f872(x94981,a860)),f323(f277(x94982,x94981,x94983),x94984)),x94985))+~P101(f323(f323(f237(f872(x94982,a860)),x94984),f323(f77(f872(x94982,a860)),f323(f277(x94981,x94982,f323(f278(x94982,x94981),x94983)),f323(f77(f872(x94981,a860)),x94985)))))
% 188.07/187.97 [9574]~P82(x95741)+P101(f323(f323(f237(x95741),f323(f73(x95741),f323(f323(f22(x95741),f323(f323(f78(x95741),x95742),x95743)),f323(f323(f78(x95741),x95744),x95745)))),f323(f323(f78(x95741),f323(f73(x95741),f323(f323(f22(x95741),x95742),x95744))),f323(f73(x95741),f323(f323(f22(x95741),x95743),x95745)))))
% 188.07/187.97 [9679]P101(f323(f323(f325(x96791),f458(x96792,x96793,x96794,x96791,x96795)),x96794))+P101(f323(f323(f237(f872(x96795,a860)),f323(f323(f39(x96791,f872(x96795,a860)),x96794),x96793)),x96792))
% 188.07/187.97 [9875]~P101(f323(f323(f237(f872(x98751,a860)),f323(x98754,f458(x98755,x98754,x98753,x98752,x98751))),x98755))+P101(f323(f323(f237(f872(x98751,a860)),f323(f323(f39(x98752,f872(x98751,a860)),x98753),x98754)),x98755))
% 188.07/187.97 [8489]E(f323(f323(f121(x84891),x84892),f323(f323(f152(x84891,x84893),f323(f323(f22(a865),x84894),f323(f189(f866(x84891)),x84892))),x84895)),f323(f323(f152(x84891,f323(f323(f121(x84891),x84892),x84893)),x84894),x84895))+P101(f323(f323(f238(a865),x84894),f323(f189(f866(x84891)),x84892)))
% 188.07/187.97 [8516]~P136(x85161)+E(f323(f323(f78(x85161),f323(f323(f79(x85161),x85162),x85163)),f323(f323(f78(x85161),f323(f323(f79(x85161),x85164),x85163)),x85165)),f323(f323(f78(x85161),f323(f323(f79(x85161),f323(f323(f78(x85161),x85162),x85164)),x85163)),x85165))
% 188.07/187.97 [9098]~P139(x90981)+E(f323(f159(x90981),f323(f323(f147(x90982,x90981),f323(f323(f8(x90981,x90981,x90982),f323(f79(x90981),x90983)),x90984)),x90985)),f323(f323(f79(x90981),x90983),f323(f159(x90981),f323(f323(f147(x90982,x90981),x90984),x90985))))
% 188.07/187.97 [9267]E(f323(f189(f866(x92671)),f323(f323(f169(x92671),f323(f323(f235(a865),f323(f189(f866(x92671)),x92672)),f323(f189(f866(x92673)),x92674))),x92672)),f323(f189(f866(x92673)),f323(f323(f169(x92673),f323(f323(f235(a865),f323(f189(f866(x92671)),x92672)),f323(f189(f866(x92673)),x92674))),x92674)))+P101(f323(x92675,f323(f323(f175(x92671,x92673),x92672),x92674)))
% 188.07/187.97 [9509]~P139(x95092)+E(f323(f323(f6(x95091,x95092),f323(f323(f7(x95091,x95092,x95092),f323(f323(f8(x95092,f872(x95092,x95092),x95091),f79(x95092)),x95093)),x95094)),x95095),f323(f323(f79(x95092),f323(f323(f6(x95091,x95092),x95093),x95095)),x95094))
% 188.07/187.97 [9510]~P63(x95102)+E(f323(f323(f6(x95101,x95102),f323(f323(f7(x95101,x95102,x95102),f323(f323(f8(x95102,f872(x95102,x95102),x95101),f281(x95102)),x95103)),x95104)),x95105),f323(f323(f281(x95102),f323(f323(f6(x95101,x95102),x95103),x95105)),x95104))
% 188.07/187.97 [9517]~P60(x95172)+E(f323(f323(f6(x95171,x95172),f323(f323(f18(x95171,x95172,x95172),f323(f323(f8(x95172,f872(x95172,x95172),x95171),f22(x95172)),x95173)),x95174)),x95175),f323(f323(f22(x95172),f323(f323(f6(x95171,x95172),x95173),x95175)),f323(f323(f6(x95171,x95172),x95174),x95175)))
% 188.07/187.97 [9518]~P72(x95182)+E(f323(f323(f6(x95181,x95182),f323(f323(f18(x95181,x95182,x95182),f323(f323(f8(x95182,f872(x95182,x95182),x95181),f78(x95182)),x95183)),x95184)),x95185),f323(f323(f78(x95182),f323(f323(f6(x95181,x95182),x95183),x95185)),f323(f323(f6(x95181,x95182),x95184),x95185)))
% 188.07/187.97 [9519]~P68(x95192)+E(f323(f323(f9(x95191,x95192),f323(f323(f18(x95191,x95192,x95192),f323(f323(f8(x95192,f872(x95192,x95192),x95191),f79(x95192)),x95193)),x95194)),x95195),f323(f323(f79(x95192),f323(f323(f9(x95191,x95192),x95193),x95195)),f323(f323(f9(x95191,x95192),x95194),x95195)))
% 188.07/187.97 [9558]~E(x95583,f188(f872(x95581,a860)))+E(f323(f323(f39(x95581,f872(x95582,a860)),x95583),f323(f323(f7(x95581,f872(x95582,a860),f872(x95582,a860)),f323(f323(f8(f872(x95582,a860),f872(f872(x95582,a860),f872(x95582,a860)),x95581),f110(f872(x95582,a860))),x95584)),x95585)),f188(f872(x95582,a860)))
% 188.07/187.97 [9559]~E(x95593,f188(f872(x95591,a860)))+E(f323(f323(f40(x95591,f872(x95592,a860)),x95593),f323(f323(f7(x95591,f872(x95592,a860),f872(x95592,a860)),f323(f323(f8(f872(x95592,a860),f872(f872(x95592,a860),f872(x95592,a860)),x95591),f22(f872(x95592,a860))),x95594)),x95595)),f246(f872(x95592,a860)))
% 188.07/187.97 [9560]~E(x95603,f188(f872(x95601,a860)))+E(f323(f323(f40(x95601,f872(x95602,a860)),x95603),f323(f323(f7(x95601,f872(x95602,a860),f872(x95602,a860)),f323(f323(f8(f872(x95602,a860),f872(f872(x95602,a860),f872(x95602,a860)),x95601),f101(f872(x95602,a860))),x95604)),x95605)),f246(f872(x95602,a860)))
% 188.07/187.97 [9582]E(x95821,f188(f872(x95822,a860)))+E(f323(f323(f39(x95822,f872(x95823,a860)),x95821),f323(f323(f7(x95822,f872(x95823,a860),f872(x95823,a860)),f323(f323(f8(f872(x95823,a860),f872(f872(x95823,a860),f872(x95823,a860)),x95822),f110(f872(x95823,a860))),x95824)),x95825)),f323(f323(f110(f872(x95823,a860)),f323(f323(f39(x95822,f872(x95823,a860)),x95821),x95824)),x95825))
% 188.07/187.97 [9583]E(x95831,f188(f872(x95832,a860)))+E(f323(f323(f40(x95832,f872(x95833,a860)),x95831),f323(f323(f7(x95832,f872(x95833,a860),f872(x95833,a860)),f323(f323(f8(f872(x95833,a860),f872(f872(x95833,a860),f872(x95833,a860)),x95832),f22(f872(x95833,a860))),x95834)),x95835)),f323(f323(f22(f872(x95833,a860)),f323(f323(f40(x95832,f872(x95833,a860)),x95831),x95834)),x95835))
% 188.07/187.97 [9584]E(x95841,f188(f872(x95842,a860)))+E(f323(f323(f40(x95842,f872(x95843,a860)),x95841),f323(f323(f7(x95842,f872(x95843,a860),f872(x95843,a860)),f323(f323(f8(f872(x95843,a860),f872(f872(x95843,a860),f872(x95843,a860)),x95842),f101(f872(x95843,a860))),x95844)),x95845)),f323(f323(f101(f872(x95843,a860)),f323(f323(f40(x95842,f872(x95843,a860)),x95841),x95844)),x95845))
% 188.07/187.97 [9149]~P101(f323(f323(f237(a865),x91491),x91494))+E(f323(f323(f22(a865),f323(f323(f78(a865),f323(f323(f79(a865),x91491),x91492)),x91493)),f323(f323(f78(a865),f323(f323(f79(a865),x91494),x91492)),x91495)),f323(f323(f22(a865),x91493),f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f22(a865),x91494),x91491)),x91492)),x91495)))
% 188.07/187.97 [9739]~P139(x97391)+E(f323(f159(x97391),f323(f323(f147(x97392,x97391),f323(f323(f7(x97392,x97391,x97391),f323(f323(f8(x97391,f872(x97391,x97391),x97392),f79(x97391)),x97393)),x97394)),x97395)),f323(f323(f79(x97391),f323(f159(x97391),f323(f323(f147(x97392,x97391),x97393),x97395))),x97394))
% 188.07/187.97 [9745]~P60(x97451)+E(f323(f159(x97451),f323(f323(f147(x97452,x97451),f323(f323(f18(x97452,x97451,x97451),f323(f323(f8(x97451,f872(x97451,x97451),x97452),f22(x97451)),x97453)),x97454)),x97455)),f323(f323(f22(x97451),f323(f159(x97451),f323(f323(f147(x97452,x97451),x97453),x97455))),f323(f159(x97451),f323(f323(f147(x97452,x97451),x97454),x97455))))
% 188.07/187.97 [9746]~P72(x97461)+E(f323(f159(x97461),f323(f323(f147(x97462,x97461),f323(f323(f18(x97462,x97461,x97461),f323(f323(f8(x97461,f872(x97461,x97461),x97462),f78(x97461)),x97463)),x97464)),x97465)),f323(f323(f78(x97461),f323(f159(x97461),f323(f323(f147(x97462,x97461),x97463),x97465))),f323(f159(x97461),f323(f323(f147(x97462,x97461),x97464),x97465))))
% 188.07/187.97 [9888]P101(f323(x98881,f323(f323(f175(x98882,x98883),x98884),x98885)))+~P101(f323(x98881,f323(f323(f175(x98882,x98883),f323(f323(f169(x98882),f323(f323(f235(a865),f323(f189(f866(x98882)),x98884)),f323(f189(f866(x98883)),x98885))),x98884)),f323(f323(f169(x98883),f323(f323(f235(a865),f323(f189(f866(x98882)),x98884)),f323(f189(f866(x98883)),x98885))),x98885))))
% 188.07/187.97 [10122]~P101(f323(f323(f325(f871(x101222,x101221)),f323(f323(f258(x101222,x101221),x101224),x101225)),f323(f278(x101221,x101222),x101223)))+P101(f323(f323(f247(x101221,x101222,f323(f323(f7(x101221,f872(f871(x101221,x101222),a860),f872(x101222,a860)),f323(f323(f8(f872(x101222,f872(f872(f871(x101221,x101222),a860),a860)),f872(f872(f871(x101221,x101222),a860),f872(x101222,a860)),x101221),f7(x101222,f872(f871(x101221,x101222),a860),a860)),f323(f323(f8(f872(x101222,f871(x101221,x101222)),f872(x101222,f872(f872(f871(x101221,x101222),a860),a860)),x101221),f323(f8(f871(x101221,x101222),f872(f872(f871(x101221,x101222),a860),a860),x101222),f325(f871(x101221,x101222)))),f258(x101221,x101222)))),x101223)),x101224),x101225))
% 188.07/187.97 [10132]P101(f323(f323(f325(f871(x101321,x101322)),f323(f323(f258(x101321,x101322),x101323),x101324)),f323(f278(x101322,x101321),x101325)))+~P101(f323(f323(f247(x101322,x101321,f323(f323(f7(x101322,f872(f871(x101322,x101321),a860),f872(x101321,a860)),f323(f323(f8(f872(x101321,f872(f872(f871(x101322,x101321),a860),a860)),f872(f872(f871(x101322,x101321),a860),f872(x101321,a860)),x101322),f7(x101321,f872(f871(x101322,x101321),a860),a860)),f323(f323(f8(f872(x101321,f871(x101322,x101321)),f872(x101321,f872(f872(f871(x101322,x101321),a860),a860)),x101322),f323(f8(f871(x101322,x101321),f872(f872(f871(x101322,x101321),a860),a860),x101321),f325(f871(x101322,x101321)))),f258(x101322,x101321)))),x101325)),x101323),x101324))
% 188.07/187.97 [9388]~P101(f323(f323(f237(a865),x93884),x93881))+E(f323(f323(f22(a865),f323(f323(f78(a865),f323(f323(f79(a865),x93881),x93882)),x93883)),f323(f323(f78(a865),f323(f323(f79(a865),x93884),x93882)),x93885)),f323(f323(f22(a865),f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f22(a865),x93881),x93884)),x93882)),x93883)),x93885))
% 188.07/187.97 [5244]E(x52441,x52442)+~E(f27(x52443,x52444,x52441),f27(x52445,x52446,x52442))
% 188.07/187.97 [5245]E(x52451,x52452)+~E(f27(x52453,x52451,x52454),f27(x52455,x52452,x52456))
% 188.07/187.97 [5246]E(x52461,x52462)+~E(f27(x52461,x52463,x52464),f27(x52462,x52465,x52466))
% 188.07/187.97 [5247]E(x52471,x52472)+~E(f26(x52473,x52474,x52471),f26(x52475,x52476,x52472))
% 188.07/187.97 [5248]E(x52481,x52482)+~E(f26(x52483,x52481,x52484),f26(x52485,x52482,x52486))
% 188.07/187.97 [5249]E(x52491,x52492)+~E(f26(x52491,x52493,x52494),f26(x52492,x52495,x52496))
% 188.07/187.97 [6673]E(f323(f180(x66731,x66732,x66733,x66734),x66735),f323(f230(x66732),x66736))+~E(f323(x66734,x66735),f323(f230(x66732),x66736))
% 188.07/187.97 [6816]E(f323(f232(f869(x68161),x68162,f200(x68161),x68163),f323(x68164,x68165)),f323(x68163,x68166))+~E(f323(x68164,x68165),f323(f230(x68162),x68166))
% 188.07/187.97 [8330]~P21(x83305,x83301,x83302,x83306)+E(f323(f71(x83301,x83301,x83301,f323(x83302,x83303)),f323(x83302,x83304)),f323(f71(x83301,x83301,x83301,f323(x83302,x83304)),f323(x83302,x83303)))
% 188.07/187.97 [8562]~P53(x85624,x85625,x85622,x85621,x85626)+E(f323(x85621,f323(x85622,x85623)),x85623)
% 188.07/187.97 [8731]P27(x87311,x87312,x87313,x87314)+~P27(x87311,x87315,f323(f71(x87312,x87315,x87311,x87316),x87313),x87314)
% 188.07/187.97 [8818]~P27(x88184,x88182,f323(f71(x88181,x88182,x88184,x88183),x88185),x88186)+P27(x88181,x88182,x88183,f323(f302(x88184,x88181,x88185),x88186))
% 188.07/187.97 [9520]P101(f323(f59(x95201),x95202))+~P101(f323(f64(x95201,x95203,x95204,x95205,x95202),x95206))
% 188.07/187.97 [9529]~P101(f323(f323(f325(x95294),x95293),f291(x95294,x95295,x95291,x95292,x95296)))+P101(f323(f323(x95291,x95292),x95293))
% 188.07/187.97 [9530]~P101(f323(f323(f325(x95304),x95303),f288(x95304,x95301,x95305,x95302,x95306)))+P101(f323(f323(x95301,x95302),x95303))
% 188.07/187.97 [9531]~P101(f323(f323(f325(x95314),x95312),f291(x95314,x95311,x95315,x95316,x95313)))+P101(f323(f323(x95311,x95312),x95313))
% 188.07/187.97 [9532]~P101(f323(f323(f325(x95324),x95322),f288(x95324,x95325,x95321,x95326,x95323)))+P101(f323(f323(x95321,x95322),x95323))
% 188.07/187.97 [5746]E(x57461,x57462)+~E(f323(f323(f258(x57463,x57464),x57465),x57461),f323(f323(f258(x57463,x57464),x57466),x57462))
% 188.07/187.97 [5748]E(x57481,x57482)+~E(f323(f323(f258(x57483,x57484),x57481),x57485),f323(f323(f258(x57483,x57484),x57482),x57486))
% 188.07/187.97 [5872]~P18(x58725,x58726,x58721)+E(f323(f323(x58721,x58722),f323(f323(x58721,x58723),x58724)),f323(f323(x58721,x58723),f323(f323(x58721,x58722),x58724)))
% 188.07/187.97 [7267]~P33(x72674,x72671,f323(f323(f144(x72674),x72672),x72675),f323(f323(f144(x72674),x72673),x72676))+P101(f323(f323(x72671,x72672),x72673))
% 188.07/187.97 [7629]P33(x76291,x76292,x76293,x76294)+~P33(x76291,x76292,f323(f323(f144(x76291),x76295),x76293),f323(f323(f144(x76291),x76296),x76294))
% 188.07/187.97 [8668]~P53(x86685,x86681,x86682,x86686,x86684)+P101(f323(f323(f325(x86681),f323(x86682,x86683)),x86684))
% 188.07/187.97 [8845]E(f323(f74(x88451,x88452,x88453,x88454,x88455),x88456),f323(x88453,x88456))+P101(f323(f323(f325(x88451),x88456),x88455))
% 188.07/187.97 [8866]~E(x88663,f323(f323(f144(x88661),x88665),x88666))+P101(f323(f323(f325(f871(f866(x88661),f866(x88661))),f323(f323(f258(f866(x88661),f866(x88661)),x88662),f323(f323(f121(x88661),x88662),x88663))),f140(x88661,x88664)))
% 188.07/187.97 [8872]E(f323(f74(x88721,x88722,x88723,x88724,x88725),x88726),f323(x88724,x88726))+~P101(f323(f323(f325(x88721),x88726),x88725))
% 188.07/187.97 [8878]E(f323(f181(x88781,x88782,x88783,x88784,x88785),x88786),f323(x88783,x88786))+P101(f323(f323(f325(x88781),x88786),f323(f166(x88781),x88784)))
% 188.07/187.97 [9102]~P35(x91021,x91022,x91023,x91025,x91026)+P35(x91021,x91022,x91023,f323(f323(f169(x91021),x91024),x91025),f323(f323(f169(x91022),x91024),x91026))
% 188.07/187.97 [9103]~P35(x91031,x91032,x91033,x91035,x91036)+P35(x91031,x91032,x91033,f323(f323(f131(x91031),x91034),x91035),f323(f323(f131(x91032),x91034),x91036))
% 188.07/187.97 [9594]~P25(x95944,x95942,x95945,x95943,x95946,x95941)+E(f323(x95941,f188(f872(x95942,a860))),x95943)
% 188.07/187.97 [9838]~E(f323(x98384,f323(f257(x98381,x98383),x98385)),f323(x98386,f323(f257(x98381,x98383),x98385)))+E(f323(f263(x98381,x98382,x98383,x98383,x98384,f32(x98383)),x98385),f323(f263(x98381,x98382,x98383,x98383,x98386,f32(x98383)),x98385))
% 188.07/187.97 [9839]~E(f323(x98394,f323(f261(x98391,x98392),x98395)),f323(x98396,f323(f261(x98391,x98392),x98395)))+E(f323(f263(x98391,x98391,x98392,x98393,f32(x98391),x98394),x98395),f323(f263(x98391,x98391,x98392,x98393,f32(x98391),x98396),x98395))
% 188.07/187.97 [9884]~E(f323(f263(x98842,x98846,x98843,x98843,x98841,f32(x98843)),x98844),f323(f263(x98842,x98846,x98843,x98843,x98845,f32(x98843)),x98844))+E(f323(x98841,f323(f257(x98842,x98843),x98844)),f323(x98845,f323(f257(x98842,x98843),x98844)))
% 188.07/187.97 [9885]~E(f323(f263(x98852,x98852,x98853,x98856,f32(x98852),x98851),x98854),f323(f263(x98852,x98852,x98853,x98856,f32(x98852),x98855),x98854))+E(f323(x98851,f323(f261(x98852,x98853),x98854)),f323(x98855,f323(f261(x98852,x98853),x98854)))
% 188.07/187.97 [8772]P101(f323(f323(f325(x87721),x87722),x87723))+~P101(f323(f323(f325(f871(x87721,x87724)),f323(f323(f258(x87721,x87724),x87722),x87725)),f323(f323(f260(x87721,x87724),x87723),x87726)))
% 188.07/187.97 [8788]P101(f323(f323(f325(x87881),x87882),f323(x87883,x87884)))+~P101(f323(f323(f325(f871(x87885,x87881)),f323(f323(f258(x87885,x87881),x87884),x87882)),f323(f323(f260(x87885,x87881),x87886),x87883)))
% 188.07/187.97 [8875]~E(f323(f189(f866(x88751)),x88754),f323(f189(f866(x88752)),x88755))+E(f181(x88751,x88752,x88753,x88754,f323(f323(f121(x88752),x88755),x88756)),f181(x88751,x88752,x88753,x88754,x88755))
% 188.07/187.97 [8876]~E(f323(f189(f866(x88761)),x88764),f323(f189(f866(x88762)),x88766))+E(f181(x88761,x88762,x88763,f323(f323(f121(x88761),x88764),x88765),x88766),f181(x88761,x88762,x88763,x88764,x88766))
% 188.07/187.97 [9120]P101(f323(f323(f325(x91201),x91204),f177(x91201,x91202,x91206)))+E(f180(x91201,x91202,f323(f323(f323(f70(x91201,f869(x91202)),x91203),x91204),f323(f230(x91202),x91205)),x91206),f323(f323(f323(f70(x91201,f869(x91202)),f180(x91201,x91202,x91203,x91206)),x91204),f323(f230(x91202),x91205)))
% 188.07/187.97 [9219]P101(f323(f323(f325(f871(x92191,x92191)),f323(f323(f258(x92191,x92191),f323(x92192,x92193)),f323(x92192,x92194))),x92195))+~P101(f323(f323(f325(f871(x92196,x92196)),f323(f323(f258(x92196,x92196),x92193),x92194)),f323(f323(f279(x92191,x92196),x92195),x92192)))
% 188.07/187.97 [9238]~P101(f323(f323(f325(f871(x92384,x92384)),f323(f323(f258(x92384,x92384),f323(x92386,x92382)),f323(x92386,x92383))),x92385))+P101(f323(f323(f325(f871(x92381,x92381)),f323(f323(f258(x92381,x92381),x92382),x92383)),f323(f323(f279(x92384,x92381),x92385),x92386)))
% 188.07/187.97 [9887]E(f323(f323(f258(x98871,x98872),f780(x98873,x98874,x98875,x98876,x98872,x98871)),f781(x98873,x98874,x98875,x98876,x98872,x98871)),x98876)+~P101(f323(f323(f325(f871(x98871,x98872)),x98876),f323(f323(f280(x98871,x98875,x98872),x98874),x98873)))
% 188.07/187.97 [10085]~P101(f323(f323(f325(f871(x100851,x100856)),x100855),f323(f323(f280(x100851,x100852,x100856),x100854),x100853)))+P101(f323(f323(f325(f871(x100851,x100852)),f323(f323(f258(x100851,x100852),f780(x100853,x100854,x100852,x100855,x100856,x100851)),f782(x100853,x100854,x100852,x100855,x100856,x100851))),x100854))
% 188.07/187.97 [10086]~P101(f323(f323(f325(f871(x100866,x100862)),x100865),f323(f323(f280(x100866,x100861,x100862),x100864),x100863)))+P101(f323(f323(f325(f871(x100861,x100862)),f323(f323(f258(x100861,x100862),f782(x100863,x100864,x100861,x100865,x100862,x100866)),f781(x100863,x100864,x100861,x100865,x100862,x100866))),x100863))
% 188.07/187.97 [6140]~E(x61406,x61404)+E(f323(f323(f323(f323(f70(x61401,x61402),x61403),x61404),x61405),x61406),x61405)
% 188.07/187.97 [6189]E(x61891,x61892)+E(f323(f323(f323(f323(f70(x61893,x61894),x61895),x61892),x61896),x61891),f323(x61895,x61891))
% 188.07/187.97 [7700]~P6(x77002)+E(f323(f323(f39(x77001,x77002),x77003),f323(f323(f7(x77001,x77004,x77002),x77005),x77006)),f323(f323(f323(f39(x77001,f872(x77004,x77002)),x77003),x77005),x77006))
% 188.07/187.97 [7701]~P6(x77012)+E(f323(f323(f40(x77011,x77012),x77013),f323(f323(f7(x77011,x77014,x77012),x77015),x77016)),f323(f323(f323(f40(x77011,f872(x77014,x77012)),x77013),x77015),x77016))
% 188.07/187.97 [8471]E(f323(f323(f39(x84711,f872(x84712,a860)),x84713),f323(f323(f8(f872(x84712,a860),f872(x84712,a860),x84711),f323(f301(x84712),x84714)),x84715)),f323(f323(f301(x84712),x84714),f323(f323(f39(x84711,f872(x84712,a860)),x84713),x84715)))+~P101(f323(f323(f325(x84711),x84716),x84713))
% 188.07/187.97 [8922]~P6(x89222)+E(f323(f323(f39(x89221,x89222),x89223),f323(f323(f8(f872(x89224,x89222),x89222,x89221),f323(f39(x89224,x89222),x89225)),f323(f7(x89224,x89221,x89222),x89226))),f323(f323(f39(x89224,x89222),x89225),f323(f323(f8(f872(x89221,x89222),x89222,x89224),f323(f39(x89221,x89222),x89223)),x89226)))
% 188.07/187.97 [8923]~P6(x89232)+E(f323(f323(f40(x89231,x89232),x89233),f323(f323(f8(f872(x89234,x89232),x89232,x89231),f323(f40(x89234,x89232),x89235)),f323(f7(x89234,x89231,x89232),x89236))),f323(f323(f40(x89234,x89232),x89235),f323(f323(f8(f872(x89231,x89232),x89232,x89234),f323(f40(x89231,x89232),x89233)),x89236)))
% 188.07/187.97 [9129]P101(f323(f323(f325(x91291),x91292),f323(f166(x91291),x91293)))+~P101(f323(f323(f325(f871(x91294,x91291)),f323(f323(f258(x91294,x91291),x91295),x91292)),f323(f166(f871(x91294,x91291)),f323(f323(f175(x91294,x91291),x91296),x91293))))
% 188.07/187.97 [9130]P101(f323(f323(f325(x91301),x91302),f323(f166(x91301),x91303)))+~P101(f323(f323(f325(f871(x91301,x91304)),f323(f323(f258(x91301,x91304),x91302),x91305)),f323(f166(f871(x91301,x91304)),f323(f323(f175(x91301,x91304),x91303),x91306))))
% 188.07/187.97 [9235]P101(f323(f323(f237(f872(x92351,a860)),f323(f277(x92352,x92351,x92353),x92354)),x92355))+~P101(f323(f323(f237(f872(f871(x92352,x92351),a860)),x92353),f323(f323(f260(x92352,x92351),x92356),f323(f16(f872(x92351,a860),x92352),x92355))))
% 188.07/187.97 [9239]~P28(x92394,x92392,x92395,f246(f872(x92394,a860)),f246(f872(x92392,a860)))+E(f323(f323(f40(x92391,f872(x92392,a860)),x92393),f323(f323(f8(f872(x92394,a860),f872(x92392,a860),x92391),f302(x92394,x92392,x92395)),x92396)),f323(f302(x92394,x92392,x92395),f323(f323(f40(x92391,f872(x92394,a860)),x92393),x92396)))
% 188.07/187.97 [9422]P101(f323(f323(f325(f871(f866(x94221),f866(x94221))),f323(f323(f258(f866(x94221),f866(x94221)),f323(f323(f144(x94221),x94222),x94223)),f323(f323(f144(x94221),x94224),x94225))),f140(x94221,x94226)))+~P101(f323(f323(f325(f871(x94221,x94221)),f323(f323(f258(x94221,x94221),x94222),x94224)),x94226))
% 188.07/187.97 [9883]E(f323(f323(f258(x98831,x98832),f697(x98833,x98834,x98835,x98832,x98831,x98836)),f698(x98833,x98834,x98835,x98832,x98831,x98836)),x98836)+P101(f323(f323(f325(x98835),x98834),f323(f323(f262(x98831,x98832,f872(x98835,a860)),x98833),x98836)))
% 188.07/187.97 [9889]E(f323(f323(f258(x98891,x98892),f699(x98893,x98894,x98892,x98891,x98895,x98896)),f700(x98893,x98894,x98892,x98891,x98895,x98896)),x98893)+~P101(f323(f323(f325(x98896),x98895),f323(f323(f262(x98891,x98892,f872(x98896,a860)),x98894),x98893)))
% 188.07/187.97 [10045]P101(f323(f323(f325(x100451),x100452),f323(f323(x100453,f699(x100454,x100453,x100455,x100456,x100452,x100451)),f700(x100454,x100453,x100455,x100456,x100452,x100451))))+~P101(f323(f323(f325(x100451),x100452),f323(f323(f262(x100456,x100455,f872(x100451,a860)),x100453),x100454)))
% 188.07/187.97 [10063]~P101(f323(f323(f325(x100631),x100632),f323(f323(x100635,f697(x100635,x100632,x100631,x100634,x100633,x100636)),f698(x100635,x100632,x100631,x100634,x100633,x100636))))+P101(f323(f323(f325(x100631),x100632),f323(f323(f262(x100633,x100634,f872(x100631,a860)),x100635),x100636)))
% 188.07/187.97 [7818]P101(f323(f323(f325(x78181),x78184),x78186))+E(f182(x78181,x78182,f323(f323(f323(f70(x78181,f869(x78182)),x78183),x78184),x78185),x78186),f182(x78181,x78182,x78183,x78186))
% 188.07/187.97 [7898]P101(f323(f323(f325(x78981),x78984),x78986))+E(f323(f302(x78981,x78982,f323(f323(f323(f70(x78981,x78982),x78983),x78984),x78985)),x78986),f323(f302(x78981,x78982,x78983),x78986))
% 188.07/187.97 [7926]P101(f323(f323(f325(x79261),x79264),f323(f166(x79261),x79266)))+E(f323(f323(f147(x79261,x79262),f323(f323(f323(f70(x79261,x79262),x79263),x79264),x79265)),x79266),f323(f323(f147(x79261,x79262),x79263),x79266))
% 188.07/187.97 [8377]E(x83771,x83772)+E(f323(f323(f152(x83773,f323(f323(f152(x83773,x83774),x83771),x83775)),x83772),x83776),f323(f323(f152(x83773,f323(f323(f152(x83773,x83774),x83772),x83776)),x83771),x83775))
% 188.07/187.97 [8928]~P101(f323(f323(f325(x89283),x89286),x89285))+E(f323(f323(f301(x89281),x89282),f323(f302(x89283,x89281,x89284),f323(f323(f22(f872(x89283,a860)),x89285),f323(f323(f301(x89283),x89286),f188(f872(x89283,a860)))))),f323(f302(x89283,x89281,f323(f323(f323(f70(x89283,x89281),x89284),x89286),x89282)),x89285))
% 188.07/187.97 [9701]E(f181(x97011,x97012,x97013,f323(f323(f121(x97011),x97014),f323(f323(f144(x97011),x97015),f113(x97011))),x97016),f323(f323(f323(f70(x97011,f869(x97012)),f181(x97011,x97012,x97013,x97014,x97016)),x97015),f323(f230(x97012),f323(f323(f158(x97012),x97016),f323(f189(f866(x97011)),x97014)))))+~P101(f323(f323(f238(a865),f323(f189(f866(x97011)),x97014)),f323(f189(f866(x97012)),x97016)))
% 188.07/187.97 [8712]~E(x87123,x87126)+E(f323(f323(f179(x87121,x87122),f323(f323(f144(f871(x87121,x87122)),f323(f323(f258(x87121,x87122),x87123),x87124)),x87125)),x87126),f323(f230(x87122),x87124))
% 188.07/187.97 [8742]E(x87421,x87422)+E(f323(f323(f179(x87423,x87424),f323(f323(f144(f871(x87423,x87424)),f323(f323(f258(x87423,x87424),x87421),x87425)),x87426)),x87422),f323(f323(f179(x87423,x87424),x87426),x87422))
% 188.07/187.97 [9001]~P101(f323(f323(x90014,x90015),x90016))+P101(f323(f323(f323(f323(f110(f872(x90011,f872(x90012,a860))),x90013),x90014),x90015),x90016))
% 188.07/187.97 [9003]~P101(f323(f323(x90033,x90035),x90036))+P101(f323(f323(f323(f323(f110(f872(x90031,f872(x90032,a860))),x90033),x90034),x90035),x90036))
% 188.07/187.97 [9289]P101(f323(f323(x92891,x92892),x92893))+~P101(f323(f323(f323(f323(f101(f872(x92894,f872(x92895,a860))),x92896),x92891),x92892),x92893))
% 188.07/187.97 [9290]P101(f323(f323(x92901,x92902),x92903))+~P101(f323(f323(f323(f323(f101(f872(x92904,f872(x92905,a860))),x92901),x92906),x92902),x92903))
% 188.07/187.97 [9723]~P72(x97232)+E(f323(f323(f6(x97231,x97232),f323(f323(f7(x97231,f872(x97233,a860),x97232),f323(f323(f8(f872(x97233,x97232),f872(f872(x97233,a860),x97232),x97231),f6(x97233,x97232)),x97234)),x97235)),x97236),f323(f323(f6(f871(x97231,x97233),x97232),f323(f262(x97231,x97233,x97232),x97234)),f323(f323(f260(x97231,x97233),x97236),f323(f16(f872(x97233,a860),x97231),x97235))))
% 188.07/187.97 [9724]~P68(x97242)+E(f323(f323(f9(x97241,x97242),f323(f323(f7(x97241,f872(x97243,a860),x97242),f323(f323(f8(f872(x97243,x97242),f872(f872(x97243,a860),x97242),x97241),f9(x97243,x97242)),x97244)),x97245)),x97246),f323(f323(f9(f871(x97241,x97243),x97242),f323(f262(x97241,x97243,x97242),x97244)),f323(f323(f260(x97241,x97243),x97246),f323(f16(f872(x97243,a860),x97241),x97245))))
% 188.07/187.97 [9866]~P72(x98662)+E(f323(f323(f6(x98661,x98662),f323(f323(f7(x98661,f872(x98663,a860),x98662),f323(f323(f8(f872(x98663,x98662),f872(f872(x98663,a860),x98662),x98661),f6(x98663,x98662)),f323(f7(x98663,x98661,x98662),x98664))),x98665)),x98666),f323(f323(f6(x98663,x98662),f323(f323(f7(x98663,f872(x98661,a860),x98662),f323(f323(f8(f872(x98661,x98662),f872(f872(x98661,a860),x98662),x98663),f6(x98661,x98662)),x98664)),x98666)),x98665))
% 188.07/187.97 [9563]~P101(f323(f323(f325(x95631),x95635),x95634))+E(f323(f323(f323(f70(x95631,f869(x95632)),f182(x95631,x95632,x95633,f323(f323(f22(f872(x95631,a860)),x95634),f323(f323(f301(x95631),x95635),f188(f872(x95631,a860)))))),x95635),x95636),f182(x95631,x95632,f323(f323(f323(f70(x95631,f869(x95632)),x95633),x95635),x95636),x95634))
% 188.07/187.97 [10142]~P101(f323(f323(f325(f871(x101421,x101422)),f323(f323(f258(x101421,x101422),x101425),x101426)),f323(f323(f110(f872(f871(x101421,x101422),a860)),x101423),x101424)))+P101(f323(f323(f323(f323(f110(f872(x101421,f872(x101422,a860))),f323(f323(f7(x101421,f872(f871(x101421,x101422),a860),f872(x101422,a860)),f323(f323(f8(f872(x101422,f872(f872(f871(x101421,x101422),a860),a860)),f872(f872(f871(x101421,x101422),a860),f872(x101422,a860)),x101421),f7(x101422,f872(f871(x101421,x101422),a860),a860)),f323(f323(f8(f872(x101422,f871(x101421,x101422)),f872(x101422,f872(f872(f871(x101421,x101422),a860),a860)),x101421),f323(f8(f871(x101421,x101422),f872(f872(f871(x101421,x101422),a860),a860),x101422),f325(f871(x101421,x101422)))),f258(x101421,x101422)))),x101423)),f323(f323(f7(x101421,f872(f871(x101421,x101422),a860),f872(x101422,a860)),f323(f323(f8(f872(x101422,f872(f872(f871(x101421,x101422),a860),a860)),f872(f872(f871(x101421,x101422),a860),f872(x101422,a860)),x101421),f7(x101422,f872(f871(x101421,x101422),a860),a860)),f323(f323(f8(f872(x101422,f871(x101421,x101422)),f872(x101422,f872(f872(f871(x101421,x101422),a860),a860)),x101421),f323(f8(f871(x101421,x101422),f872(f872(f871(x101421,x101422),a860),a860),x101422),f325(f871(x101421,x101422)))),f258(x101421,x101422)))),x101424)),x101425),x101426))
% 188.07/187.97 [10143]~P101(f323(f323(f325(f871(x101431,x101432)),f323(f323(f258(x101431,x101432),x101435),x101436)),f323(f323(f101(f872(f871(x101431,x101432),a860)),x101433),x101434)))+P101(f323(f323(f323(f323(f101(f872(x101431,f872(x101432,a860))),f323(f323(f7(x101431,f872(f871(x101431,x101432),a860),f872(x101432,a860)),f323(f323(f8(f872(x101432,f872(f872(f871(x101431,x101432),a860),a860)),f872(f872(f871(x101431,x101432),a860),f872(x101432,a860)),x101431),f7(x101432,f872(f871(x101431,x101432),a860),a860)),f323(f323(f8(f872(x101432,f871(x101431,x101432)),f872(x101432,f872(f872(f871(x101431,x101432),a860),a860)),x101431),f323(f8(f871(x101431,x101432),f872(f872(f871(x101431,x101432),a860),a860),x101432),f325(f871(x101431,x101432)))),f258(x101431,x101432)))),x101433)),f323(f323(f7(x101431,f872(f871(x101431,x101432),a860),f872(x101432,a860)),f323(f323(f8(f872(x101432,f872(f872(f871(x101431,x101432),a860),a860)),f872(f872(f871(x101431,x101432),a860),f872(x101432,a860)),x101431),f7(x101432,f872(f871(x101431,x101432),a860),a860)),f323(f323(f8(f872(x101432,f871(x101431,x101432)),f872(x101432,f872(f872(f871(x101431,x101432),a860),a860)),x101431),f323(f8(f871(x101431,x101432),f872(f872(f871(x101431,x101432),a860),a860),x101432),f325(f871(x101431,x101432)))),f258(x101431,x101432)))),x101434)),x101435),x101436))
% 188.07/187.97 [10149]P101(f323(f323(f325(f871(x101491,x101492)),f323(f323(f258(x101491,x101492),x101493),x101494)),f323(f323(f110(f872(f871(x101491,x101492),a860)),x101495),x101496)))+~P101(f323(f323(f323(f323(f110(f872(x101491,f872(x101492,a860))),f323(f323(f7(x101491,f872(f871(x101491,x101492),a860),f872(x101492,a860)),f323(f323(f8(f872(x101492,f872(f872(f871(x101491,x101492),a860),a860)),f872(f872(f871(x101491,x101492),a860),f872(x101492,a860)),x101491),f7(x101492,f872(f871(x101491,x101492),a860),a860)),f323(f323(f8(f872(x101492,f871(x101491,x101492)),f872(x101492,f872(f872(f871(x101491,x101492),a860),a860)),x101491),f323(f8(f871(x101491,x101492),f872(f872(f871(x101491,x101492),a860),a860),x101492),f325(f871(x101491,x101492)))),f258(x101491,x101492)))),x101495)),f323(f323(f7(x101491,f872(f871(x101491,x101492),a860),f872(x101492,a860)),f323(f323(f8(f872(x101492,f872(f872(f871(x101491,x101492),a860),a860)),f872(f872(f871(x101491,x101492),a860),f872(x101492,a860)),x101491),f7(x101492,f872(f871(x101491,x101492),a860),a860)),f323(f323(f8(f872(x101492,f871(x101491,x101492)),f872(x101492,f872(f872(f871(x101491,x101492),a860),a860)),x101491),f323(f8(f871(x101491,x101492),f872(f872(f871(x101491,x101492),a860),a860),x101492),f325(f871(x101491,x101492)))),f258(x101491,x101492)))),x101496)),x101493),x101494))
% 188.07/187.97 [10150]P101(f323(f323(f325(f871(x101501,x101502)),f323(f323(f258(x101501,x101502),x101503),x101504)),f323(f323(f101(f872(f871(x101501,x101502),a860)),x101505),x101506)))+~P101(f323(f323(f323(f323(f101(f872(x101501,f872(x101502,a860))),f323(f323(f7(x101501,f872(f871(x101501,x101502),a860),f872(x101502,a860)),f323(f323(f8(f872(x101502,f872(f872(f871(x101501,x101502),a860),a860)),f872(f872(f871(x101501,x101502),a860),f872(x101502,a860)),x101501),f7(x101502,f872(f871(x101501,x101502),a860),a860)),f323(f323(f8(f872(x101502,f871(x101501,x101502)),f872(x101502,f872(f872(f871(x101501,x101502),a860),a860)),x101501),f323(f8(f871(x101501,x101502),f872(f872(f871(x101501,x101502),a860),a860),x101502),f325(f871(x101501,x101502)))),f258(x101501,x101502)))),x101505)),f323(f323(f7(x101501,f872(f871(x101501,x101502),a860),f872(x101502,a860)),f323(f323(f8(f872(x101502,f872(f872(f871(x101501,x101502),a860),a860)),f872(f872(f871(x101501,x101502),a860),f872(x101502,a860)),x101501),f7(x101502,f872(f871(x101501,x101502),a860),a860)),f323(f323(f8(f872(x101502,f871(x101501,x101502)),f872(x101502,f872(f872(f871(x101501,x101502),a860),a860)),x101501),f323(f8(f871(x101501,x101502),f872(f872(f871(x101501,x101502),a860),a860),x101502),f325(f871(x101501,x101502)))),f258(x101501,x101502)))),x101506)),x101503),x101504))
% 188.07/187.97 [10138]~P101(f323(f323(f325(f871(x101382,x101383)),f323(f323(f258(x101382,x101383),x101385),x101386)),f323(f323(f39(x101381,f872(f871(x101382,x101383),a860)),f246(f872(x101381,a860))),x101384)))+P101(f323(f323(f323(f323(f39(x101381,f872(x101382,f872(x101383,a860))),f246(f872(x101381,a860))),f323(f323(f8(f872(f871(x101382,x101383),a860),f872(x101382,f872(x101383,a860)),x101381),f323(f7(x101382,f872(f871(x101382,x101383),a860),f872(x101383,a860)),f323(f323(f8(f872(x101383,f872(f872(f871(x101382,x101383),a860),a860)),f872(f872(f871(x101382,x101383),a860),f872(x101383,a860)),x101382),f7(x101383,f872(f871(x101382,x101383),a860),a860)),f323(f323(f8(f872(x101383,f871(x101382,x101383)),f872(x101383,f872(f872(f871(x101382,x101383),a860),a860)),x101382),f323(f8(f871(x101382,x101383),f872(f872(f871(x101382,x101383),a860),a860),x101383),f325(f871(x101382,x101383)))),f258(x101382,x101383))))),x101384)),x101385),x101386))
% 188.07/187.97 [10139]~P101(f323(f323(f325(f871(x101392,x101393)),f323(f323(f258(x101392,x101393),x101395),x101396)),f323(f323(f40(x101391,f872(f871(x101392,x101393),a860)),f246(f872(x101391,a860))),x101394)))+P101(f323(f323(f323(f323(f40(x101391,f872(x101392,f872(x101393,a860))),f246(f872(x101391,a860))),f323(f323(f8(f872(f871(x101392,x101393),a860),f872(x101392,f872(x101393,a860)),x101391),f323(f7(x101392,f872(f871(x101392,x101393),a860),f872(x101393,a860)),f323(f323(f8(f872(x101393,f872(f872(f871(x101392,x101393),a860),a860)),f872(f872(f871(x101392,x101393),a860),f872(x101393,a860)),x101392),f7(x101393,f872(f871(x101392,x101393),a860),a860)),f323(f323(f8(f872(x101393,f871(x101392,x101393)),f872(x101393,f872(f872(f871(x101392,x101393),a860),a860)),x101392),f323(f8(f871(x101392,x101393),f872(f872(f871(x101392,x101393),a860),a860),x101393),f325(f871(x101392,x101393)))),f258(x101392,x101393))))),x101394)),x101395),x101396))
% 188.07/187.97 [10146]P101(f323(f323(f325(f871(x101461,x101462)),f323(f323(f258(x101461,x101462),x101463),x101464)),f323(f323(f39(x101465,f872(f871(x101461,x101462),a860)),f246(f872(x101465,a860))),x101466)))+~P101(f323(f323(f323(f323(f39(x101465,f872(x101461,f872(x101462,a860))),f246(f872(x101465,a860))),f323(f323(f8(f872(f871(x101461,x101462),a860),f872(x101461,f872(x101462,a860)),x101465),f323(f7(x101461,f872(f871(x101461,x101462),a860),f872(x101462,a860)),f323(f323(f8(f872(x101462,f872(f872(f871(x101461,x101462),a860),a860)),f872(f872(f871(x101461,x101462),a860),f872(x101462,a860)),x101461),f7(x101462,f872(f871(x101461,x101462),a860),a860)),f323(f323(f8(f872(x101462,f871(x101461,x101462)),f872(x101462,f872(f872(f871(x101461,x101462),a860),a860)),x101461),f323(f8(f871(x101461,x101462),f872(f872(f871(x101461,x101462),a860),a860),x101462),f325(f871(x101461,x101462)))),f258(x101461,x101462))))),x101466)),x101463),x101464))
% 188.07/187.97 [10147]P101(f323(f323(f325(f871(x101471,x101472)),f323(f323(f258(x101471,x101472),x101473),x101474)),f323(f323(f40(x101475,f872(f871(x101471,x101472),a860)),f246(f872(x101475,a860))),x101476)))+~P101(f323(f323(f323(f323(f40(x101475,f872(x101471,f872(x101472,a860))),f246(f872(x101475,a860))),f323(f323(f8(f872(f871(x101471,x101472),a860),f872(x101471,f872(x101472,a860)),x101475),f323(f7(x101471,f872(f871(x101471,x101472),a860),f872(x101472,a860)),f323(f323(f8(f872(x101472,f872(f872(f871(x101471,x101472),a860),a860)),f872(f872(f871(x101471,x101472),a860),f872(x101472,a860)),x101471),f7(x101472,f872(f871(x101471,x101472),a860),a860)),f323(f323(f8(f872(x101472,f871(x101471,x101472)),f872(x101472,f872(f872(f871(x101471,x101472),a860),a860)),x101471),f323(f8(f871(x101471,x101472),f872(f872(f871(x101471,x101472),a860),a860),x101472),f325(f871(x101471,x101472)))),f258(x101471,x101472))))),x101476)),x101473),x101474))
% 188.07/187.97 [7377]E(f323(x73771,f323(x73772,x73773)),f323(x73774,x73773))+~E(f323(f71(x73775,x73776,x73777,x73771),x73772),x73774)
% 188.07/187.97 [9593]~P24(x95933,x95934,x95931,x95935,x95936,x95937)+E(f323(f323(x95931,x95932),x95932),x95932)
% 188.07/187.97 [9963]~E(f323(f232(f869(x99637),x99631,f200(x99637),x99635),f323(x99634,x99633)),f323(f230(x99637),x99632))+E(f323(f230(x99631),f838(x99632,x99633,x99634,x99635,x99636,x99637,x99631)),f323(x99634,x99633))
% 188.07/187.97 [9964]~E(f323(f232(f869(x99646),x99647,f200(x99646),x99641),f323(x99644,x99643)),f323(f230(x99646),x99642))+E(f323(x99641,f838(x99642,x99643,x99644,x99641,x99645,x99646,x99647)),f323(f230(x99646),x99642))
% 188.07/187.97 [5969]~E(f323(f323(f147(x59691,x59695),x59696),x59692),f323(f323(f147(x59693,x59695),x59697),x59694))+E(f323(f189(f866(x59691)),x59692),f323(f189(f866(x59693)),x59694))
% 188.07/187.97 [7453]E(x74531,x74532)+~E(f323(f323(f323(f70(x74533,f869(x74534)),x74535),x74536),f323(f230(x74534),x74531)),f323(f323(f323(f70(x74533,f869(x74534)),x74537),x74536),f323(f230(x74534),x74532)))
% 188.07/187.97 [8409]E(f323(x84091,f323(x84092,x84093)),f323(x84094,x84093))+~E(f323(f71(x84095,x84096,x84097,x84091),x84092),f323(f71(x84096,x84096,x84097,f32(x84096)),x84094))
% 188.07/187.97 [8761]~P35(x87614,x87615,x87611,f323(f323(f144(x87614),x87612),x87616),f323(f323(f144(x87615),x87613),x87617))+P101(f323(f323(x87611,x87612),x87613))
% 188.07/187.97 [9136]P35(x91361,x91362,x91363,x91364,x91365)+~P35(x91361,x91362,x91363,f323(f323(f144(x91361),x91366),x91364),f323(f323(f144(x91362),x91367),x91365))
% 188.07/187.97 [9762]P101(f323(f323(x97621,x97622),f666(x97623,x97622,x97624,x97621)))+~P101(f323(f323(f259(x97625,x97626,x97627,x97621,x97624),x97622),x97623))
% 188.07/187.97 [9783]P101(f323(f323(x97831,f666(x97832,x97833,x97831,x97834)),x97832))+~P101(f323(f323(f259(x97835,x97836,x97837,x97834,x97831),x97833),x97832))
% 188.07/187.97 [6012]E(x60121,x60122)+~E(f323(f323(f323(f90(x60123),x60124),x60125),x60121),f323(f323(f323(f90(x60123),x60126),x60127),x60122))
% 188.07/187.97 [6013]E(x60131,x60132)+~E(f323(f323(f323(f90(x60133),x60134),x60131),x60135),f323(f323(f323(f90(x60133),x60136),x60132),x60137))
% 188.07/187.97 [6014]E(x60141,x60142)+~E(f323(f323(f323(f90(x60143),x60141),x60144),x60145),f323(f323(f323(f90(x60143),x60142),x60146),x60147))
% 188.07/187.97 [8881]~P22(x88816,x88811,x88813,x88817)+E(f323(f71(x88811,x88811,x88812,f323(x88813,x88814)),f323(f71(x88811,x88811,x88812,f323(x88813,x88814)),x88815)),f323(f71(x88811,x88811,x88812,f323(x88813,x88814)),x88815))
% 188.07/187.97 [9242]~P35(x92423,x92422,x92424,f323(f323(f147(x92421,x92423),x92425),x92426),x92427)+P35(x92421,x92422,f323(f323(f8(x92423,f872(x92422,a860),x92421),x92424),x92425),x92426,x92427)
% 188.07/187.97 [9264]P35(x92641,x92642,x92643,f323(f323(f147(x92644,x92641),x92645),x92646),x92647)+~P35(x92644,x92642,f323(f323(f8(x92641,f872(x92642,a860),x92644),x92643),x92645),x92646,x92647)
% 188.07/187.97 [9681]E(f181(x96811,x96812,f323(f323(f323(f70(x96811,f869(x96812)),x96813),x96814),f323(f230(x96812),x96815)),x96816,x96817),f323(f323(f323(f70(x96811,f869(x96812)),f181(x96811,x96812,x96813,x96816,x96817)),x96814),f323(f230(x96812),x96815)))+P101(f323(f323(f325(x96811),x96814),f323(f166(x96811),x96816)))
% 188.07/187.97 [8880]~P101(f323(f323(f325(x88801),x88802),f323(f323(x88805,x88806),x88807)))+P101(f323(f323(f325(x88801),x88802),f323(f323(f262(x88803,x88804,f872(x88801,a860)),x88805),f323(f323(f258(x88803,x88804),x88806),x88807))))
% 188.07/187.97 [9164]P101(f323(f323(f323(x91641,x91642),x91643),x91644))+~P101(f323(f323(f323(f262(x91645,x91646,f872(x91647,a860)),x91641),f323(f323(f258(x91645,x91646),x91642),x91643)),x91644))
% 188.07/187.97 [9304]P101(f323(f323(f325(x93041),f323(f323(x93042,x93043),x93044)),f323(f302(f871(x93045,x93046),x93041,f323(f262(x93045,x93046,x93041),x93042)),x93047)))+~P101(f323(f323(f325(f871(x93045,x93046)),f323(f323(f258(x93045,x93046),x93043),x93044)),x93047))
% 188.07/187.97 [9640]P101(f323(f323(f325(f871(f866(x96401),f866(x96401))),f323(f323(f258(f866(x96401),f866(x96401)),f323(f323(f121(x96401),x96402),f323(f323(f144(x96401),x96403),x96404))),f323(f323(f121(x96401),x96402),f323(f323(f144(x96401),x96405),x96406)))),f140(x96401,x96407)))+~P101(f323(f323(f325(f871(x96401,x96401)),f323(f323(f258(x96401,x96401),x96403),x96405)),x96407))
% 188.07/187.97 [9703]~P35(x97031,x97033,x97034,x97036,f323(f323(f147(x97032,x97033),x97035),x97037))+P35(x97031,x97032,f323(f323(f7(x97031,f872(x97032,x97033),f872(x97032,a860)),f323(f323(f8(f872(x97033,a860),f872(f872(x97032,x97033),f872(x97032,a860)),x97031),f8(x97033,a860,x97032)),x97034)),x97035),x97036,x97037)
% 188.07/187.97 [9787]P35(x97871,x97872,x97873,x97874,f323(f323(f147(x97875,x97872),x97876),x97877))+~P35(x97871,x97875,f323(f323(f7(x97871,f872(x97875,x97872),f872(x97875,a860)),f323(f323(f8(f872(x97872,a860),f872(f872(x97875,x97872),f872(x97875,a860)),x97871),f8(x97872,a860,x97875)),x97873)),x97876),x97874,x97877)
% 188.07/187.97 [9156]E(x91561,x91562)+E(f323(f323(f323(f70(x91563,x91564),f323(f323(f323(f70(x91563,x91564),x91565),x91561),x91566)),x91562),x91567),f323(f323(f323(f70(x91563,x91564),f323(f323(f323(f70(x91563,x91564),x91565),x91562),x91567)),x91561),x91566))
% 188.07/187.97 [9398]E(f181(x93981,x93982,f323(f323(f323(f70(x93981,f869(x93982)),x93983),x93984),f323(f230(x93982),x93985)),x93986,x93987),f181(x93981,x93982,x93983,x93986,x93987))+~P101(f323(f323(f325(x93981),x93984),f323(f166(x93981),f323(f323(f169(x93981),f323(f189(f866(x93982)),x93987)),x93986))))
% 188.07/187.97 [9714]E(f181(x97141,x97142,f323(f323(f323(f70(x97141,f869(x97142)),x97143),x97144),f323(f230(x97142),x97145)),x97146,x97147),f323(f323(f323(f70(x97141,f869(x97142)),f181(x97141,x97142,x97143,x97146,x97147)),x97144),f323(f230(x97142),x97145)))+P101(f323(f323(f325(x97141),x97144),f323(f166(x97141),f323(f323(f169(x97141),f323(f189(f866(x97142)),x97147)),x97146))))
% 188.07/187.97 [10074]P101(f323(f323(f325(x100741),f643(x100742,x100743,x100744,x100745,x100746,x100747,x100741)),x100745))+P101(f323(f323(f323(f323(f40(x100741,f872(x100747,f872(x100746,a860))),x100745),x100744),x100743),x100742))
% 188.07/187.97 [10075]P101(f323(f323(f325(x100751),f463(x100752,x100753,x100754,x100755,x100756,x100757,x100751)),x100755))+~P101(f323(f323(f323(f323(f39(x100751,f872(x100757,f872(x100756,a860))),x100755),x100754),x100753),x100752))
% 188.07/187.97 [10102]P101(f323(f323(f323(x101021,f463(x101022,x101023,x101021,x101024,x101025,x101026,x101027)),x101023),x101022))+~P101(f323(f323(f323(f323(f39(x101027,f872(x101026,f872(x101025,a860))),x101024),x101021),x101023),x101022))
% 188.07/187.97 [10120]~P101(f323(f323(f323(x101205,f643(x101207,x101206,x101205,x101204,x101203,x101202,x101201)),x101206),x101207))+P101(f323(f323(f323(f323(f40(x101201,f872(x101202,f872(x101203,a860))),x101204),x101205),x101206),x101207))
% 188.07/187.97 [10137]~P101(f323(f323(f325(f871(x101371,x101373)),f323(f323(f258(x101371,x101373),x101376),x101377)),f323(f323(f280(x101371,x101372,x101373),x101374),x101375)))+P101(f323(f323(f259(x101371,x101372,x101373,f323(f323(f7(x101371,f872(f871(x101371,x101372),a860),f872(x101372,a860)),f323(f323(f8(f872(x101372,f872(f872(f871(x101371,x101372),a860),a860)),f872(f872(f871(x101371,x101372),a860),f872(x101372,a860)),x101371),f7(x101372,f872(f871(x101371,x101372),a860),a860)),f323(f323(f8(f872(x101372,f871(x101371,x101372)),f872(x101372,f872(f872(f871(x101371,x101372),a860),a860)),x101371),f323(f8(f871(x101371,x101372),f872(f872(f871(x101371,x101372),a860),a860),x101372),f325(f871(x101371,x101372)))),f258(x101371,x101372)))),x101374),f323(f323(f7(x101372,f872(f871(x101372,x101373),a860),f872(x101373,a860)),f323(f323(f8(f872(x101373,f872(f872(f871(x101372,x101373),a860),a860)),f872(f872(f871(x101372,x101373),a860),f872(x101373,a860)),x101372),f7(x101373,f872(f871(x101372,x101373),a860),a860)),f323(f323(f8(f872(x101373,f871(x101372,x101373)),f872(x101373,f872(f872(f871(x101372,x101373),a860),a860)),x101372),f323(f8(f871(x101372,x101373),f872(f872(f871(x101372,x101373),a860),a860),x101373),f325(f871(x101372,x101373)))),f258(x101372,x101373)))),x101375)),x101376),x101377))
% 188.07/187.97 [10145]P101(f323(f323(f325(f871(x101451,x101452)),f323(f323(f258(x101451,x101452),x101453),x101454)),f323(f323(f280(x101451,x101455,x101452),x101456),x101457)))+~P101(f323(f323(f259(x101451,x101455,x101452,f323(f323(f7(x101451,f872(f871(x101451,x101455),a860),f872(x101455,a860)),f323(f323(f8(f872(x101455,f872(f872(f871(x101451,x101455),a860),a860)),f872(f872(f871(x101451,x101455),a860),f872(x101455,a860)),x101451),f7(x101455,f872(f871(x101451,x101455),a860),a860)),f323(f323(f8(f872(x101455,f871(x101451,x101455)),f872(x101455,f872(f872(f871(x101451,x101455),a860),a860)),x101451),f323(f8(f871(x101451,x101455),f872(f872(f871(x101451,x101455),a860),a860),x101455),f325(f871(x101451,x101455)))),f258(x101451,x101455)))),x101456),f323(f323(f7(x101455,f872(f871(x101455,x101452),a860),f872(x101452,a860)),f323(f323(f8(f872(x101452,f872(f872(f871(x101455,x101452),a860),a860)),f872(f872(f871(x101455,x101452),a860),f872(x101452,a860)),x101455),f7(x101452,f872(f871(x101455,x101452),a860),a860)),f323(f323(f8(f872(x101452,f871(x101455,x101452)),f872(x101452,f872(f872(f871(x101455,x101452),a860),a860)),x101455),f323(f8(f871(x101455,x101452),f872(f872(f871(x101455,x101452),a860),a860),x101452),f325(f871(x101455,x101452)))),f258(x101455,x101452)))),x101457)),x101453),x101454))
% 188.07/187.97 [10084]~P139(x100842)+E(f323(f323(f6(x100841,x100842),f323(f323(f7(x100841,f872(x100843,a860),x100842),f323(f323(f8(f872(x100843,x100842),f872(f872(x100843,a860),x100842),x100841),f6(x100843,x100842)),f323(f323(f7(x100841,f872(x100843,x100842),f872(x100843,x100842)),f323(f323(f8(f872(x100842,x100842),f872(f872(x100843,x100842),f872(x100843,x100842)),x100841),f8(x100842,x100842,x100843)),f323(f323(f8(x100842,f872(x100842,x100842),x100841),f79(x100842)),x100844))),x100845))),x100846)),x100847),f323(f323(f79(x100842),f323(f323(f6(x100841,x100842),x100844),x100847)),f323(f323(f6(x100843,x100842),x100845),x100846)))
% 188.07/187.97 [9194]~P21(x91947,x91941,x91943,x91948)+E(f323(f71(x91941,x91941,x91942,f323(x91943,x91944)),f323(f71(x91941,x91941,x91942,f323(x91943,x91945)),x91946)),f323(f71(x91941,x91941,x91942,f323(x91943,x91945)),f323(f71(x91941,x91941,x91942,f323(x91943,x91944)),x91946)))
% 188.07/187.97 [10140]E(f323(f323(f258(x101401,x101402),f323(x101403,f609(x101404,x101405,x101403,x101406,x101407,x101408,x101402,x101401))),f323(x101405,f610(x101404,x101405,x101403,x101406,x101407,x101408,x101402,x101401))),x101408)+~P101(f323(f323(f325(f871(x101401,x101402)),x101408),f323(f302(f871(x101407,x101406),f871(x101401,x101402),f263(x101407,x101401,x101406,x101402,x101403,x101405)),x101404)))
% 188.07/187.97 [10154]~P101(f323(f323(f325(f871(x101548,x101547)),x101546),f323(f302(f871(x101541,x101542),f871(x101548,x101547),f263(x101541,x101548,x101542,x101547,x101545,x101544)),x101543)))+P101(f323(f323(f325(f871(x101541,x101542)),f323(f323(f258(x101541,x101542),f609(x101543,x101544,x101545,x101542,x101541,x101546,x101547,x101548)),f610(x101543,x101544,x101545,x101542,x101541,x101546,x101547,x101548))),x101543))
% 188.07/187.97 [9630]P101(f323(f323(f325(f871(f871(x96301,x96302),f871(x96301,x96302))),f323(f323(f258(f871(x96301,x96302),f871(x96301,x96302)),f323(f323(f258(x96301,x96302),x96303),x96304)),f323(f323(f258(x96301,x96302),x96305),x96306))),f315(x96301,x96302,x96307,x96308)))+~P101(f323(f323(f325(f871(x96301,x96301)),f323(f323(f258(x96301,x96301),x96303),x96305)),x96307))
% 188.07/187.97 [10131]E(f323(f135(x101311,x101312,f323(f7(x101312,x101311,x101311),x101313),f323(x101314,x101315)),x101316),f323(x101314,f323(f135(x101317,x101312,f323(f7(x101312,x101317,x101317),x101318),x101315),x101316)))+P101(f323(f323(f325(x101312),f679(x101315,x101318,x101314,x101313,x101317,x101311,x101316,x101312)),f323(f166(x101312),x101316)))
% 188.07/187.97 [10148]~E(f323(f71(x101481,x101481,x101487,f323(x101483,f679(x101485,x101488,x101484,x101483,x101487,x101481,x101486,x101482))),x101484),f323(f71(x101487,x101481,x101487,x101484),f323(x101488,f679(x101485,x101488,x101484,x101483,x101487,x101481,x101486,x101482))))+E(f323(f135(x101481,x101482,f323(f7(x101482,x101481,x101481),x101483),f323(x101484,x101485)),x101486),f323(x101484,f323(f135(x101487,x101482,f323(f7(x101482,x101487,x101487),x101488),x101485),x101486)))
% 188.07/187.97 [8414]E(f323(x84141,f323(x84142,x84143)),f323(x84144,f323(x84145,x84143)))+~E(f323(f71(x84146,x84147,x84148,x84141),x84142),f323(f71(x84149,x84147,x84148,x84144),x84145))
% 188.07/187.97 [10014]P101(f323(f323(f325(f871(x100141,x100142)),f323(f323(f258(x100141,x100142),f323(x100143,x100144)),f323(x100145,x100146))),f323(f302(f871(x100147,x100148),f871(x100141,x100142),f263(x100147,x100141,x100148,x100142,x100143,x100145)),x100149)))+~P101(f323(f323(f325(f871(x100147,x100148)),f323(f323(f258(x100147,x100148),x100144),x100146)),x100149))
% 188.07/187.97 [8706]~E(f323(x87064,f323(x87065,x87066)),f323(x87069,f323(x870610,x870611)))+E(f323(f323(f71(x87061,x87062,x87063,x87064),x87065),x87066),f323(f323(f71(x87067,x87062,x87068,x87069),x870610),x870611))
% 188.07/187.97 [4586]~P98(x45861)+~P103(x45861)+E(f101(x45861),f235(x45861))
% 188.07/187.97 [4587]~P97(x45871)+~P103(x45871)+E(f110(x45871),f236(x45871))
% 188.07/187.97 [4831]~P116(x48311)+~P90(x48311)+E(f323(f73(x48311),f323(f103(x48311),a97)),f76(x48311))
% 188.07/187.97 [5106]E(x51061,f2(a1))+E(f80(a1,x51061),f323(f77(a1),f76(a1)))+P101(f323(f323(f238(a1),f2(a1)),x51061))
% 188.07/187.97 [5309]E(x53091,f2(a1))+E(f80(a1,x53091),f76(a1))+~P101(f323(f323(f238(a1),f2(a1)),x53091))
% 188.07/187.97 [7271]~P39(x72711)+P101(f323(f59(a1),x72711))+~P101(f323(f59(a865),f323(f302(a1,a865,a104),x72711)))
% 188.07/187.97 [9592]E(x95921,f188(f872(f871(a865,a865),a860)))+~P101(f323(f59(f871(a865,a865)),x95921))+P101(f323(f323(f325(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f258(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),f188(f872(f871(a865,a865),a860))),x95921)),a34))
% 188.07/187.97 [9763]E(x97631,f2(a865))+E(x97631,f323(a112,f2(a865)))+~P101(f323(f323(f238(a865),x97631),f323(f103(a865),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)))))
% 188.07/187.97 [10042]E(x100421,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),x100421),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,x100421))+E(f42(a99,x100421,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))
% 188.07/187.97 [9894]E(x98941,f2(a99))+~E(f42(a99,x98941,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),x98941),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,x98941))
% 188.07/187.97 [4658]~P54(x46581,x46582)+P44(x46581,x46582)+~P45(a860)
% 188.07/187.97 [4596]~P140(x45961)+P30(x45961,x45962)+~E(x45962,f2(x45961))
% 188.07/187.97 [4597]~P103(x45971)+P16(x45971,x45972)+~E(x45972,f113(x45971))
% 188.07/187.97 [4606]~P116(x46061)+~E(x46062,f2(x46061))+E(f80(x46061,x46062),f2(x46061))
% 188.07/187.97 [4607]~P85(x46071)+~E(x46072,f2(x46071))+E(f80(x46071,x46072),f2(x46071))
% 188.07/187.97 [4615]~P140(x46152)+~P30(x46152,x46151)+E(x46151,f2(x46152))
% 188.07/187.97 [4649]~P116(x46492)+~E(f80(x46492,x46491),f2(x46492))+E(x46491,f2(x46492))
% 188.07/187.97 [4665]~P5(x46652)+~P5(x46651)+P5(f872(x46651,x46652))
% 188.07/187.97 [4666]~P5(x46662)+~P5(x46661)+P5(f870(x46661,x46662))
% 188.07/187.97 [4667]~P5(x46672)+~P5(x46671)+P5(f871(x46671,x46672))
% 188.07/187.97 [4668]~P61(x46682)+~P61(x46681)+P61(f872(x46681,x46682))
% 188.07/187.97 [4669]~P61(x46692)+~P61(x46691)+P61(f870(x46691,x46692))
% 188.07/187.97 [4670]~P61(x46702)+~P61(x46701)+P61(f871(x46701,x46702))
% 188.07/187.97 [4671]~P7(x46712)+~P7(x46711)+P7(f194(x46711,x46712))
% 188.07/187.97 [4672]~P141(x46722)+~P141(x46721)+P141(f871(x46721,x46722))
% 188.07/187.97 [4673]~P5(x46731)+~P92(x46732)+P92(f872(x46731,x46732))
% 188.07/187.97 [4803]~P103(x48031)+~P16(x48031,x48032)+P16(x48031,f145(x48031,x48032))
% 188.07/187.97 [5037]~P7(x50372)+~P7(x50371)+P7(f42(a1,x50371,x50372))
% 188.07/187.97 [4617]~P74(x46171)+~E(x46172,f2(x46171))+E(f323(f77(x46171),x46172),x46172)
% 188.07/187.97 [4621]~P134(x46211)+~E(x46212,f2(a1))+E(f323(f102(x46211),x46212),f2(x46211))
% 188.07/187.97 [4622]~P89(x46221)+~E(x46222,f2(a1))+E(f323(f102(x46221),x46222),f2(x46221))
% 188.07/187.97 [4646]~P59(x46461)+~E(f2(x46461),x46462)+E(f323(f77(x46461),x46462),f2(x46461))
% 188.07/187.97 [4647]~P59(x46471)+~E(x46472,f2(x46471))+E(f323(f77(x46471),x46472),f2(x46471))
% 188.07/187.97 [4648]~P82(x46481)+~E(x46482,f2(x46481))+E(f323(f73(x46481),x46482),f2(x46481))
% 188.07/187.97 [4675]~P74(x46752)+E(x46751,f2(x46752))+~E(f323(f77(x46752),x46751),x46751)
% 188.07/187.97 [4683]E(x46831,f323(a104,x46832))+~E(x46831,f2(a865))+~E(x46832,f323(f100(a1),x46831))
% 188.07/187.97 [4684]E(f323(a104,x46841),x46842)+~E(x46842,f2(a865))+~E(x46841,f323(f100(a1),x46842))
% 188.07/187.97 [4688]~P89(x46882)+E(x46881,f2(a1))+~E(f323(f102(x46882),x46881),f2(x46882))
% 188.07/187.97 [4693]~P59(x46932)+E(x46931,f2(x46932))+~E(f323(f77(x46932),x46931),f2(x46932))
% 188.07/187.97 [4694]~P82(x46942)+E(x46941,f2(x46942))+~E(f323(f73(x46942),x46941),f2(x46942))
% 188.07/187.97 [4695]~P59(x46951)+E(f2(x46951),x46952)+~E(f323(f77(x46951),x46952),f2(x46951))
% 188.07/187.97 [4877]~P103(x48771)+~P16(x48771,x48772)+P16(x48771,f323(f165(x48771),x48772))
% 188.07/187.97 [4902]~P101(x49022)+~P101(x49021)+P101(f323(f323(a322,x49021),x49022))
% 188.07/187.97 [4936]~E(f76(a865),f2(a865))+E(f323(f35(x49361),x49362),f2(a865))+~P101(f323(f59(x49361),x49362))
% 188.07/187.97 [4969]~P139(x49691)+~P110(x49691)+E(f323(f323(f248(x49691),f2(x49691)),f323(a112,x49692)),f2(x49691))
% 188.07/187.97 [5007]~P103(x50071)+P16(x50071,f132(x50071,x50072))+~P101(f323(f59(x50071),x50072))
% 188.07/187.97 [5008]~P103(x50081)+P16(x50081,f690(x50082,x50081))+~P101(f323(f59(x50081),x50082))
% 188.07/187.97 [5029]~P103(x50291)+E(f323(f166(x50291),f132(x50291,x50292)),x50292)+~P101(f323(f59(x50291),x50292))
% 188.07/187.97 [5030]~P103(x50301)+E(f323(f166(x50301),f690(x50302,x50301)),x50302)+~P101(f323(f59(x50301),x50302))
% 188.07/187.97 [5058]P101(x50581)+P101(x50582)+~P101(f323(f323(a321,x50582),x50581))
% 188.07/187.97 [5070]E(x50701,f188(f872(x50702,a860)))+~E(f323(f35(x50702),x50701),f2(a865))+~P101(f323(f59(x50702),x50701))
% 188.07/187.97 [5075]P101(x50751)+~P101(x50752)+~P101(f323(f323(a326,x50752),x50751))
% 188.07/187.97 [5124]~P71(x51241)+E(f323(f73(x51241),x51242),x51242)+P101(f323(f323(f238(x51241),x51242),f2(x51241)))
% 188.07/187.97 [5186]~P5(x51862)+~P101(f323(f55(x51862),x51861))+P101(f323(x51861,f691(x51861,x51862)))
% 188.07/187.97 [5187]~P5(x51872)+~P101(f323(f55(x51872),x51871))+P101(f323(x51871,f703(x51871,x51872)))
% 188.07/187.97 [5220]E(x52201,f113(x52202))+P101(f323(f130(x52202),f114(x52202,x52201)))+~P101(f323(f130(x52202),x52201))
% 188.07/187.97 [5225]~P103(x52251)+~P101(f323(f59(x52251),x52252))+P101(f323(f130(x52251),f132(x52251,x52252)))
% 188.07/187.97 [5226]~P103(x52261)+~P101(f323(f59(x52261),x52262))+P101(f323(f130(x52261),f690(x52262,x52261)))
% 188.07/187.97 [5232]~P134(x52321)+E(f323(f100(x52321),f323(a104,x52322)),f323(f102(x52321),x52322))+P101(f323(f323(f238(a1),x52322),f2(a1)))
% 188.07/187.97 [5260]P8(x52602,x52601)+E(f323(x52601,f490(x52601)),f323(x52601,f526(x52601)))+P101(f323(f323(x52601,f490(x52601)),f526(x52601)))
% 188.07/187.97 [5274]E(f323(f100(a1),f424(x52741,x52742)),x52741)+P101(f323(x52742,f323(a104,x52741)))+~P101(f323(x52742,f2(a865)))
% 188.07/187.97 [5286]~P5(x52861)+~P101(f323(x52862,f650(x52862,x52861)))+P101(f323(f56(x52861),x52862))
% 188.07/187.97 [5287]~P5(x52871)+~P101(f323(x52872,f659(x52872,x52871)))+P101(f323(f56(x52871),x52872))
% 188.07/187.97 [5302]~P5(x53022)+~P36(x53022,x53021,f53(x53022))+P101(f323(x53021,f705(x53021,x53022)))
% 188.07/187.97 [5318]~P116(x53181)+~E(f80(x53181,x53182),f323(f77(x53181),f76(x53181)))+P101(f323(f323(f238(x53181),x53182),f2(x53181)))
% 188.07/187.97 [5394]~E(x53942,f2(a1))+E(f217(x53941,x53942),f323(f323(f258(a1,a1),f2(a1)),f76(a1)))+P101(f323(f323(f238(a1),x53942),f2(a1)))
% 188.07/187.97 [5395]~E(x53951,f2(a1))+E(f217(x53951,x53952),f323(f323(f258(a1,a1),f2(a1)),f76(a1)))+P101(f323(f323(f238(a1),x53952),f2(a1)))
% 188.07/187.97 [5447]E(f323(f100(a1),f424(x54471,x54472)),x54471)+P101(f323(x54472,f323(a104,x54471)))+P101(f323(f323(f238(a1),x54471),f2(a1)))
% 188.07/187.97 [5510]~P116(x55101)+E(f80(x55101,x55102),f323(f77(x55101),f76(x55101)))+~P101(f323(f323(f238(x55101),x55102),f2(x55101)))
% 188.07/187.97 [5511]~P82(x55111)+E(f323(f73(x55111),x55112),f323(f77(x55111),x55112))+~P101(f323(f323(f237(x55111),x55112),f2(x55111)))
% 188.07/187.97 [5512]~P82(x55121)+E(f323(f73(x55121),x55122),f323(f77(x55121),x55122))+~P101(f323(f323(f238(x55121),x55122),f2(x55121)))
% 188.07/187.97 [5513]~P71(x55131)+E(f323(f73(x55131),x55132),f323(f77(x55131),x55132))+~P101(f323(f323(f238(x55131),x55132),f2(x55131)))
% 188.07/187.97 [5608]~P101(f323(x56081,f424(x56082,x56081)))+P101(f323(x56081,f323(a104,x56082)))+~P101(f323(x56081,f2(a865)))
% 188.07/187.97 [5615]E(x56151,f2(a865))+E(f323(a112,f853(x56152,x56151)),x56151)+~P101(f323(f323(f238(a865),x56151),f323(a112,x56152)))
% 188.07/187.97 [5619]P8(x56191,x56192)+~E(f323(x56192,f490(x56192)),f323(x56192,f526(x56192)))+~P101(f323(f323(x56192,f490(x56192)),f526(x56192)))
% 188.07/187.97 [5639]~P103(x56391)+P16(x56391,x56392)+P101(f323(f323(f237(a865),f562(x56392,x56391)),f563(x56392,x56391)))
% 188.07/187.97 [5640]~P103(x56401)+P16(x56401,x56402)+P101(f323(f323(f237(a865),f603(x56402,x56401)),f607(x56402,x56401)))
% 188.07/187.97 [5726]~P82(x57261)+~E(x57262,f2(x57261))+P101(f323(f323(f237(x57261),f323(f73(x57261),x57262)),f2(x57261)))
% 188.07/187.97 [5805]~P5(x58052)+~P5(x58051)+E(f57(x58051,x58052,f53(x58051),f53(x58052)),f53(f871(x58051,x58052)))
% 188.07/187.97 [5809]~P101(f323(x58091,f424(x58092,x58091)))+P101(f323(x58091,f323(a104,x58092)))+P101(f323(f323(f238(a1),x58092),f2(a1)))
% 188.07/187.97 [5832]~P101(f323(x58321,f323(a104,x58322)))+P101(f323(x58321,f2(a865)))+~P101(f323(f323(f238(a1),x58322),f2(a1)))
% 188.07/187.97 [6161]~P116(x61611)+~P101(f323(f323(f238(x61611),x61612),f2(x61611)))+P101(f323(f323(f238(x61611),f80(x61611,x61612)),f2(x61611)))
% 188.07/187.97 [6274]~P116(x62741)+P101(f323(f323(f237(x62741),f323(f102(x62741),x62742)),f2(x62741)))+~P101(f323(f323(f237(a1),x62742),f2(a1)))
% 188.07/187.97 [6275]~P116(x62751)+P101(f323(f323(f238(x62751),f323(f102(x62751),x62752)),f2(x62751)))+~P101(f323(f323(f238(a1),x62752),f2(a1)))
% 188.07/187.97 [6282]~P82(x62822)+E(x62821,f2(x62822))+~P101(f323(f323(f237(x62822),f323(f73(x62822),x62821)),f2(x62822)))
% 188.07/187.97 [6357]~P134(x63571)+~P101(f323(f323(f325(x63571),x63572),f109(x63571)))+P101(f323(f323(f325(x63571),f323(f77(x63571),x63572)),f109(x63571)))
% 188.07/187.97 [6390]~P116(x63901)+~P101(f323(f323(f238(x63901),f80(x63901,x63902)),f2(x63901)))+P101(f323(f323(f238(x63901),x63902),f2(x63901)))
% 188.07/187.97 [6558]~P116(x65582)+~P101(f323(f323(f237(x65582),f323(f102(x65582),x65581)),f2(x65582)))+P101(f323(f323(f237(a1),x65581),f2(a1)))
% 188.07/187.97 [6559]~P116(x65592)+~P101(f323(f323(f238(x65592),f323(f102(x65592),x65591)),f2(x65592)))+P101(f323(f323(f238(a1),x65591),f2(a1)))
% 188.07/187.97 [7058]~P74(x70581)+~P101(f323(f323(f237(x70581),x70582),f2(x70581)))+P101(f323(f323(f237(x70581),f323(f323(f78(x70581),x70582),x70582)),f2(x70581)))
% 188.07/187.97 [7059]~P116(x70591)+~P101(f323(f323(f238(x70591),x70592),f2(x70591)))+P101(f323(f323(f238(x70591),f323(f323(f78(x70591),x70592),x70592)),f2(x70591)))
% 188.07/187.97 [7060]~P74(x70601)+~P101(f323(f323(f238(x70601),x70602),f2(x70601)))+P101(f323(f323(f238(x70601),f323(f323(f78(x70601),x70602),x70602)),f2(x70601)))
% 188.07/187.97 [7623]~P74(x76231)+~P101(f323(f323(f237(x76231),f323(f323(f78(x76231),x76232),x76232)),f2(x76231)))+P101(f323(f323(f237(x76231),x76232),f2(x76231)))
% 188.07/187.97 [7624]~P116(x76241)+~P101(f323(f323(f238(x76241),f323(f323(f78(x76241),x76242),x76242)),f2(x76241)))+P101(f323(f323(f238(x76241),x76242),f2(x76241)))
% 188.07/187.97 [7625]~P74(x76251)+~P101(f323(f323(f238(x76251),f323(f323(f78(x76251),x76252),x76252)),f2(x76251)))+P101(f323(f323(f238(x76251),x76252),f2(x76251)))
% 188.07/187.97 [4733]~E(x47332,f76(a865))+~E(x47331,f76(a865))+E(f323(f323(f79(a865),x47331),x47332),f76(a865))
% 188.07/187.97 [4734]~E(x47342,f76(a1))+~E(x47341,f76(a1))+E(f323(f323(f79(a1),x47341),x47342),f76(a1))
% 188.07/187.97 [4735]~E(x47352,f2(a865))+~E(x47351,f2(a865))+E(f323(f323(f78(a865),x47351),x47352),f2(a865))
% 188.07/187.97 [4789]~P114(x47892)+E(x47891,f2(x47892))+E(f323(f323(f281(x47892),x47891),x47891),f76(x47892))
% 188.07/187.97 [4790]~P57(x47902)+E(x47901,f2(x47902))+E(f323(f323(f36(x47902),x47901),x47901),f76(x47902))
% 188.07/187.97 [4791]~P115(x47912)+E(x47911,f2(x47912))+E(f323(f323(f281(x47912),x47911),x47911),f76(x47912))
% 188.07/187.97 [4809]~P133(x48091)+~E(x48092,f76(x48091))+E(f323(f323(f79(x48091),x48092),x48092),f76(x48091))
% 188.07/187.97 [4810]~P74(x48101)+~E(x48102,f2(x48101))+E(f323(f323(f78(x48101),x48102),x48102),f2(x48101))
% 188.07/187.97 [4811]~P115(x48111)+~E(x48112,f2(x48111))+E(f323(f323(f281(x48111),x48112),x48112),f2(x48111))
% 188.07/187.97 [4856]~E(x48562,f2(a865))+~E(x48561,f2(a865))+E(f323(f77(a1),f323(f100(a1),x48561)),f323(f100(a1),x48562))
% 188.07/187.97 [4874]E(x48741,f76(a865))+E(x48742,f2(a865))+~E(f323(f323(f79(a865),x48742),x48741),x48742)
% 188.07/187.97 [4884]E(x48841,f2(a865))+E(x48842,f2(a865))+~E(f323(f323(f79(a865),x48842),x48841),f2(a865))
% 188.07/187.97 [4911]~E(x49112,f2(a865))+~E(x49111,f323(a112,f2(a865)))+E(f323(f323(f78(a865),x49111),x49112),f323(a112,f2(a865)))
% 188.07/187.97 [4912]~E(x49121,f2(a865))+~E(x49122,f323(a112,f2(a865)))+E(f323(f323(f78(a865),x49121),x49122),f323(a112,f2(a865)))
% 188.07/187.97 [4919]E(x49191,f76(a1))+E(x49192,f323(f103(a1),a97))+~E(f323(f323(f79(a1),x49191),x49192),f76(a1))
% 188.07/187.97 [4920]E(x49201,f76(a1))+E(x49202,f323(f103(a1),a97))+~E(f323(f323(f79(a1),x49202),x49201),f76(a1))
% 188.07/187.97 [4921]E(x49211,f76(a1))+E(x49211,f323(f103(a1),a97))+~E(f323(f323(f79(a1),x49212),x49211),f76(a1))
% 188.07/187.97 [4923]E(x49231,f76(a1))+E(x49231,f323(f103(a1),a97))+~E(f323(f323(f79(a1),x49231),x49232),f76(a1))
% 188.07/187.97 [4940]~P74(x49402)+E(x49401,f2(x49402))+~E(f323(f323(f78(x49402),x49401),x49401),f2(x49402))
% 188.07/187.97 [4946]~E(x49461,f323(f103(a1),a97))+~E(x49462,f323(f103(a1),a97))+E(f323(f323(f79(a1),x49461),x49462),f76(a1))
% 188.07/187.97 [4958]E(x49581,f2(a865))+E(x49582,f2(a865))+~E(f323(f323(f78(a865),x49582),x49581),f323(a112,f2(a865)))
% 188.07/187.97 [4968]~P62(x49681)+~P90(x49681)+E(f323(f323(f281(x49681),x49682),f323(f103(x49681),a81)),f2(x49681))
% 188.07/187.97 [4974]~P133(x49741)+~E(x49742,f323(f77(x49741),f76(x49741)))+E(f323(f323(f79(x49741),x49742),x49742),f76(x49741))
% 188.07/187.97 [4979]~P7(x49792)+~P7(x49791)+P7(f323(f323(f79(a1),x49791),x49792))
% 188.07/187.97 [4980]~P7(x49802)+~P7(x49801)+P7(f323(f323(f78(a1),x49801),x49802))
% 188.07/187.97 [4981]~P7(x49812)+~P7(x49811)+P7(f323(f323(f36(a1),x49811),x49812))
% 188.07/187.97 [4983]~E(x49832,f2(a1))+E(x49831,f2(a1))+E(f43(x49831,x49832),f323(f323(f258(a1,a1),f2(a1)),x49831))
% 188.07/187.97 [5005]~E(x50052,f323(a112,f2(a865)))+~E(x50051,f323(a112,f2(a865)))+E(f323(f323(f79(a865),x50051),x50052),f323(a112,f2(a865)))
% 188.07/187.97 [5020]E(x50201,f2(a865))+E(x50202,f323(a112,f2(a865)))+~E(f323(f323(f248(a865),x50202),x50201),f323(a112,f2(a865)))
% 188.07/187.97 [5021]E(x50211,f2(a865))+E(x50211,f323(a112,f2(a865)))+~E(f323(f323(f78(a865),x50212),x50211),f323(a112,f2(a865)))
% 188.07/187.97 [5022]E(x50221,f2(a865))+E(x50221,f323(a112,f2(a865)))+~E(f323(f323(f78(a865),x50221),x50222),f323(a112,f2(a865)))
% 188.07/187.97 [5031]~P62(x50311)+~P90(x50311)+E(f323(f323(f281(x50311),x50312),f323(f103(x50311),a97)),f323(f77(x50311),x50312))
% 188.07/187.97 [5050]E(x50501,f323(a104,x50502))+~E(x50501,f2(a865))+P101(f323(f323(f237(a1),f2(a1)),x50502))
% 188.07/187.97 [5051]E(f323(a104,x50511),x50512)+~E(x50512,f2(a865))+P101(f323(f323(f237(a1),f2(a1)),x50511))
% 188.07/187.97 [5066]E(x50661,f323(a112,f2(a865)))+E(x50662,f323(a112,f2(a865)))+~E(f323(f323(f78(a865),x50661),x50662),f323(a112,f2(a865)))
% 188.07/187.97 [5077]~E(x50771,f323(a104,x50772))+E(x50771,f2(a865))+P101(f323(f323(f237(a1),f2(a1)),x50772))
% 188.07/187.97 [5078]~E(f323(a104,x50782),x50781)+E(x50781,f2(a865))+P101(f323(f323(f237(a1),f2(a1)),x50782))
% 188.07/187.97 [5100]~P2(x51001)+E(f323(f61(x51001,f101(x51001)),x51002),f11(x51001,x51002))+~P101(f323(f59(x51001),x51002))
% 188.07/187.97 [5101]~P2(x51011)+E(f323(f61(x51011,f110(x51011)),x51012),f10(x51011,x51012))+~P101(f323(f59(x51011),x51012))
% 188.07/187.97 [5102]~P103(x51021)+E(f323(f61(x51021,f236(x51021)),x51022),f14(x51021,x51022))+~P101(f323(f59(x51021),x51022))
% 188.07/187.97 [5103]~P103(x51031)+E(f323(f61(x51031,f235(x51031)),x51032),f15(x51031,x51032))+~P101(f323(f59(x51031),x51032))
% 188.07/187.97 [5105]~P5(x51051)+~P101(f323(x51052,f200(x51051)))+P101(f323(f55(f869(x51051)),x51052))
% 188.07/187.97 [5179]~P5(x51792)+P101(f323(x51791,f200(x51792)))+~P101(f323(f56(f869(x51792)),x51791))
% 188.07/187.97 [5180]E(x51801,x51802)+~E(f323(f323(f22(a865),x51802),x51801),f2(a865))+~E(f323(f323(f22(a865),x51801),x51802),f2(a865))
% 188.07/187.97 [5193]P7(x51931)+~P39(x51932)+~P101(f323(f323(f325(a1),x51931),x51932))
% 188.07/187.97 [5221]~P116(x52211)+~E(f80(x52211,x52212),f76(x52211))+P101(f323(f323(f238(x52211),f2(x52211)),x52212))
% 188.07/187.97 [5233]~P90(x52331)+E(f323(f100(x52331),f323(f103(a865),x52332)),f323(f103(x52331),x52332))+P101(f323(a193,f323(f103(a1),x52332)))
% 188.07/187.97 [5239]~P44(x52391,x52392)+P45(a860)+P101(f323(f59(f871(x52391,x52391)),x52392))
% 188.07/187.97 [5311]~P103(x53111)+E(f323(f61(x53111,f235(x53111)),x53112),f12(x53111,f235(x53111),x53112))+~P101(f323(f59(x53111),x53112))
% 188.07/187.97 [5312]~P103(x53121)+E(f323(f61(x53121,f236(x53121)),x53122),f13(x53121,f236(x53121),x53122))+~P101(f323(f59(x53121),x53122))
% 188.07/187.97 [5325]E(x53251,x53252)+P101(f323(f323(f238(a865),x53252),x53251))+P101(f323(f323(f238(a865),x53251),x53252))
% 188.07/187.97 [5326]E(x53261,x53262)+P101(f323(f323(f238(a1),x53262),x53261))+P101(f323(f323(f238(a1),x53261),x53262))
% 188.07/187.97 [5381]~P90(x53811)+E(f323(f100(x53811),f323(f103(a865),x53812)),f2(x53811))+~P101(f323(a193,f323(f103(a1),x53812)))
% 188.07/187.97 [5384]~E(x53842,f323(a104,x53841))+E(x53841,f323(f100(a1),x53842))+~P101(f323(f323(f237(a1),f2(a1)),x53841))
% 188.07/187.97 [5385]~E(f323(a104,x53851),x53852)+E(x53851,f323(f100(a1),x53852))+~P101(f323(f323(f237(a1),f2(a1)),x53851))
% 188.07/187.97 [5386]~E(x53861,f323(a104,x53862))+E(f323(f100(a1),x53861),x53862)+~P101(f323(f323(f237(a1),f2(a1)),x53862))
% 188.07/187.97 [5396]E(x53961,f323(a104,x53962))+~E(x53962,f323(f100(a1),x53961))+~P101(f323(f323(f237(a1),f2(a1)),x53962))
% 188.07/187.97 [5397]E(f323(a104,x53971),x53972)+~E(x53971,f323(f100(a1),x53972))+~P101(f323(f323(f237(a1),f2(a1)),x53971))
% 188.07/187.97 [5436]~P82(x54362)+E(x54361,f2(x54362))+P101(f323(f323(f238(x54362),f2(x54362)),f323(f73(x54362),x54361)))
% 188.07/187.97 [5503]~P116(x55031)+E(f80(x55031,x55032),f76(x55031))+~P101(f323(f323(f238(x55031),f2(x55031)),x55032))
% 188.07/187.97 [5507]~P90(x55071)+E(f323(f100(x55071),f323(f103(a865),x55072)),f2(x55071))+P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x55072)))
% 188.07/187.97 [5514]~P82(x55141)+E(f323(f73(x55141),x55142),x55142)+~P101(f323(f323(f237(x55141),f2(x55141)),x55142))
% 188.07/187.97 [5515]~P82(x55151)+E(f323(f73(x55151),x55152),x55152)+~P101(f323(f323(f238(x55151),f2(x55151)),x55152))
% 188.07/187.97 [5522]E(x55221,f2(a865))+~E(f132(a865,f323(f293(a865,x55222),x55221)),f113(a865))+P101(f323(f323(f237(a865),x55221),x55222))
% 188.07/187.97 [5532]~P72(x55321)+E(f323(f323(f6(x55321,x55321),f5(x55321)),f323(f166(x55321),x55322)),f323(f159(x55321),x55322))+~P101(f323(f130(x55321),x55322))
% 188.07/187.97 [5535]~P134(x55351)+E(f323(f100(x55351),f323(a104,x55352)),f323(f102(x55351),x55352))+~P101(f323(f323(f237(a1),f2(a1)),x55352))
% 188.07/187.97 [5562]E(x55621,x55622)+P101(f323(f323(f238(a865),x55621),x55622))+~P101(f323(f323(f237(a865),x55621),x55622))
% 188.07/187.97 [5563]E(x55631,x55632)+P101(f323(f323(f238(a1),x55631),x55632))+~P101(f323(f323(f237(a1),x55631),x55632))
% 188.07/187.97 [5566]E(x55661,f76(a1))+~E(f323(f323(f79(a1),x55662),x55661),f76(a1))+~P101(f323(f323(f238(a1),f2(a1)),x55662))
% 188.07/187.97 [5567]E(x55671,f76(a1))+~E(f323(f323(f79(a1),x55671),x55672),f76(a1))+~P101(f323(f323(f238(a1),f2(a1)),x55671))
% 188.07/187.97 [5605]~P39(x56052)+P101(f323(f323(f237(a1),f2(a1)),x56051))+~P101(f323(f323(f325(a1),x56051),x56052))
% 188.07/187.97 [5624]~P54(x56241,x56242)+P38(x56241,x56242)+~P101(f323(f59(f871(x56241,x56241)),x56242))
% 188.07/187.97 [5626]~P54(x56261,x56262)+P44(x56261,x56262)+~P101(f323(f59(f871(x56261,x56261)),x56262))
% 188.07/187.97 [5670]E(x56701,f188(f872(x56702,a860)))+~P101(f323(f59(x56702),x56701))+P101(f323(f323(f238(a865),f2(a865)),f323(f35(x56702),x56701)))
% 188.07/187.97 [5697]~P101(f323(x56971,x56972))+P101(f323(x56971,f2(a865)))+P101(f323(f323(f238(a865),f331(x56972,x56971)),x56972))
% 188.07/187.97 [5720]E(x57201,f2(a865))+~E(f323(f159(a865),x57202),f2(a865))+~P101(f323(f323(f325(a865),x57201),f323(f166(a865),x57202)))
% 188.07/187.97 [5786]E(x57861,x57862)+~P101(f323(f323(f237(a865),x57862),x57861))+~P101(f323(f323(f237(a865),x57861),x57862))
% 188.07/187.97 [5787]E(x57871,x57872)+~P101(f323(f323(f237(a1),x57872),x57871))+~P101(f323(f323(f237(a1),x57871),x57872))
% 188.07/187.97 [5788]E(f323(f35(x57881),x57882),f2(a865))+~P101(f323(f59(x57881),x57882))+P101(f323(f323(f325(x57881),f488(x57882,x57881)),x57882))
% 188.07/187.97 [5797]E(f47(x57971,x57972),f43(x57971,x57972))+P101(f323(f323(f237(a1),f2(a1)),x57971))+~P101(f323(f323(f238(a1),f2(a1)),x57972))
% 188.07/187.97 [5821]~P101(f323(x58211,f422(x58211)))+P101(f323(x58211,f323(a104,x58212)))+~P101(f323(f323(f237(a1),f2(a1)),x58212))
% 188.07/187.97 [5823]P101(f323(f323(f237(a865),x58231),f807(x58232)))+~P101(f323(f59(a865),x58232))+~P101(f323(f323(f325(a865),x58231),x58232))
% 188.07/187.97 [5824]P101(f323(f323(f238(a865),x58241),f818(x58242)))+~P101(f323(f59(a865),x58242))+~P101(f323(f323(f325(a865),x58241),x58242))
% 188.07/187.97 [5853]E(x58531,x58532)+~P101(f323(f323(f238(a865),x58531),f323(a112,x58532)))+P101(f323(f323(f238(a865),x58531),x58532))
% 188.07/187.97 [5885]E(x58851,f323(a112,x58852))+~P101(f323(f323(f237(a865),x58851),f323(a112,x58852)))+P101(f323(f323(f237(a865),x58851),x58852))
% 188.07/187.97 [5898]P101(f323(x58981,f423(x58981)))+~P101(f323(x58981,f323(a104,x58982)))+~P101(f323(f323(f237(a1),f2(a1)),x58982))
% 188.07/187.97 [5912]~P101(f323(x59121,x59122))+~P101(f323(f323(f237(a1),f2(a1)),x59122))+P101(f323(x59121,f323(f100(a1),f382(x59121))))
% 188.07/187.97 [5926]~P82(x59262)+~E(x59261,f2(x59262))+~P101(f323(f323(f238(x59262),f2(x59262)),f323(f73(x59262),x59261)))
% 188.07/187.97 [5950]~P54(x59501,x59502)+P38(x59501,f323(f278(x59501,x59501),x59502))+~P101(f323(f59(f871(x59501,x59501)),x59502))
% 188.07/187.97 [5958]~P90(x59581)+E(f323(f100(x59581),f323(f103(a865),x59582)),f323(f103(x59581),x59582))+~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x59582)))
% 188.07/187.97 [5961]E(f323(a112,x59611),x59612)+~P101(f323(f323(f238(a865),x59611),x59612))+P101(f323(f323(f238(a865),f323(a112,x59611)),x59612))
% 188.07/187.97 [5974]E(f323(f323(f36(a1),x59741),x59742),f2(a1))+~P101(f323(f323(f237(a1),x59741),f2(a1)))+~P101(f323(f323(f238(a1),x59742),x59741))
% 188.07/187.97 [5985]E(f42(a1,x59851,x59852),x59851)+~P101(f323(f323(f237(a1),x59851),f2(a1)))+~P101(f323(f323(f238(a1),x59852),x59851))
% 188.07/187.97 [5998]E(f44(x59981,x59982),f43(x59981,x59982))+~P101(f323(f323(f237(a1),f2(a1)),x59981))+~P101(f323(f323(f237(a1),f2(a1)),x59982))
% 188.07/187.97 [6006]E(f323(f323(f36(a1),x60061),x60062),f2(a1))+~P101(f323(f323(f237(a1),f2(a1)),x60061))+~P101(f323(f323(f238(a1),x60061),x60062))
% 188.07/187.97 [6018]E(f42(a865,f323(f103(a865),x60181),f323(f103(a865),x60182)),f323(f103(a865),x60181))+P101(f323(a193,f323(f103(a1),x60181)))+~P101(f323(a193,f323(f103(a1),x60182)))
% 188.07/187.97 [6020]E(f42(a1,x60201,x60202),x60201)+~P101(f323(f323(f237(a1),f2(a1)),x60201))+~P101(f323(f323(f238(a1),x60201),x60202))
% 188.07/187.97 [6021]E(x60211,x60212)+~P101(f323(f323(f238(a865),x60211),f323(a112,x60212)))+~P101(f323(f323(f237(a865),x60212),x60211))
% 188.07/187.97 [6038]~P74(x60381)+~P101(f323(f323(f237(x60381),x60382),f2(x60381)))+P101(f323(f323(f237(x60381),x60382),f323(f77(x60381),x60382)))
% 188.07/187.97 [6039]~P116(x60391)+~P101(f323(f323(f238(x60391),x60392),f2(x60391)))+P101(f323(f323(f238(x60391),x60392),f323(f77(x60391),x60392)))
% 188.07/187.97 [6049]~P6(x60491)+E(f323(f323(f62(x60491,x60491,f110(x60491)),f188(x60491)),x60492),f37(x60491,x60492))+~P101(f323(f59(x60491),x60492))
% 188.07/187.97 [6050]~P6(x60501)+E(f323(f323(f62(x60501,x60501,f101(x60501)),f246(x60501)),x60502),f38(x60501,x60502))+~P101(f323(f59(x60501),x60502))
% 188.07/187.97 [6064]~P116(x60641)+~P101(f323(f323(f237(a1),f2(a1)),x60642))+P101(f323(f323(f237(x60641),f2(x60641)),f323(f102(x60641),x60642)))
% 188.07/187.97 [6065]~P119(x60651)+~P101(f323(f323(f238(a865),f2(a865)),x60652))+P101(f323(f323(f238(x60651),f2(x60651)),f323(f100(x60651),x60652)))
% 188.07/187.97 [6066]~P116(x60661)+~P101(f323(f323(f238(a1),f2(a1)),x60662))+P101(f323(f323(f238(x60661),f2(x60661)),f323(f102(x60661),x60662)))
% 188.07/187.97 [6069]~P7(x60692)+~P7(x60691)+E(f323(f302(a865,a1,f100(a1)),f294(a865,f323(a104,x60691),f323(a104,x60692))),f294(a1,x60691,x60692))
% 188.07/187.97 [6075]P101(f323(x60751,x60752))+~P101(f323(f323(f237(a1),f2(a1)),x60752))+~P101(f323(x60751,f323(f100(a1),f383(x60751))))
% 188.07/187.97 [6100]E(f323(f323(f78(a865),f323(f103(a865),x61001)),f323(f103(a865),x61002)),f323(f103(a865),x61001))+P101(f323(f323(f238(a1),x61001),a81))+~P101(f323(f323(f238(a1),x61002),a81))
% 188.07/187.97 [6104]~P116(x61041)+P101(f323(f323(f238(x61041),f2(x61041)),f80(x61041,x61042)))+~P101(f323(f323(f238(x61041),f2(x61041)),x61042))
% 188.07/187.97 [6115]~P75(x61151)+~P101(f323(f323(f237(x61151),x61152),f2(x61151)))+P101(f323(f323(f237(x61151),f2(x61151)),f323(f77(x61151),x61152)))
% 188.07/187.97 [6116]~P75(x61161)+~P101(f323(f323(f238(x61161),x61162),f2(x61161)))+P101(f323(f323(f238(x61161),f2(x61161)),f323(f77(x61161),x61162)))
% 188.07/187.97 [6119]E(x61191,f246(f872(x61192,a860)))+~E(f323(f35(x61192),x61191),f323(f35(x61192),f246(f872(x61192,a860))))+~P101(f323(f59(x61192),f246(f872(x61192,a860))))
% 188.07/187.97 [6153]~P74(x61531)+P101(f323(f323(f237(x61531),x61532),f2(x61531)))+~P101(f323(f323(f237(x61531),x61532),f323(f77(x61531),x61532)))
% 188.07/187.97 [6154]~P116(x61541)+P101(f323(f323(f238(x61541),x61542),f2(x61541)))+~P101(f323(f323(f238(x61541),x61542),f323(f77(x61541),x61542)))
% 188.07/187.97 [6163]~P90(x61631)+P101(f323(f323(f325(x61631),f323(f103(x61631),x61632)),f186(x61631)))+~P101(f323(f323(f237(a1),a81),x61632))
% 188.07/187.97 [6194]E(x61941,f2(a865))+~P101(f323(f323(f238(a865),x61941),f323(a112,x61942)))+P101(f323(f323(f238(a865),f853(x61942,x61941)),x61942))
% 188.07/187.97 [6216]~P116(x62161)+~P101(f323(f323(f238(x62161),f2(x62161)),f80(x62161,x62162)))+P101(f323(f323(f238(x62161),f2(x62161)),x62162))
% 188.07/187.97 [6218]~E(f323(f103(a865),x62182),f323(f103(a865),x62181))+P101(f323(f323(f237(a1),f323(f103(a1),x62181)),f2(a1)))+~P101(f323(a193,f323(f103(a1),x62182)))
% 188.07/187.97 [6247]E(f323(f257(a1,a1),f47(x62471,x62472)),f323(f323(f36(a1),x62471),x62472))+~P101(f323(f323(f238(a1),x62471),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x62472))
% 188.07/187.97 [6280]E(f323(f261(a1,a1),f47(x62801,x62802)),f42(a1,x62801,x62802))+~P101(f323(f323(f238(a1),x62801),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x62802))
% 188.07/187.97 [6283]~P116(x62832)+~P101(f323(f323(f237(x62832),f2(x62832)),f323(f102(x62832),x62831)))+P101(f323(f323(f237(a1),f2(a1)),x62831))
% 188.07/187.97 [6284]~P119(x62842)+~P101(f323(f323(f238(x62842),f2(x62842)),f323(f100(x62842),x62841)))+P101(f323(f323(f238(a865),f2(a865)),x62841))
% 188.07/187.97 [6285]~P116(x62852)+~P101(f323(f323(f238(x62852),f2(x62852)),f323(f102(x62852),x62851)))+P101(f323(f323(f238(a1),f2(a1)),x62851))
% 188.07/187.97 [6288]E(f323(f257(a1,a1),f44(x62881,x62882)),f323(f323(f36(a1),x62881),x62882))+~P101(f323(f323(f237(a1),f2(a1)),x62882))+~P101(f323(f323(f238(a1),f2(a1)),x62881))
% 188.07/187.97 [6303]E(f323(f261(a1,a1),f44(x63031,x63032)),f42(a1,x63031,x63032))+~P101(f323(f323(f237(a1),f2(a1)),x63032))+~P101(f323(f323(f238(a1),f2(a1)),x63031))
% 188.07/187.97 [6318]~P75(x63181)+P101(f323(f323(f237(x63181),x63182),f2(x63181)))+~P101(f323(f323(f237(x63181),f2(x63181)),f323(f77(x63181),x63182)))
% 188.07/187.97 [6319]~P75(x63191)+P101(f323(f323(f238(x63191),x63192),f2(x63191)))+~P101(f323(f323(f238(x63191),f2(x63191)),f323(f77(x63191),x63192)))
% 188.07/187.97 [6345]P101(f323(f46(x63451,x63452),f47(x63451,x63452)))+~P101(f323(f323(f238(a1),x63451),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x63452))
% 188.07/187.97 [6369]P101(f323(f46(x63691,x63692),f44(x63691,x63692)))+~P101(f323(f323(f237(a1),f2(a1)),x63691))+~P101(f323(f323(f238(a1),f2(a1)),x63692))
% 188.07/187.97 [6412]~P75(x64121)+P101(f323(f323(f237(x64121),f323(f77(x64121),x64122)),f2(x64121)))+~P101(f323(f323(f237(x64121),f2(x64121)),x64122))
% 188.07/187.97 [6413]~P75(x64131)+P101(f323(f323(f238(x64131),f323(f77(x64131),x64132)),f2(x64131)))+~P101(f323(f323(f238(x64131),f2(x64131)),x64132))
% 188.07/187.97 [6429]E(f323(f323(f22(a865),f323(a104,x64291)),f323(a104,x64292)),f323(a104,f194(x64291,x64292)))+~P101(f323(f323(f237(a1),f2(a1)),x64292))+~P101(f323(f323(f237(a1),f2(a1)),x64291))
% 188.07/187.97 [6446]P101(f323(f323(f237(a1),f2(a1)),f194(x64461,x64462)))+~P101(f323(f323(f237(a1),f2(a1)),x64462))+~P101(f323(f323(f237(a1),f2(a1)),x64461))
% 188.07/187.97 [6483]~P101(f323(x64831,x64832))+P101(f323(x64831,f2(a865)))+P101(f323(x64831,f323(f323(f78(a865),f331(x64832,x64831)),f76(a865))))
% 188.07/187.97 [6565]E(f323(f103(a865),x65651),f323(f103(a865),x65652))+~P101(f323(f323(f237(a1),f323(f103(a1),x65652)),f2(a1)))+~P101(f323(a193,f323(f103(a1),x65651)))
% 188.07/187.97 [6575]~E(x65751,f2(a865))+~E(f608(x65752,x65751),f2(a865))+E(f323(f135(a865,a865,f78(a865),x65751),x65752),f2(a865))
% 188.07/187.97 [6600]~P101(f323(f59(x66001),f547(x66002,x66001)))+~P101(f323(f59(f872(x66001,a860)),x66002))+P101(f323(f59(x66001),f37(f872(x66001,a860),x66002)))
% 188.07/187.97 [6606]E(x66061,x66062)+P101(f323(f323(f238(a1),x66061),x66062))+~P101(f323(f323(f238(a1),x66061),f323(f323(f78(a1),x66062),f76(a1))))
% 188.07/187.97 [6607]P101(f323(f323(f237(a865),f323(a104,x66071)),f323(a104,x66072)))+~P101(f323(f323(f237(a1),f2(a1)),x66072))+~P101(f323(f323(f237(a1),x66071),x66072))
% 188.07/187.97 [6608]P101(f323(f323(f237(a865),f323(a104,x66081)),f323(a104,x66082)))+~P101(f323(f323(f238(a1),f2(a1)),x66081))+~P101(f323(f323(f237(a1),x66081),x66082))
% 188.07/187.97 [6610]P101(f323(f323(f238(a865),f323(a104,x66101)),f323(a104,x66102)))+~P101(f323(f323(f237(a1),f2(a1)),x66101))+~P101(f323(f323(f238(a1),x66101),x66102))
% 188.07/187.97 [6611]P101(f323(f323(f238(a865),f323(a104,x66111)),f323(a104,x66112)))+~P101(f323(f323(f238(a1),f2(a1)),x66112))+~P101(f323(f323(f238(a1),x66111),x66112))
% 188.07/187.97 [6622]E(f42(a865,f323(a104,x66221),f323(a104,x66222)),f323(a104,f42(a1,x66221,x66222)))+~P101(f323(f323(f237(a1),f2(a1)),x66222))+~P101(f323(f323(f237(a1),f2(a1)),x66221))
% 188.07/187.97 [6644]~P75(x66441)+~P101(f323(f323(f237(x66441),f323(f77(x66441),x66442)),f2(x66441)))+P101(f323(f323(f237(x66441),f2(x66441)),x66442))
% 188.07/187.97 [6645]~P75(x66451)+~P101(f323(f323(f238(x66451),f323(f77(x66451),x66452)),f2(x66451)))+P101(f323(f323(f238(x66451),f2(x66451)),x66452))
% 188.07/187.97 [6660]~P101(f323(f323(f238(a1),a81),x66602))+~P101(f323(f323(f238(a1),x66601),x66602))+P101(f323(f323(f238(a865),f323(f103(a865),x66601)),f323(f103(a865),x66602)))
% 188.07/187.97 [6750]~P101(f323(f323(f237(a1),f2(a1)),x67501))+P101(f323(f323(f238(a865),f323(a104,x67501)),x67502))+~P101(f323(f323(f238(a1),x67501),f323(f100(a1),x67502)))
% 188.07/187.97 [6767]E(x67671,f2(a1))+E(f42(a1,x67672,x67671),f2(a1))+E(f323(f323(f22(a1),f323(f77(a1),f323(f323(f36(a1),x67672),x67671))),f76(a1)),f323(f323(f36(a1),x67672),f323(f77(a1),x67671)))
% 188.07/187.97 [6783]~P101(f323(f323(f237(a1),f2(a1)),x67831))+~P101(f323(f323(f238(a865),f323(a104,x67831)),x67832))+P101(f323(f323(f238(a1),x67831),f323(f100(a1),x67832)))
% 188.07/187.97 [6818]~P101(f323(f323(f237(a865),f323(a104,x68181)),f323(a104,x68182)))+~P101(f323(f323(f237(a1),f2(a1)),x68182))+P101(f323(f323(f237(a1),x68181),x68182))
% 188.07/187.97 [6819]~P101(f323(f323(f237(a865),f323(a104,x68191)),f323(a104,x68192)))+~P101(f323(f323(f238(a1),f2(a1)),x68191))+P101(f323(f323(f237(a1),x68191),x68192))
% 188.07/187.97 [6847]P101(f323(f323(f237(a1),x68471),x68472))+~P101(f323(f323(f237(a865),f323(f103(a865),x68471)),f323(f103(a865),x68472)))+P101(f323(f323(f237(a1),x68471),a81))
% 188.07/187.97 [6871]P101(f323(f323(f237(a1),f2(a1)),f42(a1,x68711,x68712)))+~P101(f323(f323(f237(a1),f2(a1)),x68712))+~P101(f323(f323(f237(a1),f2(a1)),x68711))
% 188.07/187.97 [6969]P101(f323(f323(f238(a1),a81),x69691))+~P101(f323(f323(f238(a1),x69692),x69691))+~P101(f323(f323(f238(a865),f323(f103(a865),x69692)),f323(f103(a865),x69691)))
% 188.07/187.97 [7020]E(f323(f323(f258(a1,a1),f323(f323(f36(a1),x70201),x70202)),f42(a1,x70201,x70202)),f47(x70201,x70202))+~P101(f323(f323(f238(a1),x70201),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x70202))
% 188.07/187.97 [7041]E(f323(f323(f258(a1,a1),f323(f323(f36(a1),x70411),x70412)),f42(a1,x70411,x70412)),f44(x70411,x70412))+~P101(f323(f323(f237(a1),f2(a1)),x70412))+~P101(f323(f323(f237(a1),f2(a1)),x70411))
% 188.07/187.97 [7092]~P93(x70922)+E(x70921,f113(x70922))+E(f323(f135(x70922,x70922,f79(x70922),f323(f134(x70922),x70921)),f323(f165(x70922),x70921)),f323(f61(x70922,f79(x70922)),f323(f166(x70922),x70921)))
% 188.07/187.97 [7204]~E(x72041,f2(a865))+E(f323(f135(a865,a865,f78(a865),x72041),x72042),f2(a865))+P101(f323(f323(f325(a865),f608(x72042,x72041)),f323(f166(a865),x72042)))
% 188.07/187.97 [7251]~P101(f323(f323(f237(a1),x72511),f2(a1)))+P101(f323(f323(f237(a1),f323(f323(f36(a1),x72511),x72512)),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x72512))
% 188.07/187.97 [7252]~P101(f323(f323(f238(a1),x72522),f2(a1)))+P101(f323(f323(f237(a1),f323(f323(f36(a1),x72521),x72522)),f2(a1)))+~P101(f323(f323(f237(a1),f2(a1)),x72521))
% 188.07/187.97 [7253]~P101(f323(f323(f238(a1),x72532),f2(a1)))+P101(f323(f323(f238(a1),f323(f323(f36(a1),x72531),x72532)),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x72531))
% 188.07/187.97 [7255]~P101(f323(f323(f238(a1),x72551),f2(a1)))+P101(f323(f323(f238(a1),f323(f323(f36(a1),x72551),x72552)),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x72552))
% 188.07/187.97 [7261]P101(f323(f323(f325(f872(x72611,a860)),f547(x72612,x72611)),x72612))+~P101(f323(f59(f872(x72611,a860)),x72612))+P101(f323(f59(x72611),f37(f872(x72611,a860),x72612)))
% 188.07/187.97 [7355]P27(x73551,x73551,x73552,f246(f872(x73551,a860)))+~E(f323(f302(x73551,x73551,x73552),f246(f872(x73551,a860))),f246(f872(x73551,a860)))+~P101(f323(f59(x73551),f246(f872(x73551,a860))))
% 188.07/187.97 [7481]~P27(x74811,x74811,x74812,f246(f872(x74811,a860)))+E(f323(f302(x74811,x74811,x74812),f246(f872(x74811,a860))),f246(f872(x74811,a860)))+~P101(f323(f59(x74811),f246(f872(x74811,a860))))
% 188.07/187.97 [7617]E(f323(f323(f36(a1),x76171),x76172),f323(f103(a1),a97))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),x76171),x76172)),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x76171))
% 188.07/187.97 [7676]~P101(f323(f323(f238(a1),x76762),f2(a1)))+~P101(f323(f323(f238(a1),f323(f323(f36(a1),x76761),x76762)),f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x76761))
% 188.07/187.97 [7681]E(f323(f323(f78(a1),x76811),x76812),f42(a1,x76811,x76812))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),x76811),x76812)),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x76811))
% 188.07/187.97 [7684]P101(f323(f323(f238(a1),x76841),f2(a1)))+~P101(f323(f323(f238(a1),f323(f323(f36(a1),x76841),x76842)),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x76842))
% 188.07/187.97 [8070]~P5(x80701)+~P101(f323(f56(f869(x80701)),x80702))+P101(f323(f56(x80701),f323(f323(f8(f869(x80701),a860,x80701),x80702),f230(x80701))))
% 188.07/187.97 [8382]~P103(x83821)+P16(x83821,x83822)+~P101(f323(f323(f237(x83821),f323(f323(f158(x83821),x83822),f562(x83822,x83821))),f323(f323(f158(x83821),x83822),f563(x83822,x83821))))
% 188.07/187.97 [8383]~P103(x83831)+P16(x83831,x83832)+~P101(f323(f323(f237(x83831),f323(f323(f158(x83831),x83832),f603(x83832,x83831))),f323(f323(f158(x83831),x83832),f607(x83832,x83831))))
% 188.07/187.97 [8528]~P5(x85281)+P101(f323(f55(f869(x85281)),x85282))+~P101(f323(f55(x85281),f323(f323(f8(f869(x85281),a860,x85281),x85282),f230(x85281))))
% 188.07/187.97 [9711]~P5(x97111)+~P5(x97112)+E(f323(f323(f147(f866(x97111),f872(x97112,x97111)),f323(f323(f8(f872(x97112,f869(x97111)),f872(x97112,x97111),f866(x97111)),f71(f869(x97111),x97111,x97112,f234(x97111))),f323(f323(f8(f866(f871(x97112,x97111)),f872(x97112,f869(x97111)),f866(x97111)),f179(x97112,x97111)),f323(f175(x97112,x97111),f53(x97112))))),f52(x97111,f323(f189(f866(x97112)),f53(x97112)),f53(x97111))),f53(f872(x97112,x97111)))
% 188.07/187.97 [5663]E(x56631,f2(a1))+~E(f42(a1,x56632,x56631),f2(a1))+E(f323(f323(f36(a1),x56632),f323(f77(a1),x56631)),f323(f77(a1),f323(f323(f36(a1),x56632),x56631)))
% 188.07/187.97 [5681]~P39(x56812)+~P39(x56811)+P39(f323(f323(f110(f872(a1,a860)),x56811),x56812))
% 188.07/187.97 [5682]~P39(x56822)+~P39(x56821)+P39(f323(f323(f101(f872(a1,a860)),x56821),x56822))
% 188.07/187.97 [5700]~P62(x57001)+~P90(x57001)+E(f323(f77(x57001),f323(f323(f281(x57001),f76(x57001)),x57002)),f323(f323(f281(x57001),f323(f103(x57001),a97)),x57002))
% 188.07/187.97 [5813]E(x58131,f2(a1))+~E(f42(a1,x58132,x58131),f2(a1))+E(f323(f323(f36(a1),f323(f77(a1),x58132)),x58131),f323(f77(a1),f323(f323(f36(a1),x58132),x58131)))
% 188.07/187.97 [5944]~P103(x59441)+P16(x59441,x59442)+P101(f323(f323(f238(a865),f563(x59442,x59441)),f323(f189(f866(x59441)),x59442)))
% 188.07/187.97 [5945]~P103(x59451)+P16(x59451,x59452)+P101(f323(f323(f238(a865),f607(x59452,x59451)),f323(f189(f866(x59451)),x59452)))
% 188.07/187.97 [6096]~P90(x60961)+~E(f323(f103(x60961),x60962),f2(x60961))+P30(x60961,f323(f103(x60961),f323(f323(f78(a1),x60962),f323(f77(a1),a81))))
% 188.07/187.97 [6097]~P90(x60971)+~E(f323(f103(x60971),x60972),f2(x60971))+P30(x60971,f323(f103(x60971),f323(f323(f78(a1),a81),f323(f77(a1),x60972))))
% 188.07/187.97 [6099]E(f323(a48,f44(f323(f77(a1),x60991),f323(f77(a1),x60992))),f43(x60991,x60992))+P101(f323(f323(f237(a1),f2(a1)),x60991))+P101(f323(f323(f238(a1),f2(a1)),x60992))
% 188.07/187.97 [6224]~E(x62242,f2(a865))+~E(x62241,f2(a865))+P101(f323(f323(f237(a1),f323(f100(a1),x62241)),f323(f77(a1),f323(f100(a1),x62242))))
% 188.07/187.97 [6251]E(f323(f323(f78(a865),f323(f103(a865),x62511)),f323(f103(a865),x62512)),f323(f103(a865),f323(f323(f78(a1),x62511),x62512)))+P101(f323(f323(f238(a1),x62511),a81))+P101(f323(f323(f238(a1),x62512),a81))
% 188.07/187.97 [6379]~P74(x63791)+~P101(f323(f323(f237(x63791),f2(x63791)),x63792))+P101(f323(f323(f237(x63791),f323(f77(x63791),x63792)),x63792))
% 188.07/187.97 [6380]~P74(x63801)+~P101(f323(f323(f238(x63801),f2(x63801)),x63802))+P101(f323(f323(f238(x63801),f323(f77(x63801),x63802)),x63802))
% 188.07/187.97 [6551]E(f323(f323(f22(a865),f323(a104,x65511)),f323(a104,x65512)),f323(a104,f323(f323(f22(a1),x65511),x65512)))+~P101(f323(f323(f237(a1),f2(a1)),x65512))+~P101(f323(f323(f237(a1),x65512),x65511))
% 188.07/187.97 [6583]E(f323(a104,f42(a1,f323(f103(a1),x65831),f323(f103(a1),x65832))),f42(a865,f323(f103(a865),x65831),f323(f103(a865),x65832)))+P101(f323(a193,f323(f103(a1),x65831)))+P101(f323(a193,f323(f103(a1),x65832)))
% 188.07/187.97 [6601]~P74(x66011)+P101(f323(f323(f237(x66011),f2(x66011)),x66012))+~P101(f323(f323(f237(x66011),f323(f77(x66011),x66012)),x66012))
% 188.07/187.97 [6602]~P74(x66021)+P101(f323(f323(f238(x66021),f2(x66021)),x66022))+~P101(f323(f323(f238(x66021),f323(f77(x66021),x66022)),x66022))
% 188.07/187.97 [6614]~P74(x66141)+~P101(f323(f323(f237(x66141),f2(x66141)),x66142))+P101(f323(f323(f237(x66141),f2(x66141)),f323(f323(f78(x66141),x66142),x66142)))
% 188.07/187.97 [6616]~P74(x66161)+~P101(f323(f323(f238(x66161),f2(x66161)),x66162))+P101(f323(f323(f238(x66161),f2(x66161)),f323(f323(f78(x66161),x66162),x66162)))
% 188.07/187.97 [6628]E(f323(f323(f78(a865),f323(a104,x66281)),f323(a104,x66282)),f323(a104,f323(f323(f78(a1),x66281),x66282)))+~P101(f323(f323(f237(a1),f2(a1)),x66282))+~P101(f323(f323(f237(a1),f2(a1)),x66281))
% 188.07/187.97 [6639]E(x66391,f2(a865))+P101(f323(f323(f238(a865),f2(a865)),x66392))+~P101(f323(f323(f238(a865),f2(a865)),f323(f323(f248(a865),x66392),x66391)))
% 188.07/187.97 [6669]~P90(x66691)+E(f323(f103(x66691),x66692),f2(x66691))+~P30(x66691,f323(f103(x66691),f323(f323(f78(a1),a81),f323(f77(a1),x66692))))
% 188.07/187.97 [6670]~P90(x66701)+E(f323(f103(x66701),x66702),f2(x66701))+~P30(x66701,f323(f103(x66701),f323(f323(f78(a1),x66702),f323(f77(a1),a81))))
% 188.07/187.97 [6728]~P101(f323(f59(x67281),x67282))+~P101(f323(f59(x67281),f246(f872(x67281,a860))))+P101(f323(f59(x67281),f323(f77(f872(x67281,a860)),x67282)))
% 188.07/187.97 [6751]~P101(f323(f323(f238(a1),f2(a1)),x67512))+~P101(f323(f323(f237(a1),x67512),x67511))+P101(f323(f323(f238(a1),f2(a1)),f323(f323(f36(a1),x67511),x67512)))
% 188.07/187.97 [6752]~P101(f323(f323(f237(a1),x67521),f2(a1)))+~P101(f323(f323(f238(a1),x67522),f2(a1)))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f36(a1),x67521),x67522)))
% 188.07/187.97 [6791]~P101(f323(f323(f237(a1),f2(a1)),x67912))+~P101(f323(f323(f237(a1),f2(a1)),x67911))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f79(a1),x67911),x67912)))
% 188.07/187.97 [6792]~P101(f323(f323(f237(a1),f2(a1)),x67922))+~P101(f323(f323(f237(a1),f2(a1)),x67921))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),x67921),x67922)))
% 188.07/187.97 [6793]~P101(f323(f323(f237(a1),f2(a1)),x67932))+~P101(f323(f323(f237(a1),f2(a1)),x67931))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f36(a1),x67931),x67932)))
% 188.07/187.97 [6794]~P101(f323(f323(f237(a1),f2(a1)),x67941))+~P101(f323(f323(f238(a1),f2(a1)),x67942))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f36(a1),x67941),x67942)))
% 188.07/187.97 [6795]~P101(f323(f323(f238(a865),f2(a865)),x67952))+~P101(f323(f323(f238(a865),f2(a865)),x67951))+P101(f323(f323(f238(a865),f2(a865)),f323(f323(f79(a865),x67951),x67952)))
% 188.07/187.97 [6859]E(x68591,f2(a1))+E(f42(a1,x68592,x68591),f2(a1))+E(f323(f323(f22(a1),f323(f77(a1),f323(f323(f36(a1),x68592),x68591))),f76(a1)),f323(f323(f36(a1),f323(f77(a1),x68592)),x68591))
% 188.07/187.97 [6912]P101(f323(f323(f238(a865),f2(a865)),x69121))+P101(f323(f323(f238(a865),f2(a865)),x69122))+~P101(f323(f323(f238(a865),f2(a865)),f323(f323(f78(a865),x69122),x69121)))
% 188.07/187.97 [6916]~P74(x69161)+P101(f323(f323(f237(x69161),f2(x69161)),x69162))+~P101(f323(f323(f237(x69161),f2(x69161)),f323(f323(f78(x69161),x69162),x69162)))
% 188.07/187.97 [6917]~P74(x69171)+P101(f323(f323(f238(x69171),f2(x69171)),x69172))+~P101(f323(f323(f238(x69171),f2(x69171)),f323(f323(f78(x69171),x69172),x69172)))
% 188.07/187.97 [6970]~P101(f323(f59(x69701),x69702))+P101(f323(f59(x69701),f246(f872(x69701,a860))))+~P101(f323(f59(x69701),f323(f77(f872(x69701,a860)),x69702)))
% 188.07/187.97 [7033]P101(f323(f323(f237(a1),x70331),f2(a1)))+~P101(f323(f323(f238(a1),x70332),f2(a1)))+~P101(f323(f323(f237(a1),f2(a1)),f323(f323(f36(a1),x70331),x70332)))
% 188.07/187.97 [7039]~P101(f323(f323(f238(a1),f2(a1)),x70391))+P101(f323(f323(f237(a1),x70391),x70392))+~P101(f323(f323(f238(a1),f2(a1)),f323(f323(f36(a1),x70392),x70391)))
% 188.07/187.97 [7040]~P101(f323(f323(f237(a1),f2(a1)),x70402))+P101(f323(f323(f237(a1),x70401),x70402))+~P101(f323(f323(f238(a1),f2(a1)),f323(f323(f36(a1),x70402),x70401)))
% 188.07/187.97 [7069]P101(f323(f323(f237(a1),f2(a1)),x70691))+~P101(f323(f323(f238(a1),f2(a1)),x70692))+~P101(f323(f323(f237(a1),f2(a1)),f323(f323(f36(a1),x70691),x70692)))
% 188.07/187.97 [7070]P101(f323(f323(f238(a1),f2(a1)),x70701))+~P101(f323(f323(f237(a1),f2(a1)),x70702))+~P101(f323(f323(f238(a1),f2(a1)),f323(f323(f36(a1),x70702),x70701)))
% 188.07/187.97 [7511]~P101(f323(f59(x75112),f246(f872(x75112,a860))))+~P101(f323(f59(x75111),f246(f872(x75111,a860))))+P101(f323(f59(f870(x75111,x75112)),f246(f872(f870(x75111,x75112),a860))))
% 188.07/187.97 [7512]~P101(f323(f59(x75122),f246(f872(x75122,a860))))+~P101(f323(f59(x75121),f246(f872(x75121,a860))))+P101(f323(f59(f871(x75121,x75122)),f246(f872(f871(x75121,x75122),a860))))
% 188.07/187.97 [7581]~P101(f323(f323(f238(a865),f323(a112,f2(a865))),x75811))+~P101(f323(f323(f238(a865),f323(a112,f2(a865))),x75812))+P101(f323(f323(f238(a865),x75811),f323(f323(f79(a865),x75812),x75811)))
% 188.07/187.97 [7582]~P101(f323(f323(f238(a865),f323(a112,f2(a865))),x75821))+~P101(f323(f323(f238(a865),f323(a112,f2(a865))),x75822))+P101(f323(f323(f238(a865),x75821),f323(f323(f79(a865),x75821),x75822)))
% 188.07/187.97 [7616]E(f323(f35(x76161),f246(f872(x76161,a860))),f323(a112,f2(a865)))+P101(f323(f59(x76162),f246(f872(x76162,a860))))+~P101(f323(f59(f872(x76162,x76161)),f246(f872(f872(x76162,x76161),a860))))
% 188.07/187.97 [7744]~P101(f323(f323(f237(a865),f323(a112,f2(a865))),x77441))+~P101(f323(f323(f237(a865),f323(a112,f2(a865))),x77442))+P101(f323(f323(f237(a865),f323(a112,f2(a865))),f323(f323(f79(a865),x77441),x77442)))
% 188.07/187.97 [7745]~P101(f323(f323(f238(a865),f323(a112,f2(a865))),x77452))+~P101(f323(f323(f238(a865),f323(a112,f2(a865))),x77451))+P101(f323(f323(f238(a865),f323(a112,f2(a865))),f323(f323(f79(a865),x77451),x77452)))
% 188.07/187.97 [8425]E(x84251,f113(x84252))+~P101(f323(f130(x84252),x84251))+E(f171(x84252,f323(f323(f8(a860,a860,x84252),a318),f323(f323(f7(x84252,x84252,a860),a320),f137(x84252,x84251))),x84251),f114(x84252,x84251))
% 188.07/187.97 [8518]~P39(x85182)+~P39(x85181)+E(f323(f302(a865,a1,f100(a1)),f323(f323(f110(f872(a865,a860)),f323(f302(a1,a865,a104),x85181)),f323(f302(a1,a865,a104),x85182))),f323(f323(f110(f872(a1,a860)),x85181),x85182))
% 188.07/187.97 [8519]~P39(x85192)+~P39(x85191)+E(f323(f302(a865,a1,f100(a1)),f323(f323(f101(f872(a865,a860)),f323(f302(a1,a865,a104),x85191)),f323(f302(a1,a865,a104),x85192))),f323(f323(f101(f872(a1,a860)),x85191),x85192))
% 188.07/187.97 [9188]~P90(x91881)+~E(f323(f103(x91881),x91882),f76(x91881))+P30(x91881,f323(f103(x91881),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f77(a1),x91882))))
% 188.07/187.97 [9420]~P90(x94201)+E(f323(f103(x94201),x94202),f76(x94201))+~P30(x94201,f323(f103(x94201),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f77(a1),x94202))))
% 188.07/187.97 [10152]E(x101521,f2(a1))+E(x101522,f2(a1))+E(f323(f263(a1,a1,a1,a1,f32(a1),f323(f79(a1),f80(a1,x101522))),f323(f323(f323(f96(f871(a1,a1)),f323(f323(a320,f80(a1,x101521)),f80(a1,x101522))),f50(x101521,x101522)),f323(f323(f262(a1,a1,f871(a1,a1)),f323(f323(f18(a1,f872(a1,f871(a1,a1)),f872(a1,f871(a1,a1))),f323(f323(f8(f872(a1,f872(f871(a1,a1),f871(a1,a1))),f872(f872(a1,f871(a1,a1)),f872(a1,f871(a1,a1))),a1),f18(a1,f871(a1,a1),f871(a1,a1))),f323(f323(f8(f871(a1,a1),f872(a1,f872(f871(a1,a1),f871(a1,a1))),a1),f323(f7(a1,f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),f323(f323(f8(a860,f872(f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),a1),f96(f871(a1,a1))),f323(f323(f7(a1,a1,a860),a320),f2(a1))))),f323(f323(f7(a1,a1,f871(a1,a1)),f323(f323(f8(a1,f872(a1,f871(a1,a1)),a1),f258(a1,a1)),f77(a1))),f2(a1))))),f323(f323(f7(a1,f872(a1,a1),f872(a1,f871(a1,a1))),f323(f323(f8(f872(a1,f871(a1,a1)),f872(f872(a1,a1),f872(a1,f871(a1,a1))),a1),f8(a1,f871(a1,a1),a1)),f323(f323(f8(a1,f872(a1,f871(a1,a1)),a1),f258(a1,a1)),f323(f323(f7(a1,a1,a1),f323(f323(f8(a1,f872(a1,a1),a1),f22(a1)),f77(a1))),f76(a1))))),f323(f22(a1),f323(f73(a1),x101522))))),f50(x101521,x101522)))),f43(x101521,x101522))
% 188.07/187.97 [10153]E(x101531,f2(a1))+E(x101532,f2(a1))+E(f323(f263(a1,a1,a1,a1,f32(a1),f323(f79(a1),f80(a1,x101532))),f323(f323(f323(f96(f871(a1,a1)),f323(f323(a321,f323(f323(a322,f323(f323(f238(a1),f2(a1)),x101532)),f323(f323(f237(a1),f2(a1)),x101531))),f323(f323(a322,f323(f323(f238(a1),x101532),f2(a1))),f323(f323(f238(a1),x101531),f2(a1))))),f50(x101531,x101532)),f323(f323(f262(a1,a1,f871(a1,a1)),f323(f323(f18(a1,f872(a1,f871(a1,a1)),f872(a1,f871(a1,a1))),f323(f323(f8(f872(a1,f872(f871(a1,a1),f871(a1,a1))),f872(f872(a1,f871(a1,a1)),f872(a1,f871(a1,a1))),a1),f18(a1,f871(a1,a1),f871(a1,a1))),f323(f323(f8(f871(a1,a1),f872(a1,f872(f871(a1,a1),f871(a1,a1))),a1),f323(f7(a1,f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),f323(f323(f8(a860,f872(f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),a1),f96(f871(a1,a1))),f323(f323(f7(a1,a1,a860),a320),f2(a1))))),f323(f323(f7(a1,a1,f871(a1,a1)),f323(f323(f8(a1,f872(a1,f871(a1,a1)),a1),f258(a1,a1)),f77(a1))),f2(a1))))),f323(f323(f7(a1,f872(a1,a1),f872(a1,f871(a1,a1))),f323(f323(f8(f872(a1,f871(a1,a1)),f872(f872(a1,a1),f872(a1,f871(a1,a1))),a1),f8(a1,f871(a1,a1),a1)),f323(f323(f8(a1,f872(a1,f871(a1,a1)),a1),f258(a1,a1)),f323(f323(f7(a1,a1,a1),f323(f323(f8(a1,f872(a1,a1),a1),f22(a1)),f77(a1))),f76(a1))))),f323(f22(a1),f323(f73(a1),x101532))))),f50(x101531,x101532)))),f43(x101531,x101532))
% 188.07/187.97 [5689]~P116(x56891)+~P90(x56891)+E(f323(f73(x56891),f323(f323(f248(x56891),f323(f103(x56891),a97)),x56892)),f76(x56891))
% 188.07/187.97 [6164]~P134(x61641)+~P101(f323(f323(f238(a1),x61642),f2(a1)))+E(f323(f77(x61641),f323(f100(x61641),f323(a104,f323(f77(a1),x61642)))),f323(f102(x61641),x61642))
% 188.07/187.97 [6362]P101(f323(f323(f237(a99),x63621),f76(a99)))+E(f323(f323(f78(a99),f76(a99)),f271(x63621,f323(f323(f36(a99),x63622),x63621))),f271(x63621,x63622))+P101(f323(f323(f238(a99),x63622),x63621))
% 188.07/187.97 [6957]~P89(x69571)+~P101(f323(f323(f325(x69571),x69572),f109(x69571)))+~E(f323(f323(f78(x69571),f323(f323(f78(x69571),f76(x69571)),x69572)),x69572),f2(x69571))
% 188.07/187.97 [7071]~P101(f323(f323(f237(a1),x70712),f2(a1)))+~P101(f323(f323(f238(a1),x70711),f2(a1)))+E(f323(f257(a1,a1),f323(a48,f44(f323(f77(a1),x70711),f323(f77(a1),x70712)))),f323(f323(f36(a1),x70711),x70712))
% 188.07/187.97 [7088]~P101(f323(f323(f237(a1),x70882),f2(a1)))+~P101(f323(f323(f238(a1),x70881),f2(a1)))+E(f323(f261(a1,a1),f323(a48,f44(f323(f77(a1),x70881),f323(f77(a1),x70882)))),f42(a1,x70881,x70882))
% 188.07/187.97 [7094]~P101(f323(f323(f238(a1),x70942),f2(a1)))+E(f323(f257(a1,a1),f323(a48,f47(f323(f77(a1),x70941),f323(f77(a1),x70942)))),f323(f323(f36(a1),x70941),x70942))+~P101(f323(f323(f238(a1),f2(a1)),x70941))
% 188.07/187.97 [7112]~P101(f323(f323(f238(a1),x71122),f2(a1)))+E(f323(f261(a1,a1),f323(a48,f47(f323(f77(a1),x71121),f323(f77(a1),x71122)))),f42(a1,x71121,x71122))+~P101(f323(f323(f238(a1),f2(a1)),x71121))
% 188.07/187.97 [7165]E(f323(f323(f36(a1),f323(f323(f248(a1),x71651),x71652)),x71651),f323(f323(f248(a1),x71651),f323(f323(f22(a865),x71652),f323(a112,f2(a865)))))+~P101(f323(f323(f238(a865),f2(a865)),x71652))+~P101(f323(f323(f238(a1),f2(a1)),x71651))
% 188.07/187.97 [7258]~P101(f323(f323(f238(a865),f2(a865)),x72581))+~P101(f323(f323(f238(a865),f2(a865)),x72582))+P101(f323(f323(f238(a865),f323(f323(f22(a865),x72581),x72582)),x72581))
% 188.07/187.97 [7259]~P101(f323(f323(f238(a865),f2(a865)),x72591))+~P101(f323(f323(f238(a865),f76(a865)),x72592))+P101(f323(f323(f238(a865),f323(f323(f36(a865),x72591),x72592)),x72591))
% 188.07/187.97 [7260]~P101(f323(f323(f238(a1),f2(a1)),x72601))+~P101(f323(f323(f238(a1),f76(a1)),x72602))+P101(f323(f323(f238(a1),f323(f323(f36(a1),x72601),x72602)),x72601))
% 188.07/187.97 [7404]E(x74041,f2(a865))+~E(x74042,f2(a1))+~P101(f323(f323(f238(a1),f2(a1)),f323(f323(f248(a1),f323(f73(a1),x74042)),x74041)))
% 188.07/187.97 [7822]~E(x78222,f113(f866(x78221)))+E(f323(f189(f866(f866(x78221))),f173(x78221,x78222)),f2(a865))+~P16(a865,f323(f162(a865),f323(f323(f147(f866(x78221),a865),f189(f866(x78221))),x78222)))
% 188.07/187.97 [8069]P101(f323(x80691,x80692))+~P101(f323(x80691,f323(a107,f684(x80691,x80692))))+~P101(f323(f323(f325(f872(f871(a865,a865),a860)),x80692),a98))
% 188.07/187.97 [8087]E(x80871,f113(f866(x80872)))+E(f323(f189(f866(x80872)),f323(f323(f158(f866(x80872)),x80871),f2(a865))),f323(f189(f866(f866(x80872))),f173(x80872,x80871)))+~P16(a865,f323(f162(a865),f323(f323(f147(f866(x80872),a865),f189(f866(x80872))),x80871)))
% 188.07/187.97 [8806]~P101(f323(f59(x88061),f323(f243(x88061),x88062)))+~P101(f323(f59(x88061),f246(f872(x88061,a860))))+P101(f323(f59(x88061),f323(f243(x88061),f323(f323(f8(a860,a860,x88061),a318),x88062))))
% 188.07/187.97 [8867]E(f323(f323(f258(a865,a865),f323(a112,f323(f323(f36(a865),f323(f323(f22(a865),x88671),x88672)),x88672))),f42(a865,f323(f323(f22(a865),x88671),x88672),x88672)),f83(f871(a865,a865),f45(x88671,x88672)))+~P101(f323(f323(f238(a865),f2(a865)),x88672))+~P101(f323(f323(f237(a865),x88672),x88671))
% 188.07/187.97 [9154]~P101(f323(f59(x91541),f323(f243(x91541),x91542)))+P101(f323(f59(x91541),f246(f872(x91541,a860))))+~P101(f323(f59(x91541),f323(f243(x91541),f323(f323(f8(a860,a860,x91541),a318),x91542))))
% 188.07/187.97 [9877]P29(x98771,x98772)+~P38(x98771,f323(f257(f872(f871(x98771,x98771),a860),f872(f871(x98771,x98771),a860)),x98772))+~P101(f323(f323(f237(f872(f871(x98771,x98771),a860)),f323(f323(f280(x98771,x98771,x98771),f323(f257(f872(f871(x98771,x98771),a860),f872(f871(x98771,x98771),a860)),x98772)),f323(f261(f872(f871(x98771,x98771),a860),f872(f871(x98771,x98771),a860)),x98772))),f323(f257(f872(f871(x98771,x98771),a860),f872(f871(x98771,x98771),a860)),x98772)))
% 188.07/187.97 [7191]~P101(f323(f323(f238(a865),f2(a865)),x71912))+P101(f323(f323(f238(a865),x71911),x71912))+E(f323(a112,f323(f323(f36(a865),f323(f323(f22(a865),x71911),x71912)),x71912)),f323(f323(f36(a865),x71911),x71912))
% 188.07/187.97 [7325]~P101(f323(f323(f238(a865),f2(a865)),x73252))+~P101(f323(f323(f237(a865),x73252),x73251))+E(f323(a112,f323(f323(f36(a865),f323(f323(f22(a865),x73251),x73252)),x73252)),f323(f323(f36(a865),x73251),x73252))
% 188.07/187.97 [8298]~P90(x82981)+~P89(x82981)+~P30(x82981,f323(f103(x82981),f323(f323(f22(a1),f323(f323(f78(a1),x82982),x82982)),a97)))
% 188.07/187.97 [9062]E(x90621,f2(a865))+E(f323(f323(f262(a865,a865,f871(a865,a865)),f323(f323(f8(a865,f872(a865,f871(a865,a865)),a865),f258(a865,a865)),a112)),f83(f871(a865,a865),f45(f323(f323(f22(a865),x90622),x90621),x90621))),f83(f871(a865,a865),f45(x90622,x90621)))+P101(f323(f323(f238(a865),x90622),x90621))
% 188.07/187.97 [9486]P101(f323(x94862,f775(x94862,x94861)))+P101(f323(x94861,f775(x94862,x94861)))+E(f323(f243(a1),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f237(a1),f2(a1)))),x94861)),f323(f243(a1),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f237(a1),f2(a1)))),x94862)))
% 188.07/187.97 [9490]~P101(f323(x94902,f775(x94902,x94901)))+~P101(f323(x94901,f775(x94902,x94901)))+E(f323(f243(a1),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f237(a1),f2(a1)))),x94901)),f323(f243(a1),f323(f323(f18(a1,a860,a860),f323(f323(f8(a860,f872(a860,a860),a1),a322),f323(f237(a1),f2(a1)))),x94902)))
% 188.07/187.97 [7539]~P63(x75391)+~P90(x75391)+E(f323(f323(f281(x75391),x75392),f323(f103(x75391),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),x75392)
% 188.07/187.97 [9187]~P90(x91871)+~E(f323(f103(x91871),x91872),f76(x91871))+P30(x91871,f323(f103(x91871),f323(f323(f78(a1),x91872),f323(f77(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 188.07/187.97 [9364]~P133(x93641)+~E(x93642,f76(x93641))+E(f323(f323(f248(x93641),x93642),f323(f103(a865),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(x93641))
% 188.07/187.97 [9365]~P133(x93651)+~E(x93652,f2(x93651))+E(f323(f323(f248(x93651),x93652),f323(f103(a865),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(x93651))
% 188.07/187.97 [9378]~P133(x93781)+~E(x93782,f323(f77(x93781),f76(x93781)))+E(f323(f323(f248(x93781),x93782),f323(f103(a865),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(x93781))
% 188.07/187.97 [9421]~P90(x94211)+E(f323(f103(x94211),x94212),f76(x94211))+~P30(x94211,f323(f103(x94211),f323(f323(f78(a1),x94212),f323(f77(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 188.07/187.97 [9813]~P116(x98132)+E(x98131,f2(x98132))+P101(f323(f323(f238(x98132),f2(x98132)),f323(f323(f248(x98132),x98131),f323(f103(a865),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))))))
% 188.07/187.97 [9876]~P116(x98762)+~E(x98761,f2(x98762))+~P101(f323(f323(f238(x98762),f2(x98762)),f323(f323(f248(x98762),x98761),f323(f103(a865),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))))))
% 188.07/187.97 [9902]P101(f323(f323(f237(a1),x99021),f2(a1)))+P101(f323(f323(f238(a1),x99022),x99021))+E(f323(f41(x99021),f44(x99022,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)))),x99021))),f44(x99022,x99021))
% 188.07/187.97 [9903]~P101(f323(f323(f238(a1),f2(a1)),x99031))+P101(f323(f323(f238(a1),x99032),x99031))+E(f323(f41(x99031),f44(x99032,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)))),x99031))),f44(x99032,x99031))
% 188.07/187.97 [9904]P101(f323(f323(f237(a1),x99041),f2(a1)))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),x99042),x99041)))+E(f323(f41(x99041),f47(x99042,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)))),x99041))),f47(x99042,x99041))
% 188.07/187.97 [9905]~P101(f323(f323(f238(a1),f2(a1)),x99051))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),x99052),x99051)))+E(f323(f41(x99051),f47(x99052,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)))),x99051))),f47(x99052,x99051))
% 188.07/187.97 [9906]~P140(x99061)+~P101(f323(f323(f237(a1),f2(a1)),x99062))+E(f323(f100(x99061),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)))),x99062))),f323(f323(f78(x99061),f323(f100(x99061),f323(a104,x99062))),f323(f100(x99061),f323(a104,x99062))))
% 188.07/187.97 [5038]~P142(x50381,x50382,x50383)+~E(x50383,f2(a1))+P101(f323(x50381,x50382))
% 188.07/187.97 [5158]~P103(x51581)+~P16(x51581,x51583)+P16(x51581,f164(x51581,x51582,x51583))
% 188.07/187.97 [5159]~P103(x51591)+~P16(x51591,x51593)+P16(x51591,f171(x51591,x51592,x51593))
% 188.07/187.97 [4744]~P59(x47442)+~E(x47443,f323(f77(x47442),x47441))+E(x47441,f323(f77(x47442),x47443))
% 188.07/187.97 [4746]~P59(x47461)+~E(f323(f77(x47461),x47463),x47462)+E(f323(f77(x47461),x47462),x47463)
% 188.07/187.97 [4821]~P87(x48213)+E(x48211,x48212)+~E(f323(f77(x48213),x48211),f323(f77(x48213),x48212))
% 188.07/187.97 [4822]~P59(x48223)+E(x48221,x48222)+~E(f323(f77(x48223),x48221),f323(f77(x48223),x48222))
% 188.07/187.97 [4823]~P103(x48233)+E(x48231,x48232)+~E(f323(f244(x48233),x48231),f323(f244(x48233),x48232))
% 188.07/187.97 [4824]~P99(x48243)+E(x48241,x48242)+~E(f323(f100(x48243),x48241),f323(f100(x48243),x48242))
% 188.07/187.97 [4825]~P103(x48253)+E(x48251,x48252)+~E(f323(f295(x48253),x48251),f323(f295(x48253),x48252))
% 188.07/187.97 [4826]~P103(x48263)+E(x48261,x48262)+~E(f323(f245(x48263),x48261),f323(f245(x48263),x48262))
% 188.07/187.97 [4827]~P89(x48273)+E(x48271,x48272)+~E(f323(f102(x48273),x48271),f323(f102(x48273),x48272))
% 188.07/187.97 [4828]~P103(x48283)+E(x48281,x48282)+~E(f323(f292(x48283),x48281),f323(f292(x48283),x48282))
% 188.07/187.97 [4927]~P5(x49271)+~P101(f323(x49272,x49273))+P101(f323(f55(x49271),x49272))
% 188.07/187.97 [4960]~P5(x49603)+P101(f323(x49601,x49602))+~P101(f323(f56(x49603),x49601))
% 188.07/187.97 [5057]~P143(x50571,x50573,x50572)+~E(x50572,f2(a1))+P101(f323(x50571,f2(a1)))
% 188.07/187.97 [5095]~E(x50951,f2(a865))+E(f803(x50951,x50952,x50953),f188(f872(x50953,a860)))+~E(f323(f35(x50953),x50952),f323(a112,x50951))
% 188.07/187.97 [5238]~E(x52382,f2(a865))+E(f323(f257(a865,a865),x52381),f2(a865))+~P101(f323(f45(x52383,x52382),x52381))
% 188.07/187.97 [5283]P101(f323(x52831,x52832))+~E(x52833,f323(f100(a1),x52832))+~P101(f323(x52831,f323(a104,x52833)))
% 188.07/187.97 [5752]~E(x57523,f2(a865))+~P101(f323(x57521,x57522))+P101(f323(x57521,f42(a865,x57522,x57523)))
% 188.07/187.97 [5913]~P5(x59133)+~P12(x59133,x59131,x59132)+P101(f323(x59131,f541(x59132,x59131,x59133)))
% 188.07/187.97 [6147]~E(x61473,f2(a865))+P101(f323(x61471,x61472))+~P101(f323(x61471,f42(a865,x61472,x61473)))
% 188.07/187.97 [6294]~P5(x62941)+P13(x62941,x62942,x62943)+~P101(f323(x62942,f542(x62943,x62942,x62941)))
% 188.07/187.97 [6817]E(x68171,f2(a865))+~P101(f323(x68172,f492(x68171,x68173,x68172)))+P101(f323(x68172,f42(a865,x68173,x68171)))
% 188.07/187.97 [6922]~P6(x69221)+~P101(f323(f323(f237(x69221),x69222),f644(x69223,x69222,x69221)))+P101(f323(f323(f237(x69221),x69222),f38(x69221,x69223)))
% 188.07/187.97 [6924]~P101(f323(x69241,x69242))+~P101(f323(x69241,f492(x69243,x69242,x69241)))+P101(f323(x69241,f42(a865,x69242,x69243)))
% 188.07/187.97 [7026]E(x70261,f113(x70262))+E(f323(f323(f144(x70262),f625(x70263,x70261,x70262)),f630(x70263,x70261,x70262)),x70261)+~P101(f323(f323(f325(f866(x70262)),x70261),f154(x70262,x70263)))
% 188.07/187.97 [7057]~P134(x70571)+~P101(f323(f323(f325(x70571),x70572),f109(x70571)))+P101(f323(f323(f325(x70571),f323(f323(f248(x70571),x70572),x70573)),f109(x70571)))
% 188.07/187.97 [7374]P38(x73741,x73742)+~P101(f323(f323(f325(x73741),x73743),f735(x73742,x73741)))+P101(f323(f323(f325(x73741),f774(x73742,x73741,x73743)),f735(x73742,x73741)))
% 188.07/187.97 [7643]E(x76431,f113(x76432))+~P101(f323(f323(f325(f866(x76432)),x76431),f154(x76432,x76433)))+P101(f323(f323(f325(f866(x76432)),f630(x76433,x76431,x76432)),f154(x76432,x76433)))
% 188.07/187.97 [7696]E(x76961,f2(a865))+E(f323(f323(f78(a865),f323(f323(f79(a865),x76961),f493(x76961,x76962,x76963))),f492(x76961,x76962,x76963)),x76962)+P101(f323(x76963,f42(a865,x76962,x76961)))
% 188.07/187.97 [7739]~P101(f323(x77393,x77392))+E(f323(f323(f78(a865),f323(f323(f79(a865),x77391),f493(x77391,x77392,x77393))),f492(x77391,x77392,x77393)),x77392)+P101(f323(x77393,f42(a865,x77392,x77391)))
% 188.07/187.97 [7880]P101(f323(f323(f238(a1),x78801),f482(x78802,x78803,x78801)))+P101(f323(f323(x78803,f323(f323(f36(a1),x78802),x78801)),f42(a1,x78802,x78801)))+~P101(f323(f323(f238(a1),x78801),f2(a1)))
% 188.07/187.97 [8147]P101(f323(f323(x81472,f323(f323(f36(a1),x81471),x81473)),f42(a1,x81471,x81473)))+~P101(f323(f323(f238(a1),x81473),f2(a1)))+P101(f323(f323(f237(a1),f482(x81471,x81472,x81473)),f2(a1)))
% 188.07/187.97 [8334]E(f323(f323(f78(a1),f323(f323(f79(a1),x83341),f483(x83342,x83343,x83341))),f482(x83342,x83343,x83341)),x83342)+P101(f323(f323(x83343,f323(f323(f36(a1),x83342),x83341)),f42(a1,x83342,x83341)))+~P101(f323(f323(f238(a1),x83341),f2(a1)))
% 188.07/187.97 [8568]~P101(f323(f323(x85681,f483(x85682,x85681,x85683)),f482(x85682,x85681,x85683)))+P101(f323(f323(x85681,f323(f323(f36(a1),x85682),x85683)),f42(a1,x85682,x85683)))+~P101(f323(f323(f238(a1),x85683),f2(a1)))
% 188.07/187.97 [8816]~P103(x88161)+~P16(x88161,x88163)+P16(x88161,f142(x88161,x88161,f5(x88161),x88162,x88163))
% 188.07/187.97 [9314]~P120(x93142)+E(x93141,f2(x93142))+~P101(f323(f323(f237(x93142),f323(f323(f78(x93142),f323(f323(f79(x93142),x93143),x93143)),f323(f323(f79(x93142),x93141),x93141))),f2(x93142)))
% 188.07/187.97 [9315]~P120(x93152)+E(x93151,f2(x93152))+~P101(f323(f323(f237(x93152),f323(f323(f78(x93152),f323(f323(f79(x93152),x93151),x93151)),f323(f323(f79(x93152),x93153),x93153))),f2(x93152)))
% 188.07/187.97 [10091]~P116(x100911)+~P101(f323(f323(f238(x100911),x100912),f2(x100911)))+P101(f323(f323(f238(x100911),f323(f323(f248(x100911),x100912),f323(a112,f323(f323(f79(a865),f323(f103(a865),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)))),x100913)))),f2(x100911)))
% 188.07/187.97 [10100]~P116(x101002)+E(x101001,f2(x101002))+~P101(f323(f323(f237(x101002),f323(f323(f78(x101002),f323(f323(f248(x101002),x101003),f323(f103(a865),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(x101002),x101001),f323(f103(a865),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(x101002)))
% 188.07/187.97 [10101]~P116(x101012)+E(x101011,f2(x101012))+~P101(f323(f323(f237(x101012),f323(f323(f78(x101012),f323(f323(f248(x101012),x101011),f323(f103(a865),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(x101012),x101013),f323(f103(a865),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(x101012)))
% 188.07/187.97 [4778]~E(x47782,x47783)+~P59(x47781)+E(f323(f323(f22(x47781),x47782),x47783),f2(x47781))
% 188.07/187.97 [4779]~E(x47792,x47793)+~P60(x47791)+E(f323(f323(f22(x47791),x47792),x47793),f2(x47791))
% 188.07/187.97 [4792]~P135(x47921)+~E(x47923,f2(x47921))+E(f323(f323(f78(x47921),x47922),x47923),x47922)
% 188.07/187.97 [4807]~P137(x48071)+~E(x48073,f2(x48071))+E(f323(f323(f79(x48071),x48072),x48073),f2(x48071))
% 188.07/187.97 [4808]~P137(x48081)+~E(x48082,f2(x48081))+E(f323(f323(f79(x48081),x48082),x48083),f2(x48081))
% 188.07/187.97 [4830]~E(x48303,f113(x48301))+~E(x48302,f113(x48301))+E(f323(f323(f121(x48301),x48302),x48303),f113(x48301))
% 188.07/187.97 [4917]~P135(x49172)+E(x49171,f2(x49172))+~E(f323(f323(f78(x49172),x49173),x49171),x49173)
% 188.07/187.97 [4918]~P59(x49181)+~E(x49182,f323(f77(x49181),x49183))+E(f323(f323(f78(x49181),x49182),x49183),f2(x49181))
% 188.07/187.97 [4925]E(x49251,f113(x49252))+E(x49253,f2(a865))+~E(f323(f323(f169(x49252),x49253),x49251),f113(x49252))
% 188.07/187.97 [4931]~P59(x49313)+E(x49311,x49312)+~E(f323(f323(f22(x49313),x49311),x49312),f2(x49313))
% 188.07/187.97 [4932]~P60(x49323)+E(x49321,x49322)+~E(f323(f323(f22(x49323),x49321),x49322),f2(x49323))
% 188.07/187.97 [4941]~P133(x49412)+E(x49411,f2(x49412))+~E(f323(f323(f248(x49412),x49411),x49413),f2(x49412))
% 188.07/187.97 [4942]~P3(x49422)+E(x49421,f188(x49422))+~E(f323(f323(f110(x49422),x49423),x49421),f188(x49422))
% 188.07/187.97 [4943]~P3(x49432)+E(x49431,f188(x49432))+~E(f323(f323(f110(x49432),x49431),x49433),f188(x49432))
% 188.07/187.97 [4944]~P95(x49442)+E(x49441,f246(x49442))+~E(f323(f323(f101(x49442),x49443),x49441),f246(x49442))
% 188.07/187.97 [4945]~P95(x49452)+E(x49451,f246(x49452))+~E(f323(f323(f101(x49452),x49451),x49453),f246(x49452))
% 188.07/187.97 [5011]~P59(x50112)+E(x50111,f323(f77(x50112),x50113))+~E(f323(f323(f78(x50112),x50111),x50113),f2(x50112))
% 188.07/187.97 [5012]~P59(x50121)+E(f323(f77(x50121),x50122),x50123)+~E(f323(f323(f78(x50121),x50122),x50123),f2(x50121))
% 188.07/187.97 [5014]~E(x50142,x50143)+~P102(x50141)+P101(f323(f323(f237(x50141),x50142),x50143))
% 188.07/187.97 [5016]~E(x50162,x50163)+~P105(x50161)+P101(f323(f323(f237(x50161),x50162),x50163))
% 188.07/187.97 [5017]~E(x50172,x50173)+~P92(x50171)+P101(f323(f323(f89(x50171),x50172),x50173))
% 188.07/187.97 [5111]~P108(x51111)+~E(x51112,f323(f77(x51111),x51113))+E(f323(f323(f79(x51111),x51112),x51112),f323(f323(f79(x51111),x51113),x51113))
% 188.07/187.97 [5119]~P103(x51191)+~P16(x51191,x51193)+P16(x51191,f323(f323(f169(x51191),x51192),x51193))
% 188.07/187.97 [5120]~P103(x51201)+~P16(x51201,x51203)+P16(x51201,f323(f323(f131(x51201),x51202),x51203))
% 188.07/187.97 [5156]E(x51561,x51562)+E(x51563,f2(a865))+~E(f323(f323(f79(a865),x51563),x51561),f323(f323(f79(a865),x51563),x51562))
% 188.07/187.97 [5157]E(x51571,x51572)+E(x51573,f2(a865))+~E(f323(f323(f79(a865),x51571),x51573),f323(f323(f79(a865),x51572),x51573))
% 188.07/187.97 [5229]~E(x52292,x52293)+~P105(x52291)+E(f294(x52291,x52292,x52293),f323(f323(f301(x52291),x52292),f188(f872(x52291,a860))))
% 188.07/187.97 [5270]E(x52701,x52702)+~P92(x52703)+~P101(f323(f323(f89(x52703),x52701),x52702))
% 188.07/187.97 [5281]~E(x52811,x52812)+~P103(x52813)+~P101(f323(f323(f238(x52813),x52811),x52812))
% 188.07/187.97 [5282]~E(x52821,x52822)+~P105(x52823)+~P101(f323(f323(f238(x52823),x52821),x52822))
% 188.07/187.97 [5292]~P105(x52921)+E(f323(f293(x52921,x52922),x52923),f188(f872(x52921,a860)))+P101(f323(f323(f238(x52921),x52922),x52923))
% 188.07/187.97 [5339]~P105(x53391)+E(f294(x53391,x53392,x53393),f188(f872(x53391,a860)))+P101(f323(f323(f237(x53391),x53392),x53393))
% 188.07/187.97 [5340]~P105(x53401)+E(f296(x53401,x53402,x53403),f188(f872(x53401,a860)))+P101(f323(f323(f238(x53401),x53402),x53403))
% 188.07/187.97 [5341]~P105(x53411)+E(f188(f872(x53411,a860)),f294(x53411,x53412,x53413))+P101(f323(f323(f237(x53411),x53412),x53413))
% 188.07/187.97 [5342]~P105(x53421)+E(f188(f872(x53421,a860)),f296(x53421,x53422,x53423))+P101(f323(f323(f238(x53421),x53422),x53423))
% 188.07/187.97 [5350]~P97(x53501)+~E(f323(f323(f110(x53501),x53502),x53503),x53503)+P101(f323(f323(f237(x53501),x53502),x53503))
% 188.07/187.97 [5351]~P98(x53511)+~E(f323(f323(f101(x53511),x53512),x53513),x53512)+P101(f323(f323(f237(x53511),x53512),x53513))
% 188.07/187.97 [5352]~P103(x53521)+~E(f323(f323(f235(x53521),x53522),x53523),x53522)+P101(f323(f323(f237(x53521),x53522),x53523))
% 188.07/187.97 [5353]~P103(x53531)+~E(f323(f323(f236(x53531),x53532),x53533),x53533)+P101(f323(f323(f237(x53531),x53532),x53533))
% 188.07/187.97 [5373]~P103(x53731)+P16(x53731,x53732)+~P16(x53731,f323(f323(f144(x53731),x53733),x53732))
% 188.07/187.97 [5374]~P103(x53741)+P16(x53741,x53742)+~P16(x53741,f323(f323(f121(x53741),x53743),x53742))
% 188.07/187.97 [5375]~P103(x53751)+P16(x53751,x53752)+~P16(x53751,f323(f323(f121(x53751),x53752),x53753))
% 188.07/187.97 [5440]~P103(x54401)+P101(f323(f323(f237(x54401),x54403),x54402))+P101(f323(f323(f237(x54401),x54402),x54403))
% 188.07/187.97 [5445]~P103(x54451)+P101(f323(f323(f238(x54451),x54453),x54452))+P101(f323(f323(f237(x54451),x54452),x54453))
% 188.07/187.97 [5483]~P97(x54831)+E(f323(f323(f110(x54831),x54832),x54833),x54832)+~P101(f323(f323(f237(x54831),x54833),x54832))
% 188.07/187.97 [5485]~P97(x54851)+E(f323(f323(f110(x54851),x54852),x54853),x54853)+~P101(f323(f323(f237(x54851),x54852),x54853))
% 188.07/187.97 [5486]~P98(x54861)+E(f323(f323(f101(x54861),x54862),x54863),x54863)+~P101(f323(f323(f237(x54861),x54863),x54862))
% 188.07/187.97 [5488]~P98(x54881)+E(f323(f323(f101(x54881),x54882),x54883),x54882)+~P101(f323(f323(f237(x54881),x54882),x54883))
% 188.07/187.97 [5489]~P103(x54891)+E(f323(f323(f235(x54891),x54892),x54893),x54893)+~P101(f323(f323(f237(x54891),x54893),x54892))
% 188.07/187.97 [5491]~P103(x54911)+E(f323(f323(f235(x54911),x54912),x54913),x54912)+~P101(f323(f323(f237(x54911),x54912),x54913))
% 188.07/187.97 [5492]~P103(x54921)+E(f323(f323(f236(x54921),x54922),x54923),x54922)+~P101(f323(f323(f237(x54921),x54923),x54922))
% 188.07/187.97 [5494]~P103(x54941)+E(f323(f323(f236(x54941),x54942),x54943),x54943)+~P101(f323(f323(f237(x54941),x54942),x54943))
% 188.07/187.97 [5501]~P114(x55012)+E(x55011,f2(x55012))+E(f323(f323(f281(x55012),f323(f77(x55012),x55013)),f323(f77(x55012),x55011)),f323(f323(f281(x55012),x55013),x55011))
% 188.07/187.97 [5546]~P105(x55461)+E(f323(f293(x55461,x55462),x55463),f188(f872(x55461,a860)))+~P101(f323(f323(f237(x55461),x55463),x55462))
% 188.07/187.97 [5578]~P105(x55781)+E(f294(x55781,x55782,x55783),f188(f872(x55781,a860)))+~P101(f323(f323(f238(x55781),x55783),x55782))
% 188.07/187.97 [5579]~P105(x55791)+E(f297(x55791,x55792,x55793),f188(f872(x55791,a860)))+~P101(f323(f323(f237(x55791),x55793),x55792))
% 188.07/187.97 [5580]~P105(x55801)+E(f296(x55801,x55802,x55803),f188(f872(x55801,a860)))+~P101(f323(f323(f237(x55801),x55803),x55802))
% 188.07/187.97 [5631]~E(f323(f323(f22(a865),x56311),x56313),x56312)+E(x56311,f323(f323(f78(a865),x56312),x56313))+~P101(f323(f323(f237(a865),x56313),x56311))
% 188.07/187.97 [5632]~E(x56321,f323(f323(f78(a865),x56323),x56322))+E(f323(f323(f22(a865),x56321),x56322),x56323)+~P101(f323(f323(f237(a865),x56322),x56321))
% 188.07/187.97 [5678]~P101(f323(x56781,x56783))+P101(f323(x56781,f375(x56781,x56782)))+~P101(f323(f323(f237(a865),x56783),x56782))
% 188.07/187.97 [5679]~P101(f323(x56791,x56793))+P101(f323(x56791,f386(x56791,x56792)))+~P101(f323(f323(f238(a865),x56793),x56792))
% 188.07/187.97 [5687]~P105(x56871)+~E(f323(f293(x56871,x56872),x56873),f188(f872(x56871,a860)))+~P101(f323(f323(f238(x56871),x56872),x56873))
% 188.07/187.97 [5692]~P102(x56921)+~P101(f323(f323(f238(x56921),x56922),x56923))+P101(f323(f323(f237(x56921),x56922),x56923))
% 188.07/187.97 [5694]~P105(x56941)+~P101(f323(f323(f238(x56941),x56942),x56943))+P101(f323(f323(f237(x56941),x56942),x56943))
% 188.07/187.97 [5800]~P105(x58001)+~E(f294(x58001,x58002,x58003),f188(f872(x58001,a860)))+~P101(f323(f323(f237(x58001),x58002),x58003))
% 188.07/187.97 [5801]~P105(x58011)+~E(f296(x58011,x58012,x58013),f188(f872(x58011,a860)))+~P101(f323(f323(f238(x58011),x58012),x58013))
% 188.07/187.97 [5802]~P105(x58021)+~E(f188(f872(x58021,a860)),f294(x58021,x58022,x58023))+~P101(f323(f323(f237(x58021),x58022),x58023))
% 188.07/187.97 [5803]~P105(x58031)+~E(f188(f872(x58031,a860)),f296(x58031,x58032,x58033))+~P101(f323(f323(f238(x58031),x58032),x58033))
% 188.07/187.97 [5811]P101(f323(x58111,x58112))+~P101(f323(x58111,f378(x58111,x58113)))+~P101(f323(f323(f237(a865),x58112),x58113))
% 188.07/187.97 [5812]P101(f323(x58121,x58122))+~P101(f323(x58121,f387(x58121,x58123)))+~P101(f323(f323(f238(a865),x58122),x58123))
% 188.07/187.97 [5820]~E(x58201,f323(a112,x58203))+P101(f323(f323(f238(a865),x58201),f323(a112,x58202)))+~P101(f323(f323(f238(a865),x58203),x58202))
% 188.07/187.97 [5836]E(x58361,x58362)+~E(f323(f323(f79(a865),x58363),x58361),f323(f323(f79(a865),x58363),x58362))+~P101(f323(f323(f238(a865),f2(a865)),x58363))
% 188.07/187.97 [5892]E(f323(x58921,f332(x58921,x58922,x58923)),f76(a865))+~E(f323(f323(f6(x58923,a865),x58921),x58922),f76(a865))+~P101(f323(f59(x58923),x58922))
% 188.07/187.97 [5904]~P6(x59041)+P101(f323(f323(f237(x59041),x59042),f37(x59041,x59043)))+~P101(f323(f323(f325(x59041),x59042),x59043))
% 188.07/187.97 [5930]~P102(x59301)+~P101(f323(f323(f238(x59301),x59303),x59302))+~P101(f323(f323(f237(x59301),x59302),x59303))
% 188.07/187.97 [5934]~P102(x59341)+~P101(f323(f323(f238(x59341),x59343),x59342))+~P101(f323(f323(f238(x59341),x59342),x59343))
% 188.07/187.97 [5937]~P103(x59371)+~P101(f323(f323(f238(x59371),x59373),x59372))+~P101(f323(f323(f237(x59371),x59372),x59373))
% 188.07/187.97 [5938]~P103(x59381)+~P101(f323(f323(f238(x59381),x59383),x59382))+~P101(f323(f323(f238(x59381),x59382),x59383))
% 188.07/187.97 [5939]~P105(x59391)+~P101(f323(f323(f238(x59391),x59393),x59392))+~P101(f323(f323(f238(x59391),x59392),x59393))
% 188.07/187.97 [5964]~E(f323(x59642,f333(x59642,x59643,x59641)),f2(a865))+E(f323(f323(f6(x59641,a865),x59642),x59643),f2(a865))+~P101(f323(f59(x59641),x59643))
% 188.07/187.97 [5965]~E(f323(x59652,f465(x59652,x59653,x59651)),f76(a865))+E(f323(f323(f9(x59651,a865),x59652),x59653),f76(a865))+~P101(f323(f59(x59651),x59653))
% 188.07/187.97 [5978]~P104(x59781)+~P101(f323(f323(f238(x59781),x59783),x59782))+P101(f323(f323(f325(x59781),x59782),f323(f295(x59781),x59783)))
% 188.07/187.97 [5979]~P104(x59791)+~P101(f323(f323(f237(x59791),x59793),x59792))+P101(f323(f323(f325(x59791),x59792),f323(f245(x59791),x59793)))
% 188.07/187.97 [5980]~P104(x59801)+~P101(f323(f323(f238(x59801),x59802),x59803))+P101(f323(f323(f325(x59801),x59802),f323(f244(x59801),x59803)))
% 188.07/187.97 [5981]~P104(x59811)+~P101(f323(f323(f237(x59811),x59812),x59813))+P101(f323(f323(f325(x59811),x59812),f323(f292(x59811),x59813)))
% 188.07/187.97 [5993]E(f323(x59931,f358(x59931,x59932,x59933)),f323(a112,f2(a865)))+~E(f323(f323(f6(x59933,a865),x59931),x59932),f323(a112,f2(a865)))+~P101(f323(f59(x59933),x59932))
% 188.07/187.97 [6076]~P6(x60761)+~P101(f323(f323(f325(x60761),x60763),x60762))+P101(f323(f323(f237(x60761),f38(x60761,x60762)),x60763))
% 188.07/187.97 [6093]~P101(f323(f323(f237(a865),x60931),x60933))+P101(f323(f323(f237(a865),x60931),x60932))+~P101(f323(f323(f237(a865),x60933),x60932))
% 188.07/187.97 [6094]~P101(f323(f323(f237(a1),x60941),x60943))+P101(f323(f323(f237(a1),x60941),x60942))+~P101(f323(f323(f237(a1),x60943),x60942))
% 188.07/187.97 [6111]~P104(x61111)+~P101(f323(f323(f325(x61111),x61113),f323(f245(x61111),x61112)))+P101(f323(f323(f237(x61111),x61112),x61113))
% 188.07/187.97 [6112]~P104(x61121)+~P101(f323(f323(f325(x61121),x61122),f323(f292(x61121),x61123)))+P101(f323(f323(f237(x61121),x61122),x61123))
% 188.07/187.97 [6113]~P104(x61131)+~P101(f323(f323(f325(x61131),x61133),f323(f295(x61131),x61132)))+P101(f323(f323(f238(x61131),x61132),x61133))
% 188.07/187.97 [6114]~P104(x61141)+~P101(f323(f323(f325(x61141),x61142),f323(f244(x61141),x61143)))+P101(f323(f323(f238(x61141),x61142),x61143))
% 188.07/187.97 [6328]~P64(x63281)+P101(f323(f323(f238(x63281),f2(x63281)),f475(x63283,x63282,x63281)))+P101(f323(f323(f237(x63281),x63282),x63283))
% 188.07/187.97 [6395]~P75(x63951)+~P101(f323(f323(f237(x63951),x63953),f323(f77(x63951),x63952)))+P101(f323(f323(f237(x63951),x63952),f323(f77(x63951),x63953)))
% 188.07/187.97 [6397]~P75(x63971)+~P101(f323(f323(f238(x63971),x63973),f323(f77(x63971),x63972)))+P101(f323(f323(f238(x63971),x63972),f323(f77(x63971),x63973)))
% 188.07/187.97 [6409]~P101(f323(f323(f238(a865),x64091),x64093))+~P101(f323(f323(f238(a865),x64093),x64092))+P101(f323(f323(f238(a865),f323(a112,x64091)),x64092))
% 188.07/187.97 [6434]~P119(x64341)+P101(f323(f323(f237(x64341),f323(f100(x64341),x64342)),f323(f100(x64341),x64343)))+~P101(f323(f323(f237(a865),x64342),x64343))
% 188.07/187.97 [6435]~P116(x64351)+P101(f323(f323(f237(x64351),f323(f102(x64351),x64352)),f323(f102(x64351),x64353)))+~P101(f323(f323(f237(a1),x64352),x64353))
% 188.07/187.97 [6437]~P116(x64371)+P101(f323(f323(f238(x64371),f323(f102(x64371),x64372)),f323(f102(x64371),x64373)))+~P101(f323(f323(f238(a1),x64372),x64373))
% 188.07/187.97 [6438]~P119(x64381)+P101(f323(f323(f238(x64381),f323(f100(x64381),x64382)),f323(f100(x64381),x64383)))+~P101(f323(f323(f238(a865),x64382),x64383))
% 188.07/187.97 [6444]~P103(x64441)+E(f323(f323(f110(f872(x64441,a860)),f323(f244(x64441),x64442)),f323(f293(x64441,x64442),x64443)),f323(f244(x64441),x64443))+~P101(f323(f323(f237(x64441),x64442),x64443))
% 188.07/187.97 [6474]~P75(x64741)+~P101(f323(f323(f237(x64741),x64743),x64742))+P101(f323(f323(f237(x64741),f323(f77(x64741),x64742)),f323(f77(x64741),x64743)))
% 188.07/187.97 [6476]~P87(x64761)+~P101(f323(f323(f237(x64761),x64763),x64762))+P101(f323(f323(f237(x64761),f323(f77(x64761),x64762)),f323(f77(x64761),x64763)))
% 188.07/187.97 [6477]~P75(x64771)+~P101(f323(f323(f238(x64771),x64773),x64772))+P101(f323(f323(f238(x64771),f323(f77(x64771),x64772)),f323(f77(x64771),x64773)))
% 188.07/187.97 [6510]~P103(x65101)+E(f323(f323(f110(f872(x65101,a860)),f323(f244(x65101),x65102)),f294(x65101,x65102,x65103)),f323(f292(x65101),x65103))+~P101(f323(f323(f237(x65101),x65102),x65103))
% 188.07/187.97 [6511]~P103(x65111)+E(f323(f323(f110(f872(x65111,a860)),f323(f292(x65111),x65112)),f297(x65111,x65112,x65113)),f323(f244(x65111),x65113))+~P101(f323(f323(f238(x65111),x65112),x65113))
% 188.07/187.97 [6512]~P103(x65121)+E(f323(f323(f110(f872(x65121,a860)),f323(f292(x65121),x65122)),f296(x65121,x65122,x65123)),f323(f292(x65121),x65123))+~P101(f323(f323(f237(x65121),x65122),x65123))
% 188.07/187.97 [6546]~P103(x65461)+E(f323(f323(f110(f872(x65461,a860)),f323(f293(x65461,x65462),x65463)),f323(f245(x65461),x65463)),f323(f245(x65461),x65462))+~P101(f323(f323(f237(x65461),x65462),x65463))
% 188.07/187.97 [6699]~P103(x66991)+E(f323(f323(f110(f872(x66991,a860)),f294(x66991,x66992,x66993)),f323(f295(x66991),x66993)),f323(f245(x66991),x66992))+~P101(f323(f323(f237(x66991),x66992),x66993))
% 188.07/187.97 [6700]~P103(x67001)+E(f323(f323(f110(f872(x67001,a860)),f297(x67001,x67002,x67003)),f323(f245(x67001),x67003)),f323(f295(x67001),x67002))+~P101(f323(f323(f238(x67001),x67002),x67003))
% 188.07/187.97 [6701]~P103(x67011)+E(f323(f323(f110(f872(x67011,a860)),f296(x67011,x67012,x67013)),f323(f295(x67011),x67013)),f323(f295(x67011),x67012))+~P101(f323(f323(f237(x67011),x67012),x67013))
% 188.07/187.97 [6719]P101(f323(x67191,x67192))+~P101(f323(f323(f237(a865),x67192),x67193))+P101(f323(f323(f325(a865),f378(x67191,x67193)),f294(a865,f2(a865),x67193)))
% 188.07/187.97 [6753]E(x67531,x67532)+~E(f323(f323(f158(x67533),x67531),f533(x67533,x67532,x67531)),f323(f323(f158(x67533),x67532),f533(x67533,x67532,x67531)))+~E(f323(f189(f866(x67533)),x67531),f323(f189(f866(x67533)),x67532))
% 188.07/187.97 [6758]~E(x67583,f323(f323(f36(a865),x67581),x67582))+~P101(f323(f323(f238(a865),f2(a865)),x67582))+P101(f323(f323(f238(a865),x67581),f323(f323(f79(a865),x67582),f323(a112,x67583))))
% 188.07/187.97 [6775]~P101(f323(x67751,x67753))+~P101(f323(f323(f237(a865),x67753),x67752))+P101(f323(f323(f325(a865),f375(x67751,x67752)),f294(a865,f2(a865),x67752)))
% 188.07/187.97 [6814]~P101(f323(x68141,x68143))+P101(f323(x68141,f380(x68141,x68142)))+~P101(f323(f323(f325(a865),x68143),f294(a865,f2(a865),x68142)))
% 188.07/187.97 [6833]~P119(x68333)+~P101(f323(f323(f237(x68333),f323(f100(x68333),x68331)),f323(f100(x68333),x68332)))+P101(f323(f323(f237(a865),x68331),x68332))
% 188.07/187.97 [6834]~P116(x68343)+~P101(f323(f323(f237(x68343),f323(f102(x68343),x68341)),f323(f102(x68343),x68342)))+P101(f323(f323(f237(a1),x68341),x68342))
% 188.07/187.97 [6836]~P119(x68363)+~P101(f323(f323(f238(x68363),f323(f100(x68363),x68361)),f323(f100(x68363),x68362)))+P101(f323(f323(f238(a865),x68361),x68362))
% 188.07/187.97 [6837]~P116(x68373)+~P101(f323(f323(f238(x68373),f323(f102(x68373),x68371)),f323(f102(x68373),x68372)))+P101(f323(f323(f238(a1),x68371),x68372))
% 188.07/187.97 [6853]~P119(x68531)+~P101(f323(f323(f238(x68531),f76(x68531)),x68532))+P101(f323(f323(f238(x68531),f76(x68531)),f323(f323(f248(x68531),x68532),f323(a112,x68533))))
% 188.07/187.97 [6855]~P75(x68551)+~P101(f323(f323(f237(x68551),f323(f77(x68551),x68553)),f323(f77(x68551),x68552)))+P101(f323(f323(f237(x68551),x68552),x68553))
% 188.07/187.97 [6856]~P87(x68561)+~P101(f323(f323(f237(x68561),f323(f77(x68561),x68563)),f323(f77(x68561),x68562)))+P101(f323(f323(f237(x68561),x68562),x68563))
% 188.07/187.97 [6857]~P75(x68571)+~P101(f323(f323(f238(x68571),f323(f77(x68571),x68573)),f323(f77(x68571),x68572)))+P101(f323(f323(f238(x68571),x68572),x68573))
% 188.07/187.97 [6881]P101(f323(x68811,x68812))+~P101(f323(x68811,f379(x68811,x68813)))+~P101(f323(f323(f325(a865),x68812),f294(a865,f2(a865),x68813)))
% 188.07/187.97 [6900]~P64(x69001)+P101(f323(f323(f238(x69001),f475(x69003,x69002,x69001)),f76(x69001)))+P101(f323(f323(f237(x69001),x69002),x69003))
% 188.07/187.97 [6919]~E(f42(a865,x69193,x69192),f42(a865,x69191,x69192))+E(f323(f323(f78(a865),x69191),f323(f323(f79(a865),x69192),f494(x69191,x69192,x69193))),x69193)+~P101(f323(f323(f237(a865),x69191),x69193))
% 188.07/187.97 [6938]E(f323(x69381,f443(x69381,x69382,x69383)),f200(x69382))+~P101(f323(f59(x69383),f177(x69383,x69382,x69381)))+P101(f323(f59(x69383),f246(f872(x69383,a860))))
% 188.07/187.97 [6977]E(f323(f323(f6(x69771,a865),x69772),x69773),f2(a865))+~P101(f323(f59(x69771),x69773))+P101(f323(f323(f325(x69771),f333(x69772,x69773,x69771)),x69773))
% 188.07/187.98 [6978]E(f323(f323(f9(x69781,a865),x69782),x69783),f76(a865))+~P101(f323(f59(x69781),x69783))+P101(f323(f323(f325(x69781),f465(x69782,x69783,x69781)),x69783))
% 188.07/187.98 [7000]~P103(x70001)+~P101(f323(f323(f237(x70001),x70002),x70003))+P101(f323(f323(f237(f872(x70001,a860)),f323(f244(x70001),x70002)),f323(f244(x70001),x70003)))
% 188.07/187.98 [7001]~P103(x70011)+~P101(f323(f323(f237(x70011),x70013),x70012))+P101(f323(f323(f237(f872(x70011,a860)),f323(f295(x70011),x70012)),f323(f295(x70011),x70013)))
% 188.07/187.98 [7002]~P105(x70021)+~P101(f323(f323(f237(x70021),x70023),x70022))+P101(f323(f323(f237(f872(x70021,a860)),f323(f245(x70021),x70022)),f323(f245(x70021),x70023)))
% 188.07/187.98 [7003]~P105(x70031)+~P101(f323(f323(f237(x70031),x70032),x70033))+P101(f323(f323(f237(f872(x70031,a860)),f323(f292(x70031),x70032)),f323(f292(x70031),x70033)))
% 188.07/187.98 [7004]~P103(x70041)+~P101(f323(f323(f238(x70041),x70042),x70043))+P101(f323(f323(f238(f872(x70041,a860)),f323(f244(x70041),x70042)),f323(f244(x70041),x70043)))
% 188.07/187.98 [7012]~P6(x70121)+P101(f323(f323(f237(x70121),x70122),f38(x70121,x70123)))+P101(f323(f323(f325(x70121),f644(x70123,x70122,x70121)),x70123))
% 188.07/187.98 [7018]~P75(x70181)+P101(f323(f323(f237(x70181),f323(f323(f22(x70181),x70182),x70183)),f2(x70181)))+~P101(f323(f323(f237(x70181),x70182),x70183))
% 188.07/187.98 [7019]~P75(x70191)+P101(f323(f323(f238(x70191),f323(f323(f22(x70191),x70192),x70193)),f2(x70191)))+~P101(f323(f323(f238(x70191),x70192),x70193))
% 188.07/187.98 [7061]P101(f323(x70611,x70612))+P101(f323(f323(f237(a865),f379(x70611,x70613)),x70613))+~P101(f323(f323(f325(a865),x70612),f294(a865,f2(a865),x70613)))
% 188.07/187.98 [7101]~E(f323(f323(f6(x71011,a865),x71012),x71013),f76(a865))+~P101(f323(f59(x71011),x71013))+P101(f323(f323(f325(x71011),f332(x71012,x71013,x71011)),x71013))
% 188.07/187.98 [7102]~P101(f323(x71021,x71023))+P101(f323(f323(f237(a865),f380(x71021,x71022)),x71022))+~P101(f323(f323(f325(a865),x71023),f294(a865,f2(a865),x71022)))
% 188.07/187.98 [7142]~P6(x71421)+P101(f323(f323(f325(x71421),f549(x71423,x71422,x71421)),x71422))+P101(f323(f323(f237(x71421),f37(x71421,x71422)),x71423))
% 188.07/187.98 [7173]~E(f323(f323(f6(x71731,a865),x71732),x71733),f323(a112,f2(a865)))+~P101(f323(f59(x71731),x71733))+P101(f323(f323(f325(x71731),f358(x71732,x71733,x71731)),x71733))
% 188.07/187.98 [7184]E(x71841,f2(a865))+P101(f323(x71842,f42(a865,x71843,x71841)))+P101(f323(f323(f238(a865),f492(x71841,x71843,x71842)),x71841))
% 188.07/187.98 [7289]~P101(f323(x72891,x72892))+P101(f323(x72891,f42(a865,x72892,x72893)))+P101(f323(f323(f238(a865),f492(x72893,x72892,x72891)),x72893))
% 188.07/187.98 [7408]E(x74081,f113(x74082))+~P101(f323(f323(f325(f866(x74082)),x74081),f154(x74082,x74083)))+P101(f323(f323(f325(x74082),f625(x74083,x74081,x74082)),x74083))
% 188.07/187.98 [7430]~P103(x74301)+E(f323(f323(f110(f872(x74301,a860)),f323(f323(f301(x74301),x74302),f188(f872(x74301,a860)))),f297(x74301,x74302,x74303)),f323(f293(x74301,x74302),x74303))+~P101(f323(f323(f238(x74301),x74302),x74303))
% 188.07/187.98 [7455]~P103(x74551)+E(f323(f323(f110(f872(x74551,a860)),f323(f323(f301(x74551),x74552),f188(f872(x74551,a860)))),f296(x74551,x74552,x74553)),f294(x74551,x74552,x74553))+~P101(f323(f323(f237(x74551),x74552),x74553))
% 188.07/187.98 [7561]~P103(x75611)+P101(f323(f323(f237(x75611),x75612),x75613))+~P101(f323(f323(f237(f872(x75611,a860)),f323(f295(x75611),x75613)),f323(f295(x75611),x75612)))
% 188.07/187.98 [7562]~P105(x75621)+P101(f323(f323(f237(x75621),x75622),x75623))+~P101(f323(f323(f237(f872(x75621,a860)),f323(f245(x75621),x75623)),f323(f245(x75621),x75622)))
% 188.07/187.98 [7563]~P103(x75631)+P101(f323(f323(f237(x75631),x75632),x75633))+~P101(f323(f323(f237(f872(x75631,a860)),f323(f244(x75631),x75632)),f323(f244(x75631),x75633)))
% 188.07/187.98 [7564]~P105(x75641)+P101(f323(f323(f237(x75641),x75642),x75643))+~P101(f323(f323(f237(f872(x75641,a860)),f323(f292(x75641),x75642)),f323(f292(x75641),x75643)))
% 188.07/187.98 [7565]~P103(x75651)+P101(f323(f323(f238(x75651),x75652),x75653))+~P101(f323(f323(f238(f872(x75651,a860)),f323(f244(x75651),x75652)),f323(f244(x75651),x75653)))
% 188.07/187.98 [7588]~P75(x75881)+~P101(f323(f323(f237(x75881),f323(f323(f22(x75881),x75882),x75883)),f2(x75881)))+P101(f323(f323(f237(x75881),x75882),x75883))
% 188.07/187.98 [7589]~P75(x75891)+~P101(f323(f323(f238(x75891),f323(f323(f22(x75891),x75892),x75893)),f2(x75891)))+P101(f323(f323(f238(x75891),x75892),x75893))
% 188.07/187.98 [7746]E(x77461,f2(a865))+~E(f323(f135(a865,a865,f78(a865),x77462),x77463),f2(a865))+~P101(f323(f323(f325(a865),x77461),f323(f166(a865),x77463)))
% 188.07/187.98 [7750]~P6(x77501)+~P101(f323(f323(f237(x77501),f549(x77503,x77502,x77501)),x77503))+P101(f323(f323(f237(x77501),f37(x77501,x77502)),x77503))
% 188.07/187.98 [7907]P101(f323(f323(f237(a1),f2(a1)),f485(x79071,x79072,x79073)))+P101(f323(f323(x79072,f323(f323(f36(a1),x79071),x79073)),f42(a1,x79071,x79073)))+~P101(f323(f323(f238(a1),f2(a1)),x79073))
% 188.07/187.98 [7994]E(x79941,x79942)+~E(f323(f189(f866(x79943)),x79941),f323(f189(f866(x79943)),x79942))+~P101(f323(f323(f262(x79943,x79943,a860),a320),f583(x79943,x79941,x79942)))
% 188.07/187.98 [8060]~P38(x80602,x80603)+E(x80601,f188(f872(x80602,a860)))+~P101(f323(f323(f237(f872(x80602,a860)),x80601),f323(f277(x80602,x80602,x80603),x80601)))
% 188.07/187.98 [8128]P40(x81281,x81282,x81283)+P101(f323(f323(f325(x81281),f585(x81283,x81282,x81281)),x81282))+P101(f323(f323(f325(f871(x81281,x81281)),f586(x81283,x81282,x81281)),x81283))
% 188.07/187.98 [8150]P101(f323(f323(x81502,f323(f323(f36(a1),x81501),x81503)),f42(a1,x81501,x81503)))+~P101(f323(f323(f238(a1),f2(a1)),x81503))+P101(f323(f323(f238(a1),f485(x81501,x81502,x81503)),x81503))
% 188.07/187.98 [8174]E(f323(f302(a865,a865,f323(f323(f7(a865,a865,a865),f22(a865)),x81741)),f323(f293(a865,x81742),x81743)),f188(f872(a865,a860)))+P101(f323(f323(f238(a865),x81741),x81743))+P101(f323(f323(f238(a865),x81742),x81743))
% 188.07/187.98 [8284]E(f323(f302(a865,a865,f323(f323(f7(a865,a865,a865),f22(a865)),x82841)),f323(f293(a865,x82842),x82843)),f323(f323(f301(a865),f2(a865)),f188(f872(a865,a860))))+P101(f323(f323(f238(a865),x82841),x82843))+~P101(f323(f323(f238(a865),x82842),x82843))
% 188.07/187.98 [8301]~P103(x83011)+E(f142(x83011,x83011,f5(x83011),x83012,x83013),x83013)+~P101(f323(f323(f325(x83011),x83012),f323(f166(x83011),x83013)))
% 188.07/187.98 [8315]P27(x83151,x83151,x83152,x83153)+~P101(f323(f59(x83151),x83153))+~P101(f323(f323(f237(f872(x83151,a860)),x83153),f323(f302(x83151,x83151,x83152),x83153)))
% 188.07/187.98 [8341]E(f323(f323(f78(a1),f323(f323(f79(a1),x83411),f487(x83412,x83413,x83411))),f485(x83412,x83413,x83411)),x83412)+P101(f323(f323(x83413,f323(f323(f36(a1),x83412),x83411)),f42(a1,x83412,x83411)))+~P101(f323(f323(f238(a1),f2(a1)),x83411))
% 188.07/187.98 [8576]~P101(f323(f323(x85761,f487(x85762,x85761,x85763)),f485(x85762,x85761,x85763)))+P101(f323(f323(x85761,f323(f323(f36(a1),x85762),x85763)),f42(a1,x85762,x85763)))+~P101(f323(f323(f238(a1),f2(a1)),x85763))
% 188.07/187.98 [9454]~P101(f323(f59(x94541),x94542))+~P101(f323(f323(f325(x94541),x94543),x94542))+P101(f323(f323(f238(a865),f323(f35(x94541),f323(f323(f22(f872(x94541,a860)),x94542),f323(f323(f301(x94541),x94543),f188(f872(x94541,a860)))))),f323(f35(x94541),x94542)))
% 188.07/187.98 [10051]P40(x100511,x100512,x100513)+~P101(f323(f323(f262(x100511,x100511,a860),f323(f323(f7(x100511,f872(x100511,a860),f872(x100511,a860)),f323(f323(f8(f872(a860,a860),f872(f872(x100511,a860),f872(x100511,a860)),x100511),f8(a860,a860,x100511)),f323(f323(f8(a860,f872(a860,a860),x100511),a322),f323(f323(f7(x100511,f872(x100511,a860),a860),f325(x100511)),x100512)))),f323(f323(f7(x100511,f872(x100511,a860),a860),f325(x100511)),x100512))),f586(x100513,x100512,x100511)))+P101(f323(f323(f325(x100511),f585(x100513,x100512,x100511)),x100512))
% 188.07/187.98 [5462]~P114(x54622)+E(x54621,f2(x54622))+E(f323(f323(f281(x54622),x54623),f323(f77(x54622),x54621)),f323(f77(x54622),f323(f323(f281(x54622),x54623),x54621)))
% 188.07/187.98 [5594]~E(x55943,f188(f872(x55941,a860)))+~E(x55942,f188(f872(x55941,a860)))+E(f323(f323(f110(f872(x55941,a860)),x55942),x55943),f188(f872(x55941,a860)))
% 188.07/187.98 [5652]~E(x56523,f2(a865))+~P101(f323(x56521,f2(a865)))+P101(f323(x56521,f323(f323(f36(a865),x56522),x56523)))
% 188.07/187.98 [5792]~P65(x57922)+E(x57921,f2(x57922))+E(f323(f323(f281(x57922),f323(f73(x57922),x57923)),f323(f73(x57922),x57921)),f323(f73(x57922),f323(f323(f281(x57922),x57923),x57921)))
% 188.07/187.98 [5954]~P101(f323(f59(x59541),x59543))+E(f323(f35(x59541),f323(f323(f301(x59541),x59542),x59543)),f323(a112,f323(f35(x59541),x59543)))+P101(f323(f323(f325(x59541),x59542),x59543))
% 188.07/187.98 [6025]~E(x60252,f2(a865))+P101(f323(x60251,f2(a865)))+~P101(f323(x60251,f323(f323(f36(a865),x60253),x60252)))
% 188.07/187.98 [6044]~P101(f323(f59(x60441),x60443))+E(f323(f35(x60441),f323(f323(f301(x60441),x60442),x60443)),f323(f35(x60441),x60443))+~P101(f323(f323(f325(x60441),x60442),x60443))
% 188.07/187.98 [6078]~P101(f323(f59(x60781),x60783))+E(f323(f35(x60781),f323(f323(f301(x60781),x60782),x60783)),f323(f323(f78(a865),f76(a865)),f323(f35(x60781),x60783)))+P101(f323(f323(f325(x60781),x60782),x60783))
% 188.07/187.98 [6192]E(f323(f323(f78(a865),x61921),f854(x61921,x61922,x61923)),x61922)+~P101(f323(x61923,f2(a865)))+P101(f323(x61923,f323(f323(f22(a865),x61922),x61921)))
% 188.07/187.98 [6193]E(f323(f323(f78(a865),x61931),f855(x61931,x61932,x61933)),x61932)+~P101(f323(x61933,f2(a865)))+P101(f323(x61933,f323(f323(f22(a865),x61932),x61931)))
% 188.07/187.98 [6239]~P6(x62391)+~P101(f323(f59(x62391),x62393))+E(f323(f323(f62(x62391,x62391,f110(x62391)),x62392),x62393),f323(f323(f110(x62391),x62392),f37(x62391,x62393)))
% 188.07/187.98 [6240]~P6(x62401)+~P101(f323(f59(x62401),x62403))+E(f323(f323(f62(x62401,x62401,f101(x62401)),x62402),x62403),f323(f323(f101(x62401),x62402),f38(x62401,x62403)))
% 188.07/187.98 [6246]~P90(x62461)+~E(f323(f103(x62461),x62462),f323(f103(x62461),x62463))+P30(x62461,f323(f103(x62461),f323(f323(f78(a1),x62462),f323(f77(a1),x62463))))
% 188.07/187.98 [6253]~P134(x62531)+E(f323(f323(f22(x62531),f323(f100(x62531),x62532)),f323(f100(x62531),x62533)),f323(f100(x62531),f323(f323(f22(a865),x62532),x62533)))+~P101(f323(f323(f237(a865),x62533),x62532))
% 188.07/187.98 [6338]E(f323(f323(f78(a865),x63381),f854(x63381,x63382,x63383)),x63382)+P101(f323(f323(f238(a865),x63382),x63381))+P101(f323(x63383,f323(f323(f22(a865),x63382),x63381)))
% 188.07/187.98 [6339]E(f323(f323(f78(a865),x63391),f855(x63391,x63392,x63393)),x63392)+P101(f323(f323(f238(a865),x63392),x63391))+P101(f323(x63393,f323(f323(f22(a865),x63392),x63391)))
% 188.07/187.98 [6354]~P116(x63541)+E(f323(f323(f79(x63541),f323(f73(x63541),x63542)),x63543),f323(f73(x63541),f323(f323(f79(x63541),x63542),x63543)))+~P101(f323(f323(f237(x63541),f2(x63541)),x63543))
% 188.07/187.98 [6355]~P64(x63551)+E(f323(f323(f281(x63551),f323(f73(x63551),x63552)),x63553),f323(f73(x63551),f323(f323(f281(x63551),x63552),x63553)))+~P101(f323(f323(f238(x63551),f2(x63551)),x63553))
% 188.07/187.98 [6363]~P2(x63631)+~P101(f323(f59(x63631),x63633))+E(f323(f323(f62(x63631,x63631,f101(x63631)),x63632),x63633),f11(x63631,f323(f323(f301(x63631),x63632),x63633)))
% 188.07/187.98 [6364]~P2(x63641)+~P101(f323(f59(x63641),x63643))+E(f323(f323(f62(x63641,x63641,f110(x63641)),x63642),x63643),f10(x63641,f323(f323(f301(x63641),x63642),x63643)))
% 188.07/187.98 [6365]~P103(x63651)+~P101(f323(f59(x63651),x63653))+E(f323(f323(f62(x63651,x63651,f236(x63651)),x63652),x63653),f14(x63651,f323(f323(f301(x63651),x63652),x63653)))
% 188.07/187.98 [6366]~P103(x63661)+~P101(f323(f59(x63661),x63663))+E(f323(f323(f62(x63661,x63661,f235(x63661)),x63662),x63663),f15(x63661,f323(f323(f301(x63661),x63662),x63663)))
% 188.07/187.98 [6411]E(x64111,f113(x64112))+~E(f173(x64112,x64113),f113(f866(x64112)))+~P101(f323(f323(f325(f866(x64112)),x64111),f323(f166(f866(x64112)),x64113)))
% 188.07/187.98 [6452]~P101(f323(f130(x64521),x64523))+P101(f323(f323(f325(x64521),x64522),f323(f166(x64521),x64523)))+P101(f323(f130(x64521),f323(f323(f144(x64521),x64522),x64523)))
% 188.07/187.98 [6463]~P93(x64631)+~P101(f323(f59(x64631),x64633))+E(f323(f61(x64631,f79(x64631)),f323(f323(f301(x64631),x64632),x64633)),f323(f323(f62(x64631,x64631,f79(x64631)),x64632),x64633))
% 188.07/187.98 [6485]~P103(x64851)+~P101(f323(f59(x64851),x64853))+E(f12(x64851,f235(x64851),f323(f323(f301(x64851),x64852),x64853)),f323(f323(f62(x64851,x64851,f235(x64851)),x64852),x64853))
% 188.07/187.98 [6486]~P103(x64861)+~P101(f323(f59(x64861),x64863))+E(f13(x64861,f236(x64861),f323(f323(f301(x64861),x64862),x64863)),f323(f323(f62(x64861,x64861,f236(x64861)),x64862),x64863))
% 188.07/187.98 [6488]P101(f323(x64881,f2(a865)))+~P101(f323(f323(f238(a865),x64882),x64883))+~P101(f323(x64881,f323(f323(f22(a865),x64882),x64883)))
% 188.07/187.98 [6508]~P82(x65081)+P101(f323(f323(f237(x65081),x65082),x65083))+~P101(f323(f323(f237(x65081),f323(f73(x65081),x65082)),x65083))
% 188.07/187.98 [6509]~P116(x65091)+P101(f323(f323(f238(x65091),x65092),x65093))+~P101(f323(f323(f238(x65091),f323(f73(x65091),x65092)),x65093))
% 188.07/187.98 [6526]E(x65261,f113(x65262))+E(f323(f134(x65262),f323(f323(f131(x65262),x65263),x65261)),f323(f323(f158(x65262),x65261),x65263))+~P101(f323(f323(f238(a865),x65263),f323(f189(f866(x65262)),x65261)))
% 188.07/187.98 [6577]~P101(f323(x65771,x65773))+P101(f323(x65771,f388(x65771,x65772)))+~P101(f323(f323(f325(a865),x65773),f323(f293(a865,f2(a865)),x65772)))
% 188.07/187.98 [6598]P101(f323(x65981,x65982))+~P101(f323(f323(f238(a865),x65982),x65983))+P101(f323(f323(f325(a865),f387(x65981,x65983)),f323(f293(a865,f2(a865)),x65983)))
% 188.07/187.98 [6613]~P119(x66131)+~P101(f323(f323(f237(x66131),f76(x66131)),x66132))+P101(f323(f323(f237(x66131),f76(x66131)),f323(f323(f248(x66131),x66132),x66133)))
% 188.07/187.98 [6615]~P119(x66151)+~P101(f323(f323(f237(x66151),f2(x66151)),x66152))+P101(f323(f323(f237(x66151),f2(x66151)),f323(f323(f248(x66151),x66152),x66153)))
% 188.07/187.98 [6617]~P119(x66171)+~P101(f323(f323(f238(x66171),f2(x66171)),x66172))+P101(f323(f323(f238(x66171),f2(x66171)),f323(f323(f248(x66171),x66172),x66173)))
% 188.07/187.98 [6641]~P101(f323(x66411,x66413))+~P101(f323(f323(f238(a865),x66413),x66412))+P101(f323(f323(f325(a865),f386(x66411,x66412)),f323(f293(a865,f2(a865)),x66412)))
% 188.07/187.98 [6648]P101(f323(f59(x66481),x66482))+~P101(f323(f59(x66481),x66483))+~P101(f323(f323(f237(f872(x66481,a860)),x66482),x66483))
% 188.07/187.98 [6656]P101(f323(x66561,x66562))+~P101(f323(x66561,f389(x66561,x66563)))+~P101(f323(f323(f325(a865),x66562),f323(f293(a865,f2(a865)),x66563)))
% 188.07/187.98 [6667]E(x66671,f2(a865))+P101(f323(x66672,f476(x66671,x66673,x66672)))+~P101(f323(x66672,f323(f323(f36(a865),x66673),x66671)))
% 188.07/187.98 [6675]~P120(x66752)+E(x66751,f2(x66752))+~E(f323(f323(f78(x66752),f323(f323(f79(x66752),x66753),x66753)),f323(f323(f79(x66752),x66751),x66751)),f2(x66752))
% 188.07/187.98 [6676]~P120(x66762)+E(x66761,f2(x66762))+~E(f323(f323(f78(x66762),f323(f323(f79(x66762),x66761),x66761)),f323(f323(f79(x66762),x66763),x66763)),f2(x66762))
% 188.07/187.98 [6720]E(x67201,f2(a865))+~P101(f323(x67202,f477(x67201,x67203,x67202)))+P101(f323(x67202,f323(f323(f36(a865),x67203),x67201)))
% 188.07/187.98 [6725]~P103(x67251)+~P16(x67251,x67253)+P16(x67251,f323(f323(f141(x67251,x67251,f5(x67251)),x67252),x67253))
% 188.07/187.98 [6768]P101(f323(x67681,f476(x67682,x67683,x67681)))+P101(f323(x67681,f2(a865)))+~P101(f323(x67681,f323(f323(f36(a865),x67683),x67682)))
% 188.07/187.98 [6774]~P90(x67741)+E(f323(f103(x67741),x67742),f323(f103(x67741),x67743))+~P30(x67741,f323(f103(x67741),f323(f323(f78(a1),x67742),f323(f77(a1),x67743))))
% 188.07/187.98 [6840]E(x68401,f2(a1))+E(x68402,f2(a1))+~P101(f323(f46(x68402,x68402),f323(f323(f258(a1,a1),x68403),x68401)))
% 188.07/187.98 [6841]E(x68411,f76(a1))+E(x68412,f2(a1))+~P101(f323(f46(x68412,x68412),f323(f323(f258(a1,a1),x68411),x68413)))
% 188.07/187.98 [6854]P101(f323(x68541,x68542))+P101(f323(f323(f238(a865),f389(x68541,x68543)),x68543))+~P101(f323(f323(f325(a865),x68542),f323(f293(a865,f2(a865)),x68543)))
% 188.07/187.98 [6876]~P101(f323(x68761,f854(x68763,x68762,x68761)))+~P101(f323(x68761,f2(a865)))+P101(f323(x68761,f323(f323(f22(a865),x68762),x68763)))
% 188.07/187.98 [6877]~P101(f323(x68771,f855(x68773,x68772,x68771)))+~P101(f323(x68771,f2(a865)))+P101(f323(x68771,f323(f323(f22(a865),x68772),x68773)))
% 188.07/187.98 [6878]~P101(f323(x68781,f477(x68783,x68782,x68781)))+~P101(f323(x68781,f2(a865)))+P101(f323(x68781,f323(f323(f36(a865),x68782),x68783)))
% 188.07/187.98 [6896]~P101(f323(x68961,x68963))+P101(f323(f323(f238(a865),f388(x68961,x68962)),x68962))+~P101(f323(f323(f325(a865),x68963),f323(f293(a865,f2(a865)),x68962)))
% 188.07/187.98 [6897]E(f323(f323(f22(a865),f323(f323(f22(a865),x68971),x68972)),f323(f323(f22(a865),x68973),x68972)),f323(f323(f22(a865),x68971),x68973))+~P101(f323(f323(f237(a865),x68972),x68971))+~P101(f323(f323(f237(a865),x68972),x68973))
% 188.07/187.98 [6932]~P75(x69321)+~P101(f323(f323(f237(x69321),f323(f77(x69321),x69323)),x69322))+P101(f323(f323(f237(x69321),f323(f77(x69321),x69322)),x69323))
% 188.07/187.98 [6934]~P82(x69341)+~P101(f323(f323(f237(x69341),f323(f73(x69341),x69342)),x69343))+P101(f323(f323(f237(x69341),f323(f77(x69341),x69342)),x69343))
% 188.07/187.98 [6936]~P75(x69361)+~P101(f323(f323(f238(x69361),f323(f77(x69361),x69363)),x69362))+P101(f323(f323(f238(x69361),f323(f77(x69361),x69362)),x69363))
% 188.07/187.98 [6937]~P116(x69371)+~P101(f323(f323(f238(x69371),f323(f73(x69371),x69372)),x69373))+P101(f323(f323(f238(x69371),f323(f77(x69371),x69372)),x69373))
% 188.07/187.98 [6971]~P101(f323(x69713,f854(x69712,x69711,x69713)))+P101(f323(f323(f238(a865),x69711),x69712))+P101(f323(x69713,f323(f323(f22(a865),x69711),x69712)))
% 188.07/187.98 [6972]~P101(f323(x69723,f855(x69722,x69721,x69723)))+P101(f323(f323(f238(a865),x69721),x69722))+P101(f323(x69723,f323(f323(f22(a865),x69721),x69722)))
% 188.07/187.98 [7022]~E(f553(x70223,x70222,x70221),f554(x70223,x70222,x70221))+E(f323(f323(f101(f872(x70221,a860)),x70222),f37(f872(x70221,a860),x70223)),f188(f872(x70221,a860)))+P101(f323(f323(f325(f872(x70221,a860)),x70222),x70223))
% 188.07/187.98 [7031]~P101(f323(f59(x70311),x70313))+P101(f323(f59(x70311),f38(f872(x70311,a860),x70312)))+~P101(f323(f323(f325(f872(x70311,a860)),x70313),x70312))
% 188.07/187.98 [7090]~P103(x70901)+E(f323(f323(f110(f872(x70901,a860)),f323(f293(x70901,x70902),x70903)),f323(f323(f301(x70901),x70903),f188(f872(x70901,a860)))),f294(x70901,x70902,x70903))+~P101(f323(f323(f237(x70901),x70902),x70903))
% 188.07/187.98 [7091]E(x70911,f2(a865))+P101(f323(f323(f238(a865),f481(x70911,x70913,x70912)),x70911))+P101(f323(x70912,f323(f323(f36(a865),x70913),x70911)))
% 188.07/187.98 [7126]E(x71261,x71262)+~P101(f323(f323(f237(f872(x71263,a860)),x71261),x71262))+P101(f323(f323(f238(f872(x71263,a860)),x71261),x71262))
% 188.07/187.98 [7139]E(x71391,x71392)+~E(f323(f189(f866(x71393)),x71391),f323(f189(f866(x71393)),x71392))+P101(f323(f323(f238(a865),f533(x71393,x71391,x71392)),f323(f189(f866(x71393)),x71392)))
% 188.07/187.98 [7185]P9(x71851,x71852,x71853)+~E(f323(f256(x71851,x71851),x71853),x71852)+~E(f323(f323(f280(x71851,x71851,x71851),f323(f278(x71851,x71851),x71853)),x71853),x71853)
% 188.07/187.98 [7257]~P101(f323(x72571,f2(a865)))+P101(f323(f323(f238(a865),f481(x72573,x72572,x72571)),x72573))+P101(f323(x72571,f323(f323(f36(a865),x72572),x72573)))
% 188.07/187.98 [7266]~P103(x72661)+E(f323(f323(f110(f872(x72661,a860)),f297(x72661,x72662,x72663)),f323(f323(f301(x72661),x72663),f188(f872(x72661,a860)))),f296(x72661,x72662,x72663))+~P101(f323(f323(f238(x72661),x72662),x72663))
% 188.07/187.98 [7363]~P101(f323(f59(x73631),x73633))+P101(f323(f323(f237(a865),f323(f35(x73631),x73632)),f323(f35(x73631),x73633)))+~P101(f323(f323(f237(f872(x73631,a860)),x73632),x73633))
% 188.07/187.98 [7364]~P101(f323(f59(x73641),x73643))+P101(f323(f323(f238(a865),f323(f35(x73641),x73642)),f323(f35(x73641),x73643)))+~P101(f323(f323(f238(f872(x73641,a860)),x73642),x73643))
% 188.07/187.98 [7499]E(x74991,x74992)+~P101(f323(f323(f237(f872(x74993,a860)),x74992),x74991))+~P101(f323(f323(f237(f872(x74993,a860)),x74991),x74992))
% 188.07/187.98 [7502]~P103(x75021)+P16(x75021,x75022)+~P16(x75021,f323(f323(f141(x75021,x75021,f5(x75021)),x75023),x75022))
% 188.07/187.98 [7570]~P101(f323(f323(f238(a865),x75703),x75702))+~P101(f323(f323(f238(a865),x75703),x75701))+P101(f323(f323(f238(a865),f323(f323(f22(a865),x75701),x75702)),f323(f323(f22(a865),x75701),x75703)))
% 188.07/187.98 [7571]~P101(f323(f323(f237(a865),x75712),x75711))+~P101(f323(f323(f238(a865),x75711),x75713))+P101(f323(f323(f238(a865),f323(f323(f22(a865),x75711),x75712)),f323(f323(f22(a865),x75713),x75712)))
% 188.07/187.98 [7586]~P101(f323(f323(f238(a1),x75862),f2(a1)))+~P101(f323(f323(f237(a1),x75863),x75861))+P101(f323(f323(f237(a1),f323(f323(f36(a1),x75861),x75862)),f323(f323(f36(a1),x75863),x75862)))
% 188.07/187.98 [7604]~P101(f323(f323(f238(a865),f2(a865)),x76043))+~P101(f323(f323(f237(a865),x76043),x76042))+P101(f323(f323(f237(a865),f323(f323(f36(a865),x76041),x76042)),f323(f323(f36(a865),x76041),x76043)))
% 188.07/187.98 [7605]~P101(f323(f323(f238(a1),f2(a1)),x76052))+~P101(f323(f323(f237(a1),x76051),x76053))+P101(f323(f323(f237(a1),f323(f323(f36(a1),x76051),x76052)),f323(f323(f36(a1),x76053),x76052)))
% 188.07/187.98 [7609]~P101(f323(f323(f238(a865),f2(a865)),x76092))+~P101(f323(f323(f238(a865),x76091),x76093))+P101(f323(f323(f238(a865),f323(f323(f79(a865),x76091),x76092)),f323(f323(f79(a865),x76093),x76092)))
% 188.07/187.98 [7610]~P101(f323(f323(f238(a865),f2(a865)),x76101))+~P101(f323(f323(f238(a865),x76102),x76103))+P101(f323(f323(f238(a865),f323(f323(f79(a865),x76101),x76102)),f323(f323(f79(a865),x76101),x76103)))
% 188.07/187.98 [7611]~P101(f323(f323(f238(a1),f2(a1)),x76111))+~P101(f323(f323(f238(a1),x76112),x76113))+P101(f323(f323(f238(a1),f323(f323(f79(a1),x76111),x76112)),f323(f323(f79(a1),x76111),x76113)))
% 188.07/187.98 [7661]E(x76611,f2(a865))+E(f323(f323(f78(a865),f323(f323(f79(a865),x76611),f477(x76611,x76612,x76613))),f481(x76611,x76612,x76613)),x76612)+P101(f323(x76613,f323(f323(f36(a865),x76612),x76611)))
% 188.07/187.98 [7719]E(f323(f323(f78(a865),f323(f323(f79(a865),x77191),f477(x77191,x77192,x77193))),f481(x77191,x77192,x77193)),x77192)+~P101(f323(x77193,f2(a865)))+P101(f323(x77193,f323(f323(f36(a865),x77192),x77191)))
% 188.07/187.98 [7737]~P101(f323(f59(x77371),x77373))+P101(f323(f323(f325(x77371),f470(x77372,x77373,x77371)),x77373))+P101(f323(f323(f238(a865),f2(a865)),f323(f323(f9(x77371,a865),x77372),x77373)))
% 188.07/187.98 [7738]~P101(f323(f59(x77381),x77383))+P101(f323(f323(f325(x77381),f489(x77382,x77383,x77381)),x77383))+P101(f323(f323(f238(a865),f2(a865)),f323(f323(f9(x77381,a865),x77382),x77383)))
% 188.07/187.98 [8027]E(x80271,f188(f872(x80272,a860)))+E(x80271,f323(f323(f301(x80272),x80273),f188(f872(x80272,a860))))+~P101(f323(f323(f237(f872(x80272,a860)),x80271),f323(f323(f301(x80272),x80273),f188(f872(x80272,a860)))))
% 188.07/187.98 [8044]~P5(x80441)+P13(x80441,x80442,x80443)+P101(f323(f323(f325(f866(x80441)),f542(x80443,x80442,x80441)),f323(f166(f866(x80441)),f52(x80441,x80443,f53(x80441)))))
% 188.07/187.98 [8062]~P101(f323(f323(f238(a865),f2(a865)),x80623))+P101(f323(f323(f237(a865),x80621),x80622))+~P101(f323(f323(f237(a865),f323(f323(f79(a865),x80623),x80621)),f323(f323(f79(a865),x80623),x80622)))
% 188.07/187.98 [8063]~P101(f323(f323(f238(a865),f2(a865)),x80633))+P101(f323(f323(f237(a865),x80631),x80632))+~P101(f323(f323(f237(a865),f323(f323(f79(a865),x80631),x80633)),f323(f323(f79(a865),x80632),x80633)))
% 188.07/187.98 [8065]~P101(f323(f323(f238(a865),f2(a865)),x80653))+P101(f323(f323(f238(a865),x80651),x80652))+~P101(f323(f323(f238(a865),f323(f323(f248(a865),x80653),x80651)),f323(f323(f248(a865),x80653),x80652)))
% 188.07/187.98 [8090]~P5(x80901)+~P12(x80901,x80903,x80902)+P101(f323(f323(f325(f866(x80901)),f541(x80902,x80903,x80901)),f323(f166(f866(x80901)),f52(x80901,x80902,f53(x80901)))))
% 188.07/187.98 [8106]~E(f323(f323(f101(f872(x81061,a860)),f554(x81063,x81062,x81061)),f553(x81063,x81062,x81061)),f188(f872(x81061,a860)))+E(f323(f323(f101(f872(x81061,a860)),x81062),f37(f872(x81061,a860),x81063)),f188(f872(x81061,a860)))+P101(f323(f323(f325(f872(x81061,a860)),x81062),x81063))
% 188.07/187.98 [8123]E(x81231,f113(x81232))+~E(f323(f135(f866(x81232),f866(x81232),f121(x81232),f113(x81232)),x81233),f113(x81232))+~P101(f323(f323(f325(f866(x81232)),x81231),f323(f166(f866(x81232)),x81233)))
% 188.07/187.98 [8179]E(x81791,f188(f872(f872(x81792,a860),a860)))+P101(f323(f323(f325(f872(x81792,a860)),f674(x81793,x81791,x81792)),x81791))+P101(f323(f323(f237(f872(x81792,a860)),f38(f872(x81792,a860),x81791)),x81793))
% 188.07/187.98 [8187]~P68(x81871)+~P72(x81871)+E(f323(f323(f6(a1,x81871),f323(f323(f8(a865,x81871,a1),x81872),a104)),f323(f302(a865,a1,f100(a1)),x81873)),f323(f323(f6(a865,x81871),x81872),x81873))
% 188.07/187.98 [8188]~P68(x81881)+~P72(x81881)+E(f323(f323(f9(a1,x81881),f323(f323(f8(a865,x81881,a1),x81882),a104)),f323(f302(a865,a1,f100(a1)),x81883)),f323(f323(f9(a865,x81881),x81882),x81883))
% 188.07/187.98 [8229]~P101(f323(f59(x82291),x82293))+~P101(f323(f323(f238(a865),f2(a865)),f323(x82292,f470(x82292,x82293,x82291))))+P101(f323(f323(f238(a865),f2(a865)),f323(f323(f9(x82291,a865),x82292),x82293)))
% 188.07/187.98 [8230]~P101(f323(f59(x82301),x82303))+~P101(f323(f323(f238(a865),f2(a865)),f323(x82302,f489(x82302,x82303,x82301))))+P101(f323(f323(f238(a865),f2(a865)),f323(f323(f9(x82301,a865),x82302),x82303)))
% 188.07/187.98 [8265]~P63(x82652)+E(x82651,f76(x82652))+E(f323(f323(f281(x82652),f323(f323(f22(x82652),f323(f323(f248(x82652),x82651),x82653)),f76(x82652))),f323(f323(f22(x82652),x82651),f76(x82652))),f323(f323(f6(a865,x82652),f323(f248(x82652),x82651)),f323(f293(a865,f2(a865)),x82653)))
% 188.07/187.98 [8326]E(x83261,f2(a865))+~P101(f323(x83263,f323(f323(f36(a865),x83262),x83261)))+P101(f323(f323(f238(a865),x83262),f323(f323(f79(a865),x83261),f323(a112,f476(x83261,x83262,x83263)))))
% 188.07/187.98 [8344]P101(f323(x83441,f2(a865)))+~P101(f323(x83441,f323(f323(f36(a865),x83442),x83443)))+P101(f323(f323(f238(a865),x83442),f323(f323(f79(a865),x83443),f323(a112,f476(x83443,x83442,x83441)))))
% 188.07/187.98 [8384]E(x83841,f2(a865))+~P101(f323(x83843,f323(f323(f36(a865),x83842),x83841)))+P101(f323(f323(f237(a865),f323(f323(f79(a865),x83841),f476(x83841,x83842,x83843))),x83842))
% 188.07/187.98 [8416]P101(f323(x84161,f2(a865)))+~P101(f323(x84161,f323(f323(f36(a865),x84163),x84162)))+P101(f323(f323(f237(a865),f323(f323(f79(a865),x84162),f476(x84162,x84163,x84161))),x84163))
% 188.07/187.98 [8419]~P103(x84191)+E(f323(f323(f141(x84191,x84191,f5(x84191)),x84192),x84193),f142(x84191,x84191,f5(x84191),x84192,x84193))+P101(f323(f323(f325(x84191),x84192),f323(f166(x84191),x84193)))
% 188.07/187.98 [8454]~E(f323(x84543,f692(x84542,x84543,x84541)),f323(x84543,f694(x84542,x84543,x84541)))+~P56(x84541,f323(x84543,f693(x84542,x84543,x84541)))+P56(x84541,f323(f323(f39(x84542,f872(x84541,f872(x84541,a860))),f246(f872(x84542,a860))),x84543))
% 188.07/187.98 [8462]E(x84621,f188(f872(f872(x84622,a860),a860)))+~P101(f323(f323(f237(f872(x84622,a860)),f674(x84623,x84621,x84622)),x84623))+P101(f323(f323(f237(f872(x84622,a860)),f38(f872(x84622,a860),x84621)),x84623))
% 188.07/187.98 [8521]~P65(x85211)+~P101(f323(f323(f238(x85211),x85212),x85213))+P101(f323(f323(f238(x85211),x85212),f323(f323(f281(x85211),f323(f323(f78(x85211),x85212),x85213)),f323(f323(f78(x85211),f76(x85211)),f76(x85211)))))
% 188.07/187.98 [8582]~P101(f323(f323(x85821,f514(x85821,x85823,x85822)),f515(x85821,x85823,x85822)))+P101(f323(f323(x85821,x85822),x85823))+~P101(f323(f311(f871(a1,a1),a49),f323(f323(f258(a1,a1),x85822),x85823)))
% 188.07/187.98 [8583]~P101(f323(f323(x85831,f516(x85831,x85833,x85832)),f517(x85831,x85833,x85832)))+P101(f323(f323(x85831,x85832),x85833))+~P101(f323(f311(f871(a1,a1),a54),f323(f323(f258(a1,a1),x85832),x85833)))
% 188.07/187.98 [8584]~P101(f323(f323(x85841,f522(x85841,x85843,x85842)),f523(x85841,x85843,x85842)))+P101(f323(f323(x85841,x85842),x85843))+~P101(f323(f311(f871(a1,a1),a226),f323(f323(f258(a1,a1),x85842),x85843)))
% 188.07/187.98 [8585]~P101(f323(f323(x85851,f524(x85851,x85853,x85852)),f525(x85851,x85853,x85852)))+P101(f323(f323(x85851,x85852),x85853))+~P101(f323(f311(f871(a865,a865),a221),f323(f323(f258(a865,a865),x85852),x85853)))
% 188.07/187.98 [8586]~P101(f323(f323(x85861,f566(x85861,x85863,x85862)),f569(x85861,x85863,x85862)))+P101(f323(f323(x85861,x85862),x85863))+~P101(f323(f311(f871(a1,a1),a176),f323(f323(f258(a1,a1),x85862),x85863)))
% 188.07/187.98 [8599]P101(f323(f323(x85991,x85992),f801(x85993,x85991)))+~P26(a859,a874,f323(f323(f301(f864(a859)),f323(f323(f323(f90(a859),x85993),a875),x85991)),f188(f872(f864(a859),a860))))+~P101(f323(f323(x85993,x85992),a796))
% 188.07/187.98 [8857]P101(f323(f323(x88571,x88572),x88573))+P101(f323(f311(f871(a865,a865),a221),f323(f323(f258(a865,a865),f524(x88571,x88573,x88572)),f525(x88571,x88573,x88572))))+~P101(f323(f311(f871(a865,a865),a221),f323(f323(f258(a865,a865),x88572),x88573)))
% 188.07/187.98 [8858]P101(f323(f323(x88581,x88582),x88583))+P101(f323(f311(f871(a1,a1),a49),f323(f323(f258(a1,a1),f514(x88581,x88583,x88582)),f515(x88581,x88583,x88582))))+~P101(f323(f311(f871(a1,a1),a49),f323(f323(f258(a1,a1),x88582),x88583)))
% 188.07/187.98 [8859]P101(f323(f323(x88591,x88592),x88593))+P101(f323(f311(f871(a1,a1),a54),f323(f323(f258(a1,a1),f516(x88591,x88593,x88592)),f517(x88591,x88593,x88592))))+~P101(f323(f311(f871(a1,a1),a54),f323(f323(f258(a1,a1),x88592),x88593)))
% 188.07/187.98 [8860]P101(f323(f323(x88601,x88602),x88603))+P101(f323(f311(f871(a1,a1),a226),f323(f323(f258(a1,a1),f522(x88601,x88603,x88602)),f523(x88601,x88603,x88602))))+~P101(f323(f311(f871(a1,a1),a226),f323(f323(f258(a1,a1),x88602),x88603)))
% 188.07/187.98 [8861]P101(f323(f323(x88611,x88612),x88613))+P101(f323(f311(f871(a1,a1),a176),f323(f323(f258(a1,a1),f566(x88611,x88613,x88612)),f569(x88611,x88613,x88612))))+~P101(f323(f311(f871(a1,a1),a176),f323(f323(f258(a1,a1),x88612),x88613)))
% 188.07/187.98 [9199]~P101(f323(f59(x91991),x91993))+P101(f323(f323(f325(f871(f872(x91991,a860),f872(x91991,a860))),f323(f323(f258(f872(x91991,a860),f872(x91991,a860)),x91992),x91993)),f298(x91991)))+~P101(f323(f323(f238(f872(x91991,a860)),x91992),x91993))
% 188.07/187.98 [9269]~P56(x92691,f323(x92693,f693(x92692,x92693,x92691)))+P56(x92691,f323(f323(f39(x92692,f872(x92691,f872(x92691,a860))),f246(f872(x92692,a860))),x92693))+~E(f323(f323(f101(f872(x92691,a860)),f252(x92691,x92691,f323(x92693,f692(x92692,x92693,x92691)))),f253(x92691,x92691,f323(x92693,f694(x92692,x92693,x92691)))),f188(f872(x92691,a860)))
% 188.07/187.98 [9467]P40(x94671,x94672,x94673)+P101(f323(f323(f325(f871(x94671,x94671)),f586(x94673,x94672,x94671)),x94673))+~P101(f323(f323(f325(f871(x94671,x94671)),f323(f323(f258(x94671,x94671),f585(x94673,x94672,x94671)),f585(x94673,x94672,x94671))),x94673))
% 188.07/187.98 [10052]P40(x100521,x100522,x100523)+~P101(f323(f323(f262(x100521,x100521,a860),f323(f323(f7(x100521,f872(x100521,a860),f872(x100521,a860)),f323(f323(f8(f872(a860,a860),f872(f872(x100521,a860),f872(x100521,a860)),x100521),f8(a860,a860,x100521)),f323(f323(f8(a860,f872(a860,a860),x100521),a322),f323(f323(f7(x100521,f872(x100521,a860),a860),f325(x100521)),x100522)))),f323(f323(f7(x100521,f872(x100521,a860),a860),f325(x100521)),x100522))),f586(x100523,x100522,x100521)))+~P101(f323(f323(f325(f871(x100521,x100521)),f323(f323(f258(x100521,x100521),f585(x100523,x100522,x100521)),f585(x100523,x100522,x100521))),x100523))
% 188.07/187.98 [5633]~P57(x56332)+E(x56331,f2(x56332))+E(f323(f323(f36(x56332),f323(f323(f79(x56332),x56333),x56331)),x56331),x56333)
% 188.07/187.98 [5634]~P57(x56342)+E(x56341,f2(x56342))+E(f323(f323(f36(x56342),f323(f323(f79(x56342),x56341),x56343)),x56341),x56343)
% 188.07/187.98 [6410]~P72(x64101)+~E(f323(x64102,f2(a865)),f2(x64101))+E(f323(f323(f6(a865,x64101),x64102),f323(f293(a865,f323(a112,f2(a865))),x64103)),f323(f323(f6(a865,x64101),x64102),f323(f293(a865,f2(a865)),x64103)))
% 188.07/187.98 [6538]~P57(x65382)+E(x65381,f2(x65382))+E(f323(f323(f36(x65382),f323(f323(f78(x65382),x65383),x65381)),x65381),f323(f323(f78(x65382),f323(f323(f36(x65382),x65383),x65381)),f76(x65382)))
% 188.07/187.98 [6539]~P57(x65392)+E(x65391,f2(x65392))+E(f323(f323(f36(x65392),f323(f323(f78(x65392),x65391),x65393)),x65391),f323(f323(f78(x65392),f323(f323(f36(x65392),x65393),x65391)),f76(x65392)))
% 188.07/187.98 [6756]~P101(f323(x67563,f2(a1)))+P101(f323(f323(f237(a865),x67561),x67562))+P101(f323(x67563,f323(f100(a1),f323(f323(f22(a865),x67562),x67561))))
% 188.07/187.98 [6860]P101(f323(f323(f238(a865),x68602),x68601))+P101(f323(f323(f237(a865),x68601),x68602))+P101(f323(x68603,f323(f100(a1),f323(f323(f22(a865),x68602),x68601))))
% 188.07/187.98 [6930]E(f323(f323(f78(a865),f323(f103(a865),x69301)),f323(f323(f78(a865),f323(f103(a865),x69302)),x69303)),f323(f323(f78(a865),f323(f103(a865),x69301)),x69303))+P101(f323(a193,f323(f103(a1),x69301)))+~P101(f323(a193,f323(f103(a1),x69302)))
% 188.07/187.98 [7009]~E(x70092,f323(f323(f36(a865),x70093),x70091))+~P101(f323(f323(f238(a865),f2(a865)),x70091))+P101(f323(f323(f237(a865),f323(f323(f79(a865),x70091),x70092)),x70093))
% 188.07/187.98 [7123]~P101(f323(f59(x71231),x71233))+~P101(f323(f59(x71231),x71232))+P101(f323(f59(x71231),f323(f323(f110(f872(x71231,a860)),x71232),x71233)))
% 188.07/187.98 [7414]~P103(x74141)+~P101(f323(f59(x74141),x74142))+E(f132(x74141,f323(f323(f22(f872(x74141,a860)),x74142),f323(f323(f301(x74141),x74143),f188(f872(x74141,a860))))),f164(x74141,x74143,f132(x74141,x74142)))
% 188.07/187.98 [7479]P101(f323(x74791,f2(a1)))+~P101(f323(f323(f238(a865),x74792),x74793))+~P101(f323(x74791,f323(f100(a1),f323(f323(f22(a865),x74792),x74793))))
% 188.07/187.98 [7496]~P101(f323(f59(x74961),x74962))+E(f323(f35(x74961),f323(f323(f22(f872(x74961,a860)),x74962),f323(f323(f301(x74961),x74963),f188(f872(x74961,a860))))),f323(f35(x74961),x74962))+P101(f323(f323(f325(x74961),x74963),x74962))
% 188.07/187.98 [7626]~P119(x76261)+~P101(f323(f323(f238(x76261),f76(x76261)),x76262))+P101(f323(f323(f238(x76261),f76(x76261)),f323(f323(f79(x76261),x76262),f323(f323(f248(x76261),x76262),x76263))))
% 188.07/187.98 [7671]~P101(f323(f59(x76711),x76713))+E(f323(f323(f22(a865),f323(f35(x76711),x76712)),f323(f35(x76711),x76713)),f323(f35(x76711),f323(f323(f22(f872(x76711,a860)),x76712),x76713)))+~P101(f323(f323(f237(f872(x76711,a860)),x76713),x76712))
% 188.07/187.98 [7728]~P101(f323(f323(f237(a865),x77282),x77283))+~P101(f323(f323(f237(a865),x77281),f323(f323(f22(a865),x77283),x77282)))+P101(f323(f323(f237(a865),f323(f323(f78(a865),x77281),x77282)),x77283))
% 188.07/187.98 [7779]P101(f323(f59(x77791),x77792))+~P101(f323(f59(x77791),x77793))+~P101(f323(f59(x77791),f323(f323(f22(f872(x77791,a860)),x77792),x77793)))
% 188.07/187.98 [7785]~P101(f323(f59(x77851),x77852))+E(f323(f35(x77851),f323(f323(f22(f872(x77851,a860)),x77852),f323(f323(f301(x77851),x77853),f188(f872(x77851,a860))))),f323(f323(f22(a865),f323(f35(x77851),x77852)),f76(a865)))+~P101(f323(f323(f325(x77851),x77853),x77852))
% 188.07/187.98 [7862]P56(x78621,x78622)+~P56(x78621,x78623)+~P101(f323(f323(f237(f872(x78621,f872(x78621,a860))),x78622),x78623))
% 188.07/187.98 [7906]~P101(f323(f323(f237(a865),x79063),x79062))+P101(f323(f323(f237(a865),x79061),f323(f323(f22(a865),x79062),x79063)))+~P101(f323(f323(f237(a865),f323(f323(f78(a865),x79061),x79063)),x79062))
% 188.07/187.98 [7924]P38(x79241,x79242)+~P38(x79241,x79243)+~P101(f323(f323(f237(f872(f871(x79241,x79241),a860)),x79242),x79243))
% 188.07/187.98 [7925]P54(x79251,x79252)+~P54(x79251,x79253)+~P101(f323(f323(f237(f872(f871(x79251,x79251),a860)),x79252),x79253))
% 188.07/187.98 [8157]~P119(x81571)+~P101(f323(f323(f238(x81571),f76(x81571)),x81572))+P101(f323(f323(f238(x81571),f323(f323(f248(x81571),x81572),x81573)),f323(f323(f79(x81571),x81572),f323(f323(f248(x81571),x81572),x81573))))
% 188.07/187.98 [8247]~P101(f323(x82471,f2(a1)))+~P101(f323(x82471,f323(f323(f22(a1),f323(f100(a1),x82472)),f323(f100(a1),x82473))))+P101(f323(x82471,f323(f100(a1),f323(f323(f22(a865),x82472),x82473))))
% 188.07/187.98 [8262]~P101(f323(f323(f237(a865),x82623),x82622))+P101(f323(x82621,f323(f323(f22(a1),f323(f100(a1),x82622)),f323(f100(a1),x82623))))+~P101(f323(x82621,f323(f100(a1),f323(f323(f22(a865),x82622),x82623))))
% 188.07/187.98 [8281]P101(f323(f323(f238(a865),x82811),x82812))+~P101(f323(x82813,f323(f323(f22(a1),f323(f100(a1),x82811)),f323(f100(a1),x82812))))+P101(f323(x82813,f323(f100(a1),f323(f323(f22(a865),x82811),x82812))))
% 188.07/187.98 [8338]~P120(x83382)+E(x83381,f2(x83382))+P101(f323(f323(f238(x83382),f2(x83382)),f323(f323(f78(x83382),f323(f323(f79(x83382),x83383),x83383)),f323(f323(f79(x83382),x83381),x83381))))
% 188.07/187.98 [8339]~P120(x83392)+E(x83391,f2(x83392))+P101(f323(f323(f238(x83392),f2(x83392)),f323(f323(f78(x83392),f323(f323(f79(x83392),x83391),x83391)),f323(f323(f79(x83392),x83393),x83393))))
% 188.07/187.98 [8437]~P101(f323(f323(f238(a865),f2(a865)),x84371))+~P101(f323(f323(f238(a1),x84372),x84373))+P101(f323(f323(f238(a1),f323(f323(f79(a1),f323(f100(a1),x84371)),x84372)),f323(f323(f79(a1),f323(f100(a1),x84371)),x84373)))
% 188.07/187.98 [8491]E(f323(f323(f101(f872(x84911,a860)),x84912),f37(f872(x84911,a860),x84913)),f188(f872(x84911,a860)))+P101(f323(f323(f325(f872(x84911,a860)),x84912),x84913))+P101(f323(f323(f325(f872(x84911,a860)),f554(x84913,x84912,x84911)),f323(f323(f301(f872(x84911,a860)),x84912),x84913)))
% 188.07/187.98 [8492]E(f323(f323(f101(f872(x84921,a860)),x84922),f37(f872(x84921,a860),x84923)),f188(f872(x84921,a860)))+P101(f323(f323(f325(f872(x84921,a860)),x84922),x84923))+P101(f323(f323(f325(f872(x84921,a860)),f553(x84923,x84922,x84921)),f323(f323(f301(f872(x84921,a860)),x84922),x84923)))
% 188.07/187.98 [8520]E(x85201,x85202)+~E(f323(f189(f866(x85203)),x85201),f323(f189(f866(x85203)),x85202))+P101(f323(f323(f325(f871(x85203,x85203)),f583(x85203,x85201,x85202)),f323(f166(f871(x85203,x85203)),f323(f323(f175(x85203,x85203),x85202),x85201))))
% 188.07/187.98 [8775]E(f299(x87751,x87752),f299(x87751,x87753))+~P101(f323(f323(f237(f872(f871(x87751,x87751),a860)),x87753),f299(x87751,x87752)))+~P101(f323(f323(f237(f872(f871(x87751,x87751),a860)),x87752),x87753))
% 188.07/187.98 [8836]~P40(x88361,f246(f872(x88361,a860)),x88363)+P101(f323(f323(f237(f872(f871(f866(x88361),f866(x88361)),a860)),f150(x88361,x88362)),f151(x88361,x88363)))+~P101(f323(f323(f237(f872(f871(x88361,x88361),a860)),x88362),x88363))
% 188.07/187.98 [9037]P38(x90371,x90372)+~P101(f323(f323(f325(x90371),x90373),f735(x90372,x90371)))+P101(f323(f323(f325(f871(x90371,x90371)),f323(f323(f258(x90371,x90371),f774(x90372,x90371,x90373)),x90373)),x90372))
% 188.07/187.98 [9072]~P101(f323(f59(x90721),x90722))+P101(f323(f59(f872(x90721,a860)),f323(f323(f58(x90721),x90722),x90723)))+~P101(f323(f323(f237(f872(f871(x90721,x90721),a860)),x90723),f323(f323(f260(x90721,x90721),x90722),f323(f16(f872(x90721,a860),x90721),x90722))))
% 188.07/187.98 [9106]P40(x91061,x91062,x91063)+P101(f323(f323(f325(x91061),f611(x91063,x91062,x91061)),x91062))+~P101(f323(f323(f237(f872(f871(x91061,x91061),a860)),x91063),f323(f323(f260(x91061,x91061),x91062),f323(f16(f872(x91061,a860),x91061),x91062))))
% 188.07/187.98 [9107]P40(x91071,x91072,x91073)+P101(f323(f323(f325(x91071),f616(x91072,x91073,x91071)),x91072))+~P101(f323(f323(f237(f872(f871(x91071,x91071),a860)),x91073),f323(f323(f260(x91071,x91071),x91072),f323(f16(f872(x91071,a860),x91071),x91072))))
% 188.07/187.98 [9141]~P65(x91411)+~P101(f323(f323(f238(x91411),x91412),x91413))+P101(f323(f323(f238(x91411),f323(f323(f281(x91411),f323(f323(f78(x91411),x91412),x91413)),f323(f323(f78(x91411),f76(x91411)),f76(x91411)))),x91413))
% 188.07/187.98 [9174]~P64(x91741)+P101(f323(f323(f237(x91741),x91742),x91743))+~P101(f323(f323(f237(x91741),f323(f323(f79(x91741),f475(x91743,x91742,x91741)),x91742)),x91743))
% 188.07/187.98 [9305]E(f323(f189(f866(f866(x93051))),f323(f129(f866(x93051),f323(f323(f8(a865,a860,f866(x93051)),f323(f238(a865),x93052)),f189(f866(x93051)))),f173(x93051,x93053))),f323(f189(f866(x93051)),f323(f323(f158(f866(x93051)),x93053),x93052)))+~P16(a865,f323(f162(a865),f323(f323(f147(f866(x93051),a865),f189(f866(x93051))),x93053)))+~P101(f323(f323(f238(a865),x93052),f323(f189(f866(f866(x93051))),x93053)))
% 188.07/187.98 [9411]~P38(x94111,x94112)+P29(x94111,f323(f323(f258(f872(f871(x94111,x94111),a860),f872(f871(x94111,x94111),a860)),x94112),x94113))+~P101(f323(f323(f237(f872(f871(x94111,x94111),a860)),f323(f323(f280(x94111,x94111,x94111),x94112),x94113)),x94112))
% 188.07/187.98 [9418]E(f323(f323(f147(f866(x94181),x94181),f323(f323(f7(f866(x94181),a865,x94181),f158(x94181)),x94182)),f323(f129(f866(x94181),f323(f323(f8(a865,a860,f866(x94181)),f323(f238(a865),x94182)),f189(f866(x94181)))),f173(x94181,x94183))),f323(f323(f158(f866(x94181)),x94183),x94182))+~P16(a865,f323(f162(a865),f323(f323(f147(f866(x94181),a865),f189(f866(x94181))),x94183)))+~P101(f323(f323(f238(a865),x94182),f323(f189(f866(f866(x94181))),x94183)))
% 188.07/187.98 [9556]P40(x95561,x95562,x95563)+~P101(f323(f323(f325(f871(x95561,x95561)),f323(f323(f258(x95561,x95561),f611(x95563,x95562,x95561)),f611(x95563,x95562,x95561))),x95563))+~P101(f323(f323(f237(f872(f871(x95561,x95561),a860)),x95563),f323(f323(f260(x95561,x95561),x95562),f323(f16(f872(x95561,a860),x95561),x95562))))
% 188.07/187.98 [9557]P40(x95571,x95572,x95573)+~P101(f323(f323(f325(f871(x95571,x95571)),f323(f323(f258(x95571,x95571),f616(x95572,x95573,x95571)),f616(x95572,x95573,x95571))),x95573))+~P101(f323(f323(f237(f872(f871(x95571,x95571),a860)),x95573),f323(f323(f260(x95571,x95571),x95572),f323(f16(f872(x95571,a860),x95571),x95572))))
% 188.07/187.98 [9734]~P134(x97341)+~P118(x97341)+E(f323(f323(f281(x97341),f323(f102(x97341),f323(f323(f71(f871(a1,a1),a1,x97342,f257(a1,a1)),f214(x97342)),x97343))),f323(f102(x97341),f323(f323(f71(f871(a1,a1),a1,x97342,f261(a1,a1)),f214(x97342)),x97343))),f227(x97342,x97341,x97343))
% 188.07/187.98 [9934]~E(x99343,f2(a865))+~E(f323(f189(f866(x99341)),f323(f323(f158(f866(x99341)),x99342),f568(x99343,x99341,x99342))),x99343)+E(f323(f323(f147(a865,f866(x99341)),f323(f323(f7(a865,f866(a865),f866(x99341)),f323(f323(f8(f872(a865,x99341),f872(f866(a865),f866(x99341)),a865),f147(a865,x99341)),f323(f7(a865,a865,x99341),f323(f323(f8(f866(x99341),f872(a865,x99341),a865),f158(x99341)),f323(f158(f866(x99341)),x99342))))),f132(a865,f323(f293(a865,f2(a865)),f323(f189(f866(f866(x99341))),x99342))))),f132(a865,f323(f293(a865,f2(a865)),x99343))),f173(x99341,x99342))
% 188.07/187.98 [9935]E(x99351,f113(f866(x99352)))+~E(f323(f189(f866(x99352)),f323(f323(f158(f866(x99352)),x99351),f568(x99353,x99352,x99351))),x99353)+E(f323(f323(f147(a865,f866(x99352)),f323(f323(f7(a865,f866(a865),f866(x99352)),f323(f323(f8(f872(a865,x99352),f872(f866(a865),f866(x99352)),a865),f147(a865,x99352)),f323(f7(a865,a865,x99352),f323(f323(f8(f866(x99352),f872(a865,x99352),a865),f158(x99352)),f323(f158(f866(x99352)),x99351))))),f132(a865,f323(f293(a865,f2(a865)),f323(f189(f866(f866(x99352))),x99351))))),f132(a865,f323(f293(a865,f2(a865)),x99353))),f173(x99352,x99351))
% 188.07/187.98 [9936]~E(x99363,f2(a865))+E(f323(f323(f147(a865,f866(x99361)),f323(f323(f7(a865,f866(a865),f866(x99361)),f323(f323(f8(f872(a865,x99361),f872(f866(a865),f866(x99361)),a865),f147(a865,x99361)),f323(f7(a865,a865,x99361),f323(f323(f8(f866(x99361),f872(a865,x99361),a865),f158(x99361)),f323(f158(f866(x99361)),x99362))))),f132(a865,f323(f293(a865,f2(a865)),f323(f189(f866(f866(x99361))),x99362))))),f132(a865,f323(f293(a865,f2(a865)),x99363))),f173(x99361,x99362))+P101(f323(f323(f238(a865),f568(x99363,x99361,x99362)),f323(f189(f866(f866(x99361))),x99362)))
% 188.07/187.98 [9937]E(x99371,f113(f866(x99372)))+E(f323(f323(f147(a865,f866(x99372)),f323(f323(f7(a865,f866(a865),f866(x99372)),f323(f323(f8(f872(a865,x99372),f872(f866(a865),f866(x99372)),a865),f147(a865,x99372)),f323(f7(a865,a865,x99372),f323(f323(f8(f866(x99372),f872(a865,x99372),a865),f158(x99372)),f323(f158(f866(x99372)),x99371))))),f132(a865,f323(f293(a865,f2(a865)),f323(f189(f866(f866(x99372))),x99371))))),f132(a865,f323(f293(a865,f2(a865)),x99373))),f173(x99372,x99371))+P101(f323(f323(f238(a865),f568(x99373,x99372,x99371)),f323(f189(f866(f866(x99372))),x99371)))
% 188.07/187.98 [7668]E(f323(f323(f78(a865),f323(f103(a865),x76681)),f323(f323(f78(a865),f323(f103(a865),x76682)),x76683)),f323(f323(f78(a865),f323(f103(a865),f323(f323(f78(a1),x76681),x76682))),x76683))+P101(f323(a193,f323(f103(a1),x76681)))+P101(f323(a193,f323(f103(a1),x76682)))
% 188.07/187.98 [8428]~P101(f323(f59(x84281),x84282))+~P101(f323(f323(f325(x84281),x84283),x84282))+E(f323(a112,f323(f35(x84281),f323(f323(f22(f872(x84281,a860)),x84282),f323(f323(f301(x84281),x84283),f188(f872(x84281,a860)))))),f323(f35(x84281),x84282))
% 188.07/187.98 [8444]~P101(f323(f59(x84441),x84442))+~P101(f323(f323(f325(x84441),x84443),x84442))+E(f323(f323(f78(a865),f76(a865)),f323(f35(x84441),f323(f323(f22(f872(x84441,a860)),x84442),f323(f323(f301(x84441),x84443),f188(f872(x84441,a860)))))),f323(f35(x84441),x84442))
% 188.07/187.98 [8530]~P103(x85301)+~P101(f323(f59(x85301),x85303))+E(f323(f323(f141(x85301,x85301,f5(x85301)),x85302),f132(x85301,f323(f323(f22(f872(x85301,a860)),x85303),f323(f323(f301(x85301),x85302),f188(f872(x85301,a860)))))),f132(x85301,f323(f323(f301(x85301),x85302),x85303)))
% 188.07/187.98 [8699]~P101(f323(f59(x86991),x86993))+~P101(f323(f59(x86991),x86992))+E(f323(f323(f78(a865),f323(f35(x86991),f323(f323(f110(f872(x86991,a860)),x86992),x86993))),f323(f35(x86991),f323(f323(f101(f872(x86991,a860)),x86992),x86993))),f323(f323(f78(a865),f323(f35(x86991),x86992)),f323(f35(x86991),x86993)))
% 188.07/187.98 [9882]~P27(x98821,f872(f872(x98821,a860),a860),f323(f323(f7(x98821,f872(f871(x98821,x98821),a860),f872(f872(x98821,a860),a860)),f323(f323(f8(f872(x98821,a860),f872(f872(f871(x98821,x98821),a860),f872(f872(x98821,a860),a860)),x98821),f58(x98821)),f323(f323(f7(x98821,f872(x98821,a860),f872(x98821,a860)),f301(x98821)),f188(f872(x98821,a860))))),x98823),x98822)+~P101(f323(f59(x98821),x98822))+E(f323(f35(f872(x98821,a860)),f323(f323(f58(x98821),x98822),x98823)),f323(f35(x98821),x98822))
% 188.07/187.98 [7937]~P90(x79371)+P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x79373)))+E(f323(f323(f248(x79371),x79372),f323(f103(a865),f323(f323(f22(a1),f323(f323(f78(a1),x79373),x79373)),a97))),f76(x79371))
% 188.07/187.98 [9396]~P90(x93961)+~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x93963)))+E(f323(f323(f248(x93961),x93962),f323(f103(a865),f323(f323(f22(a1),f323(f323(f78(a1),x93963),x93963)),a97))),f323(f323(f84(x93961,x93961),f323(f323(f248(x93961),x93962),f323(f103(a865),x93963))),f323(f323(f18(x93961,x93961,x93961),f323(f323(f8(x93961,f872(x93961,x93961),x93961),f79(x93961)),f323(f79(x93961),x93962))),f5(x93961))))
% 188.07/187.98 [9794]~P101(f323(f130(x97941),x97943))+~P101(f323(f323(f325(x97941),x97942),f323(f166(x97941),x97943)))+E(f323(f323(f131(x97941),f323(f189(f866(x97941)),f171(x97941,f323(f323(f8(a860,a860,x97941),a318),f323(f323(f7(x97941,x97941,a860),a320),x97942)),f323(f162(x97941),x97943)))),f323(f162(x97941),x97943)),f323(f323(f144(x97941),x97942),f323(f162(x97941),f171(x97941,f323(f323(f8(a860,a860,x97941),a318),f323(f323(f7(x97941,x97941,a860),a320),x97942)),x97943))))
% 188.07/187.98 [9863]P101(f323(f323(f237(f872(f871(x98631,x98631),a860)),f299(x98631,x98632)),x98633))+~P101(f323(f323(f237(f872(f871(x98631,x98631),a860)),f299(x98631,f188(f872(f871(x98631,x98631),a860)))),x98633))+~P101(f323(f323(f237(f872(f871(x98631,x98631),a860)),f323(f323(f280(x98631,x98631,x98631),f323(f323(f101(f872(f871(x98631,x98631),a860)),f299(x98631,x98632)),x98633)),x98632)),x98633))
% 188.07/187.98 [9705]~P101(f323(f59(x97051),f323(f243(x97051),x97053)))+~P101(f323(f59(x97051),f323(f243(x97051),x97052)))+P101(f323(f59(x97051),f323(f243(x97051),f323(f323(f18(x97051,a860,a860),f323(f323(f8(a860,f872(a860,a860),x97051),a321),x97052)),x97053))))
% 188.07/187.98 [9996]P101(f323(f323(f237(f872(f871(x99961,x99961),a860)),f323(f323(f280(x99961,x99961,x99961),x99962),f299(x99961,x99962))),x99963))+~P101(f323(f323(f237(f872(f871(x99961,x99961),a860)),x99962),x99963))+~P101(f323(f323(f237(f872(f871(x99961,x99961),a860)),f323(f323(f280(x99961,x99961,x99961),f323(f323(f101(f872(f871(x99961,x99961),a860)),f323(f323(f280(x99961,x99961,x99961),x99962),f299(x99961,x99962))),x99963)),x99962)),x99963))
% 188.07/187.98 [9950]~P116(x99502)+E(x99501,f2(x99502))+~E(f323(f323(f78(x99502),f323(f323(f248(x99502),x99503),f323(f103(a865),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(x99502),x99501),f323(f103(a865),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(x99502))
% 188.07/187.98 [9951]~P116(x99512)+E(x99511,f2(x99512))+~E(f323(f323(f78(x99512),f323(f323(f248(x99512),x99511),f323(f103(a865),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(x99512),x99513),f323(f103(a865),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(x99512))
% 188.07/187.98 [9956]~P101(f323(f130(x99561),x99563))+~P101(f323(f323(f325(x99561),x99562),f323(f166(x99561),x99563)))+E(f323(f162(x99561),f323(f165(x99561),f323(f323(f131(x99561),f323(f189(f866(x99561)),f171(x99561,f323(f323(f8(a860,a860,x99561),a318),f323(f323(f7(x99561,x99561,a860),a320),x99562)),x99563))),x99563))),f171(x99561,f323(f323(f8(a860,a860,x99561),a318),f323(f323(f7(x99561,x99561,a860),a320),x99562)),f323(f162(x99561),x99563)))
% 188.07/187.98 [10040]~P116(x100402)+E(x100401,f2(x100402))+P101(f323(f323(f238(x100402),f2(x100402)),f323(f323(f78(x100402),f323(f323(f248(x100402),x100403),f323(f103(a865),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(x100402),x100401),f323(f103(a865),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)))))))
% 188.07/187.98 [10041]~P116(x100412)+E(x100411,f2(x100412))+P101(f323(f323(f238(x100412),f2(x100412)),f323(f323(f78(x100412),f323(f323(f248(x100412),x100411),f323(f103(a865),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(x100412),x100413),f323(f103(a865),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)))))))
% 188.07/187.98 [10082]~P116(x100821)+P101(f323(f323(f237(x100821),f2(x100821)),x100822))+~P101(f323(f323(f237(x100821),f2(x100821)),f323(f323(f248(x100821),x100822),f323(a112,f323(f323(f79(a865),f323(f103(a865),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)))),x100823)))))
% 188.07/187.98 [5475]~P26(x54751,x54754,x54753)+P26(x54751,x54752,x54753)+~P26(x54751,x54752,x54754)
% 188.07/187.98 [4951]~E(x49512,f88(x49513,x49511))+P101(f323(x49511,x49512))+~P101(f323(x49511,x49514))
% 188.07/187.98 [6668]~P38(x66682,x66684)+~P38(x66681,x66683)+P38(f871(x66681,x66682),f315(x66681,x66682,x66683,x66684))
% 188.07/187.98 [5130]~P8(x51304,x51301)+~E(f323(x51301,x51302),f323(x51301,x51303))+P101(f323(f323(x51301,x51302),x51303))
% 188.07/187.98 [5290]~P8(x52904,x52901)+E(f323(x52901,x52902),f323(x52901,x52903))+~P101(f323(f323(x52901,x52902),x52903))
% 188.07/187.98 [5382]~P20(x53823,x53824,x53821)+E(f323(x53821,x53822),f323(f61(x53823,x53824),x53822))+~P101(f323(f59(x53823),x53822))
% 188.07/187.98 [5383]~P10(x53833,x53834,x53831)+E(f323(x53831,x53832),f323(f61(x53833,x53834),x53832))+~P101(f323(f59(x53833),x53832))
% 188.07/187.98 [5508]~P8(x55084,x55081)+~P101(f323(f323(x55081,x55083),x55082))+P101(f323(f323(x55081,x55082),x55083))
% 188.07/187.98 [5576]E(x55761,x55762)+~E(f323(f257(x55763,x55764),x55761),f323(f257(x55763,x55764),x55762))+~E(f323(f261(x55763,x55764),x55761),f323(f261(x55763,x55764),x55762))
% 188.07/187.98 [5601]E(x56011,x56012)+~P101(f323(f45(x56013,x56014),x56012))+~P101(f323(f45(x56013,x56014),x56011))
% 188.07/187.98 [5791]~P72(x57912)+E(f228(x57911,x57912,x57913,x57914),f2(x57912))+P101(f323(f59(x57911),x57914))
% 188.07/187.98 [5925]~P101(f323(f311(x59251,x59252),x59254))+P101(f323(f311(x59251,x59252),x59253))+~P101(f323(f323(x59252,x59253),x59254))
% 188.07/187.98 [6342]P50(x63421,x63422,x63423,x63424)+P101(f323(f323(x63422,x63424),x63423))+~P101(f323(f323(x63422,x63423),x63424))
% 188.07/187.98 [7774]E(x77741,f2(a865))+~P101(f323(x77742,x77743))+P101(f323(x77742,f793(x77742,x77743,x77741,x77744)))
% 188.07/187.98 [7857]~P103(x78572)+~P101(f323(f130(x78571),x78574))+P101(f323(f130(x78571),f143(x78571,x78572,x78573,x78574)))
% 188.07/187.98 [8078]~P101(f323(f59(x80782),x80784))+~P101(f323(f59(x80781),x80783))+P101(f323(f59(f870(x80781,x80782)),f310(x80781,x80782,x80783,x80784)))
% 188.07/187.98 [8079]~P101(f323(f130(x80792),x80794))+~P101(f323(f130(x80791),x80793))+P101(f323(f130(f871(x80791,x80792)),f57(x80791,x80792,x80793,x80794)))
% 188.07/187.98 [8083]P101(f323(f323(f325(f866(x80831)),f323(f323(f121(x80831),x80832),x80833)),f154(x80831,x80834)))+~P101(f323(f323(f325(f866(x80831)),x80833),f154(x80831,x80834)))+~P101(f323(f323(f325(f866(x80831)),x80832),f154(x80831,x80834)))
% 188.07/187.98 [8369]E(x83691,f2(a865))+P101(f323(x83692,x83693))+~P101(f323(x83692,f795(x83692,x83693,x83691,x83694)))
% 188.07/187.98 [8408]~P103(x84083)+~P101(f323(f130(x84081),f143(x84081,x84083,x84084,x84082)))+P101(f323(f130(x84081),x84082))
% 188.07/187.98 [8688]~P101(f323(f323(f325(f871(x86881,x86881)),f323(f323(f258(x86881,x86881),x86882),x86884)),f299(x86881,x86883)))+P101(f323(f323(f325(x86881),x86882),f312(x86881,x86883)))+~P101(f323(f323(f325(x86881),x86884),f312(x86881,x86883)))
% 188.07/187.98 [5114]~P72(x51142)+E(f323(f323(f6(x51141,x51142),x51143),x51144),f2(x51142))+P101(f323(f59(x51141),x51144))
% 188.07/187.98 [5117]~P68(x51172)+E(f323(f323(f9(x51171,x51172),x51173),x51174),f76(x51172))+P101(f323(f59(x51171),x51174))
% 188.07/187.98 [5254]~P69(x52543)+E(x52541,x52542)+~E(f323(f323(f78(x52543),x52544),x52541),f323(f323(f78(x52543),x52544),x52542))
% 188.07/187.98 [5255]~P70(x52553)+E(x52551,x52552)+~E(f323(f323(f78(x52553),x52554),x52551),f323(f323(f78(x52553),x52554),x52552))
% 188.07/187.98 [5257]~P69(x52573)+E(x52571,x52572)+~E(f323(f323(f78(x52573),x52571),x52574),f323(f323(f78(x52573),x52572),x52574))
% 188.07/187.98 [5378]~P6(x53783)+E(x53781,f188(f872(x53782,a860)))+E(f323(f323(f39(x53782,x53783),x53781),f323(f16(x53783,x53782),x53784)),x53784)
% 188.07/187.98 [5379]~P6(x53793)+E(x53791,f188(f872(x53792,a860)))+E(f323(f323(f40(x53792,x53793),x53791),f323(f16(x53793,x53792),x53794)),x53794)
% 188.07/187.98 [5589]~P105(x55893)+E(x55891,x55892)+~E(f294(x55893,x55894,x55891),f323(f323(f301(x55893),x55892),f188(f872(x55893,a860))))
% 188.07/187.98 [5590]~P105(x55903)+E(x55901,x55902)+~E(f294(x55903,x55901,x55902),f323(f323(f301(x55903),x55904),f188(f872(x55903,a860))))
% 188.07/187.98 [5650]~P36(x56503,x56501,x56504)+P36(x56503,x56501,f323(f323(f144(x56503),x56502),x56504))+P101(f323(x56501,x56502))
% 188.07/187.98 [5751]~P32(x57511,x57512,x57514)+~P101(f323(x57512,x57513))+P32(x57511,x57512,f323(f323(f144(x57511),x57513),x57514))
% 188.07/187.98 [5882]P101(f323(x58821,x58822))+~P101(f323(f251(x58823,x58821),x58824))+~P101(f323(f323(f325(x58823),x58822),x58824))
% 188.07/187.98 [5891]~P32(x58911,x58912,x58914)+~P32(x58911,x58912,x58913)+P32(x58911,x58912,f323(f323(f121(x58911),x58913),x58914))
% 188.07/187.98 [5901]P34(x59011,x59012,x59013)+~P34(x59011,x59012,f323(f323(f144(x59011),x59014),x59013))+P101(f323(x59012,x59014))
% 188.07/187.98 [5902]P36(x59021,x59022,x59023)+~P36(x59021,x59022,f323(f323(f144(x59021),x59024),x59023))+P101(f323(x59022,x59024))
% 188.07/187.98 [5975]P34(x59751,x59752,x59753)+P34(x59751,x59752,x59754)+~P34(x59751,x59752,f323(f323(f121(x59751),x59754),x59753))
% 188.07/187.98 [5994]~P72(x59941)+E(f323(f323(f6(a865,x59941),x59942),f323(f293(a865,x59943),f323(a112,x59944))),f2(x59941))+~P101(f323(f323(f238(a865),x59944),x59943))
% 188.07/187.98 [5999]~P58(x59991)+~E(f42(x59991,x59992,x59993),f42(x59991,x59994,x59993))+E(f42(x59991,f323(f77(x59991),x59992),x59993),f42(x59991,f323(f77(x59991),x59994),x59993))
% 188.07/187.98 [6067]P101(f323(x60671,x60672))+~E(f323(f129(x60673,x60671),x60674),x60674)+~P101(f323(f323(f325(x60673),x60672),f323(f166(x60673),x60674)))
% 188.07/187.98 [6086]~E(f323(f323(f78(a865),x60863),x60862),f323(f323(f78(a865),x60861),x60864))+~P101(f323(f323(f238(a865),x60863),x60864))+P101(f323(f323(f238(a865),x60861),x60862))
% 188.07/187.98 [6090]P34(x60901,x60902,x60903)+~P101(f323(x60902,x60904))+~P101(f323(f323(f325(x60901),x60904),f323(f166(x60901),x60903)))
% 188.07/187.98 [6126]~P32(x61263,x61261,x61264)+P101(f323(x61261,x61262))+~P101(f323(f323(f325(x61263),x61262),f323(f166(x61263),x61264)))
% 188.07/187.98 [6128]~E(f323(f129(x61281,x61282),x61283),f113(x61281))+~P101(f323(x61282,x61284))+~P101(f323(f323(f325(x61281),x61284),f323(f166(x61281),x61283)))
% 188.07/187.98 [6129]~E(f171(x61293,x61291,x61294),x61294)+P101(f323(x61291,x61292))+~P101(f323(f323(f325(x61293),x61292),f323(f166(x61293),x61294)))
% 188.07/187.98 [6157]~E(x61574,f188(f872(x61572,a860)))+~E(x61573,f188(f872(x61571,a860)))+E(f310(x61571,x61572,x61573,x61574),f188(f872(f870(x61571,x61572),a860)))
% 188.07/187.98 [6301]P101(f323(x63011,x63012))+~P101(f323(f153(x63013,x63011),x63014))+~P101(f323(f323(f325(x63013),x63012),f323(f166(x63013),x63014)))
% 188.07/187.98 [6567]~P72(x65671)+E(f323(f323(f6(a865,x65671),x65672),f294(a865,x65673,f323(a112,x65674))),f2(x65671))+~P101(f323(f323(f238(a865),f323(a112,x65674)),x65673))
% 188.07/187.98 [6706]~P103(x67061)+E(f323(f323(f22(f872(x67061,a860)),f323(f293(x67061,x67062),x67063)),f323(f293(x67061,x67062),x67064)),f323(f293(x67061,x67064),x67063))+~P101(f323(f323(f237(x67061),x67062),x67064))
% 188.07/187.98 [6778]~E(x67783,x67784)+E(x67781,f2(a865))+P101(f323(f323(f325(x67782),x67783),f323(f166(x67782),f163(x67782,x67781,x67784))))
% 188.07/187.98 [7055]~P101(f323(f323(f325(f866(x70551)),x70554),f154(x70551,x70553)))+P101(f323(f323(f325(x70551),x70552),x70553))+~P101(f323(f323(f325(x70551),x70552),f323(f166(x70551),x70554)))
% 188.07/187.98 [7062]~P38(x70621,x70622)+P101(f323(f323(f325(x70621),f736(x70622,x70621,x70623)),x70623))+~P101(f323(f323(f325(x70621),x70624),x70623))
% 188.07/187.98 [7118]~P72(x71181)+E(f323(f323(f323(f63(x71181,x71182,f78(x71181)),x71183),f2(x71181)),x71184),f323(f323(f6(x71182,x71181),x71183),x71184))+~P101(f323(f59(x71182),x71184))
% 188.07/187.98 [7120]~P68(x71201)+E(f323(f323(f323(f63(x71201,x71202,f79(x71201)),x71203),f76(x71201)),x71204),f323(f323(f9(x71202,x71201),x71203),x71204))+~P101(f323(f59(x71202),x71204))
% 188.07/187.98 [7148]P27(x71481,x71482,x71483,x71484)+~E(f323(f35(x71482),f323(f302(x71481,x71482,x71483),x71484)),f323(f35(x71481),x71484))+~P101(f323(f59(x71481),x71484))
% 188.07/187.98 [7331]~P72(x73311)+E(f323(f323(f78(x73311),f323(x73312,x73313)),f323(f323(f6(a865,x73311),x73312),f296(a865,x73313,x73314))),f323(f323(f6(a865,x73311),x73312),f294(a865,x73313,x73314)))+~P101(f323(f323(f237(a865),x73313),x73314))
% 188.07/187.98 [7341]~P72(x73411)+~P27(x73412,x73411,x73413,x73414)+E(f323(f323(f6(x73411,x73411),f32(x73411)),f323(f302(x73412,x73411,x73413),x73414)),f323(f323(f6(x73412,x73411),x73413),x73414))
% 188.07/187.98 [7342]~P68(x73421)+~P27(x73422,x73421,x73423,x73424)+E(f323(f323(f9(x73421,x73421),f32(x73421)),f323(f302(x73422,x73421,x73423),x73424)),f323(f323(f9(x73422,x73421),x73423),x73424))
% 188.07/187.98 [7395]E(f323(f35(f870(x73951,x73952)),f310(x73951,x73952,x73953,x73954)),f323(f323(f78(a865),f323(f35(x73951),x73953)),f323(f35(x73952),x73954)))+~P101(f323(f59(x73952),x73954))+~P101(f323(f59(x73951),x73953))
% 188.07/187.98 [7480]E(x74801,x74802)+P101(f323(f323(f325(x74803),x74801),f323(f166(x74803),f164(x74803,x74802,x74804))))+~P101(f323(f323(f325(x74803),x74801),f323(f166(x74803),x74804)))
% 188.07/187.98 [7705]~P72(x77051)+E(f323(f323(f78(x77051),f323(f323(f6(a865,x77051),x77052),f323(f293(a865,x77053),x77054))),f323(x77052,x77054)),f323(f323(f6(a865,x77051),x77052),f323(f293(a865,x77053),f323(a112,x77054))))+P101(f323(f323(f238(a865),x77054),x77053))
% 188.07/187.98 [7756]~P27(x77561,x77562,x77563,f246(f872(x77561,a860)))+~P101(f323(f59(x77562),x77564))+P101(f323(f59(x77561),f323(f303(x77561,x77562,x77563),x77564)))
% 188.07/187.98 [7872]P101(f323(f323(f325(f866(x78721)),f323(f323(f144(x78721),x78722),x78723)),f154(x78721,x78724)))+~P101(f323(f323(f325(f866(x78721)),x78723),f154(x78721,x78724)))+~P101(f323(f323(f325(x78721),x78722),x78724))
% 188.07/187.98 [7961]~E(f323(f302(x79613,x79611,x79614),f246(f872(x79613,a860))),f246(f872(x79611,a860)))+P101(f323(f59(x79611),x79612))+~P101(f323(f59(x79613),f323(f303(x79613,x79611,x79614),x79612)))
% 188.07/187.98 [8051]~P27(x80511,x80513,x80514,x80512)+P101(f323(f59(x80511),x80512))+~P101(f323(f59(x80513),f323(f302(x80511,x80513,x80514),x80512)))
% 188.07/187.98 [8072]~E(x80722,x80723)+P101(f323(f323(f325(f871(x80721,x80721)),f323(f323(f258(x80721,x80721),x80722),x80723)),f255(x80721,x80724)))+~P101(f323(f323(f325(x80721),x80722),x80724))
% 188.07/187.98 [8108]~P72(x81081)+E(f323(f323(f78(x81081),f323(f323(f6(a865,x81081),x81082),f294(a865,x81083,x81084))),f323(x81082,f323(a112,x81084))),f323(f323(f6(a865,x81081),x81082),f294(a865,x81083,f323(a112,x81084))))+P101(f323(f323(f238(a865),f323(a112,x81084)),x81083))
% 188.07/187.98 [8171]P101(f323(x81711,x81712))+~P101(f323(x81711,f323(f323(f158(x81713),x81714),f538(x81711,x81714,x81713))))+~P101(f323(f323(f325(x81713),x81712),f323(f166(x81713),x81714)))
% 188.07/187.98 [8314]~P101(f323(f323(f325(x83141),x83142),f312(x83141,x83144)))+P101(f323(f323(f325(f866(x83141)),f323(f323(f144(x83141),x83142),x83143)),f312(f866(x83141),f150(x83141,x83144))))+~P101(f323(f323(f325(f866(x83141)),x83143),f312(f866(x83141),f150(x83141,x83144))))
% 188.07/187.98 [8329]~P27(x83292,x83293,x83294,f675(x83294,x83293,x83292,x83291))+P27(x83292,x83293,x83294,f38(f872(x83292,a860),x83291))+E(x83291,f188(f872(f872(x83292,a860),a860)))
% 188.07/187.98 [8596]E(x85961,x85962)+~P101(f323(f323(f325(f871(x85963,x85963)),f323(f323(f258(x85963,x85963),x85961),x85962)),f299(x85963,x85964)))+P101(f323(f323(f325(x85963),x85961),f323(f256(x85963,x85963),x85964)))
% 188.07/187.98 [8879]E(x88791,f2(a865))+P101(f323(x88792,x88793))+P101(f323(f323(f325(x88794),f795(x88792,x88793,x88791,x88794)),f323(f166(x88794),f163(x88794,x88791,x88793))))
% 188.07/187.98 [8889]E(x88891,f2(a865))+~P101(f323(x88893,x88894))+P101(f323(f323(f325(x88892),f793(x88893,x88894,x88891,x88892)),f323(f166(x88892),f163(x88892,x88891,x88894))))
% 188.07/187.98 [8891]~P28(x88911,x88912,x88913,f246(f872(x88911,a860)),f246(f872(x88912,a860)))+~P101(f323(f59(x88912),x88914))+P101(f323(f59(x88911),f323(f303(x88911,x88912,x88913),x88914)))
% 188.07/187.98 [8895]P27(x88952,x88953,x88954,f38(f872(x88952,a860),x88951))+E(x88951,f188(f872(f872(x88952,a860),a860)))+P101(f323(f323(f325(f872(x88952,a860)),f675(x88954,x88953,x88952,x88951)),x88951))
% 188.07/187.98 [9006]~P28(x90063,x90061,x90064,f246(f872(x90063,a860)),f246(f872(x90061,a860)))+P101(f323(f59(x90061),x90062))+~P101(f323(f59(x90063),f323(f303(x90063,x90061,x90064),x90062)))
% 188.07/187.98 [9024]P101(f323(f59(x90241),x90242))+~P101(f323(f59(x90244),f323(f302(x90241,x90244,x90243),x90242)))+P101(f323(f323(f325(x90241),f357(x90243,x90244,x90242,x90241)),x90242))
% 188.07/187.98 [9118]~P6(x91182)+E(f323(f323(f62(x91181,x91182,f323(f323(f8(x91182,f872(x91182,x91182),x91181),f110(x91182)),x91183)),f188(x91182)),x91184),f323(f323(f39(x91181,x91182),x91184),x91183))+~P101(f323(f59(x91181),x91184))
% 188.07/187.98 [9119]~P6(x91192)+E(f323(f323(f62(x91191,x91192,f323(f323(f8(x91192,f872(x91192,x91192),x91191),f101(x91192)),x91193)),f246(x91192)),x91194),f323(f323(f40(x91191,x91192),x91194),x91193))+~P101(f323(f59(x91191),x91194))
% 188.07/187.98 [9202]P101(f323(x92021,x92022))+~P101(f323(x92021,f323(f323(f158(x92023),x92024),f561(x92022,x92021,x92024,x92023))))+~P101(f323(f323(f325(x92023),x92022),f323(f166(x92023),x92024)))
% 188.07/187.98 [9222]E(x92221,x92222)+~P101(f323(f323(f325(f871(x92223,x92223)),f323(f323(f258(x92223,x92223),x92221),x92222)),f299(x92223,x92224)))+P101(f323(f323(f325(f871(x92223,x92223)),f323(f323(f258(x92223,x92223),x92221),x92222)),f323(f323(f280(x92223,x92223,x92223),x92224),f299(x92223,x92224))))
% 188.07/187.98 [9270]~E(f323(f189(f866(x92701)),x92702),f323(f189(f866(x92701)),x92703))+~P101(f323(f323(f325(f871(f866(x92701),f866(x92701))),f323(f323(f258(f866(x92701),f866(x92701)),x92702),x92703)),f140(x92701,x92704)))+P101(f323(f323(f325(f871(f866(x92701),f866(x92701))),f323(f323(f258(f866(x92701),f866(x92701)),x92702),x92703)),f138(x92701,x92704)))
% 188.07/187.98 [9502]P32(x95021,f323(f323(f18(x95021,a860,a860),f323(f323(f8(a860,f872(a860,a860),x95021),a321),f323(f323(f8(a860,a860,x95021),a318),x95022))),f323(a320,x95023)),x95024)+~P101(f323(x95022,x95023))+~P36(x95021,x95022,f323(f323(f144(x95021),x95023),x95024))
% 188.07/187.98 [9667]~P32(x96671,f323(f323(f18(x96671,a860,a860),f323(f323(f8(a860,f872(a860,a860),x96671),a321),f323(f323(f8(a860,a860,x96671),a318),x96672))),f323(a320,x96673)),x96674)+~P101(f323(x96672,x96673))+P36(x96671,x96672,f323(f323(f144(x96671),x96673),x96674))
% 188.07/187.98 [9671]~P36(x96711,x96712,x96714)+~P32(x96711,f323(f323(f18(x96711,a860,a860),f323(f323(f8(a860,f872(a860,a860),x96711),a321),f323(f323(f8(a860,a860,x96711),a318),x96712))),f323(a320,x96713)),x96714)+P36(x96711,x96712,f323(f323(f144(x96711),x96713),x96714))
% 188.07/187.98 [9708]~P60(x97081)+E(f323(f323(f6(a865,x97081),f323(f323(f18(a865,x97081,x97081),f323(f323(f8(x97081,f872(x97081,x97081),a865),f22(x97081)),x97082)),f323(f323(f8(a865,x97081,a865),x97082),f323(f323(f7(a865,a865,a865),f78(a865)),f76(a865))))),f294(a865,x97083,x97084)),f2(x97081))+P101(f323(f323(f237(a865),x97083),x97084))
% 188.07/187.98 [9949]~P38(x99492,x99494)+~P27(x99492,x99491,x99493,f246(f872(x99492,a860)))+P38(x99491,f323(f302(f871(x99492,x99492),f871(x99491,x99491),f263(x99492,x99491,x99492,x99491,x99493,x99493)),x99494))
% 188.07/187.98 [10111]~E(f323(f189(f866(x101111)),x101113),f323(f189(f866(x101111)),x101112))+P101(f323(f323(f325(f871(f866(x101111),f866(x101111))),f323(f323(f258(f866(x101111),f866(x101111)),x101112),x101113)),f151(x101111,x101114)))+~P101(f323(f323(f262(x101111,x101111,a860),f323(f323(f7(x101111,f872(f871(x101111,x101111),a860),f872(x101111,a860)),f323(f323(f8(f872(x101111,f872(f872(f871(x101111,x101111),a860),a860)),f872(f872(f871(x101111,x101111),a860),f872(x101111,a860)),x101111),f7(x101111,f872(f871(x101111,x101111),a860),a860)),f323(f323(f8(f872(x101111,f871(x101111,x101111)),f872(x101111,f872(f872(f871(x101111,x101111),a860),a860)),x101111),f323(f8(f871(x101111,x101111),f872(f872(f871(x101111,x101111),a860),a860),x101111),f325(f871(x101111,x101111)))),f258(x101111,x101111)))),x101114)),f575(x101114,x101113,x101112,x101111)))
% 188.07/187.98 [6051]~P57(x60511)+~E(x60512,f2(x60511))+E(f323(f323(f36(x60511),f323(f323(f79(x60511),x60512),x60513)),f323(f323(f79(x60511),x60512),x60514)),f2(x60511))
% 188.07/187.98 [6089]E(x60891,f113(x60892))+E(x60893,f323(f323(f22(a865),f323(f189(f866(x60892)),x60891)),f76(a865)))+E(f137(x60892,f323(f323(f152(x60892,x60891),x60893),x60894)),f137(x60892,x60891))
% 188.07/187.98 [6117]E(x61171,x61172)+P101(f323(x61173,x61172))+~P101(f323(f323(f323(f301(x61174),x61171),x61173),x61172))
% 188.07/187.98 [6133]~P72(x61331)+~P101(f323(f130(x61332),x61334))+E(f323(f159(x61331),f323(f323(f147(x61332,x61331),x61333),x61334)),f323(f323(f6(x61332,x61331),x61333),f323(f166(x61332),x61334)))
% 188.07/187.98 [6150]~P68(x61502)+~P101(f323(f59(x61501),x61504))+E(f323(f323(f9(x61501,x61502),f323(f16(x61502,x61501),x61503)),x61504),f323(f323(f248(x61502),x61503),f323(f35(x61501),x61504)))
% 188.07/187.98 [6205]~P62(x62052)+E(x62051,f2(x62052))+E(f323(f323(f281(x62052),f323(f323(f79(x62052),x62053),x62051)),f323(f323(f79(x62052),x62054),x62051)),f323(f323(f281(x62052),x62053),x62054))
% 188.07/187.98 [6206]~P62(x62062)+E(x62061,f2(x62062))+E(f323(f323(f281(x62062),f323(f323(f79(x62062),x62061),x62063)),f323(f323(f79(x62062),x62061),x62064)),f323(f323(f281(x62062),x62063),x62064))
% 188.07/187.98 [6207]~P57(x62072)+E(x62071,f2(x62072))+E(f323(f323(f36(x62072),f323(f323(f79(x62072),x62073),x62071)),f323(f323(f79(x62072),x62074),x62071)),f323(f323(f36(x62072),x62073),x62074))
% 188.07/187.98 [6209]~P57(x62092)+E(x62091,f2(x62092))+E(f323(f323(f36(x62092),f323(f323(f79(x62092),x62091),x62093)),f323(f323(f79(x62092),x62091),x62094)),f323(f323(f36(x62092),x62093),x62094))
% 188.07/187.98 [6271]P101(f323(x62711,x62712))+~E(x62713,f323(f323(f78(a865),x62714),x62712))+~P101(f323(x62711,f323(f323(f22(a865),x62713),x62714)))
% 188.07/187.98 [6353]~P101(f323(x63532,x63533))+~P101(f323(f153(x63531,x63532),x63534))+P101(f323(f153(x63531,x63532),f323(f323(f144(x63531),x63533),x63534)))
% 188.07/187.98 [6393]E(x63931,f113(x63932))+~E(x63933,f323(f323(f22(a865),f323(f189(f866(x63932)),x63931)),f76(a865)))+E(f137(x63932,f323(f323(f152(x63932,x63931),x63933),x63934)),x63934)
% 188.07/187.98 [6416]~P97(x64161)+~P101(f323(f323(f237(x64161),x64162),x64164))+P101(f323(f323(f237(x64161),x64162),f323(f323(f110(x64161),x64163),x64164)))
% 188.07/187.98 [6417]~P97(x64171)+~P101(f323(f323(f237(x64171),x64172),x64173))+P101(f323(f323(f237(x64171),x64172),f323(f323(f110(x64171),x64173),x64174)))
% 188.07/187.98 [6419]~P103(x64191)+~P101(f323(f323(f237(x64191),x64192),x64194))+P101(f323(f323(f237(x64191),x64192),f323(f323(f236(x64191),x64193),x64194)))
% 188.07/187.98 [6421]~P103(x64211)+~P101(f323(f323(f237(x64211),x64212),x64213))+P101(f323(f323(f237(x64211),x64212),f323(f323(f236(x64211),x64213),x64214)))
% 188.07/187.98 [6422]~P97(x64221)+~P101(f323(f323(f238(x64221),x64222),x64224))+P101(f323(f323(f238(x64221),x64222),f323(f323(f110(x64221),x64223),x64224)))
% 188.07/187.98 [6423]~P97(x64231)+~P101(f323(f323(f238(x64231),x64232),x64233))+P101(f323(f323(f238(x64231),x64232),f323(f323(f110(x64231),x64233),x64234)))
% 188.07/187.98 [6425]~P103(x64251)+~P101(f323(f323(f238(x64251),x64252),x64254))+P101(f323(f323(f238(x64251),x64252),f323(f323(f236(x64251),x64253),x64254)))
% 188.07/187.98 [6427]~P103(x64271)+~P101(f323(f323(f238(x64271),x64272),x64273))+P101(f323(f323(f238(x64271),x64272),f323(f323(f236(x64271),x64273),x64274)))
% 188.07/187.98 [6513]~E(f323(f323(f158(x65131),x65132),x65133),x65134)+E(f323(f323(f152(x65131,x65132),x65133),x65134),x65132)+~P101(f323(f323(f238(a865),x65133),f323(f189(f866(x65131)),x65132)))
% 188.07/187.98 [6553]P101(f323(x65531,x65532))+~P101(f323(x65533,x65532))+~P101(f323(f323(f237(f872(x65534,a860)),x65533),x65531))
% 188.07/187.98 [6584]~E(f323(f323(f152(x65841,x65842),x65843),x65844),x65842)+E(f323(f323(f158(x65841),x65842),x65843),x65844)+~P101(f323(f323(f238(a865),x65843),f323(f189(f866(x65841)),x65842)))
% 188.07/187.98 [6599]~P101(f323(f153(x65991,x65992),x65994))+~P101(f323(f153(x65991,x65992),x65993))+P101(f323(f153(x65991,x65992),f323(f323(f121(x65991),x65993),x65994)))
% 188.07/187.98 [6703]E(x67031,f188(f872(x67032,a860)))+E(x67033,f188(f872(x67034,a860)))+~E(f323(f323(f260(x67034,x67032),x67033),f323(f16(f872(x67032,a860),x67034),x67031)),f188(f872(f871(x67034,x67032),a860)))
% 188.07/187.98 [6722]E(x67221,x67222)+P101(f323(f323(f325(x67223),x67221),x67224))+~P101(f323(f323(f325(x67223),x67221),f323(f323(f301(x67223),x67222),x67224)))
% 188.07/187.98 [6739]~P98(x67391)+P101(f323(f323(f237(x67391),x67392),x67393))+~P101(f323(f323(f237(x67391),x67392),f323(f323(f101(x67391),x67394),x67393)))
% 188.07/187.98 [6741]~P98(x67411)+P101(f323(f323(f237(x67411),x67412),x67413))+~P101(f323(f323(f237(x67411),x67412),f323(f323(f101(x67411),x67413),x67414)))
% 188.07/187.98 [6743]~P103(x67431)+P101(f323(f323(f237(x67431),x67432),x67433))+~P101(f323(f323(f237(x67431),x67432),f323(f323(f235(x67431),x67434),x67433)))
% 188.07/187.98 [6745]~P103(x67451)+P101(f323(f323(f237(x67451),x67452),x67453))+~P101(f323(f323(f237(x67451),x67452),f323(f323(f235(x67451),x67453),x67454)))
% 188.07/187.98 [6746]~P103(x67461)+P101(f323(f323(f238(x67461),x67462),x67463))+~P101(f323(f323(f238(x67461),x67462),f323(f323(f235(x67461),x67464),x67463)))
% 188.07/187.98 [6747]~P103(x67471)+P101(f323(f323(f238(x67471),x67472),x67473))+~P101(f323(f323(f238(x67471),x67472),f323(f323(f235(x67471),x67473),x67474)))
% 188.07/187.98 [6769]~E(f323(f323(f158(x67691),x67693),x67694),x67692)+P101(f323(f323(f325(x67691),x67692),f323(f166(x67691),x67693)))+~P101(f323(f323(f238(a865),x67694),f323(f189(f866(x67691)),x67693)))
% 188.07/187.98 [6781]~P103(x67811)+~P16(x67811,f323(f323(f144(x67811),x67812),f323(f323(f144(x67811),x67813),x67814)))+P101(f323(f323(f237(x67811),x67812),x67813))
% 188.07/187.98 [6920]~P32(x69202,x69201,x69203)+P101(f323(x69201,f323(f323(f158(x69202),x69203),x69204)))+~P101(f323(f323(f238(a865),x69204),f323(f189(f866(x69202)),x69203)))
% 188.07/187.98 [6939]E(x69391,f2(a1))+E(f323(f323(f36(a1),x69392),x69391),x69393)+~P101(f323(f46(x69392,x69391),f323(f323(f258(a1,a1),x69393),x69394)))
% 188.07/187.98 [6960]E(f42(a1,x69602,x69601),x69603)+E(x69601,f2(a1))+~P101(f323(f46(x69602,x69601),f323(f323(f258(a1,a1),x69604),x69603)))
% 188.07/187.98 [7079]P101(f323(f323(f325(x70791),x70792),x70793))+~P101(f323(f323(f325(x70791),x70792),x70794))+~P101(f323(f323(f238(f872(x70791,a860)),x70794),x70793))
% 188.07/187.98 [7080]P101(f323(f323(f325(x70801),x70802),x70803))+~P101(f323(f323(f325(x70801),x70802),x70804))+~P101(f323(f323(f237(f872(x70801,a860)),x70804),x70803))
% 188.07/187.98 [7188]P34(x71881,x71882,x71883)+~P101(f323(x71882,f323(f323(f158(x71881),x71883),x71884)))+~P101(f323(f323(f238(a865),x71884),f323(f189(f866(x71881)),x71883)))
% 188.07/187.98 [7297]~P104(x72972)+~P101(f323(f323(f238(f872(x72971,x72972)),x72973),x72974))+P101(f323(f323(f237(f872(x72971,x72972)),x72973),x72974))
% 188.07/187.98 [7383]~P26(x73831,x73832,x73834)+P26(x73831,x73832,f323(f323(f301(f864(x73831)),x73833),x73834))+~P26(x73831,x73832,f323(f323(f301(f864(x73831)),x73833),f188(f872(f864(x73831),a860))))
% 188.07/187.98 [7427]~P101(f323(f323(f325(x74271),x74272),x74274))+P101(f323(f323(f325(x74271),x74272),f37(f872(x74271,a860),x74273)))+~P101(f323(f323(f325(f872(x74271,a860)),x74274),x74273))
% 188.07/187.98 [7458]~P80(x74581)+~P101(f323(f323(f237(x74581),x74583),x74584))+P101(f323(f323(f237(x74581),f323(f323(f78(x74581),x74582),x74583)),f323(f323(f78(x74581),x74582),x74584)))
% 188.07/187.98 [7459]~P81(x74591)+~P101(f323(f323(f237(x74591),x74593),x74594))+P101(f323(f323(f237(x74591),f323(f323(f78(x74591),x74592),x74593)),f323(f323(f78(x74591),x74592),x74594)))
% 188.07/187.98 [7460]~P80(x74601)+~P101(f323(f323(f237(x74601),x74602),x74604))+P101(f323(f323(f237(x74601),f323(f323(f78(x74601),x74602),x74603)),f323(f323(f78(x74601),x74604),x74603)))
% 188.07/187.98 [7461]~P81(x74611)+~P101(f323(f323(f237(x74611),x74612),x74614))+P101(f323(f323(f237(x74611),f323(f323(f78(x74611),x74612),x74613)),f323(f323(f78(x74611),x74614),x74613)))
% 188.07/187.98 [7462]~P80(x74621)+~P101(f323(f323(f238(x74621),x74623),x74624))+P101(f323(f323(f238(x74621),f323(f323(f78(x74621),x74622),x74623)),f323(f323(f78(x74621),x74622),x74624)))
% 188.07/187.98 [7463]~P83(x74631)+~P101(f323(f323(f238(x74631),x74633),x74634))+P101(f323(f323(f238(x74631),f323(f323(f78(x74631),x74632),x74633)),f323(f323(f78(x74631),x74632),x74634)))
% 188.07/187.98 [7464]~P80(x74641)+~P101(f323(f323(f238(x74641),x74642),x74644))+P101(f323(f323(f238(x74641),f323(f323(f78(x74641),x74642),x74643)),f323(f323(f78(x74641),x74644),x74643)))
% 188.07/187.98 [7465]~P83(x74651)+~P101(f323(f323(f238(x74651),x74652),x74654))+P101(f323(f323(f238(x74651),f323(f323(f78(x74651),x74652),x74653)),f323(f323(f78(x74651),x74654),x74653)))
% 188.07/187.98 [7474]~P107(x74741)+~P91(x74741)+E(f323(f323(f22(x74741),f323(f323(f79(x74741),x74742),f323(f103(x74741),x74743))),f323(f323(f79(x74741),x74744),f323(f103(x74741),x74743))),f323(f323(f79(x74741),f323(f323(f22(x74741),x74742),x74744)),f323(f103(x74741),x74743)))
% 188.07/187.98 [7475]~P136(x74751)+~P91(x74751)+E(f323(f323(f78(x74751),f323(f323(f79(x74751),x74752),f323(f103(x74751),x74753))),f323(f323(f79(x74751),x74754),f323(f103(x74751),x74753))),f323(f323(f79(x74751),f323(f323(f78(x74751),x74752),x74754)),f323(f103(x74751),x74753)))
% 188.07/187.98 [7510]~P72(x75101)+E(f323(f323(f78(x75101),f323(x75102,x75103)),f323(f323(f6(a865,x75101),x75102),f294(a865,f323(a112,x75103),x75104))),f323(f323(f6(a865,x75101),x75102),f294(a865,x75103,x75104)))+~P101(f323(f323(f237(a865),x75103),x75104))
% 188.07/187.98 [7521]~P27(x75212,x75211,x75213,f323(f166(x75212),x75214))+~P101(f323(f130(x75212),x75214))+P101(f323(f130(x75211),f323(f323(f147(x75212,x75211),x75213),x75214)))
% 188.07/187.98 [7568]~P101(f323(f323(f237(a865),x75682),x75684))+~P101(f323(f323(f237(a865),x75681),x75683))+P101(f323(f323(f237(a865),f323(f323(f79(a865),x75681),x75682)),f323(f323(f79(a865),x75683),x75684)))
% 188.07/187.98 [7569]~P101(f323(f323(f237(a865),x75692),x75694))+~P101(f323(f323(f237(a865),x75691),x75693))+P101(f323(f323(f237(a865),f323(f323(f78(a865),x75691),x75692)),f323(f323(f78(a865),x75693),x75694)))
% 188.07/187.98 [7572]~P101(f323(f323(f238(a865),x75722),x75724))+~P101(f323(f323(f238(a865),x75721),x75723))+P101(f323(f323(f238(a865),f323(f323(f78(a865),x75721),x75722)),f323(f323(f78(a865),x75723),x75724)))
% 188.07/187.98 [7573]~P101(f323(f323(f237(a1),x75732),x75734))+~P101(f323(f323(f238(a1),x75731),x75733))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x75731),x75732)),f323(f323(f78(a1),x75733),x75734)))
% 188.07/187.98 [7621]P101(f323(f323(f325(x76211),x76212),x76213))+~P101(f323(f323(f325(x76211),x76212),f38(f872(x76211,a860),x76214)))+~P101(f323(f323(f325(f872(x76211,a860)),x76213),x76214))
% 188.07/187.98 [7637]~P101(f323(x76371,f537(x76371,x76373,x76372)))+P101(f323(x76371,f323(f323(f158(x76372),x76373),x76374)))+~P101(f323(f323(f238(a865),x76374),f323(f189(f866(x76372)),x76373)))
% 188.07/187.98 [7642]P101(f323(x76421,x76422))+~P101(f323(f323(f325(x76424),x76422),f323(f166(x76424),x76423)))+P101(f323(f323(f238(a865),f538(x76421,x76423,x76424)),f323(f189(f866(x76424)),x76423)))
% 188.07/187.98 [7690]~P104(x76901)+~P101(f323(f323(f238(f872(x76902,x76901)),x76904),x76903))+~P101(f323(f323(f237(f872(x76902,x76901)),x76903),x76904))
% 188.07/187.98 [7735]~P101(f323(x77354,x77352))+~P101(f323(f323(f325(x77351),x77352),x77353))+P101(f323(f323(f325(x77351),x77352),f323(f323(f101(f872(x77351,a860)),x77353),f323(f243(x77351),x77354))))
% 188.07/187.98 [7881]~P101(f323(f323(f325(x78811),x78813),x78814))+~P101(f323(f323(f238(f872(x78811,a860)),x78812),x78814))+P101(f323(f323(f238(f872(x78811,a860)),x78812),f323(f323(f301(x78811),x78813),x78814)))
% 188.07/187.98 [7883]E(f323(f323(f101(f872(x78831,a860)),x78832),x78833),f188(f872(x78831,a860)))+~E(f323(f323(f101(f872(x78831,a860)),f37(f872(x78831,a860),x78834)),x78833),f188(f872(x78831,a860)))+~P101(f323(f323(f325(f872(x78831,a860)),x78832),x78834))
% 188.07/187.98 [7957]P101(f323(f323(f325(x79571),x79572),x79573))+~P101(f323(f323(f237(f872(x79571,a860)),x79573),f323(f323(f301(x79571),x79572),x79574)))+P101(f323(f323(f237(f872(x79571,a860)),x79573),x79574))
% 188.07/187.98 [7974]P101(f323(f323(f325(x79742),f537(x79741,x79743,x79742)),f323(f166(x79742),x79743)))+P101(f323(x79741,f323(f323(f158(x79742),x79743),x79744)))+~P101(f323(f323(f238(a865),x79744),f323(f189(f866(x79742)),x79743)))
% 188.07/187.98 [7982]~P101(f323(f323(f237(f872(x79821,a860)),x79822),x79824))+P101(f323(f323(f237(f872(x79821,a860)),x79822),x79823))+~P101(f323(f323(f237(f872(x79821,a860)),x79824),x79823))
% 188.07/187.98 [7983]~P101(f323(f323(f238(f872(x79831,a860)),x79832),x79834))+~P101(f323(f323(f237(f872(x79831,a860)),x79834),x79833))+P101(f323(f323(f238(f872(x79831,a860)),x79832),x79833))
% 188.07/187.98 [7984]~P101(f323(f323(f237(f872(x79841,a860)),x79842),x79844))+~P101(f323(f323(f238(f872(x79841,a860)),x79844),x79843))+P101(f323(f323(f238(f872(x79841,a860)),x79842),x79843))
% 188.07/187.98 [7985]~P101(f323(f323(f238(f872(x79851,a860)),x79852),x79854))+P101(f323(f323(f238(f872(x79851,a860)),x79852),x79853))+~P101(f323(f323(f238(f872(x79851,a860)),x79854),x79853))
% 188.07/187.98 [8026]~P101(f323(f323(f325(x80261),x80264),x80263))+~P101(f323(f323(f238(f872(x80261,a860)),x80262),f323(f323(f301(x80261),x80264),x80263)))+P101(f323(f323(f238(f872(x80261,a860)),x80262),x80263))
% 188.07/187.98 [8037]~P80(x80371)+P101(f323(f323(f237(x80371),x80372),x80373))+~P101(f323(f323(f237(x80371),f323(f323(f78(x80371),x80374),x80372)),f323(f323(f78(x80371),x80374),x80373)))
% 188.07/187.98 [8039]~P80(x80391)+P101(f323(f323(f237(x80391),x80392),x80393))+~P101(f323(f323(f237(x80391),f323(f323(f78(x80391),x80392),x80394)),f323(f323(f78(x80391),x80393),x80394)))
% 188.07/187.98 [8041]~P80(x80411)+P101(f323(f323(f238(x80411),x80412),x80413))+~P101(f323(f323(f238(x80411),f323(f323(f78(x80411),x80414),x80412)),f323(f323(f78(x80411),x80414),x80413)))
% 188.07/187.98 [8043]~P80(x80431)+P101(f323(f323(f238(x80431),x80432),x80433))+~P101(f323(f323(f238(x80431),f323(f323(f78(x80431),x80432),x80434)),f323(f323(f78(x80431),x80433),x80434)))
% 188.07/187.98 [8089]P101(f323(x80891,x80892))+~E(f323(f323(f131(x80893),f323(f189(f866(x80893)),f171(x80893,x80891,x80894))),x80894),f113(x80893))+~P101(f323(f323(f325(x80893),x80892),f323(f166(x80893),x80894)))
% 188.07/187.98 [8214]P101(f323(x82141,x82142))+~P101(f323(f323(f325(x82143),x82142),f323(f166(x82143),x82144)))+P101(f323(f323(f238(a865),f323(f189(f866(x82143)),f323(f129(x82143,x82141),x82144))),f323(f189(f866(x82143)),x82144)))
% 188.07/187.98 [8704]~P101(f323(x87041,f719(x87041,x87043,x87042,x87044)))+P101(f323(x87041,f323(f323(f158(x87042),x87043),x87044)))+~P101(f323(f323(f238(a865),x87044),f323(f189(f866(x87042)),x87043)))
% 188.07/187.98 [8728]~P27(x87284,x87283,x87281,f246(f872(x87284,a860)))+E(f323(x87281,f539(x87282,x87281,x87283,x87284)),x87282)+~P101(f323(f323(f325(x87283),x87282),f323(f302(x87284,x87283,x87281),f246(f872(x87284,a860)))))
% 188.07/187.98 [8797]E(f171(x87971,x87972,x87973),f323(f323(f169(x87971),x87974),x87973))+P101(f323(f323(f238(a865),f632(x87972,x87973,x87971,x87974)),x87974))+P101(f323(f323(f238(a865),x87974),f323(f189(f866(x87971)),x87973)))
% 188.07/187.98 [8800]E(f171(x88001,x88002,x88003),f323(f323(f169(x88001),x88004),x88003))+P101(f323(f323(f238(a865),f632(x88002,x88003,x88001,x88004)),x88004))+P101(f323(x88002,f323(f323(f158(x88001),x88003),x88004)))
% 188.07/187.98 [8829]P101(f323(x88291,x88292))+~P101(f323(f323(f325(x88294),x88292),f323(f166(x88294),x88293)))+P101(f323(f323(f238(a865),f561(x88292,x88291,x88293,x88294)),f323(f189(f866(x88294)),x88293)))
% 188.07/187.98 [8831]E(f171(x88311,x88312,x88313),f323(f323(f169(x88311),x88314),x88313))+P101(f323(f323(f238(a865),x88314),f323(f189(f866(x88311)),x88313)))+P101(f323(f323(f238(a865),f632(x88312,x88313,x88311,x88314)),f323(f189(f866(x88311)),x88313)))
% 188.07/187.98 [8838]E(f171(x88381,x88382,x88383),f323(f323(f169(x88381),x88384),x88383))+P101(f323(x88382,f323(f323(f158(x88381),x88383),x88384)))+P101(f323(f323(f238(a865),f632(x88382,x88383,x88381,x88384)),f323(f189(f866(x88381)),x88383)))
% 188.07/187.98 [8864]~P119(x88644)+P101(f323(f323(f325(x88641),f783(x88642,x88643,x88641,x88644)),x88643))+P101(f323(f323(f238(x88644),f2(x88644)),f323(f323(f9(x88641,x88644),x88642),x88643)))
% 188.07/187.98 [8865]~P119(x88654)+P101(f323(f323(f325(x88651),f787(x88652,x88653,x88651,x88654)),x88653))+P101(f323(f323(f237(x88654),f2(x88654)),f323(f323(f9(x88651,x88654),x88652),x88653)))
% 188.07/187.98 [8897]~P101(f323(f59(x88971),x88974))+P101(f323(f323(f325(x88971),f615(x88972,x88973,x88974,x88971)),x88974))+P101(f323(f59(f871(x88971,x88973)),f323(f323(f260(x88971,x88973),x88974),x88972)))
% 188.07/187.98 [8925]P101(f323(f323(f325(x89252),f719(x89251,x89253,x89252,x89254)),f323(f166(x89252),x89253)))+P101(f323(x89251,f323(f323(f158(x89252),x89253),x89254)))+~P101(f323(f323(f238(a865),x89254),f323(f189(f866(x89252)),x89253)))
% 188.07/187.98 [9057]P101(f323(f323(f237(a865),x90574),f323(f189(f866(x90572)),f171(x90572,x90573,x90571))))+P101(f323(f323(f238(a865),f634(x90571,x90572,x90573,x90574)),x90574))+~P101(f323(f323(f237(a865),x90574),f323(f189(f866(x90572)),x90571)))
% 188.07/187.98 [9161]~E(f323(f323(f179(x91611,x91612),x91613),f685(x91614,x91613,x91612,x91611)),f323(f323(f179(x91611,x91612),x91614),f685(x91614,x91613,x91612,x91611)))+E(f323(f179(x91611,x91612),x91613),f323(f179(x91611,x91612),x91614))+~E(f323(f166(x91611),f323(f323(f147(f871(x91611,x91612),x91611),f257(x91611,x91612)),x91613)),f323(f166(x91611),f323(f323(f147(f871(x91611,x91612),x91611),f257(x91611,x91612)),x91614)))
% 188.07/187.98 [9205]E(f171(x92051,x92052,x92053),f323(f323(f169(x92051),x92054),x92053))+~P101(f323(x92052,f323(f323(f158(x92051),x92053),f632(x92052,x92053,x92051,x92054))))+P101(f323(f323(f238(a865),x92054),f323(f189(f866(x92051)),x92053)))
% 188.07/187.98 [9209]E(f171(x92091,x92092,x92093),f323(f323(f169(x92091),x92094),x92093))+~P101(f323(x92092,f323(f323(f158(x92091),x92093),f632(x92092,x92093,x92091,x92094))))+P101(f323(x92092,f323(f323(f158(x92091),x92093),x92094)))
% 188.07/187.98 [9216]~P101(f323(f59(x92161),x92163))+~P101(f323(f59(x92162),f323(x92164,f615(x92164,x92162,x92163,x92161))))+P101(f323(f59(f871(x92161,x92162)),f323(f323(f260(x92161,x92162),x92163),x92164)))
% 188.07/187.98 [9224]~P119(x92241)+~P101(f323(f323(f237(x92241),f2(x92241)),f323(x92243,f787(x92243,x92244,x92242,x92241))))+P101(f323(f323(f237(x92241),f2(x92241)),f323(f323(f9(x92242,x92241),x92243),x92244)))
% 188.07/187.98 [9225]~P119(x92251)+~P101(f323(f323(f238(x92251),f2(x92251)),f323(x92253,f783(x92253,x92254,x92252,x92251))))+P101(f323(f323(f238(x92251),f2(x92251)),f323(f323(f9(x92252,x92251),x92253),x92254)))
% 188.07/187.98 [9233]~E(f323(f189(f866(x92334)),x92332),f323(f189(f866(x92334)),x92333))+P101(f323(f323(f325(f871(f866(x92334),f866(x92334))),f323(f323(f258(f866(x92334),f866(x92334)),x92333),x92332)),f151(x92334,x92331)))+P101(f323(f323(f238(a865),f571(x92331,x92332,x92333,x92334)),f323(f189(f866(x92334)),x92333)))
% 188.07/187.98 [9284]~P101(f323(x92843,f323(f323(f158(x92842),x92844),f634(x92844,x92842,x92843,x92841))))+P101(f323(f323(f237(a865),x92841),f323(f189(f866(x92842)),f171(x92842,x92843,x92844))))+~P101(f323(f323(f237(a865),x92841),f323(f189(f866(x92842)),x92844)))
% 188.07/187.98 [9361]E(f323(f323(f169(x93611),f588(x93612,x93613,x93614,x93611)),x93613),f323(f323(f169(x93611),f588(x93612,x93613,x93614,x93611)),x93614))+~P101(f323(f323(f325(f871(f866(x93611),f866(x93611))),f323(f323(f258(f866(x93611),f866(x93611)),x93614),x93613)),f140(x93611,x93612)))+P101(f323(f323(f238(a865),f323(f189(f866(x93611)),x93614)),f323(f189(f866(x93611)),x93613)))
% 188.07/187.98 [9414]~P101(f323(f323(f238(a865),f2(a865)),x94143))+~P101(f323(f323(f238(a865),x94144),x94141))+P101(f323(f323(f238(a865),f323(f323(f78(a865),f323(f323(f79(a865),x94141),f42(a865,x94142,x94143))),x94144)),f323(f323(f79(a865),x94141),x94143)))
% 188.07/187.98 [9610]~P104(x96102)+~P101(f323(f323(f237(x96102),f323(x96103,f509(x96104,x96103,x96101,x96102))),f323(x96104,f509(x96104,x96103,x96101,x96102))))+P101(f323(f323(f237(f872(x96101,x96102)),x96103),x96104))
% 188.07/187.98 [9715]~P60(x97151)+E(f323(f323(f6(a865,x97151),f323(f323(f18(a865,x97151,x97151),f323(f323(f8(x97151,f872(x97151,x97151),a865),f22(x97151)),x97152)),f323(f323(f8(a865,x97151,a865),x97152),f323(f323(f7(a865,a865,a865),f78(a865)),f76(a865))))),f294(a865,x97153,x97154)),f323(f323(f22(x97151),f323(x97152,x97153)),f323(x97152,f323(f323(f78(a865),x97154),f76(a865)))))+~P101(f323(f323(f237(a865),x97153),x97154))
% 188.07/187.98 [6773]E(f323(f323(f121(x67731),x67732),x67733),x67734)+~E(x67733,f323(f323(f131(x67731),f323(f189(f866(x67731)),x67732)),x67734))+~E(f323(f323(f169(x67731),f323(f189(f866(x67731)),x67732)),x67734),x67732)
% 188.07/187.98 [6829]~P63(x68292)+E(x68291,f2(x68292))+E(f323(f323(f281(x68292),f323(f323(f248(x68292),x68293),x68294)),f323(f323(f248(x68292),x68291),x68294)),f323(f323(f248(x68292),f323(f323(f281(x68292),x68293),x68291)),x68294))
% 188.07/187.98 [6962]~E(f323(f189(f866(x69621)),x69623),f323(f189(f866(x69622)),x69624))+~P101(f323(f130(x69621),x69623))+E(f177(x69621,x69622,f323(f179(x69621,x69622),f323(f323(f175(x69621,x69622),x69623),x69624))),f323(f166(x69621),x69623))
% 188.07/187.98 [6979]~P98(x69791)+~P101(f323(f323(f237(x69791),x69793),x69794))+P101(f323(f323(f237(x69791),f323(f323(f101(x69791),x69792),x69793)),x69794))
% 188.07/187.98 [6980]~P98(x69801)+~P101(f323(f323(f237(x69801),x69802),x69804))+P101(f323(f323(f237(x69801),f323(f323(f101(x69801),x69802),x69803)),x69804))
% 188.07/187.98 [6982]~P103(x69821)+~P101(f323(f323(f237(x69821),x69823),x69824))+P101(f323(f323(f237(x69821),f323(f323(f235(x69821),x69822),x69823)),x69824))
% 188.07/187.98 [6984]~P103(x69841)+~P101(f323(f323(f237(x69841),x69842),x69844))+P101(f323(f323(f237(x69841),f323(f323(f235(x69841),x69842),x69843)),x69844))
% 188.07/187.98 [6985]~P98(x69851)+~P101(f323(f323(f238(x69851),x69853),x69854))+P101(f323(f323(f238(x69851),f323(f323(f101(x69851),x69852),x69853)),x69854))
% 188.07/187.98 [6986]~P98(x69861)+~P101(f323(f323(f238(x69861),x69862),x69864))+P101(f323(f323(f238(x69861),f323(f323(f101(x69861),x69862),x69863)),x69864))
% 188.07/187.98 [6988]~P103(x69881)+~P101(f323(f323(f238(x69881),x69883),x69884))+P101(f323(f323(f238(x69881),f323(f323(f235(x69881),x69882),x69883)),x69884))
% 188.07/187.98 [6990]~P103(x69901)+~P101(f323(f323(f238(x69901),x69902),x69904))+P101(f323(f323(f238(x69901),f323(f323(f235(x69901),x69902),x69903)),x69904))
% 188.07/187.98 [7010]~P101(f323(x70103,x70104))+~P101(f323(x70102,x70104))+P101(f323(f323(f323(f101(f872(x70101,a860)),x70102),x70103),x70104))
% 188.07/187.98 [7134]P26(x71341,x71342,x71343)+~P26(x71341,x71344,x71343)+~P101(f323(f323(f237(f872(f864(x71341),a860)),x71344),x71342))
% 188.07/187.98 [7135]P26(x71351,x71352,x71353)+~P26(x71351,x71352,x71354)+~P101(f323(f323(f237(f872(f864(x71351),a860)),x71353),x71354))
% 188.07/187.98 [7500]~P72(x75001)+E(f323(f323(f78(x75001),f323(x75002,x75003)),f323(f323(f6(a865,x75001),x75002),f323(f293(a865,f323(a112,x75003)),x75004))),f323(f323(f6(a865,x75001),x75002),f323(f293(a865,x75003),x75004)))+~P101(f323(f323(f238(a865),x75003),x75004))
% 188.07/187.98 [7529]~P97(x75291)+P101(f323(f323(f237(x75291),x75292),x75293))+~P101(f323(f323(f237(x75291),f323(f323(f110(x75291),x75294),x75292)),x75293))
% 188.07/187.98 [7531]~P97(x75311)+P101(f323(f323(f237(x75311),x75312),x75313))+~P101(f323(f323(f237(x75311),f323(f323(f110(x75311),x75312),x75314)),x75313))
% 188.07/187.98 [7533]~P103(x75331)+P101(f323(f323(f237(x75331),x75332),x75333))+~P101(f323(f323(f237(x75331),f323(f323(f236(x75331),x75334),x75332)),x75333))
% 188.07/187.98 [7535]~P103(x75351)+P101(f323(f323(f237(x75351),x75352),x75353))+~P101(f323(f323(f237(x75351),f323(f323(f236(x75351),x75352),x75354)),x75353))
% 188.07/187.98 [7536]~P103(x75361)+P101(f323(f323(f238(x75361),x75362),x75363))+~P101(f323(f323(f238(x75361),f323(f323(f236(x75361),x75364),x75362)),x75363))
% 188.07/187.98 [7537]~P103(x75371)+P101(f323(f323(f238(x75371),x75372),x75373))+~P101(f323(f323(f238(x75371),f323(f323(f236(x75371),x75372),x75374)),x75373))
% 188.07/187.98 [7613]~P101(f323(f323(f325(x76131),x76132),x76134))+P101(f323(f323(f325(x76131),x76132),x76133))+P101(f323(f323(f325(x76131),x76132),f323(f323(f22(f872(x76131,a860)),x76134),x76133)))
% 188.07/187.98 [7697]P101(f323(x76971,x76972))+P101(f323(x76973,x76972))+~P101(f323(f323(f323(f110(f872(x76974,a860)),x76973),x76971),x76972))
% 188.07/187.98 [7708]~P101(f323(f323(f325(x77081),x77082),x77084))+~P101(f323(f323(f325(x77081),x77082),x77083))+P101(f323(f323(f325(x77081),x77082),f323(f323(f101(f872(x77081,a860)),x77083),x77084)))
% 188.07/187.98 [7757]~P97(x77571)+~P101(f323(f59(x77571),x77574))+E(f323(f323(f62(x77571,x77571,f110(x77571)),x77572),f323(f323(f301(x77571),x77573),x77574)),f323(f323(f110(x77571),x77573),f323(f323(f62(x77571,x77571,f110(x77571)),x77572),x77574)))
% 188.07/187.98 [7758]~P98(x77581)+~P101(f323(f59(x77581),x77584))+E(f323(f323(f62(x77581,x77581,f101(x77581)),x77582),f323(f323(f301(x77581),x77583),x77584)),f323(f323(f101(x77581),x77583),f323(f323(f62(x77581,x77581,f101(x77581)),x77582),x77584)))
% 188.07/187.98 [7759]~P103(x77591)+~P101(f323(f59(x77591),x77594))+E(f323(f323(f62(x77591,x77591,f235(x77591)),x77592),f323(f323(f301(x77591),x77593),x77594)),f323(f323(f235(x77591),x77593),f323(f323(f62(x77591,x77591,f235(x77591)),x77592),x77594)))
% 188.07/187.98 [7760]~P103(x77601)+~P101(f323(f59(x77601),x77604))+E(f323(f323(f62(x77601,x77601,f236(x77601)),x77602),f323(f323(f301(x77601),x77603),x77604)),f323(f323(f236(x77601),x77603),f323(f323(f62(x77601,x77601,f236(x77601)),x77602),x77604)))
% 188.07/187.98 [7761]~P107(x77611)+~P91(x77611)+E(f323(f323(f22(x77611),f323(f323(f79(x77611),f323(f103(x77611),x77612)),x77613)),f323(f323(f79(x77611),f323(f103(x77611),x77612)),x77614)),f323(f323(f79(x77611),f323(f103(x77611),x77612)),f323(f323(f22(x77611),x77613),x77614)))
% 188.07/187.98 [7762]~P136(x77621)+~P91(x77621)+E(f323(f323(f78(x77621),f323(f323(f79(x77621),f323(f103(x77621),x77622)),x77623)),f323(f323(f79(x77621),f323(f103(x77621),x77622)),x77624)),f323(f323(f79(x77621),f323(f103(x77621),x77622)),f323(f323(f78(x77621),x77623),x77624)))
% 188.07/187.98 [7879]E(x78791,x78792)+P101(f323(f323(f325(x78793),x78791),f323(f166(x78793),x78794)))+~P101(f323(f323(f325(x78793),x78791),f323(f166(x78793),f323(f323(f144(x78793),x78792),x78794))))
% 188.07/187.98 [7905]~P5(x79051)+~E(f323(f189(f866(x79052)),x79053),f323(f189(f866(x79051)),f53(x79051)))+E(f323(f323(f179(x79051,x79052),f323(f323(f175(x79051,x79052),f53(x79051)),x79053)),x79054),f323(f230(x79052),f544(x79054,x79053,x79052,x79051)))
% 188.07/187.98 [8049]P51(x80491,x80492,x80493)+~P51(x80491,x80492,x80494)+~P101(f323(f323(f237(f872(f871(x80491,x80492),a860)),x80493),x80494))
% 188.07/187.98 [8092]P101(f323(f323(f325(x80921),x80922),x80923))+P101(f323(f323(f325(x80921),x80922),x80924))+~P101(f323(f323(f325(x80921),x80922),f323(f323(f110(f872(x80921,a860)),x80924),x80923)))
% 188.07/187.98 [8102]~P40(x81021,x81024,x81023)+~P101(f323(f323(f325(x81021),x81022),x81024))+P101(f323(f323(f325(f871(x81021,x81021)),f323(f323(f258(x81021,x81021),x81022),x81022)),x81023))
% 188.07/187.98 [8117]~P101(f323(f59(x81172),x81174))+~P101(f323(f59(x81171),x81173))+P101(f323(f59(f871(x81171,x81172)),f323(f323(f260(x81171,x81172),x81173),f323(f16(f872(x81172,a860),x81171),x81174))))
% 188.07/187.98 [8118]~P101(f323(f323(f325(x81181),x81182),x81184))+~P101(f323(f323(f237(f872(x81181,a860)),x81183),x81184))+P101(f323(f323(f237(f872(x81181,a860)),f323(f323(f301(x81181),x81182),x81183)),x81184))
% 188.07/187.98 [8126]~P68(x81262)+~P140(x81262)+E(f323(f323(f9(x81261,x81262),f323(f323(f8(a865,x81262,x81261),f100(x81262)),x81263)),x81264),f323(f100(x81262),f323(f323(f9(x81261,a865),x81263),x81264)))
% 188.07/187.98 [8127]~P68(x81272)+~P134(x81272)+E(f323(f323(f9(x81271,x81272),f323(f323(f8(a1,x81272,x81271),f102(x81272)),x81273)),x81274),f323(f102(x81272),f323(f323(f9(x81271,a1),x81273),x81274)))
% 188.07/187.98 [8152]E(f323(f323(f22(f872(x81521,a860)),x81522),f323(f323(f22(f872(x81521,a860)),x81523),x81524)),x81524)+~P101(f323(f323(f237(f872(x81521,a860)),x81522),x81523))+~P101(f323(f323(f237(f872(x81521,a860)),x81524),x81522))
% 188.07/187.98 [8248]~P101(f323(f59(x82481),x82484))+E(f323(f323(f22(a865),f323(f323(f6(x82481,a865),x82482),x82483)),f323(f323(f6(x82481,a865),x82482),x82484)),f323(f323(f6(x82481,a865),x82482),f323(f323(f22(f872(x82481,a860)),x82483),x82484)))+~P101(f323(f323(f237(f872(x82481,a860)),x82484),x82483))
% 188.07/187.98 [8404]~P9(x84041,x84044,x84043)+~P101(f323(f323(f325(x84041),x84042),x84044))+P101(f323(f323(f325(x84041),x84042),f323(f277(x84041,x84041,x84043),f323(f323(f301(x84041),x84042),f188(f872(x84041,a860))))))
% 188.07/187.98 [8460]~P101(f323(f323(f237(f872(x84601,a860)),x84602),x84603))+~P101(f323(f323(f237(f872(x84601,a860)),x84602),x84604))+P101(f323(f323(f237(f872(x84601,a860)),x84602),f323(f323(f101(f872(x84601,a860)),x84603),x84604)))
% 188.07/187.98 [8563]E(x85631,f188(f872(x85632,a860)))+P101(f323(f59(x85633),x85634))+~P101(f323(f59(f871(x85633,x85632)),f323(f323(f260(x85633,x85632),x85634),f323(f16(f872(x85632,a860),x85633),x85631))))
% 188.07/187.98 [8564]E(x85641,f188(f872(x85642,a860)))+P101(f323(f59(x85643),x85644))+~P101(f323(f59(f871(x85642,x85643)),f323(f323(f260(x85642,x85643),x85641),f323(f16(f872(x85643,a860),x85642),x85644))))
% 188.07/187.98 [8639]P101(f323(f323(f325(x86391),x86392),f312(x86391,x86393)))+~P101(f323(f323(f325(x86391),x86394),f312(x86391,x86393)))+~P101(f323(f323(f325(f871(x86391,x86391)),f323(f323(f258(x86391,x86391),x86392),x86394)),x86393))
% 188.07/187.98 [8696]~P38(x86961,x86964)+P101(f323(f323(f325(f871(x86961,x86961)),f323(f323(f258(x86961,x86961),x86963),x86962)),f299(x86961,x86964)))+P38(x86961,f323(f323(f301(f871(x86961,x86961)),f323(f323(f258(x86961,x86961),x86962),x86963)),x86964))
% 188.07/187.98 [8697]~P54(x86971,x86974)+P101(f323(f323(f325(f871(x86971,x86971)),f323(f323(f258(x86971,x86971),x86973),x86972)),f299(x86971,x86974)))+P54(x86971,f323(f323(f301(f871(x86971,x86971)),f323(f323(f258(x86971,x86971),x86972),x86973)),x86974))
% 188.07/187.98 [8780]~E(x87802,x87803)+~P101(f323(f323(f325(x87801),x87802),f323(f166(x87801),x87804)))+P101(f323(f323(f325(f871(x87801,x87801)),f323(f323(f258(x87801,x87801),x87802),x87803)),f323(f166(f871(x87801,x87801)),f323(f323(f175(x87801,x87801),x87804),x87804))))
% 188.07/187.98 [8862]~E(x88623,x88624)+P101(f323(f323(f262(x88621,x88621,a860),a320),x88622))+~P101(f323(f323(f325(f871(x88621,x88621)),x88622),f323(f166(f871(x88621,x88621)),f323(f323(f175(x88621,x88621),x88623),x88624))))
% 188.07/187.98 [8912]P101(f323(f323(f325(f871(f866(x89121),f866(x89121))),f323(f323(f258(f866(x89121),f866(x89121)),x89122),x89123)),f140(x89121,x89124)))+~E(f323(f323(f169(x89121),f323(f189(f866(x89121)),x89122)),x89123),x89122)+~P101(f323(f323(f238(a865),f323(f189(f866(x89121)),x89122)),f323(f189(f866(x89121)),x89123)))
% 188.07/187.98 [9004]~P101(f323(f59(x90041),x90044))+P101(f323(f323(f325(x90041),f446(x90042,x90043,x90044,x90041)),x90044))+P101(f323(f59(x90043),f323(f323(f39(x90041,f872(x90043,a860)),x90044),x90042)))
% 188.07/187.98 [9005]~P101(f323(f59(x90051),x90054))+P101(f323(f323(f325(x90051),f457(x90052,x90053,x90054,x90051)),x90054))+P101(f323(f59(x90053),f323(f323(f39(x90051,f872(x90053,a860)),x90054),x90052)))
% 188.07/187.98 [9092]P101(f323(f323(f325(f871(x90921,x90921)),x90922),f323(f323(f280(x90921,x90921,x90921),x90923),f299(x90921,x90923))))+~P101(f323(f323(f238(a865),f2(a865)),x90924))+~P101(f323(f323(f325(f871(x90921,x90921)),x90922),f323(f323(f183(f871(x90921,x90921),a860),x90924),x90923)))
% 188.07/187.98 [9100]~P38(x91001,x91002)+~P101(f323(f323(f325(f871(x91001,x91001)),f323(f323(f258(x91001,x91001),x91004),x91003)),x91002))+~P101(f323(f323(f325(f871(x91001,x91001)),f323(f323(f258(x91001,x91001),x91003),x91004)),x91002))
% 188.07/187.98 [9223]~P101(f323(f59(x92231),x92234))+E(f323(f323(f6(x92231,a865),f323(f323(f8(f872(x92232,a860),a865,x92231),f35(x92232)),x92233)),x92234),f323(f35(f871(x92231,x92232)),f323(f323(f260(x92231,x92232),x92234),x92233)))+P101(f323(f323(f325(x92231),f618(x92233,x92232,x92234,x92231)),x92234))
% 188.07/187.98 [9227]~P101(f323(f130(x92271),x92272))+P101(f323(f130(x92271),f323(f323(f152(x92271,x92272),x92273),x92274)))+P101(f323(f323(f325(x92271),x92274),f323(f323(f22(f872(x92271,a860)),f323(f166(x92271),x92272)),f323(f323(f301(x92271),f323(f323(f158(x92271),x92272),x92273)),f188(f872(x92271,a860))))))
% 188.07/187.98 [9243]~P101(f323(f59(x92432),x92433))+~P101(f323(f59(x92431),f323(x92434,f446(x92434,x92431,x92433,x92432))))+P101(f323(f59(x92431),f323(f323(f39(x92432,f872(x92431,a860)),x92433),x92434)))
% 188.07/187.98 [9244]~P101(f323(f59(x92442),x92443))+~P101(f323(f59(x92441),f323(x92444,f457(x92444,x92441,x92443,x92442))))+P101(f323(f59(x92441),f323(f323(f39(x92442,f872(x92441,a860)),x92443),x92444)))
% 188.07/187.98 [9322]~P101(f323(f323(f325(f871(x93221,x93221)),x93222),f323(f323(f280(x93221,x93221,x93221),x93224),f299(x93221,x93224))))+P101(f323(f323(f325(f871(x93221,x93221)),x93222),f323(f323(f280(x93221,x93221,x93221),x93223),f299(x93221,x93223))))+~P101(f323(f323(f237(f872(f871(x93221,x93221),a860)),x93224),x93223))
% 188.07/187.98 [9330]E(f323(f323(f169(x93301),f588(x93304,x93303,x93302,x93301)),x93303),f323(f323(f169(x93301),f588(x93304,x93303,x93302,x93301)),x93302))+~P101(f323(f323(f325(f871(f866(x93301),f866(x93301))),f323(f323(f258(f866(x93301),f866(x93301)),x93302),x93303)),f140(x93301,x93304)))+E(f323(f323(f169(x93301),f323(f189(f866(x93301)),x93302)),x93303),x93302)
% 188.07/187.98 [9346]~P101(f323(f59(x93461),x93464))+E(f323(f323(f6(x93461,a865),f323(f323(f8(f872(x93462,a860),a865,x93461),f35(x93462)),x93463)),x93464),f323(f35(f871(x93461,x93462)),f323(f323(f260(x93461,x93462),x93464),x93463)))+~P101(f323(f59(x93462),f323(x93463,f618(x93463,x93462,x93464,x93461))))
% 188.07/187.98 [9350]~E(f323(f189(f866(x93501)),x93503),f323(f189(f866(x93501)),x93502))+P101(f323(f323(f325(f871(f866(x93501),f866(x93501))),f323(f323(f258(f866(x93501),f866(x93501)),x93502),x93503)),f151(x93501,x93504)))+P101(f323(f323(f325(f871(x93501,x93501)),f575(x93504,x93503,x93502,x93501)),f323(f166(f871(x93501,x93501)),f323(f323(f175(x93501,x93501),x93502),x93503))))
% 188.07/187.98 [9426]~P101(f323(f323(f325(f871(f866(x94261),f866(x94261))),f323(f323(f258(f866(x94261),f866(x94261)),x94262),x94263)),f140(x94261,x94264)))+E(f323(f323(f169(x94261),f323(f189(f866(x94261)),x94262)),x94263),x94262)+P101(f323(f323(f238(a865),f588(x94264,x94263,x94262,x94261)),f323(f323(f235(a865),f323(f189(f866(x94261)),x94262)),f323(f189(f866(x94261)),x94263))))
% 188.07/187.98 [9427]E(f323(f179(x94271,x94272),x94273),f323(f179(x94271,x94272),x94274))+~E(f323(f166(x94271),f323(f323(f147(f871(x94271,x94272),x94271),f257(x94271,x94272)),x94273)),f323(f166(x94271),f323(f323(f147(f871(x94271,x94272),x94271),f257(x94271,x94272)),x94274)))+P101(f323(f323(f325(x94271),f685(x94273,x94274,x94272,x94271)),f323(f166(x94271),f323(f323(f147(f871(x94271,x94272),x94271),f257(x94271,x94272)),x94274))))
% 188.07/187.98 [9452]~P101(f323(f323(f325(f871(f866(x94521),f866(x94521))),f323(f323(f258(f866(x94521),f866(x94521)),x94522),x94523)),f140(x94521,x94524)))+P101(f323(f323(f238(a865),f323(f189(f866(x94521)),x94522)),f323(f189(f866(x94521)),x94523)))+P101(f323(f323(f238(a865),f588(x94524,x94523,x94522,x94521)),f323(f323(f235(a865),f323(f189(f866(x94521)),x94522)),f323(f189(f866(x94521)),x94523))))
% 188.07/187.98 [9752]~P101(f323(f323(f323(x97521,f519(x97521,x97524,x97523,x97522)),f520(x97521,x97524,x97523,x97522)),f521(x97521,x97524,x97523,x97522)))+P101(f323(f323(f323(x97521,x97522),x97523),x97524))+~P101(f323(f311(f871(f872(a1,f869(f866(a319))),f871(a1,a1)),a309),f323(f323(f258(f872(a1,f869(f866(a319))),f871(a1,a1)),x97522),f323(f323(f258(a1,a1),x97523),x97524))))
% 188.07/187.98 [9830]P101(f323(f323(f323(x98301,x98302),x98303),x98304))+P101(f323(f311(f871(f872(a1,f869(f866(a319))),f871(a1,a1)),a309),f323(f323(f258(f872(a1,f869(f866(a319))),f871(a1,a1)),f519(x98301,x98304,x98303,x98302)),f323(f323(f258(a1,a1),f520(x98301,x98304,x98303,x98302)),f521(x98301,x98304,x98303,x98302)))))+~P101(f323(f311(f871(f872(a1,f869(f866(a319))),f871(a1,a1)),a309),f323(f323(f258(f872(a1,f869(f866(a319))),f871(a1,a1)),x98302),f323(f323(f258(a1,a1),x98303),x98304))))
% 188.07/187.98 [9869]~P101(f323(f323(f325(f871(f866(x98691),f866(x98691))),f323(f323(f258(f866(x98691),f866(x98691)),x98692),x98693)),f140(x98691,x98694)))+E(f323(f323(f169(x98691),f323(f189(f866(x98691)),x98692)),x98693),x98692)+P101(f323(f323(f325(f871(x98691,x98691)),f323(f323(f258(x98691,x98691),f323(f323(f158(x98691),x98692),f588(x98694,x98693,x98692,x98691))),f323(f323(f158(x98691),x98693),f588(x98694,x98693,x98692,x98691)))),x98694))
% 188.07/187.98 [9870]~P101(f323(f323(f325(f871(f866(x98701),f866(x98701))),f323(f323(f258(f866(x98701),f866(x98701)),x98702),x98703)),f140(x98701,x98704)))+P101(f323(f323(f238(a865),f323(f189(f866(x98701)),x98702)),f323(f189(f866(x98701)),x98703)))+P101(f323(f323(f325(f871(x98701,x98701)),f323(f323(f258(x98701,x98701),f323(f323(f158(x98701),x98702),f588(x98704,x98703,x98702,x98701))),f323(f323(f158(x98701),x98703),f588(x98704,x98703,x98702,x98701)))),x98704))
% 188.07/187.98 [9927]~E(f323(f189(f866(x99271)),x99272),f323(f189(f866(x99271)),x99273))+P101(f323(f323(f325(f871(f866(x99271),f866(x99271))),f323(f323(f258(f866(x99271),f866(x99271)),x99272),x99273)),f151(x99271,x99274)))+~P101(f323(f323(f325(f871(x99271,x99271)),f323(f323(f258(x99271,x99271),f323(f323(f158(x99271),x99272),f571(x99274,x99273,x99272,x99271))),f323(f323(f158(x99271),x99273),f571(x99274,x99273,x99272,x99271)))),x99274))
% 188.07/187.98 [10060]~P72(x100601)+~P101(f323(f59(x100602),x100604))+E(f323(f159(x100601),f323(f323(f147(x100602,x100601),x100603),f88(f866(x100602),f323(f323(f18(f866(x100602),a860,a860),f323(f323(f8(a860,f872(a860,a860),f866(x100602)),a322),f323(f323(f7(f866(x100602),f872(x100602,a860),a860),f323(f323(f8(f872(x100602,a860),f872(f872(x100602,a860),a860),f866(x100602)),a320),f166(x100602))),x100604))),f130(x100602))))),f228(x100602,x100601,x100603,x100604))
% 188.07/187.98 [7343]~P62(x73432)+E(x73431,f2(x73432))+E(f323(f323(f281(x73432),f323(f323(f78(x73432),x73433),f323(f323(f79(x73432),x73434),x73431))),x73431),f323(f323(f78(x73432),x73434),f323(f323(f281(x73432),x73433),x73431)))
% 188.07/187.98 [7344]~P57(x73442)+E(x73441,f2(x73442))+E(f323(f323(f36(x73442),f323(f323(f78(x73442),x73443),f323(f323(f79(x73442),x73444),x73441))),x73441),f323(f323(f78(x73442),x73444),f323(f323(f36(x73442),x73443),x73441)))
% 188.07/187.98 [7345]~P57(x73452)+E(x73451,f2(x73452))+E(f323(f323(f36(x73452),f323(f323(f78(x73452),x73453),f323(f323(f79(x73452),x73451),x73454))),x73451),f323(f323(f78(x73452),x73454),f323(f323(f36(x73452),x73453),x73451)))
% 188.07/187.98 [7576]~P63(x75762)+E(x75761,f2(x75762))+E(f323(f323(f281(x75762),f323(f323(f22(x75762),x75763),f323(f323(f79(x75762),x75761),x75764))),x75761),f323(f323(f22(x75762),f323(f323(f281(x75762),x75763),x75761)),x75764))
% 188.07/187.98 [7577]~P62(x75772)+E(x75771,f2(x75772))+E(f323(f323(f281(x75772),f323(f323(f78(x75772),x75773),f323(f323(f79(x75772),x75774),x75771))),x75771),f323(f323(f78(x75772),f323(f323(f281(x75772),x75773),x75771)),x75774))
% 188.07/187.98 [7578]~P63(x75782)+E(x75781,f2(x75782))+E(f323(f323(f281(x75782),f323(f323(f78(x75782),x75783),f323(f323(f79(x75782),x75781),x75784))),x75781),f323(f323(f78(x75782),f323(f323(f281(x75782),x75783),x75781)),x75784))
% 188.07/187.98 [8279]~P101(f323(f153(x82791,x82793),x82794))+~P101(f323(f153(x82791,x82792),x82794))+P101(f323(f153(x82791,f323(f323(f101(f872(x82791,a860)),x82792),x82793)),x82794))
% 188.07/187.98 [8654]~E(f323(f323(f280(x86541,x86541,x86541),x86542),x86544),f188(f872(f871(x86541,x86541),a860)))+~E(f323(f323(f280(x86541,x86541,x86541),x86542),x86543),f188(f872(f871(x86541,x86541),a860)))+E(f323(f323(f280(x86541,x86541,x86541),x86542),f323(f323(f110(f872(f871(x86541,x86541),a860)),x86543),x86544)),f188(f872(f871(x86541,x86541),a860)))
% 188.07/187.98 [8781]~P101(f323(f323(f237(f872(x87811,a860)),x87813),x87814))+~P101(f323(f323(f237(f872(x87811,a860)),x87812),x87814))+P101(f323(f323(f237(f872(x87811,a860)),f323(f323(f110(f872(x87811,a860)),x87812),x87813)),x87814))
% 188.07/187.98 [9155]~P101(f323(f59(x91551),x91554))+~P101(f323(f59(x91551),x91553))+E(f323(f323(f22(a865),f323(f323(f78(a865),f323(f323(f6(x91551,a865),x91552),x91553)),f323(f323(f6(x91551,a865),x91552),x91554))),f323(f323(f6(x91551,a865),x91552),f323(f323(f101(f872(x91551,a860)),x91553),x91554))),f323(f323(f6(x91551,a865),x91552),f323(f323(f110(f872(x91551,a860)),x91553),x91554)))
% 188.07/187.98 [9240]~P101(f323(f323(f325(x92401),x92403),x92402))+~P101(f323(f323(f237(f872(x92401,a860)),x92402),f323(f323(f301(x92401),x92403),x92404)))+P101(f323(f323(f237(f872(x92401,a860)),f323(f323(f22(f872(x92401,a860)),x92402),f323(f323(f301(x92401),x92403),f188(f872(x92401,a860))))),x92404))
% 188.07/187.98 [9400]~P101(f323(f323(f325(x94001),x94003),x94002))+P101(f323(f323(f237(f872(x94001,a860)),x94002),f323(f323(f301(x94001),x94003),x94004)))+~P101(f323(f323(f237(f872(x94001,a860)),f323(f323(f22(f872(x94001,a860)),x94002),f323(f323(f301(x94001),x94003),f188(f872(x94001,a860))))),x94004))
% 188.07/187.98 [9491]~P101(f323(f323(f237(a865),x94911),x94913))+~P101(f323(f323(f238(a865),x94912),x94914))+P101(f323(f323(f325(f871(f871(a865,a865),f871(a865,a865))),f323(f323(f258(f871(a865,a865),f871(a865,a865)),f323(f323(f258(a865,a865),x94911),x94912)),f323(f323(f258(a865,a865),x94913),x94914))),a33))
% 188.07/187.98 [9492]~P101(f323(f323(f237(a865),x94922),x94924))+~P101(f323(f323(f237(a865),x94921),x94923))+P101(f323(f323(f325(f871(f871(a865,a865),f871(a865,a865))),f323(f323(f258(f871(a865,a865),f871(a865,a865)),f323(f323(f258(a865,a865),x94921),x94922)),f323(f323(f258(a865,a865),x94923),x94924))),a68))
% 188.07/187.98 [9792]~P101(f323(f323(f325(f866(x97921)),x97924),f154(x97921,x97923)))+~P101(f323(f323(f325(f866(x97921)),x97924),f154(x97921,x97922)))+P101(f323(f153(x97921,f323(f323(f101(f872(x97921,a860)),f323(f323(f7(x97921,f872(x97921,a860),a860),f325(x97921)),x97922)),f323(f323(f7(x97921,f872(x97921,a860),a860),f325(x97921)),x97923))),x97924))
% 188.07/187.98 [9892]~P27(x98921,f872(f872(x98921,a860),a860),f323(f323(f7(x98921,f872(f871(x98921,x98921),a860),f872(f872(x98921,a860),a860)),f323(f323(f8(f872(x98921,a860),f872(f872(f871(x98921,x98921),a860),f872(f872(x98921,a860),a860)),x98921),f58(x98921)),f323(f323(f7(x98921,f872(x98921,a860),f872(x98921,a860)),f301(x98921)),f188(f872(x98921,a860))))),x98923),x98922)+~P101(f323(f323(f325(x98921),x98924),x98922))+E(f323(f323(f22(f872(f872(x98921,a860),a860)),f323(f323(f58(x98921),x98922),x98923)),f323(f323(f58(x98921),f323(f323(f301(x98921),x98924),f188(f872(x98921,a860)))),x98923)),f323(f323(f58(x98921),f323(f323(f22(f872(x98921,a860)),x98922),f323(f323(f301(x98921),x98924),f188(f872(x98921,a860))))),x98923))
% 188.07/187.98 [10025]~P40(x100251,x100252,x100254)+~P101(f323(f323(f325(f871(x100251,x100251)),x100253),x100254))+P101(f323(f323(f262(x100251,x100251,a860),f323(f323(f7(x100251,f872(x100251,a860),f872(x100251,a860)),f323(f323(f8(f872(a860,a860),f872(f872(x100251,a860),f872(x100251,a860)),x100251),f8(a860,a860,x100251)),f323(f323(f8(a860,f872(a860,a860),x100251),a322),f323(f323(f7(x100251,f872(x100251,a860),a860),f325(x100251)),x100252)))),f323(f323(f7(x100251,f872(x100251,a860),a860),f325(x100251)),x100252))),x100253))
% 188.07/187.98 [10037]P101(f323(f59(x100371),x100372))+~P101(f323(f59(x100373),f323(f302(x100371,x100373,x100374),x100372)))+~P101(f323(f59(x100371),f323(f243(x100371),f323(f323(f18(x100371,a860,a860),f323(f323(f8(a860,f872(a860,a860),x100371),a322),f323(f323(f7(x100371,f872(x100371,a860),a860),f325(x100371)),x100372))),f323(f323(f7(x100371,x100373,a860),f323(f323(f8(x100373,f872(x100373,a860),x100371),a320),x100374)),f323(x100374,f357(x100374,x100373,x100372,x100371)))))))
% 188.07/187.98 [8032]~P63(x80322)+E(x80321,f2(x80322))+E(f323(f323(f281(x80322),f323(f323(f22(x80322),f323(f323(f79(x80322),x80321),x80323)),x80324)),x80321),f323(f323(f22(x80322),x80323),f323(f323(f281(x80322),x80324),x80321)))
% 188.07/187.98 [8033]~P63(x80332)+E(x80331,f2(x80332))+E(f323(f323(f281(x80332),f323(f323(f78(x80332),f323(f323(f79(x80332),x80331),x80333)),x80334)),x80331),f323(f323(f78(x80332),x80333),f323(f323(f281(x80332),x80334),x80331)))
% 188.07/187.98 [8939]~E(f323(f323(f280(x89391,x89391,x89391),x89393),x89394),f188(f872(f871(x89391,x89391),a860)))+~E(f323(f323(f280(x89391,x89391,x89391),x89392),x89394),f188(f872(f871(x89391,x89391),a860)))+E(f323(f323(f280(x89391,x89391,x89391),f323(f323(f110(f872(f871(x89391,x89391),a860)),x89392),x89393)),x89394),f188(f872(f871(x89391,x89391),a860)))
% 188.07/187.98 [9969]~P141(x99691)+~P141(x99692)+E(f323(f323(f308(x99691),f323(f323(f7(x99691,a99,f869(f866(a319))),f323(f323(f8(f872(x99692,f869(f866(a319))),f872(a99,f869(f866(a319))),x99691),f308(x99692)),f323(f323(f8(f872(x99692,f871(x99691,x99692)),f872(x99692,f869(f866(a319))),x99691),f323(f8(f871(x99691,x99692),f869(f866(a319)),x99692),x99693)),f258(x99691,x99692)))),x99694)),x99694),f323(f323(f308(f871(x99691,x99692)),x99693),x99694))
% 188.07/187.98 [9700]~P101(f323(f153(x97001,x97003),x97004))+~P101(f323(f153(x97001,x97002),x97004))+P101(f323(f153(x97001,f323(f323(f18(x97001,a860,a860),f323(f323(f8(a860,f872(a860,a860),x97001),a322),x97002)),x97003)),x97004))
% 188.07/187.98 [9961]P101(f323(x99611,f837(x99612,x99613,x99611,x99614)))+~P101(f323(f59(x99614),f323(f243(x99614),x99611)))+P101(f323(f59(x99613),f323(f243(x99613),f323(f323(f8(f872(x99614,a860),a860,x99613),f85(x99614)),f323(f323(f8(f872(x99614,a860),f872(x99614,a860),x99613),f323(f18(x99614,a860,a860),f323(f323(f8(a860,f872(a860,a860),x99614),a322),x99611))),x99612)))))
% 188.07/187.98 [9982]~P101(f323(f59(x99822),f323(f243(x99822),x99823)))+~P101(f323(f59(x99821),f323(f243(x99821),f323(f323(f7(x99821,x99822,a860),x99824),f837(x99824,x99821,x99823,x99822)))))+P101(f323(f59(x99821),f323(f243(x99821),f323(f323(f8(f872(x99822,a860),a860,x99821),f85(x99822)),f323(f323(f8(f872(x99822,a860),f872(x99822,a860),x99821),f323(f18(x99822,a860,a860),f323(f323(f8(a860,f872(a860,a860),x99822),a322),x99823))),x99824)))))
% 188.07/187.98 [5026]~E(x50262,x50264)+E(f163(x50261,x50262,x50263),f163(x50261,x50264,x50265))+~E(x50262,f2(a865))
% 188.07/187.98 [5273]E(x52731,x52732)+~E(f163(x52734,x52733,x52731),f163(x52734,x52735,x52732))+E(x52733,f2(a865))
% 188.07/187.98 [6493]E(x64931,x64932)+~E(f323(x64933,x64931),f323(x64933,x64932))+~P27(x64934,x64935,x64933,f246(f872(x64934,a860)))
% 188.07/187.98 [6652]~E(f323(x66523,x66525),f200(x66522))+~E(f323(x66524,x66525),f200(x66522))+E(f323(f180(x66521,x66522,x66523,x66524),x66525),f200(x66522))
% 188.07/187.98 [7378]E(x73781,x73782)+~P27(x73783,x73784,x73785,f246(f872(x73783,a860)))+~E(f323(f302(x73783,x73784,x73785),x73781),f323(f302(x73783,x73784,x73785),x73782))
% 188.07/187.98 [7630]P27(x76302,x76303,f605(x76304,x76303,x76302,x76301),x76301)+~E(f323(f302(x76303,x76302,x76305),x76304),x76301)+E(x76301,f188(f872(x76302,a860)))
% 188.07/187.98 [8163]~P101(f323(f323(x81633,x81632),x81635))+~P101(f323(f323(x81633,x81634),x81632))+P101(f323(f323(f325(x81631),x81632),f290(x81631,x81633,x81634,x81635)))
% 188.07/187.98 [8164]~P101(f323(f323(x81643,x81642),x81645))+~P101(f323(f323(x81643,x81644),x81642))+P101(f323(f323(f325(x81641),x81642),f287(x81641,x81643,x81644,x81645)))
% 188.07/187.98 [8468]~P27(x84681,x84682,x84683,x84684)+P28(x84681,x84682,x84683,x84684,x84685)+~E(f323(f302(x84681,x84682,x84683),x84684),x84685)
% 188.07/187.98 [8603]~P28(x86031,x86033,x86034,x86032,x86035)+~P101(f323(f59(x86033),x86035))+P101(f323(f59(x86031),x86032))
% 188.07/187.98 [8604]~P28(x86043,x86041,x86044,x86045,x86042)+~P101(f323(f59(x86043),x86045))+P101(f323(f59(x86041),x86042))
% 188.07/187.98 [8737]~P27(x87371,x87373,x87375,f246(f872(x87371,a860)))+~P27(x87373,x87372,x87374,f246(f872(x87373,a860)))+P27(x87371,x87372,f323(f71(x87373,x87372,x87371,x87374),x87375),f246(f872(x87371,a860)))
% 188.07/187.98 [9299]P101(f323(f323(f325(f871(x92991,x92991)),f323(f323(f258(x92991,x92991),x92992),x92993)),f299(x92991,x92994)))+~P101(f323(f323(f325(f871(x92991,x92991)),f323(f323(f258(x92991,x92991),x92992),x92995)),f299(x92991,x92994)))+~P101(f323(f323(f325(f871(x92991,x92991)),f323(f323(f258(x92991,x92991),x92995),x92993)),f299(x92991,x92994)))
% 188.07/187.98 [9337]~P103(x93372)+~P101(f323(f130(x93371),x93375))+P101(f323(f130(x93371),f142(x93371,x93372,x93373,x93374,x93375)))
% 188.07/187.98 [5344]~E(x53442,f113(x53441))+E(f323(f323(f121(x53441),x53442),x53443),f323(f323(f144(x53441),x53444),x53445))+~E(x53443,f323(f323(f144(x53441),x53444),x53445))
% 188.07/187.98 [5345]~E(x53452,f113(x53451))+E(f323(f323(f121(x53451),x53452),x53453),f323(f323(f144(x53451),x53454),x53455))+~E(f323(f323(f144(x53451),x53454),x53455),x53453)
% 188.07/187.98 [6450]~E(f323(f189(f866(x64501)),x64505),f323(f189(f866(x64502)),x64504))+E(f323(f323(f147(f871(x64501,x64502),x64502),f261(x64501,x64502)),x64503),x64504)+~E(f323(f323(f175(x64501,x64502),x64505),x64504),x64503)
% 188.07/187.98 [6451]~E(f323(f189(f866(x64511)),x64514),f323(f189(f866(x64512)),x64515))+E(f323(f323(f147(f871(x64511,x64512),x64511),f257(x64511,x64512)),x64513),x64514)+~E(f323(f323(f175(x64511,x64512),x64514),x64515),x64513)
% 188.07/187.98 [6921]~P103(x69211)+~P16(x69211,f323(f323(f147(x69212,x69211),x69213),x69215))+P16(x69211,f323(f323(f147(x69212,x69211),x69213),f323(f129(x69212,x69214),x69215)))
% 188.07/187.98 [6966]~P101(f323(x69663,x69665))+~P101(f323(f323(x69662,x69664),x69665))+P101(f323(f323(f92(x69661,x69662,x69663),x69664),x69665))
% 188.07/187.98 [7063]~P103(x70631)+P16(x70631,f323(f323(f147(x70632,x70631),x70633),f164(x70632,x70634,x70635)))+~P16(x70631,f323(f323(f147(x70632,x70631),x70633),x70635))
% 188.07/187.98 [7086]~P51(x70863,x70862,x70865)+~P51(x70861,x70863,x70864)+P51(x70861,x70862,f323(f323(f280(x70861,x70863,x70862),x70864),x70865))
% 188.07/187.98 [7178]E(x71781,x71782)+~P27(x71783,x71784,x71785,f246(f872(x71783,a860)))+~E(f323(f323(f147(x71783,x71784),x71785),x71781),f323(f323(f147(x71783,x71784),x71785),x71782))
% 188.07/187.98 [7329]~P101(f323(f323(f237(a865),x73291),f323(x73293,x73295)))+P101(f323(f323(f237(a865),x73291),f148(x73292,x73293,x73294)))+~P101(f323(f323(f325(x73292),x73295),f323(f166(x73292),x73294)))
% 188.07/187.98 [7330]~P101(f323(f323(f238(a865),x73301),f323(x73303,x73305)))+P101(f323(f323(f238(a865),x73301),f148(x73302,x73303,x73304)))+~P101(f323(f323(f325(x73302),x73305),f323(f166(x73302),x73304)))
% 188.07/187.98 [7729]P101(f323(x77291,x77292))+~P101(f323(x77291,x77293))+~P101(f323(f323(f325(x77294),x77292),f323(f166(x77294),f163(x77294,x77295,x77293))))
% 188.07/187.98 [7730]P101(f323(x77301,x77302))+~P101(f323(x77301,x77303))+~P101(f323(f323(f325(x77304),x77303),f323(f166(x77304),f163(x77304,x77305,x77302))))
% 188.07/187.98 [7734]~P105(x77341)+P101(f323(f323(f237(f872(x77341,a860)),f294(x77341,x77342,x77343)),f294(x77341,x77344,x77345)))+P101(f323(f323(f237(x77341),x77342),x77343))
% 188.07/187.98 [7755]~P6(x77551)+P101(f323(f323(f237(x77551),f323(f323(f40(x77552,x77551),x77553),x77554)),f323(x77554,x77555)))+~P101(f323(f323(f325(x77552),x77555),x77553))
% 188.07/187.98 [7823]~P27(x78231,x78232,x78234,x78233)+E(f323(f75(x78231,x78232,x78233,x78234),f323(x78234,x78235)),x78235)+~P101(f323(f323(f325(x78231),x78235),x78233))
% 188.07/187.98 [7824]~P27(x78241,x78242,x78244,x78243)+E(f323(f91(x78241,x78242,x78243,x78244),f323(x78244,x78245)),x78245)+~P101(f323(f323(f325(x78241),x78245),x78243))
% 188.07/187.98 [8021]~P101(f323(x80211,x80215))+P101(f323(x80211,f390(x80211,x80212,x80213,x80214)))+~P101(f323(f323(f325(x80214),x80215),x80213))
% 188.07/187.98 [8022]~P101(f323(x80221,x80225))+P101(f323(x80221,f390(x80221,x80222,x80223,x80224)))+~P101(f323(f323(f325(x80224),x80225),x80222))
% 188.07/187.98 [8115]P101(f323(f59(x81151),x81152))+~P101(f323(f59(x81153),x81154))+~P101(f323(f323(f237(f872(x81151,a860)),x81152),f323(f302(x81153,x81151,x81155),x81154)))
% 188.07/187.98 [8283]E(x82831,x82832)+~P27(x82833,x82834,x82835,f323(f323(f110(f872(x82833,a860)),f323(f166(x82833),x82831)),f323(f166(x82833),x82832)))+~E(f323(f323(f147(x82833,x82834),x82835),x82831),f323(f323(f147(x82833,x82834),x82835),x82832))
% 188.07/187.98 [8340]~P105(x83401)+~P101(f323(f323(f238(f872(x83401,a860)),f294(x83401,x83404,x83405)),f294(x83401,x83402,x83403)))+P101(f323(f323(f237(x83401),x83402),x83403))
% 188.07/187.98 [8403]~P27(x84031,x84034,x84035,f246(f872(x84031,a860)))+~P101(f323(f323(f325(x84034),f323(x84035,x84032)),f323(f302(x84031,x84034,x84035),x84033)))+P101(f323(f323(f325(x84031),x84032),x84033))
% 188.07/187.98 [8474]P101(f323(x84741,x84742))+~P101(f323(x84741,f430(x84741,x84743,x84744,x84745)))+~P101(f323(f323(f325(x84745),x84742),x84744))
% 188.07/187.98 [8475]P101(f323(x84751,x84752))+~P101(f323(x84751,f430(x84751,x84753,x84754,x84755)))+~P101(f323(f323(f325(x84755),x84752),x84753))
% 188.07/187.98 [8778]~P27(x87782,x87783,x87781,x87784)+E(f323(x87781,f323(f75(x87782,x87783,x87784,x87781),x87785)),x87785)+~P101(f323(f323(f325(x87783),x87785),f323(f302(x87782,x87783,x87781),x87784)))
% 188.07/187.98 [8884]E(x88841,f113(x88842))+E(f323(f323(f144(x88842),x88843),f570(x88844,x88843,x88845,x88841,x88842)),x88841)+~E(f323(f323(f121(x88842),x88841),x88845),f323(f323(f144(x88842),x88843),x88844))
% 188.07/187.98 [8885]E(x88851,f113(x88852))+E(f323(f323(f144(x88852),x88853),f572(x88854,x88851,x88855,x88853,x88852)),x88851)+~E(f323(f323(f121(x88852),x88851),x88854),f323(f323(f144(x88852),x88853),x88855))
% 188.07/187.98 [8901]E(f323(f323(f144(x89012),x89013),f570(x89014,x89013,x89011,x89015,x89012)),x89015)+~E(f323(f323(f121(x89012),x89015),x89011),f323(f323(f144(x89012),x89013),x89014))+E(x89011,f323(f323(f144(x89012),x89013),x89014))
% 188.07/187.98 [8902]E(f323(f323(f144(x89021),x89022),f572(x89024,x89025,x89023,x89022,x89021)),x89025)+~E(f323(f323(f121(x89021),x89025),x89024),f323(f323(f144(x89021),x89022),x89023))+E(f323(f323(f144(x89021),x89022),x89023),x89024)
% 188.07/187.98 [8975]~E(f323(f302(x89753,x89752,x89754),f246(f872(x89753,a860))),f246(f872(x89752,a860)))+~E(f323(f302(x89751,x89753,x89755),f246(f872(x89751,a860))),f246(f872(x89753,a860)))+E(f323(f302(x89751,x89752,f323(f71(x89753,x89752,x89751,x89754),x89755)),f246(f872(x89751,a860))),f246(f872(x89752,a860)))
% 188.07/187.98 [9343]E(x93431,f113(x93432))+~E(f323(f323(f121(x93432),x93431),x93433),f323(f323(f144(x93432),x93435),x93434))+E(f323(f323(f121(x93432),f572(x93433,x93431,x93434,x93435,x93432)),x93433),x93434)
% 188.07/187.98 [9344]E(x93441,f113(x93442))+~E(f323(f323(f121(x93442),x93441),x93445),f323(f323(f144(x93442),x93444),x93443))+E(f323(f323(f121(x93442),f570(x93443,x93444,x93445,x93441,x93442)),x93445),x93443)
% 188.07/187.98 [9351]E(f323(f323(f121(x93512),f570(x93514,x93513,x93511,x93515,x93512)),x93511),x93514)+~E(f323(f323(f121(x93512),x93515),x93511),f323(f323(f144(x93512),x93513),x93514))+E(x93511,f323(f323(f144(x93512),x93513),x93514))
% 188.07/187.98 [9352]~E(f323(f323(f121(x93521),x93525),x93524),f323(f323(f144(x93521),x93522),x93523))+E(f323(f323(f121(x93521),f572(x93524,x93525,x93523,x93522,x93521)),x93524),x93523)+E(f323(f323(f144(x93521),x93522),x93523),x93524)
% 188.07/187.98 [9353]E(f323(f323(f121(x93531),x93535),f576(x93533,x93532,x93534,x93535,x93531)),x93532)+E(f323(f323(f121(x93531),x93532),f573(x93533,x93532,x93534,x93535,x93531)),x93535)+~E(f323(f323(f121(x93531),x93535),x93534),f323(f323(f121(x93531),x93532),x93533))
% 188.07/187.98 [9385]~P103(x93851)+P16(x93851,f323(f323(f147(x93852,x93851),x93853),f142(x93852,x93851,x93853,x93854,x93855)))+~P16(x93851,f323(f323(f147(x93852,x93851),x93853),x93855))
% 188.07/187.98 [9397]~P55(x93975,x93971,x93974,x93973)+P101(f323(f323(x93971,x93972),f668(x93973,x93974,x93971,x93975,x93972)))+~P101(f323(f323(f325(x93975),x93972),x93974))
% 188.07/187.98 [9503]~P101(f323(f323(f325(f871(x95031,x95031)),f323(f323(f258(x95031,x95031),x95035),x95033)),f299(x95031,x95034)))+P101(f323(f323(f325(f871(x95031,x95031)),f323(f323(f258(x95031,x95031),x95032),x95033)),f323(f323(f280(x95031,x95031,x95031),x95034),f299(x95031,x95034))))+~P101(f323(f323(f325(f871(x95031,x95031)),f323(f323(f258(x95031,x95031),x95032),x95035)),f323(f323(f280(x95031,x95031,x95031),x95034),f299(x95031,x95034))))
% 188.07/187.98 [9504]~P101(f323(f323(f325(f871(x95041,x95041)),f323(f323(f258(x95041,x95041),x95042),x95045)),f299(x95041,x95044)))+P101(f323(f323(f325(f871(x95041,x95041)),f323(f323(f258(x95041,x95041),x95042),x95043)),f323(f323(f280(x95041,x95041,x95041),x95044),f299(x95041,x95044))))+~P101(f323(f323(f325(f871(x95041,x95041)),f323(f323(f258(x95041,x95041),x95045),x95043)),f323(f323(f280(x95041,x95041,x95041),x95044),f299(x95041,x95044))))
% 188.07/187.98 [9507]P101(f323(f323(f325(f871(f866(x95071),f866(x95071))),f323(f323(f258(f866(x95071),f866(x95071)),x95072),x95073)),f151(x95071,f299(x95071,x95074))))+~P101(f323(f323(f325(f871(f866(x95071),f866(x95071))),f323(f323(f258(f866(x95071),f866(x95071)),x95072),x95075)),f151(x95071,f299(x95071,x95074))))+~P101(f323(f323(f325(f871(f866(x95071),f866(x95071))),f323(f323(f258(f866(x95071),f866(x95071)),x95075),x95073)),f151(x95071,f299(x95071,x95074))))
% 188.07/187.98 [9511]E(f323(f323(f121(x95111),x95112),f573(x95113,x95112,x95114,x95115,x95111)),x95115)+E(f323(f323(f121(x95111),f576(x95113,x95112,x95114,x95115,x95111)),x95113),x95114)+~E(f323(f323(f121(x95111),x95112),x95113),f323(f323(f121(x95111),x95115),x95114))
% 188.07/187.98 [9512]E(f323(f323(f121(x95121),x95122),f576(x95123,x95124,x95125,x95122,x95121)),x95124)+E(f323(f323(f121(x95121),f573(x95123,x95124,x95125,x95122,x95121)),x95125),x95123)+~E(f323(f323(f121(x95121),x95122),x95125),f323(f323(f121(x95121),x95124),x95123))
% 188.07/187.98 [9568]P101(f323(f323(f325(f871(x95681,x95681)),f323(f323(f258(x95681,x95681),x95682),x95683)),f323(f323(f280(x95681,x95681,x95681),x95684),f299(x95681,x95684))))+~P101(f323(f323(f325(f871(x95681,x95681)),f323(f323(f258(x95681,x95681),x95682),x95685)),f323(f323(f280(x95681,x95681,x95681),x95684),f299(x95681,x95684))))+~P101(f323(f323(f325(f871(x95681,x95681)),f323(f323(f258(x95681,x95681),x95685),x95683)),f323(f323(f280(x95681,x95681,x95681),x95684),f299(x95681,x95684))))
% 188.07/187.98 [9595]P35(x95951,x95952,x95953,x95954,x95955)+~E(f323(f189(f866(x95951)),x95954),f323(f189(f866(x95952)),x95955))+~P101(f323(f323(f262(x95951,x95952,a860),x95953),f648(x95955,x95954,x95953,x95952,x95951)))
% 188.07/187.98 [9596]P35(x95961,x95962,x95963,x95964,x95965)+~E(f323(f189(f866(x95961)),x95964),f323(f189(f866(x95962)),x95965))+~P101(f323(f323(f262(x95961,x95962,a860),x95963),f656(x95963,x95965,x95964,x95962,x95961)))
% 188.07/187.98 [9601]E(f323(f323(f121(x96011),f573(x96012,x96013,x96014,x96015,x96011)),x96014),x96012)+~E(f323(f323(f121(x96011),x96013),x96012),f323(f323(f121(x96011),x96015),x96014))+E(f323(f323(f121(x96011),f576(x96012,x96013,x96014,x96015,x96011)),x96012),x96014)
% 188.07/187.98 [9616]~P103(x96162)+E(f323(f323(f141(x96161,x96162,x96163),x96164),x96165),f323(f323(f144(x96161),x96164),x96165))+P101(f323(f323(f325(x96161),f702(x96164,x96163,x96165,x96161,x96162)),f323(f166(x96161),x96165)))
% 188.07/187.98 [9621]~P55(x96211,x96214,x96213,x96212)+~P101(f323(f323(f325(x96211),x96215),x96213))+P101(f323(f323(f325(x96211),f668(x96212,x96213,x96214,x96211,x96215)),x96212))
% 188.07/187.98 [9743]~P101(f323(f323(f325(f871(f872(x97431,a860),f872(x97431,a860))),f323(f323(f258(f872(x97431,a860),f872(x97431,a860)),x97434),x97433)),f314(x97431,x97432)))+~P101(f323(f323(f325(x97431),x97435),x97434))+P101(f323(f323(f325(x97431),f721(x97432,x97433,x97434,x97431,x97435)),x97433))
% 188.07/187.98 [9755]~P103(x97552)+E(f323(f323(f141(x97551,x97552,x97553),x97554),x97555),f323(f323(f144(x97551),x97554),x97555))+~P101(f323(f323(f237(x97552),f323(x97553,x97554)),f323(x97553,f702(x97554,x97553,x97555,x97551,x97552))))
% 188.07/187.98 [9801]~P27(x98013,x98014,x98015,f246(f872(x98013,a860)))+P101(f323(x98011,x98012))+~P101(f323(x98011,f323(f91(x98013,x98014,f246(f872(x98013,a860)),x98015),f730(x98012,x98011,x98015,x98014,x98013))))
% 188.07/187.98 [9944]P35(x99441,x99442,x99443,x99444,x99445)+~E(f323(f189(f866(x99441)),x99444),f323(f189(f866(x99442)),x99445))+~P101(f323(f323(x99443,f323(f323(f158(x99441),x99444),f657(x99445,x99444,x99443,x99442,x99441))),f323(f323(f158(x99442),x99445),f657(x99445,x99444,x99443,x99442,x99441))))
% 188.07/187.98 [9945]P35(x99451,x99452,x99453,x99454,x99455)+~E(f323(f189(f866(x99451)),x99454),f323(f189(f866(x99452)),x99455))+~P101(f323(f323(x99453,f323(f323(f158(x99451),x99454),f696(x99453,x99455,x99452,x99454,x99451))),f323(f323(f158(x99452),x99455),f696(x99453,x99455,x99452,x99454,x99451))))
% 188.07/187.98 [6522]~P19(x65222,x65225,x65221)+~P101(f323(f59(x65222),x65224))+E(f323(x65221,f323(f323(f301(x65222),x65223),x65224)),f323(f323(f62(x65222,x65222,x65225),x65223),x65224))
% 188.07/187.98 [6523]~E(x65233,x65234)+~E(x65232,x65235)+E(f323(f323(f301(x65231),x65232),f323(f323(f301(x65231),x65233),f188(f872(x65231,a860)))),f323(f323(f301(x65231),x65234),f323(f323(f301(x65231),x65235),f188(f872(x65231,a860)))))
% 188.07/187.98 [6533]P101(f323(x65332,x65335))+E(f171(x65331,x65332,f323(f323(f121(x65331),x65333),x65334)),f171(x65331,x65332,x65333))+~P101(f323(f323(f325(x65331),x65335),f323(f166(x65331),x65333)))
% 188.07/187.98 [6570]E(f323(x65701,x65702),f188(f872(x65703,a860)))+~E(f323(f323(f39(x65704,f872(x65703,a860)),x65705),x65701),f188(f872(x65703,a860)))+~P101(f323(f323(f325(x65704),x65702),x65705))
% 188.07/187.98 [6571]E(f323(x65711,x65712),f246(f872(x65713,a860)))+~E(f323(f323(f40(x65714,f872(x65713,a860)),x65715),x65711),f246(f872(x65713,a860)))+~P101(f323(f323(f325(x65714),x65712),x65715))
% 188.07/187.98 [7073]~E(x70732,x70734)+~P135(x70731)+E(f323(f323(f78(x70731),f323(f323(f79(x70731),x70732),x70733)),f323(f323(f79(x70731),x70734),x70735)),f323(f323(f78(x70731),f323(f323(f79(x70731),x70732),x70735)),f323(f323(f79(x70731),x70734),x70733)))
% 188.07/187.98 [7133]~P6(x71331)+~P101(f323(f323(f325(x71334),x71333),x71335))+P101(f323(f323(f237(x71331),f323(x71332,x71333)),f323(f323(f39(x71334,x71331),x71335),x71332)))
% 188.07/187.98 [7183]~P104(x71831)+P101(f323(f323(f237(x71831),f323(x71832,x71833)),f323(x71834,x71833)))+~P101(f323(f323(f237(f872(x71835,x71831)),x71832),x71834))
% 188.07/187.98 [7298]E(x72981,x72982)+E(x72983,x72981)+~E(f323(f323(f301(x72984),x72981),f323(f323(f301(x72984),x72985),f188(f872(x72984,a860)))),f323(f323(f301(x72984),x72982),f323(f323(f301(x72984),x72983),f188(f872(x72984,a860)))))
% 188.07/187.98 [7299]E(x72991,x72992)+E(x72993,x72991)+~E(f323(f323(f301(x72994),x72993),f323(f323(f301(x72994),x72992),f188(f872(x72994,a860)))),f323(f323(f301(x72994),x72995),f323(f323(f301(x72994),x72991),f188(f872(x72994,a860)))))
% 188.07/187.98 [7300]E(x73001,x73002)+E(x73001,x73003)+~E(f323(f323(f301(x73004),x73003),f323(f323(f301(x73004),x73002),f188(f872(x73004,a860)))),f323(f323(f301(x73004),x73005),f323(f323(f301(x73004),x73001),f188(f872(x73004,a860)))))
% 188.07/187.98 [7301]E(x73011,x73012)+E(x73011,x73013)+~E(f323(f323(f301(x73014),x73011),f323(f323(f301(x73014),x73015),f188(f872(x73014,a860)))),f323(f323(f301(x73014),x73012),f323(f323(f301(x73014),x73013),f188(f872(x73014,a860)))))
% 188.07/187.98 [7834]P27(x78341,x78342,x78343,x78344)+~P27(x78341,x78342,x78343,x78345)+~P101(f323(f323(f237(f872(x78341,a860)),x78344),x78345))
% 188.07/187.98 [7863]~E(f323(x78633,x78635),x78634)+~P27(x78631,x78632,x78633,f246(f872(x78631,a860)))+E(f323(f91(x78631,x78632,f246(f872(x78631,a860)),x78633),x78634),x78635)
% 188.07/187.98 [8012]E(x80121,x80122)+~E(f323(f302(x80123,x80124,x80125),x80121),f323(f302(x80123,x80124,x80125),x80122))+~P27(x80123,x80124,x80125,f323(f323(f110(f872(x80123,a860)),x80121),x80122))
% 188.07/187.98 [8082]P101(f323(x80822,x80824))+E(f323(f323(f131(x80821),f323(f189(f866(x80821)),f171(x80821,x80822,x80823))),x80823),f323(f323(f144(x80821),x80824),x80825))+~E(f323(f323(f121(x80821),f171(x80821,x80822,x80823)),f323(f323(f144(x80821),x80824),x80825)),x80823)
% 188.07/187.98 [8112]~P27(x81121,x81122,x81123,x81125)+~P27(x81121,x81122,x81123,x81124)+P27(x81121,x81122,x81123,f323(f323(f101(f872(x81121,a860)),x81124),x81125))
% 188.07/187.98 [8223]~P72(x82231)+E(f323(f323(f78(x82231),f323(x82232,x82233)),f323(f159(x82231),f323(f323(f147(x82234,x82231),x82232),f164(x82234,x82233,x82235)))),f323(f159(x82231),f323(f323(f147(x82234,x82231),x82232),x82235)))+~P101(f323(f323(f325(x82234),x82233),f323(f166(x82234),x82235)))
% 188.07/187.98 [8313]~P103(x83131)+~P16(x83131,f323(f323(f147(x83132,x83131),x83133),x83135))+P16(x83131,f323(f323(f147(x83132,x83131),x83133),f323(f323(f141(x83132,x83131,x83133),x83134),x83135)))
% 188.07/187.98 [8399]~P6(x83991)+P101(f323(f323(f237(x83991),f323(f323(f39(x83992,x83991),x83993),x83994)),f323(f323(f39(x83992,x83991),x83995),x83994)))+~P101(f323(f323(f237(f872(x83992,a860)),x83993),x83995))
% 188.07/187.98 [8400]~P6(x84001)+P101(f323(f323(f237(x84001),f323(f323(f40(x84002,x84001),x84003),x84004)),f323(f323(f40(x84002,x84001),x84005),x84004)))+~P101(f323(f323(f237(f872(x84002,a860)),x84005),x84003))
% 188.07/187.98 [8430]~P103(x84303)+P101(f323(f130(x84301),x84302))+~P101(f323(f130(x84301),f323(f323(f141(x84301,x84303,x84304),x84305),x84302)))
% 188.07/187.98 [8575]~P103(x85751)+~P101(f323(f323(f325(x85752),x85753),f323(f166(x85752),x85754)))+~P101(f323(f130(x85752),f323(f323(f141(x85752,x85751,x85755),x85753),x85754)))
% 188.07/187.98 [8666]~P103(x86661)+P16(x86661,f323(f323(f147(x86662,x86661),x86663),x86664))+~P16(x86661,f323(f323(f147(x86662,x86661),x86663),f323(f323(f141(x86662,x86661,x86663),x86665),x86664)))
% 188.07/187.98 [8713]~P27(x87132,x87131,x87134,x87133)+E(f323(f302(x87131,x87132,f91(x87132,x87131,x87133,x87134)),f323(f302(x87132,x87131,x87134),x87135)),x87135)+~P101(f323(f323(f237(f872(x87132,a860)),x87135),x87133))
% 188.07/187.98 [8766]~P103(x87662)+E(f323(f323(f141(x87661,x87662,x87663),x87664),x87665),f142(x87661,x87662,x87663,x87664,x87665))+P101(f323(f323(f325(x87662),f323(x87663,x87664)),f323(f302(x87661,x87662,x87663),f323(f166(x87661),x87665))))
% 188.07/187.98 [8841]~P103(x88412)+E(f142(x88411,x88412,x88413,x88414,x88415),x88415)+~P101(f323(f323(f325(x88412),f323(x88413,x88414)),f323(f302(x88411,x88412,x88413),f323(f166(x88411),x88415))))
% 188.07/187.98 [8856]~P27(x88562,x88561,x88563,x88565)+P101(f323(f323(f238(f872(x88561,a860)),f323(f302(x88562,x88561,x88563),x88564)),f323(f302(x88562,x88561,x88563),x88565)))+~P101(f323(f323(f238(f872(x88562,a860)),x88564),x88565))
% 188.07/187.98 [9017]~P27(x90171,x90172,x90173,f246(f872(x90171,a860)))+~P101(f323(f323(f237(f872(x90172,a860)),x90174),f323(f302(x90171,x90172,x90173),x90175)))+P101(f323(f323(f237(f872(x90171,a860)),f323(f303(x90171,x90172,x90173),x90174)),x90175))
% 188.07/187.98 [9041]~E(f323(f302(x90413,x90411,x90414),f246(f872(x90413,a860))),f246(f872(x90411,a860)))+P101(f323(f323(f237(f872(x90411,a860)),x90412),f323(f302(x90413,x90411,x90414),x90415)))+~P101(f323(f323(f237(f872(x90413,a860)),f323(f303(x90413,x90411,x90414),x90412)),x90415))
% 188.07/187.98 [9066]~E(f323(f230(x90662),x90664),f323(f323(f179(x90661,x90662),x90665),x90663))+~P101(f323(f130(x90661),f323(f323(f147(f871(x90661,x90662),x90661),f257(x90661,x90662)),x90665)))+P101(f323(f323(f325(f871(x90661,x90662)),f323(f323(f258(x90661,x90662),x90663),x90664)),f323(f166(f871(x90661,x90662)),x90665)))
% 188.07/187.98 [9146]~P27(x91461,x91464,x91465,f246(f872(x91461,a860)))+~P101(f323(f323(f237(f872(x91464,a860)),f323(f302(x91461,x91464,x91465),x91462)),f323(f302(x91461,x91464,x91465),x91463)))+P101(f323(f323(f237(f872(x91461,a860)),x91462),x91463))
% 188.07/187.98 [9210]E(f323(f230(x92101),x92102),f323(f323(f179(x92103,x92101),x92104),x92105))+~P101(f323(f130(x92103),f323(f323(f147(f871(x92103,x92101),x92103),f257(x92103,x92101)),x92104)))+~P101(f323(f323(f325(f871(x92103,x92101)),f323(f323(f258(x92103,x92101),x92105),x92102)),f323(f166(f871(x92103,x92101)),x92104)))
% 188.07/187.98 [9212]E(f323(f323(f179(x92121,x92122),x92123),x92124),f323(f230(x92122),x92125))+~P101(f323(f130(x92121),f323(f323(f147(f871(x92121,x92122),x92121),f257(x92121,x92122)),x92123)))+~P101(f323(f323(f325(f871(x92121,x92122)),f323(f323(f258(x92121,x92122),x92124),x92125)),f323(f166(f871(x92121,x92122)),x92123)))
% 188.07/187.98 [9266]~P78(x92661)+~E(f323(x92663,f567(x92663,x92664,x92665,x92662,x92661)),f2(x92661))+E(f323(f159(x92661),f323(f323(f147(x92662,x92661),x92663),f323(f129(x92662,x92664),x92665))),f323(f159(x92661),f323(f323(f147(x92662,x92661),x92663),x92665)))
% 188.07/187.98 [9294]~P28(x92941,x92942,x92943,f246(f872(x92941,a860)),f246(f872(x92942,a860)))+~P101(f323(f323(f237(f872(x92942,a860)),x92944),f323(f302(x92941,x92942,x92943),x92945)))+P101(f323(f323(f237(f872(x92941,a860)),f323(f303(x92941,x92942,x92943),x92944)),x92945))
% 188.07/187.98 [9323]~P28(x93233,x93231,x93234,f246(f872(x93233,a860)),f246(f872(x93231,a860)))+P101(f323(f323(f237(f872(x93231,a860)),x93232),f323(f302(x93233,x93231,x93234),x93235)))+~P101(f323(f323(f237(f872(x93233,a860)),f323(f303(x93233,x93231,x93234),x93232)),x93235))
% 188.07/187.98 [9445]~P18(x94451,x94452,x94453)+~P101(f323(f59(x94451),x94455))+P101(f323(f64(x94451,x94452,x94453,x94454,x94455),f323(f323(f62(x94451,x94452,x94453),x94454),x94455)))
% 188.07/187.98 [9524]~P28(x95242,x95241,x95244,f246(f872(x95242,a860)),f246(f872(x95241,a860)))+~P28(x95241,x95243,x95245,f246(f872(x95241,a860)),f246(f872(x95243,a860)))+E(f323(f71(x95241,x95242,x95243,f91(x95242,x95241,f246(f872(x95242,a860)),x95244)),f91(x95241,x95243,f246(f872(x95241,a860)),x95245)),f91(x95242,x95243,f246(f872(x95242,a860)),f323(f71(x95241,x95243,x95242,x95245),x95244)))
% 188.07/187.98 [9525]P101(f323(x95251,f638(x95252,x95251,x95253,x95254,x95255)))+~P101(f323(f323(f237(f872(x95255,a860)),x95254),x95253))+P101(f323(f323(f237(f872(x95255,a860)),f323(f323(f101(f872(x95255,a860)),x95254),f323(f243(x95255),x95251))),f323(f323(f101(f872(x95255,a860)),x95253),f323(f243(x95255),x95252))))
% 188.07/187.98 [9539]~P78(x95391)+~P101(f323(x95394,f567(x95393,x95394,x95395,x95392,x95391)))+E(f323(f159(x95391),f323(f323(f147(x95392,x95391),x95393),f323(f129(x95392,x95394),x95395))),f323(f159(x95391),f323(f323(f147(x95392,x95391),x95393),x95395)))
% 188.07/187.98 [9619]~P6(x96195)+P101(f323(f323(f325(x96191),f640(x96192,x96193,x96191,x96194,x96195)),x96193))+P101(f323(f323(f237(x96195),x96194),f323(f323(f40(x96191,x96195),x96193),x96192)))
% 188.07/187.98 [9622]~P78(x96221)+E(f323(f159(x96221),f323(f323(f147(x96222,x96221),x96223),f323(f129(x96222,x96224),x96225))),f323(f159(x96221),f323(f323(f147(x96222,x96221),x96223),x96225)))+P101(f323(f323(f325(x96222),f567(x96223,x96224,x96225,x96222,x96221)),f323(f166(x96222),x96225)))
% 188.07/187.98 [9632]~P101(f323(x96325,f638(x96325,x96323,x96324,x96322,x96321)))+~P101(f323(f323(f237(f872(x96321,a860)),x96322),x96324))+P101(f323(f323(f237(f872(x96321,a860)),f323(f323(f101(f872(x96321,a860)),x96322),f323(f243(x96321),x96323))),f323(f323(f101(f872(x96321,a860)),x96324),f323(f243(x96321),x96325))))
% 188.07/187.98 [9647]~P27(x96475,x96473,x96474,f246(f872(x96475,a860)))+P101(f323(x96471,x96472))+P101(f323(f323(f325(x96473),f730(x96472,x96471,x96474,x96473,x96475)),f323(f302(x96475,x96473,x96474),f246(f872(x96475,a860)))))
% 188.07/187.98 [9668]P35(x96681,x96682,x96683,x96684,x96685)+~E(f323(f189(f866(x96682)),x96685),f323(f189(f866(x96681)),x96684))+P101(f323(f323(f238(a865),f657(x96685,x96684,x96683,x96682,x96681)),f323(f189(f866(x96681)),x96684)))
% 188.07/187.98 [9669]P35(x96691,x96692,x96693,x96694,x96695)+~E(f323(f189(f866(x96692)),x96695),f323(f189(f866(x96691)),x96694))+P101(f323(f323(f238(a865),f696(x96693,x96695,x96692,x96694,x96691)),f323(f189(f866(x96691)),x96694)))
% 188.07/187.98 [9702]P101(f323(f323(f325(x97021),f638(x97022,x97023,x97024,x97025,x97021)),x97025))+~P101(f323(f323(f237(f872(x97021,a860)),x97025),x97024))+P101(f323(f323(f237(f872(x97021,a860)),f323(f323(f101(f872(x97021,a860)),x97025),f323(f243(x97021),x97023))),f323(f323(f101(f872(x97021,a860)),x97024),f323(f243(x97021),x97022))))
% 188.07/187.98 [9756]~P6(x97561)+~P101(f323(f323(f237(x97561),x97562),f323(x97565,f640(x97565,x97564,x97563,x97562,x97561))))+P101(f323(f323(f237(x97561),x97562),f323(f323(f40(x97563,x97561),x97564),x97565)))
% 188.07/187.98 [9790]~P68(x97901)+~P101(f323(f59(x97902),x97905))+E(f323(f323(f323(f63(x97901,x97902,f79(x97901)),f323(f323(f18(x97902,x97901,x97901),f323(f323(f8(x97901,f872(x97901,x97901),x97902),f79(x97901)),x97903)),x97904)),f76(x97901)),x97905),f323(f323(f79(x97901),f323(f323(f323(f63(x97901,x97902,f79(x97901)),x97903),f76(x97901)),x97905)),f323(f323(f323(f63(x97901,x97902,f79(x97901)),x97904),f76(x97901)),x97905)))
% 188.07/187.98 [9851]~P101(f323(f323(f325(f871(f872(x98511,a860),f872(x98511,a860))),f323(f323(f258(f872(x98511,a860),f872(x98511,a860)),x98515),x98514)),f314(x98511,x98513)))+~P101(f323(f323(f325(x98511),x98512),x98515))+P101(f323(f323(f325(f871(x98511,x98511)),f323(f323(f258(x98511,x98511),x98512),f721(x98513,x98514,x98515,x98511,x98512))),x98513))
% 188.07/187.98 [9979]~P101(f323(f323(f325(f871(f866(x99791),f866(x99791))),f323(f323(f258(f866(x99791),f866(x99791)),f323(f323(f121(x99791),x99795),x99792)),f323(f323(f121(x99791),x99795),x99793))),f140(x99791,x99794)))+P101(f323(f323(f325(f871(f866(x99791),f866(x99791))),f323(f323(f258(f866(x99791),f866(x99791)),x99792),x99793)),f140(x99791,x99794)))+P101(f323(f323(f325(f871(x99791,x99791)),f323(f323(f258(x99791,x99791),f595(x99794,x99793,x99792,x99795,x99791)),f595(x99794,x99793,x99792,x99795,x99791))),x99794))
% 188.07/187.98 [7113]~E(f323(f189(f866(x71131)),x71133),f323(f189(f866(x71132)),x71134))+E(f323(f323(f179(x71131,x71132),f323(f323(f175(x71131,x71132),x71133),x71134)),x71135),f200(x71132))+P101(f323(f323(f325(x71131),x71135),f323(f166(x71131),x71133)))
% 188.07/187.98 [7186]~E(x71863,x71865)+E(f323(f323(f158(x71861),f323(f323(f152(x71861,x71862),x71863),x71864)),x71865),x71864)+~P101(f323(f323(f238(a865),x71863),f323(f189(f866(x71861)),x71862)))
% 188.07/187.98 [7295]~E(f323(f323(f121(x72951),x72952),x72954),f323(f323(f121(x72951),x72953),x72955))+E(f323(f323(f169(x72951),f323(f189(f866(x72951)),x72952)),x72953),x72952)+P101(f323(f323(f237(a865),f323(f189(f866(x72951)),x72953)),f323(f189(f866(x72951)),x72952)))
% 188.07/187.98 [7793]~E(f323(f323(f121(x77931),x77932),x77934),f323(f323(f121(x77931),x77933),x77935))+E(f323(f323(f169(x77931),f323(f189(f866(x77931)),x77932)),x77933),x77932)+~P101(f323(f323(f237(a865),f323(f189(f866(x77931)),x77932)),f323(f189(f866(x77931)),x77933)))
% 188.07/187.98 [7817]~P101(f323(f59(x78171),f323(x78174,x78175)))+~P101(f323(f323(f325(x78172),x78175),x78173))+P101(f323(f59(x78171),f323(f323(f40(x78172,f872(x78171,a860)),x78173),x78174)))
% 188.07/187.98 [7873]~E(f323(f189(f866(x78731)),x78732),f323(f189(f866(x78733)),x78734))+~E(f323(f323(f179(x78731,x78733),f323(f323(f175(x78731,x78733),x78732),x78734)),x78735),f200(x78733))+~P101(f323(f323(f325(x78731),x78735),f323(f166(x78731),x78732)))
% 188.07/187.98 [7996]~P40(x79961,x79963,x79965)+~P40(x79961,x79962,x79964)+P40(x79961,f323(f323(f110(f872(x79961,a860)),x79962),x79963),f323(f323(f110(f872(f871(x79961,x79961),a860)),x79964),x79965))
% 188.07/187.98 [7997]~P40(x79971,x79973,x79975)+~P40(x79971,x79972,x79974)+P40(x79971,f323(f323(f101(f872(x79971,a860)),x79972),x79973),f323(f323(f101(f872(f871(x79971,x79971),a860)),x79974),x79975))
% 188.07/187.98 [8352]E(f323(f323(f258(x83521,x83522),f323(f323(f158(x83521),x83523),x83524)),f323(f323(f158(x83522),x83525),x83524)),f323(f323(f158(f871(x83521,x83522)),f323(f323(f175(x83521,x83522),x83523),x83525)),x83524))+~P101(f323(f323(f238(a865),x83524),f323(f189(f866(x83521)),x83523)))+~P101(f323(f323(f238(a865),x83524),f323(f189(f866(x83522)),x83525)))
% 188.07/187.98 [8502]~P40(x85021,x85023,x85024)+P101(f323(f323(f325(x85021),x85022),x85023))+~P101(f323(f323(f325(f871(x85021,x85021)),f323(f323(f258(x85021,x85021),x85025),x85022)),x85024))
% 188.07/187.98 [8503]~P40(x85031,x85033,x85034)+P101(f323(f323(f325(x85031),x85032),x85033))+~P101(f323(f323(f325(f871(x85031,x85031)),f323(f323(f258(x85031,x85031),x85032),x85035)),x85034))
% 188.07/187.98 [8504]~P9(x85041,x85043,x85044)+P101(f323(f323(f325(x85041),x85042),x85043))+~P101(f323(f323(f325(f871(x85041,x85041)),f323(f323(f258(x85041,x85041),x85045),x85042)),x85044))
% 188.07/187.98 [8505]~P9(x85051,x85053,x85054)+P101(f323(f323(f325(x85051),x85052),x85053))+~P101(f323(f323(f325(f871(x85051,x85051)),f323(f323(f258(x85051,x85051),x85052),x85055)),x85054))
% 188.07/187.98 [8790]~P9(x87901,x87905,x87902)+E(f323(f277(x87901,x87901,x87902),f323(f323(f301(x87901),x87903),f188(f872(x87901,a860)))),f323(f277(x87901,x87901,x87902),f323(f323(f301(x87901),x87904),f188(f872(x87901,a860)))))+~P101(f323(f323(f325(f871(x87901,x87901)),f323(f323(f258(x87901,x87901),x87903),x87904)),x87902))
% 188.07/187.98 [8972]P101(f323(x89721,x89722))+~P101(f323(f323(f325(x89723),x89722),x89725))+P101(f323(f323(f325(x89723),f430(x89721,x89724,x89725,x89723)),f323(f323(f110(f872(x89723,a860)),x89725),x89724)))
% 188.07/187.98 [8973]P101(f323(x89731,x89732))+~P101(f323(f323(f325(x89733),x89732),x89734))+P101(f323(f323(f325(x89733),f430(x89731,x89734,x89735,x89733)),f323(f323(f110(f872(x89733,a860)),x89735),x89734)))
% 188.07/187.98 [8981]~P101(f323(x89812,x89815))+~P101(f323(f323(f325(x89811),x89815),x89814))+P101(f323(f323(f325(x89811),f390(x89812,x89813,x89814,x89811)),f323(f323(f110(f872(x89811,a860)),x89814),x89813)))
% 188.07/187.98 [8982]~P101(f323(x89822,x89825))+~P101(f323(f323(f325(x89821),x89825),x89823))+P101(f323(f323(f325(x89821),f390(x89822,x89823,x89824,x89821)),f323(f323(f110(f872(x89821,a860)),x89824),x89823)))
% 188.07/187.98 [8997]~P101(f323(f323(f237(f872(x89971,a860)),x89973),x89975))+~P101(f323(f323(f237(f872(x89971,a860)),x89972),x89974))+P101(f323(f323(f237(f872(x89971,a860)),f323(f323(f110(f872(x89971,a860)),x89972),x89973)),f323(f323(f110(f872(x89971,a860)),x89974),x89975)))
% 188.07/187.98 [8998]~P101(f323(f323(f237(f872(x89981,a860)),x89985),x89983))+~P101(f323(f323(f237(f872(x89981,a860)),x89982),x89984))+P101(f323(f323(f237(f872(x89981,a860)),f323(f323(f22(f872(x89981,a860)),x89982),x89983)),f323(f323(f22(f872(x89981,a860)),x89984),x89985)))
% 188.07/187.98 [8999]~P101(f323(f323(f237(f872(x89991,a860)),x89993),x89995))+~P101(f323(f323(f237(f872(x89991,a860)),x89992),x89994))+P101(f323(f323(f237(f872(x89991,a860)),f323(f323(f101(f872(x89991,a860)),x89992),x89993)),f323(f323(f101(f872(x89991,a860)),x89994),x89995)))
% 188.07/187.98 [9091]~E(f323(f189(f866(x90911)),x90913),f323(f189(f866(x90912)),x90914))+E(f323(f323(f179(x90911,x90912),f323(f323(f175(x90911,x90912),x90913),x90914)),x90915),f323(f230(x90912),f534(x90915,x90914,x90912,x90913,x90911)))+~P101(f323(f323(f325(x90911),x90915),f323(f166(x90911),x90913)))
% 188.07/187.98 [9095]P101(f323(f323(f325(f871(x90951,x90951)),f323(f323(f258(x90951,x90951),x90952),x90953)),f317(x90951,x90954,x90955)))+~P101(f323(f323(f237(a865),f323(x90954,x90952)),f323(x90954,x90953)))+~P101(f323(f323(f325(f871(x90951,x90951)),f323(f323(f258(x90951,x90951),x90952),x90953)),x90955))
% 188.07/187.98 [9276]P101(f323(f323(f325(f871(x92761,x92761)),f323(f323(f258(x92761,x92761),x92762),x92763)),f299(x92761,x92764)))+~P101(f323(f323(f325(f871(x92761,x92761)),f323(f323(f258(x92761,x92761),x92762),x92765)),f299(x92761,x92764)))+~P101(f323(f323(f325(f871(x92761,x92761)),f323(f323(f258(x92761,x92761),x92765),x92763)),x92764))
% 188.07/187.98 [9277]P101(f323(f323(f325(f871(x92771,x92771)),f323(f323(f258(x92771,x92771),x92772),x92773)),f299(x92771,x92774)))+~P101(f323(f323(f325(f871(x92771,x92771)),f323(f323(f258(x92771,x92771),x92775),x92773)),f299(x92771,x92774)))+~P101(f323(f323(f325(f871(x92771,x92771)),f323(f323(f258(x92771,x92771),x92772),x92775)),x92774))
% 188.07/187.98 [9374]E(x93741,x93742)+E(f323(a112,f742(x93743,x93744,x93741,x93742,x93745)),x93744)+~P101(f323(f323(f325(f871(x93745,x93745)),f323(f323(f258(x93745,x93745),x93742),x93741)),f323(f323(f183(f871(x93745,x93745),a860),x93744),x93743)))
% 188.07/187.98 [9375]E(x93751,x93752)+E(f323(a112,f744(x93753,x93754,x93751,x93752,x93755)),x93754)+~P101(f323(f323(f325(f871(x93755,x93755)),f323(f323(f258(x93755,x93755),x93752),x93751)),f323(f323(f183(f871(x93755,x93755),a860),x93754),x93753)))
% 188.07/187.98 [9376]E(x93761,f2(a865))+E(f323(a112,f742(x93762,x93761,x93763,x93764,x93765)),x93761)+~P101(f323(f323(f325(f871(x93765,x93765)),f323(f323(f258(x93765,x93765),x93764),x93763)),f323(f323(f183(f871(x93765,x93765),a860),x93761),x93762)))
% 188.07/187.98 [9377]E(x93771,f2(a865))+E(f323(a112,f744(x93772,x93771,x93773,x93774,x93775)),x93771)+~P101(f323(f323(f325(f871(x93775,x93775)),f323(f323(f258(x93775,x93775),x93774),x93773)),f323(f323(f183(f871(x93775,x93775),a860),x93771),x93772)))
% 188.07/187.98 [9394]P101(f323(f323(f325(f871(x93941,x93941)),f323(f323(f258(x93941,x93941),x93942),x93943)),f323(f323(f280(x93941,x93941,x93941),x93944),f299(x93941,x93944))))+~P101(f323(f323(f325(f871(x93941,x93941)),f323(f323(f258(x93941,x93941),x93942),x93945)),x93944))+~P101(f323(f323(f325(f871(x93941,x93941)),f323(f323(f258(x93941,x93941),x93945),x93943)),x93944))
% 188.07/187.98 [9401]~P101(f323(f323(f325(f871(x94011,x94011)),f323(f323(f258(x94011,x94011),x94012),x94015)),f299(x94011,x94014)))+P101(f323(f323(f325(f871(x94011,x94011)),f323(f323(f258(x94011,x94011),x94012),x94013)),f323(f323(f280(x94011,x94011,x94011),x94014),f299(x94011,x94014))))+~P101(f323(f323(f325(f871(x94011,x94011)),f323(f323(f258(x94011,x94011),x94015),x94013)),x94014))
% 188.07/187.98 [9439]~P9(x94391,x94395,x94392)+~P101(f323(f323(f325(f871(x94391,x94391)),f323(f323(f258(x94391,x94391),x94393),x94394)),x94392))+P101(f323(f323(f237(f872(x94391,a860)),f323(f277(x94391,x94391,x94392),f323(f323(f301(x94391),x94393),f188(f872(x94391,a860))))),f323(f277(x94391,x94391,x94392),f323(f323(f301(x94391),x94394),f188(f872(x94391,a860))))))
% 188.07/187.98 [9496]P101(f323(f323(f325(f871(x94961,x94961)),f323(f323(f258(x94961,x94961),x94962),x94963)),f323(f323(f280(x94961,x94961,x94961),x94964),f299(x94961,x94964))))+~P101(f323(f323(f325(f871(x94961,x94961)),f323(f323(f258(x94961,x94961),x94962),x94965)),f323(f323(f280(x94961,x94961,x94961),x94964),f299(x94961,x94964))))+~P101(f323(f323(f325(f871(x94961,x94961)),f323(f323(f258(x94961,x94961),x94965),x94963)),x94964))
% 188.07/187.98 [9497]P101(f323(f323(f325(f871(x94971,x94971)),f323(f323(f258(x94971,x94971),x94972),x94973)),f323(f323(f280(x94971,x94971,x94971),x94974),f299(x94971,x94974))))+~P101(f323(f323(f325(f871(x94971,x94971)),f323(f323(f258(x94971,x94971),x94975),x94973)),f323(f323(f280(x94971,x94971,x94971),x94974),f299(x94971,x94974))))+~P101(f323(f323(f325(f871(x94971,x94971)),f323(f323(f258(x94971,x94971),x94972),x94975)),x94974))
% 188.07/187.98 [9548]~P101(f323(f64(x95481,x95481,x95484,x95482,x95483),x95485))+P101(f323(f323(f325(x95481),x95482),x95483))+P101(f323(f60(x95481,x95484,f323(f323(f301(x95481),x95482),x95483)),x95485))
% 188.07/187.98 [9588]~E(f323(f302(x95883,x95882,x95885),x95884),x95881)+E(x95881,f188(f872(x95882,a860)))+P101(f323(f323(f237(f872(x95883,a860)),f323(f302(x95882,x95883,f605(x95884,x95883,x95882,x95881)),x95881)),x95884))
% 188.07/187.98 [9635]~P6(x96355)+P101(f323(f323(f325(x96351),f452(x96352,x96353,x96354,x96351,x96355)),x96354))+P101(f323(f323(f237(x96355),f323(f323(f39(x96351,x96355),x96354),x96353)),x96352))
% 188.07/187.98 [9688]P35(x96881,x96882,x96883,x96884,x96885)+~E(f323(f189(f866(x96881)),x96884),f323(f189(f866(x96882)),x96885))+P101(f323(f323(f325(f871(x96881,x96882)),f648(x96885,x96884,x96883,x96882,x96881)),f323(f166(f871(x96881,x96882)),f323(f323(f175(x96881,x96882),x96884),x96885))))
% 188.07/187.98 [9689]P35(x96891,x96892,x96893,x96894,x96895)+~E(f323(f189(f866(x96891)),x96894),f323(f189(f866(x96892)),x96895))+P101(f323(f323(f325(f871(x96891,x96892)),f656(x96893,x96895,x96894,x96892,x96891)),f323(f166(f871(x96891,x96892)),f323(f323(f175(x96891,x96892),x96894),x96895))))
% 188.07/187.98 [9828]E(x98281,x98282)+P101(f323(f323(f325(f871(x98283,x98283)),f323(f323(f258(x98283,x98283),x98281),f743(x98284,x98285,x98282,x98281,x98283))),x98284))+~P101(f323(f323(f325(f871(x98283,x98283)),f323(f323(f258(x98283,x98283),x98281),x98282)),f323(f323(f183(f871(x98283,x98283),a860),x98285),x98284)))
% 188.07/187.98 [9829]E(x98291,f2(a865))+P101(f323(f323(f325(f871(x98292,x98292)),f323(f323(f258(x98292,x98292),x98293),f743(x98294,x98291,x98295,x98293,x98292))),x98294))+~P101(f323(f323(f325(f871(x98292,x98292)),f323(f323(f258(x98292,x98292),x98293),x98295)),f323(f323(f183(f871(x98292,x98292),a860),x98291),x98294)))
% 188.07/187.98 [9872]~P6(x98721)+~P101(f323(f323(f237(x98721),f323(x98724,f452(x98725,x98724,x98723,x98722,x98721))),x98725))+P101(f323(f323(f237(x98721),f323(f323(f39(x98722,x98721),x98723),x98724)),x98725))
% 188.07/187.98 [9914]E(x99141,x99142)+P101(f323(f323(f325(f871(x99143,x99143)),f323(f323(f258(x99143,x99143),f746(x99144,x99145,x99141,x99142,x99143)),x99141)),x99144))+~P101(f323(f323(f325(f871(x99143,x99143)),f323(f323(f258(x99143,x99143),x99142),x99141)),f323(f323(f183(f871(x99143,x99143),a860),x99145),x99144)))
% 188.07/187.98 [9915]E(x99151,f2(a865))+P101(f323(f323(f325(f871(x99152,x99152)),f323(f323(f258(x99152,x99152),f746(x99153,x99151,x99154,x99155,x99152)),x99154)),x99153))+~P101(f323(f323(f325(f871(x99152,x99152)),f323(f323(f258(x99152,x99152),x99155),x99154)),f323(f323(f183(f871(x99152,x99152),a860),x99151),x99153)))
% 188.07/187.98 [9919]E(x99191,x99192)+P101(f323(f323(f325(f871(x99193,x99193)),f323(f323(f258(x99193,x99193),x99191),f746(x99194,x99195,x99192,x99191,x99193))),f323(f323(f183(f871(x99193,x99193),a860),f744(x99194,x99195,x99192,x99191,x99193)),x99194)))+~P101(f323(f323(f325(f871(x99193,x99193)),f323(f323(f258(x99193,x99193),x99191),x99192)),f323(f323(f183(f871(x99193,x99193),a860),x99195),x99194)))
% 188.07/187.98 [9920]E(x99201,f2(a865))+P101(f323(f323(f325(f871(x99202,x99202)),f323(f323(f258(x99202,x99202),x99203),f746(x99204,x99201,x99205,x99203,x99202))),f323(f323(f183(f871(x99202,x99202),a860),f744(x99204,x99201,x99205,x99203,x99202)),x99204)))+~P101(f323(f323(f325(f871(x99202,x99202)),f323(f323(f258(x99202,x99202),x99203),x99205)),f323(f323(f183(f871(x99202,x99202),a860),x99201),x99204)))
% 188.07/187.98 [9970]E(x99701,x99702)+P101(f323(f323(f325(f871(x99703,x99703)),f323(f323(f258(x99703,x99703),f743(x99704,x99705,x99701,x99702,x99703)),x99701)),f323(f323(f183(f871(x99703,x99703),a860),f742(x99704,x99705,x99701,x99702,x99703)),x99704)))+~P101(f323(f323(f325(f871(x99703,x99703)),f323(f323(f258(x99703,x99703),x99702),x99701)),f323(f323(f183(f871(x99703,x99703),a860),x99705),x99704)))
% 188.07/187.98 [9971]E(x99711,f2(a865))+P101(f323(f323(f325(f871(x99712,x99712)),f323(f323(f258(x99712,x99712),f743(x99713,x99711,x99714,x99715,x99712)),x99714)),f323(f323(f183(f871(x99712,x99712),a860),f742(x99713,x99711,x99714,x99715,x99712)),x99713)))+~P101(f323(f323(f325(f871(x99712,x99712)),f323(f323(f258(x99712,x99712),x99715),x99714)),f323(f323(f183(f871(x99712,x99712),a860),x99711),x99713)))
% 188.07/187.98 [10004]~P72(x100042)+~P101(f323(f59(x100041),x100045))+E(f323(f323(f6(x100041,x100042),f323(f323(f7(x100041,x100042,x100042),f323(f323(f18(x100041,x100042,f872(x100042,x100042)),f323(f323(f8(a860,f872(x100042,f872(x100042,x100042)),x100041),f96(x100042)),f323(f323(f7(x100041,f872(x100041,a860),a860),f325(x100041)),x100043))),x100044)),f2(x100042))),x100045),f323(f323(f6(x100041,x100042),x100044),f323(f323(f101(f872(x100041,a860)),x100045),x100043)))
% 188.07/187.98 [8571]~P72(x85711)+~P101(f323(f59(x85714),x85715))+E(f323(f323(f78(x85711),f323(x85712,x85713)),f323(f323(f6(x85714,x85711),x85712),f323(f323(f22(f872(x85714,a860)),x85715),f323(f323(f301(x85714),x85713),f188(f872(x85714,a860)))))),f323(f323(f6(x85714,x85711),x85712),f323(f323(f301(x85714),x85713),x85715)))
% 188.07/187.98 [8572]~P68(x85721)+~P101(f323(f59(x85724),x85725))+E(f323(f323(f79(x85721),f323(x85722,x85723)),f323(f323(f9(x85724,x85721),x85722),f323(f323(f22(f872(x85724,a860)),x85725),f323(f323(f301(x85724),x85723),f188(f872(x85724,a860)))))),f323(f323(f9(x85724,x85721),x85722),f323(f323(f301(x85724),x85723),x85725)))
% 188.07/187.98 [8907]~P103(x89072)+~P16(x89072,f323(f162(x89072),f323(f323(f147(x89071,x89072),x89074),x89075)))+E(f323(f129(x89071,f323(f323(f8(x89072,a860,x89071),f323(f238(x89072),x89073)),x89074)),x89075),f171(x89071,f323(f323(f8(x89072,a860,x89071),f323(f238(x89072),x89073)),x89074),x89075))
% 188.07/187.98 [8929]~P72(x89291)+E(f323(f323(f78(x89291),f323(f323(f6(a865,x89291),x89292),f294(a865,x89293,x89294))),f323(f323(f6(a865,x89291),x89292),f294(a865,f323(f323(f78(a865),x89294),f76(a865)),f323(f323(f78(a865),x89294),x89295)))),f323(f323(f6(a865,x89291),x89292),f294(a865,x89293,f323(f323(f78(a865),x89294),x89295))))+~P101(f323(f323(f237(a865),x89293),f323(f323(f78(a865),x89294),f76(a865))))
% 188.07/187.98 [8930]~P101(f323(f323(f325(x89301),x89304),x89305))+~P101(f323(f323(f237(f872(x89301,a860)),f323(f166(x89301),x89302)),x89305))+P101(f323(f323(f237(f872(x89301,a860)),f323(f166(x89301),f323(f323(f152(x89301,x89302),x89303),x89304))),x89305))
% 188.07/187.98 [9157]~P6(x91572)+~P101(f323(f59(x91571),x91575))+E(f323(f323(f62(x91571,x91572,f323(f323(f8(x91572,f872(x91572,x91572),x91571),f110(x91572)),x91573)),x91574),x91575),f323(f323(f110(x91572),x91574),f323(f323(f39(x91571,x91572),x91575),x91573)))
% 188.07/187.98 [9158]~P6(x91582)+~P101(f323(f59(x91581),x91585))+E(f323(f323(f62(x91581,x91582,f323(f323(f8(x91582,f872(x91582,x91582),x91581),f101(x91582)),x91583)),x91584),x91585),f323(f323(f101(x91582),x91584),f323(f323(f40(x91581,x91582),x91585),x91583)))
% 188.07/187.98 [9203]E(f323(x92031,x92032),f323(x92031,x92033))+P101(f323(f323(f238(a865),f323(x92031,x92032)),f323(x92031,x92033)))+~P101(f323(f323(f325(f871(x92034,x92034)),f323(f323(f258(x92034,x92034),x92032),x92033)),f146(x92034,f323(f323(f144(f872(x92034,a865)),x92031),x92035))))
% 188.07/187.98 [9236]~E(f323(x92364,x92362),f323(x92364,x92363))+~P101(f323(f323(f325(f871(x92361,x92361)),f323(f323(f258(x92361,x92361),x92362),x92363)),f146(x92361,x92365)))+P101(f323(f323(f325(f871(x92361,x92361)),f323(f323(f258(x92361,x92361),x92362),x92363)),f146(x92361,f323(f323(f144(f872(x92361,a865)),x92364),x92365))))
% 188.07/187.98 [9255]~P27(x92551,x92552,x92553,x92555)+P27(x92551,x92552,x92553,f323(f323(f301(x92551),x92554),x92555))+P101(f323(f323(f325(x92552),f323(x92553,x92554)),f323(f302(x92551,x92552,x92553),f323(f323(f22(f872(x92551,a860)),x92555),f323(f323(f301(x92551),x92554),f188(f872(x92551,a860)))))))
% 188.07/187.98 [9259]P101(f323(x92592,x92595))+~P101(f323(f323(f325(x92591),x92595),f323(f166(x92591),x92593)))+E(f323(f323(f131(x92591),f323(f189(f866(x92591)),f171(x92591,x92592,f323(f323(f121(x92591),x92593),x92594)))),f323(f323(f121(x92591),x92593),x92594)),f323(f323(f121(x92591),f323(f323(f131(x92591),f323(f189(f866(x92591)),f171(x92591,x92592,x92593))),x92593)),x92594))
% 188.07/187.98 [9262]~P101(f323(f323(f325(f871(x92621,x92621)),f323(f323(f258(x92621,x92621),x92622),x92623)),f146(x92621,x92625)))+~P101(f323(f323(f237(a865),f323(x92624,x92622)),f323(x92624,x92623)))+P101(f323(f323(f325(f871(x92621,x92621)),f323(f323(f258(x92621,x92621),x92622),x92623)),f146(x92621,f323(f323(f144(f872(x92621,a865)),x92624),x92625))))
% 188.07/187.98 [9328]P101(f323(f323(f325(f871(x93284,x93284)),f323(f323(f258(x93284,x93284),x93282),x93283)),f146(x93284,x93285)))+P101(f323(f323(f238(a865),f323(x93281,x93282)),f323(x93281,x93283)))+~P101(f323(f323(f325(f871(x93284,x93284)),f323(f323(f258(x93284,x93284),x93282),x93283)),f146(x93284,f323(f323(f144(f872(x93284,a865)),x93281),x93285))))
% 188.07/187.98 [9469]~P101(f323(f323(f325(f871(f866(x94691),f866(x94691))),f323(f323(f258(f866(x94691),f866(x94691)),x94692),x94694)),f151(x94691,x94695)))+~P101(f323(f323(f238(a865),x94693),f323(f189(f866(x94691)),x94692)))+P101(f323(f323(f325(f871(x94691,x94691)),f323(f323(f258(x94691,x94691),f323(f323(f158(x94691),x94692),x94693)),f323(f323(f158(x94691),x94694),x94693))),x94695))
% 188.07/187.98 [9716]E(x97161,f2(a1))+~P101(f323(f46(x97163,x97161),f323(f323(f258(a1,a1),x97164),x97165)))+P101(f323(f46(f323(f323(f79(a1),x97162),x97163),x97161),f323(f323(f258(a1,a1),f323(f323(f78(a1),f323(f323(f79(a1),x97162),x97164)),f323(f323(f36(a1),f323(f323(f79(a1),x97162),x97165)),x97161))),f42(a1,f323(f323(f79(a1),x97162),x97165),x97161))))
% 188.07/187.98 [9718]~P101(f323(f323(f238(a865),f2(a865)),x97183))+~P101(f323(f45(x97182,x97183),f323(f323(f258(a865,a865),x97184),x97185)))+P101(f323(f45(f323(f323(f79(a865),x97181),x97182),x97183),f323(f323(f258(a865,a865),f323(f323(f78(a865),f323(f323(f79(a865),x97181),x97184)),f323(f323(f36(a865),f323(f323(f79(a865),x97181),x97185)),x97183))),f42(a865,f323(f323(f79(a865),x97181),x97185),x97183))))
% 188.07/187.98 [10026]~P72(x100262)+~P101(f323(f59(x100261),x100264))+E(f323(f323(f6(x100261,x100262),x100263),f323(f243(x100261),f323(f323(f18(x100261,a860,a860),f323(f323(f8(a860,f872(a860,a860),x100261),a322),f323(f323(f7(x100261,f872(x100261,a860),a860),f325(x100261)),x100264))),f323(f323(f7(x100261,f872(x100261,a860),a860),f325(x100261)),x100265)))),f323(f323(f6(x100261,x100262),f323(f323(f7(x100261,x100262,x100262),f323(f323(f18(x100261,x100262,f872(x100262,x100262)),f323(f323(f8(a860,f872(x100262,f872(x100262,x100262)),x100261),f96(x100262)),f323(f323(f7(x100261,f872(x100261,a860),a860),f325(x100261)),x100265))),x100263)),f2(x100262))),x100264))
% 188.07/187.98 [8203]~E(f323(f323(f121(x82031),x82032),x82035),f323(f323(f121(x82031),x82033),x82034))+E(f323(f323(f121(x82031),f323(f323(f131(x82031),f323(f189(f866(x82031)),x82032)),x82033)),x82034),x82035)+P101(f323(f323(f237(a865),f323(f189(f866(x82031)),x82033)),f323(f189(f866(x82031)),x82032)))
% 188.07/187.98 [8402]~E(f323(f323(f121(x84022),x84023),x84021),f323(f323(f121(x84022),x84024),x84025))+E(x84021,f323(f323(f121(x84022),f323(f323(f131(x84022),f323(f189(f866(x84022)),x84023)),x84024)),x84025))+~P101(f323(f323(f237(a865),f323(f189(f866(x84022)),x84023)),f323(f189(f866(x84022)),x84024)))
% 188.07/187.98 [8485]~E(f323(f323(f78(a865),f323(f323(f79(a865),x84853),x84854)),x84851),f323(f323(f78(a865),f323(f323(f79(a865),x84852),x84854)),x84855))+~P101(f323(f323(f237(a865),x84853),x84852))+E(x84851,f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f22(a865),x84852),x84853)),x84854)),x84855))
% 188.07/187.98 [8486]~E(f323(f323(f78(a865),f323(f323(f79(a865),x84861),x84863)),x84864),f323(f323(f78(a865),f323(f323(f79(a865),x84862),x84863)),x84865))+~P101(f323(f323(f237(a865),x84862),x84861))+E(f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f22(a865),x84861),x84862)),x84863)),x84864),x84865)
% 188.07/187.98 [8657]E(f323(f323(f78(a865),f323(f323(f79(a865),x86571),x86572)),x86573),f323(f323(f78(a865),f323(f323(f79(a865),x86574),x86572)),x86575))+~P101(f323(f323(f237(a865),x86574),x86571))+~E(x86575,f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f22(a865),x86571),x86574)),x86572)),x86573))
% 188.07/187.98 [8658]E(f323(f323(f78(a865),f323(f323(f79(a865),x86581),x86582)),x86583),f323(f323(f78(a865),f323(f323(f79(a865),x86584),x86582)),x86585))+~P101(f323(f323(f237(a865),x86584),x86581))+~E(f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f22(a865),x86581),x86584)),x86582)),x86583),x86585)
% 188.07/187.98 [9523]~P62(x95232)+~P101(f323(f59(x95231),x95235))+E(f323(f323(f9(x95231,x95232),f323(f323(f18(x95231,x95232,x95232),f323(f323(f8(x95232,f872(x95232,x95232),x95231),f281(x95232)),x95233)),x95234)),x95235),f323(f323(f281(x95232),f323(f323(f9(x95231,x95232),x95233),x95235)),f323(f323(f9(x95231,x95232),x95234),x95235)))
% 188.07/187.98 [9651]~E(f749(x96515,x96514,x96513,x96512,x96511),f750(x96515,x96514,x96513,x96512,x96511))+P101(f323(f323(f325(f871(x96511,x96511)),f323(f323(f258(x96511,x96511),x96512),x96513)),f299(x96511,x96514)))+~P101(f323(f323(f325(f871(x96511,x96511)),f323(f323(f258(x96511,x96511),x96512),x96513)),f299(x96511,f323(f323(f110(f872(f871(x96511,x96511),a860)),x96514),x96515))))
% 188.07/187.98 [9652]~E(f751(x96525,x96524,x96523,x96522,x96521),f752(x96525,x96524,x96523,x96522,x96521))+P101(f323(f323(f325(f871(x96521,x96521)),f323(f323(f258(x96521,x96521),x96522),x96523)),f299(x96521,x96524)))+~P101(f323(f323(f325(f871(x96521,x96521)),f323(f323(f258(x96521,x96521),x96522),x96523)),f299(x96521,f323(f323(f110(f872(f871(x96521,x96521),a860)),x96524),x96525))))
% 188.07/187.98 [9862]P101(f323(f323(f325(f871(x98621,x98621)),f323(f323(f258(x98621,x98621),x98622),f752(x98625,x98624,x98623,x98622,x98621))),f299(x98621,x98624)))+P101(f323(f323(f325(f871(x98621,x98621)),f323(f323(f258(x98621,x98621),x98622),x98623)),f299(x98621,x98624)))+~P101(f323(f323(f325(f871(x98621,x98621)),f323(f323(f258(x98621,x98621),x98622),x98623)),f299(x98621,f323(f323(f110(f872(f871(x98621,x98621),a860)),x98624),x98625))))
% 188.07/187.98 [9941]P101(f323(f323(f325(f871(x99411,x99411)),f323(f323(f258(x99411,x99411),f750(x99415,x99414,x99413,x99412,x99411)),x99413)),f299(x99411,x99414)))+P101(f323(f323(f325(f871(x99411,x99411)),f323(f323(f258(x99411,x99411),x99412),x99413)),f299(x99411,x99414)))+~P101(f323(f323(f325(f871(x99411,x99411)),f323(f323(f258(x99411,x99411),x99412),x99413)),f299(x99411,f323(f323(f110(f872(f871(x99411,x99411),a860)),x99414),x99415))))
% 188.07/187.98 [9977]P101(f323(f323(f325(f871(x99771,x99771)),f323(f323(f258(x99771,x99771),x99772),x99773)),f299(x99771,x99774)))+P101(f323(f323(f325(f871(x99771,x99771)),f323(f323(f258(x99771,x99771),f749(x99775,x99774,x99773,x99772,x99771)),f750(x99775,x99774,x99773,x99772,x99771))),x99775))+~P101(f323(f323(f325(f871(x99771,x99771)),f323(f323(f258(x99771,x99771),x99772),x99773)),f299(x99771,f323(f323(f110(f872(f871(x99771,x99771),a860)),x99774),x99775))))
% 188.07/187.98 [9978]P101(f323(f323(f325(f871(x99781,x99781)),f323(f323(f258(x99781,x99781),x99782),x99783)),f299(x99781,x99784)))+P101(f323(f323(f325(f871(x99781,x99781)),f323(f323(f258(x99781,x99781),f752(x99785,x99784,x99783,x99782,x99781)),f751(x99785,x99784,x99783,x99782,x99781))),x99785))+~P101(f323(f323(f325(f871(x99781,x99781)),f323(f323(f258(x99781,x99781),x99782),x99783)),f299(x99781,f323(f323(f110(f872(f871(x99781,x99781),a860)),x99784),x99785))))
% 188.07/187.98 [10098]~P101(f323(f323(f325(f871(f866(x100981),f866(x100981))),f323(f323(f258(f866(x100981),f866(x100981)),x100984),x100985)),f151(x100981,x100982)))+~P101(f323(f323(f325(f871(x100981,x100981)),x100983),f323(f166(f871(x100981,x100981)),f323(f323(f175(x100981,x100981),x100984),x100985))))+P101(f323(f323(f262(x100981,x100981,a860),f323(f323(f7(x100981,f872(f871(x100981,x100981),a860),f872(x100981,a860)),f323(f323(f8(f872(x100981,f872(f872(f871(x100981,x100981),a860),a860)),f872(f872(f871(x100981,x100981),a860),f872(x100981,a860)),x100981),f7(x100981,f872(f871(x100981,x100981),a860),a860)),f323(f323(f8(f872(x100981,f871(x100981,x100981)),f872(x100981,f872(f872(f871(x100981,x100981),a860),a860)),x100981),f323(f8(f871(x100981,x100981),f872(f872(f871(x100981,x100981),a860),a860),x100981),f325(f871(x100981,x100981)))),f258(x100981,x100981)))),x100982)),x100983))
% 188.07/187.98 [9552]~P101(f323(f323(f237(a865),x95523),x95522))+~P101(f323(f323(f237(a865),f323(f323(f78(a865),f323(f323(f79(a865),x95523),x95524)),x95521)),f323(f323(f78(a865),f323(f323(f79(a865),x95522),x95524)),x95525)))+P101(f323(f323(f237(a865),x95521),f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f22(a865),x95522),x95523)),x95524)),x95525)))
% 188.07/187.98 [9553]~P101(f323(f323(f237(a865),x95533),x95532))+~P101(f323(f323(f238(a865),f323(f323(f78(a865),f323(f323(f79(a865),x95533),x95534)),x95531)),f323(f323(f78(a865),f323(f323(f79(a865),x95532),x95534)),x95535)))+P101(f323(f323(f238(a865),x95531),f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f22(a865),x95532),x95533)),x95534)),x95535)))
% 188.07/187.98 [9572]~P101(f323(f323(f237(a865),x95721),x95724))+P101(f323(f323(f237(a865),f323(f323(f78(a865),f323(f323(f79(a865),x95721),x95722)),x95723)),f323(f323(f78(a865),f323(f323(f79(a865),x95724),x95722)),x95725)))+~P101(f323(f323(f237(a865),x95723),f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f22(a865),x95724),x95721)),x95722)),x95725)))
% 188.07/187.98 [9573]~P101(f323(f323(f237(a865),x95731),x95734))+P101(f323(f323(f238(a865),f323(f323(f78(a865),f323(f323(f79(a865),x95731),x95732)),x95733)),f323(f323(f78(a865),f323(f323(f79(a865),x95734),x95732)),x95735)))+~P101(f323(f323(f238(a865),x95733),f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f22(a865),x95734),x95731)),x95732)),x95735)))
% 188.07/187.98 [9686]~P101(f323(f323(f237(a865),x96862),x96861))+~P101(f323(f323(f237(a865),f323(f323(f78(a865),f323(f323(f79(a865),x96861),x96863)),x96864)),f323(f323(f78(a865),f323(f323(f79(a865),x96862),x96863)),x96865)))+P101(f323(f323(f237(a865),f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f22(a865),x96861),x96862)),x96863)),x96864)),x96865))
% 188.07/187.98 [9687]~P101(f323(f323(f237(a865),x96872),x96871))+~P101(f323(f323(f238(a865),f323(f323(f78(a865),f323(f323(f79(a865),x96871),x96873)),x96874)),f323(f323(f78(a865),f323(f323(f79(a865),x96872),x96873)),x96875)))+P101(f323(f323(f238(a865),f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f22(a865),x96871),x96872)),x96873)),x96874)),x96875))
% 188.07/187.98 [9740]~P101(f323(f323(f237(a865),x97404),x97401))+P101(f323(f323(f237(a865),f323(f323(f78(a865),f323(f323(f79(a865),x97401),x97402)),x97403)),f323(f323(f78(a865),f323(f323(f79(a865),x97404),x97402)),x97405)))+~P101(f323(f323(f237(a865),f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f22(a865),x97401),x97404)),x97402)),x97403)),x97405))
% 188.07/187.98 [9741]~P101(f323(f323(f237(a865),x97414),x97411))+P101(f323(f323(f238(a865),f323(f323(f78(a865),f323(f323(f79(a865),x97411),x97412)),x97413)),f323(f323(f78(a865),f323(f323(f79(a865),x97414),x97412)),x97415)))+~P101(f323(f323(f238(a865),f323(f323(f78(a865),f323(f323(f79(a865),f323(f323(f22(a865),x97411),x97414)),x97412)),x97413)),x97415))
% 188.07/187.98 [9962]~P14(x99621,x99622,x99625,x99623)+~P101(f323(f323(f325(f871(x99621,x99621)),x99624),x99625))+P101(f323(f323(f262(x99621,x99621,a860),f323(f323(f7(x99621,f872(x99621,x99622),f872(x99621,a860)),f323(f323(f8(f872(x99622,a860),f872(f872(x99621,x99622),f872(x99621,a860)),x99621),f8(x99622,a860,x99621)),f323(f323(f8(x99622,f872(x99622,a860),x99621),a320),x99623))),x99623)),x99624))
% 188.07/187.98 [6761]~E(f323(x67614,x67615),f200(x67612))+E(f323(f180(x67611,x67612,x67613,x67614),x67615),f323(f230(x67612),x67616))+~E(f323(x67613,x67615),f323(f230(x67612),x67616))
% 188.07/187.98 [6861]~E(f323(x68613,x68616),f200(x68611))+E(f323(f232(f869(x68611),x68612,f200(x68611),x68613),f323(x68614,x68615)),f200(x68611))+~E(f323(x68614,x68615),f323(f230(x68612),x68616))
% 188.07/187.98 [7438]E(f323(x74381,x74382),f200(x74383))+~E(f323(f180(x74385,x74383,x74386,x74381),x74382),f323(f230(x74383),x74384))+E(f323(x74381,x74382),f323(f230(x74383),x74384))
% 188.07/187.98 [7473]~E(f323(f180(x74736,x74733,x74735,x74731),x74732),f323(f230(x74733),x74734))+E(f323(x74731,x74732),f323(f230(x74733),x74734))+E(f323(x74735,x74732),f323(f230(x74733),x74734))
% 188.07/187.98 [8365]~P21(x83656,x83651,x83652,x83654)+E(f323(f71(x83651,x83651,x83651,f323(x83652,x83653)),f323(x83654,x83655)),f323(f71(x83651,x83651,x83651,f323(x83654,x83655)),f323(x83652,x83653)))+~P101(f323(f59(x83656),x83655))
% 188.07/187.98 [8802]~P27(x88021,x88023,x88025,x88026)+~P27(x88023,x88022,x88024,f323(f302(x88021,x88023,x88025),x88026))+P27(x88021,x88022,f323(f71(x88023,x88022,x88021,x88024),x88025),x88026)
% 188.07/187.98 [9359]~P101(f323(f323(x93593,x93592),x93596))+~P101(f323(f323(x93594,x93595),x93592))+P101(f323(f323(f325(x93591),x93592),f291(x93591,x93593,x93594,x93595,x93596)))
% 188.07/187.98 [9360]~P101(f323(f323(x93604,x93602),x93606))+~P101(f323(f323(x93603,x93605),x93602))+P101(f323(f323(f325(x93601),x93602),f288(x93601,x93603,x93604,x93605,x93606)))
% 188.07/187.98 [9470]E(x94701,x94702)+E(x94703,x94704)+~P101(f323(f323(f325(f871(f866(x94705),f866(x94705))),f323(f323(f258(f866(x94705),f866(x94705)),f323(f323(f144(x94705),x94703),x94701)),f323(f323(f144(x94705),x94704),x94702))),f150(x94705,x94706)))
% 188.07/187.98 [9480]~E(x94802,x94804)+P101(f323(f323(f325(f871(f866(x94801),f866(x94801))),f323(f323(f258(f866(x94801),f866(x94801)),f323(f323(f144(x94801),x94802),x94803)),f323(f323(f144(x94801),x94804),x94805))),f138(x94801,x94806)))+~P101(f323(f323(f325(f871(f866(x94801),f866(x94801))),f323(f323(f258(f866(x94801),f866(x94801)),x94803),x94805)),f138(x94801,x94806)))
% 188.07/187.98 [9481]~E(x94812,x94814)+P101(f323(f323(f325(f871(f866(x94811),f866(x94811))),f323(f323(f258(f866(x94811),f866(x94811)),f323(f323(f144(x94811),x94812),x94813)),f323(f323(f144(x94811),x94814),x94815))),f140(x94811,x94816)))+~P101(f323(f323(f325(f871(f866(x94811),f866(x94811))),f323(f323(f258(f866(x94811),f866(x94811)),x94813),x94815)),f140(x94811,x94816)))
% 188.07/187.98 [9482]~E(x94822,x94824)+P101(f323(f323(f325(f871(f866(x94821),f866(x94821))),f323(f323(f258(f866(x94821),f866(x94821)),f323(f323(f144(x94821),x94822),x94823)),f323(f323(f144(x94821),x94824),x94825))),f150(x94821,x94826)))+~P101(f323(f323(f325(f871(f866(x94821),f866(x94821))),f323(f323(f258(f866(x94821),f866(x94821)),x94823),x94825)),f150(x94821,x94826)))
% 188.07/187.98 [9483]~E(x94832,x94834)+P101(f323(f323(f325(f871(f866(x94831),f866(x94831))),f323(f323(f258(f866(x94831),f866(x94831)),f323(f323(f121(x94831),x94832),x94833)),f323(f323(f121(x94831),x94834),x94835))),f150(x94831,x94836)))+~P101(f323(f323(f325(f871(f866(x94831),f866(x94831))),f323(f323(f258(f866(x94831),f866(x94831)),x94833),x94835)),f150(x94831,x94836)))
% 188.07/187.98 [9484]~E(x94843,x94845)+P101(f323(f323(f325(f871(f866(x94841),f866(x94841))),f323(f323(f258(f866(x94841),f866(x94841)),f323(f323(f121(x94841),x94842),x94843)),f323(f323(f121(x94841),x94844),x94845))),f150(x94841,x94846)))+~P101(f323(f323(f325(f871(f866(x94841),f866(x94841))),f323(f323(f258(f866(x94841),f866(x94841)),x94842),x94844)),f150(x94841,x94846)))
% 188.07/187.98 [9540]E(x95401,x95402)+P101(f323(f323(f325(f871(f866(x95403),f866(x95403))),f323(f323(f258(f866(x95403),f866(x95403)),x95401),x95402)),f150(x95403,x95404)))+~P101(f323(f323(f325(f871(f866(x95403),f866(x95403))),f323(f323(f258(f866(x95403),f866(x95403)),f323(f323(f144(x95403),x95405),x95401)),f323(f323(f144(x95403),x95406),x95402))),f150(x95403,x95404)))
% 188.07/187.98 [9690]~E(x96903,x96905)+P101(f323(f323(f325(f871(f866(x96901),f866(x96901))),f323(f323(f258(f866(x96901),f866(x96901)),f323(f323(f121(x96901),x96902),f323(f323(f144(x96901),x96903),f113(x96901)))),f323(f323(f121(x96901),x96904),f323(f323(f144(x96901),x96905),f113(x96901))))),f150(x96901,x96906)))+~P101(f323(f323(f325(f871(f866(x96901),f866(x96901))),f323(f323(f258(f866(x96901),f866(x96901)),x96902),x96904)),f150(x96901,x96906)))
% 188.07/187.98 [9706]E(f323(x97061,x97062),f200(x97063))+~E(f323(f232(f869(x97066),x97063,f200(x97066),x97064),f323(x97061,x97062)),f200(x97066))+E(f323(x97064,f844(x97062,x97061,x97064,x97065,x97066,x97063)),f200(x97066))
% 188.07/187.98 [9707]E(f323(x97071,x97072),f200(x97073))+~E(f323(f232(f869(x97076),x97073,f200(x97076),x97074),f323(x97071,x97072)),f200(x97076))+E(f323(f230(x97073),f844(x97072,x97071,x97074,x97075,x97076,x97073)),f323(x97071,x97072))
% 188.07/187.98 [9744]E(x97441,x97442)+E(x97443,x97444)+~P101(f323(f323(f325(f871(f866(x97445),f866(x97445))),f323(f323(f258(f866(x97445),f866(x97445)),f323(f323(f121(x97445),x97443),f323(f323(f144(x97445),x97441),f113(x97445)))),f323(f323(f121(x97445),x97444),f323(f323(f144(x97445),x97442),f113(x97445))))),f150(x97445,x97446)))
% 188.07/187.98 [9769]E(x97691,x97692)+~P101(f323(f323(f325(f871(f866(x97693),f866(x97693))),f323(f323(f258(f866(x97693),f866(x97693)),f323(f323(f121(x97693),x97691),f323(f323(f144(x97693),x97695),f113(x97693)))),f323(f323(f121(x97693),x97692),f323(f323(f144(x97693),x97696),f113(x97693))))),f150(x97693,x97694)))+P101(f323(f323(f325(f871(f866(x97693),f866(x97693))),f323(f323(f258(f866(x97693),f866(x97693)),x97691),x97692)),f150(x97693,x97694)))
% 188.07/187.98 [9807]~P101(f323(f323(f325(f871(f872(x98071,a860),f872(x98071,a860))),f323(f323(f258(f872(x98071,a860),f872(x98071,a860)),x98072),x98074)),f314(x98071,x98076)))+~P101(f323(f323(f325(f871(f872(x98071,a860),f872(x98071,a860))),f323(f323(f258(f872(x98071,a860),f872(x98071,a860)),x98073),x98075)),f314(x98071,x98076)))+P101(f323(f323(f325(f871(f872(x98071,a860),f872(x98071,a860))),f323(f323(f258(f872(x98071,a860),f872(x98071,a860)),f323(f323(f110(f872(x98071,a860)),x98072),x98073)),f323(f323(f110(f872(x98071,a860)),x98074),x98075))),f314(x98071,x98076)))
% 188.07/187.98 [5230]~E(f323(x52303,x52306),x52305)+~E(x52304,f323(f230(x52301),x52306))+E(f323(f323(f201(x52301,x52302),x52303),x52304),f323(f230(x52302),x52305))
% 188.07/187.98 [5642]~E(f323(f323(f121(x56421),x56426),x56423),x56425)+E(f323(f323(f121(x56421),x56422),x56423),f323(f323(f144(x56421),x56424),x56425))+~E(x56422,f323(f323(f144(x56421),x56424),x56426))
% 188.07/187.98 [5643]~E(f323(f323(f121(x56431),x56436),x56433),x56435)+E(f323(f323(f121(x56431),x56432),x56433),f323(f323(f121(x56431),x56434),x56435))+~E(x56432,f323(f323(f121(x56431),x56434),x56436))
% 188.07/187.98 [5645]E(f323(f323(f121(x56451),x56452),x56453),f323(f323(f144(x56451),x56454),x56455))+~E(f323(f323(f144(x56451),x56454),x56456),x56452)+~E(x56455,f323(f323(f121(x56451),x56456),x56453))
% 188.07/187.98 [5647]~E(f323(f323(f121(x56471),x56472),x56476),x56474)+E(f323(f323(f121(x56471),x56472),x56473),f323(f323(f121(x56471),x56474),x56475))+~E(x56473,f323(f323(f121(x56471),x56476),x56475))
% 188.07/187.98 [6755]E(f323(x67551,x67552),f323(x67553,x67552))+~E(f323(f323(f147(x67554,x67555),x67551),x67556),f323(f323(f147(x67554,x67555),x67553),x67556))+~P101(f323(f323(f325(x67554),x67552),f323(f166(x67554),x67556)))
% 188.07/187.98 [7136]~P21(x71364,x71365,x71366,x71361)+E(f323(f323(x71361,x71362),x71363),f323(f323(f62(x71364,x71365,x71366),x71363),x71362))+~P101(f323(f59(x71364),x71362))
% 188.07/187.98 [7202]~E(x72022,f323(x72024,x72026))+~P101(f323(f323(f325(x72023),x72026),x72025))+P101(f323(f323(f325(x72021),x72022),f323(f302(x72023,x72021,x72024),x72025)))
% 188.07/187.98 [7203]~E(f323(x72034,x72032),x72036)+~P101(f323(f323(f325(x72033),x72036),x72035))+P101(f323(f323(f325(x72031),x72032),f323(f303(x72031,x72033,x72034),x72035)))
% 188.07/187.98 [7652]~P33(x76521,x76522,x76524,x76526)+P33(x76521,x76522,f323(f323(f144(x76521),x76523),x76524),f323(f323(f144(x76521),x76525),x76526))+~P101(f323(f323(x76522,x76523),x76525))
% 188.07/187.98 [8667]~P53(x86674,x86675,x86671,x86672,x86676)+E(f323(x86671,f323(x86672,x86673)),x86673)+~P101(f323(f323(f325(x86675),x86673),x86676))
% 188.07/187.98 [9168]~P28(x91682,x91681,x91685,x91684,x91683)+E(f323(f91(x91681,x91682,x91683,f91(x91682,x91681,x91684,x91685)),x91686),f323(x91685,x91686))+~P101(f323(f323(f325(x91682),x91686),x91684))
% 188.07/187.98 [9472]E(x94721,x94722)+E(f323(f189(f866(x94723)),x94724),f323(f189(f866(x94723)),x94725))+~P101(f323(f323(f325(f871(f866(x94723),f866(x94723))),f323(f323(f258(f866(x94723),f866(x94723)),f323(f323(f144(x94723),x94721),x94724)),f323(f323(f144(x94723),x94722),x94725))),f138(x94723,x94726)))
% 188.07/187.98 [9535]~P18(x95351,x95352,x95353)+E(f323(f323(f62(x95351,x95352,x95353),x95354),x95355),x95356)+~P101(f323(f64(x95351,x95352,x95353,x95354,x95355),x95356))
% 188.07/187.98 [9543]E(f323(f189(f866(x95431)),x95432),f323(f189(f866(x95431)),x95433))+P101(f323(f323(f325(f871(f866(x95431),f866(x95431))),f323(f323(f258(f866(x95431),f866(x95431)),x95432),x95433)),f138(x95431,x95434)))+~P101(f323(f323(f325(f871(f866(x95431),f866(x95431))),f323(f323(f258(f866(x95431),f866(x95431)),f323(f323(f144(x95431),x95435),x95432)),f323(f323(f144(x95431),x95436),x95433))),f138(x95431,x95434)))
% 188.07/187.98 [9566]~P101(f323(f323(f325(f871(x95661,x95661)),f323(f323(f258(x95661,x95661),x95662),x95664)),f299(x95661,x95666)))+P101(f323(f323(f325(f871(f866(x95661),f866(x95661))),f323(f323(f258(f866(x95661),f866(x95661)),f323(f323(f144(x95661),x95662),x95663)),f323(f323(f144(x95661),x95664),x95665))),f299(f866(x95661),f150(x95661,x95666))))+~P101(f323(f323(f325(f871(f866(x95661),f866(x95661))),f323(f323(f258(f866(x95661),f866(x95661)),x95663),x95665)),f299(f866(x95661),f150(x95661,x95666))))
% 188.07/187.98 [9750]~P101(f323(x97502,x97506))+~E(f323(f129(x97501,x97502),x97503),f323(f323(f144(x97501),x97504),x97505))+~P101(f323(f323(f325(x97501),x97506),f323(f166(x97501),f714(x97505,x97504,x97503,x97502,x97501))))
% 188.07/187.98 [9751]~P101(f323(x97514,x97516))+~E(f323(f323(f144(x97511),x97512),x97513),f323(f129(x97511,x97514),x97515))+~P101(f323(f323(f325(x97511),x97516),f323(f166(x97511),f704(x97515,x97514,x97513,x97512,x97511))))
% 188.07/187.98 [10053]~P72(x100532)+E(f323(f323(f6(x100531,x100532),f323(f323(f8(f872(x100533,a860),x100532,x100531),f323(f6(x100533,x100532),x100534)),f323(f323(f8(f872(x100533,a860),f872(x100533,a860),x100531),f243(x100533)),f323(f323(f8(f872(x100533,a860),f872(x100533,a860),x100531),f323(f18(x100533,a860,a860),f323(f323(f8(a860,f872(a860,a860),x100533),a322),f323(f323(f7(x100533,f872(x100533,a860),a860),f325(x100533)),x100535)))),f323(f7(x100533,x100531,a860),f323(f323(f8(x100531,f872(x100531,a860),x100533),a320),x100536)))))),f323(f302(x100533,x100531,x100536),x100535)),f323(f323(f6(x100533,x100532),x100534),x100535))+~P101(f323(f59(x100533),x100535))
% 188.07/187.98 [6813]~P103(x68133)+P101(f323(x68132,x68135))+E(f323(f129(x68131,x68132),f323(f323(f141(x68131,x68133,x68134),x68135),x68136)),f323(f129(x68131,x68132),x68136))
% 188.07/187.98 [6815]P101(f323(x68151,x68152))+~E(f160(x68153,x68151,x68154),f323(f323(f258(f866(x68153),f866(x68153)),x68155),x68156))+~P101(f323(f323(f325(x68153),x68152),f323(f166(x68153),x68155)))
% 188.07/187.98 [6858]~P101(f323(x68582,x68586))+~E(f160(x68581,x68582,x68583),f323(f323(f258(f866(x68581),f866(x68581)),x68584),x68585))+~P101(f323(f323(f325(x68581),x68586),f323(f166(x68581),x68585)))
% 188.07/187.98 [7517]~P17(x75171,x75172,x75173)+~P101(f323(f59(x75171),x75176))+E(f323(f323(f62(x75171,x75172,x75173),x75174),f323(f323(f301(x75171),x75175),x75176)),f323(f323(f62(x75171,x75172,x75173),f323(f323(x75173,x75175),x75174)),x75176))
% 188.07/187.98 [7567]~P103(x75672)+~P101(f323(f323(f237(x75672),f323(x75673,x75674)),f323(x75673,x75675)))+E(f323(f323(f141(x75671,x75672,x75673),x75674),f323(f323(f144(x75671),x75675),x75676)),f323(f323(f144(x75671),x75674),f323(f323(f144(x75671),x75675),x75676)))
% 188.07/187.98 [7682]E(x76821,x76822)+~E(f323(f323(f260(x76823,x76824),x76821),f323(f16(f872(x76824,a860),x76823),x76825)),f323(f323(f260(x76823,x76824),x76822),f323(f16(f872(x76824,a860),x76823),x76825)))+~P101(f323(f323(f325(x76824),x76826),x76825))
% 188.07/187.98 [7747]~P17(x77471,x77472,x77473)+~P101(f323(f59(x77471),x77476))+E(f323(f323(f62(x77471,x77472,x77473),x77474),f323(f323(f301(x77471),x77475),x77476)),f323(f323(x77473,x77475),f323(f323(f62(x77471,x77472,x77473),x77474),x77476)))
% 188.07/187.98 [7864]~P18(x78641,x78642,x78643)+~P101(f323(f59(x78641),x78646))+E(f323(f323(f62(x78641,x78642,x78643),f323(f323(x78643,x78644),x78645)),x78646),f323(f323(x78643,x78644),f323(f323(f62(x78641,x78642,x78643),x78645),x78646)))
% 188.07/187.98 [7935]~P22(x79352,x79355,x79356,x79351)+~P101(f323(f59(x79352),x79354))+E(f323(x79351,f323(f323(f301(x79352),x79353),x79354)),f323(f71(x79355,x79355,x79355,f323(x79351,x79354)),f323(x79356,x79353)))
% 188.07/187.98 [7967]~P103(x79672)+P101(f323(f323(f237(x79672),f323(x79673,x79674)),f323(x79673,x79675)))+E(f323(f323(f141(x79671,x79672,x79673),x79674),f323(f323(f144(x79671),x79675),x79676)),f323(f323(f144(x79671),x79675),f323(f323(f141(x79671,x79672,x79673),x79674),x79676)))
% 188.07/187.98 [8104]~E(f323(f189(f866(x81041)),x81045),f323(f189(f866(x81042)),x81046))+~E(f323(f189(f866(x81041)),x81043),f323(f189(f866(x81042)),x81044))+E(f323(f323(f121(f871(x81041,x81042)),f323(f323(f175(x81041,x81042),x81043),x81044)),f323(f323(f175(x81041,x81042),x81045),x81046)),f323(f323(f175(x81041,x81042),f323(f323(f121(x81041),x81043),x81045)),f323(f323(f121(x81042),x81044),x81046)))
% 188.07/187.98 [8218]~E(x82182,f323(f302(x82183,x82181,x82184),x82186))+P101(f323(f323(f237(f872(x82181,a860)),x82182),f323(f302(x82183,x82181,x82184),x82185)))+~P101(f323(f323(f237(f872(x82183,a860)),x82186),x82185))
% 188.07/187.98 [8324]~P103(x83245)+E(f323(x83241,x83242),f323(x83241,x83243))+E(f323(f323(f141(x83244,x83245,x83241),x83242),f323(f323(f141(x83244,x83245,x83241),x83243),x83246)),f323(f323(f141(x83244,x83245,x83241),x83243),f323(f323(f141(x83244,x83245,x83241),x83242),x83246)))
% 188.07/187.98 [8358]~P27(x83583,x83581,x83584,x83585)+P27(x83583,x83581,f323(f323(f323(f70(x83583,x83581),x83584),x83586),x83582),x83585)+P101(f323(f323(f325(x83581),x83582),f323(f302(x83583,x83581,x83584),x83585)))
% 188.07/187.98 [8494]~P101(f323(f323(f325(x84942),x84944),f323(x84946,x84943)))+~P101(f323(f323(f325(x84941),x84943),x84945))+P101(f323(f323(f325(f871(x84941,x84942)),f323(f323(f258(x84941,x84942),x84943),x84944)),f323(f323(f260(x84941,x84942),x84945),x84946)))
% 188.07/187.98 [8970]~P72(x89702)+~P27(x89704,x89701,x89705,x89706)+E(f323(f323(f6(x89701,x89702),x89703),f323(f302(x89704,x89701,x89705),x89706)),f323(f323(f6(x89704,x89702),f323(f71(x89701,x89702,x89704,x89703),x89705)),x89706))
% 188.07/187.98 [8971]~P68(x89712)+~P27(x89714,x89711,x89715,x89716)+E(f323(f323(f9(x89711,x89712),x89713),f323(f302(x89714,x89711,x89715),x89716)),f323(f323(f9(x89714,x89712),f323(f71(x89711,x89712,x89714,x89713),x89715)),x89716))
% 188.07/187.98 [9019]~P35(x90192,x90195,x90191,x90193,x90196)+P101(f323(f323(x90191,f323(f323(f158(x90192),x90193),x90194)),f323(f323(f158(x90195),x90196),x90194)))+~P101(f323(f323(f238(a865),x90194),f323(f189(f866(x90195)),x90196)))
% 188.07/187.98 [9020]~P35(x90202,x90205,x90201,x90203,x90206)+P101(f323(f323(x90201,f323(f323(f158(x90202),x90203),x90204)),f323(f323(f158(x90205),x90206),x90204)))+~P101(f323(f323(f238(a865),x90204),f323(f189(f866(x90202)),x90203)))
% 188.07/187.98 [9031]~E(f323(f302(x90311,x90312,x90313),x90314),x90316)+E(f323(f302(x90311,x90312,x90313),f323(f302(x90312,x90311,f91(x90311,x90312,x90314,x90313)),x90315)),x90315)+~P101(f323(f323(f237(f872(x90312,a860)),x90315),x90316))
% 188.07/187.98 [9231]~P21(x92313,x92311,x92316,x92312)+~P101(f323(f59(x92313),x92314))+E(f323(f71(x92311,x92311,x92311,f323(x92312,f323(f323(f22(f872(x92313,a860)),x92314),f323(f323(f301(x92313),x92315),f188(f872(x92313,a860)))))),f323(x92316,x92315)),f323(x92312,f323(f323(f301(x92313),x92315),x92314)))
% 188.07/187.98 [9842]~E(f323(f302(x98422,x98424,x98426),f246(f872(x98422,a860))),f246(f872(x98424,a860)))+~E(f323(f302(x98421,x98423,x98425),f246(f872(x98421,a860))),f246(f872(x98423,a860)))+E(f323(f302(f871(x98421,x98422),f871(x98423,x98424),f263(x98421,x98423,x98422,x98424,x98425,x98426)),f246(f872(f871(x98421,x98422),a860))),f246(f872(f871(x98423,x98424),a860)))
% 188.07/187.98 [9890]~P27(x98903,x98904,x98905,f323(x98906,f686(x98906,x98905,x98904,x98903,x98902,x98901)))+P27(x98903,x98904,x98905,f323(f323(f40(x98902,f872(x98903,a860)),x98901),x98906))+E(x98901,f188(f872(x98902,a860)))
% 188.07/187.98 [9948]P27(x99486,x99485,x99484,f323(f323(f40(x99482,f872(x99486,a860)),x99481),x99483))+E(x99481,f188(f872(x99482,a860)))+P101(f323(f323(f325(x99482),f686(x99483,x99484,x99485,x99486,x99482,x99481)),x99481))
% 188.07/187.98 [9953]P101(f323(f323(f325(x99531),f716(x99532,x99533,x99534,x99535,x99536,x99531)),x99536))+P101(f323(f323(f237(f872(f871(x99531,x99534),a860)),f323(f323(f260(x99531,x99534),x99536),x99533)),f323(f323(f260(x99531,x99534),x99535),x99532)))+~P101(f323(f323(f237(f872(x99531,a860)),x99536),x99535))
% 188.07/187.98 [9991]P26(x99916,x99915,f323(f323(f301(f864(x99916)),f323(f323(f323(f90(x99916),x99914),x99913),x99912)),f188(f872(f864(x99916),a860))))+~P26(x99916,x99915,f323(f323(f301(f864(x99916)),f323(f323(f323(f90(x99916),x99914),x99913),x99911)),f188(f872(f864(x99916),a860))))+P101(f323(f323(x99911,f777(x99912,x99911,x99913,x99914,x99915,x99916)),f819(x99912,x99911,x99913,x99914,x99915,x99916)))
% 188.07/187.98 [9992]P26(x99926,x99925,f323(f323(f301(f864(x99926)),f323(f323(f323(f90(x99926),x99921),x99923),x99922)),f188(f872(f864(x99926),a860))))+~P26(x99926,x99925,f323(f323(f301(f864(x99926)),f323(f323(f323(f90(x99926),x99924),x99923),x99922)),f188(f872(f864(x99926),a860))))+P101(f323(f323(x99921,f851(x99921,x99922,x99923,x99924,x99925,x99926)),f858(x99921,x99922,x99923,x99924,x99925,x99926)))
% 188.07/187.98 [10029]~P26(x100291,x100292,f323(f323(f301(f864(x100291)),f323(f323(f323(f90(x100291),x100293),x100294),x100296)),f188(f872(f864(x100291),a860))))+P26(x100291,x100292,f323(f323(f301(f864(x100291)),f323(f323(f323(f90(x100291),x100293),x100294),x100295)),f188(f872(f864(x100291),a860))))+~P101(f323(f323(x100295,f777(x100295,x100296,x100294,x100293,x100292,x100291)),f819(x100295,x100296,x100294,x100293,x100292,x100291)))
% 188.07/187.98 [10030]~P26(x100301,x100302,f323(f323(f301(f864(x100301)),f323(f323(f323(f90(x100301),x100306),x100304),x100305)),f188(f872(f864(x100301),a860))))+P26(x100301,x100302,f323(f323(f301(f864(x100301)),f323(f323(f323(f90(x100301),x100303),x100304),x100305)),f188(f872(f864(x100301),a860))))+~P101(f323(f323(x100306,f851(x100303,x100305,x100304,x100306,x100302,x100301)),f858(x100303,x100305,x100304,x100306,x100302,x100301)))
% 188.07/187.98 [10064]~P101(f323(f323(f237(f872(x100642,a860)),f323(x100644,f716(x100646,x100644,x100642,x100645,x100643,x100641))),f323(x100646,f716(x100646,x100644,x100642,x100645,x100643,x100641))))+~P101(f323(f323(f237(f872(x100641,a860)),x100643),x100645))+P101(f323(f323(f237(f872(f871(x100641,x100642),a860)),f323(f323(f260(x100641,x100642),x100643),x100644)),f323(f323(f260(x100641,x100642),x100645),x100646)))
% 188.07/187.98 [7702]~P101(f323(x77021,x77025))+~P101(f323(x77026,x77024))+P101(f323(x77021,f323(f261(x77022,x77023),f323(f323(f258(x77022,x77023),x77024),x77025))))
% 188.07/187.98 [7703]~P101(f323(x77031,x77034))+~P101(f323(x77036,x77035))+P101(f323(x77031,f323(f257(x77032,x77033),f323(f323(f258(x77032,x77033),x77034),x77035))))
% 188.07/187.98 [7724]~E(f323(f189(f866(x77241)),x77243),f323(f189(f866(x77244)),x77245))+~E(f323(f323(f179(x77241,x77244),f323(f323(f175(x77241,x77244),x77243),x77245)),x77242),f323(f230(x77244),x77246))+P101(f323(f323(f325(x77241),x77242),f323(f166(x77241),x77243)))
% 188.07/187.98 [7752]~P101(f323(f323(x77524,x77526),x77525))+~P101(f323(f323(f325(x77521),x77526),x77523))+P101(f323(f323(f323(f39(x77521,f872(x77522,a860)),x77523),x77524),x77525))
% 188.07/187.98 [8055]~P101(f323(f323(f325(x80551),x80552),f323(x80555,x80556)))+~P101(f323(f323(f325(x80553),x80556),x80554))+P101(f323(f323(f325(x80551),x80552),f323(f323(f39(x80553,f872(x80551,a860)),x80554),x80555)))
% 188.07/187.98 [8097]P101(f323(f323(x80971,x80972),x80973))+~P101(f323(f323(x80974,x80972),x80973))+~P101(f323(f323(f237(f872(x80975,f872(x80976,a860))),x80974),x80971))
% 188.07/187.98 [8242]P101(f323(f323(x82421,x82422),x82423))+~P101(f323(f323(f325(x82424),x82422),x82425))+~P101(f323(f323(f323(f40(x82424,f872(x82426,a860)),x82425),x82421),x82423))
% 188.07/187.98 [8381]P101(f323(f323(f325(x83811),x83812),f323(x83813,x83814)))+~P101(f323(f323(f325(x83815),x83814),x83816))+~P101(f323(f323(f325(x83811),x83812),f323(f323(f40(x83815,f872(x83811,a860)),x83816),x83813)))
% 188.07/187.98 [8646]~P14(x86464,x86465,x86466,x86461)+E(f323(x86461,x86462),f323(x86461,x86463))+~P101(f323(f323(f325(f871(x86464,x86464)),f323(f323(f258(x86464,x86464),x86462),x86463)),x86466))
% 188.07/187.98 [8680]P101(f323(f323(f237(f872(x86801,a860)),x86802),f323(x86803,x86804)))+~P101(f323(f323(f325(x86805),x86804),x86806))+~P101(f323(f323(f237(f872(x86801,a860)),x86802),f323(f323(f40(x86805,f872(x86801,a860)),x86806),x86803)))
% 188.07/187.98 [8714]~P51(x87143,x87144,f323(f278(x87144,x87143),x87145))+E(x87141,f188(f872(x87142,a860)))+E(f323(f323(f40(x87142,f872(x87143,a860)),x87141),f323(f323(f8(f872(x87144,a860),f872(x87143,a860),x87142),f277(x87144,x87143,x87145)),x87146)),f323(f277(x87144,x87143,x87145),f323(f323(f40(x87142,f872(x87144,a860)),x87141),x87146)))
% 188.07/187.98 [8793]P101(f323(f323(f325(x87931),x87932),f323(f277(x87933,x87931,x87934),x87935)))+~P101(f323(f323(f325(x87933),x87936),x87935))+~P101(f323(f323(f325(f871(x87933,x87931)),f323(f323(f258(x87933,x87931),x87936),x87932)),x87934))
% 188.07/187.98 [9097]P101(f323(f323(f237(f872(x90971,a860)),f323(f277(x90972,x90971,x90973),x90974)),f323(f277(x90972,x90971,x90975),x90976)))+~P101(f323(f323(f237(f872(x90972,a860)),x90974),x90976))+~P101(f323(f323(f237(f872(f871(x90972,x90971),a860)),x90973),x90975))
% 188.07/187.98 [9278]~P101(f323(f323(f325(x92782),x92786),x92784))+~P101(f323(f323(f237(f872(x92781,a860)),x92783),x92785))+P101(f323(f323(f237(f872(f871(x92781,x92782),a860)),f323(f323(f260(x92781,x92782),x92783),f323(f16(f872(x92782,a860),x92781),x92784))),f323(f323(f260(x92781,x92782),x92785),f323(f16(f872(x92782,a860),x92781),x92784))))
% 188.07/187.98 [9291]~P35(x92911,x92912,x92913,x92915,x92916)+P101(f323(f323(f262(x92911,x92912,a860),x92913),x92914))+~P101(f323(f323(f325(f871(x92911,x92912)),x92914),f323(f166(f871(x92911,x92912)),f323(f323(f175(x92911,x92912),x92915),x92916))))
% 188.07/187.98 [9424]~E(x94243,x94245)+P101(f323(f323(f325(f871(f866(x94241),f866(x94241))),f323(f323(f258(f866(x94241),f866(x94241)),f323(f323(f144(x94241),x94242),x94243)),f323(f323(f144(x94241),x94244),x94245))),f150(x94241,x94246)))+~P101(f323(f323(f325(f871(x94241,x94241)),f323(f323(f258(x94241,x94241),x94242),x94244)),x94246))
% 188.07/187.98 [9431]~E(f323(f189(f866(x94311)),x94315),f323(f189(f866(x94312)),x94316))+E(f181(x94311,x94312,f182(x94311,x94312,x94313,f323(f323(f22(f872(x94311,a860)),x94314),f323(f166(x94311),x94315))),x94315,x94316),f182(x94311,x94312,f181(x94311,x94312,x94313,x94315,x94316),x94314))+~P101(f323(f323(f237(f872(x94311,a860)),f323(f166(x94311),x94315)),x94314))
% 188.07/187.98 [9432]~E(f323(f189(f866(x94321)),x94323),f323(f189(f866(x94321)),x94325))+P101(f323(f323(f325(f871(f866(x94321),f866(x94321))),f323(f323(f258(f866(x94321),f866(x94321)),f323(f323(f144(x94321),x94322),x94323)),f323(f323(f144(x94321),x94324),x94325))),f138(x94321,x94326)))+~P101(f323(f323(f325(f871(x94321,x94321)),f323(f323(f258(x94321,x94321),x94322),x94324)),x94326))
% 188.07/187.98 [9464]P101(f323(f323(f325(f871(x94641,x94641)),f323(f323(f258(x94641,x94641),x94642),x94643)),f323(f323(f183(f871(x94641,x94641),a860),f323(a112,x94644)),x94645)))+~P101(f323(f323(f325(f871(x94641,x94641)),f323(f323(f258(x94641,x94641),x94646),x94643)),x94645))+~P101(f323(f323(f325(f871(x94641,x94641)),f323(f323(f258(x94641,x94641),x94642),x94646)),f323(f323(f183(f871(x94641,x94641),a860),x94644),x94645)))
% 188.07/187.98 [9465]P101(f323(f323(f325(f871(x94651,x94651)),f323(f323(f258(x94651,x94651),x94652),x94653)),f323(f323(f183(f871(x94651,x94651),a860),f323(a112,x94654)),x94655)))+~P101(f323(f323(f325(f871(x94651,x94651)),f323(f323(f258(x94651,x94651),x94652),x94656)),x94655))+~P101(f323(f323(f325(f871(x94651,x94651)),f323(f323(f258(x94651,x94651),x94656),x94653)),f323(f323(f183(f871(x94651,x94651),a860),x94654),x94655)))
% 188.07/187.98 [9468]~P101(f323(f323(f325(x94684),x94685),x94686))+P101(f323(f323(f237(f872(x94681,a860)),x94682),x94683))+~P101(f323(f323(f237(f872(f871(x94681,x94684),a860)),f323(f323(f260(x94681,x94684),x94682),f323(f16(f872(x94684,a860),x94681),x94686))),f323(f323(f260(x94681,x94684),x94683),f323(f16(f872(x94684,a860),x94681),x94686))))
% 188.07/187.98 [9513]E(x95131,x95132)+~P101(f323(f323(f325(f871(f866(x95133),f866(x95133))),f323(f323(f258(f866(x95133),f866(x95133)),f323(f323(f144(x95133),x95131),x95135)),f323(f323(f144(x95133),x95132),x95136))),f138(x95133,x95134)))+P101(f323(f323(f325(f871(x95133,x95133)),f323(f323(f258(x95133,x95133),x95131),x95132)),x95134))
% 188.07/187.98 [9514]E(x95141,x95142)+~P101(f323(f323(f325(f871(f866(x95143),f866(x95143))),f323(f323(f258(f866(x95143),f866(x95143)),f323(f323(f144(x95143),x95141),x95145)),f323(f323(f144(x95143),x95142),x95146))),f140(x95143,x95144)))+P101(f323(f323(f325(f871(x95143,x95143)),f323(f323(f258(x95143,x95143),x95141),x95142)),x95144))
% 188.07/187.98 [9515]E(x95151,x95152)+~P101(f323(f323(f325(f871(f866(x95153),f866(x95153))),f323(f323(f258(f866(x95153),f866(x95153)),f323(f323(f144(x95153),x95151),x95155)),f323(f323(f144(x95153),x95152),x95156))),f150(x95153,x95154)))+P101(f323(f323(f325(f871(x95153,x95153)),f323(f323(f258(x95153,x95153),x95151),x95152)),x95154))
% 188.07/187.98 [9551]P101(f323(f323(f325(f871(f866(x95511),f866(x95511))),f323(f323(f258(f866(x95511),f866(x95511)),f323(f323(f144(x95511),x95512),x95513)),f323(f323(f144(x95511),x95514),x95515))),f151(x95511,x95516)))+~P101(f323(f323(f325(f871(f866(x95511),f866(x95511))),f323(f323(f258(f866(x95511),f866(x95511)),x95513),x95515)),f151(x95511,x95516)))+~P101(f323(f323(f325(f871(x95511,x95511)),f323(f323(f258(x95511,x95511),x95512),x95514)),x95516))
% 188.07/187.98 [9570]P101(f323(x95701,x95702))+~P101(f323(x95701,f449(x95701,x95703,x95704,x95705,x95706)))+~P101(f323(f323(f325(x95706),x95702),f323(f323(f39(x95705,f872(x95706,a860)),x95704),x95703)))
% 188.07/187.98 [9575]~P101(f323(f323(f325(f871(f866(x95751),f866(x95751))),f323(f323(f258(f866(x95751),f866(x95751)),f323(f323(f144(x95751),x95752),x95755)),f323(f323(f144(x95751),x95753),x95756))),f138(x95751,x95754)))+P101(f323(f323(f325(f871(f866(x95751),f866(x95751))),f323(f323(f258(f866(x95751),f866(x95751)),x95755),x95756)),f138(x95751,x95754)))+P101(f323(f323(f325(f871(x95751,x95751)),f323(f323(f258(x95751,x95751),x95752),x95753)),x95754))
% 188.07/187.98 [9576]~P101(f323(f323(f325(f871(f866(x95761),f866(x95761))),f323(f323(f258(f866(x95761),f866(x95761)),f323(f323(f144(x95761),x95762),x95765)),f323(f323(f144(x95761),x95763),x95766))),f140(x95761,x95764)))+P101(f323(f323(f325(f871(f866(x95761),f866(x95761))),f323(f323(f258(f866(x95761),f866(x95761)),x95765),x95766)),f140(x95761,x95764)))+P101(f323(f323(f325(f871(x95761,x95761)),f323(f323(f258(x95761,x95761),x95762),x95763)),x95764))
% 188.07/187.98 [9577]~P101(f323(f323(f325(f871(f866(x95771),f866(x95771))),f323(f323(f258(f866(x95771),f866(x95771)),f323(f323(f144(x95771),x95772),x95775)),f323(f323(f144(x95771),x95773),x95776))),f150(x95771,x95774)))+P101(f323(f323(f325(f871(f866(x95771),f866(x95771))),f323(f323(f258(f866(x95771),f866(x95771)),x95775),x95776)),f150(x95771,x95774)))+P101(f323(f323(f325(f871(x95771,x95771)),f323(f323(f258(x95771,x95771),x95772),x95773)),x95774))
% 188.07/187.98 [9662]P101(f323(x96621,x96622))+P101(f323(f323(f325(x96623),f450(x96621,x96624,x96625,x96623,x96626)),x96625))+~P101(f323(f323(f325(x96626),x96622),f323(f323(f39(x96623,f872(x96626,a860)),x96625),x96624)))
% 188.07/187.98 [9673]~E(x96732,x96734)+P101(f323(f323(f325(f871(f866(x96731),f866(x96731))),f323(f323(f258(f866(x96731),f866(x96731)),f323(f323(f121(x96731),x96732),f323(f323(f144(x96731),x96733),f113(x96731)))),f323(f323(f121(x96731),x96734),f323(f323(f144(x96731),x96735),f113(x96731))))),f150(x96731,x96736)))+~P101(f323(f323(f325(f871(x96731,x96731)),f323(f323(f258(x96731,x96731),x96733),x96735)),x96736))
% 188.07/187.98 [9760]E(x97601,x97602)+~P101(f323(f323(f325(f871(f866(x97603),f866(x97603))),f323(f323(f258(f866(x97603),f866(x97603)),f323(f323(f121(x97603),x97605),f323(f323(f144(x97603),x97601),f113(x97603)))),f323(f323(f121(x97603),x97606),f323(f323(f144(x97603),x97602),f113(x97603))))),f150(x97603,x97604)))+P101(f323(f323(f325(f871(x97603,x97603)),f323(f323(f258(x97603,x97603),x97601),x97602)),x97604))
% 188.07/187.98 [9788]~P101(f323(f323(f325(f871(f866(x97881),f866(x97881))),f323(f323(f258(f866(x97881),f866(x97881)),f323(f323(f121(x97881),x97885),f323(f323(f144(x97881),x97882),f113(x97881)))),f323(f323(f121(x97881),x97886),f323(f323(f144(x97881),x97883),f113(x97881))))),f150(x97881,x97884)))+P101(f323(f323(f325(f871(f866(x97881),f866(x97881))),f323(f323(f258(f866(x97881),f866(x97881)),x97885),x97886)),f150(x97881,x97884)))+P101(f323(f323(f325(f871(x97881,x97881)),f323(f323(f258(x97881,x97881),x97882),x97883)),x97884))
% 188.07/187.98 [9808]P101(f323(x98081,x98082))+P101(f323(f323(f325(x98083),f449(x98081,x98084,x98085,x98086,x98083)),f323(x98084,f450(x98081,x98084,x98085,x98086,x98083))))+~P101(f323(f323(f325(x98083),x98082),f323(f323(f39(x98086,f872(x98083,a860)),x98085),x98084)))
% 188.07/187.98 [8808]~P18(x88083,x88084,x88081)+~P101(f323(f59(x88083),x88086))+E(f323(f323(x88081,x88082),f323(f323(f62(x88083,x88084,x88081),x88085),f323(f323(f22(f872(x88083,a860)),x88086),f323(f323(f301(x88083),x88082),f188(f872(x88083,a860)))))),f323(f323(f62(x88083,x88084,x88081),x88085),f323(f323(f301(x88083),x88082),x88086)))
% 188.07/187.98 [8892]~E(f323(f323(f179(x88921,x88922),x88924),x88925),f323(f230(x88922),x88926))+~P101(f323(f323(x88923,x88925),x88926))+E(f323(f323(f179(x88921,x88922),f323(f129(f871(x88921,x88922),f323(f262(x88921,x88922,a860),x88923)),x88924)),x88925),f323(f230(x88922),x88926))
% 188.07/187.98 [9104]~P101(f323(f323(f325(x91045),x91043),x91046))+P101(f323(f323(f237(f872(x91041,a860)),f323(x91042,x91043)),x91044))+~P101(f323(f323(f237(f872(x91041,a860)),f323(f323(f39(x91045,f872(x91041,a860)),x91046),x91042)),x91044))
% 188.07/187.98 [9733]~P9(x97331,x97335,x97334)+P101(f323(f323(f325(f871(x97331,x97331)),f323(f323(f258(x97331,x97331),x97332),x97333)),x97334))+~P101(f323(f323(f325(x97331),x97336),f323(f323(f101(f872(x97331,a860)),f323(f277(x97331,x97331,x97334),f323(f323(f301(x97331),x97332),f188(f872(x97331,a860))))),f323(f277(x97331,x97331,x97334),f323(f323(f301(x97331),x97333),f188(f872(x97331,a860)))))))
% 188.07/187.98 [8531]~P107(x85312)+~E(f323(f323(f78(x85312),f323(f323(f79(x85312),x85314),x85315)),x85311),f323(f323(f78(x85312),f323(f323(f79(x85312),x85313),x85315)),x85316))+E(x85311,f323(f323(f78(x85312),f323(f323(f79(x85312),f323(f323(f22(x85312),x85313),x85314)),x85315)),x85316))
% 188.07/187.98 [8532]~P107(x85321)+~E(f323(f323(f78(x85321),f323(f323(f79(x85321),x85322),x85324)),x85325),f323(f323(f78(x85321),f323(f323(f79(x85321),x85323),x85324)),x85326))+E(f323(f323(f78(x85321),f323(f323(f79(x85321),f323(f323(f22(x85321),x85322),x85323)),x85324)),x85325),x85326)
% 188.07/187.98 [8717]~P107(x87171)+E(f323(f323(f78(x87171),f323(f323(f79(x87171),x87172),x87173)),x87174),f323(f323(f78(x87171),f323(f323(f79(x87171),x87175),x87173)),x87176))+~E(x87176,f323(f323(f78(x87171),f323(f323(f79(x87171),f323(f323(f22(x87171),x87172),x87175)),x87173)),x87174))
% 188.07/187.98 [8718]~P107(x87181)+E(f323(f323(f78(x87181),f323(f323(f79(x87181),x87182),x87183)),x87184),f323(f323(f78(x87181),f323(f323(f79(x87181),x87185),x87183)),x87186))+~E(f323(f323(f78(x87181),f323(f323(f79(x87181),f323(f323(f22(x87181),x87182),x87185)),x87183)),x87184),x87186)
% 188.07/187.98 [9043]~P101(f323(f323(x90434,x90435),x90436))+~P101(f323(f323(x90433,x90435),x90436))+P101(f323(f323(f323(f323(f101(f872(x90431,f872(x90432,a860))),x90433),x90434),x90435),x90436))
% 188.07/187.98 [9300]P101(f323(f323(x93001,x93002),x93003))+P101(f323(f323(x93004,x93002),x93003))+~P101(f323(f323(f323(f323(f110(f872(x93005,f872(x93006,a860))),x93004),x93001),x93002),x93003))
% 188.07/187.98 [9590]~P122(x95901)+~P101(f323(f323(f237(x95901),f323(f323(f78(x95901),f323(f323(f79(x95901),x95904),x95905)),x95902)),f323(f323(f78(x95901),f323(f323(f79(x95901),x95903),x95905)),x95906)))+P101(f323(f323(f237(x95901),x95902),f323(f323(f78(x95901),f323(f323(f79(x95901),f323(f323(f22(x95901),x95903),x95904)),x95905)),x95906)))
% 188.07/187.98 [9591]~P122(x95911)+~P101(f323(f323(f238(x95911),f323(f323(f78(x95911),f323(f323(f79(x95911),x95914),x95915)),x95912)),f323(f323(f78(x95911),f323(f323(f79(x95911),x95913),x95915)),x95916)))+P101(f323(f323(f238(x95911),x95912),f323(f323(f78(x95911),f323(f323(f79(x95911),f323(f323(f22(x95911),x95913),x95914)),x95915)),x95916)))
% 188.07/187.98 [9614]~P122(x96141)+P101(f323(f323(f237(x96141),f323(f323(f78(x96141),f323(f323(f79(x96141),x96142),x96143)),x96144)),f323(f323(f78(x96141),f323(f323(f79(x96141),x96145),x96143)),x96146)))+~P101(f323(f323(f237(x96141),x96144),f323(f323(f78(x96141),f323(f323(f79(x96141),f323(f323(f22(x96141),x96145),x96142)),x96143)),x96146)))
% 188.07/187.98 [9615]~P122(x96151)+P101(f323(f323(f238(x96151),f323(f323(f78(x96151),f323(f323(f79(x96151),x96152),x96153)),x96154)),f323(f323(f78(x96151),f323(f323(f79(x96151),x96155),x96153)),x96156)))+~P101(f323(f323(f238(x96151),x96154),f323(f323(f78(x96151),f323(f323(f79(x96151),f323(f323(f22(x96151),x96155),x96152)),x96153)),x96156)))
% 188.07/187.98 [9721]~P122(x97211)+~P101(f323(f323(f237(x97211),f323(f323(f78(x97211),f323(f323(f79(x97211),x97212),x97214)),x97215)),f323(f323(f78(x97211),f323(f323(f79(x97211),x97213),x97214)),x97216)))+P101(f323(f323(f237(x97211),f323(f323(f78(x97211),f323(f323(f79(x97211),f323(f323(f22(x97211),x97212),x97213)),x97214)),x97215)),x97216))
% 188.07/187.98 [9722]~P122(x97221)+~P101(f323(f323(f238(x97221),f323(f323(f78(x97221),f323(f323(f79(x97221),x97222),x97224)),x97225)),f323(f323(f78(x97221),f323(f323(f79(x97221),x97223),x97224)),x97226)))+P101(f323(f323(f238(x97221),f323(f323(f78(x97221),f323(f323(f79(x97221),f323(f323(f22(x97221),x97222),x97223)),x97224)),x97225)),x97226))
% 188.07/187.98 [9771]~P122(x97711)+P101(f323(f323(f237(x97711),f323(f323(f78(x97711),f323(f323(f79(x97711),x97712),x97713)),x97714)),f323(f323(f78(x97711),f323(f323(f79(x97711),x97715),x97713)),x97716)))+~P101(f323(f323(f237(x97711),f323(f323(f78(x97711),f323(f323(f79(x97711),f323(f323(f22(x97711),x97712),x97715)),x97713)),x97714)),x97716))
% 188.07/187.98 [9772]~P122(x97721)+P101(f323(f323(f238(x97721),f323(f323(f78(x97721),f323(f323(f79(x97721),x97722),x97723)),x97724)),f323(f323(f78(x97721),f323(f323(f79(x97721),x97725),x97723)),x97726)))+~P101(f323(f323(f238(x97721),f323(f323(f78(x97721),f323(f323(f79(x97721),f323(f323(f22(x97721),x97722),x97725)),x97723)),x97724)),x97726))
% 188.07/187.98 [9942]~P72(x99422)+~P101(f323(f59(x99421),x99426))+E(f323(f323(f6(x99421,x99422),f323(f323(f18(x99421,x99422,x99422),f323(f323(f18(x99421,x99422,f872(x99422,x99422)),f323(f323(f8(a860,f872(x99422,f872(x99422,x99422)),x99421),f96(x99422)),x99423)),x99424)),x99425)),x99426),f323(f323(f78(x99422),f323(f323(f6(x99421,x99422),x99424),f323(f323(f101(f872(x99421,a860)),x99426),f323(f243(x99421),x99423)))),f323(f323(f6(x99421,x99422),x99425),f323(f323(f101(f872(x99421,a860)),x99426),f323(f77(f872(x99421,a860)),f323(f243(x99421),x99423))))))
% 188.07/187.98 [10000]P101(f323(f323(f325(x100002),x100004),x100006))+P101(f323(f323(f325(x100002),x100005),x100006))+E(f323(f303(x100001,x100002,f323(f323(f7(x100001,x100002,x100002),f323(f323(f7(x100001,x100002,f872(x100002,x100002)),f323(f323(f8(a860,f872(x100002,f872(x100002,x100002)),x100001),f96(x100002)),f323(f323(f7(x100001,f872(x100001,a860),a860),f325(x100001)),x100003))),x100004)),x100005)),x100006),f188(f872(x100001,a860)))
% 188.07/187.98 [10001]P101(f323(f323(f325(x100012),x100015),x100016))+~P101(f323(f323(f325(x100012),x100014),x100016))+E(f323(f303(x100011,x100012,f323(f323(f7(x100011,x100012,x100012),f323(f323(f7(x100011,x100012,f872(x100012,x100012)),f323(f323(f8(a860,f872(x100012,f872(x100012,x100012)),x100011),f96(x100012)),f323(f323(f7(x100011,f872(x100011,a860),a860),f325(x100011)),x100013))),x100014)),x100015)),x100016),x100013)
% 188.07/187.98 [10002]P101(f323(f323(f325(x100022),x100024),x100026))+~P101(f323(f323(f325(x100022),x100025),x100026))+E(f323(f303(x100021,x100022,f323(f323(f7(x100021,x100022,x100022),f323(f323(f7(x100021,x100022,f872(x100022,x100022)),f323(f323(f8(a860,f872(x100022,f872(x100022,x100022)),x100021),f96(x100022)),f323(f323(f7(x100021,f872(x100021,a860),a860),f325(x100021)),x100023))),x100024)),x100025)),x100026),f323(f77(f872(x100021,a860)),x100023))
% 188.07/187.98 [10003]~P101(f323(f323(f325(x100032),x100034),x100036))+~P101(f323(f323(f325(x100032),x100035),x100036))+E(f323(f303(x100031,x100032,f323(f323(f7(x100031,x100032,x100032),f323(f323(f7(x100031,x100032,f872(x100032,x100032)),f323(f323(f8(a860,f872(x100032,f872(x100032,x100032)),x100031),f96(x100032)),f323(f323(f7(x100031,f872(x100031,a860),a860),f325(x100031)),x100033))),x100034)),x100035)),x100036),f246(f872(x100031,a860)))
% 188.07/187.98 [8565]E(x85651,x85652)+~P53(x85654,x85655,x85653,x85656,x85657)+~E(f323(x85653,x85651),f323(x85653,x85652))
% 188.07/187.98 [6964]E(f323(f232(f869(x69641),x69642,f200(x69641),x69643),f323(x69644,x69645)),f323(f230(x69641),x69646))+~E(f323(x69644,x69645),f323(f230(x69642),x69647))+~E(f323(x69643,x69647),f323(f230(x69641),x69646))
% 188.07/187.98 [8594]~P11(x85946,x85945,x85947,x85944,x85941)+E(f323(f323(x85941,x85942),x85943),x85944)+P101(f323(f59(x85945),x85943))
% 188.07/187.98 [9455]P43(x94551,x94552,x94553,x94554,x94555,f323(f323(x94553,x94556),x94557))+~E(f323(f323(x94553,x94556),x94557),x94554)+~E(x94555,f188(f872(x94551,a860)))
% 188.07/187.98 [9636]~P101(f323(x96366,x96363))+~P101(f323(f323(f325(f871(x96362,x96362)),f323(f323(f258(x96362,x96362),x96364),x96365)),f323(x96367,x96363)))+P101(f323(f323(f325(f871(f871(x96361,x96362),f871(x96361,x96362))),f323(f323(f258(f871(x96361,x96362),f871(x96361,x96362)),f323(f323(f258(x96361,x96362),x96363),x96364)),f323(f323(f258(x96361,x96362),x96363),x96365))),f275(x96361,x96362,x96366,x96367)))
% 188.07/187.98 [10055]~P43(x100552,x100557,x100553,x100556,x100551,f323(f323(x100553,x100555),x100554))+E(f323(f323(x100553,f620(x100554,x100555,x100551,x100556,x100553,x100557,x100552)),f629(x100554,x100555,x100551,x100556,x100553,x100557,x100552)),f323(f323(x100553,x100555),x100554))+E(x100551,f188(f872(x100552,a860)))
% 188.07/187.98 [10056]~P43(x100567,x100566,x100561,x100564,x100565,f323(f323(x100561,x100562),x100563))+E(f323(f323(x100561,f620(x100563,x100562,x100565,x100564,x100561,x100566,x100567)),f629(x100563,x100562,x100565,x100564,x100561,x100566,x100567)),f323(f323(x100561,x100562),x100563))+E(f323(f323(x100561,x100562),x100563),x100564)
% 188.07/187.98 [9139]~P35(x91391,x91392,x91393,x91395,x91397)+P35(x91391,x91392,x91393,f323(f323(f144(x91391),x91394),x91395),f323(f323(f144(x91392),x91396),x91397))+~P101(f323(f323(x91393,x91394),x91396))
% 188.07/187.98 [9159]P35(x91591,x91592,x91593,x91594,x91595)+~P35(x91591,x91592,x91593,f323(f323(f121(x91591),x91596),x91594),f323(f323(f121(x91592),x91597),x91595))+~E(f323(f189(f866(x91591)),x91596),f323(f189(f866(x91592)),x91597))
% 188.07/187.98 [9160]P35(x91601,x91602,x91603,x91604,x91605)+~P35(x91601,x91602,x91603,f323(f323(f121(x91601),x91604),x91606),f323(f323(f121(x91602),x91605),x91607))+~E(f323(f189(f866(x91601)),x91604),f323(f189(f866(x91602)),x91605))
% 188.07/187.98 [9362]~P35(x93621,x93622,x93623,x93625,x93627)+~P35(x93621,x93622,x93623,x93624,x93626)+P35(x93621,x93622,x93623,f323(f323(f121(x93621),x93624),x93625),f323(f323(f121(x93622),x93626),x93627))
% 188.07/187.98 [9710]~P101(f323(f64(x97101,x97104,x97105,x97106,x97103),x97107))+P101(f323(f64(x97101,x97104,x97105,x97106,f323(f323(f301(x97101),x97102),x97103)),f323(f323(x97105,x97102),x97107)))+P101(f323(f323(f325(x97101),x97102),x97103))
% 188.07/187.98 [9840]~P27(x98403,x98401,x98404,f246(f872(x98403,a860)))+E(f323(f323(f179(x98401,x98402),f323(f323(f147(f871(x98403,x98402),f871(x98401,x98402)),f323(f262(x98403,x98402,f871(x98401,x98402)),f323(f323(f8(x98401,f872(x98402,f871(x98401,x98402)),x98403),f258(x98401,x98402)),x98404))),x98405)),f323(x98404,x98406)),f323(f230(x98402),x98407))+~E(f323(f323(f179(x98403,x98402),x98405),x98406),f323(f230(x98402),x98407))
% 188.07/187.98 [10076]~P43(x100762,x100767,x100766,x100765,x100761,f323(f323(x100766,x100764),x100763))+E(x100761,f188(f872(x100762,a860)))+P101(f323(f323(f325(x100762),f620(x100763,x100764,x100761,x100765,x100766,x100767,x100762)),x100761))
% 188.07/187.98 [10077]~P43(x100775,x100777,x100771,x100774,x100776,f323(f323(x100771,x100772),x100773))+E(f323(f323(x100771,x100772),x100773),x100774)+P101(f323(f323(f325(x100775),f620(x100773,x100772,x100776,x100774,x100771,x100777,x100775)),x100776))
% 188.07/187.98 [6754]~E(x67545,x67547)+~E(x67546,x67544)+E(f323(f323(f323(f323(f70(x67541,f869(x67542)),x67543),x67544),f323(f230(x67542),x67545)),x67546),f323(f230(x67542),x67547))
% 188.07/187.98 [6880]E(x68801,x68802)+~E(f323(x68805,x68801),f323(f230(x68804),x68807))+E(f323(f323(f323(f323(f70(x68803,f869(x68804)),x68805),x68802),f323(f230(x68804),x68806)),x68801),f323(f230(x68804),x68807))
% 188.07/187.98 [7592]E(x75921,x75922)+~E(x75923,x75924)+~E(f323(f323(f323(f323(f70(x75925,f869(x75926)),x75927),x75924),f323(f230(x75926),x75921)),x75923),f323(f230(x75926),x75922))
% 188.07/187.98 [7658]E(x76581,x76582)+E(f323(x76583,x76584),f323(f230(x76585),x76581))+~E(f323(f323(f323(f323(f70(x76586,f869(x76585)),x76583),x76587),f323(f230(x76585),x76582)),x76584),f323(f230(x76585),x76581))
% 188.07/187.98 [7659]E(x76591,x76592)+E(f323(x76593,x76591),f323(f230(x76594),x76595))+~E(f323(f323(f323(f323(f70(x76596,f869(x76594)),x76593),x76592),f323(f230(x76594),x76597)),x76591),f323(f230(x76594),x76595))
% 188.07/187.98 [8832]~P23(x88324,x88325,x88326,x88327,x88321)+~P101(f323(f59(x88325),x88323))+E(f323(f323(x88321,x88322),x88323),f323(f323(f323(f63(x88324,x88325,x88326),x88322),x88327),x88323))
% 188.07/187.98 [8833]~P11(x88334,x88335,x88336,x88337,x88331)+~P101(f323(f59(x88335),x88333))+E(f323(f323(x88331,x88332),x88333),f323(f323(f323(f63(x88334,x88335,x88336),x88332),x88337),x88333))
% 188.07/187.98 [9417]~P26(x94171,x94172,f323(f323(f301(f864(x94171)),f323(f323(f323(f90(x94171),x94173),x94174),x94177)),f188(f872(f864(x94171),a860))))+P26(x94171,x94172,f323(f323(f301(f864(x94171)),f323(f323(f323(f90(x94171),x94173),f30(x94174,x94175)),x94176)),f188(f872(f864(x94171),a860))))+~P26(x94171,x94172,f323(f323(f301(f864(x94171)),f323(f323(f323(f90(x94171),x94177),x94175),x94176)),f188(f872(f864(x94171),a860))))
% 188.07/187.98 [9609]~P25(x96093,x96094,x96095,x96097,x96096,x96091)+~P101(f323(f59(x96094),x96092))+E(f323(x96091,x96092),f323(f323(f323(f63(x96093,x96094,x96095),x96096),x96097),x96092))
% 188.07/187.98 [9766]P43(x97661,x97662,x97663,x97664,x97665,f323(f323(x97663,x97666),x97667))+~P43(x97661,x97662,x97663,x97664,f323(f323(f22(f872(x97661,a860)),x97665),f323(f323(f301(x97661),x97666),f188(f872(x97661,a860)))),x97667)+~P101(f323(f323(f325(x97661),x97666),x97665))
% 188.07/187.98 [10031]~P26(x100311,x100312,f323(f323(f301(f864(x100311)),f323(f323(f323(f90(x100311),f92(x100311,x100313,x100314)),x100315),x100317)),f188(f872(f864(x100311),a860))))+P26(x100311,x100312,f323(f323(f301(f864(x100311)),f323(f323(f323(f90(x100311),x100313),f27(x100314,x100315,x100316)),x100317)),f188(f872(f864(x100311),a860))))+~P26(x100311,x100312,f323(f323(f301(f864(x100311)),f323(f323(f323(f90(x100311),f92(x100311,x100313,f323(f71(a860,a860,a861,a318),x100314))),x100316),x100317)),f188(f872(f864(x100311),a860))))
% 188.07/187.98 [10094]P26(x100947,x100946,f323(f323(f301(f864(x100947)),f323(f323(f323(f90(x100947),x100941),x100944),x100942)),f188(f872(f864(x100947),a860))))+~P26(x100947,x100946,f323(f323(f301(f864(x100947)),f323(f323(f323(f90(x100947),x100945),x100944),x100943)),f188(f872(f864(x100947),a860))))+P101(f323(f323(x100941,f348(x100942,x100941,x100943,x100944,x100945,x100946,x100947)),f356(x100942,x100941,x100943,x100944,x100945,x100946,x100947)))
% 188.07/187.98 [10103]~P43(x101032,x101033,x101034,x101035,x101031,f323(f323(x101034,x101037),x101036))+P43(x101032,x101033,x101034,x101035,f323(f323(f22(f872(x101032,a860)),x101031),f323(f323(f301(x101032),f620(x101036,x101037,x101031,x101035,x101034,x101033,x101032)),f188(f872(x101032,a860)))),f629(x101036,x101037,x101031,x101035,x101034,x101033,x101032))+E(x101031,f188(f872(x101032,a860)))
% 188.07/187.98 [10104]~P43(x101045,x101046,x101041,x101044,x101047,f323(f323(x101041,x101042),x101043))+P43(x101045,x101046,x101041,x101044,f323(f323(f22(f872(x101045,a860)),x101047),f323(f323(f301(x101045),f620(x101043,x101042,x101047,x101044,x101041,x101046,x101045)),f188(f872(x101045,a860)))),f629(x101043,x101042,x101047,x101044,x101041,x101046,x101045))+E(f323(f323(x101041,x101042),x101043),x101044)
% 188.07/187.98 [10105]~P26(x101051,x101052,f323(f323(f301(f864(x101051)),f323(f323(f323(f90(x101051),x101057),x101054),x101056)),f188(f872(f864(x101051),a860))))+P26(x101051,x101052,f323(f323(f301(f864(x101051)),f323(f323(f323(f90(x101051),x101053),x101054),x101055)),f188(f872(f864(x101051),a860))))+~P101(f323(f323(x101055,f348(x101055,x101053,x101056,x101054,x101057,x101052,x101051)),f365(x101055,x101053,x101056,x101054,x101057,x101052,x101051)))
% 188.07/187.98 [10126]~P26(x101261,x101262,f323(f323(f301(f864(x101261)),f323(f323(f323(f90(x101261),x101264),x101265),x101267)),f188(f872(f864(x101261),a860))))+~P26(x101261,x101262,f323(f323(f301(f864(x101261)),f323(f323(f323(f90(x101261),x101263),x101265),x101266)),f188(f872(f864(x101261),a860))))+P26(x101261,x101262,f323(f323(f301(f864(x101261)),f323(f323(f323(f90(x101261),f323(f323(f18(x101261,f872(a861,a860),f872(a861,a860)),f323(f323(f8(f872(a861,f872(a860,a860)),f872(f872(a861,a860),f872(a861,a860)),x101261),f18(a861,a860,a860)),f323(f323(f8(f872(a861,a860),f872(a861,f872(a860,a860)),x101261),f323(f8(a860,f872(a860,a860),a861),a321)),x101263))),x101264)),x101265),f323(f323(f18(x101261,f872(a861,a860),f872(a861,a860)),f323(f323(f8(f872(a861,f872(a860,a860)),f872(f872(a861,a860),f872(a861,a860)),x101261),f18(a861,a860,a860)),f323(f323(f8(f872(a861,a860),f872(a861,f872(a860,a860)),x101261),f323(f8(a860,f872(a860,a860),a861),a321)),x101266))),x101267))),f188(f872(f864(x101261),a860))))
% 188.07/187.98 [9147]E(f181(x91471,x91472,x91473,x91474,f323(f323(f152(x91472,x91475),x91476),x91477)),f181(x91471,x91472,x91473,x91474,x91475))+~P101(f323(f323(f238(a865),x91476),f323(f189(f866(x91472)),x91475)))+~P101(f323(f323(f237(a865),f323(f189(f866(x91471)),x91474)),x91476))
% 188.07/187.98 [9440]P101(f323(f323(f237(f872(f871(x94401,x94402),a860)),f323(f323(f280(x94401,x94403,x94402),x94404),x94405)),f323(f323(f280(x94401,x94403,x94402),x94406),x94407)))+~P101(f323(f323(f237(f872(f871(x94403,x94402),a860)),x94405),x94407))+~P101(f323(f323(f237(f872(f871(x94401,x94403),a860)),x94404),x94406))
% 188.07/187.98 [9777]~P101(f323(f323(f325(x97771),x97776),x97775))+P101(f323(f64(x97771,x97772,x97773,x97774,x97775),f323(f323(x97773,x97776),x97777)))+~P101(f323(f64(x97771,x97772,x97773,x97774,f323(f323(f22(f872(x97771,a860)),x97775),f323(f323(f301(x97771),x97776),f188(f872(x97771,a860))))),x97777))
% 188.07/187.98 [10159]~P139(x101591)+~P27(f871(x101592,x101593),x101591,f323(f262(x101592,x101593,x101591),f323(f323(f7(x101592,f872(x101593,x101591),f872(x101593,x101591)),f323(f323(f8(f872(x101591,x101591),f872(f872(x101593,x101591),f872(x101593,x101591)),x101592),f8(x101591,x101591,x101593)),f323(f323(f8(x101591,f872(x101591,x101591),x101592),f79(x101591)),x101594))),x101595)),f323(f323(f260(x101592,x101593),x101596),f323(f16(f872(x101593,a860),x101592),x101597)))+E(f323(f323(f6(x101591,x101591),f32(x101591)),f323(f243(x101591),f323(f323(f8(f872(x101592,a860),a860,x101591),f85(x101592)),f323(f323(f8(f872(x101592,f872(x101593,a860)),f872(x101592,a860),x101591),f323(f8(f872(x101593,a860),a860,x101592),f85(x101593))),f323(f323(f7(x101591,f872(x101592,f872(x101593,a860)),f872(x101592,f872(x101593,a860))),f323(f323(f8(f872(x101592,f872(f872(x101593,a860),f872(x101593,a860))),f872(f872(x101592,f872(x101593,a860)),f872(x101592,f872(x101593,a860))),x101591),f18(x101592,f872(x101593,a860),f872(x101593,a860))),f323(f323(f8(f872(x101592,f872(x101593,f872(a860,a860))),f872(x101592,f872(f872(x101593,a860),f872(x101593,a860))),x101591),f323(f8(f872(x101593,f872(a860,a860)),f872(f872(x101593,a860),f872(x101593,a860)),x101592),f18(x101593,a860,a860))),f323(f323(f8(f872(x101592,f872(x101593,a860)),f872(x101592,f872(x101593,f872(a860,a860))),x101591),f323(f8(f872(x101593,a860),f872(x101593,f872(a860,a860)),x101592),f323(f8(a860,f872(a860,a860),x101593),a322))),f323(f323(f7(x101591,f872(x101592,f872(x101593,x101591)),f872(x101592,f872(x101593,a860))),f323(f323(f8(f872(f872(x101593,x101591),f872(x101593,a860)),f872(f872(x101592,f872(x101593,x101591)),f872(x101592,f872(x101593,a860))),x101591),f8(f872(x101593,x101591),f872(x101593,a860),x101592)),f323(f323(f8(f872(x101591,a860),f872(f872(x101593,x101591),f872(x101593,a860)),x101591),f8(x101591,a860,x101593)),a320))),f323(f323(f7(x101592,f872(x101593,x101591),f872(x101593,x101591)),f323(f323(f8(f872(x101591,x101591),f872(f872(x101593,x101591),f872(x101593,x101591)),x101592),f8(x101591,x101591,x101593)),f323(f323(f8(x101591,f872(x101591,x101591),x101592),f79(x101591)),x101594))),x101595)))))),f323(f323(f7(x101592,f872(x101593,a860),f872(x101593,a860)),f323(f323(f8(f872(a860,a860),f872(f872(x101593,a860),f872(x101593,a860)),x101592),f8(a860,a860,x101593)),f323(f323(f8(a860,f872(a860,a860),x101592),a322),f323(f323(f7(x101592,f872(x101592,a860),a860),f325(x101592)),x101596)))),f323(f323(f7(x101593,f872(x101593,a860),a860),f325(x101593)),x101597))))))),f323(f323(f79(x101591),f323(f323(f6(x101592,x101591),x101594),x101596)),f323(f323(f6(x101593,x101591),x101595),x101597)))
% 188.07/187.98 [9444]~P28(x94441,x94443,x94445,x94446,x94448)+~P28(x94443,x94442,x94444,x94448,x94447)+P28(x94441,x94442,f323(f71(x94443,x94442,x94441,x94444),x94445),x94446,x94447)
% 188.07/187.98 [9474]P28(x94741,x94742,x94743,x94744,x94745)+~P28(x94746,x94741,x94747,x94748,x94744)+~P28(x94746,x94742,f323(f71(x94741,x94742,x94746,x94743),x94747),x94748,x94745)
% 188.07/187.98 [9607]~P101(f323(f323(x96074,x96076),x96078))+~P101(f323(f323(x96075,x96078),x96077))+P101(f323(f323(f259(x96071,x96072,x96073,x96074,x96075),x96076),x96077))
% 188.07/187.98 [9207]~P21(x92078,x92071,x92073,x92075)+~P101(f323(f59(x92078),x92076))+E(f323(f71(x92071,x92071,x92072,f323(x92073,x92074)),f323(f71(x92071,x92071,x92072,f323(x92075,x92076)),x92077)),f323(f71(x92071,x92071,x92072,f323(x92075,x92076)),f323(f71(x92071,x92071,x92072,f323(x92073,x92074)),x92077)))
% 188.07/187.98 [9597]~P24(x95977,x95972,x95975,x95978,x95976,x95971)+~P101(f323(f59(x95972),x95974))+E(f323(x95971,f323(f323(f301(x95972),x95973),x95974)),f323(f323(x95975,f323(x95976,x95973)),f323(x95971,x95974)))
% 188.07/187.98 [9719]~P27(x97192,x97194,x97196,x97198)+~P27(x97191,x97193,x97195,x97197)+P27(f871(x97191,x97192),f871(x97193,x97194),f263(x97191,x97193,x97192,x97194,x97195,x97196),f323(f323(f260(x97191,x97192),x97197),f323(f16(f872(x97192,a860),x97191),x97198)))
% 188.07/187.98 [9386]P101(f323(f323(f325(f871(x93861,x93862)),f323(f323(f258(x93861,x93862),x93863),x93864)),f323(f323(f280(x93861,x93865,x93862),x93866),x93867)))+~P101(f323(f323(f325(f871(x93861,x93865)),f323(f323(f258(x93861,x93865),x93863),x93868)),x93866))+~P101(f323(f323(f325(f871(x93865,x93862)),f323(f323(f258(x93865,x93862),x93868),x93864)),x93867))
% 188.07/187.98 [9578]~P101(f323(f323(f237(f872(f871(x95783,x95782),a860)),x95785),f323(f323(f260(x95783,x95782),x95788),f323(f16(f872(x95782,a860),x95783),x95787))))+~P101(f323(f323(f237(f872(f871(x95781,x95783),a860)),x95784),f323(f323(f260(x95781,x95783),x95786),f323(f16(f872(x95783,a860),x95781),x95788))))+P101(f323(f323(f237(f872(f871(x95781,x95782),a860)),f323(f323(f280(x95781,x95783,x95782),x95784),x95785)),f323(f323(f260(x95781,x95782),x95786),f323(f16(f872(x95782,a860),x95781),x95787))))
% 188.07/187.98 [9631]~E(x96313,x96315)+P101(f323(f323(f325(f871(f871(x96311,x96312),f871(x96311,x96312))),f323(f323(f258(f871(x96311,x96312),f871(x96311,x96312)),f323(f323(f258(x96311,x96312),x96313),x96314)),f323(f323(f258(x96311,x96312),x96315),x96316))),f315(x96311,x96312,x96317,x96318)))+~P101(f323(f323(f325(f871(x96312,x96312)),f323(f323(f258(x96312,x96312),x96314),x96316)),x96318))
% 188.07/187.98 [9742]E(x97421,x97422)+~P101(f323(f323(f325(f871(f871(x97423,x97425),f871(x97423,x97425))),f323(f323(f258(f871(x97423,x97425),f871(x97423,x97425)),f323(f323(f258(x97423,x97425),x97421),x97426)),f323(f323(f258(x97423,x97425),x97422),x97427))),f315(x97423,x97425,x97424,x97428)))+P101(f323(f323(f325(f871(x97423,x97423)),f323(f323(f258(x97423,x97423),x97421),x97422)),x97424))
% 188.07/187.98 [9759]~P101(f323(f323(f325(f871(f871(x97591,x97595),f871(x97591,x97595))),f323(f323(f258(f871(x97591,x97595),f871(x97591,x97595)),f323(f323(f258(x97591,x97595),x97592),x97596)),f323(f323(f258(x97591,x97595),x97593),x97597))),f315(x97591,x97595,x97594,x97598)))+P101(f323(f323(f325(f871(x97591,x97591)),f323(f323(f258(x97591,x97591),x97592),x97593)),x97594))+P101(f323(f323(f325(f871(x97595,x97595)),f323(f323(f258(x97595,x97595),x97596),x97597)),x97598))
% 188.07/187.98 [9663]~P25(x96637,x96635,x96631,x96638,x96632,x96634)+~P101(f323(f59(x96635),x96636))+E(f323(f323(x96631,f323(x96632,x96633)),f323(x96634,f323(f323(f22(f872(x96635,a860)),x96636),f323(f323(f301(x96635),x96633),f188(f872(x96635,a860)))))),f323(x96634,f323(f323(f301(x96635),x96633),x96636)))
% 188.07/187.98 [9167]~P101(f323(f323(f323(x91675,x91678),x91676),x91677))+~P101(f323(f323(f325(x91671),x91678),x91674))+P101(f323(f323(f323(f323(f39(x91671,f872(x91672,f872(x91673,a860))),x91674),x91675),x91676),x91677))
% 188.07/187.98 [9373]P101(f323(f323(f323(x93731,x93732),x93733),x93734))+~P101(f323(f323(f325(x93735),x93732),x93736))+~P101(f323(f323(f323(f323(f40(x93735,f872(x93737,f872(x93738,a860))),x93736),x93731),x93733),x93734))
% 188.07/187.98 [9571]~P23(x95713,x95712,x95714,x95718,x95711)+~P101(f323(f59(x95712),x95717))+E(f323(f323(x95711,f323(f323(f18(x95712,x95713,x95713),f323(f323(f8(x95713,f872(x95713,x95713),x95712),x95714),x95715)),x95716)),x95717),f323(f323(x95714,f323(f323(x95711,x95715),x95717)),f323(f323(x95711,x95716),x95717)))
% 188.07/187.98 [9848]~E(f323(f302(x98482,x98484,x98486),x98488),x984810)+~E(f323(f302(x98481,x98483,x98485),x98487),x98489)+E(f323(f302(f871(x98481,x98482),f871(x98483,x98484),f263(x98481,x98483,x98482,x98484,x98485,x98486)),f323(f323(f260(x98481,x98482),x98487),f323(f16(f872(x98482,a860),x98481),x98488))),f323(f323(f260(x98483,x98484),x98489),f323(f16(f872(x98484,a860),x98483),x984810)))
% 188.07/187.98 [4836]~P103(x48362)+~P16(x48362,x48361)+P16(x48362,f114(x48362,x48361))+E(x48361,f113(x48362))
% 188.07/187.98 [4837]~P103(x48372)+~P16(x48372,x48371)+P16(x48372,f612(x48371,x48372))+E(x48371,f113(x48372))
% 188.07/187.98 [5068]~P6(x50682)+E(f10(x50682,x50681),f37(x50682,x50681))+E(x50681,f188(f872(x50682,a860)))+~P101(f323(f59(x50682),x50681))
% 188.07/187.98 [5069]~P6(x50692)+E(f11(x50692,x50691),f38(x50692,x50691))+E(x50691,f188(f872(x50692,a860)))+~P101(f323(f59(x50692),x50691))
% 188.07/187.98 [5218]~P103(x52182)+~P16(x52182,x52181)+E(x52181,f113(x52182))+E(f323(f323(f144(x52182),f649(x52181,x52182)),f612(x52181,x52182)),x52181)
% 188.07/187.98 [6003]~P2(x60032)+E(x60031,f188(f872(x60032,a860)))+P101(f323(f323(f237(x60032),f11(x60032,x60031)),f10(x60032,x60031)))+~P101(f323(f59(x60032),x60031))
% 188.07/187.98 [6015]~P39(x60152)+~P39(x60151)+E(x60151,x60152)+~E(f323(f302(a1,a865,a104),x60151),f323(f302(a1,a865,a104),x60152))
% 188.07/187.98 [9021]~P116(x90211)+~P101(f323(f323(f325(x90211),x90212),f109(x90211)))+P101(f323(f323(f238(x90211),f323(f323(f78(x90211),f323(f323(f78(x90211),f76(x90211)),x90212)),x90212)),f2(x90211)))+~P101(f323(f323(f238(x90211),x90212),f2(x90211)))
% 188.07/187.98 [9261]~P116(x92611)+~P101(f323(f323(f325(x92611),x92612),f109(x92611)))+~P101(f323(f323(f238(x92611),f323(f323(f78(x92611),f323(f323(f78(x92611),f76(x92611)),x92612)),x92612)),f2(x92611)))+P101(f323(f323(f238(x92611),x92612),f2(x92611)))
% 188.07/187.98 [4892]~P139(x48922)+~P110(x48922)+E(x48921,f2(a865))+E(f323(f323(f248(x48922),f2(x48922)),x48921),f2(x48922))
% 188.07/187.98 [4895]~P139(x48951)+~P110(x48951)+~E(x48952,f2(a865))+E(f323(f323(f248(x48951),f2(x48951)),x48952),f76(x48951))
% 188.07/187.98 [5055]~P133(x50552)+E(x50551,f76(x50552))+E(x50551,f323(f77(x50552),f76(x50552)))+~E(f323(f323(f79(x50552),x50551),x50551),f76(x50552))
% 188.07/187.98 [5300]~P85(x53002)+E(x53001,f2(x53002))+E(f80(x53002,x53001),f323(f77(x53002),f76(x53002)))+P101(f323(f323(f238(x53002),f2(x53002)),x53001))
% 188.07/187.98 [5533]~P85(x55332)+E(f80(x55332,x55331),f76(x55332))+E(x55331,f2(x55332))+~P101(f323(f323(f238(x55332),f2(x55332)),x55331))
% 188.07/187.98 [5542]E(x55421,x55422)+~E(f323(f103(a865),x55421),f323(f103(a865),x55422))+P101(f323(a193,f323(f103(a1),x55422)))+P101(f323(a193,f323(f103(a1),x55421)))
% 188.07/187.98 [5592]~P89(x55921)+~E(x55922,f2(x55921))+E(f323(f323(f78(x55921),x55922),x55922),f2(x55921))+~P101(f323(f323(f325(x55921),x55922),f109(x55921)))
% 188.07/187.98 [5630]E(x56301,f2(a1))+~E(f323(f323(f36(a1),x56302),x56301),f2(a1))+P101(f323(f323(f238(a1),x56301),x56302))+P101(f323(f323(f238(a1),x56302),x56301))
% 188.07/187.98 [5661]E(x56611,f2(a1))+~E(f323(f323(f36(a1),x56612),x56611),f2(a1))+P101(f323(f323(f237(a1),x56612),f2(a1)))+P101(f323(f323(f238(a1),x56612),x56611))
% 188.07/187.98 [5695]E(x56951,f2(a1))+~E(f323(f323(f36(a1),x56952),x56951),f2(a1))+P101(f323(f323(f237(a1),f2(a1)),x56952))+P101(f323(f323(f238(a1),x56951),x56952))
% 188.07/187.98 [5729]~P89(x57292)+E(x57291,f2(x57292))+~E(f323(f323(f78(x57292),x57291),x57291),f2(x57292))+~P101(f323(f323(f325(x57292),x57291),f109(x57292)))
% 188.07/187.98 [5789]E(f323(f103(a865),x57891),f323(f103(a865),x57892))+~E(f323(f103(a1),x57892),f2(a1))+P101(f323(a193,f323(f103(a1),x57892)))+~P101(f323(a193,f323(f103(a1),x57891)))
% 188.07/187.98 [5816]~E(f323(f103(a865),x58162),f323(f103(a865),x58161))+E(f323(f103(a1),x58161),f2(a1))+P101(f323(a193,f323(f103(a1),x58161)))+~P101(f323(a193,f323(f103(a1),x58162)))
% 188.07/187.98 [5825]~P103(x58252)+E(x58251,f188(f872(x58252,a860)))+~P101(f323(f59(x58252),x58251))+P101(f323(f323(f325(x58252),f14(x58252,x58251)),x58251))
% 188.07/187.98 [5826]~P103(x58262)+E(x58261,f188(f872(x58262,a860)))+~P101(f323(f59(x58262),x58261))+P101(f323(f323(f325(x58262),f15(x58262,x58261)),x58261))
% 188.07/187.98 [5983]~P116(x59831)+~P90(x59831)+P101(f323(f323(f237(x59831),f2(x59831)),f323(f103(x59831),x59832)))+~P101(f323(f323(f237(a1),a81),x59832))
% 188.07/187.98 [5984]~P116(x59841)+~P90(x59841)+P101(f323(f323(f238(x59841),f2(x59841)),f323(f103(x59841),x59842)))+~P101(f323(f323(f238(a1),a81),x59842))
% 188.07/187.98 [6002]~P116(x60021)+~P90(x60021)+E(f323(f73(x60021),f323(f103(x60021),x60022)),f323(f103(x60021),x60022))+P101(f323(f323(f238(x60021),f323(f103(x60021),x60022)),f2(x60021)))
% 188.07/187.98 [6042]E(x60421,x60422)+~E(f323(a104,x60421),f323(a104,x60422))+~P101(f323(f323(f237(a1),f2(a1)),x60422))+~P101(f323(f323(f237(a1),f2(a1)),x60421))
% 188.07/187.98 [6231]~P90(x62312)+~P116(x62312)+~P101(f323(f323(f237(x62312),f2(x62312)),f323(f103(x62312),x62311)))+P101(f323(f323(f237(a1),a81),x62311))
% 188.07/187.98 [6232]~P90(x62322)+~P116(x62322)+~P101(f323(f323(f238(x62322),f2(x62322)),f323(f103(x62322),x62321)))+P101(f323(f323(f238(a1),a81),x62321))
% 188.07/187.98 [6237]~P116(x62371)+~P90(x62371)+P101(f323(f323(f237(x62371),f323(f103(x62371),x62372)),f2(x62371)))+~P101(f323(f323(f237(a1),x62372),a81))
% 188.07/187.98 [6238]~P116(x62381)+~P90(x62381)+P101(f323(f323(f238(x62381),f323(f103(x62381),x62382)),f2(x62381)))+~P101(f323(f323(f238(a1),x62382),a81))
% 188.07/187.98 [6544]~P90(x65442)+~P116(x65442)+~P101(f323(f323(f237(x65442),f323(f103(x65442),x65441)),f2(x65442)))+P101(f323(f323(f237(a1),x65441),a81))
% 188.07/187.98 [6545]~P90(x65452)+~P116(x65452)+~P101(f323(f323(f238(x65452),f323(f103(x65452),x65451)),f2(x65452)))+P101(f323(f323(f238(a1),x65451),a81))
% 188.07/187.98 [6635]~P116(x66351)+~P90(x66351)+E(f323(f73(x66351),f323(f103(x66351),x66352)),f323(f77(x66351),f323(f103(x66351),x66352)))+~P101(f323(f323(f238(x66351),f323(f103(x66351),x66352)),f2(x66351)))
% 188.07/187.98 [6653]E(f323(f103(a865),x66531),f323(f103(a865),x66532))+~E(f323(f103(a1),x66532),f2(a1))+~P101(f323(f323(f237(a1),f323(f103(a1),x66531)),f2(a1)))+~P101(f323(a193,f323(f103(a1),x66531)))
% 188.07/187.98 [7523]~P103(x75232)+E(x75231,f188(f872(x75232,a860)))+~P101(f323(f59(x75232),x75231))+P101(f323(f323(f237(x75232),f12(x75232,f235(x75232),x75231)),f13(x75232,f236(x75232),x75231)))
% 188.07/187.98 [7840]~P7(x78401)+~P39(x78402)+P101(f323(f323(f325(a1),x78401),x78402))+~P101(f323(f323(f325(a865),f323(a104,x78401)),f323(f302(a1,a865,a104),x78402)))
% 188.07/187.98 [8107]~P5(x81072)+P101(f323(x81071,f200(x81072)))+~P101(f323(f55(f869(x81072)),x81071))+P101(f323(f55(x81072),f323(f323(f8(f869(x81072),a860,x81072),x81071),f230(x81072))))
% 188.07/187.98 [8574]~P5(x85741)+~P101(f323(x85742,f200(x85741)))+P101(f323(f56(f869(x85741)),x85742))+~P101(f323(f56(x85741),f323(f323(f8(f869(x85741),a860,x85741),x85742),f230(x85741))))
% 188.07/187.98 [5822]~P134(x58222)+E(x58221,f2(a1))+E(f323(f77(x58222),f323(f102(x58222),f323(f77(a1),x58221))),f323(f102(x58222),x58221))+~P101(f323(f323(f238(a1),x58221),f2(a1)))
% 188.07/187.98 [5893]~P89(x58931)+~P90(x58931)+~P30(x58931,f323(f103(x58931),x58932))+P30(x58931,f323(f103(x58931),f323(f323(f78(a1),x58932),x58932)))
% 188.07/187.98 [6220]~P74(x62202)+E(x62201,f188(f872(x62202,a860)))+E(f15(x62202,f323(f302(x62202,x62202,f77(x62202)),x62201)),f323(f77(x62202),f14(x62202,x62201)))+~P101(f323(f59(x62202),x62201))
% 188.07/187.98 [6221]~P74(x62212)+E(x62211,f188(f872(x62212,a860)))+E(f14(x62212,f323(f302(x62212,x62212,f77(x62212)),x62211)),f323(f77(x62212),f15(x62212,x62211)))+~P101(f323(f59(x62212),x62211))
% 188.07/187.98 [6252]~P89(x62521)+~P90(x62521)+P30(x62521,f323(f103(x62521),x62522))+~P30(x62521,f323(f103(x62521),f323(f323(f78(a1),x62522),x62522)))
% 188.07/187.98 [6340]E(x63401,f2(a1))+E(f323(a48,f47(f323(f77(a1),x63401),f323(f77(a1),x63402))),f43(x63401,x63402))+P101(f323(f323(f237(a1),f2(a1)),x63402))+~P101(f323(f323(f237(a1),f2(a1)),x63401))
% 188.07/187.98 [8624]~P39(x86242)+~P39(x86241)+P101(f323(f323(f238(f872(a865,a860)),f323(f302(a1,a865,a104),x86241)),f323(f302(a1,a865,a104),x86242)))+~P101(f323(f323(f238(f872(a1,a860)),x86241),x86242))
% 188.07/187.98 [8851]~E(f652(x88512,x88511),f653(x88512,x88511))+~P101(f323(f130(x88511),f654(x88512,x88511)))+~P101(f323(f130(f866(x88511)),x88512))+P101(f323(f130(x88511),f323(f135(f866(x88511),f866(x88511),f121(x88511),f113(x88511)),x88512)))
% 188.07/187.98 [8940]~P39(x89402)+~P39(x89401)+~P101(f323(f323(f237(f872(a865,a860)),f323(f302(a1,a865,a104),x89401)),f323(f302(a1,a865,a104),x89402)))+P101(f323(f323(f237(f872(a1,a860)),x89401),x89402))
% 188.07/187.98 [8941]~P39(x89412)+~P39(x89411)+~P101(f323(f323(f238(f872(a865,a860)),f323(f302(a1,a865,a104),x89411)),f323(f302(a1,a865,a104),x89412)))+P101(f323(f323(f238(f872(a1,a860)),x89411),x89412))
% 188.07/187.98 [8947]~E(f652(x89472,x89471),f653(x89472,x89471))+~P101(f323(f130(f866(x89471)),x89472))+P101(f323(f130(x89471),f323(f135(f866(x89471),f866(x89471),f121(x89471),f113(x89471)),x89472)))+P101(f323(f323(f325(f866(x89471)),f654(x89472,x89471)),f323(f166(f866(x89471)),x89472)))
% 188.07/187.98 [8988]~P101(f323(f130(x89881),f654(x89882,x89881)))+~P101(f323(f130(f866(x89881)),x89882))+P101(f323(f130(x89881),f323(f135(f866(x89881),f866(x89881),f121(x89881),f113(x89881)),x89882)))+P101(f323(f323(f325(f866(x89881)),f653(x89882,x89881)),f323(f166(f866(x89881)),x89882)))
% 188.07/187.98 [8989]~P101(f323(f130(x89891),f654(x89892,x89891)))+~P101(f323(f130(f866(x89891)),x89892))+P101(f323(f130(x89891),f323(f135(f866(x89891),f866(x89891),f121(x89891),f113(x89891)),x89892)))+P101(f323(f323(f325(f866(x89891)),f652(x89892,x89891)),f323(f166(f866(x89891)),x89892)))
% 188.07/187.98 [9069]~P101(f323(f130(f866(x90691)),x90692))+P101(f323(f130(x90691),f323(f135(f866(x90691),f866(x90691),f121(x90691),f113(x90691)),x90692)))+P101(f323(f323(f325(f866(x90691)),f653(x90692,x90691)),f323(f166(f866(x90691)),x90692)))+P101(f323(f323(f325(f866(x90691)),f654(x90692,x90691)),f323(f166(f866(x90691)),x90692)))
% 188.07/187.98 [9070]~P101(f323(f130(f866(x90701)),x90702))+P101(f323(f130(x90701),f323(f135(f866(x90701),f866(x90701),f121(x90701),f113(x90701)),x90702)))+P101(f323(f323(f325(f866(x90701)),f652(x90702,x90701)),f323(f166(f866(x90701)),x90702)))+P101(f323(f323(f325(f866(x90701)),f654(x90702,x90701)),f323(f166(f866(x90701)),x90702)))
% 188.07/187.98 [9083]~E(f323(f323(f101(f872(x90831,a860)),f323(f166(x90831),f653(x90832,x90831))),f323(f166(x90831),f652(x90832,x90831))),f188(f872(x90831,a860)))+~P101(f323(f130(x90831),f654(x90832,x90831)))+~P101(f323(f130(f866(x90831)),x90832))+P101(f323(f130(x90831),f323(f135(f866(x90831),f866(x90831),f121(x90831),f113(x90831)),x90832)))
% 188.07/187.98 [9143]~E(f323(f323(f101(f872(x91431,a860)),f323(f166(x91431),f653(x91432,x91431))),f323(f166(x91431),f652(x91432,x91431))),f188(f872(x91431,a860)))+~P101(f323(f130(f866(x91431)),x91432))+P101(f323(f130(x91431),f323(f135(f866(x91431),f866(x91431),f121(x91431),f113(x91431)),x91432)))+P101(f323(f323(f325(f866(x91431)),f654(x91432,x91431)),f323(f166(f866(x91431)),x91432)))
% 188.07/187.98 [9409]E(x94091,f2(a1))+E(x94092,f2(a1))+E(f323(f323(f84(a1,f871(a1,a1)),f323(f323(a219,x94092),x94091)),f323(f323(f18(a1,a1,f871(a1,a1)),f323(f323(f8(a1,f872(a1,f871(a1,a1)),a1),f258(a1,a1)),f323(f36(a1),x94092))),f323(f36(a1),x94091))),f217(x94092,x94091))+P101(f323(f323(f238(a1),x94091),f2(a1)))
% 188.07/187.98 [8167]~P90(x81672)+~P116(x81672)+~P101(f323(f323(f237(x81672),f323(f103(x81672),x81671)),f76(x81672)))+P101(f323(f323(f237(a1),x81671),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))
% 188.07/187.98 [8168]~P90(x81682)+~P116(x81682)+~P101(f323(f323(f238(x81682),f323(f103(x81682),x81681)),f76(x81682)))+P101(f323(f323(f238(a1),x81681),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))
% 188.07/187.98 [8439]~P116(x84391)+~P90(x84391)+P101(f323(f323(f237(x84391),f323(f103(x84391),x84392)),f76(x84391)))+~P101(f323(f323(f237(a1),x84392),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))
% 188.07/187.98 [8440]~P116(x84401)+~P90(x84401)+P101(f323(f323(f238(x84401),f323(f103(x84401),x84402)),f76(x84401)))+~P101(f323(f323(f238(a1),x84402),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))
% 188.07/187.98 [8652]~P90(x86522)+~P116(x86522)+~P101(f323(f323(f237(x86522),f76(x86522)),f323(f103(x86522),x86521)))+P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),x86521))
% 188.07/187.98 [8653]~P90(x86532)+~P116(x86532)+~P101(f323(f323(f238(x86532),f76(x86532)),f323(f103(x86532),x86531)))+P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),x86531))
% 188.07/187.98 [9027]~P116(x90271)+~P90(x90271)+P101(f323(f323(f237(x90271),f76(x90271)),f323(f103(x90271),x90272)))+~P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),x90272))
% 188.07/187.98 [9028]~P116(x90281)+~P90(x90281)+P101(f323(f323(f238(x90281),f76(x90281)),f323(f103(x90281),x90282)))+~P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),x90282))
% 188.07/187.98 [9542]~P133(x95422)+E(x95421,f76(x95422))+E(x95421,f323(f77(x95422),f76(x95422)))+~E(f323(f323(f248(x95422),x95421),f323(f103(a865),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(x95422))
% 188.07/187.98 [9818]~P64(x98181)+~P90(x98181)+~P101(f323(f323(f238(x98181),f2(x98181)),x98182))+P101(f323(f323(f238(x98181),f2(x98181)),f323(f323(f281(x98181),x98182),f323(f103(x98181),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))))))
% 188.07/187.98 [9878]~P64(x98781)+~P90(x98781)+P101(f323(f323(f238(x98781),f2(x98781)),x98782))+~P101(f323(f323(f238(x98781),f2(x98781)),f323(f323(f281(x98781),x98782),f323(f103(x98781),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))))))
% 188.07/187.98 [10133]~P134(x101332)+E(x101331,f2(a1))+P101(f323(f323(f238(a1),x101331),f2(a1)))+E(f323(f323(f262(a1,a1,x101332),f323(f323(f7(a1,f872(a1,f872(x101332,x101332)),f872(a1,x101332)),f323(f323(f8(f872(f872(x101332,x101332),x101332),f872(f872(a1,f872(x101332,x101332)),f872(a1,x101332)),a1),f8(f872(x101332,x101332),x101332,a1)),f323(f323(f8(x101332,f872(f872(x101332,x101332),x101332),a1),f84(x101332,x101332)),f102(x101332)))),f323(f323(f7(a1,f872(x101332,x101332),f872(x101332,x101332)),f323(f323(f8(f872(x101332,f872(x101332,x101332)),f872(f872(x101332,x101332),f872(x101332,x101332)),a1),f18(x101332,x101332,x101332)),f323(f323(f7(a1,f872(x101332,x101332),f872(x101332,f872(x101332,x101332))),f323(f323(f8(f872(x101332,f872(x101332,x101332)),f872(f872(x101332,x101332),f872(x101332,f872(x101332,x101332))),a1),f8(x101332,f872(x101332,x101332),x101332)),f323(f323(f8(a860,f872(x101332,f872(x101332,x101332)),a1),f96(x101332)),f323(f323(f7(a1,a1,a860),a320),f2(a1))))),f323(f323(f18(x101332,x101332,x101332),f78(x101332)),f5(x101332))))),f323(f323(f7(x101332,x101332,x101332),f323(f323(f8(x101332,f872(x101332,x101332),x101332),f78(x101332)),f323(f323(f18(x101332,x101332,x101332),f78(x101332)),f5(x101332)))),f76(x101332))))),f43(x101331,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(x101332),x101331))
% 188.07/187.98 [5213]~P5(x52133)+~P36(x52133,x52132,f53(x52133))+E(x52131,f705(x52132,x52133))+~P101(f323(x52132,x52131))
% 188.07/187.98 [5370]~P5(x53701)+P36(x53701,x53702,f53(x53701))+~E(f706(x53702,x53701,x53703),x53703)+~P101(f323(x53702,x53703))
% 188.07/187.98 [4863]~P89(x48633)+~P90(x48633)+E(x48631,x48632)+~E(f323(f103(x48633),x48631),f323(f103(x48633),x48632))
% 188.07/187.98 [5982]~P5(x59821)+P36(x59821,x59822,f53(x59821))+~P101(f323(x59822,x59823))+P101(f323(x59822,f706(x59822,x59821,x59823)))
% 188.07/187.98 [5992]~P101(f323(x59921,x59922))+~P101(f323(x59921,x59923))+~P101(f323(f323(f237(a865),x59923),f331(x59922,x59921)))+P101(f323(x59921,f2(a865)))
% 188.07/187.98 [6403]P143(x64032,x64033,x64031)+E(x64031,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f799(x64031,x64033,x64032)))+P101(f323(f323(f238(a1),x64031),f2(a1)))
% 188.07/187.98 [6404]P142(x64042,x64043,x64041)+E(x64041,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f809(x64041,x64043,x64042)))+P101(f323(f323(f238(a1),x64041),f2(a1)))
% 188.07/187.98 [6524]P142(x65241,x65242,x65243)+~P101(f323(x65241,x65242))+P101(f323(f323(f237(a1),f2(a1)),f809(x65243,x65242,x65241)))+P101(f323(f323(f238(a1),x65243),f2(a1)))
% 188.07/187.98 [6550]P143(x65501,x65502,x65503)+P101(f323(f323(f237(a1),f2(a1)),f799(x65503,x65502,x65501)))+~P101(f323(x65501,f2(a1)))+P101(f323(f323(f238(a1),x65503),f2(a1)))
% 188.07/187.98 [6578]P143(x65782,x65783,x65781)+E(x65781,f2(a1))+~P101(f323(x65782,f800(x65781,x65783,x65782)))+P101(f323(f323(f238(a1),x65781),f2(a1)))
% 188.07/187.98 [6579]P142(x65792,x65793,x65791)+E(x65791,f2(a1))+~P101(f323(x65792,f809(x65791,x65793,x65792)))+P101(f323(f323(f238(a1),x65791),f2(a1)))
% 188.07/187.98 [6678]~P103(x66781)+~P6(x66781)+~P101(f323(f323(f238(x66781),x66782),f37(x66781,x66783)))+P101(f323(f323(f238(x66781),x66782),f548(x66783,x66782,x66781)))
% 188.07/187.98 [6687]P142(x66871,x66872,x66873)+~P101(f323(x66871,x66872))+~P101(f323(x66871,f809(x66873,x66872,x66871)))+P101(f323(f323(f238(a1),x66873),f2(a1)))
% 188.07/187.98 [6718]P143(x67181,x67182,x67183)+~P101(f323(x67181,f800(x67183,x67182,x67181)))+~P101(f323(x67181,f2(a1)))+P101(f323(f323(f238(a1),x67183),f2(a1)))
% 188.07/187.98 [6967]P143(x69672,x69673,x69671)+E(x69671,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f799(x69671,x69673,x69672)))+P101(f323(f323(f238(a1),x69671),f798(x69671,x69673,x69672)))
% 188.07/187.98 [6968]P142(x69682,x69683,x69681)+E(x69681,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f809(x69681,x69683,x69682)))+P101(f323(f323(f238(a1),x69681),f808(x69681,x69683,x69682)))
% 188.07/187.98 [7085]P142(x70851,x70852,x70853)+~P101(f323(x70851,x70852))+P101(f323(f323(f237(a1),f2(a1)),f809(x70853,x70852,x70851)))+P101(f323(f323(f238(a1),x70853),f808(x70853,x70852,x70851)))
% 188.07/187.98 [7104]P143(x71041,x71042,x71043)+P101(f323(f323(f237(a1),f2(a1)),f799(x71043,x71042,x71041)))+P101(f323(f323(f238(a1),x71043),f798(x71043,x71042,x71041)))+~P101(f323(x71041,f2(a1)))
% 188.07/187.98 [7137]P143(x71372,x71373,x71371)+E(x71371,f2(a1))+~P101(f323(x71372,f800(x71371,x71373,x71372)))+P101(f323(f323(f238(a1),x71371),f798(x71371,x71373,x71372)))
% 188.07/187.98 [7138]P142(x71382,x71383,x71381)+E(x71381,f2(a1))+~P101(f323(x71382,f809(x71381,x71383,x71382)))+P101(f323(f323(f238(a1),x71381),f808(x71381,x71383,x71382)))
% 188.07/187.98 [7179]P143(x71792,x71793,x71791)+E(x71791,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f799(x71791,x71793,x71792)))+~P101(f323(x71792,f802(x71791,x71793,x71792)))
% 188.07/187.98 [7180]P142(x71802,x71803,x71801)+E(x71801,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f809(x71801,x71803,x71802)))+~P101(f323(x71802,f808(x71801,x71803,x71802)))
% 188.07/187.98 [7268]P142(x72681,x72682,x72683)+~P101(f323(x72681,x72682))+~P101(f323(x72681,f809(x72683,x72682,x72681)))+P101(f323(f323(f238(a1),x72683),f808(x72683,x72682,x72681)))
% 188.07/187.98 [7284]P143(x72841,x72842,x72843)+~P101(f323(x72841,f800(x72843,x72842,x72841)))+P101(f323(f323(f238(a1),x72843),f798(x72843,x72842,x72841)))+~P101(f323(x72841,f2(a1)))
% 188.07/187.98 [7288]P142(x72881,x72882,x72883)+~P101(f323(x72881,x72882))+P101(f323(f323(f237(a1),f2(a1)),f809(x72883,x72882,x72881)))+~P101(f323(x72881,f808(x72883,x72882,x72881)))
% 188.07/187.98 [7304]P143(x73041,x73042,x73043)+P101(f323(f323(f237(a1),f2(a1)),f799(x73043,x73042,x73041)))+~P101(f323(x73041,f802(x73043,x73042,x73041)))+~P101(f323(x73041,f2(a1)))
% 188.07/187.98 [7327]P143(x73272,x73273,x73271)+E(x73271,f2(a1))+~P101(f323(x73272,f800(x73271,x73273,x73272)))+~P101(f323(x73272,f802(x73271,x73273,x73272)))
% 188.07/187.98 [7328]P142(x73282,x73283,x73281)+E(x73281,f2(a1))+~P101(f323(x73282,f809(x73281,x73283,x73282)))+~P101(f323(x73282,f808(x73281,x73283,x73282)))
% 188.07/187.98 [7419]P142(x74191,x74192,x74193)+~P101(f323(x74191,x74192))+~P101(f323(x74191,f809(x74193,x74192,x74191)))+~P101(f323(x74191,f808(x74193,x74192,x74191)))
% 188.07/187.98 [7436]P143(x74361,x74362,x74363)+~P101(f323(x74361,f800(x74363,x74362,x74361)))+~P101(f323(x74361,f802(x74363,x74362,x74361)))+~P101(f323(x74361,f2(a1)))
% 188.07/187.98 [7483]P143(x74832,x74833,x74831)+E(x74831,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f799(x74831,x74833,x74832)))+P101(f323(f323(f237(a1),f798(x74831,x74833,x74832)),f2(a1)))
% 188.07/187.98 [7484]P142(x74842,x74843,x74841)+E(x74841,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f809(x74841,x74843,x74842)))+P101(f323(f323(f237(a1),f808(x74841,x74843,x74842)),f2(a1)))
% 188.07/187.98 [7485]~P134(x74851)+~P101(f323(f323(f325(x74851),x74853),f109(x74851)))+~P101(f323(f323(f325(x74851),x74852),f109(x74851)))+P101(f323(f323(f325(x74851),f323(f323(f22(x74851),x74852),x74853)),f109(x74851)))
% 188.07/187.98 [7486]~P134(x74861)+~P101(f323(f323(f325(x74861),x74863),f109(x74861)))+~P101(f323(f323(f325(x74861),x74862),f109(x74861)))+P101(f323(f323(f325(x74861),f323(f323(f79(x74861),x74862),x74863)),f109(x74861)))
% 188.07/187.98 [7487]~P140(x74871)+~P101(f323(f323(f325(x74871),x74873),f186(x74871)))+~P101(f323(f323(f325(x74871),x74872),f186(x74871)))+P101(f323(f323(f325(x74871),f323(f323(f79(x74871),x74872),x74873)),f186(x74871)))
% 188.07/187.98 [7488]~P134(x74881)+~P101(f323(f323(f325(x74881),x74883),f109(x74881)))+~P101(f323(f323(f325(x74881),x74882),f109(x74881)))+P101(f323(f323(f325(x74881),f323(f323(f78(x74881),x74882),x74883)),f109(x74881)))
% 188.07/187.98 [7489]~P140(x74891)+~P101(f323(f323(f325(x74891),x74893),f186(x74891)))+~P101(f323(f323(f325(x74891),x74892),f186(x74891)))+P101(f323(f323(f325(x74891),f323(f323(f78(x74891),x74892),x74893)),f186(x74891)))
% 188.07/187.98 [7490]~P84(x74901)+~P101(f323(f323(f237(x74901),x74903),f2(x74901)))+~P101(f323(f323(f237(x74901),x74902),f2(x74901)))+P101(f323(f323(f237(x74901),f323(f323(f78(x74901),x74902),x74903)),f2(x74901)))
% 188.07/187.98 [7491]~P84(x74911)+~P101(f323(f323(f237(x74911),x74913),f2(x74911)))+~P101(f323(f323(f238(x74911),x74912),f2(x74911)))+P101(f323(f323(f238(x74911),f323(f323(f78(x74911),x74912),x74913)),f2(x74911)))
% 188.07/187.98 [7492]~P84(x74921)+~P101(f323(f323(f237(x74921),x74922),f2(x74921)))+~P101(f323(f323(f238(x74921),x74923),f2(x74921)))+P101(f323(f323(f238(x74921),f323(f323(f78(x74921),x74922),x74923)),f2(x74921)))
% 188.07/187.98 [7493]~P84(x74931)+~P101(f323(f323(f238(x74931),x74933),f2(x74931)))+~P101(f323(f323(f238(x74931),x74932),f2(x74931)))+P101(f323(f323(f238(x74931),f323(f323(f78(x74931),x74932),x74933)),f2(x74931)))
% 188.07/187.98 [7519]P143(x75193,x75192,x75191)+E(x75191,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x75191),f800(x75191,x75192,x75193))),f799(x75191,x75192,x75193)),x75192)+P101(f323(f323(f238(a1),x75191),f2(a1)))
% 188.07/187.98 [7520]P142(x75203,x75202,x75201)+E(x75201,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x75201),f810(x75201,x75202,x75203))),f809(x75201,x75202,x75203)),x75202)+P101(f323(f323(f238(a1),x75201),f2(a1)))
% 188.07/187.98 [7602]P142(x76021,x76022,x76023)+~P101(f323(x76021,x76022))+P101(f323(f323(f237(a1),f2(a1)),f809(x76023,x76022,x76021)))+P101(f323(f323(f237(a1),f808(x76023,x76022,x76021)),f2(a1)))
% 188.07/187.98 [7631]P143(x76311,x76312,x76313)+P101(f323(f323(f237(a1),f2(a1)),f799(x76313,x76312,x76311)))+~P101(f323(x76311,f2(a1)))+P101(f323(f323(f237(a1),f798(x76313,x76312,x76311)),f2(a1)))
% 188.07/187.98 [7640]P142(x76403,x76402,x76401)+~P101(f323(x76403,x76402))+E(f323(f323(f78(a1),f323(f323(f79(a1),x76401),f810(x76401,x76402,x76403))),f809(x76401,x76402,x76403)),x76402)+P101(f323(f323(f238(a1),x76401),f2(a1)))
% 188.07/187.98 [7647]P143(x76472,x76473,x76471)+E(x76471,f2(a1))+~P101(f323(x76472,f800(x76471,x76473,x76472)))+P101(f323(f323(f237(a1),f798(x76471,x76473,x76472)),f2(a1)))
% 188.07/187.98 [7648]P142(x76482,x76483,x76481)+E(x76481,f2(a1))+~P101(f323(x76482,f809(x76481,x76483,x76482)))+P101(f323(f323(f237(a1),f808(x76481,x76483,x76482)),f2(a1)))
% 188.07/187.98 [7653]P143(x76533,x76532,x76531)+E(f323(f323(f78(a1),f323(f323(f79(a1),x76531),f800(x76531,x76532,x76533))),f799(x76531,x76532,x76533)),x76532)+~P101(f323(x76533,f2(a1)))+P101(f323(f323(f238(a1),x76531),f2(a1)))
% 188.07/187.98 [7709]P142(x77091,x77092,x77093)+~P101(f323(x77091,x77092))+~P101(f323(x77091,f809(x77093,x77092,x77091)))+P101(f323(f323(f237(a1),f808(x77093,x77092,x77091)),f2(a1)))
% 188.07/187.98 [7713]P143(x77131,x77132,x77133)+~P101(f323(x77131,f800(x77133,x77132,x77131)))+~P101(f323(x77131,f2(a1)))+P101(f323(f323(f237(a1),f798(x77133,x77132,x77131)),f2(a1)))
% 188.07/187.98 [7780]~P120(x77801)+~P101(f323(f323(f237(x77801),f323(f323(f79(x77801),x77803),x77802)),f2(x77801)))+P101(f323(f323(f237(x77801),x77802),f2(x77801)))+P101(f323(f323(f237(x77801),x77803),f2(x77801)))
% 188.07/187.98 [7781]~P64(x77811)+~P101(f323(f323(f237(x77811),f323(f323(f281(x77811),x77813),x77812)),f2(x77811)))+P101(f323(f323(f237(x77811),x77812),f2(x77811)))+P101(f323(f323(f237(x77811),x77813),f2(x77811)))
% 188.07/187.98 [7782]~P64(x77821)+~P101(f323(f323(f238(x77821),f323(f323(f281(x77821),x77823),x77822)),f2(x77821)))+P101(f323(f323(f238(x77821),x77822),f2(x77821)))+P101(f323(f323(f238(x77821),x77823),f2(x77821)))
% 188.07/187.98 [7899]P143(x78993,x78992,x78991)+E(x78991,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x78991),f800(x78991,x78992,x78993))),f799(x78991,x78992,x78993)),x78992)+P101(f323(f323(f238(a1),x78991),f798(x78991,x78992,x78993)))
% 188.07/187.98 [7900]P142(x79003,x79002,x79001)+E(x79001,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79001),f810(x79001,x79002,x79003))),f809(x79001,x79002,x79003)),x79002)+P101(f323(f323(f238(a1),x79001),f808(x79001,x79002,x79003)))
% 188.07/187.98 [7913]P143(x79133,x79132,x79131)+E(x79131,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79131),f802(x79131,x79132,x79133))),f798(x79131,x79132,x79133)),x79132)+P101(f323(f323(f237(a1),f2(a1)),f799(x79131,x79132,x79133)))
% 188.07/187.98 [7914]P142(x79143,x79142,x79141)+E(x79141,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79141),f811(x79141,x79142,x79143))),f808(x79141,x79142,x79143)),x79142)+P101(f323(f323(f237(a1),f2(a1)),f809(x79141,x79142,x79143)))
% 188.07/187.98 [7955]P142(x79553,x79552,x79551)+~P101(f323(x79553,x79552))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79551),f810(x79551,x79552,x79553))),f809(x79551,x79552,x79553)),x79552)+P101(f323(f323(f238(a1),x79551),f808(x79551,x79552,x79553)))
% 188.07/187.98 [7964]P143(x79643,x79642,x79641)+E(f323(f323(f78(a1),f323(f323(f79(a1),x79641),f800(x79641,x79642,x79643))),f799(x79641,x79642,x79643)),x79642)+P101(f323(f323(f238(a1),x79641),f798(x79641,x79642,x79643)))+~P101(f323(x79643,f2(a1)))
% 188.07/187.98 [7970]P142(x79703,x79702,x79701)+~P101(f323(x79703,x79702))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79701),f811(x79701,x79702,x79703))),f808(x79701,x79702,x79703)),x79702)+P101(f323(f323(f237(a1),f2(a1)),f809(x79701,x79702,x79703)))
% 188.07/187.98 [7976]P143(x79763,x79762,x79761)+E(f323(f323(f78(a1),f323(f323(f79(a1),x79761),f802(x79761,x79762,x79763))),f798(x79761,x79762,x79763)),x79762)+P101(f323(f323(f237(a1),f2(a1)),f799(x79761,x79762,x79763)))+~P101(f323(x79763,f2(a1)))
% 188.07/187.98 [7987]P143(x79873,x79872,x79871)+E(x79871,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79871),f800(x79871,x79872,x79873))),f799(x79871,x79872,x79873)),x79872)+~P101(f323(x79873,f802(x79871,x79872,x79873)))
% 188.07/187.98 [7988]P142(x79883,x79882,x79881)+E(x79881,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79881),f810(x79881,x79882,x79883))),f809(x79881,x79882,x79883)),x79882)+~P101(f323(x79883,f808(x79881,x79882,x79883)))
% 188.07/187.98 [7989]P143(x79893,x79892,x79891)+E(x79891,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79891),f802(x79891,x79892,x79893))),f798(x79891,x79892,x79893)),x79892)+~P101(f323(x79893,f800(x79891,x79892,x79893)))
% 188.07/187.98 [7990]P142(x79903,x79902,x79901)+E(x79901,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79901),f811(x79901,x79902,x79903))),f808(x79901,x79902,x79903)),x79902)+~P101(f323(x79903,f809(x79901,x79902,x79903)))
% 188.07/187.98 [8047]P142(x80473,x80472,x80471)+~P101(f323(x80473,x80472))+E(f323(f323(f78(a1),f323(f323(f79(a1),x80471),f810(x80471,x80472,x80473))),f809(x80471,x80472,x80473)),x80472)+~P101(f323(x80473,f808(x80471,x80472,x80473)))
% 188.07/187.98 [8048]P142(x80483,x80482,x80481)+~P101(f323(x80483,x80482))+E(f323(f323(f78(a1),f323(f323(f79(a1),x80481),f811(x80481,x80482,x80483))),f808(x80481,x80482,x80483)),x80482)+~P101(f323(x80483,f809(x80481,x80482,x80483)))
% 188.07/187.98 [8058]P143(x80583,x80582,x80581)+E(f323(f323(f78(a1),f323(f323(f79(a1),x80581),f800(x80581,x80582,x80583))),f799(x80581,x80582,x80583)),x80582)+~P101(f323(x80583,f802(x80581,x80582,x80583)))+~P101(f323(x80583,f2(a1)))
% 188.07/187.98 [8059]P143(x80593,x80592,x80591)+E(f323(f323(f78(a1),f323(f323(f79(a1),x80591),f802(x80591,x80592,x80593))),f798(x80591,x80592,x80593)),x80592)+~P101(f323(x80593,f800(x80591,x80592,x80593)))+~P101(f323(x80593,f2(a1)))
% 188.07/187.98 [8160]P143(x81603,x81602,x81601)+E(x81601,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x81601),f800(x81601,x81602,x81603))),f799(x81601,x81602,x81603)),x81602)+P101(f323(f323(f237(a1),f798(x81601,x81602,x81603)),f2(a1)))
% 188.07/187.98 [8161]P142(x81613,x81612,x81611)+E(x81611,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x81611),f810(x81611,x81612,x81613))),f809(x81611,x81612,x81613)),x81612)+P101(f323(f323(f237(a1),f808(x81611,x81612,x81613)),f2(a1)))
% 188.07/187.98 [8202]P142(x82023,x82022,x82021)+~P101(f323(x82023,x82022))+E(f323(f323(f78(a1),f323(f323(f79(a1),x82021),f810(x82021,x82022,x82023))),f809(x82021,x82022,x82023)),x82022)+P101(f323(f323(f237(a1),f808(x82021,x82022,x82023)),f2(a1)))
% 188.07/187.98 [8207]P143(x82073,x82072,x82071)+E(f323(f323(f78(a1),f323(f323(f79(a1),x82071),f800(x82071,x82072,x82073))),f799(x82071,x82072,x82073)),x82072)+~P101(f323(x82073,f2(a1)))+P101(f323(f323(f237(a1),f798(x82071,x82072,x82073)),f2(a1)))
% 188.07/187.98 [8342]P143(x83423,x83422,x83421)+E(x83421,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x83421),f802(x83421,x83422,x83423))),f798(x83421,x83422,x83423)),x83422)+E(f323(f323(f78(a1),f323(f323(f79(a1),x83421),f800(x83421,x83422,x83423))),f799(x83421,x83422,x83423)),x83422)
% 188.07/187.98 [8343]P142(x83433,x83432,x83431)+E(x83431,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x83431),f811(x83431,x83432,x83433))),f808(x83431,x83432,x83433)),x83432)+E(f323(f323(f78(a1),f323(f323(f79(a1),x83431),f810(x83431,x83432,x83433))),f809(x83431,x83432,x83433)),x83432)
% 188.07/187.98 [8364]P142(x83643,x83642,x83641)+~P101(f323(x83643,x83642))+E(f323(f323(f78(a1),f323(f323(f79(a1),x83641),f811(x83641,x83642,x83643))),f808(x83641,x83642,x83643)),x83642)+E(f323(f323(f78(a1),f323(f323(f79(a1),x83641),f810(x83641,x83642,x83643))),f809(x83641,x83642,x83643)),x83642)
% 188.07/187.98 [8376]P143(x83763,x83762,x83761)+E(f323(f323(f78(a1),f323(f323(f79(a1),x83761),f802(x83761,x83762,x83763))),f798(x83761,x83762,x83763)),x83762)+E(f323(f323(f78(a1),f323(f323(f79(a1),x83761),f800(x83761,x83762,x83763))),f799(x83761,x83762,x83763)),x83762)+~P101(f323(x83763,f2(a1)))
% 188.07/187.98 [9036]~P120(x90361)+~E(x90363,f2(x90361))+~E(x90362,f2(x90361))+P101(f323(f323(f237(x90361),f323(f323(f78(x90361),f323(f323(f79(x90361),x90362),x90362)),f323(f323(f79(x90361),x90363),x90363))),f2(x90361)))
% 188.07/187.98 [10079]~P116(x100791)+~E(x100793,f2(x100791))+~E(x100792,f2(x100791))+P101(f323(f323(f237(x100791),f323(f323(f78(x100791),f323(f323(f248(x100791),x100792),f323(f103(a865),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(x100791),x100793),f323(f103(a865),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(x100791)))
% 188.07/187.98 [4812]~E(x48123,x48121)+~P114(x48122)+E(x48121,f2(x48122))+E(f323(f323(f281(x48122),x48123),x48121),f76(x48122))
% 188.07/187.98 [4864]~P3(x48641)+~E(x48643,f188(x48641))+~E(x48642,f188(x48641))+E(f323(f323(f110(x48641),x48642),x48643),f188(x48641))
% 188.07/187.98 [4865]~P95(x48651)+~E(x48653,f246(x48651))+~E(x48652,f246(x48651))+E(f323(f323(f101(x48651),x48652),x48653),f246(x48651))
% 188.07/187.98 [4952]~P114(x49523)+E(x49521,x49522)+E(x49522,f2(x49523))+~E(f323(f323(f281(x49523),x49521),x49522),f76(x49523))
% 188.07/187.98 [4971]~P123(x49712)+E(x49711,f2(x49712))+E(x49713,f2(x49712))+~E(f323(f323(f79(x49712),x49713),x49711),f2(x49712))
% 188.07/187.98 [4972]~P137(x49722)+E(x49721,f2(x49722))+E(x49723,f2(x49722))+~E(f323(f323(f79(x49722),x49723),x49721),f2(x49722))
% 188.07/187.98 [5337]~P108(x53373)+E(x53371,x53372)+E(x53371,f323(f77(x53373),x53372))+~E(f323(f323(f79(x53373),x53371),x53371),f323(f323(f79(x53373),x53372),x53372))
% 188.07/187.98 [5377]~P87(x53771)+E(f323(f77(x53771),x53772),x53773)+~E(f323(f323(f110(x53771),x53772),x53773),f246(x53771))+~E(f323(f323(f101(x53771),x53772),x53773),f188(x53771))
% 188.07/187.98 [5456]~P116(x54563)+E(x54561,x54562)+P101(f323(f323(f238(x54563),x54562),x54561))+P101(f323(f323(f238(x54563),x54561),x54562))
% 188.07/187.98 [5457]~P103(x54573)+E(x54571,x54572)+P101(f323(f323(f238(x54573),x54572),x54571))+P101(f323(f323(f238(x54573),x54571),x54572))
% 188.07/187.98 [5458]~E(x54582,x54583)+~P103(x54581)+P101(f323(f323(f238(x54581),x54582),x54583))+P101(f323(f323(f237(x54581),x54582),x54583))
% 188.07/187.98 [5711]~P105(x57113)+E(x57111,x57112)+~P101(f323(f323(f237(x57113),x57112),x57111))+P101(f323(f323(f238(x57113),x57112),x57111))
% 188.07/187.98 [5713]~P103(x57133)+E(x57131,x57132)+~P101(f323(f323(f237(x57133),x57131),x57132))+P101(f323(f323(f238(x57133),x57131),x57132))
% 188.07/187.98 [5719]~P105(x57193)+E(x57191,x57192)+~P101(f323(f323(f237(x57193),x57191),x57192))+P101(f323(f323(f238(x57193),x57191),x57192))
% 188.07/187.98 [5819]P142(x58191,x58192,x58193)+~P101(f323(x58191,x58192))+P101(f323(f323(f238(a1),x58193),f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x58193))
% 188.07/187.98 [5866]P143(x58661,x58662,x58663)+~P101(f323(x58661,f2(a1)))+P101(f323(f323(f238(a1),x58663),f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x58663))
% 188.07/187.98 [5870]~P2(x58701)+E(f323(f323(f110(x58701),x58702),f11(x58701,x58703)),x58702)+~P101(f323(f59(x58701),x58703))+~P101(f323(f323(f325(x58701),x58702),x58703))
% 188.07/187.98 [5871]~P2(x58711)+E(f323(f323(f101(x58711),x58712),f10(x58711,x58713)),x58712)+~P101(f323(f59(x58711),x58713))+~P101(f323(f323(f325(x58711),x58712),x58713))
% 188.07/187.98 [5905]~P2(x59051)+E(f323(f323(f110(x59051),x59052),f10(x59051,x59053)),f10(x59051,x59053))+~P101(f323(f59(x59051),x59053))+~P101(f323(f323(f325(x59051),x59052),x59053))
% 188.07/187.98 [5906]~P2(x59061)+E(f323(f323(f101(x59061),x59062),f11(x59061,x59063)),f11(x59061,x59063))+~P101(f323(f59(x59061),x59063))+~P101(f323(f323(f325(x59061),x59062),x59063))
% 188.07/187.98 [5907]~P103(x59071)+E(f323(f323(f235(x59071),x59072),f15(x59071,x59073)),f15(x59071,x59073))+~P101(f323(f59(x59071),x59073))+~P101(f323(f323(f325(x59071),x59072),x59073))
% 188.07/187.98 [5908]~P103(x59081)+E(f323(f323(f236(x59081),x59082),f14(x59081,x59083)),f14(x59081,x59083))+~P101(f323(f59(x59081),x59083))+~P101(f323(f323(f325(x59081),x59082),x59083))
% 188.07/187.98 [5949]E(x59491,x59492)+~P105(x59493)+~P101(f323(f323(f237(x59493),x59492),x59491))+~P101(f323(f323(f237(x59493),x59491),x59492))
% 188.07/187.98 [6087]~P102(x60871)+P101(f323(f323(f238(x60871),x60873),x60872))+~P101(f323(f323(f237(x60871),x60873),x60872))+P101(f323(f323(f237(x60871),x60872),x60873))
% 188.07/187.98 [6108]~P103(x61081)+~P101(f323(f59(x61081),x61083))+P101(f323(f323(f237(x61081),x61082),f14(x61081,x61083)))+~P101(f323(f323(f325(x61081),x61082),x61083))
% 188.07/187.98 [6155]~P103(x61551)+E(f323(f323(f235(x61551),x61552),f13(x61551,f236(x61551),x61553)),x61552)+~P101(f323(f59(x61551),x61553))+~P101(f323(f323(f325(x61551),x61552),x61553))
% 188.07/187.98 [6156]~P103(x61561)+E(f323(f323(f236(x61561),x61562),f12(x61561,f235(x61561),x61563)),x61562)+~P101(f323(f59(x61561),x61563))+~P101(f323(f323(f325(x61561),x61562),x61563))
% 188.07/187.98 [6293]E(x62931,x62932)+~E(f323(f323(f22(a865),x62931),x62933),f323(f323(f22(a865),x62932),x62933))+~P101(f323(f323(f237(a865),x62933),x62931))+~P101(f323(f323(f237(a865),x62933),x62932))
% 188.07/187.98 [6320]~P103(x63201)+~P101(f323(f59(x63201),x63202))+~P101(f323(f323(f325(x63201),x63203),x63202))+P101(f323(f323(f237(x63201),f15(x63201,x63202)),x63203))
% 188.07/187.98 [6383]P143(x63832,x63833,x63831)+E(x63831,f2(a1))+P101(f323(f323(f238(a1),x63831),f798(x63831,x63833,x63832)))+P101(f323(f323(f238(a1),f2(a1)),x63831))
% 188.07/187.98 [6384]P142(x63842,x63843,x63841)+E(x63841,f2(a1))+P101(f323(f323(f238(a1),x63841),f808(x63841,x63843,x63842)))+P101(f323(f323(f238(a1),f2(a1)),x63841))
% 188.07/187.98 [6385]~P103(x63851)+E(f323(f323(f235(x63851),x63852),f12(x63851,f235(x63851),x63853)),f12(x63851,f235(x63851),x63853))+~P101(f323(f59(x63851),x63853))+~P101(f323(f323(f325(x63851),x63852),x63853))
% 188.07/187.98 [6386]~P103(x63861)+E(f323(f323(f236(x63861),x63862),f13(x63861,f236(x63861),x63863)),f13(x63861,f236(x63861),x63863))+~P101(f323(f59(x63861),x63863))+~P101(f323(f323(f325(x63861),x63862),x63863))
% 188.07/187.98 [6391]~P101(f323(x63911,x63912))+P101(f323(x63911,f491(x63912,x63911,x63913)))+P101(f323(x63911,f2(a865)))+~P101(f323(f323(f238(a865),x63912),x63913))
% 188.07/187.98 [6445]~P101(f323(x64451,x64452))+~P101(f323(f59(x64453),x64452))+P101(f323(x64451,f821(x64451,x64452,x64453)))+P101(f323(x64451,f188(f872(x64453,a860))))
% 188.07/187.98 [6458]~P116(x64581)+~P90(x64581)+P101(f323(f323(f237(x64581),f323(f103(x64581),x64582)),f323(f103(x64581),x64583)))+~P101(f323(f323(f237(a1),x64582),x64583))
% 188.07/187.98 [6459]~P116(x64591)+~P90(x64591)+P101(f323(f323(f238(x64591),f323(f103(x64591),x64592)),f323(f103(x64591),x64593)))+~P101(f323(f323(f238(a1),x64592),x64593))
% 188.07/187.98 [6462]~P101(f323(x64621,x64623))+~P101(f323(f59(x64622),x64623))+P101(f323(f59(x64622),f821(x64621,x64623,x64622)))+P101(f323(x64621,f188(f872(x64622,a860))))
% 188.07/187.98 [6495]P142(x64951,x64952,x64953)+~P101(f323(x64951,x64952))+P101(f323(f323(f238(a1),x64953),f808(x64953,x64952,x64951)))+P101(f323(f323(f238(a1),f2(a1)),x64953))
% 188.07/187.98 [6530]P143(x65301,x65302,x65303)+P101(f323(f323(f238(a1),x65303),f798(x65303,x65302,x65301)))+~P101(f323(x65301,f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x65303))
% 188.07/187.98 [6561]~P104(x65611)+~P91(x65611)+E(f323(f323(f235(x65611),f323(f103(x65611),x65612)),f323(f103(x65611),x65613)),f323(f103(x65611),x65613))+P101(f323(f323(f237(x65611),f323(f103(x65611),x65612)),f323(f103(x65611),x65613)))
% 188.07/187.98 [6562]~P104(x65621)+~P91(x65621)+E(f323(f323(f236(x65621),f323(f103(x65621),x65622)),f323(f103(x65621),x65623)),f323(f103(x65621),x65622))+P101(f323(f323(f237(x65621),f323(f103(x65621),x65622)),f323(f103(x65621),x65623)))
% 188.07/187.98 [6619]P143(x66192,x66193,x66191)+E(x66191,f2(a1))+~P101(f323(x66192,f802(x66191,x66193,x66192)))+P101(f323(f323(f238(a1),f2(a1)),x66191))
% 188.07/187.98 [6620]P142(x66202,x66203,x66201)+E(x66201,f2(a1))+~P101(f323(x66202,f808(x66201,x66203,x66202)))+P101(f323(f323(f238(a1),f2(a1)),x66201))
% 188.07/187.98 [6624]P101(f323(x66241,x66242))+~P101(f323(f59(x66243),x66242))+P101(f323(x66241,f789(x66241,x66242,x66243)))+~P101(f323(x66241,f188(f872(x66243,a860))))
% 188.07/187.98 [6643]P101(f323(x66431,x66432))+P101(f323(f59(x66433),f789(x66431,x66432,x66433)))+~P101(f323(f59(x66433),x66432))+~P101(f323(x66431,f188(f872(x66433,a860))))
% 188.07/187.98 [6707]P142(x67071,x67072,x67073)+~P101(f323(x67071,x67072))+~P101(f323(x67071,f808(x67073,x67072,x67071)))+P101(f323(f323(f238(a1),f2(a1)),x67073))
% 188.07/187.98 [6737]P143(x67371,x67372,x67373)+~P101(f323(x67371,f802(x67373,x67372,x67371)))+~P101(f323(x67371,f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x67373))
% 188.07/187.98 [6845]~P90(x68453)+~P116(x68453)+~P101(f323(f323(f237(x68453),f323(f103(x68453),x68451)),f323(f103(x68453),x68452)))+P101(f323(f323(f237(a1),x68451),x68452))
% 188.07/187.98 [6846]~P90(x68463)+~P116(x68463)+~P101(f323(f323(f238(x68463),f323(f103(x68463),x68461)),f323(f103(x68463),x68462)))+P101(f323(f323(f238(a1),x68461),x68462))
% 188.07/187.98 [6872]~P103(x68721)+~P16(x68721,x68723)+P16(x68721,f323(f323(f144(x68721),x68722),x68723))+~P101(f323(f323(f237(x68721),x68722),f597(x68723,x68722,x68721)))
% 188.07/187.98 [6873]~P103(x68731)+~P16(x68731,x68733)+P16(x68731,f323(f323(f144(x68731),x68732),x68733))+~P101(f323(f323(f237(x68731),x68732),f600(x68733,x68732,x68731)))
% 188.07/187.98 [6874]~P103(x68741)+~P16(x68741,x68743)+P16(x68741,f323(f323(f144(x68741),x68742),x68743))+~P101(f323(f323(f237(x68741),x68742),f710(x68742,x68743,x68741)))
% 188.07/187.98 [6958]P143(x69582,x69583,x69581)+E(x69581,f2(a1))+P101(f323(f323(f238(a1),x69581),f2(a1)))+P101(f323(f323(f238(a1),f799(x69581,x69583,x69582)),x69581))
% 188.07/187.98 [6959]P142(x69592,x69593,x69591)+E(x69591,f2(a1))+P101(f323(f323(f238(a1),x69591),f2(a1)))+P101(f323(f323(f238(a1),f809(x69591,x69593,x69592)),x69591))
% 188.07/187.98 [6998]P143(x69982,x69983,x69981)+E(x69981,f2(a1))+P101(f323(f323(f237(a1),f798(x69981,x69983,x69982)),f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x69981))
% 188.07/187.98 [6999]P142(x69992,x69993,x69991)+E(x69991,f2(a1))+P101(f323(f323(f237(a1),f808(x69991,x69993,x69992)),f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x69991))
% 188.07/187.98 [7021]~P103(x70211)+~P16(x70211,x70213)+E(f323(f323(f141(x70211,x70211,f5(x70211)),x70212),f164(x70211,x70212,x70213)),x70213)+~P101(f323(f323(f325(x70211),x70212),f323(f166(x70211),x70213)))
% 188.07/187.98 [7068]P142(x70681,x70682,x70683)+~P101(f323(x70681,x70682))+P101(f323(f323(f238(a1),x70683),f2(a1)))+P101(f323(f323(f238(a1),f809(x70683,x70682,x70681)),x70683))
% 188.07/187.98 [7074]~P104(x70741)+~P91(x70741)+E(f323(f323(f235(x70741),f323(f103(x70741),x70742)),f323(f103(x70741),x70743)),f323(f103(x70741),x70742))+~P101(f323(f323(f237(x70741),f323(f103(x70741),x70742)),f323(f103(x70741),x70743)))
% 188.07/187.98 [7075]~P104(x70751)+~P91(x70751)+E(f323(f323(f236(x70751),f323(f103(x70751),x70752)),f323(f103(x70751),x70753)),f323(f103(x70751),x70753))+~P101(f323(f323(f237(x70751),f323(f103(x70751),x70752)),f323(f103(x70751),x70753)))
% 188.07/187.98 [7089]P143(x70891,x70892,x70893)+~P101(f323(x70891,f2(a1)))+P101(f323(f323(f238(a1),x70893),f2(a1)))+P101(f323(f323(f238(a1),f799(x70893,x70892,x70891)),x70893))
% 188.07/187.98 [7097]P142(x70971,x70972,x70973)+~P101(f323(x70971,x70972))+P101(f323(f323(f237(a1),f808(x70973,x70972,x70971)),f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x70973))
% 188.07/187.98 [7121]P143(x71211,x71212,x71213)+~P101(f323(x71211,f2(a1)))+P101(f323(f323(f237(a1),f798(x71213,x71212,x71211)),f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x71213))
% 188.07/187.98 [7149]~P101(f323(x71491,x71492))+P101(f323(x71491,f2(a865)))+~P101(f323(f323(f238(a865),x71492),x71493))+P101(f323(f323(f238(a865),f491(x71492,x71491,x71493)),x71493))
% 188.07/187.98 [7166]~P103(x71661)+~P16(x71661,x71663)+P16(x71661,f323(f323(f144(x71661),x71662),x71663))+P101(f323(f323(f325(x71661),f597(x71663,x71662,x71661)),f323(f166(x71661),x71663)))
% 188.07/187.98 [7167]~P103(x71671)+~P16(x71671,x71673)+P16(x71671,f323(f323(f144(x71671),x71672),x71673))+P101(f323(f323(f325(x71671),f600(x71673,x71672,x71671)),f323(f166(x71671),x71673)))
% 188.07/187.98 [7168]~P103(x71681)+~P16(x71681,x71683)+P16(x71681,f323(f323(f144(x71681),x71682),x71683))+P101(f323(f323(f325(x71681),f710(x71682,x71683,x71681)),f323(f166(x71681),x71683)))
% 188.07/187.98 [7272]~P103(x72721)+~P6(x72721)+~P101(f323(f323(f238(x72721),x72723),f37(x72721,x72722)))+P101(f323(f323(f325(x72721),f548(x72722,x72723,x72721)),x72722))
% 188.07/187.98 [7434]~P103(x74341)+~P6(x74341)+~P101(f323(f323(f238(x74341),f38(x74341,x74343)),x74342))+P101(f323(f323(f325(x74341),f645(x74342,x74343,x74341)),x74343))
% 188.07/187.98 [7435]~P103(x74351)+~P6(x74351)+~P101(f323(f323(f238(x74351),f38(x74351,x74353)),x74352))+P101(f323(f323(f238(x74351),f645(x74352,x74353,x74351)),x74352))
% 188.07/187.98 [7449]P143(x74492,x74493,x74491)+E(x74491,f2(a1))+P101(f323(f323(f238(a1),x74491),f798(x74491,x74493,x74492)))+P101(f323(f323(f238(a1),f799(x74491,x74493,x74492)),x74491))
% 188.07/187.98 [7450]P142(x74502,x74503,x74501)+E(x74501,f2(a1))+P101(f323(f323(f238(a1),x74501),f808(x74501,x74503,x74502)))+P101(f323(f323(f238(a1),f809(x74501,x74503,x74502)),x74501))
% 188.07/187.98 [7540]P143(x75403,x75402,x75401)+E(x75401,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x75401),f802(x75401,x75402,x75403))),f798(x75401,x75402,x75403)),x75402)+P101(f323(f323(f238(a1),f2(a1)),x75401))
% 188.07/187.98 [7541]P142(x75413,x75412,x75411)+E(x75411,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x75411),f811(x75411,x75412,x75413))),f808(x75411,x75412,x75413)),x75412)+P101(f323(f323(f238(a1),f2(a1)),x75411))
% 188.07/187.98 [7543]~P120(x75431)+~P101(f323(f323(f237(x75431),x75433),f2(x75431)))+P101(f323(f323(f237(x75431),f323(f323(f79(x75431),x75432),x75433)),f2(x75431)))+~P101(f323(f323(f237(x75431),f2(x75431)),x75432))
% 188.07/187.98 [7544]~P120(x75441)+~P101(f323(f323(f237(x75441),x75442),f2(x75441)))+P101(f323(f323(f237(x75441),f323(f323(f79(x75441),x75442),x75443)),f2(x75441)))+~P101(f323(f323(f237(x75441),f2(x75441)),x75443))
% 188.07/187.98 [7546]~P129(x75461)+~P101(f323(f323(f237(x75461),x75463),f2(x75461)))+P101(f323(f323(f237(x75461),f323(f323(f79(x75461),x75462),x75463)),f2(x75461)))+~P101(f323(f323(f237(x75461),f2(x75461)),x75462))
% 188.07/187.98 [7548]~P129(x75481)+~P101(f323(f323(f237(x75481),x75482),f2(x75481)))+P101(f323(f323(f237(x75481),f323(f323(f79(x75481),x75482),x75483)),f2(x75481)))+~P101(f323(f323(f237(x75481),f2(x75481)),x75483))
% 188.07/187.98 [7549]~P65(x75491)+~P101(f323(f323(f237(x75491),x75492),f2(x75491)))+P101(f323(f323(f237(x75491),f323(f323(f281(x75491),x75492),x75493)),f2(x75491)))+~P101(f323(f323(f238(x75491),f2(x75491)),x75493))
% 188.07/187.98 [7550]~P65(x75501)+~P101(f323(f323(f238(x75501),x75503),f2(x75501)))+P101(f323(f323(f237(x75501),f323(f323(f281(x75501),x75502),x75503)),f2(x75501)))+~P101(f323(f323(f237(x75501),f2(x75501)),x75502))
% 188.07/187.98 [7551]~P64(x75511)+~P101(f323(f323(f237(x75511),x75513),f2(x75511)))+P101(f323(f323(f237(x75511),f323(f323(f281(x75511),x75512),x75513)),f2(x75511)))+~P101(f323(f323(f237(x75511),f2(x75511)),x75512))
% 188.07/187.98 [7552]~P64(x75521)+~P101(f323(f323(f237(x75521),x75522),f2(x75521)))+P101(f323(f323(f237(x75521),f323(f323(f281(x75521),x75522),x75523)),f2(x75521)))+~P101(f323(f323(f237(x75521),f2(x75521)),x75523))
% 188.07/187.98 [7554]~P125(x75541)+~P101(f323(f323(f238(x75541),x75543),f2(x75541)))+P101(f323(f323(f238(x75541),f323(f323(f79(x75541),x75542),x75543)),f2(x75541)))+~P101(f323(f323(f238(x75541),f2(x75541)),x75542))
% 188.07/187.98 [7555]~P125(x75551)+~P101(f323(f323(f238(x75551),x75552),f2(x75551)))+P101(f323(f323(f238(x75551),f323(f323(f79(x75551),x75552),x75553)),f2(x75551)))+~P101(f323(f323(f238(x75551),f2(x75551)),x75553))
% 188.07/187.98 [7556]~P65(x75561)+~P101(f323(f323(f238(x75561),x75563),f2(x75561)))+P101(f323(f323(f238(x75561),f323(f323(f281(x75561),x75562),x75563)),f2(x75561)))+~P101(f323(f323(f238(x75561),f2(x75561)),x75562))
% 188.07/187.98 [7557]~P65(x75571)+~P101(f323(f323(f238(x75571),x75572),f2(x75571)))+P101(f323(f323(f238(x75571),f323(f323(f281(x75571),x75572),x75573)),f2(x75571)))+~P101(f323(f323(f238(x75571),f2(x75571)),x75573))
% 188.07/187.98 [7558]~P64(x75581)+~P101(f323(f323(f238(x75581),x75583),f2(x75581)))+P101(f323(f323(f238(x75581),f323(f323(f281(x75581),x75582),x75583)),f2(x75581)))+~P101(f323(f323(f238(x75581),f2(x75581)),x75582))
% 188.07/187.98 [7559]~P64(x75591)+~P101(f323(f323(f238(x75591),x75592),f2(x75591)))+P101(f323(f323(f238(x75591),f323(f323(f281(x75591),x75592),x75593)),f2(x75591)))+~P101(f323(f323(f238(x75591),f2(x75591)),x75593))
% 188.07/187.98 [7574]P142(x75741,x75742,x75743)+~P101(f323(x75741,x75742))+P101(f323(f323(f238(a1),x75743),f808(x75743,x75742,x75741)))+P101(f323(f323(f238(a1),f809(x75743,x75742,x75741)),x75743))
% 188.07/187.98 [7587]P143(x75871,x75872,x75873)+P101(f323(f323(f238(a1),x75873),f798(x75873,x75872,x75871)))+~P101(f323(x75871,f2(a1)))+P101(f323(f323(f238(a1),f799(x75873,x75872,x75871)),x75873))
% 188.07/187.98 [7638]P143(x76382,x76383,x76381)+E(x76381,f2(a1))+~P101(f323(x76382,f802(x76381,x76383,x76382)))+P101(f323(f323(f238(a1),f799(x76381,x76383,x76382)),x76381))
% 188.07/187.98 [7639]P142(x76392,x76393,x76391)+E(x76391,f2(a1))+~P101(f323(x76392,f808(x76391,x76393,x76392)))+P101(f323(f323(f238(a1),f809(x76391,x76393,x76392)),x76391))
% 188.07/187.98 [7650]P142(x76503,x76502,x76501)+~P101(f323(x76503,x76502))+E(f323(f323(f78(a1),f323(f323(f79(a1),x76501),f811(x76501,x76502,x76503))),f808(x76501,x76502,x76503)),x76502)+P101(f323(f323(f238(a1),f2(a1)),x76501))
% 188.07/187.98 [7667]P143(x76673,x76672,x76671)+E(f323(f323(f78(a1),f323(f323(f79(a1),x76671),f802(x76671,x76672,x76673))),f798(x76671,x76672,x76673)),x76672)+~P101(f323(x76673,f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x76671))
% 188.07/187.98 [7693]~P101(f323(x76931,x76933))+~P101(f323(f59(x76932),x76933))+P101(f323(f323(f325(x76932),f822(x76931,x76933,x76932)),f821(x76931,x76933,x76932)))+P101(f323(x76931,f188(f872(x76932,a860))))
% 188.07/187.98 [7704]P142(x77041,x77042,x77043)+~P101(f323(x77041,x77042))+~P101(f323(x77041,f808(x77043,x77042,x77041)))+P101(f323(f323(f238(a1),f809(x77043,x77042,x77041)),x77043))
% 188.07/187.98 [7710]P143(x77101,x77102,x77103)+~P101(f323(x77101,f802(x77103,x77102,x77101)))+~P101(f323(x77101,f2(a1)))+P101(f323(f323(f238(a1),f799(x77103,x77102,x77101)),x77103))
% 188.07/187.98 [7811]~P120(x78111)+~P101(f323(f323(f237(x78111),f323(f323(f79(x78111),x78113),x78112)),f2(x78111)))+P101(f323(f323(f237(x78111),x78112),f2(x78111)))+P101(f323(f323(f237(x78111),f2(x78111)),x78112))
% 188.07/187.98 [7812]~P120(x78121)+~P101(f323(f323(f237(x78121),f323(f323(f79(x78121),x78122),x78123)),f2(x78121)))+P101(f323(f323(f237(x78121),x78122),f2(x78121)))+P101(f323(f323(f237(x78121),f2(x78121)),x78122))
% 188.07/187.98 [7813]~P64(x78131)+~P101(f323(f323(f237(x78131),f323(f323(f281(x78131),x78133),x78132)),f2(x78131)))+P101(f323(f323(f237(x78131),x78132),f2(x78131)))+P101(f323(f323(f237(x78131),f2(x78131)),x78132))
% 188.07/187.98 [7814]~P64(x78141)+~P101(f323(f323(f237(x78141),f323(f323(f281(x78141),x78142),x78143)),f2(x78141)))+P101(f323(f323(f237(x78141),x78142),f2(x78141)))+P101(f323(f323(f237(x78141),f2(x78141)),x78142))
% 188.07/187.98 [7815]~P64(x78151)+~P101(f323(f323(f238(x78151),f323(f323(f281(x78151),x78153),x78152)),f2(x78151)))+P101(f323(f323(f238(x78151),x78152),f2(x78151)))+P101(f323(f323(f238(x78151),f2(x78151)),x78152))
% 188.07/187.98 [7816]~P64(x78161)+~P101(f323(f323(f238(x78161),f323(f323(f281(x78161),x78162),x78163)),f2(x78161)))+P101(f323(f323(f238(x78161),x78162),f2(x78161)))+P101(f323(f323(f238(x78161),f2(x78161)),x78162))
% 188.07/187.98 [7841]~P120(x78411)+~P101(f323(f323(f237(x78411),f323(f323(f79(x78411),x78412),x78413)),f2(x78411)))+P101(f323(f323(f237(x78411),f2(x78411)),x78412))+P101(f323(f323(f237(x78411),f2(x78411)),x78413))
% 188.07/187.98 [7842]~P64(x78421)+~P101(f323(f323(f237(x78421),f323(f323(f281(x78421),x78422),x78423)),f2(x78421)))+P101(f323(f323(f237(x78421),f2(x78421)),x78422))+P101(f323(f323(f237(x78421),f2(x78421)),x78423))
% 188.07/187.98 [7843]~P64(x78431)+~P101(f323(f323(f238(x78431),f323(f323(f281(x78431),x78432),x78433)),f2(x78431)))+P101(f323(f323(f238(x78431),f2(x78431)),x78432))+P101(f323(f323(f238(x78431),f2(x78431)),x78433))
% 188.07/187.98 [7865]P143(x78652,x78653,x78651)+E(x78651,f2(a1))+P101(f323(f323(f237(a1),f798(x78651,x78653,x78652)),f2(a1)))+P101(f323(f323(f238(a1),f799(x78651,x78653,x78652)),x78651))
% 188.07/187.98 [7866]P142(x78662,x78663,x78661)+E(x78661,f2(a1))+P101(f323(f323(f237(a1),f808(x78661,x78663,x78662)),f2(a1)))+P101(f323(f323(f238(a1),f809(x78661,x78663,x78662)),x78661))
% 188.07/187.98 [7874]~P119(x78741)+~P101(f323(f323(f238(x78741),x78742),f76(x78741)))+P101(f323(f323(f238(x78741),f323(f323(f248(x78741),x78742),f323(a112,x78743))),f76(x78741)))+~P101(f323(f323(f238(x78741),f2(x78741)),x78742))
% 188.07/187.98 [7930]~P103(x79301)+~E(x79303,f113(x79301))+~P16(x79301,f323(f162(x79301),x79303))+E(f323(f135(x79301,x79301,f323(f7(x79301,x79301,x79301),f236(x79301)),x79302),f323(f162(x79301),x79303)),x79302)
% 188.07/187.98 [7932]P142(x79321,x79322,x79323)+~P101(f323(x79321,x79322))+P101(f323(f323(f237(a1),f808(x79323,x79322,x79321)),f2(a1)))+P101(f323(f323(f238(a1),f809(x79323,x79322,x79321)),x79323))
% 188.07/187.98 [7939]P143(x79391,x79392,x79393)+~P101(f323(x79391,f2(a1)))+P101(f323(f323(f237(a1),f798(x79393,x79392,x79391)),f2(a1)))+P101(f323(f323(f238(a1),f799(x79393,x79392,x79391)),x79393))
% 188.07/187.98 [8155]P143(x81553,x81552,x81551)+E(x81551,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x81551),f802(x81551,x81552,x81553))),f798(x81551,x81552,x81553)),x81552)+P101(f323(f323(f238(a1),f799(x81551,x81552,x81553)),x81551))
% 188.07/187.98 [8156]P142(x81563,x81562,x81561)+E(x81561,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x81561),f811(x81561,x81562,x81563))),f808(x81561,x81562,x81563)),x81562)+P101(f323(f323(f238(a1),f809(x81561,x81562,x81563)),x81561))
% 188.07/187.98 [8193]P142(x81933,x81932,x81931)+~P101(f323(x81933,x81932))+E(f323(f323(f78(a1),f323(f323(f79(a1),x81931),f811(x81931,x81932,x81933))),f808(x81931,x81932,x81933)),x81932)+P101(f323(f323(f238(a1),f809(x81931,x81932,x81933)),x81931))
% 188.07/187.98 [8194]~P68(x81941)+~P72(x81941)+~P39(x81943)+E(f323(f323(f6(a865,x81941),f323(f323(f8(a1,x81941,a865),x81942),f100(a1))),f323(f302(a1,a865,a104),x81943)),f323(f323(f6(a1,x81941),x81942),x81943))
% 188.07/187.98 [8195]~P68(x81951)+~P72(x81951)+~P39(x81953)+E(f323(f323(f9(a865,x81951),f323(f323(f8(a1,x81951,a865),x81952),f100(a1))),f323(f302(a1,a865,a104),x81953)),f323(f323(f9(a1,x81951),x81952),x81953))
% 188.07/187.98 [8204]P143(x82043,x82042,x82041)+E(f323(f323(f78(a1),f323(f323(f79(a1),x82041),f802(x82041,x82042,x82043))),f798(x82041,x82042,x82043)),x82042)+~P101(f323(x82043,f2(a1)))+P101(f323(f323(f238(a1),f799(x82041,x82042,x82043)),x82041))
% 188.07/187.98 [8225]~E(x82252,f2(a865))+~E(f323(f257(a865,a865),x82253),f2(a865))+~E(x82251,f323(f323(f78(a865),f323(f323(f79(a865),f323(f257(a865,a865),x82253)),x82252)),f323(f261(a865,a865),x82253)))+P101(f323(f45(x82251,x82252),x82253))
% 188.07/187.98 [8280]P101(f323(x82801,x82802))+~P101(f323(f323(f325(x82803),f791(x82801,x82802,x82803)),f789(x82801,x82802,x82803)))+~P101(f323(f59(x82803),x82802))+~P101(f323(x82801,f188(f872(x82803,a860))))
% 188.07/187.98 [8908]P101(f323(x89081,x89082))+~P101(f323(f59(x89083),x89082))+~P101(f323(x89081,f323(f323(f301(x89083),f791(x89081,x89082,x89083)),f789(x89081,x89082,x89083))))+~P101(f323(x89081,f188(f872(x89083,a860))))
% 188.07/187.98 [9138]P101(f323(f323(f237(a1),x91381),f2(a1)))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),f323(f323(f79(a1),x91383),x91381)),x91382)),f2(a1)))+~P101(f323(f323(f237(a1),f2(a1)),x91382))+~P101(f323(f323(f238(a1),f2(a1)),x91383))
% 188.07/187.98 [5780]~P2(x57802)+E(x57801,f188(f872(x57802,a860)))+~P101(f323(f59(x57802),x57801))+E(f11(x57802,f323(f323(f301(x57802),x57803),x57801)),f323(f323(f101(x57802),x57803),f11(x57802,x57801)))
% 188.07/187.98 [5781]~P2(x57812)+E(x57811,f188(f872(x57812,a860)))+~P101(f323(f59(x57812),x57811))+E(f10(x57812,f323(f323(f301(x57812),x57813),x57811)),f323(f323(f110(x57812),x57813),f10(x57812,x57811)))
% 188.07/187.98 [5782]~P103(x57822)+E(x57821,f188(f872(x57822,a860)))+~P101(f323(f59(x57822),x57821))+E(f14(x57822,f323(f323(f301(x57822),x57823),x57821)),f323(f323(f236(x57822),x57823),f14(x57822,x57821)))
% 188.07/187.98 [5783]~P103(x57832)+E(x57831,f188(f872(x57832,a860)))+~P101(f323(f59(x57832),x57831))+E(f15(x57832,f323(f323(f301(x57832),x57833),x57831)),f323(f323(f235(x57832),x57833),f15(x57832,x57831)))
% 188.07/187.98 [6084]~P120(x60841)+~E(x60843,f2(x60841))+~E(x60842,f2(x60841))+E(f323(f323(f78(x60841),f323(f323(f79(x60841),x60842),x60842)),f323(f323(f79(x60841),x60843),x60843)),f2(x60841))
% 188.07/187.98 [6149]~P93(x61492)+E(x61491,f188(f872(x61492,a860)))+~P101(f323(f59(x61492),x61491))+E(f323(f61(x61492,f79(x61492)),f323(f323(f301(x61492),x61493),x61491)),f323(f323(f79(x61492),x61493),f323(f61(x61492,f79(x61492)),x61491)))
% 188.07/187.98 [6272]~P103(x62722)+E(x62721,f188(f872(x62722,a860)))+~P101(f323(f59(x62722),x62721))+E(f12(x62722,f235(x62722),f323(f323(f301(x62722),x62723),x62721)),f323(f323(f235(x62722),x62723),f12(x62722,f235(x62722),x62721)))
% 188.07/187.98 [6273]~P103(x62732)+E(x62731,f188(f872(x62732,a860)))+~P101(f323(f59(x62732),x62731))+E(f13(x62732,f236(x62732),f323(f323(f301(x62732),x62733),x62731)),f323(f323(f236(x62732),x62733),f13(x62732,f236(x62732),x62731)))
% 188.07/187.98 [6772]~P66(x67721)+~P101(f323(f59(x67721),x67723))+E(f323(f61(x67721,f79(x67721)),f323(f323(f301(x67721),x67722),x67723)),f323(f323(f62(x67721,x67721,f79(x67721)),x67722),x67723))+P101(f323(f323(f325(x67721),x67722),x67723))
% 188.07/187.98 [6852]~E(f323(f323(f78(a1),x68522),f323(f323(f79(a1),x68523),x68521)),x68523)+~P101(f323(f323(f238(a1),f2(a1)),x68523))+P101(f323(f323(f237(a1),f76(a1)),x68521))+~P101(f323(f323(f238(a1),x68522),x68523))
% 188.07/187.98 [6879]~E(f323(f323(f78(a1),x68792),f323(f323(f79(a1),x68793),x68791)),x68793)+P101(f323(f323(f237(a1),x68791),f76(a1)))+~P101(f323(f323(f237(a1),f2(a1)),x68792))+~P101(f323(f323(f238(a1),f2(a1)),x68793))
% 188.07/187.98 [6895]E(x68951,f2(a865))+~P101(f323(f45(x68953,x68951),x68952))+~P101(f323(f323(f238(a865),f2(a865)),x68951))+P101(f323(f323(f238(a865),f323(f261(a865,a865),x68952)),x68951))
% 188.07/187.98 [6925]~P132(x69251)+~P101(f323(f323(f237(x69251),x69252),f2(x69251)))+~P101(f323(f323(f237(x69251),x69253),f2(x69251)))+E(f323(f323(f79(x69251),f323(f73(x69251),x69252)),f323(f73(x69251),x69253)),f323(f73(x69251),f323(f323(f79(x69251),x69252),x69253)))
% 188.07/187.98 [6975]~P132(x69751)+~P101(f323(f323(f237(x69751),x69752),f2(x69751)))+E(f323(f323(f79(x69751),f323(f73(x69751),x69752)),f323(f73(x69751),x69753)),f323(f73(x69751),f323(f323(f79(x69751),x69752),x69753)))+~P101(f323(f323(f237(x69751),f2(x69751)),x69753))
% 188.07/187.98 [6976]~P132(x69761)+~P101(f323(f323(f237(x69761),x69763),f2(x69761)))+E(f323(f323(f79(x69761),f323(f73(x69761),x69762)),f323(f73(x69761),x69763)),f323(f73(x69761),f323(f323(f79(x69761),x69762),x69763)))+~P101(f323(f323(f237(x69761),f2(x69761)),x69762))
% 188.07/187.98 [7030]~P132(x70301)+E(f323(f323(f79(x70301),f323(f73(x70301),x70302)),f323(f73(x70301),x70303)),f323(f73(x70301),f323(f323(f79(x70301),x70302),x70303)))+~P101(f323(f323(f237(x70301),f2(x70301)),x70302))+~P101(f323(f323(f237(x70301),f2(x70301)),x70303))
% 188.07/187.98 [7047]~P122(x70471)+~P101(f323(f323(f237(x70471),x70473),f2(x70471)))+~P101(f323(f323(f237(x70471),x70472),f2(x70471)))+P101(f323(f323(f237(x70471),f2(x70471)),f323(f323(f79(x70471),x70472),x70473)))
% 188.07/187.98 [7048]~P120(x70481)+~P101(f323(f323(f237(x70481),x70483),f2(x70481)))+~P101(f323(f323(f237(x70481),x70482),f2(x70481)))+P101(f323(f323(f237(x70481),f2(x70481)),f323(f323(f79(x70481),x70482),x70483)))
% 188.07/187.98 [7049]~P65(x70491)+~P101(f323(f323(f238(x70491),x70493),f2(x70491)))+~P101(f323(f323(f237(x70491),x70492),f2(x70491)))+P101(f323(f323(f237(x70491),f2(x70491)),f323(f323(f281(x70491),x70492),x70493)))
% 188.07/187.98 [7050]~P64(x70501)+~P101(f323(f323(f237(x70501),x70503),f2(x70501)))+~P101(f323(f323(f237(x70501),x70502),f2(x70501)))+P101(f323(f323(f237(x70501),f2(x70501)),f323(f323(f281(x70501),x70502),x70503)))
% 188.07/187.98 [7051]~P120(x70511)+~P101(f323(f323(f238(x70511),x70513),f2(x70511)))+~P101(f323(f323(f238(x70511),x70512),f2(x70511)))+P101(f323(f323(f238(x70511),f2(x70511)),f323(f323(f79(x70511),x70512),x70513)))
% 188.07/187.98 [7052]~P65(x70521)+~P101(f323(f323(f238(x70521),x70523),f2(x70521)))+~P101(f323(f323(f238(x70521),x70522),f2(x70521)))+P101(f323(f323(f238(x70521),f2(x70521)),f323(f323(f281(x70521),x70522),x70523)))
% 188.07/187.98 [7053]~P64(x70531)+~P101(f323(f323(f238(x70531),x70533),f2(x70531)))+~P101(f323(f323(f238(x70531),x70532),f2(x70531)))+P101(f323(f323(f238(x70531),f2(x70531)),f323(f323(f281(x70531),x70532),x70533)))
% 188.07/187.98 [7054]~P119(x70541)+~P101(f323(f323(f238(a865),f2(a865)),x70543))+~P101(f323(f323(f238(x70541),f76(x70541)),x70542))+P101(f323(f323(f238(x70541),f76(x70541)),f323(f323(f248(x70541),x70542),x70543)))
% 188.07/187.98 [7150]~P122(x71501)+~P101(f323(f323(f237(x71501),f2(x71501)),x71503))+~P101(f323(f323(f237(x71501),f2(x71501)),x71502))+P101(f323(f323(f237(x71501),f2(x71501)),f323(f323(f79(x71501),x71502),x71503)))
% 188.07/187.98 [7151]~P120(x71511)+~P101(f323(f323(f237(x71511),f2(x71511)),x71513))+~P101(f323(f323(f237(x71511),f2(x71511)),x71512))+P101(f323(f323(f237(x71511),f2(x71511)),f323(f323(f79(x71511),x71512),x71513)))
% 188.07/187.98 [7152]~P129(x71521)+~P101(f323(f323(f237(x71521),f2(x71521)),x71523))+~P101(f323(f323(f237(x71521),f2(x71521)),x71522))+P101(f323(f323(f237(x71521),f2(x71521)),f323(f323(f79(x71521),x71522),x71523)))
% 188.07/187.98 [7154]~P65(x71541)+~P101(f323(f323(f238(x71541),f2(x71541)),x71543))+~P101(f323(f323(f237(x71541),f2(x71541)),x71542))+P101(f323(f323(f237(x71541),f2(x71541)),f323(f323(f281(x71541),x71542),x71543)))
% 188.07/187.98 [7155]~P64(x71551)+~P101(f323(f323(f237(x71551),f2(x71551)),x71553))+~P101(f323(f323(f237(x71551),f2(x71551)),x71552))+P101(f323(f323(f237(x71551),f2(x71551)),f323(f323(f281(x71551),x71552),x71553)))
% 188.07/187.98 [7156]~P119(x71561)+~P101(f323(f323(f238(x71561),f76(x71561)),x71563))+~P101(f323(f323(f238(x71561),f76(x71561)),x71562))+P101(f323(f323(f238(x71561),f76(x71561)),f323(f323(f79(x71561),x71562),x71563)))
% 188.07/187.98 [7157]~P125(x71571)+~P101(f323(f323(f238(x71571),f2(x71571)),x71573))+~P101(f323(f323(f238(x71571),f2(x71571)),x71572))+P101(f323(f323(f238(x71571),f2(x71571)),f323(f323(f79(x71571),x71572),x71573)))
% 188.07/187.98 [7160]~P84(x71601)+~P101(f323(f323(f238(x71601),f2(x71601)),x71603))+~P101(f323(f323(f238(x71601),f2(x71601)),x71602))+P101(f323(f323(f238(x71601),f2(x71601)),f323(f323(f78(x71601),x71602),x71603)))
% 188.07/187.98 [7161]~P65(x71611)+~P101(f323(f323(f238(x71611),f2(x71611)),x71613))+~P101(f323(f323(f238(x71611),f2(x71611)),x71612))+P101(f323(f323(f238(x71611),f2(x71611)),f323(f323(f281(x71611),x71612),x71613)))
% 188.07/187.98 [7162]~P64(x71621)+~P101(f323(f323(f238(x71621),f2(x71621)),x71623))+~P101(f323(f323(f238(x71621),f2(x71621)),x71622))+P101(f323(f323(f238(x71621),f2(x71621)),f323(f323(f281(x71621),x71622),x71623)))
% 188.07/187.98 [7233]~P2(x72331)+~P101(f323(f59(x72331),x72333))+E(f11(x72331,f323(f323(f301(x72331),x72332),x72333)),x72332)+~E(f323(f323(f22(f872(x72331,a860)),x72333),f323(f323(f301(x72331),x72332),f188(f872(x72331,a860)))),f188(f872(x72331,a860)))
% 188.07/187.98 [7234]~P2(x72341)+~P101(f323(f59(x72341),x72343))+E(f10(x72341,f323(f323(f301(x72341),x72342),x72343)),x72342)+~E(f323(f323(f22(f872(x72341,a860)),x72343),f323(f323(f301(x72341),x72342),f188(f872(x72341,a860)))),f188(f872(x72341,a860)))
% 188.07/187.98 [7235]~P103(x72351)+~P101(f323(f59(x72351),x72353))+E(f14(x72351,f323(f323(f301(x72351),x72352),x72353)),x72352)+~E(f323(f323(f22(f872(x72351,a860)),x72353),f323(f323(f301(x72351),x72352),f188(f872(x72351,a860)))),f188(f872(x72351,a860)))
% 188.07/187.98 [7236]~P103(x72361)+~P101(f323(f59(x72361),x72363))+E(f15(x72361,f323(f323(f301(x72361),x72362),x72363)),x72362)+~E(f323(f323(f22(f872(x72361,a860)),x72363),f323(f323(f301(x72361),x72362),f188(f872(x72361,a860)))),f188(f872(x72361,a860)))
% 188.07/187.98 [7237]~P120(x72371)+P101(f323(f323(f237(x72371),x72372),f2(x72371)))+P101(f323(f323(f237(x72371),f2(x72371)),x72373))+~P101(f323(f323(f237(x72371),f2(x72371)),f323(f323(f79(x72371),x72373),x72372)))
% 188.07/187.98 [7238]~P120(x72381)+P101(f323(f323(f237(x72381),x72382),f2(x72381)))+P101(f323(f323(f237(x72381),f2(x72381)),x72383))+~P101(f323(f323(f237(x72381),f2(x72381)),f323(f323(f79(x72381),x72382),x72383)))
% 188.07/187.98 [7239]~P64(x72391)+P101(f323(f323(f237(x72391),x72392),f2(x72391)))+P101(f323(f323(f237(x72391),f2(x72391)),x72393))+~P101(f323(f323(f237(x72391),f2(x72391)),f323(f323(f281(x72391),x72393),x72392)))
% 188.07/187.98 [7240]~P64(x72401)+P101(f323(f323(f237(x72401),x72402),f2(x72401)))+P101(f323(f323(f237(x72401),f2(x72401)),x72403))+~P101(f323(f323(f237(x72401),f2(x72401)),f323(f323(f281(x72401),x72402),x72403)))
% 188.07/187.98 [7241]~P120(x72411)+P101(f323(f323(f237(x72411),x72412),f2(x72411)))+P101(f323(f323(f237(x72411),f2(x72411)),x72412))+~P101(f323(f323(f237(x72411),f2(x72411)),f323(f323(f79(x72411),x72413),x72412)))
% 188.07/187.98 [7242]~P120(x72421)+P101(f323(f323(f237(x72421),x72422),f2(x72421)))+P101(f323(f323(f237(x72421),f2(x72421)),x72422))+~P101(f323(f323(f237(x72421),f2(x72421)),f323(f323(f79(x72421),x72422),x72423)))
% 188.07/187.98 [7243]~P64(x72431)+P101(f323(f323(f237(x72431),x72432),f2(x72431)))+P101(f323(f323(f237(x72431),f2(x72431)),x72432))+~P101(f323(f323(f237(x72431),f2(x72431)),f323(f323(f281(x72431),x72433),x72432)))
% 188.07/187.98 [7244]~P64(x72441)+P101(f323(f323(f237(x72441),x72442),f2(x72441)))+P101(f323(f323(f237(x72441),f2(x72441)),x72442))+~P101(f323(f323(f237(x72441),f2(x72441)),f323(f323(f281(x72441),x72442),x72443)))
% 188.07/187.98 [7245]~P64(x72451)+P101(f323(f323(f238(x72451),x72452),f2(x72451)))+P101(f323(f323(f238(x72451),f2(x72451)),x72453))+~P101(f323(f323(f238(x72451),f2(x72451)),f323(f323(f281(x72451),x72453),x72452)))
% 188.07/187.98 [7246]~P64(x72461)+P101(f323(f323(f238(x72461),x72462),f2(x72461)))+P101(f323(f323(f238(x72461),f2(x72461)),x72463))+~P101(f323(f323(f238(x72461),f2(x72461)),f323(f323(f281(x72461),x72462),x72463)))
% 188.07/187.98 [7247]~P64(x72471)+P101(f323(f323(f238(x72471),x72472),f2(x72471)))+P101(f323(f323(f238(x72471),f2(x72471)),x72472))+~P101(f323(f323(f238(x72471),f2(x72471)),f323(f323(f281(x72471),x72473),x72472)))
% 188.07/187.98 [7248]~P64(x72481)+P101(f323(f323(f238(x72481),x72482),f2(x72481)))+P101(f323(f323(f238(x72481),f2(x72481)),x72482))+~P101(f323(f323(f238(x72481),f2(x72481)),f323(f323(f281(x72481),x72482),x72483)))
% 188.07/187.98 [7335]~E(f323(f323(f101(f872(x73351,a860)),f323(f166(x73351),x73352)),f323(f166(x73351),x73353)),f188(f872(x73351,a860)))+~P101(f323(f130(x73351),x73353))+~P101(f323(f130(x73351),x73352))+P101(f323(f130(x73351),f323(f323(f121(x73351),x73352),x73353)))
% 188.07/187.98 [7336]~P103(x73361)+~P101(f323(f59(x73361),x73363))+E(f12(x73361,f235(x73361),f323(f323(f301(x73361),x73362),x73363)),x73362)+~E(f323(f323(f22(f872(x73361,a860)),x73363),f323(f323(f301(x73361),x73362),f188(f872(x73361,a860)))),f188(f872(x73361,a860)))
% 188.07/187.98 [7337]~P103(x73371)+~P101(f323(f59(x73371),x73373))+E(f13(x73371,f236(x73371),f323(f323(f301(x73371),x73372),x73373)),x73372)+~E(f323(f323(f22(f872(x73371,a860)),x73373),f323(f323(f301(x73371),x73372),f188(f872(x73371,a860)))),f188(f872(x73371,a860)))
% 188.07/187.98 [7353]~P82(x73531)+~P101(f323(f323(f237(x73531),x73532),x73533))+~P101(f323(f323(f237(x73531),f323(f77(x73531),x73532)),x73533))+P101(f323(f323(f237(x73531),f323(f73(x73531),x73532)),x73533))
% 188.07/187.98 [7354]~P116(x73541)+~P101(f323(f323(f238(x73541),x73542),x73543))+~P101(f323(f323(f238(x73541),f323(f77(x73541),x73542)),x73543))+P101(f323(f323(f238(x73541),f323(f73(x73541),x73542)),x73543))
% 188.07/187.98 [7424]~P125(x74241)+P101(f323(f323(f238(x74241),f2(x74241)),x74242))+~P101(f323(f323(f238(x74241),f2(x74241)),x74243))+~P101(f323(f323(f238(x74241),f2(x74241)),f323(f323(f79(x74241),x74243),x74242)))
% 188.07/187.98 [7425]~P125(x74251)+P101(f323(f323(f238(x74251),f2(x74251)),x74252))+~P101(f323(f323(f238(x74251),f2(x74251)),x74253))+~P101(f323(f323(f238(x74251),f2(x74251)),f323(f323(f79(x74251),x74252),x74253)))
% 188.07/187.98 [7726]E(x77261,x77262)+~P101(f323(f59(x77263),x77261))+~P101(f323(f323(f237(a865),f323(f35(x77263),x77261)),f323(f35(x77263),x77262)))+~P101(f323(f323(f237(f872(x77263,a860)),x77262),x77261))
% 188.07/187.98 [7870]~P101(f323(f323(f238(a1),x78701),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x78702))+~P101(f323(f323(f237(a1),x78702),x78703))+P101(f323(f323(f237(a1),f323(f323(f36(a1),x78701),x78702)),f323(f323(f36(a1),x78701),x78703)))
% 188.07/187.98 [7882]~P101(f323(f323(f237(a1),f2(a1)),x78821))+~P101(f323(f323(f238(a1),f2(a1)),x78823))+~P101(f323(f323(f237(a1),x78823),x78822))+P101(f323(f323(f237(a1),f323(f323(f36(a1),x78821),x78822)),f323(f323(f36(a1),x78821),x78823)))
% 188.07/187.98 [8017]E(f323(x80171,f432(x80172,x80171,x80173)),x80172)+~P101(f323(f323(f237(a1),x80172),f323(x80171,x80173)))+P101(f323(f323(f238(a865),f433(x80172,x80171,x80173)),x80173))+~P101(f323(f323(f237(a1),f323(x80171,f2(a865))),x80172))
% 188.07/187.98 [8018]E(f323(x80181,f445(x80182,x80181,x80183)),x80182)+~P101(f323(f323(f237(a1),x80182),f323(x80181,x80183)))+P101(f323(f323(f238(a865),f438(x80182,x80181,x80183)),x80183))+~P101(f323(f323(f237(a1),f323(x80181,f2(a865))),x80182))
% 188.07/187.98 [8116]~P101(f323(f59(x81161),x81163))+~P101(f323(f323(f238(a865),f323(f35(x81161),x81162)),f323(f35(x81161),x81163)))+~P101(f323(f323(f237(f872(x81161,a860)),x81162),x81163))+P101(f323(f323(f238(f872(x81161,a860)),x81162),x81163))
% 188.07/187.98 [8145]E(f323(f323(f78(a1),f391(x81453,x81451,x81452)),f392(x81453,x81451,x81452)),x81451)+E(f323(f323(f22(a1),x81451),x81452),x81451)+~P101(f323(f323(f238(a1),f2(a1)),x81452))+~P101(f323(f323(f325(a1),f323(f323(f22(a1),x81451),f76(a1))),x81453))
% 188.07/187.98 [8146]E(f323(f323(f22(a1),f393(x81463,x81461,x81462)),f394(x81463,x81461,x81462)),x81461)+E(f323(f323(f78(a1),x81461),x81462),x81461)+~P101(f323(f323(f238(a1),f2(a1)),x81462))+~P101(f323(f323(f325(a1),f323(f323(f78(a1),x81461),f76(a1))),x81463))
% 188.07/187.98 [8199]~P101(f323(f323(f237(a865),x81993),x81991))+P101(f323(f323(f237(a865),x81991),x81992))+~P101(f323(f323(f237(a865),x81993),x81992))+~P101(f323(f323(f237(a865),f323(f323(f22(a865),x81991),x81993)),f323(f323(f22(a865),x81992),x81993)))
% 188.07/187.98 [8200]~P101(f323(f323(f237(a865),x82003),x82001))+P101(f323(f323(f238(a865),x82001),x82002))+~P101(f323(f323(f237(a865),x82003),x82002))+~P101(f323(f323(f238(a865),f323(f323(f22(a865),x82001),x82003)),f323(f323(f22(a865),x82002),x82003)))
% 188.07/187.98 [8216]~P103(x82162)+E(x82161,f113(x82162))+~P16(x82162,f323(f162(x82162),x82161))+E(f323(f135(x82162,x82162,f323(f7(x82162,x82162,x82162),f236(x82162)),x82163),f323(f162(x82162),x82161)),f323(f323(f236(x82162),f323(f323(f158(x82162),x82161),f2(a865))),x82163))
% 188.07/187.98 [8285]E(f323(f323(f22(a1),x82851),x82852),x82851)+~P101(f323(f323(f238(a1),f2(a1)),x82852))+P101(f323(f323(f325(a1),f391(x82853,x82851,x82852)),x82853))+~P101(f323(f323(f325(a1),f323(f323(f22(a1),x82851),f76(a1))),x82853))
% 188.07/187.98 [8286]E(f323(f323(f78(a1),x82861),x82862),x82861)+~P101(f323(f323(f238(a1),f2(a1)),x82862))+P101(f323(f323(f325(a1),f393(x82863,x82861,x82862)),x82863))+~P101(f323(f323(f325(a1),f323(f323(f78(a1),x82861),f76(a1))),x82863))
% 188.07/187.98 [8362]~P101(f323(f323(f237(a1),x83621),f323(x83622,x83623)))+P101(f323(f323(f238(a865),f433(x83621,x83622,x83623)),x83623))+P101(f323(f323(f237(a865),f432(x83621,x83622,x83623)),x83623))+~P101(f323(f323(f237(a1),f323(x83622,f2(a865))),x83621))
% 188.07/187.98 [8363]~P101(f323(f323(f237(a1),x83631),f323(x83632,x83633)))+P101(f323(f323(f238(a865),f438(x83631,x83632,x83633)),x83633))+P101(f323(f323(f237(a865),f445(x83631,x83632,x83633)),x83633))+~P101(f323(f323(f237(a1),f323(x83632,f2(a865))),x83631))
% 188.07/187.98 [8433]E(f323(f323(f22(a1),x84331),x84332),x84331)+~P101(f323(f323(f238(a1),f2(a1)),x84332))+P101(f323(f323(f325(a1),f392(x84333,x84331,x84332)),f294(a1,f76(a1),x84332)))+~P101(f323(f323(f325(a1),f323(f323(f22(a1),x84331),f76(a1))),x84333))
% 188.07/187.98 [8434]E(f323(f323(f78(a1),x84341),x84342),x84341)+~P101(f323(f323(f238(a1),f2(a1)),x84342))+P101(f323(f323(f325(a1),f394(x84343,x84341,x84342)),f294(a1,f76(a1),x84342)))+~P101(f323(f323(f325(a1),f323(f323(f78(a1),x84341),f76(a1))),x84343))
% 188.07/187.98 [8566]~P119(x85661)+~P101(f323(f323(f238(x85661),x85662),f76(x85661)))+~P101(f323(f323(f238(x85661),f2(x85661)),x85662))+P101(f323(f323(f238(x85661),f323(f323(f79(x85661),x85662),f323(f323(f248(x85661),x85662),x85663))),f323(f323(f248(x85661),x85662),x85663)))
% 188.07/187.98 [8661]~P101(f323(x86611,x86612))+P101(f323(x86611,f2(a865)))+~P101(f323(f323(f238(a865),x86612),x86613))+~P101(f323(x86611,f42(a865,f323(a112,f491(x86612,x86611,x86613)),x86613)))
% 188.07/187.98 [8809]E(f525(x88091,x88092,x88093),f2(a865))+P101(f323(f323(x88091,x88093),x88092))+P101(f323(f323(x88091,f525(x88091,x88092,x88093)),f42(a865,f524(x88091,x88092,x88093),f525(x88091,x88092,x88093))))+~P101(f323(f311(f871(a865,a865),a221),f323(f323(f258(a865,a865),x88093),x88092)))
% 188.07/187.98 [8846]~P27(x88461,x88461,x88462,x88463)+E(f323(f302(x88461,x88461,x88462),x88463),x88463)+~P101(f323(f59(x88461),x88463))+~P101(f323(f323(f237(f872(x88461,a860)),f323(f302(x88461,x88461,x88462),x88463)),x88463))
% 188.07/187.98 [9082]P101(f323(f323(x90821,x90822),x90823))+~P101(f323(f323(f238(a1),f523(x90821,x90823,x90822)),f2(a1)))+P101(f323(f323(x90821,f323(f77(a1),f522(x90821,x90823,x90822))),f323(f77(a1),f523(x90821,x90823,x90822))))+~P101(f323(f311(f871(a1,a1),a226),f323(f323(f258(a1,a1),x90822),x90823)))
% 188.07/187.98 [9265]P101(f323(f323(x92651,x92652),x92653))+P101(f323(f323(x92651,f323(f323(f78(a1),f566(x92651,x92653,x92652)),f76(a1))),f569(x92651,x92653,x92652)))+~P101(f323(f323(f237(a1),f566(x92651,x92653,x92652)),f569(x92651,x92653,x92652)))+~P101(f323(f311(f871(a1,a1),a176),f323(f323(f258(a1,a1),x92652),x92653)))
% 188.07/187.98 [9695]~P5(x96952)+~P5(x96951)+~P101(f323(f56(f871(x96951,x96952)),x96953))+P101(f323(f56(x96951),f323(f323(f8(f872(x96952,a860),a860,x96951),f56(x96952)),f323(f323(f8(f872(x96952,f871(x96951,x96952)),f872(x96952,a860),x96951),f323(f8(f871(x96951,x96952),a860,x96952),x96953)),f258(x96951,x96952)))))
% 188.07/187.98 [9696]~P5(x96962)+~P5(x96961)+~P101(f323(f55(f871(x96961,x96962)),x96963))+P101(f323(f55(x96961),f323(f323(f8(f872(x96962,a860),a860,x96961),f55(x96962)),f323(f323(f8(f872(x96962,f871(x96961,x96962)),f872(x96962,a860),x96961),f323(f8(f871(x96961,x96962),a860,x96962),x96963)),f258(x96961,x96962)))))
% 188.07/187.98 [9799]~P5(x97992)+~P5(x97991)+P101(f323(f56(f871(x97991,x97992)),x97993))+~P101(f323(f56(x97991),f323(f323(f8(f872(x97992,a860),a860,x97991),f56(x97992)),f323(f323(f8(f872(x97992,f871(x97991,x97992)),f872(x97992,a860),x97991),f323(f8(f871(x97991,x97992),a860,x97992),x97993)),f258(x97991,x97992)))))
% 188.07/187.98 [9800]~P5(x98002)+~P5(x98001)+P101(f323(f55(f871(x98001,x98002)),x98003))+~P101(f323(f55(x98001),f323(f323(f8(f872(x98002,a860),a860,x98001),f55(x98002)),f323(f323(f8(f872(x98002,f871(x98001,x98002)),f872(x98002,a860),x98001),f323(f8(f871(x98001,x98002),a860,x98002),x98003)),f258(x98001,x98002)))))
% 188.07/187.98 [9967]E(f323(x99671,f432(x99672,x99671,x99673)),x99672)+~P101(f323(f323(f237(a1),x99672),f323(x99671,x99673)))+~P101(f323(f323(f237(a1),f323(f73(a1),f323(f323(f22(a1),f323(x99671,f323(f323(f78(a865),f433(x99672,x99671,x99673)),f76(a865)))),f323(x99671,f433(x99672,x99671,x99673))))),f76(a1)))+~P101(f323(f323(f237(a1),f323(x99671,f2(a865))),x99672))
% 188.07/187.98 [9968]E(f323(x99681,f445(x99682,x99681,x99683)),x99682)+~P101(f323(f323(f237(a1),x99682),f323(x99681,x99683)))+~P101(f323(f323(f237(a1),f323(f73(a1),f323(f323(f22(a1),f323(x99681,f323(f323(f78(a865),f438(x99682,x99681,x99683)),f76(a865)))),f323(x99681,f438(x99682,x99681,x99683))))),f76(a1)))+~P101(f323(f323(f237(a1),f323(x99681,f2(a865))),x99682))
% 188.07/187.98 [9972]~P101(f323(f323(f237(a1),x99721),f323(x99722,x99723)))+~P101(f323(f323(f237(a1),f323(f73(a1),f323(f323(f22(a1),f323(x99722,f323(f323(f78(a865),f433(x99721,x99722,x99723)),f76(a865)))),f323(x99722,f433(x99721,x99722,x99723))))),f76(a1)))+P101(f323(f323(f237(a865),f432(x99721,x99722,x99723)),x99723))+~P101(f323(f323(f237(a1),f323(x99722,f2(a865))),x99721))
% 188.07/187.98 [9973]~P101(f323(f323(f237(a1),x99731),f323(x99732,x99733)))+~P101(f323(f323(f237(a1),f323(f73(a1),f323(f323(f22(a1),f323(x99732,f323(f323(f78(a865),f438(x99731,x99732,x99733)),f76(a865)))),f323(x99732,f438(x99731,x99732,x99733))))),f76(a1)))+P101(f323(f323(f237(a865),f445(x99731,x99732,x99733)),x99733))+~P101(f323(f323(f237(a1),f323(x99732,f2(a865))),x99731))
% 188.07/187.98 [10027]E(x100271,x100272)+~E(f323(f135(f866(x100273),f866(x100273),f121(x100273),f113(x100273)),x100271),f323(f135(f866(x100273),f866(x100273),f121(x100273),f113(x100273)),x100272))+~E(f323(f189(f866(f866(x100273))),x100271),f323(f189(f866(f866(x100273))),x100272))+~P101(f323(f323(f262(f866(x100273),f866(x100273),a860),f323(f323(f7(f866(x100273),f872(f866(x100273),a865),f872(f866(x100273),a860)),f323(f323(f8(f872(a865,a860),f872(f872(f866(x100273),a865),f872(f866(x100273),a860)),f866(x100273)),f8(a865,a860,f866(x100273))),f323(f323(f8(a865,f872(a865,a860),f866(x100273)),a320),f189(f866(x100273))))),f189(f866(x100273)))),f598(x100271,x100272,x100273)))
% 188.07/187.98 [10028]E(x100281,x100282)+~E(f323(f135(f866(x100283),f866(x100283),f121(x100283),f113(x100283)),x100281),f323(f135(f866(x100283),f866(x100283),f121(x100283),f113(x100283)),x100282))+~E(f323(f189(f866(f866(x100283))),x100281),f323(f189(f866(f866(x100283))),x100282))+~P101(f323(f323(f262(f866(x100283),f866(x100283),a860),f323(f323(f7(f866(x100283),f872(f866(x100283),a865),f872(f866(x100283),a860)),f323(f323(f8(f872(a865,a860),f872(f872(f866(x100283),a865),f872(f866(x100283),a860)),f866(x100283)),f8(a865,a860,f866(x100283))),f323(f323(f8(a865,f872(a865,a860),f866(x100283)),a320),f189(f866(x100283))))),f189(f866(x100283)))),f599(x100282,x100281,x100283)))
% 188.07/187.98 [6759]~E(f76(a865),f2(a865))+~P101(f323(f59(x67591),x67593))+~P101(f323(f59(x67591),x67592))+E(f323(f323(f78(a865),f323(f35(x67591),x67592)),f323(f35(x67591),x67593)),f323(f35(x67591),f323(f323(f110(f872(x67591,a860)),x67592),x67593)))
% 188.07/187.98 [7169]~P98(x71691)+~P101(f323(f59(x71691),x71692))+~P101(f323(f323(f325(x71691),x71693),x71692))+P101(f323(f323(f237(x71691),f323(f61(x71691,f101(x71691)),x71692)),x71693))
% 188.07/187.98 [7170]~P103(x71701)+~P101(f323(f59(x71701),x71702))+~P101(f323(f323(f325(x71701),x71703),x71702))+P101(f323(f323(f237(x71701),f323(f61(x71701,f235(x71701)),x71702)),x71703))
% 188.07/187.98 [7418]~P101(f323(f59(x74181),x74183))+~P101(f323(f59(x74181),x74182))+~E(f323(f323(f101(f872(x74181,a860)),x74182),x74183),f188(f872(x74181,a860)))+E(f323(f323(f78(a865),f323(f35(x74181),x74182)),f323(f35(x74181),x74183)),f323(f35(x74181),f323(f323(f110(f872(x74181,a860)),x74182),x74183)))
% 188.07/187.98 [8205]~P38(x82051,x82053)+~P38(x82051,x82052)+~E(f323(f323(f101(f872(x82051,a860)),f323(f256(x82051,x82051),x82052)),f323(f254(x82051,x82051),x82053)),f188(f872(x82051,a860)))+P38(x82051,f323(f323(f110(f872(f871(x82051,x82051),a860)),x82052),x82053))
% 188.07/187.98 [8300]E(x83001,f323(f323(f36(a865),x83002),x83003))+~P101(f323(f323(f238(a865),f2(a865)),x83003))+~P101(f323(f323(f238(a865),x83002),f323(f323(f79(a865),x83003),f323(a112,x83001))))+~P101(f323(f323(f237(a865),f323(f323(f79(a865),x83003),x83001)),x83002))
% 188.07/187.98 [8431]~P101(f323(f59(x84311),x84312))+~P101(f323(f59(x84311),x84313))+E(f323(f323(f78(a865),f323(f35(x84311),x84312)),f323(f35(x84311),x84313)),f323(f35(x84311),f323(f323(f110(f872(x84311,a860)),x84312),x84313)))+P101(f323(f323(f325(x84311),f857(x84313,x84312,x84311)),f323(f323(f101(f872(x84311,a860)),x84312),x84313)))
% 188.07/187.98 [8821]~P120(x88212)+~E(x88211,f2(x88212))+~E(x88213,f2(x88212))+~P101(f323(f323(f238(x88212),f2(x88212)),f323(f323(f78(x88212),f323(f323(f79(x88212),x88213),x88213)),f323(f323(f79(x88212),x88211),x88211))))
% 188.07/187.98 [9345]~P38(x93451,x93453)+~P38(x93451,x93452)+P38(x93451,f323(f323(f110(f872(f871(x93451,x93451),a860)),x93452),x93453))+~P101(f323(f323(f237(f872(f871(x93451,x93451),a860)),f323(f323(f280(x93451,x93451,x93451),x93452),x93453)),x93452))
% 188.07/187.98 [9471]~P101(f323(x94711,x94713))+~P101(f323(f59(x94712),x94713))+P101(f323(x94711,f188(f872(x94712,a860))))+~P101(f323(x94711,f323(f323(f22(f872(x94712,a860)),f821(x94711,x94713,x94712)),f323(f323(f301(x94712),f822(x94711,x94713,x94712)),f188(f872(x94712,a860))))))
% 188.07/187.98 [9725]~P5(x97251)+~P5(x97252)+P12(x97251,f323(f323(f8(f872(x97252,x97251),a860,f866(x97251)),x97253),f323(f323(f8(f872(x97252,f869(x97251)),f872(x97252,x97251),f866(x97251)),f71(f869(x97251),x97251,x97252,f234(x97251))),f323(f323(f8(f866(f871(x97252,x97251)),f872(x97252,f869(x97251)),f866(x97251)),f179(x97252,x97251)),f323(f175(x97252,x97251),f53(x97252))))),f323(f189(f866(x97252)),f53(x97252)))+~P101(f323(f55(f872(x97252,x97251)),x97253))
% 188.07/187.98 [9726]~P5(x97261)+~P5(x97262)+P13(x97261,f323(f323(f8(f872(x97262,x97261),a860,f866(x97261)),x97263),f323(f323(f8(f872(x97262,f869(x97261)),f872(x97262,x97261),f866(x97261)),f71(f869(x97261),x97261,x97262,f234(x97261))),f323(f323(f8(f866(f871(x97262,x97261)),f872(x97262,f869(x97261)),f866(x97261)),f179(x97262,x97261)),f323(f175(x97262,x97261),f53(x97262))))),f323(f189(f866(x97262)),f53(x97262)))+~P101(f323(f56(f872(x97262,x97261)),x97263))
% 188.07/187.98 [9821]~P5(x98211)+~P5(x98212)+~P13(x98212,f323(f323(f8(f872(x98211,x98212),a860,f866(x98212)),x98213),f323(f323(f8(f872(x98211,f869(x98212)),f872(x98211,x98212),f866(x98212)),f71(f869(x98212),x98212,x98211,f234(x98212))),f323(f323(f8(f866(f871(x98211,x98212)),f872(x98211,f869(x98212)),f866(x98212)),f179(x98211,x98212)),f323(f175(x98211,x98212),f53(x98211))))),f323(f189(f866(x98211)),f53(x98211)))+P101(f323(f56(f872(x98211,x98212)),x98213))
% 188.07/187.98 [9822]~P5(x98221)+~P5(x98222)+~P12(x98222,f323(f323(f8(f872(x98221,x98222),a860,f866(x98222)),x98223),f323(f323(f8(f872(x98221,f869(x98222)),f872(x98221,x98222),f866(x98222)),f71(f869(x98222),x98222,x98221,f234(x98222))),f323(f323(f8(f866(f871(x98221,x98222)),f872(x98221,f869(x98222)),f866(x98222)),f179(x98221,x98222)),f323(f175(x98221,x98222),f53(x98221))))),f323(f189(f866(x98221)),f53(x98221)))+P101(f323(f55(f872(x98221,x98222)),x98223))
% 188.07/187.98 [8607]~P101(f323(f323(f238(a1),f2(a1)),x86073))+P101(f323(f323(f237(a1),f2(a1)),x86071))+~P101(f323(f323(f238(a1),x86072),x86073))+~P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),f323(f323(f79(a1),x86073),x86071)),x86072)))
% 188.07/187.98 [8632]~P2(x86321)+~P101(f323(f59(x86321),x86322))+E(f323(f323(f22(f872(x86321,a860)),x86322),f323(f323(f301(x86321),x86323),f188(f872(x86321,a860)))),f188(f872(x86321,a860)))+E(f323(f323(f101(x86321),x86323),f11(x86321,f323(f323(f22(f872(x86321,a860)),x86322),f323(f323(f301(x86321),x86323),f188(f872(x86321,a860)))))),f11(x86321,f323(f323(f301(x86321),x86323),x86322)))
% 188.07/187.98 [8633]~P2(x86331)+~P101(f323(f59(x86331),x86332))+E(f323(f323(f22(f872(x86331,a860)),x86332),f323(f323(f301(x86331),x86333),f188(f872(x86331,a860)))),f188(f872(x86331,a860)))+E(f323(f323(f110(x86331),x86333),f10(x86331,f323(f323(f22(f872(x86331,a860)),x86332),f323(f323(f301(x86331),x86333),f188(f872(x86331,a860)))))),f10(x86331,f323(f323(f301(x86331),x86333),x86332)))
% 188.07/187.98 [8634]~P103(x86341)+~P101(f323(f59(x86341),x86342))+E(f323(f323(f22(f872(x86341,a860)),x86342),f323(f323(f301(x86341),x86343),f188(f872(x86341,a860)))),f188(f872(x86341,a860)))+E(f323(f323(f236(x86341),x86343),f14(x86341,f323(f323(f22(f872(x86341,a860)),x86342),f323(f323(f301(x86341),x86343),f188(f872(x86341,a860)))))),f14(x86341,f323(f323(f301(x86341),x86343),x86342)))
% 188.07/187.98 [8635]~P103(x86351)+~P101(f323(f59(x86351),x86352))+E(f323(f323(f22(f872(x86351,a860)),x86352),f323(f323(f301(x86351),x86353),f188(f872(x86351,a860)))),f188(f872(x86351,a860)))+E(f323(f323(f235(x86351),x86353),f15(x86351,f323(f323(f22(f872(x86351,a860)),x86352),f323(f323(f301(x86351),x86353),f188(f872(x86351,a860)))))),f15(x86351,f323(f323(f301(x86351),x86353),x86352)))
% 188.07/187.98 [8707]~P103(x87071)+~P101(f323(f59(x87071),x87072))+E(f323(f323(f22(f872(x87071,a860)),x87072),f323(f323(f301(x87071),x87073),f188(f872(x87071,a860)))),f188(f872(x87071,a860)))+E(f323(f323(f235(x87071),x87073),f12(x87071,f235(x87071),f323(f323(f22(f872(x87071,a860)),x87072),f323(f323(f301(x87071),x87073),f188(f872(x87071,a860)))))),f12(x87071,f235(x87071),f323(f323(f301(x87071),x87073),x87072)))
% 188.07/187.98 [8708]~P103(x87081)+~P101(f323(f59(x87081),x87082))+E(f323(f323(f22(f872(x87081,a860)),x87082),f323(f323(f301(x87081),x87083),f188(f872(x87081,a860)))),f188(f872(x87081,a860)))+E(f323(f323(f236(x87081),x87083),f13(x87081,f236(x87081),f323(f323(f22(f872(x87081,a860)),x87082),f323(f323(f301(x87081),x87083),f188(f872(x87081,a860)))))),f13(x87081,f236(x87081),f323(f323(f301(x87081),x87083),x87082)))
% 188.07/187.98 [9285]E(x92851,x92852)+~E(f323(f135(f866(x92853),f866(x92853),f121(x92853),f113(x92853)),x92851),f323(f135(f866(x92853),f866(x92853),f121(x92853),f113(x92853)),x92852))+~E(f323(f189(f866(f866(x92853))),x92851),f323(f189(f866(f866(x92853))),x92852))+P101(f323(f323(f325(f871(f866(x92853),f866(x92853))),f598(x92851,x92852,x92853)),f323(f166(f871(f866(x92853),f866(x92853))),f323(f323(f175(f866(x92853),f866(x92853)),x92852),x92851))))
% 188.07/187.98 [9286]E(x92861,x92862)+~E(f323(f135(f866(x92863),f866(x92863),f121(x92863),f113(x92863)),x92861),f323(f135(f866(x92863),f866(x92863),f121(x92863),f113(x92863)),x92862))+~E(f323(f189(f866(f866(x92863))),x92861),f323(f189(f866(f866(x92863))),x92862))+P101(f323(f323(f325(f871(f866(x92863),f866(x92863))),f599(x92862,x92861,x92863)),f323(f166(f871(f866(x92863),f866(x92863))),f323(f323(f175(f866(x92863),f866(x92863)),x92861),x92862))))
% 188.07/187.98 [10114]~P96(x101142)+E(x101141,f188(f872(x101142,a860)))+~P101(f323(f59(x101142),x101141))+E(f11(x101142,f323(f243(x101142),f323(f323(f8(f872(x101142,a860),a860,x101142),f85(x101142)),f323(f323(f7(x101142,f872(x101142,a860),f872(x101142,a860)),f323(f323(f8(f872(x101142,f872(a860,a860)),f872(f872(x101142,a860),f872(x101142,a860)),x101142),f18(x101142,a860,a860)),f323(f323(f8(f872(x101142,a860),f872(x101142,f872(a860,a860)),x101142),f323(f8(a860,f872(a860,a860),x101142),a322)),f323(f323(f7(x101142,f872(x101142,x101142),f872(x101142,a860)),f323(f323(f8(f872(x101142,a860),f872(f872(x101142,x101142),f872(x101142,a860)),x101142),f8(x101142,a860,x101142)),a320)),f323(f110(x101142),x101143))))),f323(f323(f7(x101142,f872(x101142,a860),a860),f325(x101142)),x101141))))),f323(f323(f110(x101142),x101143),f11(x101142,x101141)))
% 188.07/187.98 [10115]~P96(x101152)+E(x101151,f188(f872(x101152,a860)))+~P101(f323(f59(x101152),x101151))+E(f10(x101152,f323(f243(x101152),f323(f323(f8(f872(x101152,a860),a860,x101152),f85(x101152)),f323(f323(f7(x101152,f872(x101152,a860),f872(x101152,a860)),f323(f323(f8(f872(x101152,f872(a860,a860)),f872(f872(x101152,a860),f872(x101152,a860)),x101152),f18(x101152,a860,a860)),f323(f323(f8(f872(x101152,a860),f872(x101152,f872(a860,a860)),x101152),f323(f8(a860,f872(a860,a860),x101152),a322)),f323(f323(f7(x101152,f872(x101152,x101152),f872(x101152,a860)),f323(f323(f8(f872(x101152,a860),f872(f872(x101152,x101152),f872(x101152,a860)),x101152),f8(x101152,a860,x101152)),a320)),f323(f101(x101152),x101153))))),f323(f323(f7(x101152,f872(x101152,a860),a860),f325(x101152)),x101151))))),f323(f323(f101(x101152),x101153),f10(x101152,x101151)))
% 188.07/187.98 [10116]~P73(x101162)+E(x101161,f188(f872(x101162,a860)))+~P101(f323(f59(x101162),x101161))+E(f14(x101162,f323(f243(x101162),f323(f323(f8(f872(x101162,a860),a860,x101162),f85(x101162)),f323(f323(f7(x101162,f872(x101162,a860),f872(x101162,a860)),f323(f323(f8(f872(x101162,f872(a860,a860)),f872(f872(x101162,a860),f872(x101162,a860)),x101162),f18(x101162,a860,a860)),f323(f323(f8(f872(x101162,a860),f872(x101162,f872(a860,a860)),x101162),f323(f8(a860,f872(a860,a860),x101162),a322)),f323(f323(f7(x101162,f872(x101162,x101162),f872(x101162,a860)),f323(f323(f8(f872(x101162,a860),f872(f872(x101162,x101162),f872(x101162,a860)),x101162),f8(x101162,a860,x101162)),a320)),f323(f78(x101162),x101163))))),f323(f323(f7(x101162,f872(x101162,a860),a860),f325(x101162)),x101161))))),f323(f323(f78(x101162),x101163),f14(x101162,x101161)))
% 188.07/187.98 [10117]~P73(x101172)+E(x101171,f188(f872(x101172,a860)))+~P101(f323(f59(x101172),x101171))+E(f15(x101172,f323(f243(x101172),f323(f323(f8(f872(x101172,a860),a860,x101172),f85(x101172)),f323(f323(f7(x101172,f872(x101172,a860),f872(x101172,a860)),f323(f323(f8(f872(x101172,f872(a860,a860)),f872(f872(x101172,a860),f872(x101172,a860)),x101172),f18(x101172,a860,a860)),f323(f323(f8(f872(x101172,a860),f872(x101172,f872(a860,a860)),x101172),f323(f8(a860,f872(a860,a860),x101172),a322)),f323(f323(f7(x101172,f872(x101172,x101172),f872(x101172,a860)),f323(f323(f8(f872(x101172,a860),f872(f872(x101172,x101172),f872(x101172,a860)),x101172),f8(x101172,a860,x101172)),a320)),f323(f78(x101172),x101173))))),f323(f323(f7(x101172,f872(x101172,a860),a860),f325(x101172)),x101171))))),f323(f323(f78(x101172),x101173),f15(x101172,x101171)))
% 188.07/187.98 [10118]~P103(x101182)+E(x101181,f188(f872(x101182,a860)))+~P101(f323(f59(x101182),x101181))+E(f13(x101182,f236(x101182),f323(f243(x101182),f323(f323(f8(f872(x101182,a860),a860,x101182),f85(x101182)),f323(f323(f7(x101182,f872(x101182,a860),f872(x101182,a860)),f323(f323(f8(f872(x101182,f872(a860,a860)),f872(f872(x101182,a860),f872(x101182,a860)),x101182),f18(x101182,a860,a860)),f323(f323(f8(f872(x101182,a860),f872(x101182,f872(a860,a860)),x101182),f323(f8(a860,f872(a860,a860),x101182),a322)),f323(f323(f7(x101182,f872(x101182,x101182),f872(x101182,a860)),f323(f323(f8(f872(x101182,a860),f872(f872(x101182,x101182),f872(x101182,a860)),x101182),f8(x101182,a860,x101182)),a320)),f323(f235(x101182),x101183))))),f323(f323(f7(x101182,f872(x101182,a860),a860),f325(x101182)),x101181))))),f323(f323(f235(x101182),x101183),f13(x101182,f236(x101182),x101181)))
% 188.07/187.98 [10119]~P103(x101192)+E(x101191,f188(f872(x101192,a860)))+~P101(f323(f59(x101192),x101191))+E(f12(x101192,f235(x101192),f323(f243(x101192),f323(f323(f8(f872(x101192,a860),a860,x101192),f85(x101192)),f323(f323(f7(x101192,f872(x101192,a860),f872(x101192,a860)),f323(f323(f8(f872(x101192,f872(a860,a860)),f872(f872(x101192,a860),f872(x101192,a860)),x101192),f18(x101192,a860,a860)),f323(f323(f8(f872(x101192,a860),f872(x101192,f872(a860,a860)),x101192),f323(f8(a860,f872(a860,a860),x101192),a322)),f323(f323(f7(x101192,f872(x101192,x101192),f872(x101192,a860)),f323(f323(f8(f872(x101192,a860),f872(f872(x101192,x101192),f872(x101192,a860)),x101192),f8(x101192,a860,x101192)),a320)),f323(f236(x101192),x101193))))),f323(f323(f7(x101192,f872(x101192,a860),a860),f325(x101192)),x101191))))),f323(f323(f236(x101192),x101193),f12(x101192,f235(x101192),x101191)))
% 188.07/187.98 [9871]~P116(x98711)+~E(x98713,f2(x98711))+~E(x98712,f2(x98711))+E(f323(f323(f78(x98711),f323(f323(f248(x98711),x98712),f323(f103(a865),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(x98711),x98713),f323(f103(a865),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(x98711))
% 188.07/187.98 [10011]~P119(x100111)+~P101(f323(f323(f237(x100111),f2(x100111)),x100113))+P101(f323(f323(f237(x100111),x100112),x100113))+~P101(f323(f323(f237(x100111),f323(f323(f248(x100111),x100112),f323(f103(a865),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(x100111),x100113),f323(f103(a865),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))))))
% 188.07/187.98 [10057]~P116(x100572)+~E(x100571,f2(x100572))+~E(x100573,f2(x100572))+~P101(f323(f323(f238(x100572),f2(x100572)),f323(f323(f78(x100572),f323(f323(f248(x100572),x100573),f323(f103(a865),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(x100572),x100571),f323(f103(a865),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)))))))
% 188.07/187.98 [8540]P28(x85401,x85402,f840(x85403,x85402,x85404,x85401),x85404,x85403)+~E(f323(f35(x85401),x85404),f323(f35(x85402),x85403))+~P101(f323(f59(x85402),x85403))+~P101(f323(f59(x85401),x85404))
% 188.07/187.98 [9248]E(x92481,x92482)+~E(f626(x92481,x92482,x92484,x92483),f628(x92481,x92482,x92484,x92483))+P101(f323(f323(f325(f871(f866(x92483),f866(x92483))),f323(f323(f258(f866(x92483),f866(x92483)),x92482),x92481)),f140(x92483,x92484)))+P101(f323(f323(f325(f871(f866(x92483),f866(x92483))),f323(f323(f258(f866(x92483),f866(x92483)),x92481),x92482)),f140(x92483,x92484)))
% 188.07/187.98 [4850]~P62(x48502)+~E(x48504,f2(x48502))+~E(x48501,f2(x48502))+E(x48501,f323(f323(f281(x48502),x48503),x48504))
% 188.07/187.98 [4851]~P62(x48511)+~E(x48513,f2(x48511))+~E(x48514,f2(x48511))+E(f323(f323(f281(x48511),x48512),x48513),x48514)
% 188.07/187.98 [4961]~P62(x49612)+E(x49611,f2(x49612))+~E(x49613,f2(x49612))+~E(x49611,f323(f323(f281(x49612),x49614),x49613))
% 188.07/187.98 [4962]~P62(x49622)+E(x49621,f2(x49622))+~E(x49623,f2(x49622))+~E(f323(f323(f281(x49622),x49624),x49623),x49621)
% 188.07/187.98 [5137]~P114(x51372)+E(x51371,f2(x51372))+~E(f323(f323(f281(x51372),x51373),x51371),x51374)+E(x51373,f323(f323(f79(x51372),x51374),x51371))
% 188.07/187.98 [5139]~P114(x51392)+E(x51391,f2(x51392))+~E(f323(f323(f79(x51392),x51393),x51391),x51394)+E(x51393,f323(f323(f281(x51392),x51394),x51391))
% 188.07/187.98 [5140]~P62(x51402)+E(x51401,f2(x51402))+~E(f323(f323(f281(x51402),x51403),x51401),x51404)+E(x51403,f323(f323(f79(x51402),x51404),x51401))
% 188.07/187.98 [5141]~P62(x51412)+E(x51411,f2(x51412))+~E(f323(f323(f79(x51412),x51413),x51411),x51414)+E(x51413,f323(f323(f281(x51412),x51414),x51411))
% 188.07/187.98 [5142]~P114(x51422)+E(x51421,f2(x51422))+~E(x51423,f323(f323(f281(x51422),x51424),x51421))+E(f323(f323(f79(x51422),x51423),x51421),x51424)
% 188.07/187.98 [5144]~P114(x51442)+E(x51441,f2(x51442))+~E(x51443,f323(f323(f79(x51442),x51444),x51441))+E(f323(f323(f281(x51442),x51443),x51441),x51444)
% 188.07/187.98 [5145]~P62(x51452)+E(x51451,f2(x51452))+~E(x51453,f323(f323(f281(x51452),x51454),x51451))+E(f323(f323(f79(x51452),x51453),x51451),x51454)
% 188.07/187.98 [5146]~P62(x51462)+E(x51461,f2(x51462))+~E(x51463,f323(f323(f79(x51462),x51464),x51461))+E(f323(f323(f281(x51462),x51463),x51461),x51464)
% 188.07/187.98 [5170]~P62(x51702)+~E(x51701,f2(x51702))+~E(f323(f323(f79(x51702),x51701),x51704),x51703)+E(x51701,f323(f323(f281(x51702),x51703),x51704))
% 188.07/187.98 [5171]~P62(x51711)+~E(x51714,f2(x51711))+~E(x51712,f323(f323(f79(x51711),x51714),x51713))+E(f323(f323(f281(x51711),x51712),x51713),x51714)
% 188.07/187.98 [5241]~E(x52413,x52414)+~E(x52412,x52413)+~P105(x52411)+E(f294(x52411,x52412,x52413),f323(f323(f301(x52411),x52414),f188(f872(x52411,a860))))
% 188.07/187.98 [5446]~E(f137(x54462,x54461),x54464)+~E(f114(x54462,x54461),x54463)+E(x54461,f113(x54462))+E(f323(f323(f121(x54462),x54463),f323(f323(f144(x54462),x54464),f113(x54462))),x54461)
% 188.07/187.98 [6052]~P119(x60523)+E(x60521,x60522)+~E(f323(f323(f248(x60523),x60524),x60521),f323(f323(f248(x60523),x60524),x60522))+~P101(f323(f323(f238(x60523),f76(x60523)),x60524))
% 188.07/187.98 [6053]E(x60531,x60532)+~E(f323(f323(f301(x60533),x60534),x60531),f323(f323(f301(x60533),x60534),x60532))+P101(f323(f323(f325(x60533),x60534),x60532))+P101(f323(f323(f325(x60533),x60534),x60531))
% 188.07/187.98 [6091]E(f323(x60911,x60912),f76(a865))+~E(f323(f323(f9(x60913,a865),x60911),x60914),f76(a865))+~P101(f323(f59(x60913),x60914))+~P101(f323(f323(f325(x60913),x60912),x60914))
% 188.07/187.98 [6092]E(f323(x60921,x60922),f2(a865))+~E(f323(f323(f6(x60923,a865),x60921),x60924),f2(a865))+~P101(f323(f59(x60923),x60924))+~P101(f323(f323(f325(x60923),x60922),x60924))
% 188.07/187.98 [6305]~P105(x63051)+~P101(f323(f323(f237(x63051),x63054),x63053))+P101(f323(f323(f237(x63051),x63052),x63053))+~P101(f323(f323(f237(x63051),x63052),x63054))
% 188.07/187.98 [6306]~P102(x63061)+~P101(f323(f323(f237(x63061),x63062),x63064))+P101(f323(f323(f237(x63061),x63062),x63063))+~P101(f323(f323(f237(x63061),x63064),x63063))
% 188.07/187.98 [6307]~P105(x63071)+~P101(f323(f323(f238(x63071),x63074),x63073))+P101(f323(f323(f238(x63071),x63072),x63073))+~P101(f323(f323(f237(x63071),x63072),x63074))
% 188.07/187.98 [6308]~P105(x63081)+~P101(f323(f323(f238(x63081),x63082),x63084))+P101(f323(f323(f238(x63081),x63082),x63083))+~P101(f323(f323(f237(x63081),x63084),x63083))
% 188.07/187.98 [6309]~P105(x63091)+~P101(f323(f323(f238(x63091),x63094),x63093))+P101(f323(f323(f238(x63091),x63092),x63093))+~P101(f323(f323(f238(x63091),x63092),x63094))
% 188.07/187.98 [6310]~P102(x63101)+~P101(f323(f323(f238(x63101),x63102),x63104))+P101(f323(f323(f238(x63101),x63102),x63103))+~P101(f323(f323(f237(x63101),x63104),x63103))
% 188.07/187.98 [6311]~P102(x63111)+~P101(f323(f323(f238(x63111),x63114),x63113))+P101(f323(f323(f238(x63111),x63112),x63113))+~P101(f323(f323(f237(x63111),x63112),x63114))
% 188.07/187.98 [6312]~P102(x63121)+~P101(f323(f323(f238(x63121),x63122),x63124))+P101(f323(f323(f238(x63121),x63122),x63123))+~P101(f323(f323(f238(x63121),x63124),x63123))
% 188.07/187.98 [6392]~P36(x63924,x63923,x63922)+E(x63921,f788(x63922,x63923,x63924))+~P101(f323(x63923,x63921))+~P101(f323(f323(f325(x63924),x63921),f323(f166(x63924),x63922)))
% 188.07/187.98 [6536]~P6(x65361)+~P101(f323(f323(f237(x65361),x65362),f38(x65361,x65364)))+P101(f323(f323(f237(x65361),x65362),x65363))+~P101(f323(f323(f325(x65361),x65363),x65364))
% 188.07/187.98 [6681]~P103(x66811)+~P16(x66811,f323(f323(f144(x66811),x66812),x66814))+~P101(f323(f323(f325(x66811),x66813),f323(f166(x66811),x66814)))+P101(f323(f323(f237(x66811),x66812),x66813))
% 188.07/187.98 [6770]~P6(x67701)+~P101(f323(f323(f237(x67701),f37(x67701,x67704)),x67703))+P101(f323(f323(f237(x67701),x67702),x67703))+~P101(f323(f323(f325(x67701),x67702),x67704))
% 188.07/187.98 [7172]~P103(x71721)+E(f323(f323(f110(f872(x71721,a860)),f323(f293(x71721,x71722),x71723)),f323(f293(x71721,x71723),x71724)),f323(f293(x71721,x71722),x71724))+~P101(f323(f323(f237(x71721),x71723),x71724))+~P101(f323(f323(f237(x71721),x71722),x71723))
% 188.07/187.98 [7209]P36(x72091,x72092,x72093)+~E(f790(x72093,x72092,x72091,x72094),x72094)+~P101(f323(x72092,x72094))+~P101(f323(f323(f325(x72091),x72094),f323(f166(x72091),x72093)))
% 188.07/187.98 [7283]~P103(x72831)+E(f323(f323(f110(f872(x72831,a860)),f323(f293(x72831,x72832),x72833)),f294(x72831,x72833,x72834)),f294(x72831,x72832,x72834))+~P101(f323(f323(f237(x72831),x72833),x72834))+~P101(f323(f323(f237(x72831),x72832),x72833))
% 188.07/187.98 [7346]~P103(x73461)+E(f323(f323(f110(f872(x73461,a860)),f297(x73461,x73462,x73463)),f323(f293(x73461,x73463),x73464)),f297(x73461,x73462,x73464))+~P101(f323(f323(f237(x73461),x73463),x73464))+~P101(f323(f323(f238(x73461),x73462),x73463))
% 188.07/187.98 [7366]~P103(x73661)+E(f323(f323(f110(f872(x73661,a860)),f294(x73661,x73662,x73663)),f297(x73661,x73663,x73664)),f323(f293(x73661,x73662),x73664))+~P101(f323(f323(f237(x73661),x73662),x73663))+~P101(f323(f323(f238(x73661),x73663),x73664))
% 188.07/187.98 [7398]~P103(x73981)+E(f323(f323(f110(f872(x73981,a860)),f294(x73981,x73982,x73983)),f296(x73981,x73983,x73984)),f294(x73981,x73982,x73984))+~P101(f323(f323(f237(x73981),x73983),x73984))+~P101(f323(f323(f237(x73981),x73982),x73983))
% 188.07/187.98 [7399]~P103(x73991)+E(f323(f323(f110(f872(x73991,a860)),f297(x73991,x73992,x73993)),f294(x73991,x73993,x73994)),f296(x73991,x73992,x73994))+~P101(f323(f323(f237(x73991),x73993),x73994))+~P101(f323(f323(f238(x73991),x73992),x73993))
% 188.07/187.98 [7400]~P103(x74001)+E(f323(f323(f110(f872(x74001,a860)),f296(x74001,x74002,x74003)),f297(x74001,x74003,x74004)),f297(x74001,x74002,x74004))+~P101(f323(f323(f237(x74001),x74002),x74003))+~P101(f323(f323(f238(x74001),x74003),x74004))
% 188.07/187.98 [7401]~P103(x74011)+E(f323(f323(f110(f872(x74011,a860)),f296(x74011,x74012,x74013)),f296(x74011,x74013,x74014)),f296(x74011,x74012,x74014))+~P101(f323(f323(f237(x74011),x74013),x74014))+~P101(f323(f323(f237(x74011),x74012),x74013))
% 188.07/187.98 [8189]P27(x81891,x81892,f839(x81893,x81892,x81894,x81891),x81894)+~P101(f323(f59(x81892),x81893))+~P101(f323(f59(x81891),x81894))+~P101(f323(f323(f237(a865),f323(f35(x81891),x81894)),f323(f35(x81892),x81893)))
% 188.07/187.98 [8210]P36(x82101,x82102,x82103)+~P101(f323(x82102,x82104))+P101(f323(x82102,f790(x82103,x82102,x82101,x82104)))+~P101(f323(f323(f325(x82101),x82104),f323(f166(x82101),x82103)))
% 188.07/187.98 [8263]~P68(x82631)+~E(f323(x82633,f469(x82633,x82634,x82632,x82631)),f76(x82631))+E(f323(f323(f323(f63(x82631,x82632,f79(x82631)),x82633),f76(x82631)),x82634),f76(x82631))+~P101(f323(f59(x82632),x82634))
% 188.07/187.98 [8529]~P119(x85291)+~P101(f323(f323(f237(x85291),f2(x85291)),x85293))+P101(f323(f323(f237(x85291),x85292),x85293))+~P101(f323(f323(f237(x85291),f323(f323(f248(x85291),x85292),f323(a112,x85294))),f323(f323(f248(x85291),x85293),f323(a112,x85294))))
% 188.07/187.98 [8847]P36(x88471,x88472,x88473)+~P101(f323(x88472,x88474))+~P101(f323(f323(f325(x88471),x88474),f323(f166(x88471),x88473)))+P101(f323(f323(f325(x88471),f790(x88473,x88472,x88471,x88474)),f323(f166(x88471),x88473)))
% 188.07/187.98 [8926]~P68(x89261)+E(f323(f323(f323(f63(x89261,x89262,f79(x89261)),x89263),f76(x89261)),x89264),f76(x89261))+~P101(f323(f59(x89262),x89264))+P101(f323(f323(f325(x89262),f469(x89263,x89264,x89262,x89261)),x89264))
% 188.07/187.98 [9410]~P101(f323(f323(f237(a1),x94104),f2(a1)))+P101(f323(f323(f237(a1),f323(f323(f78(a1),f323(f323(f79(a1),x94101),f42(a1,x94102,x94103))),x94104)),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x94103))+~P101(f323(f323(f238(a1),x94101),x94104))
% 188.07/187.98 [9864]~P101(f323(f59(x98641),x98642))+~P101(f323(f323(f325(x98641),x98644),x98642))+~P101(f323(f323(f325(x98641),x98643),x98642))+P101(f323(f323(f238(a865),f323(f35(x98641),f323(f323(f22(f872(x98641,a860)),f323(f323(f22(f872(x98641,a860)),x98642),f323(f323(f301(x98641),x98643),f188(f872(x98641,a860))))),f323(f323(f301(x98641),x98644),f188(f872(x98641,a860)))))),f323(f35(x98641),x98642)))
% 188.07/187.98 [6884]~P98(x68841)+~P101(f323(f323(f237(x68841),x68842),x68844))+~P101(f323(f323(f237(x68841),x68842),x68843))+P101(f323(f323(f237(x68841),x68842),f323(f323(f101(x68841),x68843),x68844)))
% 188.07/187.98 [6887]~P103(x68871)+~P101(f323(f323(f237(x68871),x68872),x68874))+~P101(f323(f323(f237(x68871),x68872),x68873))+P101(f323(f323(f237(x68871),x68872),f323(f323(f235(x68871),x68873),x68874)))
% 188.07/187.98 [6888]~P103(x68881)+~P101(f323(f323(f238(x68881),x68882),x68884))+~P101(f323(f323(f238(x68881),x68882),x68883))+P101(f323(f323(f238(x68881),x68882),f323(f323(f235(x68881),x68883),x68884)))
% 188.07/187.98 [6907]~P63(x69072)+E(x69071,f2(x69072))+E(f323(f323(f281(x69072),f323(f323(f248(x69072),x69071),x69073)),f323(f323(f248(x69072),x69071),x69074)),f323(f323(f248(x69072),x69071),f323(f323(f22(a865),x69073),x69074)))+~P101(f323(f323(f237(a865),x69074),x69073))
% 188.07/187.98 [6952]~P103(x69521)+~P16(x69521,f323(f323(f144(x69521),x69523),x69524))+P16(x69521,f323(f323(f144(x69521),x69522),f323(f323(f144(x69521),x69523),x69524)))+~P101(f323(f323(f237(x69521),x69522),x69523))
% 188.07/187.98 [6991]~P84(x69911)+~P101(f323(f323(f237(x69911),f2(x69911)),x69914))+~P101(f323(f323(f237(x69911),x69912),x69913))+P101(f323(f323(f237(x69911),x69912),f323(f323(f78(x69911),x69913),x69914)))
% 188.07/187.98 [6992]~P84(x69921)+~P101(f323(f323(f237(x69921),f2(x69921)),x69923))+~P101(f323(f323(f237(x69921),x69922),x69924))+P101(f323(f323(f237(x69921),x69922),f323(f323(f78(x69921),x69923),x69924)))
% 188.07/187.98 [6993]~P119(x69931)+~P101(f323(f323(f238(x69931),f2(x69931)),x69933))+~P101(f323(f323(f238(x69931),x69932),x69934))+P101(f323(f323(f238(x69931),x69932),f323(f323(f78(x69931),x69933),x69934)))
% 188.07/187.98 [6994]~P84(x69941)+~P101(f323(f323(f237(x69941),x69942),x69944))+~P101(f323(f323(f238(x69941),f2(x69941)),x69943))+P101(f323(f323(f238(x69941),x69942),f323(f323(f78(x69941),x69943),x69944)))
% 188.07/187.98 [6995]~P84(x69951)+~P101(f323(f323(f237(x69951),f2(x69951)),x69953))+~P101(f323(f323(f238(x69951),x69952),x69954))+P101(f323(f323(f238(x69951),x69952),f323(f323(f78(x69951),x69953),x69954)))
% 188.07/187.98 [7034]~P103(x70341)+P101(f323(f323(f237(x70341),x70342),x70343))+P101(f323(f323(f237(x70341),x70342),x70344))+~P101(f323(f323(f237(x70341),x70342),f323(f323(f236(x70341),x70344),x70343)))
% 188.07/187.98 [7035]~P103(x70351)+P101(f323(f323(f238(x70351),x70352),x70353))+P101(f323(f323(f238(x70351),x70352),x70354))+~P101(f323(f323(f238(x70351),x70352),f323(f323(f236(x70351),x70354),x70353)))
% 188.07/187.98 [7319]~P105(x73192)+~P5(x73191)+~P101(f323(f323(f238(f872(x73191,x73192)),x73193),x73194))+P101(f323(f323(f237(f872(x73191,x73192)),x73193),x73194))
% 188.07/187.98 [7686]~P65(x76861)+~P101(f323(f323(f238(x76861),x76864),f2(x76861)))+~P101(f323(f323(f237(x76861),x76863),f323(f323(f281(x76861),x76862),x76864)))+P101(f323(f323(f237(x76861),x76862),f323(f323(f79(x76861),x76863),x76864)))
% 188.07/187.98 [7687]~P65(x76871)+~P101(f323(f323(f238(x76871),x76874),f2(x76871)))+~P101(f323(f323(f237(x76871),x76873),f323(f323(f79(x76871),x76872),x76874)))+P101(f323(f323(f237(x76871),x76872),f323(f323(f281(x76871),x76873),x76874)))
% 188.07/187.98 [7688]~P65(x76881)+~P101(f323(f323(f238(x76881),x76884),f2(x76881)))+~P101(f323(f323(f238(x76881),x76883),f323(f323(f281(x76881),x76882),x76884)))+P101(f323(f323(f238(x76881),x76882),f323(f323(f79(x76881),x76883),x76884)))
% 188.07/187.98 [7689]~P65(x76891)+~P101(f323(f323(f238(x76891),x76894),f2(x76891)))+~P101(f323(f323(f238(x76891),x76893),f323(f323(f79(x76891),x76892),x76894)))+P101(f323(f323(f238(x76891),x76892),f323(f323(f281(x76891),x76893),x76894)))
% 188.07/187.98 [7794]~P122(x77941)+~P101(f323(f323(f237(x77941),x77942),f2(x77941)))+~P101(f323(f323(f237(x77941),x77944),x77943))+P101(f323(f323(f237(x77941),f323(f323(f79(x77941),x77942),x77943)),f323(f323(f79(x77941),x77942),x77944)))
% 188.07/187.98 [7795]~P120(x77951)+~P101(f323(f323(f238(x77951),x77952),f2(x77951)))+~P101(f323(f323(f237(x77951),x77954),x77953))+P101(f323(f323(f237(x77951),f323(f323(f79(x77951),x77952),x77953)),f323(f323(f79(x77951),x77952),x77954)))
% 188.07/187.98 [7796]~P122(x77961)+~P101(f323(f323(f237(x77961),x77963),f2(x77961)))+~P101(f323(f323(f237(x77961),x77964),x77962))+P101(f323(f323(f237(x77961),f323(f323(f79(x77961),x77962),x77963)),f323(f323(f79(x77961),x77964),x77963)))
% 188.07/187.98 [7797]~P64(x77971)+~P101(f323(f323(f237(x77971),x77973),f2(x77971)))+~P101(f323(f323(f237(x77971),x77974),x77972))+P101(f323(f323(f237(x77971),f323(f323(f281(x77971),x77972),x77973)),f323(f323(f281(x77971),x77974),x77973)))
% 188.07/187.98 [7801]~P120(x78011)+~P101(f323(f323(f238(x78011),x78013),f2(x78011)))+~P101(f323(f323(f238(x78011),x78014),x78012))+P101(f323(f323(f238(x78011),f323(f323(f79(x78011),x78012),x78013)),f323(f323(f79(x78011),x78014),x78013)))
% 188.07/187.98 [7802]~P120(x78021)+~P101(f323(f323(f238(x78021),x78022),f2(x78021)))+~P101(f323(f323(f238(x78021),x78024),x78023))+P101(f323(f323(f238(x78021),f323(f323(f79(x78021),x78022),x78023)),f323(f323(f79(x78021),x78022),x78024)))
% 188.07/187.98 [7803]~P65(x78031)+~P101(f323(f323(f238(x78031),x78033),f2(x78031)))+~P101(f323(f323(f238(x78031),x78034),x78032))+P101(f323(f323(f238(x78031),f323(f323(f281(x78031),x78032),x78033)),f323(f323(f281(x78031),x78034),x78033)))
% 188.07/187.98 [7804]~P119(x78041)+~P101(f323(f323(f238(x78041),f76(x78041)),x78042))+~P101(f323(f323(f237(a865),x78043),x78044))+P101(f323(f323(f237(x78041),f323(f323(f248(x78041),x78042),x78043)),f323(f323(f248(x78041),x78042),x78044)))
% 188.07/187.98 [7805]~P119(x78051)+~P101(f323(f323(f237(x78051),f76(x78051)),x78052))+~P101(f323(f323(f237(a865),x78053),x78054))+P101(f323(f323(f237(x78051),f323(f323(f248(x78051),x78052),x78053)),f323(f323(f248(x78051),x78052),x78054)))
% 188.07/187.98 [7807]~P119(x78071)+~P101(f323(f323(f238(x78071),f76(x78071)),x78072))+~P101(f323(f323(f238(a865),x78073),x78074))+P101(f323(f323(f238(x78071),f323(f323(f248(x78071),x78072),x78073)),f323(f323(f248(x78071),x78072),x78074)))
% 188.07/187.98 [7836]P101(f323(f323(f238(a865),f2(a865)),f323(x78361,x78362)))+~P101(f323(f59(x78363),x78364))+~P101(f323(f323(f325(x78363),x78362),x78364))+~P101(f323(f323(f238(a865),f2(a865)),f323(f323(f9(x78363,a865),x78361),x78364)))
% 188.07/187.98 [7844]~P120(x78441)+~P101(f323(f323(f238(x78441),f2(x78441)),x78442))+~P101(f323(f323(f237(x78441),x78443),x78444))+P101(f323(f323(f237(x78441),f323(f323(f79(x78441),x78442),x78443)),f323(f323(f79(x78441),x78442),x78444)))
% 188.07/187.98 [7845]~P131(x78451)+~P101(f323(f323(f237(x78451),x78453),x78454))+~P101(f323(f323(f237(x78451),f2(x78451)),x78452))+P101(f323(f323(f237(x78451),f323(f323(f79(x78451),x78452),x78453)),f323(f323(f79(x78451),x78452),x78454)))
% 188.07/187.98 [7846]~P130(x78461)+~P101(f323(f323(f237(x78461),x78463),x78464))+~P101(f323(f323(f237(x78461),f2(x78461)),x78462))+P101(f323(f323(f237(x78461),f323(f323(f79(x78461),x78462),x78463)),f323(f323(f79(x78461),x78462),x78464)))
% 188.07/187.98 [7847]~P131(x78471)+~P101(f323(f323(f237(x78471),x78472),x78474))+~P101(f323(f323(f237(x78471),f2(x78471)),x78473))+P101(f323(f323(f237(x78471),f323(f323(f79(x78471),x78472),x78473)),f323(f323(f79(x78471),x78474),x78473)))
% 188.07/187.98 [7848]~P119(x78481)+~P101(f323(f323(f237(x78481),x78482),x78484))+~P101(f323(f323(f237(x78481),f2(x78481)),x78482))+P101(f323(f323(f237(x78481),f323(f323(f248(x78481),x78482),x78483)),f323(f323(f248(x78481),x78484),x78483)))
% 188.07/187.98 [7849]~P64(x78491)+~P101(f323(f323(f237(x78491),x78492),x78494))+~P101(f323(f323(f237(x78491),f2(x78491)),x78493))+P101(f323(f323(f237(x78491),f323(f323(f281(x78491),x78492),x78493)),f323(f323(f281(x78491),x78494),x78493)))
% 188.07/187.98 [7851]~P125(x78511)+~P101(f323(f323(f238(x78511),x78513),x78514))+~P101(f323(f323(f238(x78511),f2(x78511)),x78512))+P101(f323(f323(f238(x78511),f323(f323(f79(x78511),x78512),x78513)),f323(f323(f79(x78511),x78512),x78514)))
% 188.07/187.98 [7852]~P117(x78521)+~P101(f323(f323(f238(x78521),x78523),x78524))+~P101(f323(f323(f238(x78521),f2(x78521)),x78522))+P101(f323(f323(f238(x78521),f323(f323(f79(x78521),x78522),x78523)),f323(f323(f79(x78521),x78522),x78524)))
% 188.07/187.98 [7853]~P120(x78531)+~P101(f323(f323(f238(x78531),x78532),x78534))+~P101(f323(f323(f238(x78531),f2(x78531)),x78533))+P101(f323(f323(f238(x78531),f323(f323(f79(x78531),x78532),x78533)),f323(f323(f79(x78531),x78534),x78533)))
% 188.07/187.98 [7854]~P125(x78541)+~P101(f323(f323(f238(x78541),x78542),x78544))+~P101(f323(f323(f238(x78541),f2(x78541)),x78543))+P101(f323(f323(f238(x78541),f323(f323(f79(x78541),x78542),x78543)),f323(f323(f79(x78541),x78544),x78543)))
% 188.07/187.98 [7855]~P120(x78551)+~P101(f323(f323(f238(x78551),x78553),x78554))+~P101(f323(f323(f238(x78551),f2(x78551)),x78552))+P101(f323(f323(f238(x78551),f323(f323(f79(x78551),x78552),x78553)),f323(f323(f79(x78551),x78552),x78554)))
% 188.07/187.98 [7856]~P65(x78561)+~P101(f323(f323(f238(x78561),x78562),x78564))+~P101(f323(f323(f238(x78561),f2(x78561)),x78563))+P101(f323(f323(f238(x78561),f323(f323(f281(x78561),x78562),x78563)),f323(f323(f281(x78561),x78564),x78563)))
% 188.07/187.98 [7901]~P104(x79012)+P101(f323(f323(f238(f872(x79011,x79012)),x79014),x79013))+~P101(f323(f323(f237(f872(x79011,x79012)),x79014),x79013))+P101(f323(f323(f237(f872(x79011,x79012)),x79013),x79014))
% 188.07/187.98 [7941]P101(f323(f323(f325(x79411),x79412),x79413))+P101(f323(f323(f325(x79411),x79412),x79414))+~P101(f323(f323(f237(f872(x79411,a860)),x79414),x79413))+P101(f323(f323(f238(f872(x79411,a860)),x79414),f323(f323(f301(x79411),x79412),x79413)))
% 188.07/187.98 [8095]P101(f323(f323(f325(x80951),x80952),x80953))+P101(f323(f323(f325(x80951),x80952),x80954))+~P101(f323(f323(f238(f872(x80951,a860)),x80954),f323(f323(f301(x80951),x80952),x80953)))+P101(f323(f323(f237(f872(x80951,a860)),x80954),x80953))
% 188.07/187.98 [8103]~P5(x81031)+P12(x81031,x81032,x81033)+~P101(f323(x81032,x81034))+~P101(f323(f323(f325(f866(x81031)),x81034),f323(f166(f866(x81031)),f52(x81031,x81033,f53(x81031)))))
% 188.07/187.98 [8113]~P13(x81133,x81131,x81134)+~P5(x81133)+P101(f323(x81131,x81132))+~P101(f323(f323(f325(f866(x81133)),x81132),f323(f166(f866(x81133)),f52(x81133,x81134,f53(x81133)))))
% 188.07/187.98 [8165]~P120(x81651)+P101(f323(f323(f238(x81651),x81653),x81652))+P101(f323(f323(f238(x81651),x81652),x81653))+~P101(f323(f323(f238(x81651),f323(f323(f79(x81651),x81654),x81652)),f323(f323(f79(x81651),x81654),x81653)))
% 188.07/187.98 [8166]~P120(x81661)+P101(f323(f323(f238(x81661),x81663),x81662))+P101(f323(f323(f238(x81661),x81662),x81663))+~P101(f323(f323(f238(x81661),f323(f323(f79(x81661),x81662),x81664)),f323(f323(f79(x81661),x81663),x81664)))
% 188.07/187.98 [8177]~P120(x81771)+P101(f323(f323(f238(x81771),x81774),f2(x81771)))+P101(f323(f323(f238(x81771),x81772),x81773))+~P101(f323(f323(f238(x81771),f323(f323(f79(x81771),x81772),x81774)),f323(f323(f79(x81771),x81773),x81774)))
% 188.07/187.98 [8178]~P120(x81781)+P101(f323(f323(f238(x81781),x81784),f2(x81781)))+P101(f323(f323(f238(x81781),x81782),x81783))+~P101(f323(f323(f238(x81781),f323(f323(f79(x81781),x81784),x81782)),f323(f323(f79(x81781),x81784),x81783)))
% 188.07/187.98 [8183]~P120(x81831)+P101(f323(f323(f238(x81831),x81832),x81833))+P101(f323(f323(f238(x81831),f2(x81831)),x81834))+~P101(f323(f323(f238(x81831),f323(f323(f79(x81831),x81834),x81833)),f323(f323(f79(x81831),x81834),x81832)))
% 188.07/187.98 [8184]~P120(x81841)+P101(f323(f323(f238(x81841),x81842),x81843))+P101(f323(f323(f238(x81841),f2(x81841)),x81844))+~P101(f323(f323(f238(x81841),f323(f323(f79(x81841),x81843),x81844)),f323(f323(f79(x81841),x81842),x81844)))
% 188.07/187.98 [8197]~P120(x81971)+P101(f323(f323(f238(x81971),x81972),f2(x81971)))+P101(f323(f323(f238(x81971),f2(x81971)),x81972))+~P101(f323(f323(f238(x81971),f323(f323(f79(x81971),x81973),x81972)),f323(f323(f79(x81971),x81974),x81972)))
% 188.07/187.98 [8198]~P120(x81981)+P101(f323(f323(f238(x81981),x81982),f2(x81981)))+P101(f323(f323(f238(x81981),f2(x81981)),x81982))+~P101(f323(f323(f238(x81981),f323(f323(f79(x81981),x81982),x81983)),f323(f323(f79(x81981),x81982),x81984)))
% 188.07/187.98 [8226]~P120(x82261)+~P101(f323(f323(f238(x82261),x82264),f2(x82261)))+P101(f323(f323(f237(x82261),x82262),x82263))+~P101(f323(f323(f237(x82261),f323(f323(f79(x82261),x82264),x82263)),f323(f323(f79(x82261),x82264),x82262)))
% 188.07/187.98 [8227]~P120(x82271)+~P101(f323(f323(f238(x82271),x82274),f2(x82271)))+P101(f323(f323(f238(x82271),x82272),x82273))+~P101(f323(f323(f238(x82271),f323(f323(f79(x82271),x82274),x82273)),f323(f323(f79(x82271),x82274),x82272)))
% 188.07/187.98 [8237]~P119(x82373)+~P101(f323(f323(f238(x82373),f76(x82373)),x82374))+P101(f323(f323(f237(a865),x82371),x82372))+~P101(f323(f323(f237(x82373),f323(f323(f248(x82373),x82374),x82371)),f323(f323(f248(x82373),x82374),x82372)))
% 188.07/187.98 [8239]~P119(x82393)+~P101(f323(f323(f238(x82393),f76(x82393)),x82394))+P101(f323(f323(f238(a865),x82391),x82392))+~P101(f323(f323(f238(x82393),f323(f323(f248(x82393),x82394),x82391)),f323(f323(f248(x82393),x82394),x82392)))
% 188.07/187.98 [8249]~P120(x82491)+P101(f323(f323(f237(x82491),x82492),x82493))+~P101(f323(f323(f238(x82491),f2(x82491)),x82494))+~P101(f323(f323(f237(x82491),f323(f323(f79(x82491),x82494),x82492)),f323(f323(f79(x82491),x82494),x82493)))
% 188.07/187.98 [8250]~P125(x82501)+P101(f323(f323(f237(x82501),x82502),x82503))+~P101(f323(f323(f238(x82501),f2(x82501)),x82504))+~P101(f323(f323(f237(x82501),f323(f323(f79(x82501),x82504),x82502)),f323(f323(f79(x82501),x82504),x82503)))
% 188.07/187.98 [8251]~P125(x82511)+P101(f323(f323(f237(x82511),x82512),x82513))+~P101(f323(f323(f238(x82511),f2(x82511)),x82514))+~P101(f323(f323(f237(x82511),f323(f323(f79(x82511),x82512),x82514)),f323(f323(f79(x82511),x82513),x82514)))
% 188.07/187.98 [8252]~P120(x82521)+P101(f323(f323(f238(x82521),x82522),x82523))+~P101(f323(f323(f238(x82521),f2(x82521)),x82524))+~P101(f323(f323(f238(x82521),f323(f323(f79(x82521),x82524),x82522)),f323(f323(f79(x82521),x82524),x82523)))
% 188.07/187.98 [8253]~P125(x82531)+P101(f323(f323(f238(x82531),x82532),x82533))+~P101(f323(f323(f237(x82531),f2(x82531)),x82534))+~P101(f323(f323(f238(x82531),f323(f323(f79(x82531),x82534),x82532)),f323(f323(f79(x82531),x82534),x82533)))
% 188.07/187.98 [8254]~P126(x82541)+P101(f323(f323(f238(x82541),x82542),x82543))+~P101(f323(f323(f237(x82541),f2(x82541)),x82544))+~P101(f323(f323(f238(x82541),f323(f323(f79(x82541),x82544),x82542)),f323(f323(f79(x82541),x82544),x82543)))
% 188.07/187.98 [8255]~P119(x82551)+~P101(f323(f323(f237(x82551),f2(x82551)),x82553))+P101(f323(f323(f238(x82551),x82552),x82553))+~P101(f323(f323(f238(x82551),f323(f323(f248(x82551),x82552),x82554)),f323(f323(f248(x82551),x82553),x82554)))
% 188.07/187.98 [8256]~P125(x82561)+P101(f323(f323(f238(x82561),x82562),x82563))+~P101(f323(f323(f237(x82561),f2(x82561)),x82564))+~P101(f323(f323(f238(x82561),f323(f323(f79(x82561),x82562),x82564)),f323(f323(f79(x82561),x82563),x82564)))
% 188.07/187.98 [8257]~P126(x82571)+P101(f323(f323(f238(x82571),x82572),x82573))+~P101(f323(f323(f237(x82571),f2(x82571)),x82574))+~P101(f323(f323(f238(x82571),f323(f323(f79(x82571),x82572),x82574)),f323(f323(f79(x82571),x82573),x82574)))
% 188.07/187.98 [8303]P101(f323(f323(f325(x83031),x83032),x83033))+~P101(f323(f323(f237(f872(x83031,a860)),x83033),x83034))+~P101(f323(f323(f238(f872(x83031,a860)),x83033),x83034))+P101(f323(f323(f238(f872(x83031,a860)),x83033),f323(f323(f301(x83031),x83032),x83034)))
% 188.07/187.98 [8554]~P5(x85541)+~P92(x85542)+~E(f323(x85543,f794(x85544,x85543,x85541,x85542)),f323(x85544,f794(x85544,x85543,x85541,x85542)))+P101(f323(f323(f89(f872(x85541,x85542)),x85543),x85544))
% 188.07/187.98 [8682]E(f323(f323(f22(a1),f396(x86821,x86822,x86823,x86824)),f397(x86821,x86822,x86823,x86824)),x86824)+~P101(f323(f323(f238(a1),f2(a1)),x86823))+~P101(f323(f323(f237(a1),x86821),x86824))+P101(f323(f323(f237(a1),x86821),f323(f323(f78(a1),x86824),x86823)))
% 188.07/187.98 [8683]E(f323(f323(f22(a1),f417(x86831,x86832,x86833,x86834)),f418(x86831,x86832,x86833,x86834)),x86834)+~P101(f323(f323(f238(a1),f2(a1)),x86833))+~P101(f323(f323(f238(a1),x86831),x86834))+P101(f323(f323(f238(a1),x86831),f323(f323(f78(a1),x86834),x86833)))
% 188.07/187.98 [8828]~E(f323(f323(f158(x88281),x88283),f637(x88284,x88283,x88281,x88282)),f323(f323(f158(x88281),x88284),f637(x88284,x88283,x88281,x88282)))+E(f323(f323(f169(x88281),x88282),x88283),f323(f323(f169(x88281),x88282),x88284))+~P101(f323(f323(f237(a865),x88282),f323(f189(f866(x88281)),x88283)))+~P101(f323(f323(f237(a865),x88282),f323(f189(f866(x88281)),x88284)))
% 188.07/187.98 [8898]~P101(f323(f323(f238(a1),f2(a1)),x88983))+~P101(f323(f323(f237(a1),x88981),x88984))+P101(f323(f323(f325(a1),f396(x88981,x88982,x88983,x88984)),x88982))+P101(f323(f323(f237(a1),x88981),f323(f323(f78(a1),x88984),x88983)))
% 188.07/187.98 [8899]~P101(f323(f323(f238(a1),f2(a1)),x88993))+~P101(f323(f323(f238(a1),x88991),x88994))+P101(f323(f323(f325(a1),f417(x88991,x88992,x88993,x88994)),x88992))+P101(f323(f323(f238(a1),x88991),f323(f323(f78(a1),x88994),x88993)))
% 188.07/187.98 [8935]~P98(x89351)+~P101(f323(f59(x89351),x89353))+~P101(f323(f323(f325(x89351),x89354),x89353))+P101(f323(f323(f237(x89351),f323(f323(f62(x89351,x89351,f101(x89351)),x89352),x89353)),f323(f323(f101(x89351),x89354),x89352)))
% 188.07/187.98 [8936]~P103(x89361)+~P101(f323(f59(x89361),x89363))+~P101(f323(f323(f325(x89361),x89364),x89363))+P101(f323(f323(f237(x89361),f323(f323(f62(x89361,x89361,f235(x89361)),x89362),x89363)),f323(f323(f235(x89361),x89364),x89362)))
% 188.07/187.98 [8980]E(f323(f323(f169(x89801),x89802),x89803),f323(f323(f169(x89801),x89802),x89804))+P101(f323(f323(f238(a865),f637(x89803,x89804,x89801,x89802)),x89802))+~P101(f323(f323(f237(a865),x89802),f323(f189(f866(x89801)),x89803)))+~P101(f323(f323(f237(a865),x89802),f323(f189(f866(x89801)),x89804)))
% 188.07/187.98 [8985]~P101(f323(f323(f238(a1),f2(a1)),x89853))+~P101(f323(f323(f237(a1),x89851),x89852))+P101(f323(f323(f325(a1),f397(x89851,x89854,x89853,x89852)),f294(a1,f76(a1),x89853)))+P101(f323(f323(f237(a1),x89851),f323(f323(f78(a1),x89852),x89853)))
% 188.07/187.98 [8986]~P101(f323(f323(f238(a1),f2(a1)),x89863))+~P101(f323(f323(f238(a1),x89861),x89862))+P101(f323(f323(f325(a1),f418(x89861,x89864,x89863,x89862)),f294(a1,f76(a1),x89863)))+P101(f323(f323(f238(a1),x89861),f323(f323(f78(a1),x89862),x89863)))
% 188.07/187.98 [9153]~E(f323(f179(x91531,x91532),x91533),f323(f179(x91531,x91532),x91534))+E(f323(f166(f871(x91531,x91532)),x91533),f323(f166(f871(x91531,x91532)),x91534))+~P101(f323(f130(x91531),f323(f323(f147(f871(x91531,x91532),x91531),f257(x91531,x91532)),x91534)))+~P101(f323(f130(x91531),f323(f323(f147(f871(x91531,x91532),x91531),f257(x91531,x91532)),x91533)))
% 188.07/187.98 [9165]E(f323(f179(x91651,x91652),x91653),f323(f179(x91651,x91652),x91654))+~E(f323(f166(f871(x91651,x91652)),x91653),f323(f166(f871(x91651,x91652)),x91654))+~P101(f323(f130(x91651),f323(f323(f147(f871(x91651,x91652),x91651),f257(x91651,x91652)),x91654)))+~P101(f323(f130(x91651),f323(f323(f147(f871(x91651,x91652),x91651),f257(x91651,x91652)),x91653)))
% 188.07/187.98 [9306]~P103(x93061)+~P101(f323(f59(x93061),x93064))+P101(f323(f323(f325(x93061),f766(x93062,x93063,x93064,x93061)),x93064))+P101(f323(f323(f237(x93061),f323(f323(f62(x93061,x93061,f236(x93061)),x93062),x93064)),f323(f323(f236(x93061),x93063),x93062)))
% 188.07/187.98 [9307]~P97(x93071)+~P101(f323(f59(x93071),x93074))+P101(f323(f323(f325(x93071),f770(x93072,x93073,x93074,x93071)),x93074))+P101(f323(f323(f237(x93071),f323(f323(f62(x93071,x93071,f110(x93071)),x93072),x93074)),f323(f323(f110(x93071),x93073),x93072)))
% 188.07/187.98 [9429]~P97(x94291)+~P101(f323(f59(x94291),x94293))+~P101(f323(f323(f237(x94291),f770(x94292,x94294,x94293,x94291)),x94294))+P101(f323(f323(f237(x94291),f323(f323(f62(x94291,x94291,f110(x94291)),x94292),x94293)),f323(f323(f110(x94291),x94294),x94292)))
% 188.07/187.98 [9430]~P103(x94301)+~P101(f323(f59(x94301),x94303))+~P101(f323(f323(f237(x94301),f766(x94302,x94304,x94303,x94301)),x94304))+P101(f323(f323(f237(x94301),f323(f323(f62(x94301,x94301,f236(x94301)),x94302),x94303)),f323(f323(f236(x94301),x94304),x94302)))
% 188.07/187.98 [9433]~P101(f323(f323(f237(a1),f2(a1)),x94334))+~P101(f323(f323(f238(a1),f2(a1)),x94333))+~P101(f323(f323(f238(a1),x94334),x94331))+P101(f323(f323(f238(a1),f323(f323(f78(a1),f323(f323(f79(a1),x94331),f42(a1,x94332,x94333))),x94334)),f323(f323(f79(a1),x94331),x94333)))
% 188.07/187.98 [9833]E(x98331,x98332)+P101(f323(f323(f325(f871(f866(x98333),f866(x98333))),f323(f323(f258(f866(x98333),f866(x98333)),x98332),x98331)),f140(x98333,x98334)))+P101(f323(f323(f325(f871(f866(x98333),f866(x98333))),f323(f323(f258(f866(x98333),f866(x98333)),x98331),x98332)),f140(x98333,x98334)))+~P101(f323(f323(f325(f871(x98333,x98333)),f323(f323(f258(x98333,x98333),f626(x98331,x98332,x98334,x98333)),f628(x98331,x98332,x98334,x98333))),x98334))
% 188.07/187.98 [9834]E(x98341,x98342)+P101(f323(f323(f325(f871(f866(x98343),f866(x98343))),f323(f323(f258(f866(x98343),f866(x98343)),x98342),x98341)),f140(x98343,x98344)))+P101(f323(f323(f325(f871(f866(x98343),f866(x98343))),f323(f323(f258(f866(x98343),f866(x98343)),x98341),x98342)),f140(x98343,x98344)))+~P101(f323(f323(f325(f871(x98343,x98343)),f323(f323(f258(x98343,x98343),f628(x98341,x98342,x98344,x98343)),f626(x98341,x98342,x98344,x98343))),x98344))
% 188.07/187.98 [7388]~P97(x73881)+~P101(f323(f323(f237(x73881),x73883),x73884))+~P101(f323(f323(f237(x73881),x73882),x73884))+P101(f323(f323(f237(x73881),f323(f323(f110(x73881),x73882),x73883)),x73884))
% 188.07/187.98 [7391]~P103(x73911)+~P101(f323(f323(f237(x73911),x73913),x73914))+~P101(f323(f323(f237(x73911),x73912),x73914))+P101(f323(f323(f237(x73911),f323(f323(f236(x73911),x73912),x73913)),x73914))
% 188.07/187.98 [7392]~P103(x73921)+~P101(f323(f323(f238(x73921),x73923),x73924))+~P101(f323(f323(f238(x73921),x73922),x73924))+P101(f323(f323(f238(x73921),f323(f323(f236(x73921),x73922),x73923)),x73924))
% 188.07/187.98 [7711]~E(x77111,x77113)+E(f132(a865,f323(f293(a865,x77111),x77112)),f323(f323(f144(a865),x77113),x77114))+~E(f132(a865,f323(f293(a865,f323(f323(f78(a865),x77111),f76(a865))),x77112)),x77114)+~P101(f323(f323(f238(a865),x77111),x77112))
% 188.07/187.98 [7720]~P103(x77201)+P101(f323(f323(f237(x77201),x77202),x77203))+P101(f323(f323(f237(x77201),x77204),x77203))+~P101(f323(f323(f237(x77201),f323(f323(f235(x77201),x77204),x77202)),x77203))
% 188.07/187.98 [7721]~P103(x77211)+P101(f323(f323(f238(x77211),x77212),x77213))+P101(f323(f323(f238(x77211),x77214),x77213))+~P101(f323(f323(f238(x77211),f323(f323(f235(x77211),x77214),x77212)),x77213))
% 188.07/187.98 [7999]~P64(x79991)+~P101(f323(f323(f238(x79991),f2(x79991)),x79993))+~P101(f323(f323(f237(x79991),x79992),f323(f323(f281(x79991),x79994),x79993)))+P101(f323(f323(f237(x79991),f323(f323(f79(x79991),x79992),x79993)),x79994))
% 188.07/187.98 [8000]~P65(x80001)+~P101(f323(f323(f238(x80001),f2(x80001)),x80003))+~P101(f323(f323(f237(x80001),x80002),f323(f323(f281(x80001),x80004),x80003)))+P101(f323(f323(f237(x80001),f323(f323(f79(x80001),x80002),x80003)),x80004))
% 188.07/187.98 [8002]~P64(x80021)+~P101(f323(f323(f238(x80021),f2(x80021)),x80023))+~P101(f323(f323(f237(x80021),x80022),f323(f323(f79(x80021),x80024),x80023)))+P101(f323(f323(f237(x80021),f323(f323(f281(x80021),x80022),x80023)),x80024))
% 188.07/187.98 [8003]~P65(x80031)+~P101(f323(f323(f238(x80031),f2(x80031)),x80033))+~P101(f323(f323(f237(x80031),x80032),f323(f323(f79(x80031),x80034),x80033)))+P101(f323(f323(f237(x80031),f323(f323(f281(x80031),x80032),x80033)),x80034))
% 188.07/187.98 [8004]~P64(x80041)+~P101(f323(f323(f238(x80041),f2(x80041)),x80043))+~P101(f323(f323(f238(x80041),x80042),f323(f323(f281(x80041),x80044),x80043)))+P101(f323(f323(f238(x80041),f323(f323(f79(x80041),x80042),x80043)),x80044))
% 188.07/187.98 [8005]~P65(x80051)+~P101(f323(f323(f238(x80051),f2(x80051)),x80053))+~P101(f323(f323(f238(x80051),x80052),f323(f323(f281(x80051),x80054),x80053)))+P101(f323(f323(f238(x80051),f323(f323(f79(x80051),x80052),x80053)),x80054))
% 188.07/187.98 [8007]~P64(x80071)+~P101(f323(f323(f238(x80071),f2(x80071)),x80073))+~P101(f323(f323(f238(x80071),x80072),f323(f323(f79(x80071),x80074),x80073)))+P101(f323(f323(f238(x80071),f323(f323(f281(x80071),x80072),x80073)),x80074))
% 188.07/187.98 [8008]~P65(x80081)+~P101(f323(f323(f238(x80081),f2(x80081)),x80083))+~P101(f323(f323(f238(x80081),x80082),f323(f323(f79(x80081),x80084),x80083)))+P101(f323(f323(f238(x80081),f323(f323(f281(x80081),x80082),x80083)),x80084))
% 188.07/187.98 [8135]~P64(x81351)+~P101(f323(f323(f238(x81351),f2(x81351)),x81354))+P101(f323(f323(f237(x81351),x81352),f323(f323(f79(x81351),x81353),x81354)))+~P101(f323(f323(f237(x81351),f323(f323(f281(x81351),x81352),x81354)),x81353))
% 188.07/187.98 [8137]~P64(x81371)+~P101(f323(f323(f238(x81371),f2(x81371)),x81374))+P101(f323(f323(f237(x81371),x81372),f323(f323(f281(x81371),x81373),x81374)))+~P101(f323(f323(f237(x81371),f323(f323(f79(x81371),x81372),x81374)),x81373))
% 188.07/187.98 [8138]~P65(x81381)+~P101(f323(f323(f238(x81381),f2(x81381)),x81384))+P101(f323(f323(f237(x81381),x81382),f323(f323(f79(x81381),x81383),x81384)))+~P101(f323(f323(f237(x81381),f323(f323(f281(x81381),x81382),x81384)),x81383))
% 188.07/187.98 [8139]~P65(x81391)+~P101(f323(f323(f238(x81391),f2(x81391)),x81394))+P101(f323(f323(f237(x81391),x81392),f323(f323(f281(x81391),x81393),x81394)))+~P101(f323(f323(f237(x81391),f323(f323(f79(x81391),x81392),x81394)),x81393))
% 188.07/187.98 [8140]~P64(x81401)+~P101(f323(f323(f238(x81401),f2(x81401)),x81404))+P101(f323(f323(f238(x81401),x81402),f323(f323(f79(x81401),x81403),x81404)))+~P101(f323(f323(f238(x81401),f323(f323(f281(x81401),x81402),x81404)),x81403))
% 188.07/187.98 [8142]~P64(x81421)+~P101(f323(f323(f238(x81421),f2(x81421)),x81424))+P101(f323(f323(f238(x81421),x81422),f323(f323(f281(x81421),x81423),x81424)))+~P101(f323(f323(f238(x81421),f323(f323(f79(x81421),x81422),x81424)),x81423))
% 188.07/187.98 [8143]~P65(x81431)+~P101(f323(f323(f238(x81431),f2(x81431)),x81434))+P101(f323(f323(f238(x81431),x81432),f323(f323(f79(x81431),x81433),x81434)))+~P101(f323(f323(f238(x81431),f323(f323(f281(x81431),x81432),x81434)),x81433))
% 188.07/187.98 [8144]~P65(x81441)+~P101(f323(f323(f238(x81441),f2(x81441)),x81444))+P101(f323(f323(f238(x81441),x81442),f323(f323(f281(x81441),x81443),x81444)))+~P101(f323(f323(f238(x81441),f323(f323(f79(x81441),x81442),x81444)),x81443))
% 188.07/187.98 [8307]~P65(x83071)+~P101(f323(f323(f238(x83071),x83073),f2(x83071)))+~P101(f323(f323(f237(x83071),f323(f323(f281(x83071),x83074),x83073)),x83072))+P101(f323(f323(f237(x83071),f323(f323(f79(x83071),x83072),x83073)),x83074))
% 188.07/187.98 [8308]~P65(x83081)+~P101(f323(f323(f238(x83081),x83083),f2(x83081)))+~P101(f323(f323(f237(x83081),f323(f323(f79(x83081),x83084),x83083)),x83082))+P101(f323(f323(f237(x83081),f323(f323(f281(x83081),x83082),x83083)),x83084))
% 188.07/187.98 [8309]~P65(x83091)+~P101(f323(f323(f238(x83091),x83093),f2(x83091)))+~P101(f323(f323(f238(x83091),f323(f323(f281(x83091),x83094),x83093)),x83092))+P101(f323(f323(f238(x83091),f323(f323(f79(x83091),x83092),x83093)),x83094))
% 188.07/187.98 [8310]~P65(x83101)+~P101(f323(f323(f238(x83101),x83103),f2(x83101)))+~P101(f323(f323(f238(x83101),f323(f323(f79(x83101),x83104),x83103)),x83102))+P101(f323(f323(f238(x83101),f323(f323(f281(x83101),x83102),x83103)),x83104))
% 188.07/187.98 [8322]~P101(f323(x83221,x83224))+~P101(f323(f323(f238(a865),x83222),f323(f323(f79(a865),x83223),f323(a112,x83224))))+P101(f323(x83221,f323(f323(f36(a865),x83222),x83223)))+~P101(f323(f323(f237(a865),f323(f323(f79(a865),x83223),x83224)),x83222))
% 188.07/187.98 [8526]~P97(x85261)+~P101(f323(f59(x85261),x85264))+~P101(f323(f323(f325(x85261),x85262),x85264))+P101(f323(f323(f237(x85261),f323(f323(f110(x85261),x85262),x85263)),f323(f323(f62(x85261,x85261,f110(x85261)),x85263),x85264)))
% 188.07/187.98 [8527]~P103(x85271)+~P101(f323(f59(x85271),x85274))+~P101(f323(f323(f325(x85271),x85272),x85274))+P101(f323(f323(f237(x85271),f323(f323(f236(x85271),x85272),x85273)),f323(f323(f62(x85271,x85271,f236(x85271)),x85273),x85274)))
% 188.07/187.98 [8684]~P101(f323(f59(x86841),x86842))+E(f323(f35(x86841),f323(f323(f22(f872(x86841,a860)),x86842),f323(f323(f301(x86841),x86843),x86844))),f323(f323(f22(a865),f323(f35(x86841),f323(f323(f22(f872(x86841,a860)),x86842),x86844))),f76(a865)))+P101(f323(f323(f325(x86841),x86843),x86844))+~P101(f323(f323(f325(x86841),x86843),x86842))
% 188.07/187.98 [8762]E(f323(f323(f78(a1),f398(x87621,x87622,x87623,x87624)),f399(x87621,x87622,x87623,x87624)),x87624)+~P101(f323(f323(f238(a1),f2(a1)),x87623))+~P101(f323(f323(f237(a1),x87624),x87621))+P101(f323(f323(f237(a1),f323(f323(f22(a1),x87624),x87623)),x87621))
% 188.07/187.98 [8763]E(f323(f323(f78(a1),f419(x87631,x87632,x87633,x87634)),f420(x87631,x87632,x87633,x87634)),x87634)+~P101(f323(f323(f238(a1),f2(a1)),x87633))+~P101(f323(f323(f238(a1),x87634),x87631))+P101(f323(f323(f238(a1),f323(f323(f22(a1),x87634),x87633)),x87631))
% 188.07/187.98 [8965]~P101(f323(f323(f238(a1),f2(a1)),x89653))+~P101(f323(f323(f237(a1),x89654),x89651))+P101(f323(f323(f325(a1),f398(x89651,x89652,x89653,x89654)),x89652))+P101(f323(f323(f237(a1),f323(f323(f22(a1),x89654),x89653)),x89651))
% 188.07/187.98 [8966]~P101(f323(f323(f238(a1),f2(a1)),x89663))+~P101(f323(f323(f238(a1),x89664),x89661))+P101(f323(f323(f325(a1),f419(x89661,x89662,x89663,x89664)),x89662))+P101(f323(f323(f238(a1),f323(f323(f22(a1),x89664),x89663)),x89661))
% 188.07/187.98 [9055]~P101(f323(f323(f238(a1),f2(a1)),x90552))+~P101(f323(f323(f237(a1),x90551),x90553))+P101(f323(f323(f325(a1),f399(x90553,x90554,x90552,x90551)),f294(a1,f76(a1),x90552)))+P101(f323(f323(f237(a1),f323(f323(f22(a1),x90551),x90552)),x90553))
% 188.07/187.98 [9056]~P101(f323(f323(f238(a1),f2(a1)),x90562))+~P101(f323(f323(f238(a1),x90561),x90563))+P101(f323(f323(f325(a1),f420(x90563,x90564,x90562,x90561)),f294(a1,f76(a1),x90562)))+P101(f323(f323(f238(a1),f323(f323(f22(a1),x90561),x90562)),x90563))
% 188.07/187.98 [9073]~P101(f323(f323(f237(a1),f2(a1)),x90734))+~P101(f323(f323(f238(a1),f2(a1)),x90733))+~P101(f323(f323(f238(a1),x90734),x90731))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),f323(f323(f79(a1),x90731),f42(a1,x90732,x90733))),x90734)))
% 188.07/187.98 [9134]~P98(x91341)+~P101(f323(f59(x91341),x91344))+~P101(f323(f323(f237(x91341),x91342),f764(x91343,x91342,x91344,x91341)))+P101(f323(f323(f237(x91341),f323(f323(f101(x91341),x91342),x91343)),f323(f323(f62(x91341,x91341,f101(x91341)),x91343),x91344)))
% 188.07/187.98 [9135]~P103(x91351)+~P101(f323(f59(x91351),x91354))+~P101(f323(f323(f237(x91351),x91352),f765(x91353,x91352,x91354,x91351)))+P101(f323(f323(f237(x91351),f323(f323(f235(x91351),x91352),x91353)),f323(f323(f62(x91351,x91351,f235(x91351)),x91353),x91354)))
% 188.07/187.98 [9151]~P101(f323(f323(f237(a1),x91514),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x91512))+~P101(f323(f323(f238(a1),x91511),x91514))+P101(f323(f323(f238(a1),f323(f323(f79(a1),x91511),x91512)),f323(f323(f78(a1),f323(f323(f79(a1),x91511),f42(a1,x91513,x91512))),x91514)))
% 188.07/187.98 [9177]P101(f323(f59(x91771),x91772))+~P101(f323(f59(x91771),x91773))+~P101(f323(f323(f325(f872(x91771,a860)),x91772),f323(f323(f58(x91771),x91773),x91774)))+~P101(f323(f323(f237(f872(f871(x91771,x91771),a860)),x91774),f323(f323(f260(x91771,x91771),x91773),f323(f16(f872(x91771,a860),x91771),x91773))))
% 188.07/187.98 [9200]~P103(x92001)+~P101(f323(f59(x92001),x92004))+P101(f323(f323(f325(x92001),f765(x92002,x92003,x92004,x92001)),x92004))+P101(f323(f323(f237(x92001),f323(f323(f235(x92001),x92003),x92002)),f323(f323(f62(x92001,x92001,f235(x92001)),x92002),x92004)))
% 188.07/187.98 [9201]~P98(x92011)+~P101(f323(f59(x92011),x92014))+P101(f323(f323(f325(x92011),f764(x92012,x92013,x92014,x92011)),x92014))+P101(f323(f323(f237(x92011),f323(f323(f101(x92011),x92013),x92012)),f323(f323(f62(x92011,x92011,f101(x92011)),x92012),x92014)))
% 188.07/187.98 [9599]~P101(f323(f59(x95992),x95994))+~P101(f323(f59(x95991),x95993))+~P101(f323(f323(f237(a865),f323(f35(x95992),x95994)),f323(f35(x95991),x95993)))+P101(f323(f323(f237(f872(x95991,a860)),f323(f302(x95992,x95991,f839(x95993,x95991,x95994,x95992)),x95994)),x95993))
% 188.07/187.98 [9247]~P101(f323(f323(f325(x92471),x92472),x92474))+P101(f323(f323(f325(x92471),x92472),x92473))+~P101(f323(f323(f238(f872(x92471,a860)),x92474),f323(f323(f301(x92471),x92472),x92473)))+P101(f323(f323(f238(f872(x92471,a860)),f323(f323(f22(f872(x92471,a860)),x92474),f323(f323(f301(x92471),x92472),f188(f872(x92471,a860))))),x92473))
% 188.07/187.98 [9407]~P101(f323(f323(f325(x94071),x94072),x94074))+P101(f323(f323(f325(x94071),x94072),x94073))+P101(f323(f323(f238(f872(x94071,a860)),x94074),f323(f323(f301(x94071),x94072),x94073)))+~P101(f323(f323(f238(f872(x94071,a860)),f323(f323(f22(f872(x94071,a860)),x94074),f323(f323(f301(x94071),x94072),f188(f872(x94071,a860))))),x94073))
% 188.07/187.98 [9436]P101(f323(f323(f325(x94361),x94362),x94363))+~P101(f323(f323(f237(f872(x94361,a860)),x94364),x94363))+P101(f323(f323(f238(f872(x94361,a860)),x94364),f323(f323(f301(x94361),x94362),x94363)))+~P101(f323(f323(f238(f872(x94361,a860)),f323(f323(f22(f872(x94361,a860)),x94364),f323(f323(f301(x94361),x94362),f188(f872(x94361,a860))))),x94363))
% 188.07/187.98 [9441]~P101(f323(f323(f325(x94411),x94413),x94412))+~P101(f323(f323(f238(f872(x94411,a860)),x94412),x94414))+P101(f323(f323(f238(f872(x94411,a860)),x94412),f323(f323(f301(x94411),x94413),x94414)))+~P101(f323(f323(f238(f872(x94411,a860)),f323(f323(f22(f872(x94411,a860)),x94412),f323(f323(f301(x94411),x94413),f188(f872(x94411,a860))))),x94414))
% 188.07/187.98 [9457]~P101(f323(f323(f237(f872(x94571,a860)),x94572),x94574))+~P101(f323(f323(f238(f872(x94571,a860)),x94572),x94574))+P101(f323(f323(f238(f872(x94571,a860)),x94572),f323(f323(f301(x94571),x94573),x94574)))+~P101(f323(f323(f238(f872(x94571,a860)),f323(f323(f22(f872(x94571,a860)),x94572),f323(f323(f301(x94571),x94573),f188(f872(x94571,a860))))),x94574))
% 188.07/187.98 [9500]~P105(x95002)+~P5(x95001)+~P101(f323(f323(f237(f872(x95001,x95002)),x95003),x95004))+P101(f323(f56(x95001),f323(f323(f18(x95001,x95002,a860),f323(f323(f8(x95002,f872(x95002,a860),x95001),f237(x95002)),x95003)),x95004)))
% 188.07/187.98 [9646]~P105(x96462)+~P5(x96461)+P101(f323(f323(f237(f872(x96461,x96462)),x96463),x96464))+~P101(f323(f56(x96461),f323(f323(f18(x96461,x96462,a860),f323(f323(f8(x96462,f872(x96462,a860),x96461),f237(x96462)),x96463)),x96464)))
% 188.07/187.98 [9819]E(f323(f323(f158(x98191),f323(f323(f158(f866(x98191)),f173(x98191,x98192)),x98193)),x98194),f323(f323(f158(x98191),f323(f323(f158(f866(x98191)),x98192),x98194)),x98193))+~P101(f323(f323(f238(a865),x98193),f323(f189(f866(f866(x98191))),f173(x98191,x98192))))+~P16(a865,f323(f162(a865),f323(f323(f147(f866(x98191),a865),f189(f866(x98191))),x98192)))+~P101(f323(f323(f238(a865),x98194),f323(f189(f866(f866(x98191))),f323(f129(f866(x98191),f323(f323(f8(a865,a860,f866(x98191)),f323(f238(a865),x98193)),f189(f866(x98191)))),x98192))))
% 188.07/187.98 [9846]~P101(f323(f323(f325(f871(a865,a865)),x98464),x98461))+~P101(f323(f323(f325(f871(f871(a865,a865),f871(a865,a865))),f323(f323(f258(f871(a865,a865),f871(a865,a865)),x98464),x98462)),a33))+~P101(f323(f323(f325(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f258(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),x98461),x98463)),a66))+P101(f323(f323(f325(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f258(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),x98461),f323(f323(f301(f871(a865,a865)),x98462),x98463))),a66))
% 188.07/187.98 [9847]~P101(f323(f323(f325(f871(a865,a865)),x98474),x98471))+~P101(f323(f323(f325(f871(f871(a865,a865),f871(a865,a865))),f323(f323(f258(f871(a865,a865),f871(a865,a865)),x98474),x98472)),a68))+~P101(f323(f323(f325(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f258(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),x98471),x98473)),a69))+P101(f323(f323(f325(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f258(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),x98471),f323(f323(f301(f871(a865,a865)),x98472),x98473))),a69))
% 188.07/187.98 [9732]~P105(x97322)+~P5(x97321)+~P101(f323(f323(f238(f872(x97321,x97322)),x97323),x97324))+P101(f323(f55(x97321),f323(f323(f8(a860,a860,x97321),a318),f323(f323(f18(x97321,x97322,a860),f323(f323(f8(x97322,f872(x97322,a860),x97321),a320),x97323)),x97324))))
% 188.07/187.98 [9860]~P101(f323(f323(f325(f871(a865,a865)),x98604),x98603))+~P101(f323(f323(f325(f871(f871(a865,a865),f871(a865,a865))),f323(f323(f258(f871(a865,a865),f871(a865,a865)),x98601),x98604)),a33))+~P101(f323(f323(f325(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f258(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),x98602),x98603)),a34))+P101(f323(f323(f325(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f258(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),f323(f323(f301(f871(a865,a865)),x98601),x98602)),x98603)),a34))
% 188.07/187.98 [9861]~P101(f323(f323(f325(f871(a865,a865)),x98614),x98613))+~P101(f323(f323(f325(f871(f871(a865,a865),f871(a865,a865))),f323(f323(f258(f871(a865,a865),f871(a865,a865)),x98611),x98614)),a68))+~P101(f323(f323(f325(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f258(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),x98612),x98613)),a67))+P101(f323(f323(f325(f871(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860))),f323(f323(f258(f872(f871(a865,a865),a860),f872(f871(a865,a865),a860)),f323(f323(f301(f871(a865,a865)),x98611),x98612)),x98613)),a67))
% 188.07/187.98 [6001]~P8(x60014,x60011)+~P101(f323(f323(x60011,x60012),x60015))+P101(f323(f323(x60011,x60012),x60013))+~P101(f323(f323(x60011,x60015),x60013))
% 188.07/187.98 [5272]~P60(x52725)+E(x52721,x52722)+~E(x52723,x52724)+~E(f323(f323(f22(x52725),x52723),x52724),f323(f323(f22(x52725),x52721),x52722))
% 188.07/187.98 [6109]~P19(x61095,x61091,x61093)+E(f323(f323(x61091,x61092),f323(x61093,x61094)),f323(x61093,x61094))+~P101(f323(f59(x61095),x61094))+~P101(f323(f323(f325(x61095),x61092),x61094))
% 188.07/187.98 [6296]~P75(x62961)+~E(f323(f323(f22(x62961),x62964),x62965),f323(f323(f22(x62961),x62962),x62963))+~P101(f323(f323(f237(x62961),x62964),x62965))+P101(f323(f323(f237(x62961),x62962),x62963))
% 188.07/187.98 [6298]~P75(x62981)+~E(f323(f323(f22(x62981),x62984),x62985),f323(f323(f22(x62981),x62982),x62983))+~P101(f323(f323(f238(x62981),x62984),x62985))+P101(f323(f323(f238(x62981),x62982),x62983))
% 188.07/187.98 [7250]~E(x72502,f323(f323(f144(x72501),x72504),x72505))+P101(f323(f323(f325(f866(x72501)),x72502),f154(x72501,x72503)))+~P101(f323(f323(f325(f866(x72501)),x72505),f154(x72501,x72503)))+~P101(f323(f323(f325(x72501),x72504),x72503))
% 188.07/187.98 [7662]~E(f323(f189(f866(x76621)),x76623),f323(f189(f866(x76622)),x76624))+~E(f323(f323(f147(f871(x76621,x76622),x76622),f261(x76621,x76622)),x76625),x76624)+~E(f323(f323(f147(f871(x76621,x76622),x76621),f257(x76621,x76622)),x76625),x76623)+E(f323(f323(f175(x76621,x76622),x76623),x76624),x76625)
% 188.07/187.98 [7995]~P105(x79951)+P101(f323(f323(f238(f872(x79951,a860)),f294(x79951,x79952,x79953)),f294(x79951,x79954,x79955)))+~P101(f323(f323(f237(x79951),x79954),x79955))+P101(f323(f323(f237(x79951),x79952),x79953))
% 188.07/187.98 [8088]~P105(x80881)+P101(f323(f323(f237(f872(x80881,a860)),f294(x80881,x80882,x80883)),f294(x80881,x80884,x80885)))+~P101(f323(f323(f237(x80881),x80883),x80885))+~P101(f323(f323(f237(x80881),x80884),x80882))
% 188.07/187.98 [8212]~P103(x82121)+P101(f323(f323(f237(x82121),x82122),x82123))+P101(f323(f323(f237(x82121),x82124),x82123))+~P101(f323(f323(f237(f872(x82121,a860)),f323(f293(x82121,x82123),x82122)),f323(f293(x82121,x82124),x82125)))
% 188.07/187.98 [8213]~P103(x82131)+P101(f323(f323(f237(x82131),x82132),x82133))+P101(f323(f323(f237(x82131),x82132),x82134))+~P101(f323(f323(f237(f872(x82131,a860)),f323(f293(x82131,x82133),x82132)),f323(f293(x82131,x82135),x82134)))
% 188.07/187.98 [8445]~P105(x84451)+~P101(f323(f323(f237(f872(x84451,a860)),f294(x84451,x84454,x84452)),f294(x84451,x84455,x84453)))+P101(f323(f323(f237(x84451),x84452),x84453))+~P101(f323(f323(f237(x84451),x84454),x84452))
% 188.07/187.98 [8446]~P105(x84461)+~P101(f323(f323(f238(f872(x84461,a860)),f294(x84461,x84464,x84462)),f294(x84461,x84465,x84463)))+P101(f323(f323(f237(x84461),x84462),x84463))+~P101(f323(f323(f237(x84461),x84464),x84462))
% 188.07/187.98 [8447]~P105(x84471)+~P101(f323(f323(f237(f872(x84471,a860)),f294(x84471,x84473,x84474)),f294(x84471,x84472,x84475)))+P101(f323(f323(f237(x84471),x84472),x84473))+~P101(f323(f323(f237(x84471),x84473),x84474))
% 188.07/187.98 [8448]~P105(x84481)+~P101(f323(f323(f238(f872(x84481,a860)),f294(x84481,x84483,x84484)),f294(x84481,x84482,x84485)))+P101(f323(f323(f237(x84481),x84482),x84483))+~P101(f323(f323(f237(x84481),x84483),x84484))
% 188.07/187.98 [6000]~P19(x60002,x60005,x60003)+E(x60001,f188(f872(x60002,a860)))+~P101(f323(f59(x60002),x60001))+E(f323(x60003,f323(f323(f301(x60002),x60004),x60001)),f323(f323(x60005,x60004),f323(x60003,x60001)))
% 188.07/187.98 [6757]~E(x67571,x67572)+~E(f323(f323(f101(f872(x67573,a860)),x67574),x67575),f188(f872(x67573,a860)))+~P101(f323(f323(f325(x67573),x67572),x67575))+~P101(f323(f323(f325(x67573),x67571),x67574))
% 188.07/187.98 [6839]~P20(x68392,x68395,x68391)+~P101(f323(f59(x68392),x68394))+E(f323(x68391,f323(f323(f301(x68392),x68393),x68394)),f323(f323(f62(x68392,x68392,x68395),x68393),x68394))+P101(f323(f323(f325(x68392),x68393),x68394))
% 188.07/187.98 [6903]~P72(x69032)+~P101(f323(f59(x69031),x69035))+E(f323(f323(f6(x69031,x69032),x69033),f323(f323(f301(x69031),x69034),x69035)),f323(f323(f78(x69032),f323(x69033,x69034)),f323(f323(f6(x69031,x69032),x69033),x69035)))+P101(f323(f323(f325(x69031),x69034),x69035))
% 188.07/187.98 [6905]~P68(x69052)+~P101(f323(f59(x69051),x69055))+E(f323(f323(f9(x69051,x69052),x69053),f323(f323(f301(x69051),x69054),x69055)),f323(f323(f79(x69052),f323(x69053,x69054)),f323(f323(f9(x69051,x69052),x69053),x69055)))+P101(f323(f323(f325(x69051),x69054),x69055))
% 188.07/187.98 [7403]~P20(x74032,x74035,x74031)+~P101(f323(f59(x74032),x74034))+E(f323(x74031,f323(f323(f301(x74032),x74033),x74034)),x74033)+~E(f323(f323(f22(f872(x74032,a860)),x74034),f323(f323(f301(x74032),x74033),f188(f872(x74032,a860)))),f188(f872(x74032,a860)))
% 188.07/187.98 [7764]~P97(x77641)+~P101(f323(f323(f237(x77641),x77643),x77645))+~P101(f323(f323(f237(x77641),x77642),x77644))+P101(f323(f323(f237(x77641),f323(f323(f110(x77641),x77642),x77643)),f323(f323(f110(x77641),x77644),x77645)))
% 188.07/187.98 [7765]~P98(x77651)+~P101(f323(f323(f237(x77651),x77653),x77655))+~P101(f323(f323(f237(x77651),x77652),x77654))+P101(f323(f323(f237(x77651),f323(f323(f101(x77651),x77652),x77653)),f323(f323(f101(x77651),x77654),x77655)))
% 188.07/187.98 [7766]~P81(x77661)+~P101(f323(f323(f237(x77661),x77663),x77665))+~P101(f323(f323(f237(x77661),x77662),x77664))+P101(f323(f323(f237(x77661),f323(f323(f78(x77661),x77662),x77663)),f323(f323(f78(x77661),x77664),x77665)))
% 188.07/187.98 [7767]~P103(x77671)+~P101(f323(f323(f237(x77671),x77673),x77675))+~P101(f323(f323(f237(x77671),x77672),x77674))+P101(f323(f323(f237(x77671),f323(f323(f235(x77671),x77672),x77673)),f323(f323(f235(x77671),x77674),x77675)))
% 188.07/187.98 [7768]~P103(x77681)+~P101(f323(f323(f237(x77681),x77683),x77685))+~P101(f323(f323(f237(x77681),x77682),x77684))+P101(f323(f323(f237(x77681),f323(f323(f236(x77681),x77682),x77683)),f323(f323(f236(x77681),x77684),x77685)))
% 188.07/187.98 [7769]~P83(x77691)+~P101(f323(f323(f237(x77691),x77693),x77695))+~P101(f323(f323(f238(x77691),x77692),x77694))+P101(f323(f323(f238(x77691),f323(f323(f78(x77691),x77692),x77693)),f323(f323(f78(x77691),x77694),x77695)))
% 188.07/187.98 [7770]~P83(x77701)+~P101(f323(f323(f237(x77701),x77702),x77704))+~P101(f323(f323(f238(x77701),x77703),x77705))+P101(f323(f323(f238(x77701),f323(f323(f78(x77701),x77702),x77703)),f323(f323(f78(x77701),x77704),x77705)))
% 188.07/187.98 [7771]~P83(x77711)+~P101(f323(f323(f238(x77711),x77713),x77715))+~P101(f323(f323(f238(x77711),x77712),x77714))+P101(f323(f323(f238(x77711),f323(f323(f78(x77711),x77712),x77713)),f323(f323(f78(x77711),x77714),x77715)))
% 188.07/187.98 [7912]~P135(x79125)+E(x79121,x79122)+E(x79123,x79124)+~E(f323(f323(f78(x79125),f323(f323(f79(x79125),x79123),x79121)),f323(f323(f79(x79125),x79124),x79122)),f323(f323(f78(x79125),f323(f323(f79(x79125),x79123),x79122)),f323(f323(f79(x79125),x79124),x79121)))
% 188.07/187.98 [8110]~P103(x81104)+~P101(f323(f130(x81101),x81103))+P101(f323(f323(f325(x81101),x81102),f323(f166(x81101),x81103)))+P101(f323(f130(x81101),f323(f323(f141(x81101,x81104,x81105),x81102),x81103)))
% 188.07/187.98 [8258]~P60(x82581)+E(f323(f323(f22(x82581),f323(f323(f6(a865,x82581),x82582),f323(f293(a865,x82583),x82584))),f323(f323(f6(a865,x82581),x82582),f323(f293(a865,x82583),x82585))),f323(f323(f6(a865,x82581),x82582),f323(f293(a865,x82585),x82584)))+~P101(f323(f323(f237(a865),x82585),x82584))+~P101(f323(f323(f237(a865),x82583),x82585))
% 188.07/187.98 [8259]~P72(x82591)+E(f323(f323(f78(x82591),f323(f323(f6(a865,x82591),x82592),f323(f293(a865,x82593),x82594))),f323(f323(f6(a865,x82591),x82592),f323(f293(a865,x82594),x82595))),f323(f323(f6(a865,x82591),x82592),f323(f293(a865,x82593),x82595)))+~P101(f323(f323(f237(a865),x82594),x82595))+~P101(f323(f323(f237(a865),x82593),x82594))
% 188.07/187.98 [8588]~P63(x85882)+E(x85881,f2(x85882))+E(x85883,f2(x85882))+E(f323(f323(f281(x85882),f323(f323(f22(x85882),f323(f323(f79(x85882),x85884),x85881)),f323(f323(f79(x85882),x85885),x85883))),f323(f323(f79(x85882),x85883),x85881)),f323(f323(f22(x85882),f323(f323(f281(x85882),x85884),x85883)),f323(f323(f281(x85882),x85885),x85881)))
% 188.07/187.98 [8589]~P63(x85892)+E(x85891,f2(x85892))+E(x85893,f2(x85892))+E(f323(f323(f281(x85892),f323(f323(f78(x85892),f323(f323(f79(x85892),x85894),x85891)),f323(f323(f79(x85892),x85895),x85893))),f323(f323(f79(x85892),x85893),x85891)),f323(f323(f78(x85892),f323(f323(f281(x85892),x85894),x85893)),f323(f323(f281(x85892),x85895),x85891)))
% 188.07/187.98 [8598]~E(x85982,f323(x85983,x85981))+E(x85981,f539(x85982,x85983,x85984,x85985))+~P27(x85985,x85984,x85983,f246(f872(x85985,a860)))+~P101(f323(f323(f325(x85984),x85982),f323(f302(x85985,x85984,x85983),f246(f872(x85985,a860)))))
% 188.07/187.98 [8813]~P116(x88131)+~P101(f323(f323(f238(x88131),f323(f73(x88131),x88132)),x88134))+P101(f323(f323(f238(x88131),f323(f323(f79(x88131),f323(f73(x88131),x88132)),f323(f73(x88131),x88133))),f323(f323(f79(x88131),x88134),x88135)))+~P101(f323(f323(f238(x88131),f323(f73(x88131),x88133)),x88135))
% 188.07/187.98 [8927]~P27(x89271,x89273,x89275,x89272)+~P101(f323(f59(x89273),x89274))+P101(f323(f323(f237(a865),f323(f35(x89271),x89272)),f323(f35(x89273),x89274)))+~P101(f323(f323(f237(f872(x89273,a860)),f323(f302(x89271,x89273,x89275),x89272)),x89274))
% 188.07/187.98 [8994]~P72(x89942)+~P27(x89941,x89941,x89944,x89945)+~P101(f323(f59(x89941),x89945))+E(f323(f323(f6(x89941,x89942),f323(f71(x89941,x89942,x89941,x89943),x89944)),x89945),f323(f323(f6(x89941,x89942),x89943),f323(f302(x89941,x89941,x89944),x89945)))
% 188.07/187.98 [8995]~P68(x89952)+~P27(x89951,x89951,x89954,x89955)+~P101(f323(f59(x89951),x89955))+E(f323(f323(f9(x89951,x89952),f323(f71(x89951,x89952,x89951,x89953),x89954)),x89955),f323(f323(f9(x89951,x89952),x89953),f323(f302(x89951,x89951,x89954),x89955)))
% 188.07/187.98 [9113]~P38(x91131,x91132)+~P101(f323(f323(f325(x91131),x91133),x91134))+~P101(f323(f323(f325(x91131),x91135),x91134))+~P101(f323(f323(f325(f871(x91131,x91131)),f323(f323(f258(x91131,x91131),x91135),f736(x91132,x91131,x91134))),x91132))
% 188.07/187.98 [9150]~P27(x91502,x91503,x91505,x91501)+E(x91501,f188(f872(x91502,a860)))+E(f323(f302(x91503,x91502,f596(x91504,x91503,x91502,x91501)),x91504),x91501)+~P101(f323(f323(f237(f872(x91503,a860)),f323(f302(x91502,x91503,x91505),x91501)),x91504))
% 188.07/187.98 [9628]~P103(x96285)+~P6(x96285)+P101(f323(f323(f325(x96281),f451(x96282,x96283,x96281,x96284,x96285)),x96283))+~P101(f323(f323(f238(x96285),x96284),f323(f323(f39(x96281,x96285),x96283),x96282)))
% 188.07/187.98 [9633]~P103(x96331)+~P6(x96331)+P101(f323(f323(f238(x96331),x96332),f323(x96333,f451(x96333,x96334,x96335,x96332,x96331))))+~P101(f323(f323(f238(x96331),x96332),f323(f323(f39(x96335,x96331),x96334),x96333)))
% 188.07/187.98 [9712]~P66(x97121)+~P101(f323(f64(x97121,x97121,f79(x97121),x97122,x97123),x97125))+P101(f323(f323(f325(x97121),x97122),x97123))+P101(f323(f64(x97121,x97121,f79(x97121),x97124,f323(f323(f301(x97121),x97122),x97123)),f323(f323(f79(x97121),x97124),x97125)))
% 188.07/187.98 [9928]~P72(x99282)+~P101(f323(f59(x99281),x99285))+E(f323(f323(f6(x99281,x99282),f323(f323(f7(x99281,x99282,x99282),f323(f323(f18(x99281,x99282,f872(x99282,x99282)),f323(f323(f8(a860,f872(x99282,f872(x99282,x99282)),x99281),f96(x99282)),f323(a320,x99283))),x99284)),f2(x99282))),x99285),f2(x99282))+P101(f323(f323(f325(x99281),x99283),x99285))
% 188.07/187.98 [9929]~P68(x99292)+~P101(f323(f59(x99291),x99295))+E(f323(f323(f9(x99291,x99292),f323(f323(f7(x99291,x99292,x99292),f323(f323(f18(x99291,x99292,f872(x99292,x99292)),f323(f323(f8(a860,f872(x99292,f872(x99292,x99292)),x99291),f96(x99292)),f323(a320,x99293))),x99294)),f76(x99292))),x99295),f76(x99292))+P101(f323(f323(f325(x99291),x99293),x99295))
% 188.07/187.98 [9930]~P72(x99302)+~P101(f323(f59(x99301),x99305))+E(f323(f323(f6(x99301,x99302),f323(f323(f7(x99301,x99302,x99302),f323(f323(f18(x99301,x99302,f872(x99302,x99302)),f323(f323(f8(a860,f872(x99302,f872(x99302,x99302)),x99301),f96(x99302)),f323(a320,x99303))),x99304)),f2(x99302))),x99305),f323(x99304,x99303))+~P101(f323(f323(f325(x99301),x99303),x99305))
% 188.07/187.98 [9931]~P68(x99312)+~P101(f323(f59(x99311),x99315))+E(f323(f323(f9(x99311,x99312),f323(f323(f7(x99311,x99312,x99312),f323(f323(f18(x99311,x99312,f872(x99312,x99312)),f323(f323(f8(a860,f872(x99312,f872(x99312,x99312)),x99311),f96(x99312)),f323(a320,x99313))),x99314)),f76(x99312))),x99315),f323(x99314,x99313))+~P101(f323(f323(f325(x99311),x99313),x99315))
% 188.07/187.98 [9986]~P72(x99862)+~P101(f323(f59(x99861),x99865))+E(f323(f323(f6(x99861,x99862),f323(f323(f7(x99861,x99862,x99862),f323(f323(f18(x99861,x99862,f872(x99862,x99862)),f323(f323(f8(a860,f872(x99862,f872(x99862,x99862)),x99861),f96(x99862)),f323(f323(f7(x99861,x99861,a860),a320),x99863))),x99864)),f2(x99862))),x99865),f2(x99862))+P101(f323(f323(f325(x99861),x99863),x99865))
% 188.07/187.98 [9987]~P68(x99872)+~P101(f323(f59(x99871),x99875))+E(f323(f323(f9(x99871,x99872),f323(f323(f7(x99871,x99872,x99872),f323(f323(f18(x99871,x99872,f872(x99872,x99872)),f323(f323(f8(a860,f872(x99872,f872(x99872,x99872)),x99871),f96(x99872)),f323(f323(f7(x99871,x99871,a860),a320),x99873))),x99874)),f76(x99872))),x99875),f76(x99872))+P101(f323(f323(f325(x99871),x99873),x99875))
% 188.07/187.98 [9989]~P72(x99892)+~P101(f323(f59(x99891),x99895))+E(f323(f323(f6(x99891,x99892),f323(f323(f7(x99891,x99892,x99892),f323(f323(f18(x99891,x99892,f872(x99892,x99892)),f323(f323(f8(a860,f872(x99892,f872(x99892,x99892)),x99891),f96(x99892)),f323(f323(f7(x99891,x99891,a860),a320),x99893))),x99894)),f2(x99892))),x99895),f323(x99894,x99893))+~P101(f323(f323(f325(x99891),x99893),x99895))
% 188.07/187.98 [9990]~P68(x99902)+~P101(f323(f59(x99901),x99905))+E(f323(f323(f9(x99901,x99902),f323(f323(f7(x99901,x99902,x99902),f323(f323(f18(x99901,x99902,f872(x99902,x99902)),f323(f323(f8(a860,f872(x99902,f872(x99902,x99902)),x99901),f96(x99902)),f323(f323(f7(x99901,x99901,a860),a320),x99903))),x99904)),f76(x99902))),x99905),f323(x99904,x99903))+~P101(f323(f323(f325(x99901),x99903),x99905))
% 188.07/187.98 [7763]~P60(x77632)+~P101(f323(f59(x77631),x77634))+E(f323(f323(f6(x77631,x77632),x77633),f323(f323(f22(f872(x77631,a860)),x77634),f323(f323(f301(x77631),x77635),f188(f872(x77631,a860))))),f323(f323(f6(x77631,x77632),x77633),x77634))+P101(f323(f323(f325(x77631),x77635),x77634))
% 188.07/187.98 [8266]~P107(x82662)+~P101(f323(f59(x82661),x82664))+E(f323(f323(f6(x82661,x82662),x82663),f323(f323(f22(f872(x82661,a860)),x82664),f323(f323(f301(x82661),x82665),f188(f872(x82661,a860))))),f323(f323(f22(x82662),f323(f323(f6(x82661,x82662),x82663),x82664)),f323(x82663,x82665)))+~P101(f323(f323(f325(x82661),x82665),x82664))
% 188.07/187.98 [8267]~P60(x82672)+~P101(f323(f59(x82671),x82674))+E(f323(f323(f6(x82671,x82672),x82673),f323(f323(f22(f872(x82671,a860)),x82674),f323(f323(f301(x82671),x82675),f188(f872(x82671,a860))))),f323(f323(f22(x82672),f323(f323(f6(x82671,x82672),x82673),x82674)),f323(x82673,x82675)))+~P101(f323(f323(f325(x82671),x82675),x82674))
% 188.07/187.98 [8299]~P60(x82991)+~P101(f323(f59(x82992),x82994))+E(f323(f323(f22(x82991),f323(f323(f6(x82992,x82991),x82993),x82994)),f323(f323(f6(x82992,x82991),x82993),x82995)),f323(f323(f6(x82992,x82991),x82993),f323(f323(f22(f872(x82992,a860)),x82994),x82995)))+~P101(f323(f323(f237(f872(x82992,a860)),x82995),x82994))
% 188.07/187.98 [8319]P101(f323(f59(x83191),f323(x83192,x83193)))+~P101(f323(f59(x83194),x83195))+~P101(f323(f323(f325(x83194),x83193),x83195))+~P101(f323(f59(x83191),f323(f323(f39(x83194,f872(x83191,a860)),x83195),x83192)))
% 188.07/187.98 [8774]~P9(x87741,x87745,x87744)+~E(f323(f277(x87741,x87741,x87744),f323(f323(f301(x87741),x87742),f188(f872(x87741,a860)))),f323(f277(x87741,x87741,x87744),f323(f323(f301(x87741),x87743),f188(f872(x87741,a860)))))+~P101(f323(f323(f325(x87741),x87743),x87745))+P101(f323(f323(f325(f871(x87741,x87741)),f323(f323(f258(x87741,x87741),x87742),x87743)),x87744))
% 188.07/187.98 [9071]~P101(f323(x90711,x90715))+P101(f323(x90711,f414(x90711,x90712,x90713,x90714)))+P101(f323(x90711,f404(x90711,x90712,x90713,x90714)))+~P101(f323(f323(f325(x90714),x90715),f323(f323(f110(f872(x90714,a860)),x90713),x90712)))
% 188.07/187.98 [9252]~P101(f323(x92521,x92525))+P101(f323(x92521,f404(x92521,x92522,x92523,x92524)))+P101(f323(f323(f325(x92524),f414(x92521,x92522,x92523,x92524)),x92522))+~P101(f323(f323(f325(x92524),x92525),f323(f323(f110(f872(x92524,a860)),x92523),x92522)))
% 188.07/187.98 [9253]~P101(f323(x92531,x92535))+P101(f323(x92531,f414(x92531,x92532,x92533,x92534)))+P101(f323(f323(f325(x92534),f404(x92531,x92532,x92533,x92534)),x92533))+~P101(f323(f323(f325(x92534),x92535),f323(f323(f110(f872(x92534,a860)),x92533),x92532)))
% 188.07/187.98 [9257]P101(f323(x92571,x92572))+~P101(f323(x92571,f455(x92571,x92573,x92574,x92575)))+~P101(f323(x92571,f439(x92571,x92573,x92574,x92575)))+~P101(f323(f323(f325(x92575),x92572),f323(f323(f110(f872(x92575,a860)),x92574),x92573)))
% 188.07/187.98 [9301]E(x93011,x93012)+~P101(f323(f323(f325(f871(x93013,x93013)),f323(f323(f258(x93013,x93013),x93011),x93012)),f299(x93013,x93015)))+P101(f323(f323(f325(x93013),x93011),x93014))+~P101(f323(f323(f237(f872(f871(x93013,x93013),a860)),x93015),f323(f323(f260(x93013,x93013),x93014),f323(f16(f872(x93013,a860),x93013),x93014))))
% 188.07/187.98 [9319]P101(f323(x93191,x93192))+~P101(f323(x93191,f439(x93191,x93194,x93195,x93193)))+P101(f323(f323(f325(x93193),f455(x93191,x93194,x93195,x93193)),x93194))+~P101(f323(f323(f325(x93193),x93192),f323(f323(f110(f872(x93193,a860)),x93195),x93194)))
% 188.07/187.98 [9320]P101(f323(x93201,x93202))+~P101(f323(x93201,f455(x93201,x93204,x93205,x93203)))+P101(f323(f323(f325(x93203),f439(x93201,x93204,x93205,x93203)),x93205))+~P101(f323(f323(f325(x93203),x93202),f323(f323(f110(f872(x93203,a860)),x93205),x93204)))
% 188.07/187.98 [9381]P101(f323(x93811,x93812))+P101(f323(f323(f325(x93813),f455(x93811,x93814,x93815,x93813)),x93814))+P101(f323(f323(f325(x93813),f439(x93811,x93814,x93815,x93813)),x93815))+~P101(f323(f323(f325(x93813),x93812),f323(f323(f110(f872(x93813,a860)),x93815),x93814)))
% 188.07/187.98 [9383]~P101(f323(x93832,x93835))+P101(f323(f323(f325(x93831),f414(x93832,x93833,x93834,x93831)),x93833))+P101(f323(f323(f325(x93831),f404(x93832,x93833,x93834,x93831)),x93834))+~P101(f323(f323(f325(x93831),x93835),f323(f323(f110(f872(x93831,a860)),x93834),x93833)))
% 188.07/187.98 [9533]~P9(x95331,x95335,x95334)+~P101(f323(f323(f325(x95331),x95333),x95335))+P101(f323(f323(f325(f871(x95331,x95331)),f323(f323(f258(x95331,x95331),x95332),x95333)),x95334))+~P101(f323(f323(f237(f872(x95331,a860)),f323(f277(x95331,x95331,x95334),f323(f323(f301(x95331),x95333),f188(f872(x95331,a860))))),f323(f277(x95331,x95331,x95334),f323(f323(f301(x95331),x95332),f188(f872(x95331,a860))))))
% 188.07/187.98 [9659]~P103(x96595)+~P6(x96595)+P101(f323(f323(f325(x96591),f635(x96592,x96593,x96594,x96591,x96595)),x96594))+~P101(f323(f323(f238(x96595),f323(f323(f40(x96591,x96595),x96594),x96593)),x96592))
% 188.07/187.98 [9692]~P81(x96925)+~P78(x96925)+P101(f323(f323(f325(x96921),f560(x96922,x96923,x96924,x96921,x96925)),f323(f166(x96921),x96924)))+P101(f323(f323(f237(x96925),f323(f159(x96925),f323(f323(f147(x96921,x96925),x96923),x96924))),f323(f159(x96925),f323(f323(f147(x96921,x96925),x96922),x96924))))
% 188.07/187.98 [9809]~P103(x98091)+~P6(x98091)+P101(f323(f323(f238(x98091),f323(x98092,f635(x98093,x98092,x98094,x98095,x98091))),x98093))+~P101(f323(f323(f238(x98091),f323(f323(f40(x98095,x98091),x98094),x98092)),x98093))
% 188.07/187.98 [9946]~P81(x99461)+~P78(x99461)+~P101(f323(f323(f237(x99461),f323(x99463,f560(x99465,x99463,x99464,x99462,x99461))),f323(x99465,f560(x99465,x99463,x99464,x99462,x99461))))+P101(f323(f323(f237(x99461),f323(f159(x99461),f323(f323(f147(x99462,x99461),x99463),x99464))),f323(f159(x99461),f323(f323(f147(x99462,x99461),x99465),x99464))))
% 188.07/187.98 [8612]~P72(x86121)+~P101(f323(f59(x86124),x86125))+~P101(f323(f323(f325(x86124),x86123),x86125))+E(f323(f323(f78(x86121),f323(x86122,x86123)),f323(f323(f6(x86124,x86121),x86122),f323(f323(f22(f872(x86124,a860)),x86125),f323(f323(f301(x86124),x86123),f188(f872(x86124,a860)))))),f323(f323(f6(x86124,x86121),x86122),x86125))
% 188.07/187.98 [8613]~P68(x86131)+~P101(f323(f59(x86134),x86135))+~P101(f323(f323(f325(x86134),x86133),x86135))+E(f323(f323(f79(x86131),f323(x86132,x86133)),f323(f323(f9(x86134,x86131),x86132),f323(f323(f22(f872(x86134,a860)),x86135),f323(f323(f301(x86134),x86133),f188(f872(x86134,a860)))))),f323(f323(f9(x86134,x86131),x86132),x86135))
% 188.07/187.98 [8673]~P20(x86731,x86734,x86735)+~P101(f323(f59(x86731),x86732))+E(f323(f323(f22(f872(x86731,a860)),x86732),f323(f323(f301(x86731),x86733),f188(f872(x86731,a860)))),f188(f872(x86731,a860)))+E(f323(f323(x86734,x86733),f323(x86735,f323(f323(f22(f872(x86731,a860)),x86732),f323(f323(f301(x86731),x86733),f188(f872(x86731,a860)))))),f323(x86735,f323(f323(f301(x86731),x86733),x86732)))
% 188.07/187.98 [9051]~P68(x90511)+~P101(f323(f59(x90512),x90515))+~P101(f323(f59(x90512),x90514))+E(f323(f323(f79(x90511),f323(f323(f9(x90512,x90511),x90513),f323(f323(f110(f872(x90512,a860)),x90514),x90515))),f323(f323(f9(x90512,x90511),x90513),f323(f323(f101(f872(x90512,a860)),x90514),x90515))),f323(f323(f79(x90511),f323(f323(f9(x90512,x90511),x90513),x90514)),f323(f323(f9(x90512,x90511),x90513),x90515)))
% 188.07/187.98 [9052]~P72(x90521)+~P101(f323(f59(x90522),x90525))+~P101(f323(f59(x90522),x90524))+E(f323(f323(f78(x90521),f323(f323(f6(x90522,x90521),x90523),f323(f323(f110(f872(x90522,a860)),x90524),x90525))),f323(f323(f6(x90522,x90521),x90523),f323(f323(f101(f872(x90522,a860)),x90524),x90525))),f323(f323(f78(x90521),f323(f323(f6(x90522,x90521),x90523),x90524)),f323(f323(f6(x90522,x90521),x90523),x90525)))
% 188.07/187.98 [9190]~P60(x91901)+~P101(f323(f59(x91902),x91905))+~P101(f323(f59(x91902),x91904))+E(f323(f323(f22(x91901),f323(f323(f78(x91901),f323(f323(f6(x91902,x91901),x91903),x91904)),f323(f323(f6(x91902,x91901),x91903),x91905))),f323(f323(f6(x91902,x91901),x91903),f323(f323(f101(f872(x91902,a860)),x91904),x91905))),f323(f323(f6(x91902,x91901),x91903),f323(f323(f110(f872(x91902,a860)),x91904),x91905)))
% 188.07/187.98 [9393]~P27(x93931,x93932,x93933,x93935)+~P27(x93931,x93932,x93933,x93934)+P27(x93931,x93932,x93933,f323(f323(f110(f872(x93931,a860)),x93934),x93935))+~E(f323(f323(f101(f872(x93932,a860)),f323(f302(x93931,x93932,x93933),f323(f323(f22(f872(x93931,a860)),x93934),x93935))),f323(f302(x93931,x93932,x93933),f323(f323(f22(f872(x93931,a860)),x93935),x93934))),f188(f872(x93932,a860)))
% 188.07/187.98 [9508]E(x95081,f2(a1))+~P101(f323(f323(f238(a1),f2(a1)),x95083))+~P101(f323(f46(x95082,x95081),f323(f323(f258(a1,a1),x95084),x95085)))+P101(f323(f46(x95082,f323(f323(f79(a1),x95081),x95083)),f323(f323(f258(a1,a1),f323(f323(f36(a1),x95084),x95083)),f323(f323(f78(a1),f323(f323(f79(a1),x95081),f42(a1,x95084,x95083))),x95085))))
% 188.07/187.98 [9516]~P101(f323(f323(f238(a865),f2(a865)),x95163))+~P101(f323(f323(f238(a865),f2(a865)),x95162))+~P101(f323(f45(x95161,x95162),f323(f323(f258(a865,a865),x95164),x95165)))+P101(f323(f45(x95161,f323(f323(f79(a865),x95162),x95163)),f323(f323(f258(a865,a865),f323(f323(f36(a865),x95164),x95163)),f323(f323(f78(a865),f323(f323(f79(a865),x95162),f42(a865,x95164,x95163))),x95165))))
% 188.07/187.98 [9567]~P68(x95671)+~P101(f323(f59(x95672),x95675))+~P101(f323(f59(x95672),x95674))+E(f323(f323(f79(x95671),f323(f323(f323(f63(x95671,x95672,f79(x95671)),x95673),f76(x95671)),f323(f323(f110(f872(x95672,a860)),x95674),x95675))),f323(f323(f323(f63(x95671,x95672,f79(x95671)),x95673),f76(x95671)),f323(f323(f101(f872(x95672,a860)),x95674),x95675))),f323(f323(f79(x95671),f323(f323(f323(f63(x95671,x95672,f79(x95671)),x95673),f76(x95671)),x95674)),f323(f323(f323(f63(x95671,x95672,f79(x95671)),x95673),f76(x95671)),x95675)))
% 188.07/187.98 [9569]~E(f323(f323(f169(x95691),x95695),x95692),f323(f323(f169(x95691),x95695),x95693))+P101(f323(f323(f325(f871(f866(x95691),f866(x95691))),f323(f323(f258(f866(x95691),f866(x95691)),x95692),x95693)),f140(x95691,x95694)))+~P101(f323(f323(f238(a865),x95695),f323(f323(f235(a865),f323(f189(f866(x95691)),x95692)),f323(f189(f866(x95691)),x95693))))+~P101(f323(f323(f325(f871(x95691,x95691)),f323(f323(f258(x95691,x95691),f323(f323(f158(x95691),x95692),x95695)),f323(f323(f158(x95691),x95693),x95695))),x95694))
% 188.07/187.98 [9680]~P81(x96805)+~P140(x96805)+P101(f323(f323(f325(x96801),f377(x96802,x96803,x96804,x96801,x96805)),x96804))+P101(f323(f323(f237(x96805),f323(f323(f6(x96801,x96805),x96803),x96804)),f323(f323(f79(x96805),f323(f100(x96805),f323(f35(x96801),x96804))),x96802)))
% 188.07/187.98 [9874]~P81(x98741)+~P140(x98741)+~P101(f323(f323(f237(x98741),f323(x98743,f377(x98745,x98743,x98744,x98742,x98741))),x98745))+P101(f323(f323(f237(x98741),f323(f323(f6(x98742,x98741),x98743),x98744)),f323(f323(f79(x98741),f323(f100(x98741),f323(f35(x98742),x98744))),x98745)))
% 188.07/187.98 [8642]E(f323(f323(f121(x86421),x86422),x86423),f323(f323(f121(x86421),x86424),x86425))+~E(f323(f323(f169(x86421),f323(f189(f866(x86421)),x86422)),x86424),x86422)+~E(f323(f323(f121(x86421),f323(f323(f131(x86421),f323(f189(f866(x86421)),x86422)),x86424)),x86425),x86423)+P101(f323(f323(f237(a865),f323(f189(f866(x86421)),x86424)),f323(f189(f866(x86421)),x86422)))
% 188.07/187.98 [8773]E(f323(f323(f121(x87731),x87732),x87733),f323(f323(f121(x87731),x87734),x87735))+~E(f323(f323(f169(x87731),f323(f189(f866(x87731)),x87732)),x87734),x87732)+~E(x87733,f323(f323(f121(x87731),f323(f323(f131(x87731),f323(f189(f866(x87731)),x87732)),x87734)),x87735))+~P101(f323(f323(f237(a865),f323(f189(f866(x87731)),x87732)),f323(f189(f866(x87731)),x87734)))
% 188.07/187.98 [10007]~P101(f323(x100075,x100074))+~P101(f323(f59(x100072),f323(f243(x100072),x100075)))+P101(f323(f59(x100071),f323(f243(x100071),f323(f323(f7(x100071,x100072,a860),x100073),x100074))))+~P101(f323(f59(x100071),f323(f243(x100071),f323(f323(f8(f872(x100072,a860),a860,x100071),f85(x100072)),f323(f323(f8(f872(x100072,a860),f872(x100072,a860),x100071),f323(f18(x100072,a860,a860),f323(f323(f8(a860,f872(a860,a860),x100072),a322),x100075))),x100073)))))
% 188.07/187.98 [8426]~P21(x84265,x84261,x84266,x84262)+E(f323(f71(x84261,x84261,x84261,f323(x84262,x84263)),f323(x84262,x84264)),f323(f71(x84261,x84261,x84261,f323(x84262,x84264)),f323(x84262,x84263)))+~P101(f323(f59(x84265),x84264))+~P101(f323(f59(x84265),x84263))
% 188.07/187.98 [7819]~P27(x78191,x78192,x78194,x78193)+~E(f323(x78194,x78196),x78195)+E(f323(f75(x78191,x78192,x78193,x78194),x78195),x78196)+~P101(f323(f323(f325(x78191),x78196),x78193))
% 188.07/187.98 [7820]~P27(x78201,x78202,x78204,x78203)+~E(f323(x78204,x78206),x78205)+E(f323(f91(x78201,x78202,x78203,x78204),x78205),x78206)+~P101(f323(f323(f325(x78201),x78206),x78203))
% 188.07/187.98 [8016]~P22(x80166,x80161,x80164,x80162)+E(f323(f71(x80161,x80161,x80161,f323(x80162,x80163)),f323(x80164,x80165)),f323(x80162,x80163))+~P101(f323(f59(x80166),x80163))+~P101(f323(f323(f325(x80166),x80165),x80163))
% 188.07/187.98 [9140]E(x91401,x91402)+~E(f323(f91(x91403,x91404,x91405,x91406),x91401),f323(f91(x91403,x91404,x91405,x91406),x91402))+~P101(f323(f323(f325(x91404),x91402),f323(f302(x91403,x91404,x91406),x91405)))+~P101(f323(f323(f325(x91404),x91401),f323(f302(x91403,x91404,x91406),x91405)))
% 188.07/187.98 [9237]~P21(x92373,x92371,x92376,x92372)+E(f323(f71(x92371,x92371,x92371,f323(x92372,f323(f323(f22(f872(x92373,a860)),x92374),f323(f323(f301(x92373),x92375),f188(f872(x92373,a860)))))),f323(x92376,x92375)),f323(x92372,x92374))+~P101(f323(f59(x92373),x92374))+~P101(f323(f323(f325(x92373),x92375),x92374))
% 188.07/187.98 [6908]~P58(x69081)+~E(f42(x69081,x69083,x69084),f42(x69081,x69086,x69084))+~E(f42(x69081,x69082,x69084),f42(x69081,x69085,x69084))+E(f42(x69081,f323(f323(f22(x69081),x69082),x69083),x69084),f42(x69081,f323(f323(f22(x69081),x69085),x69086),x69084))
% 188.07/187.98 [6909]~P57(x69091)+~E(f42(x69091,x69093,x69094),f42(x69091,x69096,x69094))+~E(f42(x69091,x69092,x69094),f42(x69091,x69095,x69094))+E(f42(x69091,f323(f323(f79(x69091),x69092),x69093),x69094),f42(x69091,f323(f323(f79(x69091),x69095),x69096),x69094))
% 188.07/187.98 [6910]~P57(x69101)+~E(f42(x69101,x69103,x69104),f42(x69101,x69106,x69104))+~E(f42(x69101,x69102,x69104),f42(x69101,x69105,x69104))+E(f42(x69101,f323(f323(f78(x69101),x69102),x69103),x69104),f42(x69101,f323(f323(f78(x69101),x69105),x69106),x69104))
% 188.07/187.98 [7715]~P18(x77151,x77152,x77153)+~P101(f323(f59(x77151),x77156))+E(f323(f323(f62(x77151,x77152,x77153),x77154),f323(f323(f301(x77151),x77155),x77156)),f323(f323(f62(x77151,x77152,x77153),f323(f323(x77153,x77155),x77154)),x77156))+P101(f323(f323(f325(x77151),x77155),x77156))
% 188.07/187.98 [7777]~P6(x77771)+P101(f323(f323(f237(x77771),x77772),f323(x77773,x77774)))+~P101(f323(f323(f325(x77775),x77774),x77776))+~P101(f323(f323(f237(x77771),x77772),f323(f323(f40(x77775,x77771),x77776),x77773)))
% 188.07/187.98 [7938]~P18(x79381,x79382,x79383)+~P101(f323(f59(x79381),x79386))+E(f323(f323(f62(x79381,x79382,x79383),x79384),f323(f323(f301(x79381),x79385),x79386)),f323(f323(x79383,x79385),f323(f323(f62(x79381,x79382,x79383),x79384),x79386)))+P101(f323(f323(f325(x79381),x79385),x79386))
% 188.07/187.98 [8031]~P103(x80313)+~P101(f323(x80312,x80315))+~P16(x80313,f323(f323(f147(x80311,x80313),x80314),x80316))+E(f323(f129(x80311,x80312),f323(f323(f141(x80311,x80313,x80314),x80315),x80316)),f323(f323(f141(x80311,x80313,x80314),x80315),f323(f129(x80311,x80312),x80316)))
% 188.07/187.98 [8052]E(x80521,x80522)+E(x80523,f2(a1))+~P101(f323(f46(x80524,x80523),f323(f323(f258(a1,a1),x80525),x80522)))+~P101(f323(f46(x80524,x80523),f323(f323(f258(a1,a1),x80526),x80521)))
% 188.07/187.98 [8053]E(x80531,x80532)+E(x80533,f2(a1))+~P101(f323(f46(x80534,x80533),f323(f323(f258(a1,a1),x80532),x80535)))+~P101(f323(f46(x80534,x80533),f323(f323(f258(a1,a1),x80531),x80536)))
% 188.07/187.98 [8073]~P21(x80732,x80735,x80736,x80731)+~P101(f323(f59(x80732),x80734))+E(f323(x80731,f323(f323(f301(x80732),x80733),x80734)),f323(f71(x80735,x80735,x80735,f323(x80731,x80734)),f323(x80736,x80733)))+P101(f323(f323(f325(x80732),x80733),x80734))
% 188.07/187.98 [8302]~P22(x83025,x83021,x83026,x83022)+E(f323(f71(x83021,x83021,x83021,f323(x83022,x83023)),f323(x83022,x83024)),f323(x83022,x83023))+~P101(f323(f59(x83025),x83023))+~P101(f323(f323(f237(f872(x83025,a860)),x83024),x83023))
% 188.07/187.98 [9438]~P27(x94381,x94382,x94384,x94383)+~P101(f323(f323(f325(x94382),x94385),f323(f302(x94381,x94382,x94384),x94383)))+P101(f323(f323(f325(x94381),f323(f75(x94381,x94382,x94383,x94384),x94385)),x94386))+~P101(f323(f323(f237(f872(x94381,a860)),x94383),x94386))
% 188.07/187.98 [9820]~P72(x98202)+~E(f369(x98201,x98203,x98205,x98206,x98204,x98202),f370(x98201,x98203,x98205,x98206,x98204,x98202))+~P101(f323(f59(x98204),x98206))+E(f323(f323(f6(x98201,x98202),x98203),f323(f302(x98204,x98201,x98205),x98206)),f323(f323(f6(x98204,x98202),f323(f71(x98201,x98202,x98204,x98203),x98205)),x98206))
% 188.07/187.98 [9856]~P72(x98566)+E(f323(x98561,f369(x98562,x98563,x98561,x98564,x98565,x98566)),f323(x98561,f370(x98562,x98563,x98561,x98564,x98565,x98566)))+E(f323(f323(f6(x98562,x98566),x98563),f323(f302(x98565,x98562,x98561),x98564)),f323(f323(f6(x98565,x98566),f323(f71(x98562,x98566,x98565,x98563),x98561)),x98564))+~P101(f323(f59(x98565),x98564))
% 188.07/187.98 [9896]~P72(x98962)+~E(f323(x98963,f323(x98965,f370(x98961,x98963,x98965,x98966,x98964,x98962))),f2(x98962))+~P101(f323(f59(x98964),x98966))+E(f323(f323(f6(x98961,x98962),x98963),f323(f302(x98964,x98961,x98965),x98966)),f323(f323(f6(x98964,x98962),f323(f71(x98961,x98962,x98964,x98963),x98965)),x98966))
% 188.07/187.98 [9954]~P72(x99542)+~P101(f323(f59(x99544),x99546))+E(f323(f323(f6(x99541,x99542),x99543),f323(f302(x99544,x99541,x99545),x99546)),f323(f323(f6(x99544,x99542),f323(f71(x99541,x99542,x99544,x99543),x99545)),x99546))+P101(f323(f323(f325(x99544),f370(x99541,x99543,x99545,x99546,x99544,x99542)),x99546))
% 188.07/187.98 [9955]~P72(x99552)+~P101(f323(f59(x99554),x99556))+E(f323(f323(f6(x99551,x99552),x99553),f323(f302(x99554,x99551,x99555),x99556)),f323(f323(f6(x99554,x99552),f323(f71(x99551,x99552,x99554,x99553),x99555)),x99556))+P101(f323(f323(f325(x99554),f369(x99551,x99553,x99555,x99556,x99554,x99552)),x99556))
% 188.07/187.98 [10065]~P68(x100651)+~P101(f323(f59(x100652),x100656))+E(f323(f323(f323(f63(x100651,x100652,f79(x100651)),f323(f323(f18(x100652,f872(x100653,a860),x100651),f323(f323(f7(x100652,x100651,f872(f872(x100653,a860),x100651)),f323(f323(f8(f872(x100653,x100651),f872(x100651,f872(f872(x100653,a860),x100651)),x100652),f63(x100651,x100653,f79(x100651))),x100654)),f76(x100651))),x100655)),f76(x100651)),x100656),f323(f323(f323(f63(x100651,f871(x100652,x100653),f79(x100651)),f323(f262(x100652,x100653,x100651),x100654)),f76(x100651)),f323(f323(f260(x100652,x100653),x100656),x100655)))+P101(f323(f323(f325(x100652),f621(x100654,x100655,x100653,x100656,x100652,x100651)),x100656))
% 188.07/187.98 [10083]~P68(x100831)+~P101(f323(f59(x100832),x100836))+E(f323(f323(f323(f63(x100831,x100832,f79(x100831)),f323(f323(f18(x100832,f872(x100833,a860),x100831),f323(f323(f7(x100832,x100831,f872(f872(x100833,a860),x100831)),f323(f323(f8(f872(x100833,x100831),f872(x100831,f872(f872(x100833,a860),x100831)),x100832),f63(x100831,x100833,f79(x100831))),x100834)),f76(x100831))),x100835)),f76(x100831)),x100836),f323(f323(f323(f63(x100831,f871(x100832,x100833),f79(x100831)),f323(f262(x100832,x100833,x100831),x100834)),f76(x100831)),f323(f323(f260(x100832,x100833),x100836),x100835)))+~P101(f323(f59(x100833),f323(x100835,f621(x100834,x100835,x100833,x100836,x100832,x100831))))
% 188.07/187.98 [8211]~P22(x82112,x82115,x82116,x82111)+~P101(f323(f59(x82112),x82114))+~P101(f323(f59(x82112),x82113))+E(f323(x82111,f323(f323(f110(f872(x82112,a860)),x82113),x82114)),f323(f71(x82115,x82115,x82115,f323(x82111,x82113)),f323(x82111,x82114)))
% 188.07/187.98 [8427]~P6(x84271)+P101(f323(f323(f237(x84271),f323(x84272,x84273)),x84274))+~P101(f323(f323(f325(x84275),x84273),x84276))+~P101(f323(f323(f237(x84271),f323(f323(f39(x84275,x84271),x84276),x84272)),x84274))
% 188.07/187.98 [8854]~P27(x88542,x88541,x88543,x88546)+E(f323(f323(f22(f872(x88541,a860)),f323(f302(x88542,x88541,x88543),x88544)),f323(f302(x88542,x88541,x88543),x88545)),f323(f302(x88542,x88541,x88543),f323(f323(f22(f872(x88542,a860)),x88544),x88545)))+~P101(f323(f323(f237(f872(x88542,a860)),x88545),x88546))+~P101(f323(f323(f237(f872(x88542,a860)),x88544),x88546))
% 188.07/187.98 [8855]~P27(x88552,x88551,x88553,x88556)+E(f323(f323(f101(f872(x88551,a860)),f323(f302(x88552,x88551,x88553),x88554)),f323(f302(x88552,x88551,x88553),x88555)),f323(f302(x88552,x88551,x88553),f323(f323(f101(f872(x88552,a860)),x88554),x88555)))+~P101(f323(f323(f237(f872(x88552,a860)),x88555),x88556))+~P101(f323(f323(f237(f872(x88552,a860)),x88554),x88556))
% 188.07/187.98 [9115]E(x91151,x91152)+~P51(x91153,x91154,x91155)+~P101(f323(f323(f325(f871(x91153,x91154)),f323(f323(f258(x91153,x91154),x91156),x91152)),x91155))+~P101(f323(f323(f325(f871(x91153,x91154)),f323(f323(f258(x91153,x91154),x91156),x91151)),x91155))
% 188.07/187.98 [9891]~P66(x98911)+~E(f323(x98913,f497(x98914,x98916,x98913,x98915,x98912,x98911)),f323(x98916,f497(x98914,x98916,x98913,x98915,x98912,x98911)))+~P101(f323(f59(x98912),x98915))+E(f323(f323(f323(f63(x98911,x98912,f79(x98911)),x98913),x98914),x98915),f323(f323(f323(f63(x98911,x98912,f79(x98911)),x98916),x98914),x98915))
% 188.07/187.98 [9952]~P66(x99521)+~P101(f323(f59(x99522),x99525))+E(f323(f323(f323(f63(x99521,x99522,f79(x99521)),x99523),x99524),x99525),f323(f323(f323(f63(x99521,x99522,f79(x99521)),x99526),x99524),x99525))+P101(f323(f323(f325(x99522),f497(x99524,x99523,x99526,x99525,x99522,x99521)),x99525))
% 188.07/187.98 [8656]~P66(x86561)+~P101(f323(f59(x86562),x86566))+P101(f323(f323(f325(x86562),x86565),x86566))+E(f323(f323(f323(f63(x86561,x86562,f79(x86561)),x86563),x86564),f323(f323(f301(x86562),x86565),x86566)),f323(f323(f79(x86561),f323(x86563,x86565)),f323(f323(f323(f63(x86561,x86562,f79(x86561)),x86563),x86564),x86566)))
% 188.07/187.98 [8709]~P9(x87091,x87096,x87093)+~P14(x87091,f872(x87092,a860),x87093,x87095)+~P101(f323(f323(f325(x87091),x87094),x87096))+E(f323(f323(f39(x87091,f872(x87092,a860)),f323(f277(x87091,x87091,x87093),f323(f323(f301(x87091),x87094),f188(f872(x87091,a860))))),x87095),f323(x87095,x87094))
% 188.07/187.98 [8830]~P18(x88303,x88304,x88301)+~P101(f323(f59(x88303),x88306))+~P101(f323(f323(f325(x88303),x88302),x88306))+E(f323(f323(x88301,x88302),f323(f323(f62(x88303,x88304,x88301),x88305),f323(f323(f22(f872(x88303,a860)),x88306),f323(f323(f301(x88303),x88302),f188(f872(x88303,a860)))))),f323(f323(f62(x88303,x88304,x88301),x88305),x88306))
% 188.07/187.98 [9126]~P21(x91263,x91261,x91266,x91262)+~P101(f323(f59(x91263),x91265))+~P101(f323(f59(x91263),x91264))+E(f323(f71(x91261,x91261,x91261,f323(x91262,f323(f323(f110(f872(x91263,a860)),x91264),x91265))),f323(x91262,f323(f323(f101(f872(x91263,a860)),x91264),x91265))),f323(f71(x91261,x91261,x91261,f323(x91262,x91264)),f323(x91262,x91265)))
% 188.07/187.98 [9461]~E(x94613,f323(f323(f152(x94611,x94612),x94615),x94616))+P101(f323(f323(f325(f871(f866(x94611),f866(x94611))),f323(f323(f258(f866(x94611),f866(x94611)),x94612),x94613)),f150(x94611,x94614)))+~P101(f323(f323(f238(a865),x94615),f323(f189(f866(x94611)),x94612)))+~P101(f323(f323(f325(f871(x94611,x94611)),f323(f323(f258(x94611,x94611),f323(f323(f158(x94611),x94612),x94615)),x94616)),x94614))
% 188.07/187.98 [9965]~P72(x99652)+~P101(f323(f59(x99651),x99656))+P101(f323(f323(f325(x99651),f619(x99654,x99655,x99653,x99656,x99651,x99652)),x99656))+E(f323(f323(f6(x99651,x99652),f323(f323(f18(x99651,f872(x99653,a860),x99652),f323(f323(f8(f872(x99653,x99652),f872(f872(x99653,a860),x99652),x99651),f6(x99653,x99652)),x99654)),x99655)),x99656),f323(f323(f6(f871(x99651,x99653),x99652),f323(f262(x99651,x99653,x99652),x99654)),f323(f323(f260(x99651,x99653),x99656),x99655)))
% 188.07/187.98 [9966]~P68(x99662)+~P101(f323(f59(x99661),x99666))+P101(f323(f323(f325(x99661),f617(x99664,x99665,x99663,x99666,x99661,x99662)),x99666))+E(f323(f323(f9(x99661,x99662),f323(f323(f18(x99661,f872(x99663,a860),x99662),f323(f323(f8(f872(x99663,x99662),f872(f872(x99663,a860),x99662),x99661),f9(x99663,x99662)),x99664)),x99665)),x99666),f323(f323(f9(f871(x99661,x99663),x99662),f323(f262(x99661,x99663,x99662),x99664)),f323(f323(f260(x99661,x99663),x99666),x99665)))
% 188.07/187.98 [10005]~P72(x100052)+~P101(f323(f59(x100051),x100056))+~P101(f323(f59(x100053),f323(x100055,f619(x100054,x100055,x100053,x100056,x100051,x100052))))+E(f323(f323(f6(x100051,x100052),f323(f323(f18(x100051,f872(x100053,a860),x100052),f323(f323(f8(f872(x100053,x100052),f872(f872(x100053,a860),x100052),x100051),f6(x100053,x100052)),x100054)),x100055)),x100056),f323(f323(f6(f871(x100051,x100053),x100052),f323(f262(x100051,x100053,x100052),x100054)),f323(f323(f260(x100051,x100053),x100056),x100055)))
% 188.07/187.98 [10006]~P68(x100062)+~P101(f323(f59(x100061),x100066))+~P101(f323(f59(x100063),f323(x100065,f617(x100064,x100065,x100063,x100066,x100061,x100062))))+E(f323(f323(f9(x100061,x100062),f323(f323(f18(x100061,f872(x100063,a860),x100062),f323(f323(f8(f872(x100063,x100062),f872(f872(x100063,a860),x100062),x100061),f9(x100063,x100062)),x100064)),x100065)),x100066),f323(f323(f9(f871(x100061,x100063),x100062),f323(f262(x100061,x100063,x100062),x100064)),f323(f323(f260(x100061,x100063),x100066),x100065)))
% 188.07/187.98 [9988]~P68(x99882)+~P101(f323(f59(x99881),x99886))+P101(f323(f323(f325(x99881),x99883),x99886))+E(f323(f323(f9(x99881,x99882),f323(f323(f7(x99881,x99882,x99882),f323(f323(f18(x99881,x99882,f872(x99882,x99882)),f323(f323(f8(a860,f872(x99882,f872(x99882,x99882)),x99881),f96(x99882)),f323(f323(f7(x99881,x99881,a860),a320),x99883))),x99884)),x99885)),x99886),f323(f323(f248(x99882),x99885),f323(f35(x99881),x99886)))
% 188.07/187.98 [9993]~P68(x99932)+~P101(f323(f59(x99931),x99936))+~P101(f323(f323(f325(x99931),x99933),x99936))+E(f323(f323(f9(x99931,x99932),f323(f323(f7(x99931,x99932,x99932),f323(f323(f18(x99931,x99932,f872(x99932,x99932)),f323(f323(f8(a860,f872(x99932,f872(x99932,x99932)),x99931),f96(x99932)),f323(f323(f7(x99931,x99931,a860),a320),x99933))),x99934)),x99935)),x99936),f323(f323(f79(x99932),f323(x99934,x99933)),f323(f323(f248(x99932),x99935),f323(f323(f22(a865),f323(f35(x99931),x99936)),f76(a865)))))
% 188.07/187.98 [10058]~P101(f323(f59(x100581),x100585))+~P101(f323(f59(x100582),x100583))+P101(f323(f323(f325(x100582),f371(x100586,x100584,x100583,x100582,x100585,x100581)),x100583))+E(f323(f323(f6(x100581,a865),f323(f323(f8(f872(x100582,a860),a865,x100581),f35(x100582)),f323(f323(f8(f872(x100582,a860),f872(x100582,a860),x100581),f243(x100582)),f323(f323(f8(f872(x100582,a860),f872(x100582,a860),x100581),f323(f18(x100582,a860,a860),f323(f323(f8(a860,f872(a860,a860),x100582),a322),f323(f323(f7(x100582,f872(x100582,a860),a860),f325(x100582)),x100583)))),x100584)))),x100585),f323(f323(f79(a865),x100586),f323(f35(x100582),x100583)))
% 188.07/187.98 [10059]~P101(f323(f59(x100591),x100595))+~P101(f323(f59(x100592),x100593))+P101(f323(f323(f325(x100592),f372(x100596,x100594,x100593,x100592,x100595,x100591)),x100593))+E(f323(f323(f6(x100591,a865),f323(f323(f8(f872(x100592,a860),a865,x100591),f35(x100592)),f323(f323(f8(f872(x100592,a860),f872(x100592,a860),x100591),f243(x100592)),f323(f323(f8(f872(x100592,a860),f872(x100592,a860),x100591),f323(f18(x100592,a860,a860),f323(f323(f8(a860,f872(a860,a860),x100592),a322),f323(f323(f7(x100592,f872(x100592,a860),a860),f325(x100592)),x100593)))),x100594)))),x100595),f323(f323(f6(x100592,a865),x100596),x100593))
% 188.07/187.98 [10090]~P101(f323(f59(x100902),x100903))+~P101(f323(f59(x100901),x100905))+~E(f323(f35(x100901),f323(f243(x100901),f323(f323(f18(x100901,a860,a860),f323(f323(f8(a860,f872(a860,a860),x100901),a322),f323(f323(f7(x100901,f872(x100901,a860),a860),f325(x100901)),x100905))),f323(f323(f7(x100901,x100902,a860),x100904),f371(x100906,x100904,x100903,x100902,x100905,x100901))))),x100906)+E(f323(f323(f6(x100901,a865),f323(f323(f8(f872(x100902,a860),a865,x100901),f35(x100902)),f323(f323(f8(f872(x100902,a860),f872(x100902,a860),x100901),f243(x100902)),f323(f323(f8(f872(x100902,a860),f872(x100902,a860),x100901),f323(f18(x100902,a860,a860),f323(f323(f8(a860,f872(a860,a860),x100902),a322),f323(f323(f7(x100902,f872(x100902,a860),a860),f325(x100902)),x100903)))),x100904)))),x100905),f323(f323(f79(a865),x100906),f323(f35(x100902),x100903)))
% 188.07/187.98 [10092]~P101(f323(f59(x100922),x100923))+~P101(f323(f59(x100921),x100925))+~E(f323(f35(x100921),f323(f243(x100921),f323(f323(f18(x100921,a860,a860),f323(f323(f8(a860,f872(a860,a860),x100921),a322),f323(f323(f7(x100921,f872(x100921,a860),a860),f325(x100921)),x100925))),f323(f323(f7(x100921,x100922,a860),x100924),f372(x100926,x100924,x100923,x100922,x100925,x100921))))),f323(x100926,f372(x100926,x100924,x100923,x100922,x100925,x100921)))+E(f323(f323(f6(x100921,a865),f323(f323(f8(f872(x100922,a860),a865,x100921),f35(x100922)),f323(f323(f8(f872(x100922,a860),f872(x100922,a860),x100921),f243(x100922)),f323(f323(f8(f872(x100922,a860),f872(x100922,a860),x100921),f323(f18(x100922,a860,a860),f323(f323(f8(a860,f872(a860,a860),x100922),a322),f323(f323(f7(x100922,f872(x100922,a860),a860),f325(x100922)),x100923)))),x100924)))),x100925),f323(f323(f6(x100922,a865),x100926),x100923))
% 188.07/187.98 [9747]E(x97471,x97472)+~P18(x97473,x97474,x97475)+~P101(f323(f64(x97473,x97474,x97475,x97476,x97477),x97472))+~P101(f323(f64(x97473,x97474,x97475,x97476,x97477),x97471))
% 188.07/187.98 [9537]P101(f323(x95371,x95372))+~P101(f323(f323(f325(x95377),x95372),f323(x95376,x95374)))+~P101(f323(x95371,f448(x95371,x95376,x95375,x95373,x95377)))+~P101(f323(f323(f325(x95373),x95374),x95375))
% 188.07/187.98 [9980]~P18(x99807,x99806,x99801)+E(f323(f323(x99801,x99802),f768(x99802,x99803,x99804,x99805,x99801,x99806,x99807)),x99803)+~P101(f323(f64(x99807,x99806,x99801,x99805,x99804),x99803))+~P101(f323(f323(f325(x99807),x99802),x99804))
% 188.07/187.98 [10044]~P18(x100441,x100442,x100443)+~P101(f323(f64(x100441,x100442,x100443,x100444,x100445),x100447))+P101(f323(f64(x100441,x100442,x100443,x100444,f323(f323(f22(f872(x100441,a860)),x100445),f323(f323(f301(x100441),x100446),f188(f872(x100441,a860))))),f768(x100446,x100447,x100445,x100444,x100443,x100442,x100441)))+~P101(f323(f323(f325(x100441),x100446),x100445))
% 188.07/187.98 [9197]P28(x91971,x91972,x91973,x91974,x91975)+~P28(x91971,x91972,x91973,x91976,x91977)+~E(f323(f302(x91971,x91972,x91973),x91974),x91975)+~P101(f323(f323(f237(f872(x91971,a860)),x91974),x91976))
% 188.07/187.98 [9428]~P28(x94281,x94282,x94283,x94285,x94287)+~P28(x94281,x94282,x94283,x94284,x94286)+P28(x94281,x94282,x94283,f323(f323(f110(f872(x94281,a860)),x94284),x94285),f323(f323(f110(f872(x94282,a860)),x94286),x94287))+~E(f323(f323(f101(f872(x94282,a860)),x94286),x94287),f188(f872(x94282,a860)))
% 188.07/187.98 [9434]~P66(x94341)+~P27(x94345,x94342,x94346,x94347)+~P101(f323(f59(x94345),x94347))+E(f323(f323(f323(f63(x94341,x94342,f79(x94341)),x94343),x94344),f323(f302(x94345,x94342,x94346),x94347)),f323(f323(f323(f63(x94341,x94345,f79(x94341)),f323(f71(x94342,x94341,x94345,x94343),x94346)),x94344),x94347))
% 188.07/187.98 [9561]~E(f323(f323(f301(x95611),x95615),x95616),f323(f323(f301(x95611),x95612),x95613))+~P101(f323(f64(x95611,x95611,x95614,x95612,x95613),x95617))+P101(f323(f323(f325(x95611),x95612),x95613))+P101(f323(f60(x95611,x95614,f323(f323(f301(x95611),x95615),x95616)),x95617))
% 188.07/187.98 [9645]P101(f323(x96451,x96452))+~P101(f323(f323(f325(x96453),x96452),f323(x96454,x96457)))+~P101(f323(f323(f325(x96456),x96457),x96455))+P101(f323(f323(f325(x96453),f448(x96451,x96454,x96455,x96456,x96453)),f323(f323(f39(x96456,f872(x96453,a860)),x96455),x96454)))
% 188.07/187.98 [9660]~P27(x96602,x96601,x96605,x96604)+~P27(x96601,x96603,x96606,f323(f302(x96602,x96601,x96605),x96604))+E(f323(f323(f71(x96601,x96602,x96603,f75(x96602,x96601,x96604,x96605)),f75(x96601,x96603,f323(f302(x96602,x96601,x96605),x96604),x96606)),x96607),f323(f75(x96602,x96603,x96604,f323(f71(x96601,x96603,x96602,x96606),x96605)),x96607))+~P101(f323(f323(f325(x96603),x96607),f323(f302(x96601,x96603,x96606),f323(f302(x96602,x96601,x96605),x96604))))
% 188.07/187.98 [9661]~P27(x96612,x96611,x96615,x96614)+~P27(x96611,x96613,x96616,f323(f302(x96612,x96611,x96615),x96614))+E(f323(f323(f71(x96611,x96612,x96613,f91(x96612,x96611,x96614,x96615)),f91(x96611,x96613,f323(f302(x96612,x96611,x96615),x96614),x96616)),x96617),f323(f91(x96612,x96613,x96614,f323(f71(x96611,x96613,x96612,x96616),x96615)),x96617))+~P101(f323(f323(f325(x96613),x96617),f323(f302(x96611,x96613,x96616),f323(f302(x96612,x96611,x96615),x96614))))
% 188.07/187.98 [9981]~P18(x99817,x99816,x99811)+E(f323(f323(x99811,x99812),f769(x99813,x99814,x99812,x99815,x99811,x99816,x99817)),x99813)+P101(f323(f323(f325(x99817),x99812),x99814))+~P101(f323(f64(x99817,x99816,x99811,x99815,f323(f323(f301(x99817),x99812),x99814)),x99813))
% 188.07/187.98 [10043]~P18(x100431,x100434,x100435)+P101(f323(f64(x100431,x100434,x100435,x100436,x100433),f769(x100437,x100433,x100432,x100436,x100435,x100434,x100431)))+P101(f323(f323(f325(x100431),x100432),x100433))+~P101(f323(f64(x100431,x100434,x100435,x100436,f323(f323(f301(x100431),x100432),x100433)),x100437))
% 188.07/187.98 [9729]E(x97291,f2(a1))+~P101(f323(f46(x97293,x97291),f323(f323(f258(a1,a1),x97295),x97297)))+~P101(f323(f46(x97292,x97291),f323(f323(f258(a1,a1),x97294),x97296)))+P101(f323(f46(f323(f323(f78(a1),x97292),x97293),x97291),f323(f323(f258(a1,a1),f323(f323(f78(a1),f323(f323(f78(a1),x97294),x97295)),f323(f323(f36(a1),f323(f323(f78(a1),x97296),x97297)),x97291))),f42(a1,f323(f323(f78(a1),x97296),x97297),x97291))))
% 188.07/187.98 [9731]~P101(f323(f323(f238(a865),f2(a865)),x97313))+~P101(f323(f45(x97312,x97313),f323(f323(f258(a865,a865),x97315),x97317)))+~P101(f323(f45(x97311,x97313),f323(f323(f258(a865,a865),x97314),x97316)))+P101(f323(f45(f323(f323(f78(a865),x97311),x97312),x97313),f323(f323(f258(a865,a865),f323(f323(f78(a865),f323(f323(f78(a865),x97314),x97315)),f323(f323(f36(a865),f323(f323(f78(a865),x97316),x97317)),x97313))),f42(a865,f323(f323(f78(a865),x97316),x97317),x97313))))
% 188.07/187.98 [10089]~P72(x100892)+~P101(f323(f59(x100893),x100895))+~P101(f323(f59(x100891),x100897))+E(f323(f323(f6(x100891,x100892),f323(f323(f18(x100891,f872(x100893,a860),x100892),f323(f323(f8(f872(x100893,x100892),f872(f872(x100893,a860),x100892),x100891),f6(x100893,x100892)),x100894)),f323(f323(f8(f872(x100893,a860),f872(x100893,a860),x100891),f243(x100893)),f323(f323(f8(f872(x100893,a860),f872(x100893,a860),x100891),f323(f18(x100893,a860,a860),f323(f323(f8(a860,f872(a860,a860),x100893),a322),f323(f323(f7(x100893,f872(x100893,a860),a860),f325(x100893)),x100895)))),x100896)))),x100897),f323(f323(f6(x100893,x100892),f323(f323(f18(x100893,f872(x100891,a860),x100892),f323(f323(f8(f872(x100891,x100892),f872(f872(x100891,a860),x100892),x100893),f6(x100891,x100892)),f323(f7(x100891,x100893,x100892),x100894))),f323(f323(f8(f872(x100891,a860),f872(x100891,a860),x100893),f243(x100891)),f323(f323(f8(f872(x100891,a860),f872(x100891,a860),x100893),f323(f18(x100891,a860,a860),f323(f323(f8(a860,f872(a860,a860),x100891),a322),f323(f323(f7(x100891,f872(x100891,a860),a860),f325(x100891)),x100897)))),f323(f7(x100891,x100893,a860),x100896))))),x100895))
% 188.07/187.98 [9598]~P24(x95987,x95986,x95981,x95988,x95982,x95984)+E(f323(f323(x95981,f323(x95982,x95983)),f323(x95984,x95985)),f323(x95984,x95985))+~P101(f323(f59(x95986),x95985))+~P101(f323(f323(f325(x95986),x95983),x95985))
% 188.07/187.98 [9602]~P15(x96026,x96021,x96022,x96028,x96023,x96024)+~P9(x96026,x96027,x96028)+P14(x96021,x96022,x96023,f323(x96024,x96025))+~P101(f323(f323(f325(x96026),x96025),x96027))
% 188.07/187.98 [9220]~P21(x92207,x92201,x92208,x92203)+~P101(f323(f59(x92207),x92205))+~P101(f323(f59(x92207),x92204))+E(f323(f71(x92201,x92201,x92202,f323(x92203,x92204)),f323(f71(x92201,x92201,x92202,f323(x92203,x92205)),x92206)),f323(f71(x92201,x92201,x92202,f323(x92203,x92205)),f323(f71(x92201,x92201,x92202,f323(x92203,x92204)),x92206)))
% 188.07/187.98 [9229]~P35(x92291,x92292,x92293,x92294,x92297)+P35(x92291,x92292,x92293,f323(f323(f152(x92291,x92294),x92295),x92296),f323(f323(f152(x92292,x92297),x92295),x92298))+~P101(f323(f323(x92293,x92296),x92298))+~P101(f323(f323(f238(a865),x92295),f323(f189(f866(x92291)),x92294)))
% 188.07/187.98 [9230]~P35(x92301,x92302,x92303,x92304,x92307)+P35(x92301,x92302,x92303,f323(f323(f152(x92301,x92304),x92305),x92306),f323(f323(f152(x92302,x92307),x92305),x92308))+~P101(f323(f323(x92303,x92306),x92308))+~P101(f323(f323(f238(a865),x92305),f323(f189(f866(x92302)),x92307)))
% 188.07/187.98 [9308]~P27(x93082,x93082,x93085,x93086)+~P23(x93083,x93082,x93087,x93088,x93081)+~P101(f323(f59(x93082),x93086))+E(f323(f323(x93081,f323(f71(x93082,x93083,x93082,x93084),x93085)),x93086),f323(f323(x93081,x93084),f323(f302(x93082,x93082,x93085),x93086)))
% 188.07/187.98 [9562]P28(x95621,x95622,x95623,x95624,x95625)+~P28(x95622,x95626,x95627,x95625,x95628)+~P28(x95621,x95626,f323(f71(x95622,x95626,x95621,x95627),x95623),x95624,x95628)+~P101(f323(f323(f237(f872(x95622,a860)),f323(f302(x95621,x95622,x95623),x95624)),x95625))
% 188.07/187.98 [9600]~P25(x96007,x96002,x96005,x96008,x96006,x96001)+~P101(f323(f59(x96002),x96004))+E(f323(x96001,f323(f323(f301(x96002),x96003),x96004)),f323(f323(x96005,f323(x96006,x96003)),f323(x96001,x96004)))+P101(f323(f323(f325(x96002),x96003),x96004))
% 188.07/187.98 [9611]~P24(x96116,x96115,x96111,x96117,x96118,x96112)+E(f323(f323(x96111,f323(x96112,x96113)),f323(x96112,x96114)),f323(x96112,x96114))+~P101(f323(f59(x96115),x96114))+~P101(f323(f323(f237(f872(x96115,a860)),x96113),x96114))
% 188.07/187.98 [10087]P26(x100878,x100877,f323(f323(f301(f864(x100878)),f323(f323(f323(f90(x100878),x100874),x100875),x100873)),f188(f872(f864(x100878),a860))))+~P26(x100878,x100877,f323(f323(f301(f864(x100878)),f323(f323(f323(f90(x100878),x100876),x100875),x100871)),f188(f872(f864(x100878),a860))))+~P101(f323(f323(x100876,x100872),f356(x100873,x100874,x100871,x100875,x100876,x100877,x100878)))+P101(f323(f323(x100871,x100872),f365(x100873,x100874,x100871,x100875,x100876,x100877,x100878)))
% 188.07/187.98 [9206]P101(f323(f323(f325(f871(f866(x92061),f866(x92061))),f323(f323(f258(f866(x92061),f866(x92061)),x92062),x92063)),f150(x92061,x92064)))+~E(x92063,f323(f323(f121(x92061),x92065),f323(f323(f144(x92061),x92066),x92067)))+~E(x92062,f323(f323(f121(x92061),x92065),f323(f323(f144(x92061),x92068),x92067)))+~P101(f323(f323(f325(f871(x92061,x92061)),f323(f323(f258(x92061,x92061),x92068),x92066)),x92064))
% 188.07/187.98 [9605]~P24(x96056,x96052,x96055,x96057,x96058,x96051)+~P101(f323(f59(x96052),x96054))+~P101(f323(f59(x96052),x96053))+E(f323(x96051,f323(f323(f110(f872(x96052,a860)),x96053),x96054)),f323(f323(x96055,f323(x96051,x96053)),f323(x96051,x96054)))
% 188.07/187.98 [10130]~P27(x101304,x101302,x101305,x101308)+E(f323(f323(f40(x101301,f872(x101302,a860)),x101303),f323(f323(f8(f872(x101304,a860),f872(x101302,a860),x101301),f302(x101304,x101302,x101305)),x101306)),f323(f302(x101304,x101302,x101305),f323(f323(f40(x101301,f872(x101304,a860)),x101303),x101306)))+~P101(f323(f323(f325(x101301),x101307),x101303))+P101(f323(f323(f325(x101301),f646(x101307,x101306,x101303,x101301,x101308,x101305,x101302,x101304)),x101303))
% 188.07/187.98 [10151]~P27(x101514,x101512,x101515,x101517)+E(f323(f323(f40(x101511,f872(x101512,a860)),x101513),f323(f323(f8(f872(x101514,a860),f872(x101512,a860),x101511),f302(x101514,x101512,x101515)),x101516)),f323(f302(x101514,x101512,x101515),f323(f323(f40(x101511,f872(x101514,a860)),x101513),x101516)))+~P101(f323(f323(f325(x101511),x101518),x101513))+~P101(f323(f323(f237(f872(x101514,a860)),f323(x101516,f646(x101518,x101516,x101513,x101511,x101517,x101515,x101512,x101514))),x101517))
% 188.07/187.98 [9670]~P25(x96707,x96705,x96701,x96708,x96702,x96704)+~P101(f323(f59(x96705),x96706))+~P101(f323(f323(f325(x96705),x96703),x96706))+E(f323(f323(x96701,f323(x96702,x96703)),f323(x96704,f323(f323(f22(f872(x96705,a860)),x96706),f323(f323(f301(x96705),x96703),f188(f872(x96705,a860)))))),f323(x96704,x96706))
% 188.07/187.98 [9678]~P25(x96786,x96783,x96781,x96787,x96788,x96782)+~P101(f323(f59(x96783),x96785))+~P101(f323(f59(x96783),x96784))+E(f323(f323(x96781,f323(x96782,f323(f323(f110(f872(x96783,a860)),x96784),x96785))),f323(x96782,f323(f323(f101(f872(x96783,a860)),x96784),x96785))),f323(f323(x96781,f323(x96782,x96784)),f323(x96782,x96785)))
% 188.07/187.98 [9770]P43(x97701,x97702,x97703,x97704,x97705,f323(f323(x97703,x97706),x97707))+~P43(x97701,x97702,x97703,x97704,f323(f323(f22(f872(x97701,a860)),x97705),f323(f323(f301(x97701),x97708),f188(f872(x97701,a860)))),x97709)+~E(f323(f323(x97703,x97706),x97707),f323(f323(x97703,x97708),x97709))+~P101(f323(f323(f325(x97701),x97708),x97705))
% 188.07/187.98 [10162]P26(x101621,x101622,f323(f323(f301(f864(x101621)),f323(f323(f323(f90(x101621),f323(x101623,f815(x101624,x101625,x101626,x101627,x101623,x101622,x101621,x101628,x101629))),f323(x101627,f815(x101624,x101625,x101626,x101627,x101623,x101622,x101621,x101628,x101629))),f323(x101626,f815(x101624,x101625,x101626,x101627,x101623,x101622,x101621,x101628,x101629)))),f188(f872(f864(x101621),a860))))+~P101(f323(f59(x101629),x101628))+~P26(x101621,x101622,f323(f302(x101629,f864(x101621),f323(f323(f18(x101629,f872(x101621,f872(a861,a860)),f864(x101621)),f323(f323(f18(x101629,a862,f872(f872(x101621,f872(a861,a860)),f864(x101621))),f323(f323(f8(f872(x101621,f872(a861,a860)),f872(a862,f872(f872(x101621,f872(a861,a860)),f864(x101621))),x101629),f90(x101621)),x101623)),x101627)),x101626)),x101628))+P26(x101621,x101622,f323(f302(x101629,f864(x101621),f323(f323(f18(x101629,f872(x101621,f872(a861,a860)),f864(x101621)),f323(f323(f18(x101629,a862,f872(f872(x101621,f872(a861,a860)),f864(x101621))),f323(f323(f8(f872(x101621,f872(a861,a860)),f872(a862,f872(f872(x101621,f872(a861,a860)),f864(x101621))),x101629),f90(x101621)),x101625)),x101627)),x101624)),x101628))
% 188.07/187.98 [10163]~P26(x101631,x101632,f323(f323(f301(f864(x101631)),f323(f323(f323(f90(x101631),f323(x101634,f815(x101636,x101634,x101638,x101635,x101639,x101632,x101631,x101637,x101633))),f323(x101635,f815(x101636,x101634,x101638,x101635,x101639,x101632,x101631,x101637,x101633))),f323(x101636,f815(x101636,x101634,x101638,x101635,x101639,x101632,x101631,x101637,x101633)))),f188(f872(f864(x101631),a860))))+~P101(f323(f59(x101633),x101637))+~P26(x101631,x101632,f323(f302(x101633,f864(x101631),f323(f323(f18(x101633,f872(x101631,f872(a861,a860)),f864(x101631)),f323(f323(f18(x101633,a862,f872(f872(x101631,f872(a861,a860)),f864(x101631))),f323(f323(f8(f872(x101631,f872(a861,a860)),f872(a862,f872(f872(x101631,f872(a861,a860)),f864(x101631))),x101633),f90(x101631)),x101639)),x101635)),x101638)),x101637))+P26(x101631,x101632,f323(f302(x101633,f864(x101631),f323(f323(f18(x101633,f872(x101631,f872(a861,a860)),f864(x101631)),f323(f323(f18(x101633,a862,f872(f872(x101631,f872(a861,a860)),f864(x101631))),f323(f323(f8(f872(x101631,f872(a861,a860)),f872(a862,f872(f872(x101631,f872(a861,a860)),f864(x101631))),x101633),f90(x101631)),x101634)),x101635)),x101636)),x101637))
% 188.07/187.98 [9704]~P15(x97046,x97047,x97048,x97049,x970410,x97041)+E(f323(f323(x97041,x97042),x97043),f323(f323(x97041,x97044),x97045))+~P101(f323(f323(f325(f871(x97047,x97047)),f323(f323(f258(x97047,x97047),x97043),x97045)),x970410))+~P101(f323(f323(f325(f871(x97046,x97046)),f323(f323(f258(x97046,x97046),x97042),x97044)),x97049))
% 188.07/187.98 [9310]~P2(x93102)+E(x93101,f188(f872(x93102,a860)))+~P101(f323(f59(x93102),x93101))+P101(f323(f323(f325(x93102),f11(x93102,x93101)),x93101))+~P101(f323(f323(f325(x93102),f323(f323(f101(x93102),f824(x93101,x93102)),f825(x93101,x93102))),f323(f323(f301(x93102),f824(x93101,x93102)),f323(f323(f301(x93102),f825(x93101,x93102)),f188(f872(x93102,a860))))))
% 188.07/187.98 [9311]~P2(x93112)+E(x93111,f188(f872(x93112,a860)))+~P101(f323(f59(x93112),x93111))+P101(f323(f323(f325(x93112),f10(x93112,x93111)),x93111))+~P101(f323(f323(f325(x93112),f323(f323(f110(x93112),f826(x93111,x93112)),f827(x93111,x93112))),f323(f323(f301(x93112),f826(x93111,x93112)),f323(f323(f301(x93112),f827(x93111,x93112)),f188(f872(x93112,a860))))))
% 188.07/187.98 [9342]~P66(x93422)+E(x93421,f188(f872(x93422,a860)))+~P101(f323(f59(x93422),x93421))+P101(f323(f323(f325(x93422),f323(f61(x93422,f79(x93422)),x93421)),x93421))+~P101(f323(f323(f325(x93422),f323(f323(f79(x93422),f845(x93421,x93422)),f846(x93421,x93422))),f323(f323(f301(x93422),f845(x93421,x93422)),f323(f323(f301(x93422),f846(x93421,x93422)),f188(f872(x93422,a860))))))
% 188.07/187.98 [9347]~P103(x93472)+E(x93471,f188(f872(x93472,a860)))+~P101(f323(f59(x93472),x93471))+P101(f323(f323(f325(x93472),f12(x93472,f235(x93472),x93471)),x93471))+~P101(f323(f323(f325(x93472),f323(f323(f235(x93472),f343(x93471,x93472)),f346(x93471,x93472))),f323(f323(f301(x93472),f343(x93471,x93472)),f323(f323(f301(x93472),f346(x93471,x93472)),f188(f872(x93472,a860))))))
% 188.07/187.98 [9348]~P103(x93482)+E(x93481,f188(f872(x93482,a860)))+~P101(f323(f59(x93482),x93481))+P101(f323(f323(f325(x93482),f13(x93482,f236(x93482),x93481)),x93481))+~P101(f323(f323(f325(x93482),f323(f323(f236(x93482),f344(x93481,x93482)),f345(x93481,x93482))),f323(f323(f301(x93482),f344(x93481,x93482)),f323(f323(f301(x93482),f345(x93481,x93482)),f188(f872(x93482,a860))))))
% 188.07/187.98 [6481]~P84(x64812)+E(x64811,f2(x64812))+~E(f323(f323(f78(x64812),x64813),x64811),f2(x64812))+~P101(f323(f323(f237(x64812),f2(x64812)),x64813))+~P101(f323(f323(f237(x64812),f2(x64812)),x64811))
% 188.07/187.98 [6482]~P84(x64822)+E(x64821,f2(x64822))+~E(f323(f323(f78(x64822),x64821),x64823),f2(x64822))+~P101(f323(f323(f237(x64822),f2(x64822)),x64823))+~P101(f323(f323(f237(x64822),f2(x64822)),x64821))
% 188.07/187.98 [7008]~P103(x70082)+~P16(x70082,x70081)+E(x70081,f113(x70082))+~P101(f323(f323(f325(x70082),x70083),f323(f166(x70082),f612(x70081,x70082))))+P101(f323(f323(f237(x70082),f649(x70081,x70082)),x70083))
% 188.07/187.98 [7174]~P103(x71741)+E(f15(x71741,x71742),x71743)+~P101(f323(f59(x71741),x71742))+~P101(f323(f323(f237(x71741),x71743),f499(x71743,x71742,x71741)))+~P101(f323(f323(f325(x71741),x71743),x71742))
% 188.07/187.98 [7205]~P103(x72051)+~P16(x72051,x72052)+~P16(x72051,x72053)+P16(x72051,f323(f323(f121(x72051),x72052),x72053))+P101(f323(f323(f325(x72051),f601(x72053,x72052,x72051)),f323(f166(x72051),x72052)))
% 188.07/187.98 [7206]~P103(x72061)+~P16(x72061,x72062)+~P16(x72061,x72063)+P16(x72061,f323(f323(f121(x72061),x72062),x72063))+P101(f323(f323(f325(x72061),f602(x72063,x72062,x72061)),f323(f166(x72061),x72063)))
% 188.07/187.98 [7262]~P103(x72621)+E(f14(x72621,x72622),x72623)+~P101(f323(f59(x72621),x72622))+P101(f323(f323(f325(x72621),f500(x72623,x72622,x72621)),x72622))+~P101(f323(f323(f325(x72621),x72623),x72622))
% 188.07/187.98 [7263]~P103(x72631)+E(f15(x72631,x72632),x72633)+~P101(f323(f59(x72631),x72632))+P101(f323(f323(f325(x72631),f499(x72633,x72632,x72631)),x72632))+~P101(f323(f323(f325(x72631),x72633),x72632))
% 188.07/187.98 [7839]~P103(x78391)+E(f14(x78391,x78392),x78393)+~P101(f323(f59(x78391),x78392))+~P101(f323(f323(f325(x78391),x78393),x78392))+~P101(f323(f323(f237(x78391),f500(x78393,x78392,x78391)),x78393))
% 188.07/187.98 [8158]~P103(x81581)+~P16(x81581,x81582)+~P16(x81581,x81583)+P16(x81581,f323(f323(f121(x81581),x81582),x81583))+~P101(f323(f323(f237(x81581),f601(x81583,x81582,x81581)),f602(x81583,x81582,x81581)))
% 188.07/187.98 [8950]~P2(x89502)+E(x89501,f188(f872(x89502,a860)))+~E(f323(f323(f101(x89502),f323(x89503,f823(x89501,x89503,x89502))),f323(x89503,f828(x89501,x89503,x89502))),f323(x89503,f323(f323(f101(x89502),f823(x89501,x89503,x89502)),f828(x89501,x89503,x89502))))+E(f11(x89502,f323(f302(x89502,x89502,x89503),x89501)),f323(x89503,f11(x89502,x89501)))+~P101(f323(f59(x89502),x89501))
% 188.07/187.98 [8951]~P2(x89512)+E(x89511,f188(f872(x89512,a860)))+~E(f323(f323(f110(x89512),f323(x89513,f829(x89511,x89513,x89512))),f323(x89513,f830(x89511,x89513,x89512))),f323(x89513,f323(f323(f110(x89512),f829(x89511,x89513,x89512)),f830(x89511,x89513,x89512))))+E(f10(x89512,f323(f302(x89512,x89512,x89513),x89511)),f323(x89513,f10(x89512,x89511)))+~P101(f323(f59(x89512),x89511))
% 188.07/187.98 [8952]~P103(x89522)+E(x89521,f188(f872(x89522,a860)))+~E(f323(f323(f236(x89522),f323(x89523,f339(x89521,x89523,x89522))),f323(x89523,f353(x89521,x89523,x89522))),f323(x89523,f323(f323(f236(x89522),f339(x89521,x89523,x89522)),f353(x89521,x89523,x89522))))+E(f14(x89522,f323(f302(x89522,x89522,x89523),x89521)),f323(x89523,f14(x89522,x89521)))+~P101(f323(f59(x89522),x89521))
% 188.07/187.98 [8953]~P103(x89532)+E(x89531,f188(f872(x89532,a860)))+~E(f323(f323(f235(x89532),f323(x89533,f354(x89531,x89533,x89532))),f323(x89533,f355(x89531,x89533,x89532))),f323(x89533,f323(f323(f235(x89532),f354(x89531,x89533,x89532)),f355(x89531,x89533,x89532))))+E(f15(x89532,f323(f302(x89532,x89532,x89533),x89531)),f323(x89533,f15(x89532,x89531)))+~P101(f323(f59(x89532),x89531))
% 188.07/187.98 [9022]~P103(x90222)+E(x90221,f188(f872(x90222,a860)))+~E(f323(f323(f235(x90222),f323(x90223,f340(x90221,x90223,x90222))),f323(x90223,f352(x90221,x90223,x90222))),f323(x90223,f323(f323(f235(x90222),f340(x90221,x90223,x90222)),f352(x90221,x90223,x90222))))+E(f12(x90222,f235(x90222),f323(f302(x90222,x90222,x90223),x90221)),f323(x90223,f12(x90222,f235(x90222),x90221)))+~P101(f323(f59(x90222),x90221))
% 188.07/187.98 [9023]~P103(x90232)+E(x90231,f188(f872(x90232,a860)))+~E(f323(f323(f236(x90232),f323(x90233,f341(x90231,x90233,x90232))),f323(x90233,f351(x90231,x90233,x90232))),f323(x90233,f323(f323(f236(x90232),f341(x90231,x90233,x90232)),f351(x90231,x90233,x90232))))+E(f13(x90232,f236(x90232),f323(f302(x90232,x90232,x90233),x90231)),f323(x90233,f13(x90232,f236(x90232),x90231)))+~P101(f323(f59(x90232),x90231))
% 188.07/187.98 [6497]~P66(x64972)+E(x64971,f188(f872(x64972,a860)))+~P101(f323(f59(x64972),x64971))+E(f323(f61(x64972,f79(x64972)),f323(f323(f301(x64972),x64973),x64971)),f323(f323(f79(x64972),x64973),f323(f61(x64972,f79(x64972)),x64971)))+P101(f323(f323(f325(x64972),x64973),x64971))
% 188.07/187.98 [7014]~P2(x70142)+E(f323(f323(f110(x70142),f10(x70142,x70141)),f10(x70142,x70143)),f10(x70142,x70143))+E(x70141,f188(f872(x70142,a860)))+~P101(f323(f59(x70142),x70143))+~P101(f323(f323(f237(f872(x70142,a860)),x70141),x70143))
% 188.07/187.98 [7015]~P2(x70152)+E(f323(f323(f101(x70152),f11(x70152,x70151)),f11(x70152,x70153)),f11(x70152,x70153))+E(x70151,f188(f872(x70152,a860)))+~P101(f323(f59(x70152),x70153))+~P101(f323(f323(f237(f872(x70152,a860)),x70151),x70153))
% 188.07/187.98 [7016]~P103(x70162)+E(f323(f323(f235(x70162),f15(x70162,x70161)),f15(x70162,x70163)),f15(x70162,x70163))+E(x70161,f188(f872(x70162,a860)))+~P101(f323(f59(x70162),x70163))+~P101(f323(f323(f237(f872(x70162,a860)),x70161),x70163))
% 188.07/187.98 [7017]~P103(x70172)+E(f323(f323(f236(x70172),f14(x70172,x70171)),f14(x70172,x70173)),f14(x70172,x70173))+E(x70171,f188(f872(x70172,a860)))+~P101(f323(f59(x70172),x70173))+~P101(f323(f323(f237(f872(x70172,a860)),x70171),x70173))
% 188.07/187.98 [7311]~P103(x73112)+E(x73111,f188(f872(x73112,a860)))+~P101(f323(f59(x73112),x73113))+P101(f323(f323(f237(x73112),f14(x73112,x73111)),f14(x73112,x73113)))+~P101(f323(f323(f237(f872(x73112,a860)),x73111),x73113))
% 188.07/187.98 [7312]~P103(x73122)+E(x73121,f188(f872(x73122,a860)))+~P101(f323(f59(x73122),x73123))+P101(f323(f323(f237(x73122),f15(x73122,x73123)),f15(x73122,x73121)))+~P101(f323(f323(f237(f872(x73122,a860)),x73121),x73123))
% 188.07/187.98 [7370]~P2(x73701)+E(f11(x73701,x73702),x73703)+~P101(f323(f59(x73701),x73702))+~E(f323(f323(f22(f872(x73701,a860)),x73702),f323(f323(f301(x73701),x73703),f188(f872(x73701,a860)))),f188(f872(x73701,a860)))+~P101(f323(f323(f325(x73701),x73703),x73702))
% 188.07/187.98 [7371]~P2(x73711)+E(f10(x73711,x73712),x73713)+~P101(f323(f59(x73711),x73712))+~E(f323(f323(f22(f872(x73711,a860)),x73712),f323(f323(f301(x73711),x73713),f188(f872(x73711,a860)))),f188(f872(x73711,a860)))+~P101(f323(f323(f325(x73711),x73713),x73712))
% 188.07/187.98 [7372]~P103(x73721)+E(f14(x73721,x73722),x73723)+~P101(f323(f59(x73721),x73722))+~E(f323(f323(f22(f872(x73721,a860)),x73722),f323(f323(f301(x73721),x73723),f188(f872(x73721,a860)))),f188(f872(x73721,a860)))+~P101(f323(f323(f325(x73721),x73723),x73722))
% 188.07/187.98 [7373]~P103(x73731)+E(f15(x73731,x73732),x73733)+~P101(f323(f59(x73731),x73732))+~E(f323(f323(f22(f872(x73731,a860)),x73732),f323(f323(f301(x73731),x73733),f188(f872(x73731,a860)))),f188(f872(x73731,a860)))+~P101(f323(f323(f325(x73731),x73733),x73732))
% 188.07/187.98 [7470]~P103(x74701)+E(f12(x74701,f235(x74701),x74702),x74703)+~P101(f323(f59(x74701),x74702))+~E(f323(f323(f22(f872(x74701,a860)),x74702),f323(f323(f301(x74701),x74703),f188(f872(x74701,a860)))),f188(f872(x74701,a860)))+~P101(f323(f323(f325(x74701),x74703),x74702))
% 188.07/187.98 [7471]~P103(x74711)+E(f13(x74711,f236(x74711),x74712),x74713)+~P101(f323(f59(x74711),x74712))+~E(f323(f323(f22(f872(x74711,a860)),x74712),f323(f323(f301(x74711),x74713),f188(f872(x74711,a860)))),f188(f872(x74711,a860)))+~P101(f323(f323(f325(x74711),x74713),x74712))
% 188.07/187.98 [7507]~P98(x75072)+E(x75071,f188(f872(x75072,a860)))+~P101(f323(f59(x75072),x75071))+~P101(f323(f323(f237(x75072),x75073),f832(x75073,x75071,x75072)))+P101(f323(f323(f237(x75072),x75073),f323(f61(x75072,f101(x75072)),x75071)))
% 188.07/187.98 [7508]~P103(x75082)+E(x75081,f188(f872(x75082,a860)))+~P101(f323(f59(x75082),x75081))+~P101(f323(f323(f237(x75082),x75083),f334(x75083,x75081,x75082)))+P101(f323(f323(f237(x75082),x75083),f323(f61(x75082,f235(x75082)),x75081)))
% 188.07/187.98 [7509]~P103(x75092)+E(x75091,f188(f872(x75092,a860)))+~P101(f323(f59(x75092),x75091))+~P101(f323(f323(f238(x75092),x75093),f335(x75093,x75091,x75092)))+P101(f323(f323(f238(x75092),x75093),f323(f61(x75092,f235(x75092)),x75091)))
% 188.07/187.98 [7594]~P98(x75942)+E(x75941,f188(f872(x75942,a860)))+~P101(f323(f59(x75942),x75941))+P101(f323(f323(f325(x75942),f832(x75943,x75941,x75942)),x75941))+P101(f323(f323(f237(x75942),x75943),f323(f61(x75942,f101(x75942)),x75941)))
% 188.07/187.98 [7595]~P103(x75952)+E(x75951,f188(f872(x75952,a860)))+~P101(f323(f59(x75952),x75951))+P101(f323(f323(f325(x75952),f334(x75953,x75951,x75952)),x75951))+P101(f323(f323(f237(x75952),x75953),f323(f61(x75952,f235(x75952)),x75951)))
% 188.07/187.98 [7596]~P103(x75962)+E(x75961,f188(f872(x75962,a860)))+~P101(f323(f59(x75962),x75961))+P101(f323(f323(f325(x75962),f335(x75963,x75961,x75962)),x75961))+P101(f323(f323(f238(x75962),x75963),f323(f61(x75962,f235(x75962)),x75961)))
% 188.07/187.98 [7717]~P103(x77172)+E(x77171,f188(f872(x77172,a860)))+E(f323(f323(f235(x77172),f12(x77172,f235(x77172),x77171)),f12(x77172,f235(x77172),x77173)),f12(x77172,f235(x77172),x77173))+~P101(f323(f59(x77172),x77173))+~P101(f323(f323(f237(f872(x77172,a860)),x77171),x77173))
% 188.07/187.98 [7718]~P103(x77182)+E(x77181,f188(f872(x77182,a860)))+E(f323(f323(f236(x77182),f13(x77182,f236(x77182),x77181)),f13(x77182,f236(x77182),x77183)),f13(x77182,f236(x77182),x77183))+~P101(f323(f59(x77182),x77183))+~P101(f323(f323(f237(f872(x77182,a860)),x77181),x77183))
% 188.07/187.98 [7920]~E(f557(x79201,x79203,x79202),f558(x79201,x79203,x79202))+~E(f323(f35(x79202),f559(x79201,x79203,x79202)),x79201)+E(f323(f323(f79(a865),x79201),f323(f35(f872(x79202,a860)),x79203)),f323(f35(x79202),f37(f872(x79202,a860),x79203)))+~P101(f323(f59(x79202),f37(f872(x79202,a860),x79203)))+~P101(f323(f59(f872(x79202,a860)),x79203))
% 188.07/187.98 [8093]~P103(x80932)+E(x80931,f188(f872(x80932,a860)))+~P101(f323(f59(x80932),x80933))+P101(f323(f323(f237(x80932),f323(f61(x80932,f235(x80932)),x80933)),f323(f61(x80932,f235(x80932)),x80931)))+~P101(f323(f323(f237(f872(x80932,a860)),x80931),x80933))
% 188.07/187.98 [8401]~E(f557(x84011,x84013,x84012),f558(x84011,x84013,x84012))+E(f323(f323(f79(a865),x84011),f323(f35(f872(x84012,a860)),x84013)),f323(f35(x84012),f37(f872(x84012,a860),x84013)))+P101(f323(f323(f325(f872(x84012,a860)),f559(x84011,x84013,x84012)),x84013))+~P101(f323(f59(x84012),f37(f872(x84012,a860),x84013)))+~P101(f323(f59(f872(x84012,a860)),x84013))
% 188.07/187.98 [8423]~E(f323(f35(x84232),f559(x84231,x84233,x84232)),x84231)+E(f323(f323(f79(a865),x84231),f323(f35(f872(x84232,a860)),x84233)),f323(f35(x84232),f37(f872(x84232,a860),x84233)))+P101(f323(f323(f325(f872(x84232,a860)),f558(x84231,x84233,x84232)),x84233))+~P101(f323(f59(x84232),f37(f872(x84232,a860),x84233)))+~P101(f323(f59(f872(x84232,a860)),x84233))
% 188.07/187.98 [8424]~E(f323(f35(x84242),f559(x84241,x84243,x84242)),x84241)+E(f323(f323(f79(a865),x84241),f323(f35(f872(x84242,a860)),x84243)),f323(f35(x84242),f37(f872(x84242,a860),x84243)))+P101(f323(f323(f325(f872(x84242,a860)),f557(x84241,x84243,x84242)),x84243))+~P101(f323(f59(x84242),f37(f872(x84242,a860),x84243)))+~P101(f323(f59(f872(x84242,a860)),x84243))
% 188.07/187.98 [8449]~E(f323(f35(x84492),f559(x84491,x84493,x84492)),x84491)+~E(f323(f323(f101(f872(x84492,a860)),f558(x84491,x84493,x84492)),f557(x84491,x84493,x84492)),f188(f872(x84492,a860)))+E(f323(f323(f79(a865),x84491),f323(f35(f872(x84492,a860)),x84493)),f323(f35(x84492),f37(f872(x84492,a860),x84493)))+~P101(f323(f59(f872(x84492,a860)),x84493))+~P101(f323(f59(x84492),f37(f872(x84492,a860),x84493)))
% 188.07/187.98 [8715]E(f323(f323(f79(a865),x87151),f323(f35(f872(x87152,a860)),x87153)),f323(f35(x87152),f37(f872(x87152,a860),x87153)))+P101(f323(f323(f325(f872(x87152,a860)),f559(x87151,x87153,x87152)),x87153))+P101(f323(f323(f325(f872(x87152,a860)),f558(x87151,x87153,x87152)),x87153))+~P101(f323(f59(f872(x87152,a860)),x87153))+~P101(f323(f59(x87152),f37(f872(x87152,a860),x87153)))
% 188.07/187.98 [8716]E(f323(f323(f79(a865),x87161),f323(f35(f872(x87162,a860)),x87163)),f323(f35(x87162),f37(f872(x87162,a860),x87163)))+P101(f323(f323(f325(f872(x87162,a860)),f559(x87161,x87163,x87162)),x87163))+P101(f323(f323(f325(f872(x87162,a860)),f557(x87161,x87163,x87162)),x87163))+~P101(f323(f59(f872(x87162,a860)),x87163))+~P101(f323(f59(x87162),f37(f872(x87162,a860),x87163)))
% 188.07/187.98 [8743]~E(f323(f323(f101(f872(x87432,a860)),f558(x87431,x87433,x87432)),f557(x87431,x87433,x87432)),f188(f872(x87432,a860)))+E(f323(f323(f79(a865),x87431),f323(f35(f872(x87432,a860)),x87433)),f323(f35(x87432),f37(f872(x87432,a860),x87433)))+~P101(f323(f59(f872(x87432,a860)),x87433))+P101(f323(f323(f325(f872(x87432,a860)),f559(x87431,x87433,x87432)),x87433))+~P101(f323(f59(x87432),f37(f872(x87432,a860),x87433)))
% 188.07/187.98 [8996]~P93(x89962)+E(x89961,f188(f872(x89962,a860)))+~E(f323(f323(f79(x89962),f323(x89963,f842(x89961,x89963,x89962))),f323(x89963,f847(x89961,x89963,x89962))),f323(x89963,f323(f323(f79(x89962),f842(x89961,x89963,x89962)),f847(x89961,x89963,x89962))))+~P101(f323(f59(x89962),x89961))+E(f323(f61(x89962,f79(x89962)),f323(f302(x89962,x89962,x89963),x89961)),f323(x89963,f323(f61(x89962,f79(x89962)),x89961)))
% 188.07/187.98 [9926]P101(f323(f323(x99261,x99262),x99263))+P101(f323(f323(f238(a1),f516(x99261,x99263,x99262)),f517(x99261,x99263,x99262)))+P101(f323(f323(f237(a1),f517(x99261,x99263,x99262)),f2(a1)))+P101(f323(f323(x99261,f516(x99261,x99263,x99262)),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)))),f517(x99261,x99263,x99262))))+~P101(f323(f311(f871(a1,a1),a54),f323(f323(f258(a1,a1),x99262),x99263)))
% 188.07/187.98 [9932]P101(f323(f323(x99321,x99322),x99323))+P101(f323(f323(f237(a1),f515(x99321,x99323,x99322)),f2(a1)))+P101(f323(f323(x99321,f514(x99321,x99323,x99322)),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(x99321,x99323,x99322))))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),f514(x99321,x99323,x99322)),f515(x99321,x99323,x99322))))+~P101(f323(f311(f871(a1,a1),a49),f323(f323(f258(a1,a1),x99322),x99323)))
% 188.07/187.98 [7890]~P116(x78901)+~P101(f323(f323(f237(x78901),x78902),f76(x78901)))+~P101(f323(f323(f237(x78901),f2(x78901)),x78902))+~P101(f323(f323(f237(x78901),f2(x78901)),x78903))+P101(f323(f323(f237(x78901),f323(f323(f79(x78901),x78902),x78903)),x78903))
% 188.07/187.98 [7891]~P116(x78911)+~P101(f323(f323(f237(x78911),x78913),f76(x78911)))+~P101(f323(f323(f237(x78911),f2(x78911)),x78913))+~P101(f323(f323(f237(x78911),f2(x78911)),x78912))+P101(f323(f323(f237(x78911),f323(f323(f79(x78911),x78912),x78913)),x78912))
% 188.07/187.98 [8243]~P103(x82432)+E(x82431,f188(f872(x82432,a860)))+~P101(f323(f59(x82432),x82431))+P101(f323(f323(f325(x82432),f336(x82433,x82431,x82432)),x82431))+~P101(f323(f323(f237(x82432),f323(f61(x82432,f235(x82432)),x82431)),x82433))
% 188.07/187.98 [8244]~P103(x82442)+E(x82441,f188(f872(x82442,a860)))+~P101(f323(f59(x82442),x82441))+P101(f323(f323(f325(x82442),f338(x82443,x82441,x82442)),x82441))+~P101(f323(f323(f238(x82442),f323(f61(x82442,f235(x82442)),x82441)),x82443))
% 188.07/187.98 [8245]~P103(x82452)+E(x82451,f188(f872(x82452,a860)))+~P101(f323(f59(x82452),x82451))+P101(f323(f323(f237(x82452),f336(x82453,x82451,x82452)),x82453))+~P101(f323(f323(f237(x82452),f323(f61(x82452,f235(x82452)),x82451)),x82453))
% 188.07/187.98 [8246]~P103(x82462)+E(x82461,f188(f872(x82462,a860)))+~P101(f323(f59(x82462),x82461))+P101(f323(f323(f238(x82462),f338(x82463,x82461,x82462)),x82463))+~P101(f323(f323(f238(x82462),f323(f61(x82462,f235(x82462)),x82461)),x82463))
% 188.07/187.98 [8336]~P101(f323(x83361,x83363))+P101(f323(x83361,f405(x83361,x83362)))+P101(f323(x83361,f395(x83361,x83362)))+~P101(f323(f323(f238(a1),f2(a1)),x83362))+P101(f323(x83361,f323(f323(f22(a1),f395(x83361,x83362)),f323(f323(f79(a1),f406(x83361,x83362)),x83362))))
% 188.07/187.98 [8548]~P101(f323(x85481,x85483))+P101(f323(x85481,f395(x85481,x85482)))+~P101(f323(f323(f238(a1),f2(a1)),x85482))+P101(f323(f323(f325(a1),f405(x85481,x85482)),f294(a1,f76(a1),x85482)))+P101(f323(x85481,f323(f323(f22(a1),f395(x85481,x85482)),f323(f323(f79(a1),f406(x85481,x85482)),x85482))))
% 188.07/187.98 [8765]~P101(f323(x87651,x87653))+~P101(f323(x87651,f395(x87651,x87652)))+P101(f323(x87651,f405(x87651,x87652)))+~P101(f323(f323(f238(a1),f2(a1)),x87652))+~P101(f323(x87651,f323(f323(f22(a1),f395(x87651,x87652)),f323(f323(f79(a1),f406(x87651,x87652)),x87652))))
% 188.07/187.98 [8890]~P101(f323(x88901,x88903))+~P101(f323(x88901,f395(x88901,x88902)))+~P101(f323(f323(f238(a1),f2(a1)),x88902))+P101(f323(f323(f325(a1),f405(x88901,x88902)),f294(a1,f76(a1),x88902)))+~P101(f323(x88901,f323(f323(f22(a1),f395(x88901,x88902)),f323(f323(f79(a1),f406(x88901,x88902)),x88902))))
% 188.07/187.98 [8669]~P2(x86691)+~P101(f323(f59(x86691),x86692))+E(f323(f323(f22(f872(x86691,a860)),x86692),f323(f323(f301(x86691),x86693),f188(f872(x86691,a860)))),f188(f872(x86691,a860)))+~P101(f323(f323(f325(x86691),x86693),x86692))+E(f323(f323(f101(x86691),x86693),f11(x86691,f323(f323(f22(f872(x86691,a860)),x86692),f323(f323(f301(x86691),x86693),f188(f872(x86691,a860)))))),f11(x86691,x86692))
% 188.07/187.98 [8670]~P2(x86701)+~P101(f323(f59(x86701),x86702))+E(f323(f323(f22(f872(x86701,a860)),x86702),f323(f323(f301(x86701),x86703),f188(f872(x86701,a860)))),f188(f872(x86701,a860)))+~P101(f323(f323(f325(x86701),x86703),x86702))+E(f323(f323(f110(x86701),x86703),f10(x86701,f323(f323(f22(f872(x86701,a860)),x86702),f323(f323(f301(x86701),x86703),f188(f872(x86701,a860)))))),f10(x86701,x86702))
% 188.07/187.98 [8671]~P103(x86711)+~P101(f323(f59(x86711),x86712))+E(f323(f323(f22(f872(x86711,a860)),x86712),f323(f323(f301(x86711),x86713),f188(f872(x86711,a860)))),f188(f872(x86711,a860)))+~P101(f323(f323(f325(x86711),x86713),x86712))+E(f323(f323(f236(x86711),x86713),f14(x86711,f323(f323(f22(f872(x86711,a860)),x86712),f323(f323(f301(x86711),x86713),f188(f872(x86711,a860)))))),f14(x86711,x86712))
% 188.07/187.98 [8672]~P103(x86721)+~P101(f323(f59(x86721),x86722))+E(f323(f323(f22(f872(x86721,a860)),x86722),f323(f323(f301(x86721),x86723),f188(f872(x86721,a860)))),f188(f872(x86721,a860)))+~P101(f323(f323(f325(x86721),x86723),x86722))+E(f323(f323(f235(x86721),x86723),f15(x86721,f323(f323(f22(f872(x86721,a860)),x86722),f323(f323(f301(x86721),x86723),f188(f872(x86721,a860)))))),f15(x86721,x86722))
% 188.07/187.98 [8735]~P103(x87351)+~P101(f323(f59(x87351),x87352))+E(f323(f323(f22(f872(x87351,a860)),x87352),f323(f323(f301(x87351),x87353),f188(f872(x87351,a860)))),f188(f872(x87351,a860)))+~P101(f323(f323(f325(x87351),x87353),x87352))+E(f323(f323(f235(x87351),x87353),f12(x87351,f235(x87351),f323(f323(f22(f872(x87351,a860)),x87352),f323(f323(f301(x87351),x87353),f188(f872(x87351,a860)))))),f12(x87351,f235(x87351),x87352))
% 188.07/187.98 [8736]~P103(x87361)+~P101(f323(f59(x87361),x87362))+E(f323(f323(f22(f872(x87361,a860)),x87362),f323(f323(f301(x87361),x87363),f188(f872(x87361,a860)))),f188(f872(x87361,a860)))+~P101(f323(f323(f325(x87361),x87363),x87362))+E(f323(f323(f236(x87361),x87363),f13(x87361,f236(x87361),f323(f323(f22(f872(x87361,a860)),x87362),f323(f323(f301(x87361),x87363),f188(f872(x87361,a860)))))),f13(x87361,f236(x87361),x87362))
% 188.07/187.98 [8752]~P2(x87521)+~P101(f323(f59(x87521),x87523))+~P101(f323(f59(x87521),x87522))+E(f323(f323(f101(f872(x87521,a860)),x87522),x87523),f188(f872(x87521,a860)))+E(f323(f323(f110(x87521),f10(x87521,f323(f323(f110(f872(x87521,a860)),x87522),x87523))),f10(x87521,f323(f323(f101(f872(x87521,a860)),x87522),x87523))),f323(f323(f110(x87521),f10(x87521,x87522)),f10(x87521,x87523)))
% 188.07/187.98 [8753]~P2(x87531)+~P101(f323(f59(x87531),x87533))+~P101(f323(f59(x87531),x87532))+E(f323(f323(f101(f872(x87531,a860)),x87532),x87533),f188(f872(x87531,a860)))+E(f323(f323(f101(x87531),f11(x87531,f323(f323(f110(f872(x87531,a860)),x87532),x87533))),f11(x87531,f323(f323(f101(f872(x87531,a860)),x87532),x87533))),f323(f323(f101(x87531),f11(x87531,x87532)),f11(x87531,x87533)))
% 188.07/187.98 [8754]~P103(x87541)+~P101(f323(f59(x87541),x87543))+~P101(f323(f59(x87541),x87542))+E(f323(f323(f101(f872(x87541,a860)),x87542),x87543),f188(f872(x87541,a860)))+E(f323(f323(f235(x87541),f15(x87541,f323(f323(f110(f872(x87541,a860)),x87542),x87543))),f15(x87541,f323(f323(f101(f872(x87541,a860)),x87542),x87543))),f323(f323(f235(x87541),f15(x87541,x87542)),f15(x87541,x87543)))
% 188.07/187.98 [8755]~P103(x87551)+~P101(f323(f59(x87551),x87553))+~P101(f323(f59(x87551),x87552))+E(f323(f323(f101(f872(x87551,a860)),x87552),x87553),f188(f872(x87551,a860)))+E(f323(f323(f236(x87551),f14(x87551,f323(f323(f110(f872(x87551,a860)),x87552),x87553))),f14(x87551,f323(f323(f101(f872(x87551,a860)),x87552),x87553))),f323(f323(f236(x87551),f14(x87551,x87552)),f14(x87551,x87553)))
% 188.07/187.98 [8968]~P103(x89681)+~P101(f323(f59(x89681),x89683))+~P101(f323(f59(x89681),x89682))+E(f323(f323(f101(f872(x89681,a860)),x89682),x89683),f188(f872(x89681,a860)))+E(f323(f323(f235(x89681),f12(x89681,f235(x89681),f323(f323(f110(f872(x89681,a860)),x89682),x89683))),f12(x89681,f235(x89681),f323(f323(f101(f872(x89681,a860)),x89682),x89683))),f323(f323(f235(x89681),f12(x89681,f235(x89681),x89682)),f12(x89681,f235(x89681),x89683)))
% 188.07/187.98 [8969]~P103(x89691)+~P101(f323(f59(x89691),x89693))+~P101(f323(f59(x89691),x89692))+E(f323(f323(f101(f872(x89691,a860)),x89692),x89693),f188(f872(x89691,a860)))+E(f323(f323(f236(x89691),f13(x89691,f236(x89691),f323(f323(f110(f872(x89691,a860)),x89692),x89693))),f13(x89691,f236(x89691),f323(f323(f101(f872(x89691,a860)),x89692),x89693))),f323(f323(f236(x89691),f13(x89691,f236(x89691),x89692)),f13(x89691,f236(x89691),x89693)))
% 188.07/187.98 [9767]~P119(x97673)+E(x97671,x97672)+~P101(f323(f323(f237(x97673),f2(x97673)),x97672))+~P101(f323(f323(f237(x97673),f2(x97673)),x97671))+~E(f323(f323(f248(x97673),x97671),f323(f103(a865),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(x97673),x97672),f323(f103(a865),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)))))
% 188.07/187.98 [6300]E(f332(x63001,x63002,x63003),x63004)+E(f323(x63001,x63004),f2(a865))+~E(f323(f323(f6(x63003,a865),x63001),x63002),f76(a865))+~P101(f323(f59(x63003),x63002))+~P101(f323(f323(f325(x63003),x63004),x63002))
% 188.07/187.98 [6361]E(f358(x63611,x63612,x63613),x63614)+E(f323(x63611,x63614),f2(a865))+~E(f323(f323(f6(x63613,a865),x63611),x63612),f323(a112,f2(a865)))+~P101(f323(f59(x63613),x63612))+~P101(f323(f323(f325(x63613),x63614),x63612))
% 188.07/187.98 [6466]~P103(x64661)+~P6(x64661)+P101(f323(f323(f238(x64661),x64662),f37(x64661,x64663)))+~P101(f323(f323(f238(x64661),x64662),x64664))+~P101(f323(f323(f325(x64661),x64664),x64663))
% 188.07/187.98 [6638]~P103(x66381)+~P6(x66381)+~P101(f323(f323(f238(x66381),x66384),x66383))+P101(f323(f323(f238(x66381),f38(x66381,x66382)),x66383))+~P101(f323(f323(f325(x66381),x66384),x66382))
% 188.07/187.98 [6894]~P119(x68943)+E(x68941,x68942)+~E(f323(f323(f248(x68943),x68941),f323(a112,x68944)),f323(f323(f248(x68943),x68942),f323(a112,x68944)))+~P101(f323(f323(f237(x68943),f2(x68943)),x68942))+~P101(f323(f323(f237(x68943),f2(x68943)),x68941))
% 188.07/187.98 [7103]~E(f361(x71032,x71033,x71031,x71034),x71034)+~E(f323(x71032,x71034),f76(a865))+E(f323(f323(f6(x71031,a865),x71032),x71033),f76(a865))+~P101(f323(f59(x71031),x71033))+~P101(f323(f323(f325(x71031),x71034),x71033))
% 188.07/187.98 [7110]~P112(x71104)+~P123(x71104)+E(f323(x71101,f466(x71101,x71102,x71103,x71104)),f2(x71104))+~E(f323(f323(f9(x71103,x71104),x71101),x71102),f2(x71104))+~P101(f323(f59(x71103),x71102))
% 188.07/187.98 [7196]~E(f359(x71962,x71963,x71961,x71964),x71964)+~E(f323(x71962,x71964),f323(a112,f2(a865)))+E(f323(f323(f6(x71961,a865),x71962),x71963),f323(a112,f2(a865)))+~P101(f323(f59(x71961),x71963))+~P101(f323(f323(f325(x71961),x71964),x71963))
% 188.07/187.98 [7931]~E(f323(x79312,x79314),f76(a865))+~E(f323(x79312,f361(x79312,x79313,x79311,x79314)),f2(a865))+E(f323(f323(f6(x79311,a865),x79312),x79313),f76(a865))+~P101(f323(f59(x79311),x79313))+~P101(f323(f323(f325(x79311),x79314),x79313))
% 188.07/187.98 [7969]~E(f323(x79692,x79694),f323(a112,f2(a865)))+~E(f323(x79692,f359(x79692,x79693,x79691,x79694)),f2(a865))+E(f323(f323(f6(x79691,a865),x79692),x79693),f323(a112,f2(a865)))+~P101(f323(f59(x79691),x79693))+~P101(f323(f323(f325(x79691),x79694),x79693))
% 188.07/187.98 [8515]~P103(x85151)+~P16(x85151,x85154)+P16(x85151,x85152)+~E(x85152,f323(f323(f144(x85151),x85153),x85154))+~P101(f323(f323(f237(x85151),x85153),f651(x85152,x85151,x85154,x85153)))
% 188.07/187.98 [8552]E(x85521,x85522)+E(f323(f323(f22(a1),f407(x85523,x85522,x85524,x85521)),f408(x85523,x85522,x85524,x85521)),x85521)+~E(f323(f323(f78(a1),x85521),x85524),x85522)+~P101(f323(f323(f238(a1),f2(a1)),x85524))+~P101(f323(f323(f325(a1),x85522),x85523))
% 188.07/187.98 [8553]E(x85531,x85532)+E(f323(f323(f78(a1),f410(x85533,x85532,x85534,x85531)),f411(x85533,x85532,x85534,x85531)),x85531)+~E(f323(f323(f22(a1),x85531),x85534),x85532)+~P101(f323(f323(f238(a1),f2(a1)),x85534))+~P101(f323(f323(f325(a1),x85532),x85533))
% 188.07/187.98 [8750]E(f323(x87501,f757(x87502,x87501,x87503,x87504)),x87502)+P101(f323(f323(f237(a865),x87504),f758(x87502,x87501,x87503,x87504)))+~P101(f323(f323(f237(a1),x87502),f323(x87501,x87503)))+~P101(f323(f323(f238(a865),x87504),x87503))+~P101(f323(f323(f237(a1),f323(x87501,x87504)),x87502))
% 188.07/187.98 [8751]~P103(x87511)+~P16(x87511,x87513)+P16(x87511,x87512)+~E(x87512,f323(f323(f144(x87511),x87514),x87513))+P101(f323(f323(f325(x87511),f651(x87512,x87511,x87513,x87514)),f323(f166(x87511),x87513)))
% 188.07/187.98 [8769]~P112(x87694)+~P123(x87694)+~E(f323(f323(f9(x87691,x87694),x87692),x87693),f2(x87694))+~P101(f323(f59(x87691),x87693))+P101(f323(f323(f325(x87691),f466(x87692,x87693,x87691,x87694)),x87693))
% 188.07/187.98 [8805]~E(f323(x88052,x88054),f76(a865))+E(f323(f323(f6(x88051,a865),x88052),x88053),f76(a865))+~P101(f323(f59(x88051),x88053))+~P101(f323(f323(f325(x88051),x88054),x88053))+P101(f323(f323(f325(x88051),f361(x88052,x88053,x88051,x88054)),x88053))
% 188.07/187.98 [8814]E(x88141,x88142)+~E(f323(f323(f78(a1),x88142),x88144),x88141)+~P101(f323(f323(f238(a1),f2(a1)),x88144))+~P101(f323(f323(f325(a1),x88141),x88143))+P101(f323(f323(f325(a1),f407(x88143,x88141,x88144,x88142)),x88143))
% 188.07/187.98 [8815]E(x88151,x88152)+~E(f323(f323(f22(a1),x88152),x88154),x88151)+~P101(f323(f323(f238(a1),f2(a1)),x88154))+~P101(f323(f323(f325(a1),x88151),x88153))+P101(f323(f323(f325(a1),f410(x88153,x88151,x88154,x88152)),x88153))
% 188.07/187.98 [8817]~E(f323(x88172,x88174),f323(a112,f2(a865)))+E(f323(f323(f6(x88171,a865),x88172),x88173),f323(a112,f2(a865)))+~P101(f323(f59(x88171),x88173))+~P101(f323(f323(f325(x88171),x88174),x88173))+P101(f323(f323(f325(x88171),f359(x88172,x88173,x88171,x88174)),x88173))
% 188.07/187.98 [8822]P55(x88222,x88223,x88224,x88221)+E(x88221,f188(f872(x88222,a860)))+~P101(f323(f59(x88222),x88224))+~P101(f323(f59(x88222),x88221))+P101(f323(f323(f325(x88222),f664(x88221,x88224,x88223,x88222)),x88224))
% 188.07/187.98 [8903]E(x89031,x89032)+~E(f323(f323(f78(a1),x89032),x89034),x89031)+~P101(f323(f323(f238(a1),f2(a1)),x89034))+~P101(f323(f323(f325(a1),x89031),x89033))+P101(f323(f323(f325(a1),f408(x89033,x89031,x89034,x89032)),f294(a1,f76(a1),x89034)))
% 188.07/187.98 [8904]E(x89041,x89042)+~E(f323(f323(f22(a1),x89042),x89044),x89041)+~P101(f323(f323(f238(a1),f2(a1)),x89044))+~P101(f323(f323(f325(a1),x89041),x89043))+P101(f323(f323(f325(a1),f411(x89043,x89041,x89044,x89042)),f294(a1,f76(a1),x89044)))
% 188.07/187.98 [8974]P101(f323(f323(f237(a865),x89741),f757(x89742,x89743,x89744,x89741)))+~P101(f323(f323(f237(a1),x89742),f323(x89743,x89744)))+P101(f323(f323(f237(a865),x89741),f758(x89742,x89743,x89744,x89741)))+~P101(f323(f323(f238(a865),x89741),x89744))+~P101(f323(f323(f237(a1),f323(x89743,x89741)),x89742))
% 188.07/187.98 [9089]E(f323(x90891,f757(x90892,x90891,x90893,x90894)),x90892)+~P101(f323(f323(f237(a1),x90892),f323(x90891,x90893)))+P101(f323(f323(f238(a865),f758(x90892,x90891,x90893,x90894)),x90893))+~P101(f323(f323(f238(a865),x90894),x90893))+~P101(f323(f323(f237(a1),f323(x90891,x90894)),x90892))
% 188.07/187.98 [9217]~P101(f323(f323(f237(a1),x92172),f323(x92173,x92174)))+P101(f323(f323(f237(a865),x92171),f758(x92172,x92173,x92174,x92171)))+P101(f323(f323(f237(a865),f757(x92172,x92173,x92174,x92171)),x92174))+~P101(f323(f323(f238(a865),x92171),x92174))+~P101(f323(f323(f237(a1),f323(x92173,x92171)),x92172))
% 188.07/187.98 [9218]~P101(f323(f323(f237(a1),x92182),f323(x92183,x92184)))+P101(f323(f323(f237(a865),x92181),f757(x92182,x92183,x92184,x92181)))+P101(f323(f323(f238(a865),f758(x92182,x92183,x92184,x92181)),x92184))+~P101(f323(f323(f238(a865),x92181),x92184))+~P101(f323(f323(f237(a1),f323(x92183,x92181)),x92182))
% 188.07/187.98 [9325]~P101(f323(f323(f237(a1),x93251),f323(x93252,x93253)))+P101(f323(f323(f238(a865),f758(x93251,x93252,x93253,x93254)),x93253))+~P101(f323(f323(f238(a865),x93254),x93253))+~P101(f323(f323(f237(a1),f323(x93252,x93254)),x93251))+P101(f323(f323(f237(a865),f757(x93251,x93252,x93253,x93254)),x93253))
% 188.07/187.98 [9403]E(x94031,f188(f872(x94032,a860)))+~P101(f323(f59(x94032),x94034))+~P101(f323(f59(x94032),x94031))+P101(f323(f323(f325(f871(f872(x94032,a860),f872(x94032,a860))),f323(f323(f258(f872(x94032,a860),f872(x94032,a860)),x94034),x94031)),f314(x94032,x94033)))+P101(f323(f323(f325(x94032),f670(x94033,x94031,x94034,x94032)),x94034))
% 188.07/187.98 [9404]E(x94041,f188(f872(x94042,a860)))+~P101(f323(f59(x94042),x94044))+~P101(f323(f59(x94042),x94041))+P101(f323(f323(f325(f871(f872(x94042,a860),f872(x94042,a860))),f323(f323(f258(f872(x94042,a860),f872(x94042,a860)),x94044),x94041)),f314(x94042,x94043)))+P101(f323(f323(f325(x94042),f722(x94043,x94041,x94044,x94042)),x94044))
% 188.07/187.98 [10066]E(f323(x100661,f757(x100662,x100661,x100663,x100664)),x100662)+~P101(f323(f323(f237(a1),x100662),f323(x100661,x100663)))+~P101(f323(f323(f237(a1),f323(f73(a1),f323(f323(f22(a1),f323(x100661,f323(f323(f78(a865),f758(x100662,x100661,x100663,x100664)),f76(a865)))),f323(x100661,f758(x100662,x100661,x100663,x100664))))),f76(a1)))+~P101(f323(f323(f238(a865),x100664),x100663))+~P101(f323(f323(f237(a1),f323(x100661,x100664)),x100662))
% 188.07/187.98 [10067]~P101(f323(f323(f237(a1),x100672),f323(x100673,x100674)))+P101(f323(f323(f237(a865),x100671),f757(x100672,x100673,x100674,x100671)))+~P101(f323(f323(f237(a1),f323(f73(a1),f323(f323(f22(a1),f323(x100673,f323(f323(f78(a865),f758(x100672,x100673,x100674,x100671)),f76(a865)))),f323(x100673,f758(x100672,x100673,x100674,x100671))))),f76(a1)))+~P101(f323(f323(f238(a865),x100671),x100674))+~P101(f323(f323(f237(a1),f323(x100673,x100671)),x100672))
% 188.07/187.98 [10068]~P101(f323(f323(f237(a1),x100681),f323(x100682,x100683)))+~P101(f323(f323(f237(a1),f323(f73(a1),f323(f323(f22(a1),f323(x100682,f323(f323(f78(a865),f758(x100681,x100682,x100683,x100684)),f76(a865)))),f323(x100682,f758(x100681,x100682,x100683,x100684))))),f76(a1)))+~P101(f323(f323(f238(a865),x100684),x100683))+~P101(f323(f323(f237(a1),f323(x100682,x100684)),x100681))+P101(f323(f323(f237(a865),f757(x100681,x100682,x100683,x100684)),x100683))
% 188.07/187.98 [7163]~P64(x71631)+P101(f323(f323(f238(x71631),x71632),f2(x71631)))+~P101(f323(f323(f237(x71631),x71633),f2(x71631)))+P101(f323(f323(f238(x71631),f2(x71631)),x71632))+P101(f323(f323(f237(x71631),x71633),f323(f323(f281(x71631),x71634),x71632)))
% 188.07/187.98 [7164]~P64(x71641)+P101(f323(f323(f238(x71641),x71642),f2(x71641)))+~P101(f323(f323(f238(x71641),x71643),f2(x71641)))+P101(f323(f323(f238(x71641),f2(x71641)),x71642))+P101(f323(f323(f238(x71641),x71643),f323(f323(f281(x71641),x71644),x71642)))
% 188.07/187.98 [7409]~P64(x74091)+P101(f323(f323(f237(x74091),x74092),f2(x74091)))+P101(f323(f323(f238(x74091),x74093),f2(x74091)))+P101(f323(f323(f238(x74091),f2(x74091)),x74093))+~P101(f323(f323(f237(x74091),x74092),f323(f323(f281(x74091),x74094),x74093)))
% 188.07/187.98 [7410]~P64(x74101)+P101(f323(f323(f238(x74101),x74102),f2(x74101)))+P101(f323(f323(f238(x74101),x74103),f2(x74101)))+P101(f323(f323(f238(x74101),f2(x74101)),x74103))+~P101(f323(f323(f238(x74101),x74102),f323(f323(f281(x74101),x74104),x74103)))
% 188.07/187.98 [7527]E(x75271,x75272)+~E(f323(f323(f158(x75273),x75274),x75271),f323(f323(f158(x75273),x75274),x75272))+~P101(f323(f130(x75273),x75274))+~P101(f323(f323(f238(a865),x75272),f323(f189(f866(x75273)),x75274)))+~P101(f323(f323(f238(a865),x75271),f323(f189(f866(x75273)),x75274)))
% 188.07/187.98 [7892]~P64(x78921)+~P101(f323(f323(f237(x78921),x78923),f2(x78921)))+P101(f323(f323(f238(x78921),f2(x78921)),x78922))+~P101(f323(f323(f237(x78921),x78924),f323(f323(f79(x78921),x78923),x78922)))+P101(f323(f323(f237(x78921),x78923),f323(f323(f281(x78921),x78924),x78922)))
% 188.07/187.98 [7893]~P64(x78931)+~P101(f323(f323(f238(x78931),x78933),f2(x78931)))+P101(f323(f323(f238(x78931),f2(x78931)),x78932))+~P101(f323(f323(f238(x78931),x78934),f323(f323(f79(x78931),x78933),x78932)))+P101(f323(f323(f238(x78931),x78933),f323(f323(f281(x78931),x78934),x78932)))
% 188.07/187.98 [7894]~P64(x78941)+~P101(f323(f323(f238(x78941),x78942),f2(x78941)))+P101(f323(f323(f238(x78941),f2(x78941)),x78942))+~P101(f323(f323(f237(x78941),x78944),f323(f323(f79(x78941),x78943),x78942)))+P101(f323(f323(f237(x78941),x78943),f323(f323(f281(x78941),x78944),x78942)))
% 188.07/187.98 [7895]~P64(x78951)+~P101(f323(f323(f238(x78951),x78952),f2(x78951)))+P101(f323(f323(f238(x78951),f2(x78951)),x78952))+~P101(f323(f323(f237(x78951),x78954),f323(f323(f281(x78951),x78953),x78952)))+P101(f323(f323(f237(x78951),x78953),f323(f323(f79(x78951),x78954),x78952)))
% 188.07/187.98 [7896]~P64(x78961)+~P101(f323(f323(f238(x78961),x78962),f2(x78961)))+P101(f323(f323(f238(x78961),f2(x78961)),x78962))+~P101(f323(f323(f238(x78961),x78964),f323(f323(f79(x78961),x78963),x78962)))+P101(f323(f323(f238(x78961),x78963),f323(f323(f281(x78961),x78964),x78962)))
% 188.07/187.98 [7897]~P64(x78971)+~P101(f323(f323(f238(x78971),x78972),f2(x78971)))+P101(f323(f323(f238(x78971),f2(x78971)),x78972))+~P101(f323(f323(f238(x78971),x78974),f323(f323(f281(x78971),x78973),x78972)))+P101(f323(f323(f238(x78971),x78973),f323(f323(f79(x78971),x78974),x78972)))
% 188.07/187.98 [8035]~P103(x80351)+~P16(x80351,x80352)+~P101(f323(f323(f237(a865),x80353),x80354))+P101(f323(f323(f237(x80351),f323(f323(f158(x80351),x80352),x80353)),f323(f323(f158(x80351),x80352),x80354)))+~P101(f323(f323(f238(a865),x80354),f323(f189(f866(x80351)),x80352)))
% 188.07/187.98 [8084]~P119(x80841)+~P101(f323(f323(f237(x80841),x80842),f76(x80841)))+~P101(f323(f323(f237(x80841),f2(x80841)),x80842))+~P101(f323(f323(f237(a865),x80844),x80843))+P101(f323(f323(f237(x80841),f323(f323(f248(x80841),x80842),x80843)),f323(f323(f248(x80841),x80842),x80844)))
% 188.07/187.98 [8085]~P119(x80851)+~P101(f323(f323(f238(x80851),x80852),f76(x80851)))+~P101(f323(f323(f238(x80851),f2(x80851)),x80852))+~P101(f323(f323(f238(a865),x80854),x80853))+P101(f323(f323(f238(x80851),f323(f323(f248(x80851),x80852),x80853)),f323(f323(f248(x80851),x80852),x80854)))
% 188.07/187.98 [8086]~P119(x80861)+~P101(f323(f323(f237(x80861),f2(x80861)),x80862))+~P101(f323(f323(f238(a865),f2(a865)),x80863))+~P101(f323(f323(f238(x80861),x80862),x80864))+P101(f323(f323(f238(x80861),f323(f323(f248(x80861),x80862),x80863)),f323(f323(f248(x80861),x80864),x80863)))
% 188.07/187.98 [8105]~P103(x81051)+~P16(x81051,f323(f162(x81051),x81052))+~P101(f323(f323(f237(a865),x81054),x81053))+P101(f323(f323(f237(x81051),f323(f323(f158(x81051),x81052),x81053)),f323(f323(f158(x81051),x81052),x81054)))+~P101(f323(f323(f238(a865),x81053),f323(f189(f866(x81051)),x81052)))
% 188.07/187.98 [8356]~P64(x83561)+~P101(f323(f323(f237(x83561),x83562),f2(x83561)))+~P101(f323(f323(f237(x83561),x83563),x83564))+~P101(f323(f323(f238(x83561),f2(x83561)),f323(f323(f79(x83561),x83563),x83564)))+P101(f323(f323(f237(x83561),f323(f323(f281(x83561),x83562),x83563)),f323(f323(f281(x83561),x83562),x83564)))
% 188.07/187.98 [8357]~P65(x83571)+~P101(f323(f323(f238(x83571),x83572),f2(x83571)))+~P101(f323(f323(f238(x83571),x83573),x83574))+~P101(f323(f323(f238(x83571),f2(x83571)),f323(f323(f79(x83571),x83573),x83574)))+P101(f323(f323(f238(x83571),f323(f323(f281(x83571),x83572),x83573)),f323(f323(f281(x83571),x83572),x83574)))
% 188.07/187.98 [8367]~P65(x83671)+~P101(f323(f323(f237(x83671),x83674),x83673))+~P101(f323(f323(f237(x83671),f2(x83671)),x83672))+~P101(f323(f323(f238(x83671),f2(x83671)),f323(f323(f79(x83671),x83673),x83674)))+P101(f323(f323(f237(x83671),f323(f323(f281(x83671),x83672),x83673)),f323(f323(f281(x83671),x83672),x83674)))
% 188.07/187.98 [8368]~P65(x83681)+~P101(f323(f323(f238(x83681),x83684),x83683))+~P101(f323(f323(f238(x83681),f2(x83681)),x83682))+~P101(f323(f323(f238(x83681),f2(x83681)),f323(f323(f79(x83681),x83683),x83684)))+P101(f323(f323(f238(x83681),f323(f323(f281(x83681),x83682),x83683)),f323(f323(f281(x83681),x83682),x83684)))
% 188.07/187.98 [8464]P101(f323(x84641,x84642))+~P101(f323(f59(x84644),x84642))+P101(f323(x84641,f835(x84641,x84643,x84642,x84644)))+~P101(f323(x84641,f188(f872(x84644,a860))))+~P101(f323(f323(f237(f872(x84644,a860)),x84642),x84643))
% 188.07/187.98 [8473]P101(f323(x84731,x84732))+P101(f323(f59(x84733),f835(x84731,x84734,x84732,x84733)))+~P101(f323(f59(x84733),x84732))+~P101(f323(x84731,f188(f872(x84733,a860))))+~P101(f323(f323(f237(f872(x84733,a860)),x84732),x84734))
% 188.07/187.98 [8745]E(f323(f323(f78(a1),f412(x87451,x87452,x87453,x87454)),f413(x87451,x87452,x87453,x87454)),x87454)+~P101(f323(f323(f238(a1),f2(a1)),x87453))+~P101(f323(f323(f238(a1),x87452),x87454))+~P101(f323(f323(f325(a1),x87452),x87451))+P101(f323(f323(f238(a1),x87452),f323(f323(f22(a1),x87454),x87453)))
% 188.07/187.98 [8956]~P101(f323(f323(f238(a1),f2(a1)),x89563))+~P101(f323(f323(f238(a1),x89562),x89564))+~P101(f323(f323(f325(a1),x89562),x89561))+P101(f323(f323(f325(a1),f412(x89561,x89562,x89563,x89564)),x89561))+P101(f323(f323(f238(a1),x89562),f323(f323(f22(a1),x89564),x89563)))
% 188.07/187.98 [8967]P101(f323(x89671,x89672))+~P101(f323(f59(x89673),x89672))+P101(f323(f323(f325(x89673),f836(x89671,x89674,x89672,x89673)),x89674))+~P101(f323(x89671,f188(f872(x89673,a860))))+~P101(f323(f323(f237(f872(x89673,a860)),x89672),x89674))
% 188.07/187.98 [8984]E(f323(f323(f78(a1),f400(x89841,x89842,x89843,x89844)),f401(x89841,x89842,x89843,x89844)),x89844)+~P101(f323(f323(f238(a1),f2(a1)),x89843))+~P101(f323(f323(f237(a1),x89842),x89844))+P101(f323(f323(f237(a1),x89842),f323(f323(f22(a1),x89844),x89843)))+~P101(f323(f323(f325(a1),f323(f323(f22(a1),x89842),f76(a1))),x89841))
% 188.07/187.98 [9040]~P101(f323(f323(f238(a1),f2(a1)),x90403))+~P101(f323(f323(f238(a1),x90401),x90402))+~P101(f323(f323(f325(a1),x90401),x90404))+P101(f323(f323(f325(a1),f413(x90404,x90401,x90403,x90402)),f294(a1,f76(a1),x90403)))+P101(f323(f323(f238(a1),x90401),f323(f323(f22(a1),x90402),x90403)))
% 188.07/187.98 [9133]~P101(f323(f323(f238(a1),f2(a1)),x91333))+~P101(f323(f323(f237(a1),x91332),x91334))+P101(f323(f323(f325(a1),f400(x91331,x91332,x91333,x91334)),x91331))+P101(f323(f323(f237(a1),x91332),f323(f323(f22(a1),x91334),x91333)))+~P101(f323(f323(f325(a1),f323(f323(f22(a1),x91332),f76(a1))),x91331))
% 188.07/187.98 [9178]~P101(f323(f323(f238(a1),f2(a1)),x91783))+~P101(f323(f323(f237(a1),x91781),x91782))+P101(f323(f323(f325(a1),f401(x91784,x91781,x91783,x91782)),f294(a1,f76(a1),x91783)))+P101(f323(f323(f237(a1),x91781),f323(f323(f22(a1),x91782),x91783)))+~P101(f323(f323(f325(a1),f323(f323(f22(a1),x91781),f76(a1))),x91784))
% 188.07/187.98 [9406]P101(f323(x94061,x94062))+~P101(f323(f323(f325(x94063),f836(x94061,x94064,x94062,x94063)),f835(x94061,x94064,x94062,x94063)))+~P101(f323(f59(x94063),x94062))+~P101(f323(x94061,f188(f872(x94063,a860))))+~P101(f323(f323(f237(f872(x94063,a860)),x94062),x94064))
% 188.07/187.98 [9625]P101(f323(x96251,x96252))+~P101(f323(f59(x96253),x96252))+~P101(f323(x96251,f323(f323(f301(x96253),f836(x96251,x96254,x96252,x96253)),f835(x96251,x96254,x96252,x96253))))+~P101(f323(x96251,f188(f872(x96253,a860))))+~P101(f323(f323(f237(f872(x96253,a860)),x96252),x96254))
% 188.07/187.98 [7663]~P64(x76631)+P101(f323(f323(f238(x76631),x76632),f2(x76631)))+~P101(f323(f323(f237(x76631),f2(x76631)),x76634))+P101(f323(f323(f238(x76631),f2(x76631)),x76632))+P101(f323(f323(f237(x76631),f323(f323(f281(x76631),x76633),x76632)),x76634))
% 188.07/187.98 [7664]~P64(x76641)+P101(f323(f323(f238(x76641),x76642),f2(x76641)))+P101(f323(f323(f238(x76641),f2(x76641)),x76642))+~P101(f323(f323(f238(x76641),f2(x76641)),x76644))+P101(f323(f323(f238(x76641),f323(f323(f281(x76641),x76643),x76642)),x76644))
% 188.07/187.98 [7944]~P101(f323(f323(f237(a1),x79444),f2(a1)))+~E(x79442,f323(f323(f78(a1),f323(f323(f79(a1),x79441),x79443)),x79444))+P101(f323(f323(f238(a1),f2(a1)),x79441))+~P101(f323(f323(f238(a1),x79441),x79444))+P101(f323(f46(x79442,x79441),f323(f323(f258(a1,a1),x79443),x79444)))
% 188.07/187.98 [7978]~P101(f323(x79781,x79784))+P101(f323(x79781,f428(x79782,x79781,x79783)))+~P101(f323(f323(f237(a1),f2(a1)),x79782))+~P101(f323(f323(f238(a1),f2(a1)),x79783))+P101(f323(x79781,f323(f323(f22(a1),x79784),f323(f323(f79(a1),x79782),x79783))))
% 188.07/187.98 [7979]~P101(f323(x79791,x79794))+P101(f323(x79791,f431(x79792,x79791,x79793)))+~P101(f323(f323(f237(a1),f2(a1)),x79792))+~P101(f323(f323(f238(a1),f2(a1)),x79793))+P101(f323(x79791,f323(f323(f78(a1),x79794),f323(f323(f79(a1),x79792),x79793))))
% 188.07/187.98 [7980]~P64(x79801)+P101(f323(f323(f238(x79801),x79802),f2(x79801)))+P101(f323(f323(f238(x79801),f2(x79801)),x79802))+P101(f323(f323(f237(x79801),f2(x79801)),x79803))+~P101(f323(f323(f237(x79801),f323(f323(f281(x79801),x79804),x79802)),x79803))
% 188.07/187.98 [7981]~P64(x79811)+P101(f323(f323(f238(x79811),x79812),f2(x79811)))+P101(f323(f323(f238(x79811),f2(x79811)),x79812))+P101(f323(f323(f238(x79811),f2(x79811)),x79813))+~P101(f323(f323(f238(x79811),f323(f323(f281(x79811),x79814),x79812)),x79813))
% 188.07/187.98 [8030]~E(x80301,f323(f323(f78(a1),f323(f323(f79(a1),x80302),x80303)),x80304))+~P101(f323(f323(f237(a1),f2(a1)),x80304))+~P101(f323(f323(f238(a1),f2(a1)),x80302))+~P101(f323(f323(f238(a1),x80304),x80302))+P101(f323(f46(x80301,x80302),f323(f323(f258(a1,a1),x80303),x80304)))
% 188.07/187.98 [8148]~P64(x81481)+P101(f323(f323(f238(x81481),x81482),f2(x81481)))+~P101(f323(f323(f237(x81481),f2(x81481)),x81484))+~P101(f323(f323(f237(x81481),x81483),f323(f323(f79(x81481),x81484),x81482)))+P101(f323(f323(f237(x81481),f323(f323(f281(x81481),x81483),x81482)),x81484))
% 188.07/187.98 [8149]~P64(x81491)+P101(f323(f323(f238(x81491),x81492),f2(x81491)))+~P101(f323(f323(f238(x81491),f2(x81491)),x81494))+~P101(f323(f323(f238(x81491),x81493),f323(f323(f79(x81491),x81494),x81492)))+P101(f323(f323(f238(x81491),f323(f323(f281(x81491),x81493),x81492)),x81494))
% 188.07/187.98 [8233]~P64(x82331)+P101(f323(f323(f238(x82331),x82332),f2(x82331)))+~P101(f323(f323(f237(x82331),x82333),f2(x82331)))+P101(f323(f323(f237(x82331),x82333),f323(f323(f281(x82331),x82334),x82332)))+~P101(f323(f323(f237(x82331),f323(f323(f79(x82331),x82333),x82332)),x82334))
% 188.07/187.98 [8234]~P64(x82341)+P101(f323(f323(f238(x82341),x82342),f2(x82341)))+~P101(f323(f323(f238(x82341),x82343),f2(x82341)))+P101(f323(f323(f238(x82341),x82343),f323(f323(f281(x82341),x82344),x82342)))+~P101(f323(f323(f238(x82341),f323(f323(f79(x82341),x82343),x82342)),x82344))
% 188.07/187.98 [8390]~P64(x83901)+~P101(f323(f323(f238(x83901),x83902),f2(x83901)))+P101(f323(f323(f238(x83901),f2(x83901)),x83902))+~P101(f323(f323(f237(x83901),f323(f323(f281(x83901),x83904),x83902)),x83903))+P101(f323(f323(f237(x83901),f323(f323(f79(x83901),x83903),x83902)),x83904))
% 188.07/187.98 [8391]~P64(x83911)+~P101(f323(f323(f238(x83911),x83912),f2(x83911)))+P101(f323(f323(f238(x83911),f2(x83911)),x83912))+~P101(f323(f323(f237(x83911),f323(f323(f79(x83911),x83914),x83912)),x83913))+P101(f323(f323(f237(x83911),f323(f323(f281(x83911),x83913),x83912)),x83914))
% 188.07/187.98 [8392]~P64(x83921)+~P101(f323(f323(f238(x83921),x83922),f2(x83921)))+P101(f323(f323(f238(x83921),f2(x83921)),x83922))+~P101(f323(f323(f238(x83921),f323(f323(f281(x83921),x83924),x83922)),x83923))+P101(f323(f323(f238(x83921),f323(f323(f79(x83921),x83923),x83922)),x83924))
% 188.07/187.98 [8393]~P64(x83931)+~P101(f323(f323(f238(x83931),x83932),f2(x83931)))+P101(f323(f323(f238(x83931),f2(x83931)),x83932))+~P101(f323(f323(f238(x83931),f323(f323(f79(x83931),x83934),x83932)),x83933))+P101(f323(f323(f238(x83931),f323(f323(f281(x83931),x83933),x83932)),x83934))
% 188.07/187.98 [8410]~P64(x84101)+~P101(f323(f323(f237(x84101),f2(x84101)),x84104))+P101(f323(f323(f238(x84101),f2(x84101)),x84102))+~P101(f323(f323(f237(x84101),f323(f323(f79(x84101),x84104),x84102)),x84103))+P101(f323(f323(f237(x84101),f323(f323(f281(x84101),x84103),x84102)),x84104))
% 188.07/187.98 [8411]~P64(x84111)+~P101(f323(f323(f238(x84111),f2(x84111)),x84114))+P101(f323(f323(f238(x84111),f2(x84111)),x84112))+~P101(f323(f323(f238(x84111),f323(f323(f79(x84111),x84114),x84112)),x84113))+P101(f323(f323(f238(x84111),f323(f323(f281(x84111),x84113),x84112)),x84114))
% 188.07/187.98 [8481]~P64(x84811)+~P101(f323(f323(f238(x84811),x84814),f2(x84811)))+~P101(f323(f323(f237(x84811),x84813),f323(f323(f79(x84811),x84812),x84814)))+P101(f323(f323(f237(x84811),x84812),f323(f323(f281(x84811),x84813),x84814)))+~P101(f323(f323(f237(x84811),f323(f323(f79(x84811),x84812),x84814)),x84813))
% 188.07/187.98 [8482]~P64(x84821)+~P101(f323(f323(f237(x84821),x84822),f2(x84821)))+~P101(f323(f323(f237(x84821),x84823),f323(f323(f79(x84821),x84822),x84824)))+P101(f323(f323(f237(x84821),x84822),f323(f323(f281(x84821),x84823),x84824)))+~P101(f323(f323(f237(x84821),f323(f323(f79(x84821),x84822),x84824)),x84823))
% 188.07/187.98 [8483]~P64(x84831)+~P101(f323(f323(f238(x84831),x84834),f2(x84831)))+~P101(f323(f323(f238(x84831),x84833),f323(f323(f79(x84831),x84832),x84834)))+P101(f323(f323(f238(x84831),x84832),f323(f323(f281(x84831),x84833),x84834)))+~P101(f323(f323(f238(x84831),f323(f323(f79(x84831),x84832),x84834)),x84833))
% 188.07/187.98 [8484]~P64(x84841)+~P101(f323(f323(f238(x84841),x84842),f2(x84841)))+~P101(f323(f323(f238(x84841),x84843),f323(f323(f79(x84841),x84842),x84844)))+P101(f323(f323(f238(x84841),x84842),f323(f323(f281(x84841),x84843),x84844)))+~P101(f323(f323(f238(x84841),f323(f323(f79(x84841),x84842),x84844)),x84843))
% 188.07/187.98 [8608]~P64(x86081)+~P101(f323(f323(f238(x86081),x86083),f2(x86081)))+~P101(f323(f323(f237(x86081),x86082),f323(f323(f79(x86081),x86084),x86083)))+~P101(f323(f323(f237(x86081),f323(f323(f79(x86081),x86084),x86083)),x86082))+P101(f323(f323(f237(x86081),f323(f323(f281(x86081),x86082),x86083)),x86084))
% 188.07/187.98 [8609]~P64(x86091)+~P101(f323(f323(f238(x86091),x86093),f2(x86091)))+~P101(f323(f323(f238(x86091),x86092),f323(f323(f79(x86091),x86094),x86093)))+~P101(f323(f323(f238(x86091),f323(f323(f79(x86091),x86094),x86093)),x86092))+P101(f323(f323(f238(x86091),f323(f323(f281(x86091),x86092),x86093)),x86094))
% 188.07/187.98 [8627]~P64(x86271)+~P101(f323(f323(f237(x86271),f2(x86271)),x86274))+~P101(f323(f323(f237(x86271),x86272),f323(f323(f79(x86271),x86274),x86273)))+~P101(f323(f323(f237(x86271),f323(f323(f79(x86271),x86274),x86273)),x86272))+P101(f323(f323(f237(x86271),f323(f323(f281(x86271),x86272),x86273)),x86274))
% 188.07/187.98 [8628]~P64(x86281)+~P101(f323(f323(f238(x86281),f2(x86281)),x86284))+~P101(f323(f323(f238(x86281),x86282),f323(f323(f79(x86281),x86284),x86283)))+~P101(f323(f323(f238(x86281),f323(f323(f79(x86281),x86284),x86283)),x86282))+P101(f323(f323(f238(x86281),f323(f323(f281(x86281),x86282),x86283)),x86284))
% 188.07/187.98 [8807]E(f323(f323(f22(a1),f415(x88071,x88072,x88073,x88074)),f416(x88071,x88072,x88073,x88074)),x88074)+~P101(f323(f323(f238(a1),f2(a1)),x88073))+~P101(f323(f323(f325(a1),x88072),x88071))+~P101(f323(f323(f238(a1),x88074),x88072))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x88074),x88073)),x88072))
% 188.07/187.98 [8886]~P101(f323(x88861,x88862))+~P101(f323(f323(f237(a1),f2(a1)),x88863))+~P101(f323(f323(f238(a1),f2(a1)),x88864))+~P101(f323(x88861,f323(f323(f22(a1),f428(x88863,x88861,x88864)),x88864)))+P101(f323(x88861,f323(f323(f22(a1),x88862),f323(f323(f79(a1),x88863),x88864))))
% 188.07/187.98 [8887]~P101(f323(x88871,x88872))+~P101(f323(f323(f237(a1),f2(a1)),x88873))+~P101(f323(f323(f238(a1),f2(a1)),x88874))+~P101(f323(x88871,f323(f323(f78(a1),f431(x88873,x88871,x88874)),x88874)))+P101(f323(x88871,f323(f323(f78(a1),x88872),f323(f323(f79(a1),x88873),x88874))))
% 188.07/187.98 [9033]~P101(f323(f323(f238(a1),f2(a1)),x90333))+~P101(f323(f323(f325(a1),x90332),x90331))+~P101(f323(f323(f238(a1),x90334),x90332))+P101(f323(f323(f325(a1),f415(x90331,x90332,x90333,x90334)),x90331))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x90334),x90333)),x90332))
% 188.07/187.98 [9054]E(f323(f323(f22(a1),f402(x90541,x90542,x90543,x90544)),f403(x90541,x90542,x90543,x90544)),x90544)+~P101(f323(f323(f238(a1),f2(a1)),x90543))+~P101(f323(f323(f237(a1),x90544),x90542))+~P101(f323(f323(f325(a1),f323(f323(f78(a1),x90542),f76(a1))),x90541))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x90544),x90543)),x90542))
% 188.07/187.98 [9081]~P101(f323(f323(f238(a1),f2(a1)),x90812))+~P101(f323(f323(f325(a1),x90813),x90814))+~P101(f323(f323(f238(a1),x90811),x90813))+P101(f323(f323(f325(a1),f416(x90814,x90813,x90812,x90811)),f294(a1,f76(a1),x90812)))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x90811),x90812)),x90813))
% 188.07/187.98 [9173]~P101(f323(f323(f238(a1),f2(a1)),x91733))+~P101(f323(f323(f237(a1),x91734),x91732))+P101(f323(f323(f325(a1),f402(x91731,x91732,x91733,x91734)),x91731))+~P101(f323(f323(f325(a1),f323(f323(f78(a1),x91732),f76(a1))),x91731))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x91734),x91733)),x91732))
% 188.07/187.98 [9213]~P101(f323(f323(f238(a1),f2(a1)),x92132))+~P101(f323(f323(f237(a1),x92131),x92133))+P101(f323(f323(f325(a1),f403(x92134,x92133,x92132,x92131)),f294(a1,f76(a1),x92132)))+~P101(f323(f323(f325(a1),f323(f323(f78(a1),x92133),f76(a1))),x92134))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x92131),x92132)),x92133))
% 188.07/187.98 [9499]~P38(x94991,x94993)+~P29(x94991,x94994)+P38(x94991,f323(f323(f110(f872(f871(x94991,x94991),a860)),x94992),x94993))+~P101(f323(f323(f237(f872(f871(x94991,x94991),a860)),x94992),f323(f257(f872(f871(x94991,x94991),a860),f872(f871(x94991,x94991),a860)),x94994)))+~P101(f323(f323(f237(f872(f871(x94991,x94991),a860)),x94993),f323(f261(f872(f871(x94991,x94991),a860),f872(f871(x94991,x94991),a860)),x94994)))
% 188.07/187.98 [9796]~E(f323(f519(x97961,x97964,x97963,x97962),f521(x97961,x97964,x97963,x97962)),f200(f866(a319)))+P101(f323(f323(f238(a1),f520(x97961,x97964,x97963,x97962)),f521(x97961,x97964,x97963,x97962)))+P101(f323(f323(f323(x97961,x97962),x97963),x97964))+P101(f323(f323(f323(x97961,f519(x97961,x97964,x97963,x97962)),f520(x97961,x97964,x97963,x97962)),f323(f323(f78(a1),f521(x97961,x97964,x97963,x97962)),f76(a1))))+~P101(f323(f311(f871(f872(a1,f869(f866(a319))),f871(a1,a1)),a309),f323(f323(f258(f872(a1,f869(f866(a319))),f871(a1,a1)),x97962),f323(f323(f258(a1,a1),x97963),x97964))))
% 188.07/187.98 [9895]~P20(x98952,x98954,x98953)+E(x98951,f188(f872(x98952,a860)))+~P101(f323(f59(x98952),x98951))+P101(f323(f323(f325(x98952),f323(x98953,x98951)),x98951))+~P101(f323(f323(f325(x98952),f323(f323(x98954,f814(x98951,x98953,x98954,x98952)),f816(x98951,x98953,x98954,x98952))),f323(f323(f301(x98952),f814(x98951,x98953,x98954,x98952)),f323(f323(f301(x98952),f816(x98951,x98953,x98954,x98952)),f188(f872(x98952,a860))))))
% 188.07/187.98 [9826]~P105(x98262)+~P5(x98261)+~P101(f323(f323(f237(f872(x98261,x98262)),x98263),x98264))+P101(f323(f323(f238(f872(x98261,x98262)),x98263),x98264))+~P101(f323(f55(x98261),f323(f323(f8(a860,a860,x98261),a318),f323(f323(f18(x98261,x98262,a860),f323(f323(f8(x98262,f872(x98262,a860),x98261),a320),x98263)),x98264))))
% 188.07/187.98 [9412]~P51(x94121,x94121,x94124)+P101(f323(f323(f325(f871(x94121,x94121)),f323(f323(f258(x94121,x94121),x94122),x94123)),f299(x94121,x94124)))+P101(f323(f323(f325(f871(x94121,x94121)),f323(f323(f258(x94121,x94121),x94123),x94122)),f299(x94121,x94124)))+~P101(f323(f323(f325(f871(x94121,x94121)),f323(f323(f258(x94121,x94121),x94125),x94122)),f299(x94121,x94124)))+~P101(f323(f323(f325(f871(x94121,x94121)),f323(f323(f258(x94121,x94121),x94125),x94123)),f299(x94121,x94124)))
% 188.07/187.98 [5599]E(x55991,f2(a865))+~E(f323(f35(x55992),x55995),x55991)+E(f323(f35(x55992),x55993),f323(a112,x55991))+~E(x55993,f323(f323(f301(x55992),x55994),x55995))+P101(f323(f323(f325(x55992),x55994),x55995))
% 188.07/187.98 [5723]~P63(x57232)+E(x57231,f2(x57232))+E(x57233,f2(x57232))+~E(f323(f323(f281(x57232),x57234),x57233),f323(f323(f281(x57232),x57235),x57231))+E(f323(f323(f79(x57232),x57234),x57231),f323(f323(f79(x57232),x57235),x57233))
% 188.07/187.98 [5724]~P63(x57242)+E(x57241,f2(x57242))+E(x57243,f2(x57242))+~E(f323(f323(f79(x57242),x57244),x57243),f323(f323(f79(x57242),x57245),x57241))+E(f323(f323(f281(x57242),x57244),x57241),f323(f323(f281(x57242),x57245),x57243))
% 188.07/187.98 [5790]~E(f323(f35(x57901),x57905),x57903)+~E(x57905,f188(f872(x57901,a860)))+E(f323(f35(x57901),x57902),f323(a112,x57903))+~E(x57902,f323(f323(f301(x57901),x57904),x57905))+P101(f323(f323(f325(x57901),x57904),x57905))
% 188.07/187.98 [6010]~P112(x60102)+~E(f323(x60103,x60105),f2(x60102))+E(f323(f323(f9(x60101,x60102),x60103),x60104),f2(x60102))+~P101(f323(f59(x60101),x60104))+~P101(f323(f323(f325(x60101),x60105),x60104))
% 188.07/187.98 [6374]~P103(x63743)+E(x63741,x63742)+~E(f323(f293(x63743,x63744),x63741),f323(f293(x63743,x63745),x63742))+~P101(f323(f323(f238(x63743),x63745),x63742))+~P101(f323(f323(f238(x63743),x63744),x63741))
% 188.07/187.98 [6375]~P103(x63753)+E(x63751,x63752)+~E(f323(f293(x63753,x63751),x63754),f323(f293(x63753,x63752),x63755))+~P101(f323(f323(f238(x63753),x63752),x63755))+~P101(f323(f323(f238(x63753),x63751),x63754))
% 188.07/187.98 [7426]~P103(x74261)+~P16(x74261,f323(f323(f121(x74261),x74264),x74265))+~P101(f323(f323(f325(x74261),x74263),f323(f166(x74261),x74265)))+~P101(f323(f323(f325(x74261),x74262),f323(f166(x74261),x74264)))+P101(f323(f323(f237(x74261),x74262),x74263))
% 188.07/187.98 [8517]~P105(x85171)+~P101(f323(f323(f238(f872(x85171,a860)),f294(x85171,x85175,x85172)),f294(x85171,x85174,x85173)))+~P101(f323(f323(f237(x85171),x85175),x85172))+P101(f323(f323(f238(x85171),x85172),x85173))+P101(f323(f323(f238(x85171),x85174),x85175))
% 188.07/187.98 [9938]~P19(x99382,x99385,x99383)+E(x99381,f188(f872(x99382,a860)))+~E(f323(f323(x99385,f323(x99384,f849(x99381,x99384,x99383,x99385,x99382))),f323(x99384,f850(x99381,x99384,x99383,x99385,x99382))),f323(x99384,f323(f323(x99385,f849(x99381,x99384,x99383,x99385,x99382)),f850(x99381,x99384,x99383,x99385,x99382))))+E(f323(x99383,f323(f302(x99382,x99382,x99384),x99381)),f323(x99384,f323(x99383,x99381)))+~P101(f323(f59(x99382),x99381))
% 188.07/187.98 [6371]~P20(x63712,x63715,x63713)+E(x63711,f188(f872(x63712,a860)))+~P101(f323(f59(x63712),x63711))+E(f323(x63713,f323(f323(f301(x63712),x63714),x63711)),f323(f323(x63715,x63714),f323(x63713,x63711)))+P101(f323(f323(f325(x63712),x63714),x63711))
% 188.07/187.98 [7187]~P19(x71872,x71873,x71874)+E(f323(f323(x71873,f323(x71874,x71871)),f323(x71874,x71875)),f323(x71874,x71875))+E(x71871,f188(f872(x71872,a860)))+~P101(f323(f59(x71872),x71875))+~P101(f323(f323(f237(f872(x71872,a860)),x71871),x71875))
% 188.07/187.98 [7402]~P5(x74024)+~P92(x74025)+E(f323(x74021,x74022),f323(x74023,x74022))+~P101(f323(f323(f325(x74024),x74022),f323(f166(x74024),f53(x74024))))+~P101(f323(f323(f89(f872(x74024,x74025)),x74021),x74023))
% 188.07/187.98 [7560]~P20(x75604,x75605,x75601)+E(f323(x75601,x75602),x75603)+~P101(f323(f59(x75604),x75602))+~E(f323(f323(f22(f872(x75604,a860)),x75602),f323(f323(f301(x75604),x75603),f188(f872(x75604,a860)))),f188(f872(x75604,a860)))+~P101(f323(f323(f325(x75604),x75603),x75602))
% 188.07/187.98 [7646]E(x76461,x76462)+~E(f323(f189(f866(x76463)),x76462),f323(f189(f866(x76464)),x76465))+~E(f323(f189(f866(x76463)),x76461),f323(f189(f866(x76464)),x76465))+~E(f323(f179(x76464,x76463),f323(f323(f175(x76464,x76463),x76465),x76461)),f323(f179(x76464,x76463),f323(f323(f175(x76464,x76463),x76465),x76462)))+~P101(f323(f130(x76464),x76465))
% 188.07/187.98 [8488]E(x84881,x84882)+~P9(x84883,x84884,x84885)+E(f323(f323(f101(f872(x84883,a860)),x84881),x84882),f188(f872(x84883,a860)))+~P101(f323(f323(f325(f872(x84883,a860)),x84882),f323(f323(f58(x84883),x84884),x84885)))+~P101(f323(f323(f325(f872(x84883,a860)),x84881),f323(f323(f58(x84883),x84884),x84885)))
% 188.07/187.98 [9295]~P72(x92952)+~E(f323(x92953,f434(x92953,x92954,x92955,x92951,x92952)),f2(x92952))+E(f323(f323(f6(x92951,x92952),x92953),x92954),f323(f323(f6(x92951,x92952),x92953),x92955))+~P101(f323(f59(x92951),x92955))+~P101(f323(f323(f237(f872(x92951,a860)),x92954),x92955))
% 188.07/187.98 [9296]~P72(x92962)+~E(f323(x92963,f435(x92963,x92964,x92965,x92961,x92962)),f2(x92962))+E(f323(f323(f6(x92961,x92962),x92963),x92964),f323(f323(f6(x92961,x92962),x92963),x92965))+~P101(f323(f59(x92961),x92965))+~P101(f323(f323(f237(f872(x92961,a860)),x92964),x92965))
% 188.07/187.98 [9297]~P68(x92972)+~E(f323(x92973,f478(x92973,x92974,x92975,x92971,x92972)),f76(x92972))+E(f323(f323(f9(x92971,x92972),x92973),x92974),f323(f323(f9(x92971,x92972),x92973),x92975))+~P101(f323(f59(x92971),x92975))+~P101(f323(f323(f237(f872(x92971,a860)),x92974),x92975))
% 188.07/187.98 [9298]~P68(x92982)+~E(f323(x92983,f480(x92983,x92984,x92985,x92981,x92982)),f76(x92982))+E(f323(f323(f9(x92981,x92982),x92983),x92984),f323(f323(f9(x92981,x92982),x92983),x92985))+~P101(f323(f59(x92981),x92985))+~P101(f323(f323(f237(f872(x92981,a860)),x92984),x92985))
% 188.07/187.98 [9775]~P84(x97751)+~P101(f323(f59(x97752),x97755))+~P101(f323(f323(f237(x97751),f2(x97751)),f323(x97753,f363(x97753,x97754,x97755,x97752,x97751))))+P101(f323(f323(f237(x97751),f323(f323(f6(x97752,x97751),x97753),x97754)),f323(f323(f6(x97752,x97751),x97753),x97755)))+~P101(f323(f323(f237(f872(x97752,a860)),x97754),x97755))
% 188.07/187.98 [7423]E(x74231,f2(a865))+P101(f323(x74232,x74233))+~E(x74234,f323(f323(f78(a865),f323(f323(f79(a865),x74231),x74233)),x74235))+~P101(f323(f323(f238(a865),x74235),x74231))+~P101(f323(x74232,f323(f323(f36(a865),x74234),x74231)))
% 188.07/187.98 [7501]E(x75011,f2(a865))+P101(f323(x75012,x75013))+~P101(f323(x75012,f42(a865,x75014,x75011)))+~E(x75014,f323(f323(f78(a865),f323(f323(f79(a865),x75011),x75015)),x75013))+~P101(f323(f323(f238(a865),x75013),x75011))
% 188.07/187.98 [7790]~P63(x77903)+E(f323(x77901,x77902),f2(x77903))+~P101(f323(f59(x77904),x77905))+E(f323(f323(f9(x77904,x77903),x77901),f323(f323(f22(f872(x77904,a860)),x77905),f323(f323(f301(x77904),x77902),f188(f872(x77904,a860))))),f323(f323(f9(x77904,x77903),x77901),x77905))+P101(f323(f323(f325(x77904),x77902),x77905))
% 188.07/187.98 [8190]~P72(x81901)+~P101(f323(f59(x81902),x81905))+~P101(f323(f59(x81902),x81904))+~E(f323(f323(f101(f872(x81902,a860)),x81904),x81905),f188(f872(x81902,a860)))+E(f323(f323(f78(x81901),f323(f323(f6(x81902,x81901),x81903),x81904)),f323(f323(f6(x81902,x81901),x81903),x81905)),f323(f323(f6(x81902,x81901),x81903),f323(f323(f110(f872(x81902,a860)),x81904),x81905)))
% 188.07/187.98 [8192]~P68(x81921)+~P101(f323(f59(x81922),x81925))+~P101(f323(f59(x81922),x81924))+~E(f323(f323(f101(f872(x81922,a860)),x81924),x81925),f188(f872(x81922,a860)))+E(f323(f323(f79(x81921),f323(f323(f9(x81922,x81921),x81923),x81924)),f323(f323(f9(x81922,x81921),x81923),x81925)),f323(f323(f9(x81922,x81921),x81923),f323(f323(f110(f872(x81922,a860)),x81924),x81925)))
% 188.07/187.98 [8288]~P63(x82883)+E(f323(x82881,x82882),f2(x82883))+~P101(f323(f59(x82884),x82885))+E(f323(f323(f9(x82884,x82883),x82881),f323(f323(f22(f872(x82884,a860)),x82885),f323(f323(f301(x82884),x82882),f188(f872(x82884,a860))))),f323(f323(f281(x82883),f323(f323(f9(x82884,x82883),x82881),x82885)),f323(x82881,x82882)))+~P101(f323(f323(f325(x82884),x82882),x82885))
% 188.07/187.98 [9009]~P9(x90091,x90095,x90094)+~E(f323(f323(f58(x90091),f323(f323(f301(x90091),x90092),f188(f872(x90091,a860)))),x90094),f323(f323(f58(x90091),f323(f323(f301(x90091),x90093),f188(f872(x90091,a860)))),x90094))+~P101(f323(f323(f325(x90091),x90093),x90095))+~P101(f323(f323(f325(x90091),x90092),x90095))+P101(f323(f323(f325(f871(x90091,x90091)),f323(f323(f258(x90091,x90091),x90092),x90093)),x90094))
% 188.07/187.98 [9032]~P9(x90321,x90325,x90323)+E(f323(f323(f58(x90321),f323(f323(f301(x90321),x90322),f188(f872(x90321,a860)))),x90323),f323(f323(f58(x90321),f323(f323(f301(x90321),x90324),f188(f872(x90321,a860)))),x90323))+~P101(f323(f323(f325(x90321),x90324),x90325))+~P101(f323(f323(f325(x90321),x90322),x90325))+~P101(f323(f323(f325(f871(x90321,x90321)),f323(f323(f258(x90321,x90321),x90322),x90324)),x90323))
% 188.07/187.98 [9324]~P68(x93241)+~P101(f323(f59(x93242),x93245))+~P101(f323(f59(x93242),x93244))+~E(f323(f323(f101(f872(x93242,a860)),x93244),x93245),f188(f872(x93242,a860)))+E(f323(f323(f79(x93241),f323(f323(f323(f63(x93241,x93242,f79(x93241)),x93243),f76(x93241)),x93244)),f323(f323(f323(f63(x93241,x93242,f79(x93241)),x93243),f76(x93241)),x93245)),f323(f323(f323(f63(x93241,x93242,f79(x93241)),x93243),f76(x93241)),f323(f323(f110(f872(x93242,a860)),x93244),x93245)))
% 188.07/187.98 [9333]~P72(x93331)+~E(f323(x93333,f362(x93333,x93335,x93334,x93332,x93331)),f2(x93331))+~P101(f323(f59(x93332),x93334))+~P101(f323(f59(x93332),x93335))+E(f323(f323(f78(x93331),f323(f323(f6(x93332,x93331),x93333),x93334)),f323(f323(f6(x93332,x93331),x93333),x93335)),f323(f323(f6(x93332,x93331),x93333),f323(f323(f110(f872(x93332,a860)),x93334),x93335)))
% 188.07/187.98 [9334]~P72(x93341)+~E(f323(x93343,f364(x93343,x93345,x93344,x93342,x93341)),f2(x93341))+~P101(f323(f59(x93342),x93344))+~P101(f323(f59(x93342),x93345))+E(f323(f323(f78(x93341),f323(f323(f6(x93342,x93341),x93343),x93344)),f323(f323(f6(x93342,x93341),x93343),x93345)),f323(f323(f6(x93342,x93341),x93343),f323(f323(f110(f872(x93342,a860)),x93344),x93345)))
% 188.07/187.98 [9335]~P68(x93351)+~E(f323(x93353,f472(x93353,x93355,x93354,x93352,x93351)),f76(x93351))+~P101(f323(f59(x93352),x93354))+~P101(f323(f59(x93352),x93355))+E(f323(f323(f79(x93351),f323(f323(f9(x93352,x93351),x93353),x93354)),f323(f323(f9(x93352,x93351),x93353),x93355)),f323(f323(f9(x93352,x93351),x93353),f323(f323(f110(f872(x93352,a860)),x93354),x93355)))
% 188.07/187.98 [9336]~P68(x93361)+~E(f323(x93363,f473(x93363,x93365,x93364,x93362,x93361)),f76(x93361))+~P101(f323(f59(x93362),x93364))+~P101(f323(f59(x93362),x93365))+E(f323(f323(f79(x93361),f323(f323(f9(x93362,x93361),x93363),x93364)),f323(f323(f9(x93362,x93361),x93363),x93365)),f323(f323(f9(x93362,x93361),x93363),f323(f323(f110(f872(x93362,a860)),x93364),x93365)))
% 188.07/187.98 [9544]~P68(x95441)+~E(f323(x95443,f848(x95443,x95445,x95444,x95442,x95441)),f76(x95441))+~P101(f323(f59(x95442),x95444))+~P101(f323(f59(x95442),x95445))+E(f323(f323(f79(x95441),f323(f323(f323(f63(x95441,x95442,f79(x95441)),x95443),f76(x95441)),x95444)),f323(f323(f323(f63(x95441,x95442,f79(x95441)),x95443),f76(x95441)),x95445)),f323(f323(f323(f63(x95441,x95442,f79(x95441)),x95443),f76(x95441)),f323(f323(f110(f872(x95442,a860)),x95444),x95445)))
% 188.07/187.98 [9653]~P72(x96532)+E(f323(f323(f6(x96531,x96532),x96533),x96534),f323(f323(f6(x96531,x96532),x96533),x96535))+~P101(f323(f59(x96531),x96535))+~P101(f323(f323(f237(f872(x96531,a860)),x96534),x96535))+P101(f323(f323(f325(x96531),f434(x96533,x96534,x96535,x96531,x96532)),f323(f323(f22(f872(x96531,a860)),x96535),x96534)))
% 188.07/187.98 [9654]~P72(x96542)+E(f323(f323(f6(x96541,x96542),x96543),x96544),f323(f323(f6(x96541,x96542),x96543),x96545))+~P101(f323(f59(x96541),x96545))+~P101(f323(f323(f237(f872(x96541,a860)),x96544),x96545))+P101(f323(f323(f325(x96541),f435(x96543,x96544,x96545,x96541,x96542)),f323(f323(f22(f872(x96541,a860)),x96545),x96544)))
% 188.07/187.98 [9655]~P68(x96552)+E(f323(f323(f9(x96551,x96552),x96553),x96554),f323(f323(f9(x96551,x96552),x96553),x96555))+~P101(f323(f59(x96551),x96555))+~P101(f323(f323(f237(f872(x96551,a860)),x96554),x96555))+P101(f323(f323(f325(x96551),f478(x96553,x96554,x96555,x96551,x96552)),f323(f323(f22(f872(x96551,a860)),x96555),x96554)))
% 188.07/187.98 [9656]~P68(x96562)+E(f323(f323(f9(x96561,x96562),x96563),x96564),f323(f323(f9(x96561,x96562),x96563),x96565))+~P101(f323(f59(x96561),x96565))+~P101(f323(f323(f237(f872(x96561,a860)),x96564),x96565))+P101(f323(f323(f325(x96561),f480(x96563,x96564,x96565,x96561,x96562)),f323(f323(f22(f872(x96561,a860)),x96565),x96564)))
% 188.07/187.98 [9674]~P72(x96741)+~P101(f323(f59(x96742),x96744))+~P101(f323(f59(x96742),x96745))+E(f323(f323(f78(x96741),f323(f323(f6(x96742,x96741),x96743),x96744)),f323(f323(f6(x96742,x96741),x96743),x96745)),f323(f323(f6(x96742,x96741),x96743),f323(f323(f110(f872(x96742,a860)),x96744),x96745)))+P101(f323(f323(f325(x96742),f362(x96743,x96745,x96744,x96742,x96741)),f323(f323(f101(f872(x96742,a860)),x96744),x96745)))
% 188.07/187.98 [9675]~P72(x96751)+~P101(f323(f59(x96752),x96754))+~P101(f323(f59(x96752),x96755))+E(f323(f323(f78(x96751),f323(f323(f6(x96752,x96751),x96753),x96754)),f323(f323(f6(x96752,x96751),x96753),x96755)),f323(f323(f6(x96752,x96751),x96753),f323(f323(f110(f872(x96752,a860)),x96754),x96755)))+P101(f323(f323(f325(x96752),f364(x96753,x96755,x96754,x96752,x96751)),f323(f323(f101(f872(x96752,a860)),x96754),x96755)))
% 188.07/187.98 [9676]~P68(x96761)+~P101(f323(f59(x96762),x96764))+~P101(f323(f59(x96762),x96765))+E(f323(f323(f79(x96761),f323(f323(f9(x96762,x96761),x96763),x96764)),f323(f323(f9(x96762,x96761),x96763),x96765)),f323(f323(f9(x96762,x96761),x96763),f323(f323(f110(f872(x96762,a860)),x96764),x96765)))+P101(f323(f323(f325(x96762),f472(x96763,x96765,x96764,x96762,x96761)),f323(f323(f101(f872(x96762,a860)),x96764),x96765)))
% 188.07/187.98 [9677]~P68(x96771)+~P101(f323(f59(x96772),x96774))+~P101(f323(f59(x96772),x96775))+E(f323(f323(f79(x96771),f323(f323(f9(x96772,x96771),x96773),x96774)),f323(f323(f9(x96772,x96771),x96773),x96775)),f323(f323(f9(x96772,x96771),x96773),f323(f323(f110(f872(x96772,a860)),x96774),x96775)))+P101(f323(f323(f325(x96772),f473(x96773,x96775,x96774,x96772,x96771)),f323(f323(f101(f872(x96772,a860)),x96774),x96775)))
% 188.07/187.98 [9684]~P84(x96845)+~P101(f323(f59(x96841),x96844))+P101(f323(f323(f237(x96845),f323(f323(f6(x96841,x96845),x96842),x96843)),f323(f323(f6(x96841,x96845),x96842),x96844)))+~P101(f323(f323(f237(f872(x96841,a860)),x96843),x96844))+P101(f323(f323(f325(x96841),f363(x96842,x96843,x96844,x96841,x96845)),f323(f323(f22(f872(x96841,a860)),x96844),x96843)))
% 188.07/187.98 [9738]~P68(x97381)+~P101(f323(f59(x97382),x97384))+~P101(f323(f59(x97382),x97385))+E(f323(f323(f79(x97381),f323(f323(f323(f63(x97381,x97382,f79(x97381)),x97383),f76(x97381)),x97384)),f323(f323(f323(f63(x97381,x97382,f79(x97381)),x97383),f76(x97381)),x97385)),f323(f323(f323(f63(x97381,x97382,f79(x97381)),x97383),f76(x97381)),f323(f323(f110(f872(x97382,a860)),x97384),x97385)))+P101(f323(f323(f325(x97382),f848(x97383,x97385,x97384,x97382,x97381)),f323(f323(f101(f872(x97382,a860)),x97384),x97385)))
% 188.07/187.98 [8700]~P20(x87001,x87004,x87005)+~P101(f323(f59(x87001),x87002))+E(f323(f323(f22(f872(x87001,a860)),x87002),f323(f323(f301(x87001),x87003),f188(f872(x87001,a860)))),f188(f872(x87001,a860)))+~P101(f323(f323(f325(x87001),x87003),x87002))+E(f323(f323(x87004,x87003),f323(x87005,f323(f323(f22(f872(x87001,a860)),x87002),f323(f323(f301(x87001),x87003),f188(f872(x87001,a860)))))),f323(x87005,x87002))
% 188.07/187.98 [8779]~P20(x87791,x87794,x87795)+~P101(f323(f59(x87791),x87793))+~P101(f323(f59(x87791),x87792))+E(f323(f323(f101(f872(x87791,a860)),x87792),x87793),f188(f872(x87791,a860)))+E(f323(f323(x87794,f323(x87795,f323(f323(f110(f872(x87791,a860)),x87792),x87793))),f323(x87795,f323(f323(f101(f872(x87791,a860)),x87792),x87793))),f323(f323(x87794,f323(x87795,x87792)),f323(x87795,x87793)))
% 188.07/187.98 [9338]~P101(f323(f323(f237(a1),x93384),f2(a1)))+~P101(f323(f323(f238(a1),x93383),x93385))+P101(f323(f323(f237(a1),x93381),x93382))+~P101(f323(f323(f238(a1),x93383),x93384))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),f323(f323(f79(a1),x93383),x93382)),x93385)),f323(f323(f78(a1),f323(f323(f79(a1),x93383),x93381)),x93384)))
% 188.07/187.98 [9340]~P101(f323(f323(f237(a1),f2(a1)),x93405))+P101(f323(f323(f237(a1),x93401),x93402))+~P101(f323(f323(f238(a1),x93403),x93404))+~P101(f323(f323(f238(a1),x93405),x93404))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),f323(f323(f79(a1),x93404),x93401)),x93405)),f323(f323(f78(a1),f323(f323(f79(a1),x93404),x93402)),x93403)))
% 188.07/187.98 [9453]~P63(x94535)+E(f323(x94531,f474(x94531,x94532,x94533,x94534,x94535)),f2(x94535))+~P101(f323(f59(x94534),x94533))+~P101(f323(f59(x94534),x94532))+E(f323(f323(f281(x94535),f323(f323(f79(x94535),f323(f323(f9(x94534,x94535),x94531),x94533)),f323(f323(f9(x94534,x94535),x94531),x94532))),f323(f323(f9(x94534,x94535),x94531),f323(f323(f101(f872(x94534,a860)),x94533),x94532))),f323(f323(f9(x94534,x94535),x94531),f323(f323(f110(f872(x94534,a860)),x94533),x94532)))
% 188.07/187.98 [9730]~P63(x97301)+~P101(f323(f59(x97302),x97304))+~P101(f323(f59(x97302),x97305))+E(f323(f323(f281(x97301),f323(f323(f79(x97301),f323(f323(f9(x97302,x97301),x97303),x97304)),f323(f323(f9(x97302,x97301),x97303),x97305))),f323(f323(f9(x97302,x97301),x97303),f323(f323(f101(f872(x97302,a860)),x97304),x97305))),f323(f323(f9(x97302,x97301),x97303),f323(f323(f110(f872(x97302,a860)),x97304),x97305)))+P101(f323(f323(f325(x97302),f474(x97303,x97305,x97304,x97302,x97301)),f323(f323(f101(f872(x97302,a860)),x97304),x97305)))
% 188.07/187.98 [9053]E(f323(f323(f121(x90531),x90532),x90533),f323(f323(f121(x90531),x90534),x90535))+~E(f323(f323(f169(x90531),f323(f189(f866(x90531)),x90534)),x90532),x90534)+~E(f323(f323(f169(x90531),f323(f189(f866(x90531)),x90532)),x90534),x90532)+~E(x90535,f323(f323(f121(x90531),f323(f323(f131(x90531),f323(f189(f866(x90531)),x90534)),x90532)),x90533))+~E(f323(f323(f121(x90531),f323(f323(f131(x90531),f323(f189(f866(x90531)),x90532)),x90534)),x90535),x90533)
% 188.07/187.98 [9451]~P103(x94512)+E(f323(f323(f141(x94511,x94512,x94513),x94514),f164(x94511,x94514,x94515)),x94515)+~P16(x94512,f323(f323(f147(x94511,x94512),x94513),x94515))+~P101(f323(f323(f325(x94511),x94514),f323(f166(x94511),x94515)))+~E(f323(f134(x94511),f323(f129(x94511,f323(f323(f8(x94512,a860,x94511),f323(a320,f323(x94513,x94514))),x94513)),x94515)),x94514)
% 188.07/187.98 [9793]~P66(x97931)+~P101(f323(f64(x97931,x97931,f79(x97931),x97932,x97933),x97935))+~P101(f323(f323(f325(x97931),x97934),x97933))+P101(f323(f323(f325(x97931),x97932),x97933))+P101(f323(f64(x97931,x97931,f79(x97931),x97934,f323(f323(f301(x97931),x97932),f323(f323(f22(f872(x97931,a860)),x97933),f323(f323(f301(x97931),x97934),f188(f872(x97931,a860)))))),x97935))
% 188.07/187.98 [7195]E(x71951,x71952)+~P27(x71954,x71955,x71953,x71956)+~E(f323(x71953,x71951),f323(x71953,x71952))+~P101(f323(f323(f325(x71954),x71952),x71956))+~P101(f323(f323(f325(x71954),x71951),x71956))
% 188.07/187.98 [6461]~P135(x64614)+E(x64611,x64612)+~E(x64615,x64616)+E(x64613,f2(x64614))+~E(f323(f323(f78(x64614),x64615),f323(f323(f79(x64614),x64613),x64611)),f323(f323(f78(x64614),x64616),f323(f323(f79(x64614),x64613),x64612)))
% 188.07/187.98 [7482]~P103(x74821)+~P6(x74821)+~P101(f323(f323(f238(x74821),x74822),f323(x74825,x74826)))+~P101(f323(f323(f325(x74823),x74826),x74824))+P101(f323(f323(f238(x74821),x74822),f323(f323(f39(x74823,x74821),x74824),x74825)))
% 188.07/187.98 [9789]~P27(x97892,x97891,x97893,x97894)+~P27(x97891,x97892,x97896,x97895)+P28(x97891,x97892,f813(x97893,x97894,x97895,x97896,x97892,x97891),x97895,x97894)+~P101(f323(f323(f237(f872(x97892,a860)),f323(f302(x97891,x97892,x97896),x97895)),x97894))+~P101(f323(f323(f237(f872(x97891,a860)),f323(f302(x97892,x97891,x97893),x97894)),x97895))
% 188.07/187.98 [8159]~P103(x81591)+~P6(x81591)+~P101(f323(f323(f238(x81591),f323(x81594,x81596)),x81595))+~P101(f323(f323(f325(x81592),x81596),x81593))+P101(f323(f323(f238(x81591),f323(f323(f40(x81592,x81591),x81593),x81594)),x81595))
% 188.07/187.98 [8417]~P21(x84172,x84175,x84176,x84171)+~P101(f323(f59(x84172),x84174))+~P101(f323(f59(x84172),x84173))+~E(f323(f323(f101(f872(x84172,a860)),x84173),x84174),f188(f872(x84172,a860)))+E(f323(x84171,f323(f323(f110(f872(x84172,a860)),x84173),x84174)),f323(f71(x84175,x84175,x84175,f323(x84171,x84173)),f323(x84171,x84174)))
% 188.07/187.98 [8749]E(x87491,x87492)+~P53(x87494,x87495,x87496,x87493,x87497)+~E(f323(x87493,x87491),f323(x87493,x87492))+~P101(f323(f323(f325(x87495),x87492),x87497))+~P101(f323(f323(f325(x87495),x87491),x87497))
% 188.07/187.98 [10035]~P101(f323(x100352,x100354))+~E(x100355,f323(f129(x100351,x100352),x100357))+E(f323(f129(x100351,x100352),x100353),f323(f323(f144(x100351),x100354),x100355))+~E(x100353,f323(f323(f121(x100351),x100356),f323(f323(f144(x100351),x100354),x100357)))+P101(f323(x100352,f717(x100355,x100354,x100353,x100352,x100351,x100356,x100357)))
% 188.07/187.98 [10036]~P101(f323(x100364,x100362))+~E(x100363,f323(f129(x100361,x100364),x100367))+E(f323(f323(f144(x100361),x100362),x100363),f323(f129(x100361,x100364),x100365))+~E(x100365,f323(f323(f121(x100361),x100366),f323(f323(f144(x100361),x100362),x100367)))+P101(f323(x100364,f715(x100365,x100364,x100363,x100362,x100361,x100366,x100367)))
% 188.07/187.98 [10069]~P101(f323(x100692,x100694))+~E(x100695,f323(f129(x100691,x100692),x100697))+E(f323(f129(x100691,x100692),x100693),f323(f323(f144(x100691),x100694),x100695))+~E(x100693,f323(f323(f121(x100691),x100696),f323(f323(f144(x100691),x100694),x100697)))+P101(f323(f323(f325(x100691),f717(x100695,x100694,x100693,x100692,x100691,x100696,x100697)),f323(f166(x100691),x100696)))
% 188.07/187.98 [10070]~P101(f323(x100704,x100702))+~E(x100703,f323(f129(x100701,x100704),x100707))+E(f323(f323(f144(x100701),x100702),x100703),f323(f129(x100701,x100704),x100705))+~E(x100705,f323(f323(f121(x100701),x100706),f323(f323(f144(x100701),x100702),x100707)))+P101(f323(f323(f325(x100701),f715(x100705,x100704,x100703,x100702,x100701,x100706,x100707)),f323(f166(x100701),x100706)))
% 188.07/187.98 [10073]~P9(x100731,x100737,x100736)+~P14(x100731,f872(x100735,a860),x100736,x100734)+P101(f323(f323(f325(x100731),f503(x100732,x100733,x100734,x100735,x100736,x100737,x100731)),x100737))+~P101(f323(f323(f325(f872(x100731,a860)),x100733),f323(f323(f58(x100731),x100737),x100736)))+P101(f323(f323(f325(f872(x100735,a860)),f323(f323(f39(x100731,f872(x100735,a860)),x100733),x100734)),x100732))
% 188.07/187.98 [10121]~P9(x101212,x101216,x101217)+~P14(x101212,f872(x101211,a860),x101217,x101214)+~P101(f323(f323(f325(f872(x101212,a860)),x101213),f323(f323(f58(x101212),x101216),x101217)))+~P101(f323(f323(f325(f872(x101211,a860)),f323(x101214,f503(x101215,x101213,x101214,x101211,x101217,x101216,x101212))),x101215))+P101(f323(f323(f325(f872(x101211,a860)),f323(f323(f39(x101212,f872(x101211,a860)),x101213),x101214)),x101215))
% 188.07/187.98 [8335]~P68(x83352)+~P27(x83351,x83355,x83358,x83354)+~E(x83353,f323(f71(x83355,x83352,x83351,x83356),x83358))+~E(x83357,f323(f302(x83351,x83355,x83358),x83354))+E(f323(f323(f9(x83351,x83352),x83353),x83354),f323(f323(f9(x83355,x83352),x83356),x83357))
% 188.07/187.98 [10125]~P68(x101252)+~P27(x101255,x101251,x101258,x101257)+~E(f323(x101256,f479(x101253,x101256,x101254,x101257,x101258,x101251,x101255,x101252)),f323(f323(f71(x101251,x101252,x101255,x101253),x101258),f479(x101253,x101256,x101254,x101257,x101258,x101251,x101255,x101252)))+~E(x101254,f323(f302(x101255,x101251,x101258),x101257))+E(f323(f323(f9(x101251,x101252),x101253),x101254),f323(f323(f9(x101255,x101252),x101256),x101257))
% 188.07/187.98 [10128]~P72(x101282)+~P27(x101281,x101285,x101288,x101284)+~E(x101287,f323(f302(x101281,x101285,x101288),x101284))+E(f323(f323(f6(x101281,x101282),x101283),x101284),f323(f323(f6(x101285,x101282),x101286),x101287))+P101(f323(f323(f325(x101281),f728(x101286,x101283,x101287,x101284,x101288,x101285,x101281,x101282)),x101284))
% 188.07/187.98 [10129]~P68(x101292)+~P27(x101291,x101295,x101298,x101294)+~E(x101297,f323(f302(x101291,x101295,x101298),x101294))+E(f323(f323(f9(x101291,x101292),x101293),x101294),f323(f323(f9(x101295,x101292),x101296),x101297))+P101(f323(f323(f325(x101291),f479(x101296,x101293,x101297,x101294,x101298,x101295,x101291,x101292)),x101294))
% 188.07/187.98 [10134]~P72(x101342)+~P27(x101345,x101341,x101348,x101347)+~E(x101344,f323(f302(x101345,x101341,x101348),x101347))+~E(f323(x101346,f728(x101343,x101346,x101344,x101347,x101348,x101341,x101345,x101342)),f323(x101343,f323(x101348,f728(x101343,x101346,x101344,x101347,x101348,x101341,x101345,x101342))))+E(f323(f323(f6(x101341,x101342),x101343),x101344),f323(f323(f6(x101345,x101342),x101346),x101347))
% 188.07/187.98 [9505]~E(f323(f189(f866(x95052)),x95055),f323(f189(f866(x95051)),x95053))+~E(f323(f189(f866(x95052)),x95054),f323(f189(f866(x95051)),x95053))+~E(f323(f323(f323(f70(x95051,f869(x95052)),f323(f179(x95051,x95052),f323(f323(f175(x95051,x95052),x95053),x95054))),x95056),f323(f230(x95052),x95057)),f323(f323(f323(f70(x95051,f869(x95052)),f323(f179(x95051,x95052),f323(f323(f175(x95051,x95052),x95053),x95055))),x95056),f323(f230(x95052),x95058)))+E(f323(f179(x95051,x95052),f323(f323(f175(x95051,x95052),x95053),x95054)),f323(f179(x95051,x95052),f323(f323(f175(x95051,x95052),x95053),x95055)))+P101(f323(f323(f325(x95051),x95056),f323(f166(x95051),x95053)))
% 188.07/187.98 [9620]~P25(x96206,x96202,x96205,x96207,x96208,x96201)+~P101(f323(f59(x96202),x96204))+~P101(f323(f59(x96202),x96203))+~E(f323(f323(f101(f872(x96202,a860)),x96203),x96204),f188(f872(x96202,a860)))+E(f323(x96201,f323(f323(f110(f872(x96202,a860)),x96203),x96204)),f323(f323(x96205,f323(x96201,x96203)),f323(x96201,x96204)))
% 188.07/187.98 [10022]~P25(x100228,x100222,x100225,x100227,x100226,x100221)+~E(f323(x100226,f852(x100224,x100223,x100221,x100226,x100227,x100225,x100222)),x100227)+~P101(f323(f59(x100222),x100223))+~P101(f323(f59(x100222),x100224))+E(f323(x100221,f323(f323(f110(f872(x100222,a860)),x100223),x100224)),f323(f323(x100225,f323(x100221,x100223)),f323(x100221,x100224)))
% 188.07/187.98 [10078]~P25(x100788,x100782,x100785,x100787,x100786,x100781)+~P101(f323(f59(x100782),x100783))+~P101(f323(f59(x100782),x100784))+E(f323(x100781,f323(f323(f110(f872(x100782,a860)),x100783),x100784)),f323(f323(x100785,f323(x100781,x100783)),f323(x100781,x100784)))+P101(f323(f323(f325(x100782),f852(x100784,x100783,x100781,x100786,x100787,x100785,x100782)),f323(f323(f101(f872(x100782,a860)),x100783),x100784)))
% 188.07/187.98 [9780]~P9(x97804,x97808,x97805)+~P9(x97801,x97809,x97803)+~P15(x97801,x97804,f872(x97802,a860),x97803,x97805,x97807)+P14(x97801,f872(x97802,a860),x97803,f323(f323(f8(f872(x97804,f872(x97802,a860)),f872(x97802,a860),x97801),f323(f39(x97804,f872(x97802,a860)),f323(f277(x97804,x97804,x97805),f323(f323(f301(x97804),x97806),f188(f872(x97804,a860)))))),x97807))+~P101(f323(f323(f325(x97804),x97806),x97808))
% 188.07/187.98 [5406]~P103(x54063)+~P16(x54063,x54061)+E(x54061,f690(x54062,x54063))+~E(f323(f166(x54063),x54061),x54062)+~P101(f323(f59(x54063),x54062))+~P101(f323(f130(x54063),x54061))
% 188.07/187.98 [5039]~P123(x50392)+~P124(x50392)+~P138(x50392)+~P110(x50392)+E(x50391,f2(x50392))+~E(f323(f323(f248(x50392),x50391),x50393),f2(x50392))
% 188.07/187.98 [5040]~P123(x50402)+~P124(x50402)+~P138(x50402)+~P110(x50402)+~E(x50401,f2(a865))+~E(f323(f323(f248(x50402),x50403),x50401),f2(x50402))
% 188.07/187.98 [6443]~P84(x64431)+~E(x64433,f2(x64431))+~E(x64432,f2(x64431))+E(f323(f323(f78(x64431),x64432),x64433),f2(x64431))+~P101(f323(f323(f237(x64431),f2(x64431)),x64433))+~P101(f323(f323(f237(x64431),f2(x64431)),x64432))
% 188.07/187.98 [8812]~E(f323(f257(a865,a865),x88123),f2(a865))+~E(x88121,f323(f323(f78(a865),f323(f323(f79(a865),f323(f257(a865,a865),x88123)),x88122)),f323(f261(a865,a865),x88123)))+P101(f323(f45(x88121,x88122),x88123))+~P101(f323(f323(f237(a865),f323(f261(a865,a865),x88123)),f2(a865)))+P101(f323(f323(f238(a865),f2(a865)),x88122))+~P101(f323(f323(f238(a865),x88122),f323(f261(a865,a865),x88123)))
% 188.07/187.98 [8820]E(x88201,f2(a865))+~E(x88202,f323(f323(f78(a865),f323(f323(f79(a865),f323(f257(a865,a865),x88203)),x88201)),f323(f261(a865,a865),x88203)))+P101(f323(f45(x88202,x88201),x88203))+~P101(f323(f323(f238(a865),f2(a865)),x88201))+~P101(f323(f323(f237(a865),f2(a865)),f323(f261(a865,a865),x88203)))+~P101(f323(f323(f238(a865),f323(f261(a865,a865),x88203)),x88201))
% 188.07/187.98 [8837]~E(f323(f257(a865,a865),x88373),f2(a865))+~E(x88371,f323(f323(f78(a865),f323(f323(f79(a865),f323(f257(a865,a865),x88373)),x88372)),f323(f261(a865,a865),x88373)))+P101(f323(f45(x88371,x88372),x88373))+~P101(f323(f323(f238(a865),f2(a865)),x88372))+~P101(f323(f323(f237(a865),f2(a865)),f323(f261(a865,a865),x88373)))+~P101(f323(f323(f238(a865),f323(f261(a865,a865),x88373)),x88372))
% 188.07/187.98 [6823]~P2(x68232)+E(x68231,f188(f872(x68232,a860)))+E(x68233,f188(f872(x68232,a860)))+~P101(f323(f59(x68232),x68231))+~P101(f323(f59(x68232),x68233))+E(f11(x68232,f323(f323(f110(f872(x68232,a860)),x68233),x68231)),f323(f323(f101(x68232),f11(x68232,x68233)),f11(x68232,x68231)))
% 188.07/187.98 [6824]~P2(x68242)+E(x68241,f188(f872(x68242,a860)))+E(x68243,f188(f872(x68242,a860)))+~P101(f323(f59(x68242),x68241))+~P101(f323(f59(x68242),x68243))+E(f10(x68242,f323(f323(f110(f872(x68242,a860)),x68243),x68241)),f323(f323(f110(x68242),f10(x68242,x68243)),f10(x68242,x68241)))
% 188.07/187.98 [6825]~P103(x68252)+E(x68251,f188(f872(x68252,a860)))+E(x68253,f188(f872(x68252,a860)))+~P101(f323(f59(x68252),x68251))+~P101(f323(f59(x68252),x68253))+E(f14(x68252,f323(f323(f110(f872(x68252,a860)),x68253),x68251)),f323(f323(f236(x68252),f14(x68252,x68253)),f14(x68252,x68251)))
% 188.07/187.98 [6826]~P103(x68262)+E(x68261,f188(f872(x68262,a860)))+E(x68263,f188(f872(x68262,a860)))+~P101(f323(f59(x68262),x68261))+~P101(f323(f59(x68262),x68263))+E(f15(x68262,f323(f323(f110(f872(x68262,a860)),x68263),x68261)),f323(f323(f235(x68262),f15(x68262,x68263)),f15(x68262,x68261)))
% 188.07/187.98 [7457]~P93(x74572)+E(x74571,f188(f872(x74572,a860)))+E(x74573,f188(f872(x74572,a860)))+~P101(f323(f59(x74572),x74571))+~P101(f323(f59(x74572),x74573))+E(f323(f323(f79(x74572),f323(f61(x74572,f79(x74572)),x74573)),f323(f61(x74572,f79(x74572)),x74571)),f323(f61(x74572,f79(x74572)),f323(f323(f110(f872(x74572,a860)),x74573),x74571)))
% 188.07/187.98 [7614]~P103(x76142)+E(x76141,f188(f872(x76142,a860)))+E(x76143,f188(f872(x76142,a860)))+~P101(f323(f59(x76142),x76141))+~P101(f323(f59(x76142),x76143))+E(f323(f323(f235(x76142),f12(x76142,f235(x76142),x76143)),f12(x76142,f235(x76142),x76141)),f12(x76142,f235(x76142),f323(f323(f110(f872(x76142,a860)),x76143),x76141)))
% 188.07/187.98 [7615]~P103(x76152)+E(x76151,f188(f872(x76152,a860)))+E(x76153,f188(f872(x76152,a860)))+~P101(f323(f59(x76152),x76151))+~P101(f323(f59(x76152),x76153))+E(f323(f323(f236(x76152),f13(x76152,f236(x76152),x76153)),f13(x76152,f236(x76152),x76151)),f13(x76152,f236(x76152),f323(f323(f110(f872(x76152,a860)),x76153),x76151)))
% 188.07/187.98 [8649]~P101(f323(x86491,x86493))+P101(f323(x86491,f409(x86491,x86492)))+P101(f323(x86491,f395(x86491,x86492)))+~P101(f323(f323(f238(a1),f2(a1)),x86492))+~P101(f323(f323(f325(a1),x86493),f294(a1,f76(a1),x86492)))+P101(f323(x86491,f323(f323(f22(a1),f395(x86491,x86492)),f323(f323(f79(a1),f406(x86491,x86492)),x86492))))
% 188.07/187.98 [8949]~P101(f323(x89491,x89493))+~P101(f323(x89491,f395(x89491,x89492)))+P101(f323(x89491,f409(x89491,x89492)))+~P101(f323(f323(f238(a1),f2(a1)),x89492))+~P101(f323(f323(f325(a1),x89493),f294(a1,f76(a1),x89492)))+~P101(f323(x89491,f323(f323(f22(a1),f395(x89491,x89492)),f323(f323(f79(a1),f406(x89491,x89492)),x89492))))
% 188.07/187.98 [10155]~P96(x101552)+E(x101551,f188(f872(x101552,a860)))+E(x101553,f188(f872(x101552,a860)))+~P101(f323(f59(x101552),x101551))+~P101(f323(f59(x101552),x101553))+E(f11(x101552,f323(f243(x101552),f323(f323(f8(f872(x101552,a860),a860,x101552),f85(x101552)),f323(f323(f8(f872(x101552,f872(x101552,a860)),f872(x101552,a860),x101552),f323(f8(f872(x101552,a860),a860,x101552),f85(x101552))),f323(f323(f7(x101552,f872(x101552,f872(x101552,a860)),f872(x101552,f872(x101552,a860))),f323(f323(f8(f872(x101552,f872(f872(x101552,a860),f872(x101552,a860))),f872(f872(x101552,f872(x101552,a860)),f872(x101552,f872(x101552,a860))),x101552),f18(x101552,f872(x101552,a860),f872(x101552,a860))),f323(f323(f8(f872(x101552,f872(x101552,f872(a860,a860))),f872(x101552,f872(f872(x101552,a860),f872(x101552,a860))),x101552),f323(f8(f872(x101552,f872(a860,a860)),f872(f872(x101552,a860),f872(x101552,a860)),x101552),f18(x101552,a860,a860))),f323(f323(f8(f872(x101552,f872(x101552,a860)),f872(x101552,f872(x101552,f872(a860,a860))),x101552),f323(f8(f872(x101552,a860),f872(x101552,f872(a860,a860)),x101552),f323(f8(a860,f872(a860,a860),x101552),a322))),f323(f323(f7(x101552,f872(x101552,f872(x101552,x101552)),f872(x101552,f872(x101552,a860))),f323(f323(f8(f872(f872(x101552,x101552),f872(x101552,a860)),f872(f872(x101552,f872(x101552,x101552)),f872(x101552,f872(x101552,a860))),x101552),f8(f872(x101552,x101552),f872(x101552,a860),x101552)),f323(f323(f8(f872(x101552,a860),f872(f872(x101552,x101552),f872(x101552,a860)),x101552),f8(x101552,a860,x101552)),a320))),f110(x101552)))))),f323(f323(f7(x101552,f872(x101552,a860),f872(x101552,a860)),f323(f323(f8(f872(a860,a860),f872(f872(x101552,a860),f872(x101552,a860)),x101552),f8(a860,a860,x101552)),f323(f323(f8(a860,f872(a860,a860),x101552),a322),f323(f323(f7(x101552,f872(x101552,a860),a860),f325(x101552)),x101553)))),f323(f323(f7(x101552,f872(x101552,a860),a860),f325(x101552)),x101551))))))),f323(f323(f110(x101552),f11(x101552,x101553)),f11(x101552,x101551)))
% 188.07/187.98 [10156]~P96(x101562)+E(x101561,f188(f872(x101562,a860)))+E(x101563,f188(f872(x101562,a860)))+~P101(f323(f59(x101562),x101561))+~P101(f323(f59(x101562),x101563))+E(f10(x101562,f323(f243(x101562),f323(f323(f8(f872(x101562,a860),a860,x101562),f85(x101562)),f323(f323(f8(f872(x101562,f872(x101562,a860)),f872(x101562,a860),x101562),f323(f8(f872(x101562,a860),a860,x101562),f85(x101562))),f323(f323(f7(x101562,f872(x101562,f872(x101562,a860)),f872(x101562,f872(x101562,a860))),f323(f323(f8(f872(x101562,f872(f872(x101562,a860),f872(x101562,a860))),f872(f872(x101562,f872(x101562,a860)),f872(x101562,f872(x101562,a860))),x101562),f18(x101562,f872(x101562,a860),f872(x101562,a860))),f323(f323(f8(f872(x101562,f872(x101562,f872(a860,a860))),f872(x101562,f872(f872(x101562,a860),f872(x101562,a860))),x101562),f323(f8(f872(x101562,f872(a860,a860)),f872(f872(x101562,a860),f872(x101562,a860)),x101562),f18(x101562,a860,a860))),f323(f323(f8(f872(x101562,f872(x101562,a860)),f872(x101562,f872(x101562,f872(a860,a860))),x101562),f323(f8(f872(x101562,a860),f872(x101562,f872(a860,a860)),x101562),f323(f8(a860,f872(a860,a860),x101562),a322))),f323(f323(f7(x101562,f872(x101562,f872(x101562,x101562)),f872(x101562,f872(x101562,a860))),f323(f323(f8(f872(f872(x101562,x101562),f872(x101562,a860)),f872(f872(x101562,f872(x101562,x101562)),f872(x101562,f872(x101562,a860))),x101562),f8(f872(x101562,x101562),f872(x101562,a860),x101562)),f323(f323(f8(f872(x101562,a860),f872(f872(x101562,x101562),f872(x101562,a860)),x101562),f8(x101562,a860,x101562)),a320))),f101(x101562)))))),f323(f323(f7(x101562,f872(x101562,a860),f872(x101562,a860)),f323(f323(f8(f872(a860,a860),f872(f872(x101562,a860),f872(x101562,a860)),x101562),f8(a860,a860,x101562)),f323(f323(f8(a860,f872(a860,a860),x101562),a322),f323(f323(f7(x101562,f872(x101562,a860),a860),f325(x101562)),x101563)))),f323(f323(f7(x101562,f872(x101562,a860),a860),f325(x101562)),x101561))))))),f323(f323(f101(x101562),f10(x101562,x101563)),f10(x101562,x101561)))
% 188.07/187.98 [10157]~P103(x101572)+E(x101571,f188(f872(x101572,a860)))+E(x101573,f188(f872(x101572,a860)))+~P101(f323(f59(x101572),x101571))+~P101(f323(f59(x101572),x101573))+E(f13(x101572,f236(x101572),f323(f243(x101572),f323(f323(f8(f872(x101572,a860),a860,x101572),f85(x101572)),f323(f323(f8(f872(x101572,f872(x101572,a860)),f872(x101572,a860),x101572),f323(f8(f872(x101572,a860),a860,x101572),f85(x101572))),f323(f323(f7(x101572,f872(x101572,f872(x101572,a860)),f872(x101572,f872(x101572,a860))),f323(f323(f8(f872(x101572,f872(f872(x101572,a860),f872(x101572,a860))),f872(f872(x101572,f872(x101572,a860)),f872(x101572,f872(x101572,a860))),x101572),f18(x101572,f872(x101572,a860),f872(x101572,a860))),f323(f323(f8(f872(x101572,f872(x101572,f872(a860,a860))),f872(x101572,f872(f872(x101572,a860),f872(x101572,a860))),x101572),f323(f8(f872(x101572,f872(a860,a860)),f872(f872(x101572,a860),f872(x101572,a860)),x101572),f18(x101572,a860,a860))),f323(f323(f8(f872(x101572,f872(x101572,a860)),f872(x101572,f872(x101572,f872(a860,a860))),x101572),f323(f8(f872(x101572,a860),f872(x101572,f872(a860,a860)),x101572),f323(f8(a860,f872(a860,a860),x101572),a322))),f323(f323(f7(x101572,f872(x101572,f872(x101572,x101572)),f872(x101572,f872(x101572,a860))),f323(f323(f8(f872(f872(x101572,x101572),f872(x101572,a860)),f872(f872(x101572,f872(x101572,x101572)),f872(x101572,f872(x101572,a860))),x101572),f8(f872(x101572,x101572),f872(x101572,a860),x101572)),f323(f323(f8(f872(x101572,a860),f872(f872(x101572,x101572),f872(x101572,a860)),x101572),f8(x101572,a860,x101572)),a320))),f235(x101572)))))),f323(f323(f7(x101572,f872(x101572,a860),f872(x101572,a860)),f323(f323(f8(f872(a860,a860),f872(f872(x101572,a860),f872(x101572,a860)),x101572),f8(a860,a860,x101572)),f323(f323(f8(a860,f872(a860,a860),x101572),a322),f323(f323(f7(x101572,f872(x101572,a860),a860),f325(x101572)),x101573)))),f323(f323(f7(x101572,f872(x101572,a860),a860),f325(x101572)),x101571))))))),f323(f323(f235(x101572),f13(x101572,f236(x101572),x101573)),f13(x101572,f236(x101572),x101571)))
% 188.07/187.98 [10158]~P103(x101582)+E(x101581,f188(f872(x101582,a860)))+E(x101583,f188(f872(x101582,a860)))+~P101(f323(f59(x101582),x101581))+~P101(f323(f59(x101582),x101583))+E(f12(x101582,f235(x101582),f323(f243(x101582),f323(f323(f8(f872(x101582,a860),a860,x101582),f85(x101582)),f323(f323(f8(f872(x101582,f872(x101582,a860)),f872(x101582,a860),x101582),f323(f8(f872(x101582,a860),a860,x101582),f85(x101582))),f323(f323(f7(x101582,f872(x101582,f872(x101582,a860)),f872(x101582,f872(x101582,a860))),f323(f323(f8(f872(x101582,f872(f872(x101582,a860),f872(x101582,a860))),f872(f872(x101582,f872(x101582,a860)),f872(x101582,f872(x101582,a860))),x101582),f18(x101582,f872(x101582,a860),f872(x101582,a860))),f323(f323(f8(f872(x101582,f872(x101582,f872(a860,a860))),f872(x101582,f872(f872(x101582,a860),f872(x101582,a860))),x101582),f323(f8(f872(x101582,f872(a860,a860)),f872(f872(x101582,a860),f872(x101582,a860)),x101582),f18(x101582,a860,a860))),f323(f323(f8(f872(x101582,f872(x101582,a860)),f872(x101582,f872(x101582,f872(a860,a860))),x101582),f323(f8(f872(x101582,a860),f872(x101582,f872(a860,a860)),x101582),f323(f8(a860,f872(a860,a860),x101582),a322))),f323(f323(f7(x101582,f872(x101582,f872(x101582,x101582)),f872(x101582,f872(x101582,a860))),f323(f323(f8(f872(f872(x101582,x101582),f872(x101582,a860)),f872(f872(x101582,f872(x101582,x101582)),f872(x101582,f872(x101582,a860))),x101582),f8(f872(x101582,x101582),f872(x101582,a860),x101582)),f323(f323(f8(f872(x101582,a860),f872(f872(x101582,x101582),f872(x101582,a860)),x101582),f8(x101582,a860,x101582)),a320))),f236(x101582)))))),f323(f323(f7(x101582,f872(x101582,a860),f872(x101582,a860)),f323(f323(f8(f872(a860,a860),f872(f872(x101582,a860),f872(x101582,a860)),x101582),f8(a860,a860,x101582)),f323(f323(f8(a860,f872(a860,a860),x101582),a322),f323(f323(f7(x101582,f872(x101582,a860),a860),f325(x101582)),x101583)))),f323(f323(f7(x101582,f872(x101582,a860),a860),f325(x101582)),x101581))))))),f323(f323(f236(x101582),f12(x101582,f235(x101582),x101583)),f12(x101582,f235(x101582),x101581)))
% 188.07/187.98 [7146]~P119(x71463)+E(x71461,x71462)+~E(f323(f323(f248(x71463),x71461),x71464),f323(f323(f248(x71463),x71462),x71464))+~P101(f323(f323(f237(x71463),f2(x71463)),x71462))+~P101(f323(f323(f237(x71463),f2(x71463)),x71461))+~P101(f323(f323(f238(a865),f2(a865)),x71464))
% 188.07/187.98 [7415]~P98(x74152)+E(x74151,f188(f872(x74152,a860)))+~P101(f323(f59(x74152),x74151))+~P101(f323(f323(f325(x74152),x74154),x74151))+P101(f323(f323(f237(x74152),x74153),x74154))+~P101(f323(f323(f237(x74152),x74153),f323(f61(x74152,f101(x74152)),x74151)))
% 188.07/187.98 [7416]~P103(x74162)+E(x74161,f188(f872(x74162,a860)))+~P101(f323(f59(x74162),x74161))+~P101(f323(f323(f325(x74162),x74164),x74161))+P101(f323(f323(f237(x74162),x74163),x74164))+~P101(f323(f323(f237(x74162),x74163),f323(f61(x74162,f235(x74162)),x74161)))
% 188.07/187.98 [7417]~P103(x74172)+E(x74171,f188(f872(x74172,a860)))+~P101(f323(f59(x74172),x74171))+~P101(f323(f323(f325(x74172),x74174),x74171))+P101(f323(f323(f238(x74172),x74173),x74174))+~P101(f323(f323(f238(x74172),x74173),f323(f61(x74172,f235(x74172)),x74171)))
% 188.07/187.98 [7317]E(x73171,f2(a1))+E(f323(f323(f36(a1),x73172),x73171),x73173)+~P101(f323(f323(f237(a1),x73174),f2(a1)))+~E(x73172,f323(f323(f78(a1),f323(f323(f79(a1),x73171),x73173)),x73174))+P101(f323(f323(f238(a1),f2(a1)),x73171))+~P101(f323(f323(f238(a1),x73171),x73174))
% 188.07/187.98 [7332]E(f42(a1,x73322,x73321),x73323)+E(x73321,f2(a1))+~P101(f323(f323(f237(a1),x73323),f2(a1)))+~E(x73322,f323(f323(f78(a1),f323(f323(f79(a1),x73321),x73324)),x73323))+P101(f323(f323(f238(a1),f2(a1)),x73321))+~P101(f323(f323(f238(a1),x73321),x73323))
% 188.07/187.98 [7456]E(x74561,f2(a1))+E(f323(f323(f36(a1),x74562),x74561),x74563)+~E(x74562,f323(f323(f78(a1),f323(f323(f79(a1),x74561),x74563)),x74564))+~P101(f323(f323(f237(a1),f2(a1)),x74564))+~P101(f323(f323(f238(a1),f2(a1)),x74561))+~P101(f323(f323(f238(a1),x74564),x74561))
% 188.07/187.98 [7478]E(f42(a1,x74782,x74781),x74783)+E(x74781,f2(a1))+~E(x74782,f323(f323(f78(a1),f323(f323(f79(a1),x74781),x74784)),x74783))+~P101(f323(f323(f237(a1),f2(a1)),x74783))+~P101(f323(f323(f238(a1),f2(a1)),x74781))+~P101(f323(f323(f238(a1),x74783),x74781))
% 188.07/187.98 [7618]~P103(x76182)+E(x76181,f188(f872(x76182,a860)))+~P101(f323(f59(x76182),x76181))+~P101(f323(f323(f237(x76182),x76184),x76183))+~P101(f323(f323(f325(x76182),x76184),x76181))+P101(f323(f323(f237(x76182),f323(f61(x76182,f235(x76182)),x76181)),x76183))
% 188.07/187.98 [7619]~P103(x76192)+E(x76191,f188(f872(x76192,a860)))+~P101(f323(f59(x76192),x76191))+~P101(f323(f323(f238(x76192),x76194),x76193))+~P101(f323(f323(f325(x76192),x76194),x76191))+P101(f323(f323(f238(x76192),f323(f61(x76192,f235(x76192)),x76191)),x76193))
% 188.07/187.98 [8185]~P101(f323(f323(f237(a1),x81854),f2(a1)))+~E(x81851,f323(f323(f78(a1),f323(f323(f79(a1),x81852),x81853)),x81854))+~P101(f323(f323(f237(a1),f2(a1)),x81854))+~P101(f323(f323(f238(a1),x81854),x81852))+~P101(f323(f323(f238(a1),x81852),x81854))+P101(f323(f46(x81851,x81852),f323(f323(f258(a1,a1),x81853),x81854)))
% 188.07/187.98 [9144]~P5(x91443)+~P5(x91444)+E(x91441,x91442)+~E(f323(f189(f866(x91443)),x91442),f323(f189(f866(x91444)),f53(x91444)))+~E(f323(f189(f866(x91443)),x91441),f323(f189(f866(x91444)),f53(x91444)))+~E(f323(f71(f869(x91443),x91443,x91444,f234(x91443)),f323(f179(x91444,x91443),f323(f323(f175(x91444,x91443),f53(x91444)),x91441))),f323(f71(f869(x91443),x91443,x91444,f234(x91443)),f323(f179(x91444,x91443),f323(f323(f175(x91444,x91443),f53(x91444)),x91442))))
% 188.07/187.98 [8353]~P105(x83531)+P101(f323(f323(f238(f872(x83531,a860)),f294(x83531,x83532,x83533)),f294(x83531,x83534,x83535)))+~P101(f323(f323(f237(x83531),x83534),x83532))+~P101(f323(f323(f237(x83531),x83534),x83535))+~P101(f323(f323(f237(x83531),x83533),x83535))+~P101(f323(f323(f238(x83531),x83533),x83535))
% 188.07/187.98 [8354]~P105(x83541)+P101(f323(f323(f238(f872(x83541,a860)),f294(x83541,x83542,x83543)),f294(x83541,x83544,x83545)))+~P101(f323(f323(f237(x83541),x83543),x83545))+~P101(f323(f323(f237(x83541),x83544),x83545))+~P101(f323(f323(f237(x83541),x83544),x83542))+~P101(f323(f323(f238(x83541),x83544),x83542))
% 188.07/187.98 [9208]P55(x92082,x92083,x92084,x92081)+E(x92081,f188(f872(x92082,a860)))+~P101(f323(f59(x92082),x92084))+~P101(f323(f59(x92082),x92081))+~P101(f323(f323(x92083,f664(x92081,x92084,x92083,x92082)),x92085))+~P101(f323(f323(f325(x92082),x92085),x92081))
% 188.07/187.98 [9356]~E(x93563,x93565)+~P68(x93561)+~P72(x93561)+~P39(x93563)+E(f323(f323(f6(a1,x93561),x93562),x93563),f323(f323(f6(a1,x93561),x93564),x93565))+P101(f323(f323(f237(a1),f2(a1)),f436(x93562,x93564,x93563,x93565,x93561)))
% 188.07/187.98 [9357]~E(x93573,x93575)+~P68(x93571)+~P72(x93571)+~P39(x93573)+E(f323(f323(f9(a1,x93571),x93572),x93573),f323(f323(f9(a1,x93571),x93574),x93575))+P101(f323(f323(f237(a1),f2(a1)),f484(x93572,x93574,x93573,x93575,x93571)))
% 188.07/187.98 [9527]~E(x95275,x95273)+~P68(x95271)+~P72(x95271)+~P39(x95275)+~E(f323(x95272,f436(x95274,x95272,x95275,x95273,x95271)),f323(x95274,f436(x95274,x95272,x95275,x95273,x95271)))+E(f323(f323(f6(a1,x95271),x95272),x95273),f323(f323(f6(a1,x95271),x95274),x95275))
% 188.07/187.98 [9528]~E(x95285,x95283)+~P68(x95281)+~P72(x95281)+~P39(x95285)+~E(f323(x95282,f484(x95284,x95282,x95285,x95283,x95281)),f323(x95284,f484(x95284,x95282,x95285,x95283,x95281)))+E(f323(f323(f9(a1,x95281),x95282),x95283),f323(f323(f9(a1,x95281),x95284),x95285))
% 188.07/187.98 [9617]~P75(x96173)+E(f323(x96171,x96172),f2(x96173))+~E(f323(f323(f6(x96174,x96173),x96171),x96175),f2(x96173))+~P101(f323(f59(x96174),x96175))+P101(f323(f323(f325(x96174),f367(x96172,x96171,x96175,x96174,x96173)),x96175))+~P101(f323(f323(f325(x96174),x96172),x96175))
% 188.07/187.98 [9754]~P75(x97543)+E(f323(x97541,x97542),f2(x97543))+~E(f323(f323(f6(x97544,x97543),x97541),x97545),f2(x97543))+~P101(f323(f59(x97544),x97545))+~P101(f323(f323(f325(x97544),x97542),x97545))+~P101(f323(f323(f237(x97543),f2(x97543)),f323(x97541,f367(x97542,x97541,x97545,x97544,x97543))))
% 188.07/187.98 [8268]~P131(x82681)+~P101(f323(f323(f237(x82681),x82683),x82685))+~P101(f323(f323(f237(x82681),x82682),x82684))+~P101(f323(f323(f237(x82681),f2(x82681)),x82683))+~P101(f323(f323(f237(x82681),f2(x82681)),x82684))+P101(f323(f323(f237(x82681),f323(f323(f79(x82681),x82682),x82683)),f323(f323(f79(x82681),x82684),x82685)))
% 188.07/187.98 [8269]~P131(x82691)+~P101(f323(f323(f237(x82691),x82693),x82695))+~P101(f323(f323(f237(x82691),x82692),x82694))+~P101(f323(f323(f237(x82691),f2(x82691)),x82693))+~P101(f323(f323(f237(x82691),f2(x82691)),x82692))+P101(f323(f323(f237(x82691),f323(f323(f79(x82691),x82692),x82693)),f323(f323(f79(x82691),x82694),x82695)))
% 188.07/187.99 [8270]~P65(x82701)+~P101(f323(f323(f238(x82701),f2(x82701)),x82705))+~P101(f323(f323(f237(x82701),x82705),x82703))+~P101(f323(f323(f237(x82701),x82702),x82704))+~P101(f323(f323(f237(x82701),f2(x82701)),x82702))+P101(f323(f323(f237(x82701),f323(f323(f281(x82701),x82702),x82703)),f323(f323(f281(x82701),x82704),x82705)))
% 188.07/187.99 [8271]~P125(x82711)+~P101(f323(f323(f237(x82711),x82713),x82715))+~P101(f323(f323(f237(x82711),f2(x82711)),x82712))+~P101(f323(f323(f238(x82711),x82712),x82714))+~P101(f323(f323(f238(x82711),f2(x82711)),x82713))+P101(f323(f323(f238(x82711),f323(f323(f79(x82711),x82712),x82713)),f323(f323(f79(x82711),x82714),x82715)))
% 188.07/187.99 [8272]~P125(x82721)+~P101(f323(f323(f237(x82721),x82722),x82724))+~P101(f323(f323(f237(x82721),f2(x82721)),x82723))+~P101(f323(f323(f238(x82721),x82723),x82725))+~P101(f323(f323(f238(x82721),f2(x82721)),x82722))+P101(f323(f323(f238(x82721),f323(f323(f79(x82721),x82722),x82723)),f323(f323(f79(x82721),x82724),x82725)))
% 188.07/187.99 [8273]~P125(x82731)+~P101(f323(f323(f237(x82731),f2(x82731)),x82733))+~P101(f323(f323(f237(x82731),f2(x82731)),x82732))+~P101(f323(f323(f238(x82731),x82733),x82735))+~P101(f323(f323(f238(x82731),x82732),x82734))+P101(f323(f323(f238(x82731),f323(f323(f79(x82731),x82732),x82733)),f323(f323(f79(x82731),x82734),x82735)))
% 188.07/187.99 [8274]~P125(x82741)+~P101(f323(f323(f237(x82741),f2(x82741)),x82743))+~P101(f323(f323(f238(x82741),x82743),x82745))+~P101(f323(f323(f238(x82741),x82742),x82744))+~P101(f323(f323(f238(x82741),f2(x82741)),x82744))+P101(f323(f323(f238(x82741),f323(f323(f79(x82741),x82742),x82743)),f323(f323(f79(x82741),x82744),x82745)))
% 188.07/187.99 [8275]~P65(x82751)+~P101(f323(f323(f237(x82751),x82755),x82753))+~P101(f323(f323(f237(x82751),f2(x82751)),x82752))+~P101(f323(f323(f238(x82751),x82752),x82754))+~P101(f323(f323(f238(x82751),f2(x82751)),x82755))+P101(f323(f323(f238(x82751),f323(f323(f281(x82751),x82752),x82753)),f323(f323(f281(x82751),x82754),x82755)))
% 188.07/187.99 [8276]~P65(x82761)+~P101(f323(f323(f237(x82761),x82762),x82764))+~P101(f323(f323(f238(x82761),x82765),x82763))+~P101(f323(f323(f238(x82761),f2(x82761)),x82765))+~P101(f323(f323(f238(x82761),f2(x82761)),x82762))+P101(f323(f323(f238(x82761),f323(f323(f281(x82761),x82762),x82763)),f323(f323(f281(x82761),x82764),x82765)))
% 188.07/187.99 [9657]~P83(x96575)+~P72(x96575)+E(x96571,f188(f872(x96572,a860)))+~P101(f323(f59(x96572),x96571))+P101(f323(f323(f325(x96572),f437(x96573,x96574,x96571,x96572,x96575)),x96571))+P101(f323(f323(f238(x96575),f323(f323(f6(x96572,x96575),x96574),x96571)),f323(f323(f6(x96572,x96575),x96573),x96571)))
% 188.07/187.99 [9776]~P81(x97761)+~P72(x97761)+~P101(f323(f59(x97762),x97765))+~P101(f323(f323(f237(x97761),f2(x97761)),f323(x97763,f368(x97763,x97764,x97765,x97762,x97761))))+P101(f323(f323(f237(x97761),f323(f323(f6(x97762,x97761),x97763),x97764)),f323(f323(f6(x97762,x97761),x97763),x97765)))+~P101(f323(f323(f237(f872(x97762,a860)),x97764),x97765))
% 188.07/187.99 [9943]~P83(x99433)+~P72(x99433)+E(x99431,f188(f872(x99432,a860)))+~P101(f323(f59(x99432),x99431))+~P101(f323(f323(f238(x99433),f323(x99434,f437(x99435,x99434,x99431,x99432,x99433))),f323(x99435,f437(x99435,x99434,x99431,x99432,x99433))))+P101(f323(f323(f238(x99433),f323(f323(f6(x99432,x99433),x99434),x99431)),f323(f323(f6(x99432,x99433),x99435),x99431)))
% 188.07/187.99 [7005]~P19(x70052,x70055,x70054)+E(x70051,f188(f872(x70052,a860)))+E(x70053,f188(f872(x70052,a860)))+~P101(f323(f59(x70052),x70051))+~P101(f323(f59(x70052),x70053))+E(f323(x70054,f323(f323(f110(f872(x70052,a860)),x70053),x70051)),f323(f323(x70055,f323(x70054,x70053)),f323(x70054,x70051)))
% 188.07/187.99 [7584]~P143(x75841,x75843,x75844)+P101(f323(x75841,x75842))+~P101(f323(f323(f238(a1),x75844),f2(a1)))+~P101(f323(f323(f237(a1),x75845),f2(a1)))+~E(x75843,f323(f323(f78(a1),f323(f323(f79(a1),x75844),x75842)),x75845))+~P101(f323(f323(f238(a1),x75844),x75845))
% 188.07/187.99 [7585]~P142(x75851,x75853,x75854)+P101(f323(x75851,x75852))+~P101(f323(f323(f238(a1),x75854),f2(a1)))+~P101(f323(f323(f237(a1),x75852),f2(a1)))+~E(x75853,f323(f323(f78(a1),f323(f323(f79(a1),x75854),x75855)),x75852))+~P101(f323(f323(f238(a1),x75854),x75852))
% 188.07/187.99 [7627]~P143(x76271,x76273,x76274)+P101(f323(x76271,x76272))+~E(x76273,f323(f323(f78(a1),f323(f323(f79(a1),x76274),x76272)),x76275))+~P101(f323(f323(f237(a1),f2(a1)),x76275))+~P101(f323(f323(f238(a1),f2(a1)),x76274))+~P101(f323(f323(f238(a1),x76275),x76274))
% 188.07/187.99 [7628]~P142(x76281,x76283,x76284)+P101(f323(x76281,x76282))+~E(x76283,f323(f323(f78(a1),f323(f323(f79(a1),x76284),x76285)),x76282))+~P101(f323(f323(f237(a1),f2(a1)),x76282))+~P101(f323(f323(f238(a1),f2(a1)),x76284))+~P101(f323(f323(f238(a1),x76282),x76284))
% 188.07/187.99 [8559]P101(f323(f323(x85591,x85592),x85593))+~P101(f323(f323(x85591,f323(f323(f36(a1),x85594),x85595)),f42(a1,x85594,x85595)))+~P101(f323(f323(f238(a1),x85595),f2(a1)))+~P101(f323(f323(f237(a1),x85593),f2(a1)))+~E(x85594,f323(f323(f78(a1),f323(f323(f79(a1),x85595),x85592)),x85593))+~P101(f323(f323(f238(a1),x85595),x85593))
% 188.07/187.99 [8569]P101(f323(f323(x85691,x85692),x85693))+~P101(f323(f323(x85691,f323(f323(f36(a1),x85694),x85695)),f42(a1,x85694,x85695)))+~E(x85694,f323(f323(f78(a1),f323(f323(f79(a1),x85695),x85692)),x85693))+~P101(f323(f323(f237(a1),f2(a1)),x85693))+~P101(f323(f323(f238(a1),f2(a1)),x85695))+~P101(f323(f323(f238(a1),x85693),x85695))
% 188.07/187.99 [8826]E(x88261,x88262)+~P52(x88263,x88265,x88264)+~P101(f323(f323(f325(x88263),x88262),x88265))+~P101(f323(f323(f325(x88263),x88261),x88265))+P101(f323(f323(f325(f871(x88263,x88263)),f323(f323(f258(x88263,x88263),x88261),x88262)),x88264))+P101(f323(f323(f325(f871(x88263,x88263)),f323(f323(f258(x88263,x88263),x88262),x88261)),x88264))
% 188.07/187.99 [9685]~P81(x96855)+~P72(x96855)+~P101(f323(f59(x96851),x96854))+P101(f323(f323(f237(x96855),f323(f323(f6(x96851,x96855),x96852),x96853)),f323(f323(f6(x96851,x96855),x96852),x96854)))+~P101(f323(f323(f237(f872(x96851,a860)),x96853),x96854))+P101(f323(f323(f325(x96851),f368(x96852,x96853,x96854,x96851,x96855)),f323(f323(f22(f872(x96851,a860)),x96854),x96853)))
% 188.07/187.99 [9784]E(x97841,f188(f872(x97842,a860)))+~P101(f323(f59(x97842),x97843))+~P101(f323(f59(x97842),x97841))+P101(f323(f323(f325(f871(f872(x97842,a860),f872(x97842,a860))),f323(f323(f258(f872(x97842,a860),f872(x97842,a860)),x97843),x97841)),f314(x97842,x97844)))+~P101(f323(f323(f325(x97842),x97845),x97841))+~P101(f323(f323(f325(f871(x97842,x97842)),f323(f323(f258(x97842,x97842),f670(x97844,x97841,x97843,x97842)),x97845)),x97844))
% 188.07/187.99 [9785]E(x97851,f188(f872(x97852,a860)))+~P101(f323(f59(x97852),x97853))+~P101(f323(f59(x97852),x97851))+P101(f323(f323(f325(f871(f872(x97852,a860),f872(x97852,a860))),f323(f323(f258(f872(x97852,a860),f872(x97852,a860)),x97853),x97851)),f314(x97852,x97854)))+~P101(f323(f323(f325(x97852),x97855),x97851))+~P101(f323(f323(f325(f871(x97852,x97852)),f323(f323(f258(x97852,x97852),f722(x97854,x97851,x97853,x97852)),x97855)),x97854))
% 188.07/187.99 [9947]~P75(x99471)+~E(f323(f323(f6(x99475,x99471),x99472),x99476),x99474)+~P101(f323(f59(x99475),x99476))+P101(f323(f323(f325(x99475),f373(x99473,x99474,x99472,x99476,x99475,x99471)),x99476))+P101(f323(f323(f237(x99471),f323(x99472,x99473)),x99474))+~P101(f323(f323(f325(x99475),x99473),x99476))
% 188.07/187.99 [9994]~P75(x99941)+~E(f323(f323(f6(x99945,x99941),x99942),x99946),x99944)+~P101(f323(f59(x99945),x99946))+~P101(f323(f323(f325(x99945),x99943),x99946))+~P101(f323(f323(f237(x99941),f2(x99941)),f323(x99942,f373(x99943,x99944,x99942,x99946,x99945,x99941))))+P101(f323(f323(f237(x99941),f323(x99942,x99943)),x99944))
% 188.07/187.99 [10107]~E(x101075,x101078)+~E(x101074,x101077)+~P104(x101071)+~P72(x101072)+E(f323(f323(f6(x101071,x101072),x101073),f323(f293(x101071,x101074),x101075)),f323(f323(f6(x101071,x101072),x101076),f323(f293(x101071,x101077),x101078)))+P101(f323(f323(f237(x101071),x101074),f727(x101073,x101076,x101075,x101078,x101074,x101077,x101071,x101072)))
% 188.07/187.99 [10124]~E(x101247,x101244)+~E(x101248,x101245)+~P104(x101241)+~P72(x101242)+~E(f323(x101243,f727(x101246,x101243,x101248,x101245,x101247,x101244,x101241,x101242)),f323(x101246,f727(x101246,x101243,x101248,x101245,x101247,x101244,x101241,x101242)))+E(f323(f323(f6(x101241,x101242),x101243),f323(f293(x101241,x101244),x101245)),f323(f323(f6(x101241,x101242),x101246),f323(f293(x101241,x101247),x101248)))
% 188.07/187.99 [10127]~E(x101274,x101277)+~E(x101275,x101278)+~P104(x101271)+~P72(x101272)+E(f323(f323(f6(x101271,x101272),x101273),f323(f293(x101271,x101274),x101275)),f323(f323(f6(x101271,x101272),x101276),f323(f293(x101271,x101277),x101278)))+P101(f323(f323(f238(x101271),f727(x101273,x101276,x101275,x101278,x101274,x101277,x101271,x101272)),x101275))
% 188.07/187.99 [9791]~P9(x97915,x97919,x97916)+~P9(x97911,x979110,x97913)+~P15(x97911,x97915,f872(x97912,a860),x97913,x97916,x97918)+~P101(f323(f323(f325(x97915),x97917),x97919))+~P101(f323(f323(f325(x97911),x97914),x979110))+E(f323(f323(f39(x97911,f872(x97912,a860)),f323(f277(x97911,x97911,x97913),f323(f323(f301(x97911),x97914),f188(f872(x97911,a860))))),f323(f323(f8(f872(x97915,f872(x97912,a860)),f872(x97912,a860),x97911),f323(f39(x97915,f872(x97912,a860)),f323(f277(x97915,x97915,x97916),f323(f323(f301(x97915),x97917),f188(f872(x97915,a860)))))),x97918)),f323(f323(x97918,x97914),x97917))
% 188.07/187.99 [5572]~P103(x55723)+~P16(x55723,x55722)+~P16(x55723,x55721)+E(x55721,x55722)+~E(f323(f166(x55723),x55721),f323(f166(x55723),x55722))+~P101(f323(f130(x55723),x55722))+~P101(f323(f130(x55723),x55721))
% 188.07/187.99 [4924]~P123(x49242)+~P124(x49242)+~P138(x49242)+~P110(x49242)+~E(x49243,f2(x49242))+E(x49241,f2(a865))+E(f323(f323(f248(x49242),x49243),x49241),f2(x49242))
% 188.07/187.99 [9087]E(x90871,f2(a865))+~E(x90872,f323(f323(f78(a865),f323(f323(f79(a865),f323(f257(a865,a865),x90873)),x90871)),f323(f261(a865,a865),x90873)))+P101(f323(f45(x90872,x90871),x90873))+~P101(f323(f323(f237(a865),f323(f261(a865,a865),x90873)),f2(a865)))+~P101(f323(f323(f237(a865),f2(a865)),f323(f261(a865,a865),x90873)))+~P101(f323(f323(f238(a865),x90871),f323(f261(a865,a865),x90873)))+~P101(f323(f323(f238(a865),f323(f261(a865,a865),x90873)),x90871))
% 188.07/187.99 [9096]~E(f323(f257(a865,a865),x90963),f2(a865))+~E(x90961,f323(f323(f78(a865),f323(f323(f79(a865),f323(f257(a865,a865),x90963)),x90962)),f323(f261(a865,a865),x90963)))+P101(f323(f45(x90961,x90962),x90963))+~P101(f323(f323(f237(a865),f323(f261(a865,a865),x90963)),f2(a865)))+~P101(f323(f323(f237(a865),f2(a865)),f323(f261(a865,a865),x90963)))+~P101(f323(f323(f238(a865),x90962),f323(f261(a865,a865),x90963)))+~P101(f323(f323(f238(a865),f323(f261(a865,a865),x90963)),x90962))
% 188.07/187.99 [7940]~P66(x79402)+E(x79401,f188(f872(x79402,a860)))+E(x79403,f188(f872(x79402,a860)))+~P101(f323(f59(x79402),x79401))+~P101(f323(f59(x79402),x79403))+~E(f323(f323(f101(f872(x79402,a860)),x79403),x79401),f188(f872(x79402,a860)))+E(f323(f323(f79(x79402),f323(f61(x79402,f79(x79402)),x79403)),f323(f61(x79402,f79(x79402)),x79401)),f323(f61(x79402,f79(x79402)),f323(f323(f110(f872(x79402,a860)),x79403),x79401)))
% 188.07/187.99 [7723]E(x77231,f2(a1))+E(f323(f323(f36(a1),x77232),x77231),x77233)+~P101(f323(f323(f237(a1),x77234),f2(a1)))+~E(x77232,f323(f323(f78(a1),f323(f323(f79(a1),x77231),x77233)),x77234))+~P101(f323(f323(f237(a1),f2(a1)),x77234))+~P101(f323(f323(f238(a1),x77234),x77231))+~P101(f323(f323(f238(a1),x77231),x77234))
% 188.07/187.99 [7732]E(f42(a1,x77322,x77321),x77323)+E(x77321,f2(a1))+~P101(f323(f323(f237(a1),x77323),f2(a1)))+~E(x77322,f323(f323(f78(a1),f323(f323(f79(a1),x77321),x77324)),x77323))+~P101(f323(f323(f237(a1),f2(a1)),x77323))+~P101(f323(f323(f238(a1),x77323),x77321))+~P101(f323(f323(f238(a1),x77321),x77323))
% 188.07/187.99 [7636]~P20(x76362,x76365,x76364)+E(x76361,f188(f872(x76362,a860)))+E(x76363,f188(f872(x76362,a860)))+~P101(f323(f59(x76362),x76361))+~P101(f323(f59(x76362),x76363))+~E(f323(f323(f101(f872(x76362,a860)),x76363),x76361),f188(f872(x76362,a860)))+E(f323(x76364,f323(f323(f110(f872(x76362,a860)),x76363),x76361)),f323(f323(x76365,f323(x76364,x76363)),f323(x76364,x76361)))
% 188.07/187.99 [9329]~P27(x93293,x93291,x93295,x93294)+~P27(x93291,x93293,x93296,x93292)+E(f323(f35(x93291),x93292),f323(f35(x93293),x93294))+~P101(f323(f59(x93293),x93294))+~P101(f323(f59(x93291),x93292))+~P101(f323(f323(f237(f872(x93293,a860)),f323(f302(x93291,x93293,x93296),x93292)),x93294))+~P101(f323(f323(f237(f872(x93291,a860)),f323(f302(x93293,x93291,x93295),x93294)),x93292))
% 188.07/187.99 [9272]~P101(f323(f323(f238(a1),f323(f323(f78(a1),f323(f323(f79(a1),x92725),x92721)),x92726)),f2(a1)))+~E(f323(f323(f78(a1),f323(f323(f79(a1),x92723),x92722)),x92724),f323(f323(f78(a1),f323(f323(f79(a1),x92725),x92721)),x92726))+~P101(f323(f323(f237(a1),f2(a1)),x92726))+~P101(f323(f323(f238(a1),f2(a1)),x92725))+~P101(f323(f323(f237(a1),x92725),x92723))+~P101(f323(f323(f238(a1),x92724),x92723))+P101(f323(f323(f237(a1),x92721),x92722))
% 188.07/187.99 [9039]~E(f323(f323(f78(a1),f323(f323(f79(a1),x90393),x90391)),x90394),f323(f323(f78(a1),f323(f323(f79(a1),x90395),x90392)),x90396))+~P101(f323(f323(f237(a1),f2(a1)),x90394))+~P101(f323(f323(f238(a1),f2(a1)),x90395))+~P101(f323(f323(f237(a1),x90395),x90393))+~P101(f323(f323(f238(a1),x90396),x90395))+P101(f323(f323(f237(a1),x90391),x90392))+~P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),f323(f323(f79(a1),x90395),x90392)),x90396)))
% 188.07/187.99 [9214]~P127(x92141)+~E(f323(f323(f78(x92141),x92142),x92144),f76(x92141))+~P101(f323(f323(f237(x92141),x92145),x92146))+~P101(f323(f323(f237(x92141),x92143),x92146))+~P101(f323(f323(f237(x92141),f2(x92141)),x92144))+~P101(f323(f323(f237(x92141),f2(x92141)),x92142))+P101(f323(f323(f237(x92141),f323(f323(f78(x92141),f323(f323(f79(x92141),x92142),x92143)),f323(f323(f79(x92141),x92144),x92145))),x92146))
% 188.07/187.99 [9215]~P128(x92151)+~E(f323(f323(f78(x92151),x92152),x92154),f76(x92151))+~P101(f323(f323(f237(x92151),f2(x92151)),x92154))+~P101(f323(f323(f237(x92151),f2(x92151)),x92152))+~P101(f323(f323(f238(x92151),x92155),x92156))+~P101(f323(f323(f238(x92151),x92153),x92156))+P101(f323(f323(f238(x92151),f323(f323(f78(x92151),f323(f323(f79(x92151),x92152),x92153)),f323(f323(f79(x92151),x92154),x92155))),x92156))
% 188.07/187.99 [10038]~P9(x100387,x100386,x100385)+E(x100381,x100382)+~P14(x100387,f872(x100384,a860),x100385,x100383)+E(f323(x100383,f510(x100381,x100382,x100383,x100384,x100385,x100386,x100387)),f323(x100383,f511(x100381,x100382,x100383,x100384,x100385,x100386,x100387)))+~E(f323(f323(f39(x100387,f872(x100384,a860)),x100381),x100383),f323(f323(f39(x100387,f872(x100384,a860)),x100382),x100383))+~P101(f323(f323(f325(f872(x100387,a860)),x100382),f323(f323(f58(x100387),x100386),x100385)))+~P101(f323(f323(f325(f872(x100387,a860)),x100381),f323(f323(f58(x100387),x100386),x100385)))
% 188.07/187.99 [10071]~P9(x100713,x100717,x100716)+E(x100711,x100712)+~P14(x100713,f872(x100715,a860),x100716,x100714)+~E(f323(f323(f39(x100713,f872(x100715,a860)),x100711),x100714),f323(f323(f39(x100713,f872(x100715,a860)),x100712),x100714))+P101(f323(f323(f325(x100713),f511(x100711,x100712,x100714,x100715,x100716,x100717,x100713)),x100717))+~P101(f323(f323(f325(f872(x100713,a860)),x100712),f323(f323(f58(x100713),x100717),x100716)))+~P101(f323(f323(f325(f872(x100713,a860)),x100711),f323(f323(f58(x100713),x100717),x100716)))
% 188.07/187.99 [10072]~P9(x100723,x100727,x100726)+E(x100721,x100722)+~P14(x100723,f872(x100725,a860),x100726,x100724)+~E(f323(f323(f39(x100723,f872(x100725,a860)),x100721),x100724),f323(f323(f39(x100723,f872(x100725,a860)),x100722),x100724))+P101(f323(f323(f325(x100723),f510(x100721,x100722,x100724,x100725,x100726,x100727,x100723)),x100727))+~P101(f323(f323(f325(f872(x100723,a860)),x100722),f323(f323(f58(x100723),x100727),x100726)))+~P101(f323(f323(f325(f872(x100723,a860)),x100721),f323(f323(f58(x100723),x100727),x100726)))
% 188.07/187.99 [10141]E(x101411,x101412)+~P9(x101413,x101416,x101417)+~P14(x101413,f872(x101414,a860),x101417,x101415)+~E(f323(f323(f39(x101413,f872(x101414,a860)),x101411),x101415),f323(f323(f39(x101413,f872(x101414,a860)),x101412),x101415))+~P101(f323(f323(f325(f871(x101413,x101413)),f323(f323(f258(x101413,x101413),f511(x101411,x101412,x101415,x101414,x101417,x101416,x101413)),f510(x101411,x101412,x101415,x101414,x101417,x101416,x101413))),x101417))+~P101(f323(f323(f325(f872(x101413,a860)),x101412),f323(f323(f58(x101413),x101416),x101417)))+~P101(f323(f323(f325(f872(x101413,a860)),x101411),f323(f323(f58(x101413),x101416),x101417)))
% 188.07/187.99 [9038]~P9(x90381,x90387,x90384)+~E(x90385,x90386)+~P101(f323(f323(f325(x90381),x90383),x90386))+~P101(f323(f323(f325(x90381),x90382),x90385))+~P101(f323(f323(f325(f872(x90381,a860)),x90386),f323(f323(f58(x90381),x90387),x90384)))+~P101(f323(f323(f325(f872(x90381,a860)),x90385),f323(f323(f58(x90381),x90387),x90384)))+P101(f323(f323(f325(f871(x90381,x90381)),f323(f323(f258(x90381,x90381),x90382),x90383)),x90384))
% 188.07/187.99 [9176]E(x91761,x91762)+~P9(x91763,x91764,x91765)+~P101(f323(f323(f325(x91763),x91766),x91762))+~P101(f323(f323(f325(x91763),x91767),x91761))+~P101(f323(f323(f325(f872(x91763,a860)),x91762),f323(f323(f58(x91763),x91764),x91765)))+~P101(f323(f323(f325(f872(x91763,a860)),x91761),f323(f323(f58(x91763),x91764),x91765)))+~P101(f323(f323(f325(f871(x91763,x91763)),f323(f323(f258(x91763,x91763),x91767),x91766)),x91765))
% 188.07/187.99 [10160]~P9(x101609,x101608,x101607)+~P9(x101601,x1016011,x1016010)+~P15(x101601,x101609,f872(x101606,a860),x1016010,x101607,x101605)+P101(f323(f323(f325(x101601),f504(x101602,x101603,x101604,x101605,x101606,x101607,x101608,x101609,x1016010,x1016011,x101601)),x1016011))+~P101(f323(f323(f325(f872(x101609,a860)),x101603),f323(f323(f58(x101609),x101608),x101607)))+~P101(f323(f323(f325(f872(x101601,a860)),x101604),f323(f323(f58(x101601),x1016011),x1016010)))+P101(f323(f323(f325(f872(x101606,a860)),f323(f323(f39(x101601,f872(x101606,a860)),x101604),f323(f323(f8(f872(x101609,f872(x101606,a860)),f872(x101606,a860),x101601),f323(f39(x101609,f872(x101606,a860)),x101603)),x101605))),x101602))
% 188.07/187.99 [10161]~P9(x1016111,x1016110,x101619)+~P9(x101611,x101618,x101617)+~P15(x1016111,x101611,f872(x101616,a860),x101619,x101617,x101615)+P101(f323(f323(f325(x101611),f505(x101612,x101613,x101614,x101615,x101616,x101617,x101618,x101611,x101619,x1016110,x1016111)),x101618))+~P101(f323(f323(f325(f872(x1016111,a860)),x101614),f323(f323(f58(x1016111),x1016110),x101619)))+~P101(f323(f323(f325(f872(x101611,a860)),x101613),f323(f323(f58(x101611),x101618),x101617)))+P101(f323(f323(f325(f872(x101616,a860)),f323(f323(f39(x1016111,f872(x101616,a860)),x101614),f323(f323(f8(f872(x101611,f872(x101616,a860)),f872(x101616,a860),x1016111),f323(f39(x101611,f872(x101616,a860)),x101613)),x101615))),x101612))
% 188.07/187.99 [10164]~P9(x101642,x101648,x101649)+~P9(x101644,x1016410,x1016411)+~P15(x101642,x101644,f872(x101641,a860),x101649,x1016411,x101646)+~P101(f323(f323(f325(f872(x101642,a860)),x101643),f323(f323(f58(x101642),x101648),x101649)))+~P101(f323(f323(f325(f872(x101644,a860)),x101645),f323(f323(f58(x101644),x1016410),x1016411)))+~P101(f323(f323(f325(f872(x101641,a860)),f323(f323(x101646,f504(x101647,x101645,x101643,x101646,x101641,x1016411,x1016410,x101644,x101649,x101648,x101642)),f505(x101647,x101645,x101643,x101646,x101641,x1016411,x1016410,x101644,x101649,x101648,x101642))),x101647))+P101(f323(f323(f325(f872(x101641,a860)),f323(f323(f39(x101642,f872(x101641,a860)),x101643),f323(f323(f8(f872(x101644,f872(x101641,a860)),f872(x101641,a860),x101642),f323(f39(x101644,f872(x101641,a860)),x101645)),x101646))),x101647))
% 188.07/187.99 [9074]E(x90741,x90742)+~P103(x90744)+~P27(x90743,x90744,x90745,f323(f323(f110(f872(x90743,a860)),f323(f166(x90743),x90741)),f323(f166(x90743),x90742)))+~E(f323(f166(x90743),x90741),f323(f166(x90743),x90742))+~P16(x90744,f323(f323(f147(x90743,x90744),x90745),x90742))+~P16(x90744,f323(f323(f147(x90743,x90744),x90745),x90741))+~P101(f323(f130(x90744),f323(f323(f147(x90743,x90744),x90745),x90742)))+~P101(f323(f130(x90744),f323(f323(f147(x90743,x90744),x90745),x90741)))
% 188.07/187.99 %EqnAxiom
% 188.07/187.99 [1]E(x11,x11)
% 188.07/187.99 [2]E(x22,x21)+~E(x21,x22)
% 188.07/187.99 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 188.07/187.99 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 188.07/187.99 [5]~E(x51,x52)+E(f100(x51),f100(x52))
% 188.07/187.99 [6]~E(x61,x62)+E(f22(x61),f22(x62))
% 188.07/187.99 [7]~E(x71,x72)+E(f188(x71),f188(x72))
% 188.07/187.99 [8]~E(x81,x82)+E(f323(x81,x83),f323(x82,x83))
% 188.07/187.99 [9]~E(x91,x92)+E(f323(x93,x91),f323(x93,x92))
% 188.07/187.99 [10]~E(x101,x102)+E(f28(x101),f28(x102))
% 188.07/187.99 [11]~E(x111,x112)+E(f758(x111,x113,x114,x115),f758(x112,x113,x114,x115))
% 188.07/187.99 [12]~E(x121,x122)+E(f758(x123,x121,x124,x125),f758(x123,x122,x124,x125))
% 188.07/187.99 [13]~E(x131,x132)+E(f758(x133,x134,x131,x135),f758(x133,x134,x132,x135))
% 188.07/187.99 [14]~E(x141,x142)+E(f758(x143,x144,x145,x141),f758(x143,x144,x145,x142))
% 188.07/187.99 [15]~E(x151,x152)+E(f101(x151),f101(x152))
% 188.07/187.99 [16]~E(x161,x162)+E(f235(x161),f235(x162))
% 188.07/187.99 [17]~E(x171,x172)+E(f110(x171),f110(x172))
% 188.07/187.99 [18]~E(x181,x182)+E(f236(x181),f236(x182))
% 188.07/187.99 [19]~E(x191,x192)+E(f102(x191),f102(x192))
% 188.07/187.99 [20]~E(x201,x202)+E(f32(x201),f32(x202))
% 188.07/187.99 [21]~E(x211,x212)+E(f82(x211),f82(x212))
% 188.07/187.99 [22]~E(x221,x222)+E(f76(x221),f76(x222))
% 188.07/187.99 [23]~E(x231,x232)+E(f302(x231,x233,x234),f302(x232,x233,x234))
% 188.07/187.99 [24]~E(x241,x242)+E(f302(x243,x241,x244),f302(x243,x242,x244))
% 188.07/187.99 [25]~E(x251,x252)+E(f302(x253,x254,x251),f302(x253,x254,x252))
% 188.07/187.99 [26]~E(x261,x262)+E(f505(x261,x263,x264,x265,x266,x267,x268,x269,x2610,x2611,x2612),f505(x262,x263,x264,x265,x266,x267,x268,x269,x2610,x2611,x2612))
% 188.07/187.99 [27]~E(x271,x272)+E(f505(x273,x271,x274,x275,x276,x277,x278,x279,x2710,x2711,x2712),f505(x273,x272,x274,x275,x276,x277,x278,x279,x2710,x2711,x2712))
% 188.07/187.99 [28]~E(x281,x282)+E(f505(x283,x284,x281,x285,x286,x287,x288,x289,x2810,x2811,x2812),f505(x283,x284,x282,x285,x286,x287,x288,x289,x2810,x2811,x2812))
% 188.07/187.99 [29]~E(x291,x292)+E(f505(x293,x294,x295,x291,x296,x297,x298,x299,x2910,x2911,x2912),f505(x293,x294,x295,x292,x296,x297,x298,x299,x2910,x2911,x2912))
% 188.07/187.99 [30]~E(x301,x302)+E(f505(x303,x304,x305,x306,x301,x307,x308,x309,x3010,x3011,x3012),f505(x303,x304,x305,x306,x302,x307,x308,x309,x3010,x3011,x3012))
% 188.07/187.99 [31]~E(x311,x312)+E(f505(x313,x314,x315,x316,x317,x311,x318,x319,x3110,x3111,x3112),f505(x313,x314,x315,x316,x317,x312,x318,x319,x3110,x3111,x3112))
% 188.07/187.99 [32]~E(x321,x322)+E(f505(x323,x324,x325,x326,x327,x328,x321,x329,x3210,x3211,x3212),f505(x323,x324,x325,x326,x327,x328,x322,x329,x3210,x3211,x3212))
% 188.07/187.99 [33]~E(x331,x332)+E(f505(x333,x334,x335,x336,x337,x338,x339,x331,x3310,x3311,x3312),f505(x333,x334,x335,x336,x337,x338,x339,x332,x3310,x3311,x3312))
% 188.07/187.99 [34]~E(x341,x342)+E(f505(x343,x344,x345,x346,x347,x348,x349,x3410,x341,x3411,x3412),f505(x343,x344,x345,x346,x347,x348,x349,x3410,x342,x3411,x3412))
% 188.07/187.99 [35]~E(x351,x352)+E(f505(x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x351,x3512),f505(x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x352,x3512))
% 188.07/187.99 [36]~E(x361,x362)+E(f505(x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612,x361),f505(x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612,x362))
% 188.07/187.99 [37]~E(x371,x372)+E(f257(x371,x373),f257(x372,x373))
% 188.07/187.99 [38]~E(x381,x382)+E(f257(x383,x381),f257(x383,x382))
% 188.07/187.99 [39]~E(x391,x392)+E(f79(x391),f79(x392))
% 188.07/187.99 [40]~E(x401,x402)+E(f504(x401,x403,x404,x405,x406,x407,x408,x409,x4010,x4011,x4012),f504(x402,x403,x404,x405,x406,x407,x408,x409,x4010,x4011,x4012))
% 188.07/187.99 [41]~E(x411,x412)+E(f504(x413,x411,x414,x415,x416,x417,x418,x419,x4110,x4111,x4112),f504(x413,x412,x414,x415,x416,x417,x418,x419,x4110,x4111,x4112))
% 188.07/187.99 [42]~E(x421,x422)+E(f504(x423,x424,x421,x425,x426,x427,x428,x429,x4210,x4211,x4212),f504(x423,x424,x422,x425,x426,x427,x428,x429,x4210,x4211,x4212))
% 188.07/187.99 [43]~E(x431,x432)+E(f504(x433,x434,x435,x431,x436,x437,x438,x439,x4310,x4311,x4312),f504(x433,x434,x435,x432,x436,x437,x438,x439,x4310,x4311,x4312))
% 188.07/187.99 [44]~E(x441,x442)+E(f504(x443,x444,x445,x446,x441,x447,x448,x449,x4410,x4411,x4412),f504(x443,x444,x445,x446,x442,x447,x448,x449,x4410,x4411,x4412))
% 188.07/187.99 [45]~E(x451,x452)+E(f504(x453,x454,x455,x456,x457,x451,x458,x459,x4510,x4511,x4512),f504(x453,x454,x455,x456,x457,x452,x458,x459,x4510,x4511,x4512))
% 188.07/187.99 [46]~E(x461,x462)+E(f504(x463,x464,x465,x466,x467,x468,x461,x469,x4610,x4611,x4612),f504(x463,x464,x465,x466,x467,x468,x462,x469,x4610,x4611,x4612))
% 188.07/187.99 [47]~E(x471,x472)+E(f504(x473,x474,x475,x476,x477,x478,x479,x471,x4710,x4711,x4712),f504(x473,x474,x475,x476,x477,x478,x479,x472,x4710,x4711,x4712))
% 188.07/187.99 [48]~E(x481,x482)+E(f504(x483,x484,x485,x486,x487,x488,x489,x4810,x481,x4811,x4812),f504(x483,x484,x485,x486,x487,x488,x489,x4810,x482,x4811,x4812))
% 188.07/187.99 [49]~E(x491,x492)+E(f504(x493,x494,x495,x496,x497,x498,x499,x4910,x4911,x491,x4912),f504(x493,x494,x495,x496,x497,x498,x499,x4910,x4911,x492,x4912))
% 188.07/187.99 [50]~E(x501,x502)+E(f504(x503,x504,x505,x506,x507,x508,x509,x5010,x5011,x5012,x501),f504(x503,x504,x505,x506,x507,x508,x509,x5010,x5011,x5012,x502))
% 188.07/187.99 [51]~E(x511,x512)+E(f111(x511),f111(x512))
% 188.07/187.99 [52]~E(x521,x522)+E(f325(x521),f325(x522))
% 188.07/187.99 [53]~E(x531,x532)+E(f872(x531,x533),f872(x532,x533))
% 188.07/187.99 [54]~E(x541,x542)+E(f872(x543,x541),f872(x543,x542))
% 188.07/187.99 [55]~E(x551,x552)+E(f4(x551),f4(x552))
% 188.07/187.99 [56]~E(x561,x562)+E(f78(x561),f78(x562))
% 188.07/187.99 [57]~E(x571,x572)+E(f864(x571),f864(x572))
% 188.07/187.99 [58]~E(x581,x582)+E(f869(x581),f869(x582))
% 188.07/187.99 [59]~E(x591,x592)+E(f866(x591),f866(x592))
% 188.07/187.99 [60]~E(x601,x602)+E(f867(x601),f867(x602))
% 188.07/187.99 [61]~E(x611,x612)+E(f238(x611),f238(x612))
% 188.07/187.99 [62]~E(x621,x622)+E(f59(x621),f59(x622))
% 188.07/187.99 [63]~E(x631,x632)+E(f90(x631),f90(x632))
% 188.07/187.99 [64]~E(x641,x642)+E(f36(x641),f36(x642))
% 188.07/187.99 [65]~E(x651,x652)+E(f77(x651),f77(x652))
% 188.07/187.99 [66]~E(x661,x662)+E(f73(x661),f73(x662))
% 188.07/187.99 [67]~E(x671,x672)+E(f189(x671),f189(x672))
% 188.07/187.99 [68]~E(x681,x682)+E(f237(x681),f237(x682))
% 188.07/187.99 [69]~E(x691,x692)+E(f103(x691),f103(x692))
% 188.07/187.99 [70]~E(x701,x702)+E(f137(x701,x703),f137(x702,x703))
% 188.07/187.99 [71]~E(x711,x712)+E(f137(x713,x711),f137(x713,x712))
% 188.07/187.99 [72]~E(x721,x722)+E(f144(x721),f144(x722))
% 188.07/187.99 [73]~E(x731,x732)+E(f871(x731,x733),f871(x732,x733))
% 188.07/187.99 [74]~E(x741,x742)+E(f871(x743,x741),f871(x743,x742))
% 188.07/187.99 [75]~E(x751,x752)+E(f301(x751),f301(x752))
% 188.07/187.99 [76]~E(x761,x762)+E(f311(x761,x763),f311(x762,x763))
% 188.07/187.99 [77]~E(x771,x772)+E(f311(x773,x771),f311(x773,x772))
% 188.07/187.99 [78]~E(x781,x782)+E(f757(x781,x783,x784,x785),f757(x782,x783,x784,x785))
% 188.07/187.99 [79]~E(x791,x792)+E(f757(x793,x791,x794,x795),f757(x793,x792,x794,x795))
% 188.07/187.99 [80]~E(x801,x802)+E(f757(x803,x804,x801,x805),f757(x803,x804,x802,x805))
% 188.07/187.99 [81]~E(x811,x812)+E(f757(x813,x814,x815,x811),f757(x813,x814,x815,x812))
% 188.07/187.99 [82]~E(x821,x822)+E(f141(x821,x823,x824),f141(x822,x823,x824))
% 188.07/187.99 [83]~E(x831,x832)+E(f141(x833,x831,x834),f141(x833,x832,x834))
% 188.07/187.99 [84]~E(x841,x842)+E(f141(x843,x844,x841),f141(x843,x844,x842))
% 188.07/187.99 [85]~E(x851,x852)+E(f129(x851,x853),f129(x852,x853))
% 188.07/187.99 [86]~E(x861,x862)+E(f129(x863,x861),f129(x863,x862))
% 188.07/187.99 [87]~E(x871,x872)+E(f248(x871),f248(x872))
% 188.07/187.99 [88]~E(x881,x882)+E(f200(x881),f200(x882))
% 188.07/187.99 [89]~E(x891,x892)+E(f621(x891,x893,x894,x895,x896,x897),f621(x892,x893,x894,x895,x896,x897))
% 188.07/187.99 [90]~E(x901,x902)+E(f621(x903,x901,x904,x905,x906,x907),f621(x903,x902,x904,x905,x906,x907))
% 188.07/187.99 [91]~E(x911,x912)+E(f621(x913,x914,x911,x915,x916,x917),f621(x913,x914,x912,x915,x916,x917))
% 188.07/187.99 [92]~E(x921,x922)+E(f621(x923,x924,x925,x921,x926,x927),f621(x923,x924,x925,x922,x926,x927))
% 188.07/187.99 [93]~E(x931,x932)+E(f621(x933,x934,x935,x936,x931,x937),f621(x933,x934,x935,x936,x932,x937))
% 188.07/187.99 [94]~E(x941,x942)+E(f621(x943,x944,x945,x946,x947,x941),f621(x943,x944,x945,x946,x947,x942))
% 188.07/187.99 [95]~E(x951,x952)+E(f121(x951),f121(x952))
% 188.07/187.99 [96]~E(x961,x962)+E(f58(x961),f58(x962))
% 188.07/187.99 [97]~E(x971,x972)+E(f260(x971,x973),f260(x972,x973))
% 188.07/187.99 [98]~E(x981,x982)+E(f260(x983,x981),f260(x983,x982))
% 188.07/187.99 [99]~E(x991,x992)+E(f14(x991,x993),f14(x992,x993))
% 188.07/187.99 [100]~E(x1001,x1002)+E(f14(x1003,x1001),f14(x1003,x1002))
% 188.07/187.99 [101]~E(x1011,x1012)+E(f443(x1011,x1013,x1014),f443(x1012,x1013,x1014))
% 188.07/187.99 [102]~E(x1021,x1022)+E(f443(x1023,x1021,x1024),f443(x1023,x1022,x1024))
% 188.07/187.99 [103]~E(x1031,x1032)+E(f443(x1033,x1034,x1031),f443(x1033,x1034,x1032))
% 188.07/187.99 [104]~E(x1041,x1042)+E(f398(x1041,x1043,x1044,x1045),f398(x1042,x1043,x1044,x1045))
% 188.07/187.99 [105]~E(x1051,x1052)+E(f398(x1053,x1051,x1054,x1055),f398(x1053,x1052,x1054,x1055))
% 188.07/187.99 [106]~E(x1061,x1062)+E(f398(x1063,x1064,x1061,x1065),f398(x1063,x1064,x1062,x1065))
% 188.07/187.99 [107]~E(x1071,x1072)+E(f398(x1073,x1074,x1075,x1071),f398(x1073,x1074,x1075,x1072))
% 188.07/187.99 [108]~E(x1081,x1082)+E(f262(x1081,x1083,x1084),f262(x1082,x1083,x1084))
% 188.07/187.99 [109]~E(x1091,x1092)+E(f262(x1093,x1091,x1094),f262(x1093,x1092,x1094))
% 188.07/187.99 [110]~E(x1101,x1102)+E(f262(x1103,x1104,x1101),f262(x1103,x1104,x1102))
% 188.07/187.99 [111]~E(x1111,x1112)+E(f281(x1111),f281(x1112))
% 188.07/187.99 [112]~E(x1121,x1122)+E(f258(x1121,x1123),f258(x1122,x1123))
% 188.07/187.99 [113]~E(x1131,x1132)+E(f258(x1133,x1131),f258(x1133,x1132))
% 188.07/187.99 [114]~E(x1141,x1142)+E(f63(x1141,x1143,x1144),f63(x1142,x1143,x1144))
% 188.07/187.99 [115]~E(x1151,x1152)+E(f63(x1153,x1151,x1154),f63(x1153,x1152,x1154))
% 188.07/187.99 [116]~E(x1161,x1162)+E(f63(x1163,x1164,x1161),f63(x1163,x1164,x1162))
% 188.07/187.99 [117]~E(x1171,x1172)+E(f38(x1171,x1173),f38(x1172,x1173))
% 188.07/187.99 [118]~E(x1181,x1182)+E(f38(x1183,x1181),f38(x1183,x1182))
% 188.07/187.99 [119]~E(x1191,x1192)+E(f40(x1191,x1193),f40(x1192,x1193))
% 188.07/187.99 [120]~E(x1201,x1202)+E(f40(x1203,x1201),f40(x1203,x1202))
% 188.07/187.99 [121]~E(x1211,x1212)+E(f8(x1211,x1213,x1214),f8(x1212,x1213,x1214))
% 188.07/187.99 [122]~E(x1221,x1222)+E(f8(x1223,x1221,x1224),f8(x1223,x1222,x1224))
% 188.07/187.99 [123]~E(x1231,x1232)+E(f8(x1233,x1234,x1231),f8(x1233,x1234,x1232))
% 188.07/187.99 [124]~E(x1241,x1242)+E(f147(x1241,x1243),f147(x1242,x1243))
% 188.07/187.99 [125]~E(x1251,x1252)+E(f147(x1253,x1251),f147(x1253,x1252))
% 188.07/187.99 [126]~E(x1261,x1262)+E(f135(x1261,x1263,x1264,x1265),f135(x1262,x1263,x1264,x1265))
% 188.07/187.99 [127]~E(x1271,x1272)+E(f135(x1273,x1271,x1274,x1275),f135(x1273,x1272,x1274,x1275))
% 188.07/187.99 [128]~E(x1281,x1282)+E(f135(x1283,x1284,x1281,x1285),f135(x1283,x1284,x1282,x1285))
% 188.07/187.99 [129]~E(x1291,x1292)+E(f135(x1293,x1294,x1295,x1291),f135(x1293,x1294,x1295,x1292))
% 188.07/187.99 [130]~E(x1301,x1302)+E(f513(x1301,x1303,x1304,x1305),f513(x1302,x1303,x1304,x1305))
% 188.07/187.99 [131]~E(x1311,x1312)+E(f513(x1313,x1311,x1314,x1315),f513(x1313,x1312,x1314,x1315))
% 188.07/187.99 [132]~E(x1321,x1322)+E(f513(x1323,x1324,x1321,x1325),f513(x1323,x1324,x1322,x1325))
% 188.07/187.99 [133]~E(x1331,x1332)+E(f513(x1333,x1334,x1335,x1331),f513(x1333,x1334,x1335,x1332))
% 188.07/187.99 [134]~E(x1341,x1342)+E(f559(x1341,x1343,x1344),f559(x1342,x1343,x1344))
% 188.07/187.99 [135]~E(x1351,x1352)+E(f559(x1353,x1351,x1354),f559(x1353,x1352,x1354))
% 188.07/187.99 [136]~E(x1361,x1362)+E(f559(x1363,x1364,x1361),f559(x1363,x1364,x1362))
% 188.07/187.99 [137]~E(x1371,x1372)+E(f9(x1371,x1373),f9(x1372,x1373))
% 188.07/187.99 [138]~E(x1381,x1382)+E(f9(x1383,x1381),f9(x1383,x1382))
% 188.07/187.99 [139]~E(x1391,x1392)+E(f71(x1391,x1393,x1394,x1395),f71(x1392,x1393,x1394,x1395))
% 188.07/187.99 [140]~E(x1401,x1402)+E(f71(x1403,x1401,x1404,x1405),f71(x1403,x1402,x1404,x1405))
% 188.07/187.99 [141]~E(x1411,x1412)+E(f71(x1413,x1414,x1411,x1415),f71(x1413,x1414,x1412,x1415))
% 188.07/187.99 [142]~E(x1421,x1422)+E(f71(x1423,x1424,x1425,x1421),f71(x1423,x1424,x1425,x1422))
% 188.07/187.99 [143]~E(x1431,x1432)+E(f362(x1431,x1433,x1434,x1435,x1436),f362(x1432,x1433,x1434,x1435,x1436))
% 188.07/187.99 [144]~E(x1441,x1442)+E(f362(x1443,x1441,x1444,x1445,x1446),f362(x1443,x1442,x1444,x1445,x1446))
% 188.07/187.99 [145]~E(x1451,x1452)+E(f362(x1453,x1454,x1451,x1455,x1456),f362(x1453,x1454,x1452,x1455,x1456))
% 188.07/187.99 [146]~E(x1461,x1462)+E(f362(x1463,x1464,x1465,x1461,x1466),f362(x1463,x1464,x1465,x1462,x1466))
% 188.07/187.99 [147]~E(x1471,x1472)+E(f362(x1473,x1474,x1475,x1476,x1471),f362(x1473,x1474,x1475,x1476,x1472))
% 188.07/187.99 [148]~E(x1481,x1482)+E(f261(x1481,x1483),f261(x1482,x1483))
% 188.07/187.99 [149]~E(x1491,x1492)+E(f261(x1493,x1491),f261(x1493,x1492))
% 188.07/187.99 [150]~E(x1501,x1502)+E(f134(x1501),f134(x1502))
% 188.07/187.99 [151]~E(x1511,x1512)+E(f113(x1511),f113(x1512))
% 188.07/187.99 [152]~E(x1521,x1522)+E(f246(x1521),f246(x1522))
% 188.07/187.99 [153]~E(x1531,x1532)+E(f35(x1531),f35(x1532))
% 188.07/187.99 [154]~E(x1541,x1542)+E(f802(x1541,x1543,x1544),f802(x1542,x1543,x1544))
% 188.15/187.99 [155]~E(x1551,x1552)+E(f802(x1553,x1551,x1554),f802(x1553,x1552,x1554))
% 188.15/187.99 [156]~E(x1561,x1562)+E(f802(x1563,x1564,x1561),f802(x1563,x1564,x1562))
% 188.15/187.99 [157]~E(x1571,x1572)+E(f183(x1571,x1573),f183(x1572,x1573))
% 188.15/187.99 [158]~E(x1581,x1582)+E(f183(x1583,x1581),f183(x1583,x1582))
% 188.15/187.99 [159]~E(x1591,x1592)+E(f130(x1591),f130(x1592))
% 188.15/187.99 [160]~E(x1601,x1602)+E(f42(x1601,x1603,x1604),f42(x1602,x1603,x1604))
% 188.15/187.99 [161]~E(x1611,x1612)+E(f42(x1613,x1611,x1614),f42(x1613,x1612,x1614))
% 188.15/187.99 [162]~E(x1621,x1622)+E(f42(x1623,x1624,x1621),f42(x1623,x1624,x1622))
% 188.15/187.99 [163]~E(x1631,x1632)+E(f105(x1631),f105(x1632))
% 188.15/187.99 [164]~E(x1641,x1642)+E(f106(x1641),f106(x1642))
% 188.15/187.99 [165]~E(x1651,x1652)+E(f324(x1651),f324(x1652))
% 188.15/187.99 [166]~E(x1661,x1662)+E(f7(x1661,x1663,x1664),f7(x1662,x1663,x1664))
% 188.15/187.99 [167]~E(x1671,x1672)+E(f7(x1673,x1671,x1674),f7(x1673,x1672,x1674))
% 188.15/187.99 [168]~E(x1681,x1682)+E(f7(x1683,x1684,x1681),f7(x1683,x1684,x1682))
% 188.15/187.99 [169]~E(x1691,x1692)+E(f169(x1691),f169(x1692))
% 188.15/187.99 [170]~E(x1701,x1702)+E(f299(x1701,x1703),f299(x1702,x1703))
% 188.15/187.99 [171]~E(x1711,x1712)+E(f299(x1713,x1711),f299(x1713,x1712))
% 188.15/187.99 [172]~E(x1721,x1722)+E(f39(x1721,x1723),f39(x1722,x1723))
% 188.15/187.99 [173]~E(x1731,x1732)+E(f39(x1733,x1731),f39(x1733,x1732))
% 188.15/187.99 [174]~E(x1741,x1742)+E(f243(x1741),f243(x1742))
% 188.15/187.99 [175]~E(x1751,x1752)+E(f694(x1751,x1753,x1754),f694(x1752,x1753,x1754))
% 188.15/187.99 [176]~E(x1761,x1762)+E(f694(x1763,x1761,x1764),f694(x1763,x1762,x1764))
% 188.15/187.99 [177]~E(x1771,x1772)+E(f694(x1773,x1774,x1771),f694(x1773,x1774,x1772))
% 188.15/187.99 [178]~E(x1781,x1782)+E(f5(x1781),f5(x1782))
% 188.15/187.99 [179]~E(x1791,x1792)+E(f62(x1791,x1793,x1794),f62(x1792,x1793,x1794))
% 188.15/187.99 [180]~E(x1801,x1802)+E(f62(x1803,x1801,x1804),f62(x1803,x1802,x1804))
% 188.15/187.99 [181]~E(x1811,x1812)+E(f62(x1813,x1814,x1811),f62(x1813,x1814,x1812))
% 188.15/187.99 [182]~E(x1821,x1822)+E(f159(x1821),f159(x1822))
% 188.15/187.99 [183]~E(x1831,x1832)+E(f18(x1831,x1833,x1834),f18(x1832,x1833,x1834))
% 188.15/187.99 [184]~E(x1841,x1842)+E(f18(x1843,x1841,x1844),f18(x1843,x1842,x1844))
% 188.15/187.99 [185]~E(x1851,x1852)+E(f18(x1853,x1854,x1851),f18(x1853,x1854,x1852))
% 188.15/187.99 [186]~E(x1861,x1862)+E(f264(x1861,x1863,x1864,x1865),f264(x1862,x1863,x1864,x1865))
% 188.15/187.99 [187]~E(x1871,x1872)+E(f264(x1873,x1871,x1874,x1875),f264(x1873,x1872,x1874,x1875))
% 188.15/187.99 [188]~E(x1881,x1882)+E(f264(x1883,x1884,x1881,x1885),f264(x1883,x1884,x1882,x1885))
% 188.15/187.99 [189]~E(x1891,x1892)+E(f264(x1893,x1894,x1895,x1891),f264(x1893,x1894,x1895,x1892))
% 188.15/187.99 [190]~E(x1901,x1902)+E(f37(x1901,x1903),f37(x1902,x1903))
% 188.15/187.99 [191]~E(x1911,x1912)+E(f37(x1913,x1911),f37(x1913,x1912))
% 188.15/187.99 [192]~E(x1921,x1922)+E(f230(x1921),f230(x1922))
% 188.15/187.99 [193]~E(x1931,x1932)+E(f294(x1931,x1933,x1934),f294(x1932,x1933,x1934))
% 188.15/187.99 [194]~E(x1941,x1942)+E(f294(x1943,x1941,x1944),f294(x1943,x1942,x1944))
% 188.15/187.99 [195]~E(x1951,x1952)+E(f294(x1953,x1954,x1951),f294(x1953,x1954,x1952))
% 188.15/187.99 [196]~E(x1961,x1962)+E(f27(x1961,x1963,x1964),f27(x1962,x1963,x1964))
% 188.15/187.99 [197]~E(x1971,x1972)+E(f27(x1973,x1971,x1974),f27(x1973,x1972,x1974))
% 188.15/187.99 [198]~E(x1981,x1982)+E(f27(x1983,x1984,x1981),f27(x1983,x1984,x1982))
% 188.15/187.99 [199]~E(x1991,x1992)+E(f197(x1991,x1993,x1994,x1995),f197(x1992,x1993,x1994,x1995))
% 188.15/187.99 [200]~E(x2001,x2002)+E(f197(x2003,x2001,x2004,x2005),f197(x2003,x2002,x2004,x2005))
% 188.15/187.99 [201]~E(x2011,x2012)+E(f197(x2013,x2014,x2011,x2015),f197(x2013,x2014,x2012,x2015))
% 188.15/187.99 [202]~E(x2021,x2022)+E(f197(x2023,x2024,x2025,x2021),f197(x2023,x2024,x2025,x2022))
% 188.15/187.99 [203]~E(x2031,x2032)+E(f232(x2031,x2033,x2034,x2035),f232(x2032,x2033,x2034,x2035))
% 188.15/187.99 [204]~E(x2041,x2042)+E(f232(x2043,x2041,x2044,x2045),f232(x2043,x2042,x2044,x2045))
% 188.15/187.99 [205]~E(x2051,x2052)+E(f232(x2053,x2054,x2051,x2055),f232(x2053,x2054,x2052,x2055))
% 188.15/187.99 [206]~E(x2061,x2062)+E(f232(x2063,x2064,x2065,x2061),f232(x2063,x2064,x2065,x2062))
% 188.15/187.99 [207]~E(x2071,x2072)+E(f716(x2071,x2073,x2074,x2075,x2076,x2077),f716(x2072,x2073,x2074,x2075,x2076,x2077))
% 188.15/187.99 [208]~E(x2081,x2082)+E(f716(x2083,x2081,x2084,x2085,x2086,x2087),f716(x2083,x2082,x2084,x2085,x2086,x2087))
% 188.15/187.99 [209]~E(x2091,x2092)+E(f716(x2093,x2094,x2091,x2095,x2096,x2097),f716(x2093,x2094,x2092,x2095,x2096,x2097))
% 188.15/187.99 [210]~E(x2101,x2102)+E(f716(x2103,x2104,x2105,x2101,x2106,x2107),f716(x2103,x2104,x2105,x2102,x2106,x2107))
% 188.15/187.99 [211]~E(x2111,x2112)+E(f716(x2113,x2114,x2115,x2116,x2111,x2117),f716(x2113,x2114,x2115,x2116,x2112,x2117))
% 188.15/187.99 [212]~E(x2121,x2122)+E(f716(x2123,x2124,x2125,x2126,x2127,x2121),f716(x2123,x2124,x2125,x2126,x2127,x2122))
% 188.15/187.99 [213]~E(x2131,x2132)+E(f800(x2131,x2133,x2134),f800(x2132,x2133,x2134))
% 188.15/187.99 [214]~E(x2141,x2142)+E(f800(x2143,x2141,x2144),f800(x2143,x2142,x2144))
% 188.15/187.99 [215]~E(x2151,x2152)+E(f800(x2153,x2154,x2151),f800(x2153,x2154,x2152))
% 188.15/187.99 [216]~E(x2161,x2162)+E(f395(x2161,x2163),f395(x2162,x2163))
% 188.15/187.99 [217]~E(x2171,x2172)+E(f395(x2173,x2171),f395(x2173,x2172))
% 188.15/187.99 [218]~E(x2181,x2182)+E(f131(x2181),f131(x2182))
% 188.15/187.99 [219]~E(x2191,x2192)+E(f6(x2191,x2193),f6(x2192,x2193))
% 188.15/187.99 [220]~E(x2201,x2202)+E(f6(x2203,x2201),f6(x2203,x2202))
% 188.15/187.99 [221]~E(x2211,x2212)+E(f158(x2211),f158(x2212))
% 188.15/187.99 [222]~E(x2221,x2222)+E(f11(x2221,x2223),f11(x2222,x2223))
% 188.15/187.99 [223]~E(x2231,x2232)+E(f11(x2233,x2231),f11(x2233,x2232))
% 188.15/187.99 [224]~E(x2241,x2242)+E(f91(x2241,x2243,x2244,x2245),f91(x2242,x2243,x2244,x2245))
% 188.15/187.99 [225]~E(x2251,x2252)+E(f91(x2253,x2251,x2254,x2255),f91(x2253,x2252,x2254,x2255))
% 188.15/187.99 [226]~E(x2261,x2262)+E(f91(x2263,x2264,x2261,x2265),f91(x2263,x2264,x2262,x2265))
% 188.15/187.99 [227]~E(x2271,x2272)+E(f91(x2273,x2274,x2275,x2271),f91(x2273,x2274,x2275,x2272))
% 188.15/187.99 [228]~E(x2281,x2282)+E(f10(x2281,x2283),f10(x2282,x2283))
% 188.15/187.99 [229]~E(x2291,x2292)+E(f10(x2293,x2291),f10(x2293,x2292))
% 188.15/187.99 [230]~E(x2301,x2302)+E(f96(x2301),f96(x2302))
% 188.15/187.99 [231]~E(x2311,x2312)+E(f175(x2311,x2313),f175(x2312,x2313))
% 188.15/187.99 [232]~E(x2321,x2322)+E(f175(x2323,x2321),f175(x2323,x2322))
% 188.15/187.99 [233]~E(x2331,x2332)+E(f162(x2331),f162(x2332))
% 188.15/187.99 [234]~E(x2341,x2342)+E(f799(x2341,x2343,x2344),f799(x2342,x2343,x2344))
% 188.15/187.99 [235]~E(x2351,x2352)+E(f799(x2353,x2351,x2354),f799(x2353,x2352,x2354))
% 188.15/187.99 [236]~E(x2361,x2362)+E(f799(x2363,x2364,x2361),f799(x2363,x2364,x2362))
% 188.15/187.99 [237]~E(x2371,x2372)+E(f280(x2371,x2373,x2374),f280(x2372,x2373,x2374))
% 188.15/187.99 [238]~E(x2381,x2382)+E(f280(x2383,x2381,x2384),f280(x2383,x2382,x2384))
% 188.15/187.99 [239]~E(x2391,x2392)+E(f280(x2393,x2394,x2391),f280(x2393,x2394,x2392))
% 188.15/187.99 [240]~E(x2401,x2402)+E(f44(x2401,x2403),f44(x2402,x2403))
% 188.15/187.99 [241]~E(x2411,x2412)+E(f44(x2413,x2411),f44(x2413,x2412))
% 188.15/187.99 [242]~E(x2421,x2422)+E(f457(x2421,x2423,x2424,x2425),f457(x2422,x2423,x2424,x2425))
% 188.15/187.99 [243]~E(x2431,x2432)+E(f457(x2433,x2431,x2434,x2435),f457(x2433,x2432,x2434,x2435))
% 188.15/187.99 [244]~E(x2441,x2442)+E(f457(x2443,x2444,x2441,x2445),f457(x2443,x2444,x2442,x2445))
% 188.15/187.99 [245]~E(x2451,x2452)+E(f457(x2453,x2454,x2455,x2451),f457(x2453,x2454,x2455,x2452))
% 188.15/187.99 [246]~E(x2461,x2462)+E(f292(x2461),f292(x2462))
% 188.15/187.99 [247]~E(x2471,x2472)+E(f698(x2471,x2473,x2474,x2475,x2476,x2477),f698(x2472,x2473,x2474,x2475,x2476,x2477))
% 188.15/187.99 [248]~E(x2481,x2482)+E(f698(x2483,x2481,x2484,x2485,x2486,x2487),f698(x2483,x2482,x2484,x2485,x2486,x2487))
% 188.15/187.99 [249]~E(x2491,x2492)+E(f698(x2493,x2494,x2491,x2495,x2496,x2497),f698(x2493,x2494,x2492,x2495,x2496,x2497))
% 188.15/187.99 [250]~E(x2501,x2502)+E(f698(x2503,x2504,x2505,x2501,x2506,x2507),f698(x2503,x2504,x2505,x2502,x2506,x2507))
% 188.15/187.99 [251]~E(x2511,x2512)+E(f698(x2513,x2514,x2515,x2516,x2511,x2517),f698(x2513,x2514,x2515,x2516,x2512,x2517))
% 188.15/187.99 [252]~E(x2521,x2522)+E(f698(x2523,x2524,x2525,x2526,x2527,x2521),f698(x2523,x2524,x2525,x2526,x2527,x2522))
% 188.15/187.99 [253]~E(x2531,x2532)+E(f514(x2531,x2533,x2534),f514(x2532,x2533,x2534))
% 188.15/187.99 [254]~E(x2541,x2542)+E(f514(x2543,x2541,x2544),f514(x2543,x2542,x2544))
% 188.15/187.99 [255]~E(x2551,x2552)+E(f514(x2553,x2554,x2551),f514(x2553,x2554,x2552))
% 188.15/187.99 [256]~E(x2561,x2562)+E(f166(x2561),f166(x2562))
% 188.15/187.99 [257]~E(x2571,x2572)+E(f446(x2571,x2573,x2574,x2575),f446(x2572,x2573,x2574,x2575))
% 188.15/187.99 [258]~E(x2581,x2582)+E(f446(x2583,x2581,x2584,x2585),f446(x2583,x2582,x2584,x2585))
% 188.15/187.99 [259]~E(x2591,x2592)+E(f446(x2593,x2594,x2591,x2595),f446(x2593,x2594,x2592,x2595))
% 188.15/187.99 [260]~E(x2601,x2602)+E(f446(x2603,x2604,x2605,x2601),f446(x2603,x2604,x2605,x2602))
% 188.15/187.99 [261]~E(x2611,x2612)+E(f697(x2611,x2613,x2614,x2615,x2616,x2617),f697(x2612,x2613,x2614,x2615,x2616,x2617))
% 188.15/187.99 [262]~E(x2621,x2622)+E(f697(x2623,x2621,x2624,x2625,x2626,x2627),f697(x2623,x2622,x2624,x2625,x2626,x2627))
% 188.15/187.99 [263]~E(x2631,x2632)+E(f697(x2633,x2634,x2631,x2635,x2636,x2637),f697(x2633,x2634,x2632,x2635,x2636,x2637))
% 188.15/187.99 [264]~E(x2641,x2642)+E(f697(x2643,x2644,x2645,x2641,x2646,x2647),f697(x2643,x2644,x2645,x2642,x2646,x2647))
% 188.15/187.99 [265]~E(x2651,x2652)+E(f697(x2653,x2654,x2655,x2656,x2651,x2657),f697(x2653,x2654,x2655,x2656,x2652,x2657))
% 188.15/187.99 [266]~E(x2661,x2662)+E(f697(x2663,x2664,x2665,x2666,x2667,x2661),f697(x2663,x2664,x2665,x2666,x2667,x2662))
% 188.15/187.99 [267]~E(x2671,x2672)+E(f332(x2671,x2673,x2674),f332(x2672,x2673,x2674))
% 188.15/187.99 [268]~E(x2681,x2682)+E(f332(x2683,x2681,x2684),f332(x2683,x2682,x2684))
% 188.15/187.99 [269]~E(x2691,x2692)+E(f332(x2693,x2694,x2691),f332(x2693,x2694,x2692))
% 188.15/187.99 [270]~E(x2701,x2702)+E(f153(x2701,x2703),f153(x2702,x2703))
% 188.15/187.99 [271]~E(x2711,x2712)+E(f153(x2713,x2711),f153(x2713,x2712))
% 188.15/187.99 [272]~E(x2721,x2722)+E(f145(x2721,x2723),f145(x2722,x2723))
% 188.15/187.99 [273]~E(x2731,x2732)+E(f145(x2733,x2731),f145(x2733,x2732))
% 188.15/187.99 [274]~E(x2741,x2742)+E(f56(x2741),f56(x2742))
% 188.15/187.99 [275]~E(x2751,x2752)+E(f303(x2751,x2753,x2754),f303(x2752,x2753,x2754))
% 188.15/187.99 [276]~E(x2761,x2762)+E(f303(x2763,x2761,x2764),f303(x2763,x2762,x2764))
% 188.15/187.99 [277]~E(x2771,x2772)+E(f303(x2773,x2774,x2771),f303(x2773,x2774,x2772))
% 188.15/187.99 [278]~E(x2781,x2782)+E(f114(x2781,x2783),f114(x2782,x2783))
% 188.15/187.99 [279]~E(x2791,x2792)+E(f114(x2793,x2791),f114(x2793,x2792))
% 188.15/187.99 [280]~E(x2801,x2802)+E(f163(x2801,x2803,x2804),f163(x2802,x2803,x2804))
% 188.15/187.99 [281]~E(x2811,x2812)+E(f163(x2813,x2811,x2814),f163(x2813,x2812,x2814))
% 188.15/187.99 [282]~E(x2821,x2822)+E(f163(x2823,x2824,x2821),f163(x2823,x2824,x2822))
% 188.15/187.99 [283]~E(x2831,x2832)+E(f191(x2831),f191(x2832))
% 188.15/187.99 [284]~E(x2841,x2842)+E(f70(x2841,x2843),f70(x2842,x2843))
% 188.15/187.99 [285]~E(x2851,x2852)+E(f70(x2853,x2851),f70(x2853,x2852))
% 188.15/187.99 [286]~E(x2861,x2862)+E(f115(x2861),f115(x2862))
% 188.15/187.99 [287]~E(x2871,x2872)+E(f870(x2871,x2873),f870(x2872,x2873))
% 188.15/187.99 [288]~E(x2881,x2882)+E(f870(x2883,x2881),f870(x2883,x2882))
% 188.15/187.99 [289]~E(x2891,x2892)+E(f277(x2891,x2893,x2894),f277(x2892,x2893,x2894))
% 188.15/187.99 [290]~E(x2901,x2902)+E(f277(x2903,x2901,x2904),f277(x2903,x2902,x2904))
% 188.15/187.99 [291]~E(x2911,x2912)+E(f277(x2913,x2914,x2911),f277(x2913,x2914,x2912))
% 188.15/187.99 [292]~E(x2921,x2922)+E(f256(x2921,x2923),f256(x2922,x2923))
% 188.15/187.99 [293]~E(x2931,x2932)+E(f256(x2933,x2931),f256(x2933,x2932))
% 188.15/187.99 [294]~E(x2941,x2942)+E(f293(x2941,x2943),f293(x2942,x2943))
% 188.15/187.99 [295]~E(x2951,x2952)+E(f293(x2953,x2951),f293(x2953,x2952))
% 188.15/187.99 [296]~E(x2961,x2962)+E(f161(x2961),f161(x2962))
% 188.15/187.99 [297]~E(x2971,x2972)+E(f267(x2971,x2973),f267(x2972,x2973))
% 188.15/187.99 [298]~E(x2981,x2982)+E(f267(x2983,x2981),f267(x2983,x2982))
% 188.15/187.99 [299]~E(x2991,x2992)+E(f808(x2991,x2993,x2994),f808(x2992,x2993,x2994))
% 188.15/187.99 [300]~E(x3001,x3002)+E(f808(x3003,x3001,x3004),f808(x3003,x3002,x3004))
% 188.15/187.99 [301]~E(x3011,x3012)+E(f808(x3013,x3014,x3011),f808(x3013,x3014,x3012))
% 188.15/187.99 [302]~E(x3021,x3022)+E(f263(x3021,x3023,x3024,x3025,x3026,x3027),f263(x3022,x3023,x3024,x3025,x3026,x3027))
% 188.15/187.99 [303]~E(x3031,x3032)+E(f263(x3033,x3031,x3034,x3035,x3036,x3037),f263(x3033,x3032,x3034,x3035,x3036,x3037))
% 188.15/187.99 [304]~E(x3041,x3042)+E(f263(x3043,x3044,x3041,x3045,x3046,x3047),f263(x3043,x3044,x3042,x3045,x3046,x3047))
% 188.15/187.99 [305]~E(x3051,x3052)+E(f263(x3053,x3054,x3055,x3051,x3056,x3057),f263(x3053,x3054,x3055,x3052,x3056,x3057))
% 188.15/187.99 [306]~E(x3061,x3062)+E(f263(x3063,x3064,x3065,x3066,x3061,x3067),f263(x3063,x3064,x3065,x3066,x3062,x3067))
% 188.15/187.99 [307]~E(x3071,x3072)+E(f263(x3073,x3074,x3075,x3076,x3077,x3071),f263(x3073,x3074,x3075,x3076,x3077,x3072))
% 188.15/187.99 [308]~E(x3081,x3082)+E(f165(x3081),f165(x3082))
% 188.15/187.99 [309]~E(x3091,x3092)+E(f179(x3091,x3093),f179(x3092,x3093))
% 188.15/187.99 [310]~E(x3101,x3102)+E(f179(x3103,x3101),f179(x3103,x3102))
% 188.15/187.99 [311]~E(x3111,x3112)+E(f132(x3111,x3113),f132(x3112,x3113))
% 188.15/187.99 [312]~E(x3121,x3122)+E(f132(x3123,x3121),f132(x3123,x3122))
% 188.15/187.99 [313]~E(x3131,x3132)+E(f245(x3131),f245(x3132))
% 188.15/187.99 [314]~E(x3141,x3142)+E(f414(x3141,x3143,x3144,x3145),f414(x3142,x3143,x3144,x3145))
% 188.15/187.99 [315]~E(x3151,x3152)+E(f414(x3153,x3151,x3154,x3155),f414(x3153,x3152,x3154,x3155))
% 188.15/187.99 [316]~E(x3161,x3162)+E(f414(x3163,x3164,x3161,x3165),f414(x3163,x3164,x3162,x3165))
% 188.15/187.99 [317]~E(x3171,x3172)+E(f414(x3173,x3174,x3175,x3171),f414(x3173,x3174,x3175,x3172))
% 188.15/187.99 [318]~E(x3181,x3182)+E(f25(x3181,x3183),f25(x3182,x3183))
% 188.15/187.99 [319]~E(x3191,x3192)+E(f25(x3193,x3191),f25(x3193,x3192))
% 188.15/187.99 [320]~E(x3201,x3202)+E(f47(x3201,x3203),f47(x3202,x3203))
% 188.15/187.99 [321]~E(x3211,x3212)+E(f47(x3213,x3211),f47(x3213,x3212))
% 188.15/187.99 [322]~E(x3221,x3222)+E(f164(x3221,x3223,x3224),f164(x3222,x3223,x3224))
% 188.15/187.99 [323]~E(x3231,x3232)+E(f164(x3233,x3231,x3234),f164(x3233,x3232,x3234))
% 188.15/187.99 [324]~E(x3241,x3242)+E(f164(x3243,x3244,x3241),f164(x3243,x3244,x3242))
% 188.15/187.99 [325]~E(x3251,x3252)+E(f249(x3251,x3253,x3254),f249(x3252,x3253,x3254))
% 188.15/187.99 [326]~E(x3261,x3262)+E(f249(x3263,x3261,x3264),f249(x3263,x3262,x3264))
% 188.15/187.99 [327]~E(x3271,x3272)+E(f249(x3273,x3274,x3271),f249(x3273,x3274,x3272))
% 188.15/187.99 [328]~E(x3281,x3282)+E(f278(x3281,x3283),f278(x3282,x3283))
% 188.15/187.99 [329]~E(x3291,x3292)+E(f278(x3293,x3291),f278(x3293,x3292))
% 188.15/187.99 [330]~E(x3301,x3302)+E(f809(x3301,x3303,x3304),f809(x3302,x3303,x3304))
% 188.15/187.99 [331]~E(x3311,x3312)+E(f809(x3313,x3311,x3314),f809(x3313,x3312,x3314))
% 188.15/187.99 [332]~E(x3321,x3322)+E(f809(x3323,x3324,x3321),f809(x3323,x3324,x3322))
% 188.15/187.99 [333]~E(x3331,x3332)+E(f160(x3331,x3333,x3334),f160(x3332,x3333,x3334))
% 188.15/187.99 [334]~E(x3341,x3342)+E(f160(x3343,x3341,x3344),f160(x3343,x3342,x3344))
% 188.15/187.99 [335]~E(x3351,x3352)+E(f160(x3353,x3354,x3351),f160(x3353,x3354,x3352))
% 188.15/187.99 [336]~E(x3361,x3362)+E(f438(x3361,x3363,x3364),f438(x3362,x3363,x3364))
% 188.15/187.99 [337]~E(x3371,x3372)+E(f438(x3373,x3371,x3374),f438(x3373,x3372,x3374))
% 188.15/187.99 [338]~E(x3381,x3382)+E(f438(x3383,x3384,x3381),f438(x3383,x3384,x3382))
% 188.15/187.99 [339]~E(x3391,x3392)+E(f300(x3391),f300(x3392))
% 188.15/187.99 [340]~E(x3401,x3402)+E(f16(x3401,x3403),f16(x3402,x3403))
% 188.15/187.99 [341]~E(x3411,x3412)+E(f16(x3413,x3411),f16(x3413,x3412))
% 188.15/187.99 [342]~E(x3421,x3422)+E(f57(x3421,x3423,x3424,x3425),f57(x3422,x3423,x3424,x3425))
% 188.15/187.99 [343]~E(x3431,x3432)+E(f57(x3433,x3431,x3434,x3435),f57(x3433,x3432,x3434,x3435))
% 188.15/187.99 [344]~E(x3441,x3442)+E(f57(x3443,x3444,x3441,x3445),f57(x3443,x3444,x3442,x3445))
% 188.15/187.99 [345]~E(x3451,x3452)+E(f57(x3453,x3454,x3455,x3451),f57(x3453,x3454,x3455,x3452))
% 188.15/187.99 [346]~E(x3461,x3462)+E(f314(x3461,x3463),f314(x3462,x3463))
% 188.15/187.99 [347]~E(x3471,x3472)+E(f314(x3473,x3471),f314(x3473,x3472))
% 188.15/187.99 [348]~E(x3481,x3482)+E(f84(x3481,x3483),f84(x3482,x3483))
% 188.15/187.99 [349]~E(x3491,x3492)+E(f84(x3493,x3491),f84(x3493,x3492))
% 188.15/187.99 [350]~E(x3501,x3502)+E(f316(x3501,x3503),f316(x3502,x3503))
% 188.15/187.99 [351]~E(x3511,x3512)+E(f316(x3513,x3511),f316(x3513,x3512))
% 188.15/187.99 [352]~E(x3521,x3522)+E(f616(x3521,x3523,x3524),f616(x3522,x3523,x3524))
% 188.15/187.99 [353]~E(x3531,x3532)+E(f616(x3533,x3531,x3534),f616(x3533,x3532,x3534))
% 188.15/187.99 [354]~E(x3541,x3542)+E(f616(x3543,x3544,x3541),f616(x3543,x3544,x3542))
% 188.15/187.99 [355]~E(x3551,x3552)+E(f744(x3551,x3553,x3554,x3555,x3556),f744(x3552,x3553,x3554,x3555,x3556))
% 188.15/187.99 [356]~E(x3561,x3562)+E(f744(x3563,x3561,x3564,x3565,x3566),f744(x3563,x3562,x3564,x3565,x3566))
% 188.15/187.99 [357]~E(x3571,x3572)+E(f744(x3573,x3574,x3571,x3575,x3576),f744(x3573,x3574,x3572,x3575,x3576))
% 188.15/187.99 [358]~E(x3581,x3582)+E(f744(x3583,x3584,x3585,x3581,x3586),f744(x3583,x3584,x3585,x3582,x3586))
% 188.15/187.99 [359]~E(x3591,x3592)+E(f744(x3593,x3594,x3595,x3596,x3591),f744(x3593,x3594,x3595,x3596,x3592))
% 188.15/187.99 [360]~E(x3601,x3602)+E(f149(x3601,x3603,x3604,x3605),f149(x3602,x3603,x3604,x3605))
% 188.15/187.99 [361]~E(x3611,x3612)+E(f149(x3613,x3611,x3614,x3615),f149(x3613,x3612,x3614,x3615))
% 188.15/187.99 [362]~E(x3621,x3622)+E(f149(x3623,x3624,x3621,x3625),f149(x3623,x3624,x3622,x3625))
% 188.15/187.99 [363]~E(x3631,x3632)+E(f149(x3633,x3634,x3635,x3631),f149(x3633,x3634,x3635,x3632))
% 188.15/187.99 [364]~E(x3641,x3642)+E(f312(x3641,x3643),f312(x3642,x3643))
% 188.15/187.99 [365]~E(x3651,x3652)+E(f312(x3653,x3651),f312(x3653,x3652))
% 188.15/187.99 [366]~E(x3661,x3662)+E(f180(x3661,x3663,x3664,x3665),f180(x3662,x3663,x3664,x3665))
% 188.15/187.99 [367]~E(x3671,x3672)+E(f180(x3673,x3671,x3674,x3675),f180(x3673,x3672,x3674,x3675))
% 188.15/187.99 [368]~E(x3681,x3682)+E(f180(x3683,x3684,x3681,x3685),f180(x3683,x3684,x3682,x3685))
% 188.15/187.99 [369]~E(x3691,x3692)+E(f180(x3693,x3694,x3695,x3691),f180(x3693,x3694,x3695,x3692))
% 188.15/187.99 [370]~E(x3701,x3702)+E(f671(x3701,x3703),f671(x3702,x3703))
% 188.15/187.99 [371]~E(x3711,x3712)+E(f671(x3713,x3711),f671(x3713,x3712))
% 188.15/187.99 [372]~E(x3721,x3722)+E(f43(x3721,x3723),f43(x3722,x3723))
% 188.15/187.99 [373]~E(x3731,x3732)+E(f43(x3733,x3731),f43(x3733,x3732))
% 188.15/187.99 [374]~E(x3741,x3742)+E(f337(x3741,x3743),f337(x3742,x3743))
% 188.15/187.99 [375]~E(x3751,x3752)+E(f337(x3753,x3751),f337(x3753,x3752))
% 188.15/187.99 [376]~E(x3761,x3762)+E(f61(x3761,x3763),f61(x3762,x3763))
% 188.15/187.99 [377]~E(x3771,x3772)+E(f61(x3773,x3771),f61(x3773,x3772))
% 188.15/187.99 [378]~E(x3781,x3782)+E(f171(x3781,x3783,x3784),f171(x3782,x3783,x3784))
% 188.15/187.99 [379]~E(x3791,x3792)+E(f171(x3793,x3791,x3794),f171(x3793,x3792,x3794))
% 188.15/187.99 [380]~E(x3801,x3802)+E(f171(x3803,x3804,x3801),f171(x3803,x3804,x3802))
% 188.15/187.99 [381]~E(x3811,x3812)+E(f140(x3811,x3813),f140(x3812,x3813))
% 188.15/187.99 [382]~E(x3821,x3822)+E(f140(x3823,x3821),f140(x3823,x3822))
% 188.15/187.99 [383]~E(x3831,x3832)+E(f515(x3831,x3833,x3834),f515(x3832,x3833,x3834))
% 188.15/187.99 [384]~E(x3841,x3842)+E(f515(x3843,x3841,x3844),f515(x3843,x3842,x3844))
% 188.15/187.99 [385]~E(x3851,x3852)+E(f515(x3853,x3854,x3851),f515(x3853,x3854,x3852))
% 188.15/187.99 [386]~E(x3861,x3862)+E(f437(x3861,x3863,x3864,x3865,x3866),f437(x3862,x3863,x3864,x3865,x3866))
% 188.15/187.99 [387]~E(x3871,x3872)+E(f437(x3873,x3871,x3874,x3875,x3876),f437(x3873,x3872,x3874,x3875,x3876))
% 188.15/187.99 [388]~E(x3881,x3882)+E(f437(x3883,x3884,x3881,x3885,x3886),f437(x3883,x3884,x3882,x3885,x3886))
% 188.15/187.99 [389]~E(x3891,x3892)+E(f437(x3893,x3894,x3895,x3891,x3896),f437(x3893,x3894,x3895,x3892,x3896))
% 188.15/187.99 [390]~E(x3901,x3902)+E(f437(x3903,x3904,x3905,x3906,x3901),f437(x3903,x3904,x3905,x3906,x3902))
% 188.15/187.99 [391]~E(x3911,x3912)+E(f674(x3911,x3913,x3914),f674(x3912,x3913,x3914))
% 188.15/187.99 [392]~E(x3921,x3922)+E(f674(x3923,x3921,x3924),f674(x3923,x3922,x3924))
% 188.15/187.99 [393]~E(x3931,x3932)+E(f674(x3933,x3934,x3931),f674(x3933,x3934,x3932))
% 188.15/187.99 [394]~E(x3941,x3942)+E(f15(x3941,x3943),f15(x3942,x3943))
% 188.15/187.99 [395]~E(x3951,x3952)+E(f15(x3953,x3951),f15(x3953,x3952))
% 188.15/187.99 [396]~E(x3961,x3962)+E(f150(x3961,x3963),f150(x3962,x3963))
% 188.15/187.99 [397]~E(x3971,x3972)+E(f150(x3973,x3971),f150(x3973,x3972))
% 188.15/187.99 [398]~E(x3981,x3982)+E(f83(x3981,x3983),f83(x3982,x3983))
% 188.15/187.99 [399]~E(x3991,x3992)+E(f83(x3993,x3991),f83(x3993,x3992))
% 188.15/187.99 [400]~E(x4001,x4002)+E(f645(x4001,x4003,x4004),f645(x4002,x4003,x4004))
% 188.15/187.99 [401]~E(x4011,x4012)+E(f645(x4013,x4011,x4014),f645(x4013,x4012,x4014))
% 188.15/187.99 [402]~E(x4021,x4022)+E(f645(x4023,x4024,x4021),f645(x4023,x4024,x4022))
% 188.15/187.99 [403]~E(x4031,x4032)+E(f88(x4031,x4033),f88(x4032,x4033))
% 188.15/187.99 [404]~E(x4041,x4042)+E(f88(x4043,x4041),f88(x4043,x4042))
% 188.15/187.99 [405]~E(x4051,x4052)+E(f172(x4051,x4053),f172(x4052,x4053))
% 188.15/187.99 [406]~E(x4061,x4062)+E(f172(x4063,x4061),f172(x4063,x4062))
% 188.15/187.99 [407]~E(x4071,x4072)+E(f146(x4071,x4073),f146(x4072,x4073))
% 188.15/187.99 [408]~E(x4081,x4082)+E(f146(x4083,x4081),f146(x4083,x4082))
% 188.15/187.99 [409]~E(x4091,x4092)+E(f138(x4091,x4093),f138(x4092,x4093))
% 188.15/187.99 [410]~E(x4101,x4102)+E(f138(x4103,x4101),f138(x4103,x4102))
% 188.15/187.99 [411]~E(x4111,x4112)+E(f310(x4111,x4113,x4114,x4115),f310(x4112,x4113,x4114,x4115))
% 188.15/187.99 [412]~E(x4121,x4122)+E(f310(x4123,x4121,x4124,x4125),f310(x4123,x4122,x4124,x4125))
% 188.15/187.99 [413]~E(x4131,x4132)+E(f310(x4133,x4134,x4131,x4135),f310(x4133,x4134,x4132,x4135))
% 188.15/187.99 [414]~E(x4141,x4142)+E(f310(x4143,x4144,x4145,x4141),f310(x4143,x4144,x4145,x4142))
% 188.15/187.99 [415]~E(x4151,x4152)+E(f53(x4151),f53(x4152))
% 188.15/187.99 [416]~E(x4161,x4162)+E(f591(x4161,x4163,x4164,x4165),f591(x4162,x4163,x4164,x4165))
% 188.15/187.99 [417]~E(x4171,x4172)+E(f591(x4173,x4171,x4174,x4175),f591(x4173,x4172,x4174,x4175))
% 188.15/187.99 [418]~E(x4181,x4182)+E(f591(x4183,x4184,x4181,x4185),f591(x4183,x4184,x4182,x4185))
% 188.15/187.99 [419]~E(x4191,x4192)+E(f591(x4193,x4194,x4195,x4191),f591(x4193,x4194,x4195,x4192))
% 188.15/187.99 [420]~E(x4201,x4202)+E(f548(x4201,x4203,x4204),f548(x4202,x4203,x4204))
% 188.15/187.99 [421]~E(x4211,x4212)+E(f548(x4213,x4211,x4214),f548(x4213,x4212,x4214))
% 188.15/187.99 [422]~E(x4221,x4222)+E(f548(x4223,x4224,x4221),f548(x4223,x4224,x4222))
% 188.15/187.99 [423]~E(x4231,x4232)+E(f12(x4231,x4233,x4234),f12(x4232,x4233,x4234))
% 188.15/187.99 [424]~E(x4241,x4242)+E(f12(x4243,x4241,x4244),f12(x4243,x4242,x4244))
% 188.15/187.99 [425]~E(x4251,x4252)+E(f12(x4253,x4254,x4251),f12(x4253,x4254,x4252))
% 188.15/187.99 [426]~E(x4261,x4262)+E(f451(x4261,x4263,x4264,x4265,x4266),f451(x4262,x4263,x4264,x4265,x4266))
% 188.15/187.99 [427]~E(x4271,x4272)+E(f451(x4273,x4271,x4274,x4275,x4276),f451(x4273,x4272,x4274,x4275,x4276))
% 188.15/187.99 [428]~E(x4281,x4282)+E(f451(x4283,x4284,x4281,x4285,x4286),f451(x4283,x4284,x4282,x4285,x4286))
% 188.15/187.99 [429]~E(x4291,x4292)+E(f451(x4293,x4294,x4295,x4291,x4296),f451(x4293,x4294,x4295,x4292,x4296))
% 188.15/187.99 [430]~E(x4301,x4302)+E(f451(x4303,x4304,x4305,x4306,x4301),f451(x4303,x4304,x4305,x4306,x4302))
% 188.15/187.99 [431]~E(x4311,x4312)+E(f45(x4311,x4313),f45(x4312,x4313))
% 188.15/187.99 [432]~E(x4321,x4322)+E(f45(x4323,x4321),f45(x4323,x4322))
% 188.15/187.99 [433]~E(x4331,x4332)+E(f678(x4331,x4333,x4334,x4335),f678(x4332,x4333,x4334,x4335))
% 188.15/187.99 [434]~E(x4341,x4342)+E(f678(x4343,x4341,x4344,x4345),f678(x4343,x4342,x4344,x4345))
% 188.15/187.99 [435]~E(x4351,x4352)+E(f678(x4353,x4354,x4351,x4355),f678(x4353,x4354,x4352,x4355))
% 188.15/187.99 [436]~E(x4361,x4362)+E(f678(x4363,x4364,x4365,x4361),f678(x4363,x4364,x4365,x4362))
% 188.15/187.99 [437]~E(x4371,x4372)+E(f638(x4371,x4373,x4374,x4375,x4376),f638(x4372,x4373,x4374,x4375,x4376))
% 188.15/187.99 [438]~E(x4381,x4382)+E(f638(x4383,x4381,x4384,x4385,x4386),f638(x4383,x4382,x4384,x4385,x4386))
% 188.15/187.99 [439]~E(x4391,x4392)+E(f638(x4393,x4394,x4391,x4395,x4396),f638(x4393,x4394,x4392,x4395,x4396))
% 188.15/187.99 [440]~E(x4401,x4402)+E(f638(x4403,x4404,x4405,x4401,x4406),f638(x4403,x4404,x4405,x4402,x4406))
% 188.15/187.99 [441]~E(x4411,x4412)+E(f638(x4413,x4414,x4415,x4416,x4411),f638(x4413,x4414,x4415,x4416,x4412))
% 188.15/187.99 [442]~E(x4421,x4422)+E(f177(x4421,x4423,x4424),f177(x4422,x4423,x4424))
% 188.15/187.99 [443]~E(x4431,x4432)+E(f177(x4433,x4431,x4434),f177(x4433,x4432,x4434))
% 188.15/187.99 [444]~E(x4441,x4442)+E(f177(x4443,x4444,x4441),f177(x4443,x4444,x4442))
% 188.15/187.99 [445]~E(x4451,x4452)+E(f125(x4451,x4453),f125(x4452,x4453))
% 188.15/187.99 [446]~E(x4461,x4462)+E(f125(x4463,x4461),f125(x4463,x4462))
% 188.15/187.99 [447]~E(x4471,x4472)+E(f206(x4471),f206(x4472))
% 188.15/187.99 [448]~E(x4481,x4482)+E(f305(x4481,x4483,x4484),f305(x4482,x4483,x4484))
% 188.15/187.99 [449]~E(x4491,x4492)+E(f305(x4493,x4491,x4494),f305(x4493,x4492,x4494))
% 188.15/187.99 [450]~E(x4501,x4502)+E(f305(x4503,x4504,x4501),f305(x4503,x4504,x4502))
% 188.15/187.99 [451]~E(x4511,x4512)+E(f279(x4511,x4513),f279(x4512,x4513))
% 188.15/187.99 [452]~E(x4521,x4522)+E(f279(x4523,x4521),f279(x4523,x4522))
% 188.15/187.99 [453]~E(x4531,x4532)+E(f506(x4531,x4533),f506(x4532,x4533))
% 188.15/187.99 [454]~E(x4541,x4542)+E(f506(x4543,x4541),f506(x4543,x4542))
% 188.15/187.99 [455]~E(x4551,x4552)+E(f400(x4551,x4553,x4554,x4555),f400(x4552,x4553,x4554,x4555))
% 188.15/187.99 [456]~E(x4561,x4562)+E(f400(x4563,x4561,x4564,x4565),f400(x4563,x4562,x4564,x4565))
% 188.15/187.99 [457]~E(x4571,x4572)+E(f400(x4573,x4574,x4571,x4575),f400(x4573,x4574,x4572,x4575))
% 188.15/187.99 [458]~E(x4581,x4582)+E(f400(x4583,x4584,x4585,x4581),f400(x4583,x4584,x4585,x4582))
% 188.15/187.99 [459]~E(x4591,x4592)+E(f491(x4591,x4593,x4594),f491(x4592,x4593,x4594))
% 188.15/187.99 [460]~E(x4601,x4602)+E(f491(x4603,x4601,x4604),f491(x4603,x4602,x4604))
% 188.15/187.99 [461]~E(x4611,x4612)+E(f491(x4613,x4614,x4611),f491(x4613,x4614,x4612))
% 188.15/187.99 [462]~E(x4621,x4622)+E(f201(x4621,x4623),f201(x4622,x4623))
% 188.15/187.99 [463]~E(x4631,x4632)+E(f201(x4633,x4631),f201(x4633,x4632))
% 188.15/187.99 [464]~E(x4641,x4642)+E(f271(x4641,x4643),f271(x4642,x4643))
% 188.15/187.99 [465]~E(x4651,x4652)+E(f271(x4653,x4651),f271(x4653,x4652))
% 188.15/187.99 [466]~E(x4661,x4662)+E(f798(x4661,x4663,x4664),f798(x4662,x4663,x4664))
% 188.15/187.99 [467]~E(x4671,x4672)+E(f798(x4673,x4671,x4674),f798(x4673,x4672,x4674))
% 188.15/187.99 [468]~E(x4681,x4682)+E(f798(x4683,x4684,x4681),f798(x4683,x4684,x4682))
% 188.15/187.99 [469]~E(x4691,x4692)+E(f173(x4691,x4693),f173(x4692,x4693))
% 188.15/187.99 [470]~E(x4701,x4702)+E(f173(x4703,x4701),f173(x4703,x4702))
% 188.15/187.99 [471]~E(x4711,x4712)+E(f85(x4711),f85(x4712))
% 188.15/187.99 [472]~E(x4721,x4722)+E(f731(x4721,x4723,x4724,x4725,x4726),f731(x4722,x4723,x4724,x4725,x4726))
% 188.15/187.99 [473]~E(x4731,x4732)+E(f731(x4733,x4731,x4734,x4735,x4736),f731(x4733,x4732,x4734,x4735,x4736))
% 188.15/187.99 [474]~E(x4741,x4742)+E(f731(x4743,x4744,x4741,x4745,x4746),f731(x4743,x4744,x4742,x4745,x4746))
% 188.15/187.99 [475]~E(x4751,x4752)+E(f731(x4753,x4754,x4755,x4751,x4756),f731(x4753,x4754,x4755,x4752,x4756))
% 188.15/187.99 [476]~E(x4761,x4762)+E(f731(x4763,x4764,x4765,x4766,x4761),f731(x4763,x4764,x4765,x4766,x4762))
% 188.15/187.99 [477]~E(x4771,x4772)+E(f64(x4771,x4773,x4774,x4775,x4776),f64(x4772,x4773,x4774,x4775,x4776))
% 188.15/187.99 [478]~E(x4781,x4782)+E(f64(x4783,x4781,x4784,x4785,x4786),f64(x4783,x4782,x4784,x4785,x4786))
% 188.15/187.99 [479]~E(x4791,x4792)+E(f64(x4793,x4794,x4791,x4795,x4796),f64(x4793,x4794,x4792,x4795,x4796))
% 188.15/187.99 [480]~E(x4801,x4802)+E(f64(x4803,x4804,x4805,x4801,x4806),f64(x4803,x4804,x4805,x4802,x4806))
% 188.15/187.99 [481]~E(x4811,x4812)+E(f64(x4813,x4814,x4815,x4816,x4811),f64(x4813,x4814,x4815,x4816,x4812))
% 188.15/187.99 [482]~E(x4821,x4822)+E(f298(x4821),f298(x4822))
% 188.15/187.99 [483]~E(x4831,x4832)+E(f331(x4831,x4833),f331(x4832,x4833))
% 188.15/187.99 [484]~E(x4841,x4842)+E(f331(x4843,x4841),f331(x4843,x4842))
% 188.15/187.99 [485]~E(x4851,x4852)+E(f642(x4851,x4853,x4854,x4855,x4856),f642(x4852,x4853,x4854,x4855,x4856))
% 188.15/187.99 [486]~E(x4861,x4862)+E(f642(x4863,x4861,x4864,x4865,x4866),f642(x4863,x4862,x4864,x4865,x4866))
% 188.15/187.99 [487]~E(x4871,x4872)+E(f642(x4873,x4874,x4871,x4875,x4876),f642(x4873,x4874,x4872,x4875,x4876))
% 188.15/187.99 [488]~E(x4881,x4882)+E(f642(x4883,x4884,x4885,x4881,x4886),f642(x4883,x4884,x4885,x4882,x4886))
% 188.15/187.99 [489]~E(x4891,x4892)+E(f642(x4893,x4894,x4895,x4896,x4891),f642(x4893,x4894,x4895,x4896,x4892))
% 188.15/187.99 [490]~E(x4901,x4902)+E(f522(x4901,x4903,x4904),f522(x4902,x4903,x4904))
% 188.15/187.99 [491]~E(x4911,x4912)+E(f522(x4913,x4911,x4914),f522(x4913,x4912,x4914))
% 188.15/187.99 [492]~E(x4921,x4922)+E(f522(x4923,x4924,x4921),f522(x4923,x4924,x4922))
% 188.15/187.99 [493]~E(x4931,x4932)+E(f151(x4931,x4933),f151(x4932,x4933))
% 188.15/187.99 [494]~E(x4941,x4942)+E(f151(x4943,x4941),f151(x4943,x4942))
% 188.15/187.99 [495]~E(x4951,x4952)+E(f806(x4951,x4953),f806(x4952,x4953))
% 188.15/187.99 [496]~E(x4961,x4962)+E(f806(x4963,x4961),f806(x4963,x4962))
% 188.15/187.99 [497]~E(x4971,x4972)+E(f296(x4971,x4973,x4974),f296(x4972,x4973,x4974))
% 188.15/187.99 [498]~E(x4981,x4982)+E(f296(x4983,x4981,x4984),f296(x4983,x4982,x4984))
% 188.15/187.99 [499]~E(x4991,x4992)+E(f296(x4993,x4994,x4991),f296(x4993,x4994,x4992))
% 188.15/187.99 [500]~E(x5001,x5002)+E(f244(x5001),f244(x5002))
% 188.15/187.99 [501]~E(x5011,x5012)+E(f109(x5011),f109(x5012))
% 188.15/187.99 [502]~E(x5021,x5022)+E(f13(x5021,x5023,x5024),f13(x5022,x5023,x5024))
% 188.15/187.99 [503]~E(x5031,x5032)+E(f13(x5033,x5031,x5034),f13(x5033,x5032,x5034))
% 188.15/187.99 [504]~E(x5041,x5042)+E(f13(x5043,x5044,x5041),f13(x5043,x5044,x5042))
% 188.15/187.99 [505]~E(x5051,x5052)+E(f648(x5051,x5053,x5054,x5055,x5056),f648(x5052,x5053,x5054,x5055,x5056))
% 188.15/187.99 [506]~E(x5061,x5062)+E(f648(x5063,x5061,x5064,x5065,x5066),f648(x5063,x5062,x5064,x5065,x5066))
% 188.15/187.99 [507]~E(x5071,x5072)+E(f648(x5073,x5074,x5071,x5075,x5076),f648(x5073,x5074,x5072,x5075,x5076))
% 188.15/187.99 [508]~E(x5081,x5082)+E(f648(x5083,x5084,x5085,x5081,x5086),f648(x5083,x5084,x5085,x5082,x5086))
% 188.15/187.99 [509]~E(x5091,x5092)+E(f648(x5093,x5094,x5095,x5096,x5091),f648(x5093,x5094,x5095,x5096,x5092))
% 188.15/187.99 [510]~E(x5101,x5102)+E(f127(x5101,x5103,x5104,x5105),f127(x5102,x5103,x5104,x5105))
% 188.15/187.99 [511]~E(x5111,x5112)+E(f127(x5113,x5111,x5114,x5115),f127(x5113,x5112,x5114,x5115))
% 188.15/187.99 [512]~E(x5121,x5122)+E(f127(x5123,x5124,x5121,x5125),f127(x5123,x5124,x5122,x5125))
% 188.15/187.99 [513]~E(x5131,x5132)+E(f127(x5133,x5134,x5135,x5131),f127(x5133,x5134,x5135,x5132))
% 188.15/187.99 [514]~E(x5141,x5142)+E(f481(x5141,x5143,x5144),f481(x5142,x5143,x5144))
% 188.15/187.99 [515]~E(x5151,x5152)+E(f481(x5153,x5151,x5154),f481(x5153,x5152,x5154))
% 188.15/187.99 [516]~E(x5161,x5162)+E(f481(x5163,x5164,x5161),f481(x5163,x5164,x5162))
% 188.15/187.99 [517]~E(x5171,x5172)+E(f142(x5171,x5173,x5174,x5175,x5176),f142(x5172,x5173,x5174,x5175,x5176))
% 188.15/187.99 [518]~E(x5181,x5182)+E(f142(x5183,x5181,x5184,x5185,x5186),f142(x5183,x5182,x5184,x5185,x5186))
% 188.15/187.99 [519]~E(x5191,x5192)+E(f142(x5193,x5194,x5191,x5195,x5196),f142(x5193,x5194,x5192,x5195,x5196))
% 188.15/187.99 [520]~E(x5201,x5202)+E(f142(x5203,x5204,x5205,x5201,x5206),f142(x5203,x5204,x5205,x5202,x5206))
% 188.15/187.99 [521]~E(x5211,x5212)+E(f142(x5213,x5214,x5215,x5216,x5211),f142(x5213,x5214,x5215,x5216,x5212))
% 188.15/187.99 [522]~E(x5221,x5222)+E(f29(x5221,x5223),f29(x5222,x5223))
% 188.15/187.99 [523]~E(x5231,x5232)+E(f29(x5233,x5231),f29(x5233,x5232))
% 188.15/187.99 [524]~E(x5241,x5242)+E(f755(x5241,x5243,x5244,x5245,x5246),f755(x5242,x5243,x5244,x5245,x5246))
% 188.15/187.99 [525]~E(x5251,x5252)+E(f755(x5253,x5251,x5254,x5255,x5256),f755(x5253,x5252,x5254,x5255,x5256))
% 188.15/187.99 [526]~E(x5261,x5262)+E(f755(x5263,x5264,x5261,x5265,x5266),f755(x5263,x5264,x5262,x5265,x5266))
% 188.15/187.99 [527]~E(x5271,x5272)+E(f755(x5273,x5274,x5275,x5271,x5276),f755(x5273,x5274,x5275,x5272,x5276))
% 188.15/187.99 [528]~E(x5281,x5282)+E(f755(x5283,x5284,x5285,x5286,x5281),f755(x5283,x5284,x5285,x5286,x5282))
% 188.15/187.99 [529]~E(x5291,x5292)+E(f369(x5291,x5293,x5294,x5295,x5296,x5297),f369(x5292,x5293,x5294,x5295,x5296,x5297))
% 188.15/187.99 [530]~E(x5301,x5302)+E(f369(x5303,x5301,x5304,x5305,x5306,x5307),f369(x5303,x5302,x5304,x5305,x5306,x5307))
% 188.15/187.99 [531]~E(x5311,x5312)+E(f369(x5313,x5314,x5311,x5315,x5316,x5317),f369(x5313,x5314,x5312,x5315,x5316,x5317))
% 188.15/187.99 [532]~E(x5321,x5322)+E(f369(x5323,x5324,x5325,x5321,x5326,x5327),f369(x5323,x5324,x5325,x5322,x5326,x5327))
% 188.15/187.99 [533]~E(x5331,x5332)+E(f369(x5333,x5334,x5335,x5336,x5331,x5337),f369(x5333,x5334,x5335,x5336,x5332,x5337))
% 188.15/187.99 [534]~E(x5341,x5342)+E(f369(x5343,x5344,x5345,x5346,x5347,x5341),f369(x5343,x5344,x5345,x5346,x5347,x5342))
% 188.15/187.99 [535]~E(x5351,x5352)+E(f641(x5351,x5353,x5354,x5355,x5356),f641(x5352,x5353,x5354,x5355,x5356))
% 188.15/187.99 [536]~E(x5361,x5362)+E(f641(x5363,x5361,x5364,x5365,x5366),f641(x5363,x5362,x5364,x5365,x5366))
% 188.15/187.99 [537]~E(x5371,x5372)+E(f641(x5373,x5374,x5371,x5375,x5376),f641(x5373,x5374,x5372,x5375,x5376))
% 188.15/187.99 [538]~E(x5381,x5382)+E(f641(x5383,x5384,x5385,x5381,x5386),f641(x5383,x5384,x5385,x5382,x5386))
% 188.15/187.99 [539]~E(x5391,x5392)+E(f641(x5393,x5394,x5395,x5396,x5391),f641(x5393,x5394,x5395,x5396,x5392))
% 188.15/187.99 [540]~E(x5401,x5402)+E(f525(x5401,x5403,x5404),f525(x5402,x5403,x5404))
% 188.15/187.99 [541]~E(x5411,x5412)+E(f525(x5413,x5411,x5414),f525(x5413,x5412,x5414))
% 188.15/187.99 [542]~E(x5421,x5422)+E(f525(x5423,x5424,x5421),f525(x5423,x5424,x5422))
% 188.15/187.99 [543]~E(x5431,x5432)+E(f211(x5431,x5433,x5434,x5435),f211(x5432,x5433,x5434,x5435))
% 188.15/187.99 [544]~E(x5441,x5442)+E(f211(x5443,x5441,x5444,x5445),f211(x5443,x5442,x5444,x5445))
% 188.15/187.99 [545]~E(x5451,x5452)+E(f211(x5453,x5454,x5451,x5455),f211(x5453,x5454,x5452,x5455))
% 188.15/187.99 [546]~E(x5461,x5462)+E(f211(x5463,x5464,x5465,x5461),f211(x5463,x5464,x5465,x5462))
% 188.15/187.99 [547]~E(x5471,x5472)+E(f341(x5471,x5473,x5474),f341(x5472,x5473,x5474))
% 188.15/187.99 [548]~E(x5481,x5482)+E(f341(x5483,x5481,x5484),f341(x5483,x5482,x5484))
% 188.15/187.99 [549]~E(x5491,x5492)+E(f341(x5493,x5494,x5491),f341(x5493,x5494,x5492))
% 188.15/187.99 [550]~E(x5501,x5502)+E(f810(x5501,x5503,x5504),f810(x5502,x5503,x5504))
% 188.15/187.99 [551]~E(x5511,x5512)+E(f810(x5513,x5511,x5514),f810(x5513,x5512,x5514))
% 188.15/187.99 [552]~E(x5521,x5522)+E(f810(x5523,x5524,x5521),f810(x5523,x5524,x5522))
% 188.15/187.99 [553]~E(x5531,x5532)+E(f733(x5531,x5533,x5534),f733(x5532,x5533,x5534))
% 188.15/187.99 [554]~E(x5541,x5542)+E(f733(x5543,x5541,x5544),f733(x5543,x5542,x5544))
% 188.15/187.99 [555]~E(x5551,x5552)+E(f733(x5553,x5554,x5551),f733(x5553,x5554,x5552))
% 188.15/187.99 [556]~E(x5561,x5562)+E(f198(x5561,x5563,x5564,x5565),f198(x5562,x5563,x5564,x5565))
% 188.15/187.99 [557]~E(x5571,x5572)+E(f198(x5573,x5571,x5574,x5575),f198(x5573,x5572,x5574,x5575))
% 188.15/187.99 [558]~E(x5581,x5582)+E(f198(x5583,x5584,x5581,x5585),f198(x5583,x5584,x5582,x5585))
% 188.15/187.99 [559]~E(x5591,x5592)+E(f198(x5593,x5594,x5595,x5591),f198(x5593,x5594,x5595,x5592))
% 188.15/187.99 [560]~E(x5601,x5602)+E(f767(x5601,x5603,x5604,x5605,x5606),f767(x5602,x5603,x5604,x5605,x5606))
% 188.15/187.99 [561]~E(x5611,x5612)+E(f767(x5613,x5611,x5614,x5615,x5616),f767(x5613,x5612,x5614,x5615,x5616))
% 188.15/187.99 [562]~E(x5621,x5622)+E(f767(x5623,x5624,x5621,x5625,x5626),f767(x5623,x5624,x5622,x5625,x5626))
% 188.15/187.99 [563]~E(x5631,x5632)+E(f767(x5633,x5634,x5635,x5631,x5636),f767(x5633,x5634,x5635,x5632,x5636))
% 188.15/187.99 [564]~E(x5641,x5642)+E(f767(x5643,x5644,x5645,x5646,x5641),f767(x5643,x5644,x5645,x5646,x5642))
% 188.15/187.99 [565]~E(x5651,x5652)+E(f732(x5651,x5653,x5654),f732(x5652,x5653,x5654))
% 188.15/187.99 [566]~E(x5661,x5662)+E(f732(x5663,x5661,x5664),f732(x5663,x5662,x5664))
% 188.15/187.99 [567]~E(x5671,x5672)+E(f732(x5673,x5674,x5671),f732(x5673,x5674,x5672))
% 188.15/187.99 [568]~E(x5681,x5682)+E(f701(x5681,x5683,x5684,x5685),f701(x5682,x5683,x5684,x5685))
% 188.15/187.99 [569]~E(x5691,x5692)+E(f701(x5693,x5691,x5694,x5695),f701(x5693,x5692,x5694,x5695))
% 188.15/187.99 [570]~E(x5701,x5702)+E(f701(x5703,x5704,x5701,x5705),f701(x5703,x5704,x5702,x5705))
% 188.15/187.99 [571]~E(x5711,x5712)+E(f701(x5713,x5714,x5715,x5711),f701(x5713,x5714,x5715,x5712))
% 188.15/187.99 [572]~E(x5721,x5722)+E(f308(x5721),f308(x5722))
% 188.15/187.99 [573]~E(x5731,x5732)+E(f742(x5731,x5733,x5734,x5735,x5736),f742(x5732,x5733,x5734,x5735,x5736))
% 188.15/187.99 [574]~E(x5741,x5742)+E(f742(x5743,x5741,x5744,x5745,x5746),f742(x5743,x5742,x5744,x5745,x5746))
% 188.15/187.99 [575]~E(x5751,x5752)+E(f742(x5753,x5754,x5751,x5755,x5756),f742(x5753,x5754,x5752,x5755,x5756))
% 188.15/187.99 [576]~E(x5761,x5762)+E(f742(x5763,x5764,x5765,x5761,x5766),f742(x5763,x5764,x5765,x5762,x5766))
% 188.15/187.99 [577]~E(x5771,x5772)+E(f742(x5773,x5774,x5775,x5776,x5771),f742(x5773,x5774,x5775,x5776,x5772))
% 188.15/187.99 [578]~E(x5781,x5782)+E(f30(x5781,x5783),f30(x5782,x5783))
% 188.15/187.99 [579]~E(x5791,x5792)+E(f30(x5793,x5791),f30(x5793,x5792))
% 188.15/187.99 [580]~E(x5801,x5802)+E(f602(x5801,x5803,x5804),f602(x5802,x5803,x5804))
% 188.15/187.99 [581]~E(x5811,x5812)+E(f602(x5813,x5811,x5814),f602(x5813,x5812,x5814))
% 188.15/187.99 [582]~E(x5821,x5822)+E(f602(x5823,x5824,x5821),f602(x5823,x5824,x5822))
% 188.15/187.99 [583]~E(x5831,x5832)+E(f229(x5831,x5833),f229(x5832,x5833))
% 188.15/187.99 [584]~E(x5841,x5842)+E(f229(x5843,x5841),f229(x5843,x5842))
% 188.15/187.99 [585]~E(x5851,x5852)+E(f581(x5851,x5853),f581(x5852,x5853))
% 188.15/187.99 [586]~E(x5861,x5862)+E(f581(x5863,x5861),f581(x5863,x5862))
% 188.15/187.99 [587]~E(x5871,x5872)+E(f353(x5871,x5873,x5874),f353(x5872,x5873,x5874))
% 188.15/187.99 [588]~E(x5881,x5882)+E(f353(x5883,x5881,x5884),f353(x5883,x5882,x5884))
% 188.15/187.99 [589]~E(x5891,x5892)+E(f353(x5893,x5894,x5891),f353(x5893,x5894,x5892))
% 188.15/187.99 [590]~E(x5901,x5902)+E(f190(x5901,x5903,x5904,x5905),f190(x5902,x5903,x5904,x5905))
% 188.15/187.99 [591]~E(x5911,x5912)+E(f190(x5913,x5911,x5914,x5915),f190(x5913,x5912,x5914,x5915))
% 188.15/187.99 [592]~E(x5921,x5922)+E(f190(x5923,x5924,x5921,x5925),f190(x5923,x5924,x5922,x5925))
% 188.15/187.99 [593]~E(x5931,x5932)+E(f190(x5933,x5934,x5935,x5931),f190(x5933,x5934,x5935,x5932))
% 188.15/187.99 [594]~E(x5941,x5942)+E(f482(x5941,x5943,x5944),f482(x5942,x5943,x5944))
% 188.15/187.99 [595]~E(x5951,x5952)+E(f482(x5953,x5951,x5954),f482(x5953,x5952,x5954))
% 188.15/187.99 [596]~E(x5961,x5962)+E(f482(x5963,x5964,x5961),f482(x5963,x5964,x5962))
% 188.15/187.99 [597]~E(x5971,x5972)+E(f75(x5971,x5973,x5974,x5975),f75(x5972,x5973,x5974,x5975))
% 188.15/187.99 [598]~E(x5981,x5982)+E(f75(x5983,x5981,x5984,x5985),f75(x5983,x5982,x5984,x5985))
% 188.15/187.99 [599]~E(x5991,x5992)+E(f75(x5993,x5994,x5991,x5995),f75(x5993,x5994,x5992,x5995))
% 188.15/187.99 [600]~E(x6001,x6002)+E(f75(x6003,x6004,x6005,x6001),f75(x6003,x6004,x6005,x6002))
% 188.15/187.99 [601]~E(x6011,x6012)+E(f632(x6011,x6013,x6014,x6015),f632(x6012,x6013,x6014,x6015))
% 188.15/187.99 [602]~E(x6021,x6022)+E(f632(x6023,x6021,x6024,x6025),f632(x6023,x6022,x6024,x6025))
% 188.15/187.99 [603]~E(x6031,x6032)+E(f632(x6033,x6034,x6031,x6035),f632(x6033,x6034,x6032,x6035))
% 188.15/187.99 [604]~E(x6041,x6042)+E(f632(x6043,x6044,x6045,x6041),f632(x6043,x6044,x6045,x6042))
% 188.15/187.99 [605]~E(x6051,x6052)+E(f531(x6051),f531(x6052))
% 188.15/187.99 [606]~E(x6061,x6062)+E(f789(x6061,x6063,x6064),f789(x6062,x6063,x6064))
% 188.15/187.99 [607]~E(x6071,x6072)+E(f789(x6073,x6071,x6074),f789(x6073,x6072,x6074))
% 188.15/187.99 [608]~E(x6081,x6082)+E(f789(x6083,x6084,x6081),f789(x6083,x6084,x6082))
% 188.15/187.99 [609]~E(x6091,x6092)+E(f218(x6091,x6093),f218(x6092,x6093))
% 188.15/187.99 [610]~E(x6101,x6102)+E(f218(x6103,x6101),f218(x6103,x6102))
% 188.15/187.99 [611]~E(x6111,x6112)+E(f470(x6111,x6113,x6114),f470(x6112,x6113,x6114))
% 188.15/187.99 [612]~E(x6121,x6122)+E(f470(x6123,x6121,x6124),f470(x6123,x6122,x6124))
% 188.15/187.99 [613]~E(x6131,x6132)+E(f470(x6133,x6134,x6131),f470(x6133,x6134,x6132))
% 188.15/187.99 [614]~E(x6141,x6142)+E(f676(x6141,x6143,x6144,x6145),f676(x6142,x6143,x6144,x6145))
% 188.15/187.99 [615]~E(x6151,x6152)+E(f676(x6153,x6151,x6154,x6155),f676(x6153,x6152,x6154,x6155))
% 188.15/187.99 [616]~E(x6161,x6162)+E(f676(x6163,x6164,x6161,x6165),f676(x6163,x6164,x6162,x6165))
% 188.15/187.99 [617]~E(x6171,x6172)+E(f676(x6173,x6174,x6175,x6171),f676(x6173,x6174,x6175,x6172))
% 188.15/187.99 [618]~E(x6181,x6182)+E(f370(x6181,x6183,x6184,x6185,x6186,x6187),f370(x6182,x6183,x6184,x6185,x6186,x6187))
% 188.15/187.99 [619]~E(x6191,x6192)+E(f370(x6193,x6191,x6194,x6195,x6196,x6197),f370(x6193,x6192,x6194,x6195,x6196,x6197))
% 188.15/187.99 [620]~E(x6201,x6202)+E(f370(x6203,x6204,x6201,x6205,x6206,x6207),f370(x6203,x6204,x6202,x6205,x6206,x6207))
% 188.15/187.99 [621]~E(x6211,x6212)+E(f370(x6213,x6214,x6215,x6211,x6216,x6217),f370(x6213,x6214,x6215,x6212,x6216,x6217))
% 188.15/187.99 [622]~E(x6221,x6222)+E(f370(x6223,x6224,x6225,x6226,x6221,x6227),f370(x6223,x6224,x6225,x6226,x6222,x6227))
% 188.15/187.99 [623]~E(x6231,x6232)+E(f370(x6233,x6234,x6235,x6236,x6237,x6231),f370(x6233,x6234,x6235,x6236,x6237,x6232))
% 188.15/187.99 [624]~E(x6241,x6242)+E(f409(x6241,x6243),f409(x6242,x6243))
% 188.15/187.99 [625]~E(x6251,x6252)+E(f409(x6253,x6251),f409(x6253,x6252))
% 188.15/187.99 [626]~E(x6261,x6262)+E(f752(x6261,x6263,x6264,x6265,x6266),f752(x6262,x6263,x6264,x6265,x6266))
% 188.15/187.99 [627]~E(x6271,x6272)+E(f752(x6273,x6271,x6274,x6275,x6276),f752(x6273,x6272,x6274,x6275,x6276))
% 188.15/187.99 [628]~E(x6281,x6282)+E(f752(x6283,x6284,x6281,x6285,x6286),f752(x6283,x6284,x6282,x6285,x6286))
% 188.15/187.99 [629]~E(x6291,x6292)+E(f752(x6293,x6294,x6295,x6291,x6296),f752(x6293,x6294,x6295,x6292,x6296))
% 188.15/187.99 [630]~E(x6301,x6302)+E(f752(x6303,x6304,x6305,x6306,x6301),f752(x6303,x6304,x6305,x6306,x6302))
% 188.15/187.99 [631]~E(x6311,x6312)+E(f745(x6311,x6313,x6314,x6315,x6316),f745(x6312,x6313,x6314,x6315,x6316))
% 188.15/187.99 [632]~E(x6321,x6322)+E(f745(x6323,x6321,x6324,x6325,x6326),f745(x6323,x6322,x6324,x6325,x6326))
% 188.15/187.99 [633]~E(x6331,x6332)+E(f745(x6333,x6334,x6331,x6335,x6336),f745(x6333,x6334,x6332,x6335,x6336))
% 188.15/187.99 [634]~E(x6341,x6342)+E(f745(x6343,x6344,x6345,x6341,x6346),f745(x6343,x6344,x6345,x6342,x6346))
% 188.15/187.99 [635]~E(x6351,x6352)+E(f745(x6353,x6354,x6355,x6356,x6351),f745(x6353,x6354,x6355,x6356,x6352))
% 188.15/187.99 [636]~E(x6361,x6362)+E(f181(x6361,x6363,x6364,x6365,x6366),f181(x6362,x6363,x6364,x6365,x6366))
% 188.15/187.99 [637]~E(x6371,x6372)+E(f181(x6373,x6371,x6374,x6375,x6376),f181(x6373,x6372,x6374,x6375,x6376))
% 188.15/187.99 [638]~E(x6381,x6382)+E(f181(x6383,x6384,x6381,x6385,x6386),f181(x6383,x6384,x6382,x6385,x6386))
% 188.15/187.99 [639]~E(x6391,x6392)+E(f181(x6393,x6394,x6395,x6391,x6396),f181(x6393,x6394,x6395,x6392,x6396))
% 188.15/187.99 [640]~E(x6401,x6402)+E(f181(x6403,x6404,x6405,x6406,x6401),f181(x6403,x6404,x6405,x6406,x6402))
% 188.15/187.99 [641]~E(x6411,x6412)+E(f65(x6411,x6413,x6414),f65(x6412,x6413,x6414))
% 188.15/187.99 [642]~E(x6421,x6422)+E(f65(x6423,x6421,x6424),f65(x6423,x6422,x6424))
% 188.15/187.99 [643]~E(x6431,x6432)+E(f65(x6433,x6434,x6431),f65(x6433,x6434,x6432))
% 188.15/187.99 [644]~E(x6441,x6442)+E(f814(x6441,x6443,x6444,x6445),f814(x6442,x6443,x6444,x6445))
% 188.15/187.99 [645]~E(x6451,x6452)+E(f814(x6453,x6451,x6454,x6455),f814(x6453,x6452,x6454,x6455))
% 188.15/187.99 [646]~E(x6461,x6462)+E(f814(x6463,x6464,x6461,x6465),f814(x6463,x6464,x6462,x6465))
% 188.15/187.99 [647]~E(x6471,x6472)+E(f814(x6473,x6474,x6475,x6471),f814(x6473,x6474,x6475,x6472))
% 188.15/187.99 [648]~E(x6481,x6482)+E(f476(x6481,x6483,x6484),f476(x6482,x6483,x6484))
% 188.15/187.99 [649]~E(x6491,x6492)+E(f476(x6493,x6491,x6494),f476(x6493,x6492,x6494))
% 188.15/187.99 [650]~E(x6501,x6502)+E(f476(x6503,x6504,x6501),f476(x6503,x6504,x6502))
% 188.15/187.99 [651]~E(x6511,x6512)+E(f297(x6511,x6513,x6514),f297(x6512,x6513,x6514))
% 188.15/187.99 [652]~E(x6521,x6522)+E(f297(x6523,x6521,x6524),f297(x6523,x6522,x6524))
% 188.15/187.99 [653]~E(x6531,x6532)+E(f297(x6533,x6534,x6531),f297(x6533,x6534,x6532))
% 188.15/187.99 [654]~E(x6541,x6542)+E(f335(x6541,x6543,x6544),f335(x6542,x6543,x6544))
% 188.15/187.99 [655]~E(x6551,x6552)+E(f335(x6553,x6551,x6554),f335(x6553,x6552,x6554))
% 188.15/187.99 [656]~E(x6561,x6562)+E(f335(x6563,x6564,x6561),f335(x6563,x6564,x6562))
% 188.15/187.99 [657]~E(x6571,x6572)+E(f182(x6571,x6573,x6574,x6575),f182(x6572,x6573,x6574,x6575))
% 188.15/187.99 [658]~E(x6581,x6582)+E(f182(x6583,x6581,x6584,x6585),f182(x6583,x6582,x6584,x6585))
% 188.15/187.99 [659]~E(x6591,x6592)+E(f182(x6593,x6594,x6591,x6595),f182(x6593,x6594,x6592,x6595))
% 188.15/187.99 [660]~E(x6601,x6602)+E(f182(x6603,x6604,x6605,x6601),f182(x6603,x6604,x6605,x6602))
% 188.15/187.99 [661]~E(x6611,x6612)+E(f52(x6611,x6613,x6614),f52(x6612,x6613,x6614))
% 188.15/187.99 [662]~E(x6621,x6622)+E(f52(x6623,x6621,x6624),f52(x6623,x6622,x6624))
% 188.15/187.99 [663]~E(x6631,x6632)+E(f52(x6633,x6634,x6631),f52(x6633,x6634,x6632))
% 188.15/187.99 [664]~E(x6641,x6642)+E(f122(x6641),f122(x6642))
% 188.15/187.99 [665]~E(x6651,x6652)+E(f167(x6651,x6653,x6654),f167(x6652,x6653,x6654))
% 188.15/187.99 [666]~E(x6661,x6662)+E(f167(x6663,x6661,x6664),f167(x6663,x6662,x6664))
% 188.15/187.99 [667]~E(x6671,x6672)+E(f167(x6673,x6674,x6671),f167(x6673,x6674,x6672))
% 188.15/187.99 [668]~E(x6681,x6682)+E(f776(x6681,x6683,x6684,x6685,x6686),f776(x6682,x6683,x6684,x6685,x6686))
% 188.15/187.99 [669]~E(x6691,x6692)+E(f776(x6693,x6691,x6694,x6695,x6696),f776(x6693,x6692,x6694,x6695,x6696))
% 188.15/187.99 [670]~E(x6701,x6702)+E(f776(x6703,x6704,x6701,x6705,x6706),f776(x6703,x6704,x6702,x6705,x6706))
% 188.15/187.99 [671]~E(x6711,x6712)+E(f776(x6713,x6714,x6715,x6711,x6716),f776(x6713,x6714,x6715,x6712,x6716))
% 188.15/187.99 [672]~E(x6721,x6722)+E(f776(x6723,x6724,x6725,x6726,x6721),f776(x6723,x6724,x6725,x6726,x6722))
% 188.15/187.99 [673]~E(x6731,x6732)+E(f46(x6731,x6733),f46(x6732,x6733))
% 188.15/187.99 [674]~E(x6741,x6742)+E(f46(x6743,x6741),f46(x6743,x6742))
% 188.15/187.99 [675]~E(x6751,x6752)+E(f154(x6751,x6753),f154(x6752,x6753))
% 188.15/187.99 [676]~E(x6761,x6762)+E(f154(x6763,x6761),f154(x6763,x6762))
% 188.15/187.99 [677]~E(x6771,x6772)+E(f841(x6771,x6773,x6774,x6775,x6776),f841(x6772,x6773,x6774,x6775,x6776))
% 188.15/187.99 [678]~E(x6781,x6782)+E(f841(x6783,x6781,x6784,x6785,x6786),f841(x6783,x6782,x6784,x6785,x6786))
% 188.15/187.99 [679]~E(x6791,x6792)+E(f841(x6793,x6794,x6791,x6795,x6796),f841(x6793,x6794,x6792,x6795,x6796))
% 188.15/187.99 [680]~E(x6801,x6802)+E(f841(x6803,x6804,x6805,x6801,x6806),f841(x6803,x6804,x6805,x6802,x6806))
% 188.15/187.99 [681]~E(x6811,x6812)+E(f841(x6813,x6814,x6815,x6816,x6811),f841(x6813,x6814,x6815,x6816,x6812))
% 188.15/187.99 [682]~E(x6821,x6822)+E(f735(x6821,x6823),f735(x6822,x6823))
% 188.15/187.99 [683]~E(x6831,x6832)+E(f735(x6833,x6831),f735(x6833,x6832))
% 188.15/187.99 [684]~E(x6841,x6842)+E(f539(x6841,x6843,x6844,x6845),f539(x6842,x6843,x6844,x6845))
% 188.15/187.99 [685]~E(x6851,x6852)+E(f539(x6853,x6851,x6854,x6855),f539(x6853,x6852,x6854,x6855))
% 188.15/187.99 [686]~E(x6861,x6862)+E(f539(x6863,x6864,x6861,x6865),f539(x6863,x6864,x6862,x6865))
% 188.15/187.99 [687]~E(x6871,x6872)+E(f539(x6873,x6874,x6875,x6871),f539(x6873,x6874,x6875,x6872))
% 188.15/187.99 [688]~E(x6881,x6882)+E(f556(x6881,x6883,x6884),f556(x6882,x6883,x6884))
% 188.15/187.99 [689]~E(x6891,x6892)+E(f556(x6893,x6891,x6894),f556(x6893,x6892,x6894))
% 188.15/187.99 [690]~E(x6901,x6902)+E(f556(x6903,x6904,x6901),f556(x6903,x6904,x6902))
% 188.15/187.99 [691]~E(x6911,x6912)+E(f594(x6911,x6913,x6914,x6915),f594(x6912,x6913,x6914,x6915))
% 188.15/187.99 [692]~E(x6921,x6922)+E(f594(x6923,x6921,x6924,x6925),f594(x6923,x6922,x6924,x6925))
% 188.15/187.99 [693]~E(x6931,x6932)+E(f594(x6933,x6934,x6931,x6935),f594(x6933,x6934,x6932,x6935))
% 188.15/187.99 [694]~E(x6941,x6942)+E(f594(x6943,x6944,x6945,x6941),f594(x6943,x6944,x6945,x6942))
% 188.15/187.99 [695]~E(x6951,x6952)+E(f126(x6951,x6953,x6954,x6955,x6956),f126(x6952,x6953,x6954,x6955,x6956))
% 188.15/187.99 [696]~E(x6961,x6962)+E(f126(x6963,x6961,x6964,x6965,x6966),f126(x6963,x6962,x6964,x6965,x6966))
% 188.15/187.99 [697]~E(x6971,x6972)+E(f126(x6973,x6974,x6971,x6975,x6976),f126(x6973,x6974,x6972,x6975,x6976))
% 188.15/187.99 [698]~E(x6981,x6982)+E(f126(x6983,x6984,x6985,x6981,x6986),f126(x6983,x6984,x6985,x6982,x6986))
% 188.15/187.99 [699]~E(x6991,x6992)+E(f126(x6993,x6994,x6995,x6996,x6991),f126(x6993,x6994,x6995,x6996,x6992))
% 188.15/187.99 [700]~E(x7001,x7002)+E(f555(x7001,x7003,x7004),f555(x7002,x7003,x7004))
% 188.15/187.99 [701]~E(x7011,x7012)+E(f555(x7013,x7011,x7014),f555(x7013,x7012,x7014))
% 188.15/187.99 [702]~E(x7021,x7022)+E(f555(x7023,x7024,x7021),f555(x7023,x7024,x7022))
% 188.15/187.99 [703]~E(x7031,x7032)+E(f801(x7031,x7033),f801(x7032,x7033))
% 188.15/187.99 [704]~E(x7041,x7042)+E(f801(x7043,x7041),f801(x7043,x7042))
% 188.15/187.99 [705]~E(x7051,x7052)+E(f406(x7051,x7053),f406(x7052,x7053))
% 188.15/187.99 [706]~E(x7061,x7062)+E(f406(x7063,x7061),f406(x7063,x7062))
% 188.15/187.99 [707]~E(x7071,x7072)+E(f512(x7071,x7073,x7074),f512(x7072,x7073,x7074))
% 188.15/187.99 [708]~E(x7081,x7082)+E(f512(x7083,x7081,x7084),f512(x7083,x7082,x7084))
% 188.15/187.99 [709]~E(x7091,x7092)+E(f512(x7093,x7094,x7091),f512(x7093,x7094,x7092))
% 188.15/187.99 [710]~E(x7101,x7102)+E(f396(x7101,x7103,x7104,x7105),f396(x7102,x7103,x7104,x7105))
% 188.15/187.99 [711]~E(x7111,x7112)+E(f396(x7113,x7111,x7114,x7115),f396(x7113,x7112,x7114,x7115))
% 188.15/187.99 [712]~E(x7121,x7122)+E(f396(x7123,x7124,x7121,x7125),f396(x7123,x7124,x7122,x7125))
% 188.15/187.99 [713]~E(x7131,x7132)+E(f396(x7133,x7134,x7135,x7131),f396(x7133,x7134,x7135,x7132))
% 188.15/187.99 [714]~E(x7141,x7142)+E(f542(x7141,x7143,x7144),f542(x7142,x7143,x7144))
% 188.15/187.99 [715]~E(x7151,x7152)+E(f542(x7153,x7151,x7154),f542(x7153,x7152,x7154))
% 188.15/187.99 [716]~E(x7161,x7162)+E(f542(x7163,x7164,x7161),f542(x7163,x7164,x7162))
% 188.15/187.99 [717]~E(x7171,x7172)+E(f336(x7171,x7173,x7174),f336(x7172,x7173,x7174))
% 188.15/187.99 [718]~E(x7181,x7182)+E(f336(x7183,x7181,x7184),f336(x7183,x7182,x7184))
% 188.15/187.99 [719]~E(x7191,x7192)+E(f336(x7193,x7194,x7191),f336(x7193,x7194,x7192))
% 188.15/187.99 [720]~E(x7201,x7202)+E(f536(x7201,x7203,x7204,x7205,x7206),f536(x7202,x7203,x7204,x7205,x7206))
% 188.15/187.99 [721]~E(x7211,x7212)+E(f536(x7213,x7211,x7214,x7215,x7216),f536(x7213,x7212,x7214,x7215,x7216))
% 188.15/187.99 [722]~E(x7221,x7222)+E(f536(x7223,x7224,x7221,x7225,x7226),f536(x7223,x7224,x7222,x7225,x7226))
% 188.15/187.99 [723]~E(x7231,x7232)+E(f536(x7233,x7234,x7235,x7231,x7236),f536(x7233,x7234,x7235,x7232,x7236))
% 188.15/187.99 [724]~E(x7241,x7242)+E(f536(x7243,x7244,x7245,x7246,x7241),f536(x7243,x7244,x7245,x7246,x7242))
% 188.15/187.99 [725]~E(x7251,x7252)+E(f254(x7251,x7253),f254(x7252,x7253))
% 188.15/187.99 [726]~E(x7261,x7262)+E(f254(x7263,x7261),f254(x7263,x7262))
% 188.15/187.99 [727]~E(x7271,x7272)+E(f80(x7271,x7273),f80(x7272,x7273))
% 188.15/187.99 [728]~E(x7281,x7282)+E(f80(x7283,x7281),f80(x7283,x7282))
% 188.15/187.99 [729]~E(x7291,x7292)+E(f234(x7291),f234(x7292))
% 188.15/187.99 [730]~E(x7301,x7302)+E(f255(x7301,x7303),f255(x7302,x7303))
% 188.15/187.99 [731]~E(x7311,x7312)+E(f255(x7313,x7311),f255(x7313,x7312))
% 188.15/187.99 [732]~E(x7321,x7322)+E(f228(x7321,x7323,x7324,x7325),f228(x7322,x7323,x7324,x7325))
% 188.15/187.99 [733]~E(x7331,x7332)+E(f228(x7333,x7331,x7334,x7335),f228(x7333,x7332,x7334,x7335))
% 188.15/187.99 [734]~E(x7341,x7342)+E(f228(x7343,x7344,x7341,x7345),f228(x7343,x7344,x7342,x7345))
% 188.15/187.99 [735]~E(x7351,x7352)+E(f228(x7353,x7354,x7355,x7351),f228(x7353,x7354,x7355,x7352))
% 188.15/187.99 [736]~E(x7361,x7362)+E(f766(x7361,x7363,x7364,x7365),f766(x7362,x7363,x7364,x7365))
% 188.15/187.99 [737]~E(x7371,x7372)+E(f766(x7373,x7371,x7374,x7375),f766(x7373,x7372,x7374,x7375))
% 188.15/187.99 [738]~E(x7381,x7382)+E(f766(x7383,x7384,x7381,x7385),f766(x7383,x7384,x7382,x7385))
% 188.15/187.99 [739]~E(x7391,x7392)+E(f766(x7393,x7394,x7395,x7391),f766(x7393,x7394,x7395,x7392))
% 188.15/187.99 [740]~E(x7401,x7402)+E(f392(x7401,x7403,x7404),f392(x7402,x7403,x7404))
% 188.15/187.99 [741]~E(x7411,x7412)+E(f392(x7413,x7411,x7414),f392(x7413,x7412,x7414))
% 188.15/187.99 [742]~E(x7421,x7422)+E(f392(x7423,x7424,x7421),f392(x7423,x7424,x7422))
% 188.15/187.99 [743]~E(x7431,x7432)+E(f666(x7431,x7433,x7434,x7435),f666(x7432,x7433,x7434,x7435))
% 188.15/187.99 [744]~E(x7441,x7442)+E(f666(x7443,x7441,x7444,x7445),f666(x7443,x7442,x7444,x7445))
% 188.15/187.99 [745]~E(x7451,x7452)+E(f666(x7453,x7454,x7451,x7455),f666(x7453,x7454,x7452,x7455))
% 188.15/187.99 [746]~E(x7461,x7462)+E(f666(x7463,x7464,x7465,x7461),f666(x7463,x7464,x7465,x7462))
% 188.15/187.99 [747]~E(x7471,x7472)+E(f613(x7471,x7473,x7474),f613(x7472,x7473,x7474))
% 188.15/187.99 [748]~E(x7481,x7482)+E(f613(x7483,x7481,x7484),f613(x7483,x7482,x7484))
% 188.15/187.99 [749]~E(x7491,x7492)+E(f613(x7493,x7494,x7491),f613(x7493,x7494,x7492))
% 188.15/187.99 [750]~E(x7501,x7502)+E(f573(x7501,x7503,x7504,x7505,x7506),f573(x7502,x7503,x7504,x7505,x7506))
% 188.15/187.99 [751]~E(x7511,x7512)+E(f573(x7513,x7511,x7514,x7515,x7516),f573(x7513,x7512,x7514,x7515,x7516))
% 188.15/187.99 [752]~E(x7521,x7522)+E(f573(x7523,x7524,x7521,x7525,x7526),f573(x7523,x7524,x7522,x7525,x7526))
% 188.15/187.99 [753]~E(x7531,x7532)+E(f573(x7533,x7534,x7535,x7531,x7536),f573(x7533,x7534,x7535,x7532,x7536))
% 188.15/187.99 [754]~E(x7541,x7542)+E(f573(x7543,x7544,x7545,x7546,x7541),f573(x7543,x7544,x7545,x7546,x7542))
% 188.15/187.99 [755]~E(x7551,x7552)+E(f653(x7551,x7553),f653(x7552,x7553))
% 188.15/187.99 [756]~E(x7561,x7562)+E(f653(x7563,x7561),f653(x7563,x7562))
% 188.15/187.99 [757]~E(x7571,x7572)+E(f217(x7571,x7573),f217(x7572,x7573))
% 188.15/187.99 [758]~E(x7581,x7582)+E(f217(x7583,x7581),f217(x7583,x7582))
% 188.15/187.99 [759]~E(x7591,x7592)+E(f554(x7591,x7593,x7594),f554(x7592,x7593,x7594))
% 188.15/187.99 [760]~E(x7601,x7602)+E(f554(x7603,x7601,x7604),f554(x7603,x7602,x7604))
% 188.15/187.99 [761]~E(x7611,x7612)+E(f554(x7613,x7614,x7611),f554(x7613,x7614,x7612))
% 188.15/187.99 [762]~E(x7621,x7622)+E(f89(x7621),f89(x7622))
% 188.15/187.99 [763]~E(x7631,x7632)+E(f247(x7631,x7633,x7634),f247(x7632,x7633,x7634))
% 188.15/187.99 [764]~E(x7641,x7642)+E(f247(x7643,x7641,x7644),f247(x7643,x7642,x7644))
% 188.15/187.99 [765]~E(x7651,x7652)+E(f247(x7653,x7654,x7651),f247(x7653,x7654,x7652))
% 188.15/187.99 [766]~E(x7661,x7662)+E(f584(x7661,x7663,x7664,x7665),f584(x7662,x7663,x7664,x7665))
% 188.15/187.99 [767]~E(x7671,x7672)+E(f584(x7673,x7671,x7674,x7675),f584(x7673,x7672,x7674,x7675))
% 188.15/187.99 [768]~E(x7681,x7682)+E(f584(x7683,x7684,x7681,x7685),f584(x7683,x7684,x7682,x7685))
% 188.15/187.99 [769]~E(x7691,x7692)+E(f584(x7693,x7694,x7695,x7691),f584(x7693,x7694,x7695,x7692))
% 188.15/187.99 [770]~E(x7701,x7702)+E(f60(x7701,x7703,x7704),f60(x7702,x7703,x7704))
% 188.15/187.99 [771]~E(x7711,x7712)+E(f60(x7713,x7711,x7714),f60(x7713,x7712,x7714))
% 188.15/187.99 [772]~E(x7721,x7722)+E(f60(x7723,x7724,x7721),f60(x7723,x7724,x7722))
% 188.15/187.99 [773]~E(x7731,x7732)+E(f571(x7731,x7733,x7734,x7735),f571(x7732,x7733,x7734,x7735))
% 188.15/187.99 [774]~E(x7741,x7742)+E(f571(x7743,x7741,x7744,x7745),f571(x7743,x7742,x7744,x7745))
% 188.15/187.99 [775]~E(x7751,x7752)+E(f571(x7753,x7754,x7751,x7755),f571(x7753,x7754,x7752,x7755))
% 188.15/187.99 [776]~E(x7761,x7762)+E(f571(x7763,x7764,x7765,x7761),f571(x7763,x7764,x7765,x7762))
% 188.15/187.99 [777]~E(x7771,x7772)+E(f838(x7771,x7773,x7774,x7775,x7776,x7777,x7778),f838(x7772,x7773,x7774,x7775,x7776,x7777,x7778))
% 188.15/187.99 [778]~E(x7781,x7782)+E(f838(x7783,x7781,x7784,x7785,x7786,x7787,x7788),f838(x7783,x7782,x7784,x7785,x7786,x7787,x7788))
% 188.15/187.99 [779]~E(x7791,x7792)+E(f838(x7793,x7794,x7791,x7795,x7796,x7797,x7798),f838(x7793,x7794,x7792,x7795,x7796,x7797,x7798))
% 188.15/187.99 [780]~E(x7801,x7802)+E(f838(x7803,x7804,x7805,x7801,x7806,x7807,x7808),f838(x7803,x7804,x7805,x7802,x7806,x7807,x7808))
% 188.15/187.99 [781]~E(x7811,x7812)+E(f838(x7813,x7814,x7815,x7816,x7811,x7817,x7818),f838(x7813,x7814,x7815,x7816,x7812,x7817,x7818))
% 188.15/187.99 [782]~E(x7821,x7822)+E(f838(x7823,x7824,x7825,x7826,x7827,x7821,x7828),f838(x7823,x7824,x7825,x7826,x7827,x7822,x7828))
% 188.15/187.99 [783]~E(x7831,x7832)+E(f838(x7833,x7834,x7835,x7836,x7837,x7838,x7831),f838(x7833,x7834,x7835,x7836,x7837,x7838,x7832))
% 188.15/187.99 [784]~E(x7841,x7842)+E(f458(x7841,x7843,x7844,x7845,x7846),f458(x7842,x7843,x7844,x7845,x7846))
% 188.15/187.99 [785]~E(x7851,x7852)+E(f458(x7853,x7851,x7854,x7855,x7856),f458(x7853,x7852,x7854,x7855,x7856))
% 188.15/187.99 [786]~E(x7861,x7862)+E(f458(x7863,x7864,x7861,x7865,x7866),f458(x7863,x7864,x7862,x7865,x7866))
% 188.15/187.99 [787]~E(x7871,x7872)+E(f458(x7873,x7874,x7875,x7871,x7876),f458(x7873,x7874,x7875,x7872,x7876))
% 188.15/187.99 [788]~E(x7881,x7882)+E(f458(x7883,x7884,x7885,x7886,x7881),f458(x7883,x7884,x7885,x7886,x7882))
% 188.15/187.99 [789]~E(x7891,x7892)+E(f743(x7891,x7893,x7894,x7895,x7896),f743(x7892,x7893,x7894,x7895,x7896))
% 188.15/187.99 [790]~E(x7901,x7902)+E(f743(x7903,x7901,x7904,x7905,x7906),f743(x7903,x7902,x7904,x7905,x7906))
% 188.15/187.99 [791]~E(x7911,x7912)+E(f743(x7913,x7914,x7911,x7915,x7916),f743(x7913,x7914,x7912,x7915,x7916))
% 188.15/187.99 [792]~E(x7921,x7922)+E(f743(x7923,x7924,x7925,x7921,x7926),f743(x7923,x7924,x7925,x7922,x7926))
% 188.15/187.99 [793]~E(x7931,x7932)+E(f743(x7933,x7934,x7935,x7936,x7931),f743(x7933,x7934,x7935,x7936,x7932))
% 188.15/187.99 [794]~E(x7941,x7942)+E(f611(x7941,x7943,x7944),f611(x7942,x7943,x7944))
% 188.15/187.99 [795]~E(x7951,x7952)+E(f611(x7953,x7951,x7954),f611(x7953,x7952,x7954))
% 188.15/187.99 [796]~E(x7961,x7962)+E(f611(x7963,x7964,x7961),f611(x7963,x7964,x7962))
% 188.15/187.99 [797]~E(x7971,x7972)+E(f624(x7971,x7973,x7974),f624(x7972,x7973,x7974))
% 188.15/187.99 [798]~E(x7981,x7982)+E(f624(x7983,x7981,x7984),f624(x7983,x7982,x7984))
% 188.15/187.99 [799]~E(x7991,x7992)+E(f624(x7993,x7994,x7991),f624(x7993,x7994,x7992))
% 188.15/187.99 [800]~E(x8001,x8002)+E(f157(x8001,x8003,x8004,x8005),f157(x8002,x8003,x8004,x8005))
% 188.15/187.99 [801]~E(x8011,x8012)+E(f157(x8013,x8011,x8014,x8015),f157(x8013,x8012,x8014,x8015))
% 188.15/187.99 [802]~E(x8021,x8022)+E(f157(x8023,x8024,x8021,x8025),f157(x8023,x8024,x8022,x8025))
% 188.15/187.99 [803]~E(x8031,x8032)+E(f157(x8033,x8034,x8035,x8031),f157(x8033,x8034,x8035,x8032))
% 188.15/187.99 [804]~E(x8041,x8042)+E(f346(x8041,x8043),f346(x8042,x8043))
% 188.15/187.99 [805]~E(x8051,x8052)+E(f346(x8053,x8051),f346(x8053,x8052))
% 188.15/187.99 [806]~E(x8061,x8062)+E(f55(x8061),f55(x8062))
% 188.15/187.99 [807]~E(x8071,x8072)+E(f123(x8071,x8073,x8074),f123(x8072,x8073,x8074))
% 188.15/187.99 [808]~E(x8081,x8082)+E(f123(x8083,x8081,x8084),f123(x8083,x8082,x8084))
% 188.15/187.99 [809]~E(x8091,x8092)+E(f123(x8093,x8094,x8091),f123(x8093,x8094,x8092))
% 188.15/187.99 [810]~E(x8101,x8102)+E(f527(x8101,x8103,x8104),f527(x8102,x8103,x8104))
% 188.15/187.99 [811]~E(x8111,x8112)+E(f527(x8113,x8111,x8114),f527(x8113,x8112,x8114))
% 188.15/187.99 [812]~E(x8121,x8122)+E(f527(x8123,x8124,x8121),f527(x8123,x8124,x8122))
% 188.15/187.99 [813]~E(x8131,x8132)+E(f588(x8131,x8133,x8134,x8135),f588(x8132,x8133,x8134,x8135))
% 188.15/187.99 [814]~E(x8141,x8142)+E(f588(x8143,x8141,x8144,x8145),f588(x8143,x8142,x8144,x8145))
% 188.15/187.99 [815]~E(x8151,x8152)+E(f588(x8153,x8154,x8151,x8155),f588(x8153,x8154,x8152,x8155))
% 188.15/187.99 [816]~E(x8161,x8162)+E(f588(x8163,x8164,x8165,x8161),f588(x8163,x8164,x8165,x8162))
% 188.15/187.99 [817]~E(x8171,x8172)+E(f521(x8171,x8173,x8174,x8175),f521(x8172,x8173,x8174,x8175))
% 188.15/187.99 [818]~E(x8181,x8182)+E(f521(x8183,x8181,x8184,x8185),f521(x8183,x8182,x8184,x8185))
% 188.15/187.99 [819]~E(x8191,x8192)+E(f521(x8193,x8194,x8191,x8195),f521(x8193,x8194,x8192,x8195))
% 188.15/187.99 [820]~E(x8201,x8202)+E(f521(x8203,x8204,x8205,x8201),f521(x8203,x8204,x8205,x8202))
% 188.15/187.99 [821]~E(x8211,x8212)+E(f711(x8211,x8213,x8214),f711(x8212,x8213,x8214))
% 188.15/187.99 [822]~E(x8221,x8222)+E(f711(x8223,x8221,x8224),f711(x8223,x8222,x8224))
% 188.15/187.99 [823]~E(x8231,x8232)+E(f711(x8233,x8234,x8231),f711(x8233,x8234,x8232))
% 188.15/187.99 [824]~E(x8241,x8242)+E(f295(x8241),f295(x8242))
% 188.15/187.99 [825]~E(x8251,x8252)+E(f568(x8251,x8253,x8254),f568(x8252,x8253,x8254))
% 188.15/187.99 [826]~E(x8261,x8262)+E(f568(x8263,x8261,x8264),f568(x8263,x8262,x8264))
% 188.15/187.99 [827]~E(x8271,x8272)+E(f568(x8273,x8274,x8271),f568(x8273,x8274,x8272))
% 188.15/187.99 [828]~E(x8281,x8282)+E(f471(x8281,x8283,x8284),f471(x8282,x8283,x8284))
% 188.15/187.99 [829]~E(x8291,x8292)+E(f471(x8293,x8291,x8294),f471(x8293,x8292,x8294))
% 188.15/187.99 [830]~E(x8301,x8302)+E(f471(x8303,x8304,x8301),f471(x8303,x8304,x8302))
% 188.15/187.99 [831]~E(x8311,x8312)+E(f366(x8311,x8313,x8314),f366(x8312,x8313,x8314))
% 188.15/187.99 [832]~E(x8321,x8322)+E(f366(x8323,x8321,x8324),f366(x8323,x8322,x8324))
% 188.15/187.99 [833]~E(x8331,x8332)+E(f366(x8333,x8334,x8331),f366(x8333,x8334,x8332))
% 188.15/187.99 [834]~E(x8341,x8342)+E(f707(x8341,x8343,x8344),f707(x8342,x8343,x8344))
% 188.15/187.99 [835]~E(x8351,x8352)+E(f707(x8353,x8351,x8354),f707(x8353,x8352,x8354))
% 188.15/187.99 [836]~E(x8361,x8362)+E(f707(x8363,x8364,x8361),f707(x8363,x8364,x8362))
% 188.15/187.99 [837]~E(x8371,x8372)+E(f282(x8371,x8373),f282(x8372,x8373))
% 188.15/187.99 [838]~E(x8381,x8382)+E(f282(x8383,x8381),f282(x8383,x8382))
% 188.15/187.99 [839]~E(x8391,x8392)+E(f854(x8391,x8393,x8394),f854(x8392,x8393,x8394))
% 188.15/187.99 [840]~E(x8401,x8402)+E(f854(x8403,x8401,x8404),f854(x8403,x8402,x8404))
% 188.15/187.99 [841]~E(x8411,x8412)+E(f854(x8413,x8414,x8411),f854(x8413,x8414,x8412))
% 188.15/187.99 [842]~E(x8421,x8422)+E(f519(x8421,x8423,x8424,x8425),f519(x8422,x8423,x8424,x8425))
% 188.15/187.99 [843]~E(x8431,x8432)+E(f519(x8433,x8431,x8434,x8435),f519(x8433,x8432,x8434,x8435))
% 188.15/187.99 [844]~E(x8441,x8442)+E(f519(x8443,x8444,x8441,x8445),f519(x8443,x8444,x8442,x8445))
% 188.15/187.99 [845]~E(x8451,x8452)+E(f519(x8453,x8454,x8455,x8451),f519(x8453,x8454,x8455,x8452))
% 188.15/187.99 [846]~E(x8461,x8462)+E(f532(x8461,x8463),f532(x8462,x8463))
% 188.15/187.99 [847]~E(x8471,x8472)+E(f532(x8473,x8471),f532(x8473,x8472))
% 188.15/187.99 [848]~E(x8481,x8482)+E(f368(x8481,x8483,x8484,x8485,x8486),f368(x8482,x8483,x8484,x8485,x8486))
% 188.15/187.99 [849]~E(x8491,x8492)+E(f368(x8493,x8491,x8494,x8495,x8496),f368(x8493,x8492,x8494,x8495,x8496))
% 188.15/187.99 [850]~E(x8501,x8502)+E(f368(x8503,x8504,x8501,x8505,x8506),f368(x8503,x8504,x8502,x8505,x8506))
% 188.15/187.99 [851]~E(x8511,x8512)+E(f368(x8513,x8514,x8515,x8511,x8516),f368(x8513,x8514,x8515,x8512,x8516))
% 188.15/187.99 [852]~E(x8521,x8522)+E(f368(x8523,x8524,x8525,x8526,x8521),f368(x8523,x8524,x8525,x8526,x8522))
% 188.15/187.99 [853]~E(x8531,x8532)+E(f469(x8531,x8533,x8534,x8535),f469(x8532,x8533,x8534,x8535))
% 188.15/187.99 [854]~E(x8541,x8542)+E(f469(x8543,x8541,x8544,x8545),f469(x8543,x8542,x8544,x8545))
% 188.15/187.99 [855]~E(x8551,x8552)+E(f469(x8553,x8554,x8551,x8555),f469(x8553,x8554,x8552,x8555))
% 188.15/187.99 [856]~E(x8561,x8562)+E(f469(x8563,x8564,x8565,x8561),f469(x8563,x8564,x8565,x8562))
% 188.15/187.99 [857]~E(x8571,x8572)+E(f855(x8571,x8573,x8574),f855(x8572,x8573,x8574))
% 188.15/187.99 [858]~E(x8581,x8582)+E(f855(x8583,x8581,x8584),f855(x8583,x8582,x8584))
% 188.15/187.99 [859]~E(x8591,x8592)+E(f855(x8593,x8594,x8591),f855(x8593,x8594,x8592))
% 188.15/187.99 [860]~E(x8601,x8602)+E(f355(x8601,x8603,x8604),f355(x8602,x8603,x8604))
% 188.15/187.99 [861]~E(x8611,x8612)+E(f355(x8613,x8611,x8614),f355(x8613,x8612,x8614))
% 188.15/187.99 [862]~E(x8621,x8622)+E(f355(x8623,x8624,x8621),f355(x8623,x8624,x8622))
% 188.15/187.99 [863]~E(x8631,x8632)+E(f354(x8631,x8633,x8634),f354(x8632,x8633,x8634))
% 188.15/187.99 [864]~E(x8641,x8642)+E(f354(x8643,x8641,x8644),f354(x8643,x8642,x8644))
% 188.15/187.99 [865]~E(x8651,x8652)+E(f354(x8653,x8654,x8651),f354(x8653,x8654,x8652))
% 188.15/187.99 [866]~E(x8661,x8662)+E(f576(x8661,x8663,x8664,x8665,x8666),f576(x8662,x8663,x8664,x8665,x8666))
% 188.15/187.99 [867]~E(x8671,x8672)+E(f576(x8673,x8671,x8674,x8675,x8676),f576(x8673,x8672,x8674,x8675,x8676))
% 188.15/187.99 [868]~E(x8681,x8682)+E(f576(x8683,x8684,x8681,x8685,x8686),f576(x8683,x8684,x8682,x8685,x8686))
% 188.15/187.99 [869]~E(x8691,x8692)+E(f576(x8693,x8694,x8695,x8691,x8696),f576(x8693,x8694,x8695,x8692,x8696))
% 188.15/187.99 [870]~E(x8701,x8702)+E(f576(x8703,x8704,x8705,x8706,x8701),f576(x8703,x8704,x8705,x8706,x8702))
% 188.15/187.99 [871]~E(x8711,x8712)+E(f822(x8711,x8713,x8714),f822(x8712,x8713,x8714))
% 188.15/187.99 [872]~E(x8721,x8722)+E(f822(x8723,x8721,x8724),f822(x8723,x8722,x8724))
% 188.15/187.99 [873]~E(x8731,x8732)+E(f822(x8733,x8734,x8731),f822(x8733,x8734,x8732))
% 188.15/187.99 [874]~E(x8741,x8742)+E(f495(x8741,x8743,x8744,x8745),f495(x8742,x8743,x8744,x8745))
% 188.15/187.99 [875]~E(x8751,x8752)+E(f495(x8753,x8751,x8754,x8755),f495(x8753,x8752,x8754,x8755))
% 188.15/187.99 [876]~E(x8761,x8762)+E(f495(x8763,x8764,x8761,x8765),f495(x8763,x8764,x8762,x8765))
% 188.15/187.99 [877]~E(x8771,x8772)+E(f495(x8773,x8774,x8775,x8771),f495(x8773,x8774,x8775,x8772))
% 188.15/187.99 [878]~E(x8781,x8782)+E(f585(x8781,x8783,x8784),f585(x8782,x8783,x8784))
% 188.15/187.99 [879]~E(x8791,x8792)+E(f585(x8793,x8791,x8794),f585(x8793,x8792,x8794))
% 188.15/187.99 [880]~E(x8801,x8802)+E(f585(x8803,x8804,x8801),f585(x8803,x8804,x8802))
% 188.15/187.99 [881]~E(x8811,x8812)+E(f269(x8811,x8813),f269(x8812,x8813))
% 188.15/187.99 [882]~E(x8821,x8822)+E(f269(x8823,x8821),f269(x8823,x8822))
% 188.15/187.99 [883]~E(x8831,x8832)+E(f719(x8831,x8833,x8834,x8835),f719(x8832,x8833,x8834,x8835))
% 188.15/187.99 [884]~E(x8841,x8842)+E(f719(x8843,x8841,x8844,x8845),f719(x8843,x8842,x8844,x8845))
% 188.15/187.99 [885]~E(x8851,x8852)+E(f719(x8853,x8854,x8851,x8855),f719(x8853,x8854,x8852,x8855))
% 188.15/187.99 [886]~E(x8861,x8862)+E(f719(x8863,x8864,x8865,x8861),f719(x8863,x8864,x8865,x8862))
% 188.15/187.99 [887]~E(x8871,x8872)+E(f699(x8871,x8873,x8874,x8875,x8876,x8877),f699(x8872,x8873,x8874,x8875,x8876,x8877))
% 188.15/187.99 [888]~E(x8881,x8882)+E(f699(x8883,x8881,x8884,x8885,x8886,x8887),f699(x8883,x8882,x8884,x8885,x8886,x8887))
% 188.15/187.99 [889]~E(x8891,x8892)+E(f699(x8893,x8894,x8891,x8895,x8896,x8897),f699(x8893,x8894,x8892,x8895,x8896,x8897))
% 188.15/187.99 [890]~E(x8901,x8902)+E(f699(x8903,x8904,x8905,x8901,x8906,x8907),f699(x8903,x8904,x8905,x8902,x8906,x8907))
% 188.15/187.99 [891]~E(x8911,x8912)+E(f699(x8913,x8914,x8915,x8916,x8911,x8917),f699(x8913,x8914,x8915,x8916,x8912,x8917))
% 188.15/187.99 [892]~E(x8921,x8922)+E(f699(x8923,x8924,x8925,x8926,x8927,x8921),f699(x8923,x8924,x8925,x8926,x8927,x8922))
% 188.15/187.99 [893]~E(x8931,x8932)+E(f170(x8931,x8933,x8934),f170(x8932,x8933,x8934))
% 188.15/187.99 [894]~E(x8941,x8942)+E(f170(x8943,x8941,x8944),f170(x8943,x8942,x8944))
% 188.15/187.99 [895]~E(x8951,x8952)+E(f170(x8953,x8954,x8951),f170(x8953,x8954,x8952))
% 188.15/187.99 [896]~E(x8961,x8962)+E(f709(x8961,x8963,x8964),f709(x8962,x8963,x8964))
% 188.15/187.99 [897]~E(x8971,x8972)+E(f709(x8973,x8971,x8974),f709(x8973,x8972,x8974))
% 188.15/187.99 [898]~E(x8981,x8982)+E(f709(x8983,x8984,x8981),f709(x8983,x8984,x8982))
% 188.15/187.99 [899]~E(x8991,x8992)+E(f192(x8991,x8993),f192(x8992,x8993))
% 188.15/187.99 [900]~E(x9001,x9002)+E(f192(x9003,x9001),f192(x9003,x9002))
% 188.15/187.99 [901]~E(x9011,x9012)+E(f372(x9011,x9013,x9014,x9015,x9016,x9017),f372(x9012,x9013,x9014,x9015,x9016,x9017))
% 188.15/187.99 [902]~E(x9021,x9022)+E(f372(x9023,x9021,x9024,x9025,x9026,x9027),f372(x9023,x9022,x9024,x9025,x9026,x9027))
% 188.15/187.99 [903]~E(x9031,x9032)+E(f372(x9033,x9034,x9031,x9035,x9036,x9037),f372(x9033,x9034,x9032,x9035,x9036,x9037))
% 188.15/187.99 [904]~E(x9041,x9042)+E(f372(x9043,x9044,x9045,x9041,x9046,x9047),f372(x9043,x9044,x9045,x9042,x9046,x9047))
% 188.15/187.99 [905]~E(x9051,x9052)+E(f372(x9053,x9054,x9055,x9056,x9051,x9057),f372(x9053,x9054,x9055,x9056,x9052,x9057))
% 188.15/187.99 [906]~E(x9061,x9062)+E(f372(x9063,x9064,x9065,x9066,x9067,x9061),f372(x9063,x9064,x9065,x9066,x9067,x9062))
% 188.15/187.99 [907]~E(x9071,x9072)+E(f118(x9071,x9073),f118(x9072,x9073))
% 188.15/187.99 [908]~E(x9081,x9082)+E(f118(x9083,x9081),f118(x9083,x9082))
% 188.15/187.99 [909]~E(x9091,x9092)+E(f540(x9091,x9093),f540(x9092,x9093))
% 188.15/187.99 [910]~E(x9101,x9102)+E(f540(x9103,x9101),f540(x9103,x9102))
% 188.15/187.99 [911]~E(x9111,x9112)+E(f152(x9111,x9113),f152(x9112,x9113))
% 188.15/187.99 [912]~E(x9121,x9122)+E(f152(x9123,x9121),f152(x9123,x9122))
% 188.15/187.99 [913]~E(x9131,x9132)+E(f546(x9131,x9133),f546(x9132,x9133))
% 188.15/187.99 [914]~E(x9141,x9142)+E(f546(x9143,x9141),f546(x9143,x9142))
% 188.15/187.99 [915]~E(x9151,x9152)+E(f213(x9151,x9153,x9154,x9155,x9156,x9157,x9158),f213(x9152,x9153,x9154,x9155,x9156,x9157,x9158))
% 188.15/187.99 [916]~E(x9161,x9162)+E(f213(x9163,x9161,x9164,x9165,x9166,x9167,x9168),f213(x9163,x9162,x9164,x9165,x9166,x9167,x9168))
% 188.15/187.99 [917]~E(x9171,x9172)+E(f213(x9173,x9174,x9171,x9175,x9176,x9177,x9178),f213(x9173,x9174,x9172,x9175,x9176,x9177,x9178))
% 188.15/187.99 [918]~E(x9181,x9182)+E(f213(x9183,x9184,x9185,x9181,x9186,x9187,x9188),f213(x9183,x9184,x9185,x9182,x9186,x9187,x9188))
% 188.15/187.99 [919]~E(x9191,x9192)+E(f213(x9193,x9194,x9195,x9196,x9191,x9197,x9198),f213(x9193,x9194,x9195,x9196,x9192,x9197,x9198))
% 188.15/187.99 [920]~E(x9201,x9202)+E(f213(x9203,x9204,x9205,x9206,x9207,x9201,x9208),f213(x9203,x9204,x9205,x9206,x9207,x9202,x9208))
% 188.15/187.99 [921]~E(x9211,x9212)+E(f213(x9213,x9214,x9215,x9216,x9217,x9218,x9211),f213(x9213,x9214,x9215,x9216,x9217,x9218,x9212))
% 188.15/187.99 [922]~E(x9221,x9222)+E(f185(x9221,x9223,x9224,x9225),f185(x9222,x9223,x9224,x9225))
% 188.15/187.99 [923]~E(x9231,x9232)+E(f185(x9233,x9231,x9234,x9235),f185(x9233,x9232,x9234,x9235))
% 188.15/187.99 [924]~E(x9241,x9242)+E(f185(x9243,x9244,x9241,x9245),f185(x9243,x9244,x9242,x9245))
% 188.15/187.99 [925]~E(x9251,x9252)+E(f185(x9253,x9254,x9255,x9251),f185(x9253,x9254,x9255,x9252))
% 188.15/187.99 [926]~E(x9261,x9262)+E(f793(x9261,x9263,x9264,x9265),f793(x9262,x9263,x9264,x9265))
% 188.15/187.99 [927]~E(x9271,x9272)+E(f793(x9273,x9271,x9274,x9275),f793(x9273,x9272,x9274,x9275))
% 188.15/187.99 [928]~E(x9281,x9282)+E(f793(x9283,x9284,x9281,x9285),f793(x9283,x9284,x9282,x9285))
% 188.15/187.99 [929]~E(x9291,x9292)+E(f793(x9293,x9294,x9295,x9291),f793(x9293,x9294,x9295,x9292))
% 188.15/187.99 [930]~E(x9301,x9302)+E(f690(x9301,x9303),f690(x9302,x9303))
% 188.15/187.99 [931]~E(x9311,x9312)+E(f690(x9313,x9311),f690(x9313,x9312))
% 188.15/187.99 [932]~E(x9321,x9322)+E(f661(x9321,x9323,x9324),f661(x9322,x9323,x9324))
% 188.15/187.99 [933]~E(x9331,x9332)+E(f661(x9333,x9331,x9334),f661(x9333,x9332,x9334))
% 188.15/187.99 [934]~E(x9341,x9342)+E(f661(x9343,x9344,x9341),f661(x9343,x9344,x9342))
% 188.15/187.99 [935]~E(x9351,x9352)+E(f570(x9351,x9353,x9354,x9355,x9356),f570(x9352,x9353,x9354,x9355,x9356))
% 188.15/187.99 [936]~E(x9361,x9362)+E(f570(x9363,x9361,x9364,x9365,x9366),f570(x9363,x9362,x9364,x9365,x9366))
% 188.15/187.99 [937]~E(x9371,x9372)+E(f570(x9373,x9374,x9371,x9375,x9376),f570(x9373,x9374,x9372,x9375,x9376))
% 188.15/187.99 [938]~E(x9381,x9382)+E(f570(x9383,x9384,x9385,x9381,x9386),f570(x9383,x9384,x9385,x9382,x9386))
% 188.15/187.99 [939]~E(x9391,x9392)+E(f570(x9393,x9394,x9395,x9396,x9391),f570(x9393,x9394,x9395,x9396,x9392))
% 188.15/187.99 [940]~E(x9401,x9402)+E(f618(x9401,x9403,x9404,x9405),f618(x9402,x9403,x9404,x9405))
% 188.15/187.99 [941]~E(x9411,x9412)+E(f618(x9413,x9411,x9414,x9415),f618(x9413,x9412,x9414,x9415))
% 188.15/187.99 [942]~E(x9421,x9422)+E(f618(x9423,x9424,x9421,x9425),f618(x9423,x9424,x9422,x9425))
% 188.15/187.99 [943]~E(x9431,x9432)+E(f618(x9433,x9434,x9435,x9431),f618(x9433,x9434,x9435,x9432))
% 188.15/187.99 [944]~E(x9441,x9442)+E(f379(x9441,x9443),f379(x9442,x9443))
% 188.15/187.99 [945]~E(x9451,x9452)+E(f379(x9453,x9451),f379(x9453,x9452))
% 188.15/187.99 [946]~E(x9461,x9462)+E(f225(x9461,x9463,x9464),f225(x9462,x9463,x9464))
% 188.15/187.99 [947]~E(x9471,x9472)+E(f225(x9473,x9471,x9474),f225(x9473,x9472,x9474))
% 188.15/187.99 [948]~E(x9481,x9482)+E(f225(x9483,x9484,x9481),f225(x9483,x9484,x9482))
% 188.15/187.99 [949]~E(x9491,x9492)+E(f143(x9491,x9493,x9494,x9495),f143(x9492,x9493,x9494,x9495))
% 188.15/187.99 [950]~E(x9501,x9502)+E(f143(x9503,x9501,x9504,x9505),f143(x9503,x9502,x9504,x9505))
% 188.15/187.99 [951]~E(x9511,x9512)+E(f143(x9513,x9514,x9511,x9515),f143(x9513,x9514,x9512,x9515))
% 188.15/187.99 [952]~E(x9521,x9522)+E(f143(x9523,x9524,x9525,x9521),f143(x9523,x9524,x9525,x9522))
% 188.15/187.99 [953]~E(x9531,x9532)+E(f593(x9531,x9533,x9534,x9535),f593(x9532,x9533,x9534,x9535))
% 188.15/187.99 [954]~E(x9541,x9542)+E(f593(x9543,x9541,x9544,x9545),f593(x9543,x9542,x9544,x9545))
% 188.15/187.99 [955]~E(x9551,x9552)+E(f593(x9553,x9554,x9551,x9555),f593(x9553,x9554,x9552,x9555))
% 188.15/187.99 [956]~E(x9561,x9562)+E(f593(x9563,x9564,x9565,x9561),f593(x9563,x9564,x9565,x9562))
% 188.15/187.99 [957]~E(x9571,x9572)+E(f768(x9571,x9573,x9574,x9575,x9576,x9577,x9578),f768(x9572,x9573,x9574,x9575,x9576,x9577,x9578))
% 188.15/187.99 [958]~E(x9581,x9582)+E(f768(x9583,x9581,x9584,x9585,x9586,x9587,x9588),f768(x9583,x9582,x9584,x9585,x9586,x9587,x9588))
% 188.15/187.99 [959]~E(x9591,x9592)+E(f768(x9593,x9594,x9591,x9595,x9596,x9597,x9598),f768(x9593,x9594,x9592,x9595,x9596,x9597,x9598))
% 188.15/187.99 [960]~E(x9601,x9602)+E(f768(x9603,x9604,x9605,x9601,x9606,x9607,x9608),f768(x9603,x9604,x9605,x9602,x9606,x9607,x9608))
% 188.15/187.99 [961]~E(x9611,x9612)+E(f768(x9613,x9614,x9615,x9616,x9611,x9617,x9618),f768(x9613,x9614,x9615,x9616,x9612,x9617,x9618))
% 188.15/187.99 [962]~E(x9621,x9622)+E(f768(x9623,x9624,x9625,x9626,x9627,x9621,x9628),f768(x9623,x9624,x9625,x9626,x9627,x9622,x9628))
% 188.15/187.99 [963]~E(x9631,x9632)+E(f768(x9633,x9634,x9635,x9636,x9637,x9638,x9631),f768(x9633,x9634,x9635,x9636,x9637,x9638,x9632))
% 188.15/187.99 [964]~E(x9641,x9642)+E(f199(x9641,x9643,x9644,x9645),f199(x9642,x9643,x9644,x9645))
% 188.15/187.99 [965]~E(x9651,x9652)+E(f199(x9653,x9651,x9654,x9655),f199(x9653,x9652,x9654,x9655))
% 188.15/187.99 [966]~E(x9661,x9662)+E(f199(x9663,x9664,x9661,x9665),f199(x9663,x9664,x9662,x9665))
% 188.15/187.99 [967]~E(x9671,x9672)+E(f199(x9673,x9674,x9675,x9671),f199(x9673,x9674,x9675,x9672))
% 188.15/187.99 [968]~E(x9681,x9682)+E(f380(x9681,x9683),f380(x9682,x9683))
% 188.15/187.99 [969]~E(x9691,x9692)+E(f380(x9693,x9691),f380(x9693,x9692))
% 188.15/187.99 [970]~E(x9701,x9702)+E(f455(x9701,x9703,x9704,x9705),f455(x9702,x9703,x9704,x9705))
% 188.15/187.99 [971]~E(x9711,x9712)+E(f455(x9713,x9711,x9714,x9715),f455(x9713,x9712,x9714,x9715))
% 188.15/187.99 [972]~E(x9721,x9722)+E(f455(x9723,x9724,x9721,x9725),f455(x9723,x9724,x9722,x9725))
% 188.15/187.99 [973]~E(x9731,x9732)+E(f455(x9733,x9734,x9735,x9731),f455(x9733,x9734,x9735,x9732))
% 188.15/187.99 [974]~E(x9741,x9742)+E(f287(x9741,x9743,x9744,x9745),f287(x9742,x9743,x9744,x9745))
% 188.15/187.99 [975]~E(x9751,x9752)+E(f287(x9753,x9751,x9754,x9755),f287(x9753,x9752,x9754,x9755))
% 188.15/187.99 [976]~E(x9761,x9762)+E(f287(x9763,x9764,x9761,x9765),f287(x9763,x9764,x9762,x9765))
% 188.15/187.99 [977]~E(x9771,x9772)+E(f287(x9773,x9774,x9775,x9771),f287(x9773,x9774,x9775,x9772))
% 188.15/187.99 [978]~E(x9781,x9782)+E(f557(x9781,x9783,x9784),f557(x9782,x9783,x9784))
% 188.15/187.99 [979]~E(x9791,x9792)+E(f557(x9793,x9791,x9794),f557(x9793,x9792,x9794))
% 188.15/187.99 [980]~E(x9801,x9802)+E(f557(x9803,x9804,x9801),f557(x9803,x9804,x9802))
% 188.15/187.99 [981]~E(x9811,x9812)+E(f116(x9811,x9813,x9814),f116(x9812,x9813,x9814))
% 188.15/187.99 [982]~E(x9821,x9822)+E(f116(x9823,x9821,x9824),f116(x9823,x9822,x9824))
% 188.15/187.99 [983]~E(x9831,x9832)+E(f116(x9833,x9834,x9831),f116(x9833,x9834,x9832))
% 188.15/187.99 [984]~E(x9841,x9842)+E(f51(x9841,x9843),f51(x9842,x9843))
% 188.15/187.99 [985]~E(x9851,x9852)+E(f51(x9853,x9851),f51(x9853,x9852))
% 188.15/187.99 [986]~E(x9861,x9862)+E(f479(x9861,x9863,x9864,x9865,x9866,x9867,x9868,x9869),f479(x9862,x9863,x9864,x9865,x9866,x9867,x9868,x9869))
% 188.15/187.99 [987]~E(x9871,x9872)+E(f479(x9873,x9871,x9874,x9875,x9876,x9877,x9878,x9879),f479(x9873,x9872,x9874,x9875,x9876,x9877,x9878,x9879))
% 188.15/187.99 [988]~E(x9881,x9882)+E(f479(x9883,x9884,x9881,x9885,x9886,x9887,x9888,x9889),f479(x9883,x9884,x9882,x9885,x9886,x9887,x9888,x9889))
% 188.15/187.99 [989]~E(x9891,x9892)+E(f479(x9893,x9894,x9895,x9891,x9896,x9897,x9898,x9899),f479(x9893,x9894,x9895,x9892,x9896,x9897,x9898,x9899))
% 188.15/187.99 [990]~E(x9901,x9902)+E(f479(x9903,x9904,x9905,x9906,x9901,x9907,x9908,x9909),f479(x9903,x9904,x9905,x9906,x9902,x9907,x9908,x9909))
% 188.15/187.99 [991]~E(x9911,x9912)+E(f479(x9913,x9914,x9915,x9916,x9917,x9911,x9918,x9919),f479(x9913,x9914,x9915,x9916,x9917,x9912,x9918,x9919))
% 188.15/187.99 [992]~E(x9921,x9922)+E(f479(x9923,x9924,x9925,x9926,x9927,x9928,x9921,x9929),f479(x9923,x9924,x9925,x9926,x9927,x9928,x9922,x9929))
% 188.15/187.99 [993]~E(x9931,x9932)+E(f479(x9933,x9934,x9935,x9936,x9937,x9938,x9939,x9931),f479(x9933,x9934,x9935,x9936,x9937,x9938,x9939,x9932))
% 188.15/187.99 [994]~E(x9941,x9942)+E(f407(x9941,x9943,x9944,x9945),f407(x9942,x9943,x9944,x9945))
% 188.15/187.99 [995]~E(x9951,x9952)+E(f407(x9953,x9951,x9954,x9955),f407(x9953,x9952,x9954,x9955))
% 188.15/187.99 [996]~E(x9961,x9962)+E(f407(x9963,x9964,x9961,x9965),f407(x9963,x9964,x9962,x9965))
% 188.15/187.99 [997]~E(x9971,x9972)+E(f407(x9973,x9974,x9975,x9971),f407(x9973,x9974,x9975,x9972))
% 188.15/187.99 [998]~E(x9981,x9982)+E(f344(x9981,x9983),f344(x9982,x9983))
% 188.15/187.99 [999]~E(x9991,x9992)+E(f344(x9993,x9991),f344(x9993,x9992))
% 188.15/187.99 [1000]~E(x10001,x10002)+E(f517(x10001,x10003,x10004),f517(x10002,x10003,x10004))
% 188.15/187.99 [1001]~E(x10011,x10012)+E(f517(x10013,x10011,x10014),f517(x10013,x10012,x10014))
% 188.15/187.99 [1002]~E(x10021,x10022)+E(f517(x10023,x10024,x10021),f517(x10023,x10024,x10022))
% 188.15/187.99 [1003]~E(x10031,x10032)+E(f251(x10031,x10033),f251(x10032,x10033))
% 188.15/187.99 [1004]~E(x10041,x10042)+E(f251(x10043,x10041),f251(x10043,x10042))
% 188.15/187.99 [1005]~E(x10051,x10052)+E(f748(x10051,x10053,x10054,x10055),f748(x10052,x10053,x10054,x10055))
% 188.15/187.99 [1006]~E(x10061,x10062)+E(f748(x10063,x10061,x10064,x10065),f748(x10063,x10062,x10064,x10065))
% 188.15/187.99 [1007]~E(x10071,x10072)+E(f748(x10073,x10074,x10071,x10075),f748(x10073,x10074,x10072,x10075))
% 188.15/187.99 [1008]~E(x10081,x10082)+E(f748(x10083,x10084,x10085,x10081),f748(x10083,x10084,x10085,x10082))
% 188.15/187.99 [1009]~E(x10091,x10092)+E(f670(x10091,x10093,x10094,x10095),f670(x10092,x10093,x10094,x10095))
% 188.15/187.99 [1010]~E(x10101,x10102)+E(f670(x10103,x10101,x10104,x10105),f670(x10103,x10102,x10104,x10105))
% 188.15/187.99 [1011]~E(x10111,x10112)+E(f670(x10113,x10114,x10111,x10115),f670(x10113,x10114,x10112,x10115))
% 188.15/187.99 [1012]~E(x10121,x10122)+E(f670(x10123,x10124,x10125,x10121),f670(x10123,x10124,x10125,x10122))
% 188.15/187.99 [1013]~E(x10131,x10132)+E(f762(x10131,x10133,x10134),f762(x10132,x10133,x10134))
% 188.15/187.99 [1014]~E(x10141,x10142)+E(f762(x10143,x10141,x10144),f762(x10143,x10142,x10144))
% 188.15/187.99 [1015]~E(x10151,x10152)+E(f762(x10153,x10154,x10151),f762(x10153,x10154,x10152))
% 188.15/187.99 [1016]~E(x10161,x10162)+E(f333(x10161,x10163,x10164),f333(x10162,x10163,x10164))
% 188.15/187.99 [1017]~E(x10171,x10172)+E(f333(x10173,x10171,x10174),f333(x10173,x10172,x10174))
% 188.15/187.99 [1018]~E(x10181,x10182)+E(f333(x10183,x10184,x10181),f333(x10183,x10184,x10182))
% 188.15/187.99 [1019]~E(x10191,x10192)+E(f41(x10191),f41(x10192))
% 188.15/187.99 [1020]~E(x10201,x10202)+E(f700(x10201,x10203,x10204,x10205,x10206,x10207),f700(x10202,x10203,x10204,x10205,x10206,x10207))
% 188.15/187.99 [1021]~E(x10211,x10212)+E(f700(x10213,x10211,x10214,x10215,x10216,x10217),f700(x10213,x10212,x10214,x10215,x10216,x10217))
% 188.15/187.99 [1022]~E(x10221,x10222)+E(f700(x10223,x10224,x10221,x10225,x10226,x10227),f700(x10223,x10224,x10222,x10225,x10226,x10227))
% 188.15/187.99 [1023]~E(x10231,x10232)+E(f700(x10233,x10234,x10235,x10231,x10236,x10237),f700(x10233,x10234,x10235,x10232,x10236,x10237))
% 188.15/187.99 [1024]~E(x10241,x10242)+E(f700(x10243,x10244,x10245,x10246,x10241,x10247),f700(x10243,x10244,x10245,x10246,x10242,x10247))
% 188.15/187.99 [1025]~E(x10251,x10252)+E(f700(x10253,x10254,x10255,x10256,x10257,x10251),f700(x10253,x10254,x10255,x10256,x10257,x10252))
% 188.15/187.99 [1026]~E(x10261,x10262)+E(f600(x10261,x10263,x10264),f600(x10262,x10263,x10264))
% 188.15/187.99 [1027]~E(x10271,x10272)+E(f600(x10273,x10271,x10274),f600(x10273,x10272,x10274))
% 188.15/187.99 [1028]~E(x10281,x10282)+E(f600(x10283,x10284,x10281),f600(x10283,x10284,x10282))
% 188.15/187.99 [1029]~E(x10291,x10292)+E(f376(x10291,x10293),f376(x10292,x10293))
% 188.15/187.99 [1030]~E(x10301,x10302)+E(f376(x10303,x10301),f376(x10303,x10302))
% 188.15/187.99 [1031]~E(x10311,x10312)+E(f50(x10311,x10313),f50(x10312,x10313))
% 188.15/187.99 [1032]~E(x10321,x10322)+E(f50(x10323,x10321),f50(x10323,x10322))
% 188.15/187.99 [1033]~E(x10331,x10332)+E(f612(x10331,x10333),f612(x10332,x10333))
% 188.15/187.99 [1034]~E(x10341,x10342)+E(f612(x10343,x10341),f612(x10343,x10342))
% 188.15/187.99 [1035]~E(x10351,x10352)+E(f351(x10351,x10353,x10354),f351(x10352,x10353,x10354))
% 188.15/187.99 [1036]~E(x10361,x10362)+E(f351(x10363,x10361,x10364),f351(x10363,x10362,x10364))
% 188.15/187.99 [1037]~E(x10371,x10372)+E(f351(x10373,x10374,x10371),f351(x10373,x10374,x10372))
% 188.15/187.99 [1038]~E(x10381,x10382)+E(f360(x10381,x10383),f360(x10382,x10383))
% 188.15/187.99 [1039]~E(x10391,x10392)+E(f360(x10393,x10391),f360(x10393,x10392))
% 188.15/187.99 [1040]~E(x10401,x10402)+E(f826(x10401,x10403),f826(x10402,x10403))
% 188.15/187.99 [1041]~E(x10411,x10412)+E(f826(x10413,x10411),f826(x10413,x10412))
% 188.15/187.99 [1042]~E(x10421,x10422)+E(f26(x10421,x10423,x10424),f26(x10422,x10423,x10424))
% 188.15/187.99 [1043]~E(x10431,x10432)+E(f26(x10433,x10431,x10434),f26(x10433,x10432,x10434))
% 188.15/187.99 [1044]~E(x10441,x10442)+E(f26(x10443,x10444,x10441),f26(x10443,x10444,x10442))
% 188.15/187.99 [1045]~E(x10451,x10452)+E(f492(x10451,x10453,x10454),f492(x10452,x10453,x10454))
% 188.15/187.99 [1046]~E(x10461,x10462)+E(f492(x10463,x10461,x10464),f492(x10463,x10462,x10464))
% 188.15/187.99 [1047]~E(x10471,x10472)+E(f492(x10473,x10474,x10471),f492(x10473,x10474,x10472))
% 188.15/187.99 [1048]~E(x10481,x10482)+E(f759(x10481,x10483,x10484),f759(x10482,x10483,x10484))
% 188.15/187.99 [1049]~E(x10491,x10492)+E(f759(x10493,x10491,x10494),f759(x10493,x10492,x10494))
% 188.15/187.99 [1050]~E(x10501,x10502)+E(f759(x10503,x10504,x10501),f759(x10503,x10504,x10502))
% 188.15/187.99 [1051]~E(x10511,x10512)+E(f529(x10511,x10513,x10514,x10515,x10516),f529(x10512,x10513,x10514,x10515,x10516))
% 188.15/187.99 [1052]~E(x10521,x10522)+E(f529(x10523,x10521,x10524,x10525,x10526),f529(x10523,x10522,x10524,x10525,x10526))
% 188.15/187.99 [1053]~E(x10531,x10532)+E(f529(x10533,x10534,x10531,x10535,x10536),f529(x10533,x10534,x10532,x10535,x10536))
% 188.15/187.99 [1054]~E(x10541,x10542)+E(f529(x10543,x10544,x10545,x10541,x10546),f529(x10543,x10544,x10545,x10542,x10546))
% 188.15/187.99 [1055]~E(x10551,x10552)+E(f529(x10553,x10554,x10555,x10556,x10551),f529(x10553,x10554,x10555,x10556,x10552))
% 188.15/187.99 [1056]~E(x10561,x10562)+E(f364(x10561,x10563,x10564,x10565,x10566),f364(x10562,x10563,x10564,x10565,x10566))
% 188.15/187.99 [1057]~E(x10571,x10572)+E(f364(x10573,x10571,x10574,x10575,x10576),f364(x10573,x10572,x10574,x10575,x10576))
% 188.15/187.99 [1058]~E(x10581,x10582)+E(f364(x10583,x10584,x10581,x10585,x10586),f364(x10583,x10584,x10582,x10585,x10586))
% 188.15/187.99 [1059]~E(x10591,x10592)+E(f364(x10593,x10594,x10595,x10591,x10596),f364(x10593,x10594,x10595,x10592,x10596))
% 188.15/187.99 [1060]~E(x10601,x10602)+E(f364(x10603,x10604,x10605,x10606,x10601),f364(x10603,x10604,x10605,x10606,x10602))
% 188.15/187.99 [1061]~E(x10611,x10612)+E(f718(x10611,x10613,x10614),f718(x10612,x10613,x10614))
% 188.15/187.99 [1062]~E(x10621,x10622)+E(f718(x10623,x10621,x10624),f718(x10623,x10622,x10624))
% 188.15/187.99 [1063]~E(x10631,x10632)+E(f718(x10633,x10634,x10631),f718(x10633,x10634,x10632))
% 188.15/187.99 [1064]~E(x10641,x10642)+E(f259(x10641,x10643,x10644,x10645,x10646),f259(x10642,x10643,x10644,x10645,x10646))
% 188.15/187.99 [1065]~E(x10651,x10652)+E(f259(x10653,x10651,x10654,x10655,x10656),f259(x10653,x10652,x10654,x10655,x10656))
% 188.15/187.99 [1066]~E(x10661,x10662)+E(f259(x10663,x10664,x10661,x10665,x10666),f259(x10663,x10664,x10662,x10665,x10666))
% 188.15/187.99 [1067]~E(x10671,x10672)+E(f259(x10673,x10674,x10675,x10671,x10676),f259(x10673,x10674,x10675,x10672,x10676))
% 188.15/187.99 [1068]~E(x10681,x10682)+E(f259(x10683,x10684,x10685,x10686,x10681),f259(x10683,x10684,x10685,x10686,x10682))
% 188.15/187.99 [1069]~E(x10691,x10692)+E(f373(x10691,x10693,x10694,x10695,x10696,x10697),f373(x10692,x10693,x10694,x10695,x10696,x10697))
% 188.15/187.99 [1070]~E(x10701,x10702)+E(f373(x10703,x10701,x10704,x10705,x10706,x10707),f373(x10703,x10702,x10704,x10705,x10706,x10707))
% 188.15/187.99 [1071]~E(x10711,x10712)+E(f373(x10713,x10714,x10711,x10715,x10716,x10717),f373(x10713,x10714,x10712,x10715,x10716,x10717))
% 188.15/187.99 [1072]~E(x10721,x10722)+E(f373(x10723,x10724,x10725,x10721,x10726,x10727),f373(x10723,x10724,x10725,x10722,x10726,x10727))
% 188.15/187.99 [1073]~E(x10731,x10732)+E(f373(x10733,x10734,x10735,x10736,x10731,x10737),f373(x10733,x10734,x10735,x10736,x10732,x10737))
% 188.15/187.99 [1074]~E(x10741,x10742)+E(f373(x10743,x10744,x10745,x10746,x10747,x10741),f373(x10743,x10744,x10745,x10746,x10747,x10742))
% 188.15/187.99 [1075]~E(x10751,x10752)+E(f625(x10751,x10753,x10754),f625(x10752,x10753,x10754))
% 188.15/187.99 [1076]~E(x10761,x10762)+E(f625(x10763,x10761,x10764),f625(x10763,x10762,x10764))
% 188.15/187.99 [1077]~E(x10771,x10772)+E(f625(x10773,x10774,x10771),f625(x10773,x10774,x10772))
% 188.15/187.99 [1078]~E(x10781,x10782)+E(f736(x10781,x10783,x10784),f736(x10782,x10783,x10784))
% 188.15/187.99 [1079]~E(x10791,x10792)+E(f736(x10793,x10791,x10794),f736(x10793,x10792,x10794))
% 188.15/187.99 [1080]~E(x10801,x10802)+E(f736(x10803,x10804,x10801),f736(x10803,x10804,x10802))
% 188.15/187.99 [1081]~E(x10811,x10812)+E(f433(x10811,x10813,x10814),f433(x10812,x10813,x10814))
% 188.15/187.99 [1082]~E(x10821,x10822)+E(f433(x10823,x10821,x10824),f433(x10823,x10822,x10824))
% 188.15/187.99 [1083]~E(x10831,x10832)+E(f433(x10833,x10834,x10831),f433(x10833,x10834,x10832))
% 188.15/187.99 [1084]~E(x10841,x10842)+E(f839(x10841,x10843,x10844,x10845),f839(x10842,x10843,x10844,x10845))
% 188.15/187.99 [1085]~E(x10851,x10852)+E(f839(x10853,x10851,x10854,x10855),f839(x10853,x10852,x10854,x10855))
% 188.15/187.99 [1086]~E(x10861,x10862)+E(f839(x10863,x10864,x10861,x10865),f839(x10863,x10864,x10862,x10865))
% 188.15/187.99 [1087]~E(x10871,x10872)+E(f839(x10873,x10874,x10875,x10871),f839(x10873,x10874,x10875,x10872))
% 188.15/187.99 [1088]~E(x10881,x10882)+E(f553(x10881,x10883,x10884),f553(x10882,x10883,x10884))
% 188.15/187.99 [1089]~E(x10891,x10892)+E(f553(x10893,x10891,x10894),f553(x10893,x10892,x10894))
% 188.15/187.99 [1090]~E(x10901,x10902)+E(f553(x10903,x10904,x10901),f553(x10903,x10904,x10902))
% 188.15/187.99 [1091]~E(x10911,x10912)+E(f31(x10911,x10913,x10914,x10915,x10916,x10917,x10918,x10919,x109110,x109111),f31(x10912,x10913,x10914,x10915,x10916,x10917,x10918,x10919,x109110,x109111))
% 188.15/187.99 [1092]~E(x10921,x10922)+E(f31(x10923,x10921,x10924,x10925,x10926,x10927,x10928,x10929,x109210,x109211),f31(x10923,x10922,x10924,x10925,x10926,x10927,x10928,x10929,x109210,x109211))
% 188.15/187.99 [1093]~E(x10931,x10932)+E(f31(x10933,x10934,x10931,x10935,x10936,x10937,x10938,x10939,x109310,x109311),f31(x10933,x10934,x10932,x10935,x10936,x10937,x10938,x10939,x109310,x109311))
% 188.15/187.99 [1094]~E(x10941,x10942)+E(f31(x10943,x10944,x10945,x10941,x10946,x10947,x10948,x10949,x109410,x109411),f31(x10943,x10944,x10945,x10942,x10946,x10947,x10948,x10949,x109410,x109411))
% 188.15/187.99 [1095]~E(x10951,x10952)+E(f31(x10953,x10954,x10955,x10956,x10951,x10957,x10958,x10959,x109510,x109511),f31(x10953,x10954,x10955,x10956,x10952,x10957,x10958,x10959,x109510,x109511))
% 188.15/187.99 [1096]~E(x10961,x10962)+E(f31(x10963,x10964,x10965,x10966,x10967,x10961,x10968,x10969,x109610,x109611),f31(x10963,x10964,x10965,x10966,x10967,x10962,x10968,x10969,x109610,x109611))
% 188.15/187.99 [1097]~E(x10971,x10972)+E(f31(x10973,x10974,x10975,x10976,x10977,x10978,x10971,x10979,x109710,x109711),f31(x10973,x10974,x10975,x10976,x10977,x10978,x10972,x10979,x109710,x109711))
% 188.15/187.99 [1098]~E(x10981,x10982)+E(f31(x10983,x10984,x10985,x10986,x10987,x10988,x10989,x10981,x109810,x109811),f31(x10983,x10984,x10985,x10986,x10987,x10988,x10989,x10982,x109810,x109811))
% 188.15/187.99 [1099]~E(x10991,x10992)+E(f31(x10993,x10994,x10995,x10996,x10997,x10998,x10999,x109910,x10991,x109911),f31(x10993,x10994,x10995,x10996,x10997,x10998,x10999,x109910,x10992,x109911))
% 188.15/187.99 [1100]~E(x11001,x11002)+E(f31(x11003,x11004,x11005,x11006,x11007,x11008,x11009,x110010,x110011,x11001),f31(x11003,x11004,x11005,x11006,x11007,x11008,x11009,x110010,x110011,x11002))
% 188.15/187.99 [1101]~E(x11011,x11012)+E(f385(x11011),f385(x11012))
% 188.15/187.99 [1102]~E(x11021,x11022)+E(f760(x11021,x11023,x11024),f760(x11022,x11023,x11024))
% 188.15/187.99 [1103]~E(x11031,x11032)+E(f760(x11033,x11031,x11034),f760(x11033,x11032,x11034))
% 188.15/187.99 [1104]~E(x11041,x11042)+E(f760(x11043,x11044,x11041),f760(x11043,x11044,x11042))
% 188.15/187.99 [1105]~E(x11051,x11052)+E(f647(x11051,x11053,x11054),f647(x11052,x11053,x11054))
% 188.15/187.99 [1106]~E(x11061,x11062)+E(f647(x11063,x11061,x11064),f647(x11063,x11062,x11064))
% 188.15/187.99 [1107]~E(x11071,x11072)+E(f647(x11073,x11074,x11071),f647(x11073,x11074,x11072))
% 188.15/187.99 [1108]~E(x11081,x11082)+E(f74(x11081,x11083,x11084,x11085,x11086),f74(x11082,x11083,x11084,x11085,x11086))
% 188.15/187.99 [1109]~E(x11091,x11092)+E(f74(x11093,x11091,x11094,x11095,x11096),f74(x11093,x11092,x11094,x11095,x11096))
% 188.15/187.99 [1110]~E(x11101,x11102)+E(f74(x11103,x11104,x11101,x11105,x11106),f74(x11103,x11104,x11102,x11105,x11106))
% 188.15/187.99 [1111]~E(x11111,x11112)+E(f74(x11113,x11114,x11115,x11111,x11116),f74(x11113,x11114,x11115,x11112,x11116))
% 188.15/187.99 [1112]~E(x11121,x11122)+E(f74(x11123,x11124,x11125,x11126,x11121),f74(x11123,x11124,x11125,x11126,x11122))
% 188.15/187.99 [1113]~E(x11131,x11132)+E(f276(x11131),f276(x11132))
% 188.15/187.99 [1114]~E(x11141,x11142)+E(f772(x11141,x11143,x11144),f772(x11142,x11143,x11144))
% 188.15/187.99 [1115]~E(x11151,x11152)+E(f772(x11153,x11151,x11154),f772(x11153,x11152,x11154))
% 188.15/187.99 [1116]~E(x11161,x11162)+E(f772(x11163,x11164,x11161),f772(x11163,x11164,x11162))
% 188.15/187.99 [1117]~E(x11171,x11172)+E(f220(x11171,x11173),f220(x11172,x11173))
% 188.15/187.99 [1118]~E(x11181,x11182)+E(f220(x11183,x11181),f220(x11183,x11182))
% 188.15/187.99 [1119]~E(x11191,x11192)+E(f371(x11191,x11193,x11194,x11195,x11196,x11197),f371(x11192,x11193,x11194,x11195,x11196,x11197))
% 188.15/187.99 [1120]~E(x11201,x11202)+E(f371(x11203,x11201,x11204,x11205,x11206,x11207),f371(x11203,x11202,x11204,x11205,x11206,x11207))
% 188.15/187.99 [1121]~E(x11211,x11212)+E(f371(x11213,x11214,x11211,x11215,x11216,x11217),f371(x11213,x11214,x11212,x11215,x11216,x11217))
% 188.15/187.99 [1122]~E(x11221,x11222)+E(f371(x11223,x11224,x11225,x11221,x11226,x11227),f371(x11223,x11224,x11225,x11222,x11226,x11227))
% 188.15/187.99 [1123]~E(x11231,x11232)+E(f371(x11233,x11234,x11235,x11236,x11231,x11237),f371(x11233,x11234,x11235,x11236,x11232,x11237))
% 188.15/187.99 [1124]~E(x11241,x11242)+E(f371(x11243,x11244,x11245,x11246,x11247,x11241),f371(x11243,x11244,x11245,x11246,x11247,x11242))
% 188.15/187.99 [1125]~E(x11251,x11252)+E(f803(x11251,x11253,x11254),f803(x11252,x11253,x11254))
% 188.15/187.99 [1126]~E(x11261,x11262)+E(f803(x11263,x11261,x11264),f803(x11263,x11262,x11264))
% 188.15/187.99 [1127]~E(x11271,x11272)+E(f803(x11273,x11274,x11271),f803(x11273,x11274,x11272))
% 188.15/187.99 [1128]~E(x11281,x11282)+E(f811(x11281,x11283,x11284),f811(x11282,x11283,x11284))
% 188.15/187.99 [1129]~E(x11291,x11292)+E(f811(x11293,x11291,x11294),f811(x11293,x11292,x11294))
% 188.15/187.99 [1130]~E(x11301,x11302)+E(f811(x11303,x11304,x11301),f811(x11303,x11304,x11302))
% 188.15/187.99 [1131]~E(x11311,x11312)+E(f178(x11311,x11313,x11314),f178(x11312,x11313,x11314))
% 188.15/187.99 [1132]~E(x11321,x11322)+E(f178(x11323,x11321,x11324),f178(x11323,x11322,x11324))
% 188.15/187.99 [1133]~E(x11331,x11332)+E(f178(x11333,x11334,x11331),f178(x11333,x11334,x11332))
% 188.15/187.99 [1134]~E(x11341,x11342)+E(f634(x11341,x11343,x11344,x11345),f634(x11342,x11343,x11344,x11345))
% 188.15/187.99 [1135]~E(x11351,x11352)+E(f634(x11353,x11351,x11354,x11355),f634(x11353,x11352,x11354,x11355))
% 188.15/187.99 [1136]~E(x11361,x11362)+E(f634(x11363,x11364,x11361,x11365),f634(x11363,x11364,x11362,x11365))
% 188.15/187.99 [1137]~E(x11371,x11372)+E(f634(x11373,x11374,x11375,x11371),f634(x11373,x11374,x11375,x11372))
% 188.15/187.99 [1138]~E(x11381,x11382)+E(f490(x11381),f490(x11382))
% 188.15/187.99 [1139]~E(x11391,x11392)+E(f419(x11391,x11393,x11394,x11395),f419(x11392,x11393,x11394,x11395))
% 188.15/187.99 [1140]~E(x11401,x11402)+E(f419(x11403,x11401,x11404,x11405),f419(x11403,x11402,x11404,x11405))
% 188.15/187.99 [1141]~E(x11411,x11412)+E(f419(x11413,x11414,x11411,x11415),f419(x11413,x11414,x11412,x11415))
% 188.15/187.99 [1142]~E(x11421,x11422)+E(f419(x11423,x11424,x11425,x11421),f419(x11423,x11424,x11425,x11422))
% 188.15/187.99 [1143]~E(x11431,x11432)+E(f734(x11431,x11433),f734(x11432,x11433))
% 188.15/187.99 [1144]~E(x11441,x11442)+E(f734(x11443,x11441),f734(x11443,x11442))
% 188.15/187.99 [1145]~E(x11451,x11452)+E(f148(x11451,x11453,x11454),f148(x11452,x11453,x11454))
% 188.15/187.99 [1146]~E(x11461,x11462)+E(f148(x11463,x11461,x11464),f148(x11463,x11462,x11464))
% 188.15/187.99 [1147]~E(x11471,x11472)+E(f148(x11473,x11474,x11471),f148(x11473,x11474,x11472))
% 188.15/187.99 [1148]~E(x11481,x11482)+E(f603(x11481,x11483),f603(x11482,x11483))
% 188.15/187.99 [1149]~E(x11491,x11492)+E(f603(x11493,x11491),f603(x11493,x11492))
% 188.15/187.99 [1150]~E(x11501,x11502)+E(f782(x11501,x11503,x11504,x11505,x11506,x11507),f782(x11502,x11503,x11504,x11505,x11506,x11507))
% 188.15/187.99 [1151]~E(x11511,x11512)+E(f782(x11513,x11511,x11514,x11515,x11516,x11517),f782(x11513,x11512,x11514,x11515,x11516,x11517))
% 188.15/187.99 [1152]~E(x11521,x11522)+E(f782(x11523,x11524,x11521,x11525,x11526,x11527),f782(x11523,x11524,x11522,x11525,x11526,x11527))
% 188.15/187.99 [1153]~E(x11531,x11532)+E(f782(x11533,x11534,x11535,x11531,x11536,x11537),f782(x11533,x11534,x11535,x11532,x11536,x11537))
% 188.15/187.99 [1154]~E(x11541,x11542)+E(f782(x11543,x11544,x11545,x11546,x11541,x11547),f782(x11543,x11544,x11545,x11546,x11542,x11547))
% 188.15/187.99 [1155]~E(x11551,x11552)+E(f782(x11553,x11554,x11555,x11556,x11557,x11551),f782(x11553,x11554,x11555,x11556,x11557,x11552))
% 188.15/187.99 [1156]~E(x11561,x11562)+E(f483(x11561,x11563,x11564),f483(x11562,x11563,x11564))
% 188.15/187.99 [1157]~E(x11571,x11572)+E(f483(x11573,x11571,x11574),f483(x11573,x11572,x11574))
% 188.15/187.99 [1158]~E(x11581,x11582)+E(f483(x11583,x11584,x11581),f483(x11583,x11584,x11582))
% 188.15/187.99 [1159]~E(x11591,x11592)+E(f184(x11591,x11593,x11594),f184(x11592,x11593,x11594))
% 188.15/187.99 [1160]~E(x11601,x11602)+E(f184(x11603,x11601,x11604),f184(x11603,x11602,x11604))
% 188.15/187.99 [1161]~E(x11611,x11612)+E(f184(x11613,x11614,x11611),f184(x11613,x11614,x11612))
% 188.15/187.99 [1162]~E(x11621,x11622)+E(f393(x11621,x11623,x11624),f393(x11622,x11623,x11624))
% 188.15/187.99 [1163]~E(x11631,x11632)+E(f393(x11633,x11631,x11634),f393(x11633,x11632,x11634))
% 188.15/187.99 [1164]~E(x11641,x11642)+E(f393(x11643,x11644,x11641),f393(x11643,x11644,x11642))
% 188.15/187.99 [1165]~E(x11651,x11652)+E(f831(x11651,x11653,x11654,x11655),f831(x11652,x11653,x11654,x11655))
% 188.15/187.99 [1166]~E(x11661,x11662)+E(f831(x11663,x11661,x11664,x11665),f831(x11663,x11662,x11664,x11665))
% 188.15/187.99 [1167]~E(x11671,x11672)+E(f831(x11673,x11674,x11671,x11675),f831(x11673,x11674,x11672,x11675))
% 188.15/187.99 [1168]~E(x11681,x11682)+E(f831(x11683,x11684,x11685,x11681),f831(x11683,x11684,x11685,x11682))
% 188.15/187.99 [1169]~E(x11691,x11692)+E(f834(x11691,x11693),f834(x11692,x11693))
% 188.15/187.99 [1170]~E(x11701,x11702)+E(f834(x11703,x11701),f834(x11703,x11702))
% 188.15/187.99 [1171]~E(x11711,x11712)+E(f627(x11711,x11713,x11714),f627(x11712,x11713,x11714))
% 188.15/187.99 [1172]~E(x11721,x11722)+E(f627(x11723,x11721,x11724),f627(x11723,x11722,x11724))
% 188.15/187.99 [1173]~E(x11731,x11732)+E(f627(x11733,x11734,x11731),f627(x11733,x11734,x11732))
% 188.15/187.99 [1174]~E(x11741,x11742)+E(f497(x11741,x11743,x11744,x11745,x11746,x11747),f497(x11742,x11743,x11744,x11745,x11746,x11747))
% 188.15/187.99 [1175]~E(x11751,x11752)+E(f497(x11753,x11751,x11754,x11755,x11756,x11757),f497(x11753,x11752,x11754,x11755,x11756,x11757))
% 188.15/187.99 [1176]~E(x11761,x11762)+E(f497(x11763,x11764,x11761,x11765,x11766,x11767),f497(x11763,x11764,x11762,x11765,x11766,x11767))
% 188.15/187.99 [1177]~E(x11771,x11772)+E(f497(x11773,x11774,x11775,x11771,x11776,x11777),f497(x11773,x11774,x11775,x11772,x11776,x11777))
% 188.15/187.99 [1178]~E(x11781,x11782)+E(f497(x11783,x11784,x11785,x11786,x11781,x11787),f497(x11783,x11784,x11785,x11786,x11782,x11787))
% 188.15/187.99 [1179]~E(x11791,x11792)+E(f497(x11793,x11794,x11795,x11796,x11797,x11791),f497(x11793,x11794,x11795,x11796,x11797,x11792))
% 188.15/187.99 [1180]~E(x11801,x11802)+E(f473(x11801,x11803,x11804,x11805,x11806),f473(x11802,x11803,x11804,x11805,x11806))
% 188.15/187.99 [1181]~E(x11811,x11812)+E(f473(x11813,x11811,x11814,x11815,x11816),f473(x11813,x11812,x11814,x11815,x11816))
% 188.15/187.99 [1182]~E(x11821,x11822)+E(f473(x11823,x11824,x11821,x11825,x11826),f473(x11823,x11824,x11822,x11825,x11826))
% 188.15/187.99 [1183]~E(x11831,x11832)+E(f473(x11833,x11834,x11835,x11831,x11836),f473(x11833,x11834,x11835,x11832,x11836))
% 188.15/187.99 [1184]~E(x11841,x11842)+E(f473(x11843,x11844,x11845,x11846,x11841),f473(x11843,x11844,x11845,x11846,x11842))
% 188.15/187.99 [1185]~E(x11851,x11852)+E(f210(x11851),f210(x11852))
% 188.15/187.99 [1186]~E(x11861,x11862)+E(f812(x11861,x11863,x11864,x11865,x11866),f812(x11862,x11863,x11864,x11865,x11866))
% 188.15/187.99 [1187]~E(x11871,x11872)+E(f812(x11873,x11871,x11874,x11875,x11876),f812(x11873,x11872,x11874,x11875,x11876))
% 188.15/187.99 [1188]~E(x11881,x11882)+E(f812(x11883,x11884,x11881,x11885,x11886),f812(x11883,x11884,x11882,x11885,x11886))
% 188.15/187.99 [1189]~E(x11891,x11892)+E(f812(x11893,x11894,x11895,x11891,x11896),f812(x11893,x11894,x11895,x11892,x11896))
% 188.15/187.99 [1190]~E(x11901,x11902)+E(f812(x11903,x11904,x11905,x11906,x11901),f812(x11903,x11904,x11905,x11906,x11902))
% 188.15/187.99 [1191]~E(x11911,x11912)+E(f597(x11911,x11913,x11914),f597(x11912,x11913,x11914))
% 188.15/187.99 [1192]~E(x11921,x11922)+E(f597(x11923,x11921,x11924),f597(x11923,x11922,x11924))
% 188.15/187.99 [1193]~E(x11931,x11932)+E(f597(x11933,x11934,x11931),f597(x11933,x11934,x11932))
% 188.15/187.99 [1194]~E(x11941,x11942)+E(f350(x11941,x11943),f350(x11942,x11943))
% 188.15/187.99 [1195]~E(x11951,x11952)+E(f350(x11953,x11951),f350(x11953,x11952))
% 188.15/187.99 [1196]~E(x11961,x11962)+E(f685(x11961,x11963,x11964,x11965),f685(x11962,x11963,x11964,x11965))
% 188.15/187.99 [1197]~E(x11971,x11972)+E(f685(x11973,x11971,x11974,x11975),f685(x11973,x11972,x11974,x11975))
% 188.15/187.99 [1198]~E(x11981,x11982)+E(f685(x11983,x11984,x11981,x11985),f685(x11983,x11984,x11982,x11985))
% 188.15/187.99 [1199]~E(x11991,x11992)+E(f685(x11993,x11994,x11995,x11991),f685(x11993,x11994,x11995,x11992))
% 188.15/187.99 [1200]~E(x12001,x12002)+E(f652(x12001,x12003),f652(x12002,x12003))
% 188.15/187.99 [1201]~E(x12011,x12012)+E(f652(x12013,x12011),f652(x12013,x12012))
% 188.15/187.99 [1202]~E(x12021,x12022)+E(f523(x12021,x12023,x12024),f523(x12022,x12023,x12024))
% 188.15/187.99 [1203]~E(x12031,x12032)+E(f523(x12033,x12031,x12034),f523(x12033,x12032,x12034))
% 188.15/187.99 [1204]~E(x12041,x12042)+E(f523(x12043,x12044,x12041),f523(x12043,x12044,x12042))
% 188.15/187.99 [1205]~E(x12051,x12052)+E(f202(x12051,x12053),f202(x12052,x12053))
% 188.15/187.99 [1206]~E(x12061,x12062)+E(f202(x12063,x12061),f202(x12063,x12062))
% 188.15/187.99 [1207]~E(x12071,x12072)+E(f543(x12071,x12073,x12074),f543(x12072,x12073,x12074))
% 188.15/187.99 [1208]~E(x12081,x12082)+E(f543(x12083,x12081,x12084),f543(x12083,x12082,x12084))
% 188.15/187.99 [1209]~E(x12091,x12092)+E(f543(x12093,x12094,x12091),f543(x12093,x12094,x12092))
% 188.15/187.99 [1210]~E(x12101,x12102)+E(f92(x12101,x12103,x12104),f92(x12102,x12103,x12104))
% 188.15/187.99 [1211]~E(x12111,x12112)+E(f92(x12113,x12111,x12114),f92(x12113,x12112,x12114))
% 188.15/187.99 [1212]~E(x12121,x12122)+E(f92(x12123,x12124,x12121),f92(x12123,x12124,x12122))
% 188.15/187.99 [1213]~E(x12131,x12132)+E(f537(x12131,x12133,x12134),f537(x12132,x12133,x12134))
% 188.15/187.99 [1214]~E(x12141,x12142)+E(f537(x12143,x12141,x12144),f537(x12143,x12142,x12144))
% 188.15/187.99 [1215]~E(x12151,x12152)+E(f537(x12153,x12154,x12151),f537(x12153,x12154,x12152))
% 188.15/187.99 [1216]~E(x12161,x12162)+E(f420(x12161,x12163,x12164,x12165),f420(x12162,x12163,x12164,x12165))
% 188.15/187.99 [1217]~E(x12171,x12172)+E(f420(x12173,x12171,x12174,x12175),f420(x12173,x12172,x12174,x12175))
% 188.15/187.99 [1218]~E(x12181,x12182)+E(f420(x12183,x12184,x12181,x12185),f420(x12183,x12184,x12182,x12185))
% 188.15/187.99 [1219]~E(x12191,x12192)+E(f420(x12193,x12194,x12195,x12191),f420(x12193,x12194,x12195,x12192))
% 188.15/187.99 [1220]~E(x12201,x12202)+E(f835(x12201,x12203,x12204,x12205),f835(x12202,x12203,x12204,x12205))
% 188.15/187.99 [1221]~E(x12211,x12212)+E(f835(x12213,x12211,x12214,x12215),f835(x12213,x12212,x12214,x12215))
% 188.15/187.99 [1222]~E(x12221,x12222)+E(f835(x12223,x12224,x12221,x12225),f835(x12223,x12224,x12222,x12225))
% 188.15/187.99 [1223]~E(x12231,x12232)+E(f835(x12233,x12234,x12235,x12231),f835(x12233,x12234,x12235,x12232))
% 188.15/187.99 [1224]~E(x12241,x12242)+E(f477(x12241,x12243,x12244),f477(x12242,x12243,x12244))
% 188.15/187.99 [1225]~E(x12251,x12252)+E(f477(x12253,x12251,x12254),f477(x12253,x12252,x12254))
% 188.15/187.99 [1226]~E(x12261,x12262)+E(f477(x12263,x12264,x12261),f477(x12263,x12264,x12262))
% 188.15/187.99 [1227]~E(x12271,x12272)+E(f549(x12271,x12273,x12274),f549(x12272,x12273,x12274))
% 188.15/187.99 [1228]~E(x12281,x12282)+E(f549(x12283,x12281,x12284),f549(x12283,x12282,x12284))
% 188.15/187.99 [1229]~E(x12291,x12292)+E(f549(x12293,x12294,x12291),f549(x12293,x12294,x12292))
% 188.15/187.99 [1230]~E(x12301,x12302)+E(f416(x12301,x12303,x12304,x12305),f416(x12302,x12303,x12304,x12305))
% 188.15/187.99 [1231]~E(x12311,x12312)+E(f416(x12313,x12311,x12314,x12315),f416(x12313,x12312,x12314,x12315))
% 188.15/187.99 [1232]~E(x12321,x12322)+E(f416(x12323,x12324,x12321,x12325),f416(x12323,x12324,x12322,x12325))
% 188.15/187.99 [1233]~E(x12331,x12332)+E(f416(x12333,x12334,x12335,x12331),f416(x12333,x12334,x12335,x12332))
% 188.15/187.99 [1234]~E(x12341,x12342)+E(f783(x12341,x12343,x12344,x12345),f783(x12342,x12343,x12344,x12345))
% 188.15/187.99 [1235]~E(x12351,x12352)+E(f783(x12353,x12351,x12354,x12355),f783(x12353,x12352,x12354,x12355))
% 188.15/187.99 [1236]~E(x12361,x12362)+E(f783(x12363,x12364,x12361,x12365),f783(x12363,x12364,x12362,x12365))
% 188.15/187.99 [1237]~E(x12371,x12372)+E(f783(x12373,x12374,x12375,x12371),f783(x12373,x12374,x12375,x12372))
% 188.15/187.99 [1238]~E(x12381,x12382)+E(f657(x12381,x12383,x12384,x12385,x12386),f657(x12382,x12383,x12384,x12385,x12386))
% 188.15/187.99 [1239]~E(x12391,x12392)+E(f657(x12393,x12391,x12394,x12395,x12396),f657(x12393,x12392,x12394,x12395,x12396))
% 188.15/187.99 [1240]~E(x12401,x12402)+E(f657(x12403,x12404,x12401,x12405,x12406),f657(x12403,x12404,x12402,x12405,x12406))
% 188.15/187.99 [1241]~E(x12411,x12412)+E(f657(x12413,x12414,x12415,x12411,x12416),f657(x12413,x12414,x12415,x12412,x12416))
% 188.15/187.99 [1242]~E(x12421,x12422)+E(f657(x12423,x12424,x12425,x12426,x12421),f657(x12423,x12424,x12425,x12426,x12422))
% 188.15/187.99 [1243]~E(x12431,x12432)+E(f689(x12431,x12433),f689(x12432,x12433))
% 188.15/187.99 [1244]~E(x12441,x12442)+E(f689(x12443,x12441),f689(x12443,x12442))
% 188.15/187.99 [1245]~E(x12451,x12452)+E(f411(x12451,x12453,x12454,x12455),f411(x12452,x12453,x12454,x12455))
% 188.15/187.99 [1246]~E(x12461,x12462)+E(f411(x12463,x12461,x12464,x12465),f411(x12463,x12462,x12464,x12465))
% 188.15/187.99 [1247]~E(x12471,x12472)+E(f411(x12473,x12474,x12471,x12475),f411(x12473,x12474,x12472,x12475))
% 188.15/187.99 [1248]~E(x12481,x12482)+E(f411(x12483,x12484,x12485,x12481),f411(x12483,x12484,x12485,x12482))
% 188.15/187.99 [1249]~E(x12491,x12492)+E(f795(x12491,x12493,x12494,x12495),f795(x12492,x12493,x12494,x12495))
% 188.15/187.99 [1250]~E(x12501,x12502)+E(f795(x12503,x12501,x12504,x12505),f795(x12503,x12502,x12504,x12505))
% 188.15/187.99 [1251]~E(x12511,x12512)+E(f795(x12513,x12514,x12511,x12515),f795(x12513,x12514,x12512,x12515))
% 188.15/187.99 [1252]~E(x12521,x12522)+E(f795(x12523,x12524,x12525,x12521),f795(x12523,x12524,x12525,x12522))
% 188.15/187.99 [1253]~E(x12531,x12532)+E(f488(x12531,x12533),f488(x12532,x12533))
% 188.15/187.99 [1254]~E(x12541,x12542)+E(f488(x12543,x12541),f488(x12543,x12542))
% 188.15/187.99 [1255]~E(x12551,x12552)+E(f460(x12551,x12553,x12554,x12555),f460(x12552,x12553,x12554,x12555))
% 188.15/187.99 [1256]~E(x12561,x12562)+E(f460(x12563,x12561,x12564,x12565),f460(x12563,x12562,x12564,x12565))
% 188.15/187.99 [1257]~E(x12571,x12572)+E(f460(x12573,x12574,x12571,x12575),f460(x12573,x12574,x12572,x12575))
% 188.15/187.99 [1258]~E(x12581,x12582)+E(f460(x12583,x12584,x12585,x12581),f460(x12583,x12584,x12585,x12582))
% 188.15/187.99 [1259]~E(x12591,x12592)+E(f558(x12591,x12593,x12594),f558(x12592,x12593,x12594))
% 188.15/187.99 [1260]~E(x12601,x12602)+E(f558(x12603,x12601,x12604),f558(x12603,x12602,x12604))
% 188.15/187.99 [1261]~E(x12611,x12612)+E(f558(x12613,x12614,x12611),f558(x12613,x12614,x12612))
% 188.15/187.99 [1262]~E(x12621,x12622)+E(f214(x12621),f214(x12622))
% 188.15/187.99 [1263]~E(x12631,x12632)+E(f511(x12631,x12633,x12634,x12635,x12636,x12637,x12638),f511(x12632,x12633,x12634,x12635,x12636,x12637,x12638))
% 188.15/187.99 [1264]~E(x12641,x12642)+E(f511(x12643,x12641,x12644,x12645,x12646,x12647,x12648),f511(x12643,x12642,x12644,x12645,x12646,x12647,x12648))
% 188.15/187.99 [1265]~E(x12651,x12652)+E(f511(x12653,x12654,x12651,x12655,x12656,x12657,x12658),f511(x12653,x12654,x12652,x12655,x12656,x12657,x12658))
% 188.15/187.99 [1266]~E(x12661,x12662)+E(f511(x12663,x12664,x12665,x12661,x12666,x12667,x12668),f511(x12663,x12664,x12665,x12662,x12666,x12667,x12668))
% 188.15/187.99 [1267]~E(x12671,x12672)+E(f511(x12673,x12674,x12675,x12676,x12671,x12677,x12678),f511(x12673,x12674,x12675,x12676,x12672,x12677,x12678))
% 188.15/187.99 [1268]~E(x12681,x12682)+E(f511(x12683,x12684,x12685,x12686,x12687,x12681,x12688),f511(x12683,x12684,x12685,x12686,x12687,x12682,x12688))
% 188.15/187.99 [1269]~E(x12691,x12692)+E(f511(x12693,x12694,x12695,x12696,x12697,x12698,x12691),f511(x12693,x12694,x12695,x12696,x12697,x12698,x12692))
% 188.15/187.99 [1270]~E(x12701,x12702)+E(f120(x12701),f120(x12702))
% 188.15/187.99 [1271]~E(x12711,x12712)+E(f655(x12711,x12713,x12714,x12715,x12716),f655(x12712,x12713,x12714,x12715,x12716))
% 188.15/187.99 [1272]~E(x12721,x12722)+E(f655(x12723,x12721,x12724,x12725,x12726),f655(x12723,x12722,x12724,x12725,x12726))
% 188.15/187.99 [1273]~E(x12731,x12732)+E(f655(x12733,x12734,x12731,x12735,x12736),f655(x12733,x12734,x12732,x12735,x12736))
% 188.15/187.99 [1274]~E(x12741,x12742)+E(f655(x12743,x12744,x12745,x12741,x12746),f655(x12743,x12744,x12745,x12742,x12746))
% 188.15/187.99 [1275]~E(x12751,x12752)+E(f655(x12753,x12754,x12755,x12756,x12751),f655(x12753,x12754,x12755,x12756,x12752))
% 188.15/187.99 [1276]~E(x12761,x12762)+E(f212(x12761,x12763,x12764,x12765),f212(x12762,x12763,x12764,x12765))
% 188.15/187.99 [1277]~E(x12771,x12772)+E(f212(x12773,x12771,x12774,x12775),f212(x12773,x12772,x12774,x12775))
% 188.15/187.99 [1278]~E(x12781,x12782)+E(f212(x12783,x12784,x12781,x12785),f212(x12783,x12784,x12782,x12785))
% 188.15/187.99 [1279]~E(x12791,x12792)+E(f212(x12793,x12794,x12795,x12791),f212(x12793,x12794,x12795,x12792))
% 188.15/187.99 [1280]~E(x12801,x12802)+E(f361(x12801,x12803,x12804,x12805),f361(x12802,x12803,x12804,x12805))
% 188.15/187.99 [1281]~E(x12811,x12812)+E(f361(x12813,x12811,x12814,x12815),f361(x12813,x12812,x12814,x12815))
% 188.15/187.99 [1282]~E(x12821,x12822)+E(f361(x12823,x12824,x12821,x12825),f361(x12823,x12824,x12822,x12825))
% 188.15/187.99 [1283]~E(x12831,x12832)+E(f361(x12833,x12834,x12835,x12831),f361(x12833,x12834,x12835,x12832))
% 188.15/187.99 [1284]~E(x12841,x12842)+E(f686(x12841,x12843,x12844,x12845,x12846,x12847),f686(x12842,x12843,x12844,x12845,x12846,x12847))
% 188.15/187.99 [1285]~E(x12851,x12852)+E(f686(x12853,x12851,x12854,x12855,x12856,x12857),f686(x12853,x12852,x12854,x12855,x12856,x12857))
% 188.15/187.99 [1286]~E(x12861,x12862)+E(f686(x12863,x12864,x12861,x12865,x12866,x12867),f686(x12863,x12864,x12862,x12865,x12866,x12867))
% 188.15/187.99 [1287]~E(x12871,x12872)+E(f686(x12873,x12874,x12875,x12871,x12876,x12877),f686(x12873,x12874,x12875,x12872,x12876,x12877))
% 188.15/187.99 [1288]~E(x12881,x12882)+E(f686(x12883,x12884,x12885,x12886,x12881,x12887),f686(x12883,x12884,x12885,x12886,x12882,x12887))
% 188.15/187.99 [1289]~E(x12891,x12892)+E(f686(x12893,x12894,x12895,x12896,x12897,x12891),f686(x12893,x12894,x12895,x12896,x12897,x12892))
% 188.15/187.99 [1290]~E(x12901,x12902)+E(f623(x12901,x12903,x12904),f623(x12902,x12903,x12904))
% 188.15/187.99 [1291]~E(x12911,x12912)+E(f623(x12913,x12911,x12914),f623(x12913,x12912,x12914))
% 188.15/187.99 [1292]~E(x12921,x12922)+E(f623(x12923,x12924,x12921),f623(x12923,x12924,x12922))
% 188.15/187.99 [1293]~E(x12931,x12932)+E(f186(x12931),f186(x12932))
% 188.15/187.99 [1294]~E(x12941,x12942)+E(f765(x12941,x12943,x12944,x12945),f765(x12942,x12943,x12944,x12945))
% 188.15/187.99 [1295]~E(x12951,x12952)+E(f765(x12953,x12951,x12954,x12955),f765(x12953,x12952,x12954,x12955))
% 188.15/187.99 [1296]~E(x12961,x12962)+E(f765(x12963,x12964,x12961,x12965),f765(x12963,x12964,x12962,x12965))
% 188.15/187.99 [1297]~E(x12971,x12972)+E(f765(x12973,x12974,x12975,x12971),f765(x12973,x12974,x12975,x12972))
% 188.15/187.99 [1298]~E(x12981,x12982)+E(f754(x12981,x12983,x12984,x12985,x12986),f754(x12982,x12983,x12984,x12985,x12986))
% 188.15/187.99 [1299]~E(x12991,x12992)+E(f754(x12993,x12991,x12994,x12995,x12996),f754(x12993,x12992,x12994,x12995,x12996))
% 188.15/187.99 [1300]~E(x13001,x13002)+E(f754(x13003,x13004,x13001,x13005,x13006),f754(x13003,x13004,x13002,x13005,x13006))
% 188.15/187.99 [1301]~E(x13011,x13012)+E(f754(x13013,x13014,x13015,x13011,x13016),f754(x13013,x13014,x13015,x13012,x13016))
% 188.15/187.99 [1302]~E(x13021,x13022)+E(f754(x13023,x13024,x13025,x13026,x13021),f754(x13023,x13024,x13025,x13026,x13022))
% 188.15/187.99 [1303]~E(x13031,x13032)+E(f381(x13031),f381(x13032))
% 188.15/187.99 [1304]~E(x13041,x13042)+E(f382(x13041),f382(x13042))
% 188.15/187.99 [1305]~E(x13051,x13052)+E(f375(x13051,x13053),f375(x13052,x13053))
% 188.15/187.99 [1306]~E(x13061,x13062)+E(f375(x13063,x13061),f375(x13063,x13062))
% 188.15/187.99 [1307]~E(x13071,x13072)+E(f493(x13071,x13073,x13074),f493(x13072,x13073,x13074))
% 188.15/187.99 [1308]~E(x13081,x13082)+E(f493(x13083,x13081,x13084),f493(x13083,x13082,x13084))
% 188.15/187.99 [1309]~E(x13091,x13092)+E(f493(x13093,x13094,x13091),f493(x13093,x13094,x13092))
% 188.15/187.99 [1310]~E(x13101,x13102)+E(f417(x13101,x13103,x13104,x13105),f417(x13102,x13103,x13104,x13105))
% 188.15/187.99 [1311]~E(x13111,x13112)+E(f417(x13113,x13111,x13114,x13115),f417(x13113,x13112,x13114,x13115))
% 188.15/187.99 [1312]~E(x13121,x13122)+E(f417(x13123,x13124,x13121,x13125),f417(x13123,x13124,x13122,x13125))
% 188.15/187.99 [1313]~E(x13131,x13132)+E(f417(x13133,x13134,x13135,x13131),f417(x13133,x13134,x13135,x13132))
% 188.15/187.99 [1314]~E(x13141,x13142)+E(f636(x13141,x13143,x13144,x13145),f636(x13142,x13143,x13144,x13145))
% 188.15/187.99 [1315]~E(x13151,x13152)+E(f636(x13153,x13151,x13154,x13155),f636(x13153,x13152,x13154,x13155))
% 188.15/187.99 [1316]~E(x13161,x13162)+E(f636(x13163,x13164,x13161,x13165),f636(x13163,x13164,x13162,x13165))
% 188.15/187.99 [1317]~E(x13171,x13172)+E(f636(x13173,x13174,x13175,x13171),f636(x13173,x13174,x13175,x13172))
% 188.15/187.99 [1318]~E(x13181,x13182)+E(f377(x13181,x13183,x13184,x13185,x13186),f377(x13182,x13183,x13184,x13185,x13186))
% 188.15/187.99 [1319]~E(x13191,x13192)+E(f377(x13193,x13191,x13194,x13195,x13196),f377(x13193,x13192,x13194,x13195,x13196))
% 188.15/187.99 [1320]~E(x13201,x13202)+E(f377(x13203,x13204,x13201,x13205,x13206),f377(x13203,x13204,x13202,x13205,x13206))
% 188.15/187.99 [1321]~E(x13211,x13212)+E(f377(x13213,x13214,x13215,x13211,x13216),f377(x13213,x13214,x13215,x13212,x13216))
% 188.15/187.99 [1322]~E(x13221,x13222)+E(f377(x13223,x13224,x13225,x13226,x13221),f377(x13223,x13224,x13225,x13226,x13222))
% 188.15/187.99 [1323]~E(x13231,x13232)+E(f620(x13231,x13233,x13234,x13235,x13236,x13237,x13238),f620(x13232,x13233,x13234,x13235,x13236,x13237,x13238))
% 188.15/187.99 [1324]~E(x13241,x13242)+E(f620(x13243,x13241,x13244,x13245,x13246,x13247,x13248),f620(x13243,x13242,x13244,x13245,x13246,x13247,x13248))
% 188.15/187.99 [1325]~E(x13251,x13252)+E(f620(x13253,x13254,x13251,x13255,x13256,x13257,x13258),f620(x13253,x13254,x13252,x13255,x13256,x13257,x13258))
% 188.15/187.99 [1326]~E(x13261,x13262)+E(f620(x13263,x13264,x13265,x13261,x13266,x13267,x13268),f620(x13263,x13264,x13265,x13262,x13266,x13267,x13268))
% 188.15/187.99 [1327]~E(x13271,x13272)+E(f620(x13273,x13274,x13275,x13276,x13271,x13277,x13278),f620(x13273,x13274,x13275,x13276,x13272,x13277,x13278))
% 188.15/187.99 [1328]~E(x13281,x13282)+E(f620(x13283,x13284,x13285,x13286,x13287,x13281,x13288),f620(x13283,x13284,x13285,x13286,x13287,x13282,x13288))
% 188.15/187.99 [1329]~E(x13291,x13292)+E(f620(x13293,x13294,x13295,x13296,x13297,x13298,x13291),f620(x13293,x13294,x13295,x13296,x13297,x13298,x13292))
% 188.15/187.99 [1330]~E(x13301,x13302)+E(f633(x13301,x13303,x13304,x13305),f633(x13302,x13303,x13304,x13305))
% 188.15/187.99 [1331]~E(x13311,x13312)+E(f633(x13313,x13311,x13314,x13315),f633(x13313,x13312,x13314,x13315))
% 188.15/187.99 [1332]~E(x13321,x13322)+E(f633(x13323,x13324,x13321,x13325),f633(x13323,x13324,x13322,x13325))
% 188.15/187.99 [1333]~E(x13331,x13332)+E(f633(x13333,x13334,x13335,x13331),f633(x13333,x13334,x13335,x13332))
% 188.15/187.99 [1334]~E(x13341,x13342)+E(f227(x13341,x13343,x13344),f227(x13342,x13343,x13344))
% 188.15/187.99 [1335]~E(x13351,x13352)+E(f227(x13353,x13351,x13354),f227(x13353,x13352,x13354))
% 188.15/187.99 [1336]~E(x13361,x13362)+E(f227(x13363,x13364,x13361),f227(x13363,x13364,x13362))
% 188.15/187.99 [1337]~E(x13371,x13372)+E(f580(x13371,x13373,x13374,x13375,x13376),f580(x13372,x13373,x13374,x13375,x13376))
% 188.15/187.99 [1338]~E(x13381,x13382)+E(f580(x13383,x13381,x13384,x13385,x13386),f580(x13383,x13382,x13384,x13385,x13386))
% 188.15/187.99 [1339]~E(x13391,x13392)+E(f580(x13393,x13394,x13391,x13395,x13396),f580(x13393,x13394,x13392,x13395,x13396))
% 188.15/187.99 [1340]~E(x13401,x13402)+E(f580(x13403,x13404,x13405,x13401,x13406),f580(x13403,x13404,x13405,x13402,x13406))
% 188.15/187.99 [1341]~E(x13411,x13412)+E(f580(x13413,x13414,x13415,x13416,x13411),f580(x13413,x13414,x13415,x13416,x13412))
% 188.15/187.99 [1342]~E(x13421,x13422)+E(f643(x13421,x13423,x13424,x13425,x13426,x13427,x13428),f643(x13422,x13423,x13424,x13425,x13426,x13427,x13428))
% 188.15/187.99 [1343]~E(x13431,x13432)+E(f643(x13433,x13431,x13434,x13435,x13436,x13437,x13438),f643(x13433,x13432,x13434,x13435,x13436,x13437,x13438))
% 188.15/187.99 [1344]~E(x13441,x13442)+E(f643(x13443,x13444,x13441,x13445,x13446,x13447,x13448),f643(x13443,x13444,x13442,x13445,x13446,x13447,x13448))
% 188.15/187.99 [1345]~E(x13451,x13452)+E(f643(x13453,x13454,x13455,x13451,x13456,x13457,x13458),f643(x13453,x13454,x13455,x13452,x13456,x13457,x13458))
% 188.15/187.99 [1346]~E(x13461,x13462)+E(f643(x13463,x13464,x13465,x13466,x13461,x13467,x13468),f643(x13463,x13464,x13465,x13466,x13462,x13467,x13468))
% 188.15/187.99 [1347]~E(x13471,x13472)+E(f643(x13473,x13474,x13475,x13476,x13477,x13471,x13478),f643(x13473,x13474,x13475,x13476,x13477,x13472,x13478))
% 188.15/187.99 [1348]~E(x13481,x13482)+E(f643(x13483,x13484,x13485,x13486,x13487,x13488,x13481),f643(x13483,x13484,x13485,x13486,x13487,x13488,x13482))
% 188.15/187.99 [1349]~E(x13491,x13492)+E(f640(x13491,x13493,x13494,x13495,x13496),f640(x13492,x13493,x13494,x13495,x13496))
% 188.15/187.99 [1350]~E(x13501,x13502)+E(f640(x13503,x13501,x13504,x13505,x13506),f640(x13503,x13502,x13504,x13505,x13506))
% 188.15/187.99 [1351]~E(x13511,x13512)+E(f640(x13513,x13514,x13511,x13515,x13516),f640(x13513,x13514,x13512,x13515,x13516))
% 188.15/187.99 [1352]~E(x13521,x13522)+E(f640(x13523,x13524,x13525,x13521,x13526),f640(x13523,x13524,x13525,x13522,x13526))
% 188.15/187.99 [1353]~E(x13531,x13532)+E(f640(x13533,x13534,x13535,x13536,x13531),f640(x13533,x13534,x13535,x13536,x13532))
% 188.15/187.99 [1354]~E(x13541,x13542)+E(f816(x13541,x13543,x13544,x13545),f816(x13542,x13543,x13544,x13545))
% 188.15/187.99 [1355]~E(x13551,x13552)+E(f816(x13553,x13551,x13554,x13555),f816(x13553,x13552,x13554,x13555))
% 188.15/187.99 [1356]~E(x13561,x13562)+E(f816(x13563,x13564,x13561,x13565),f816(x13563,x13564,x13562,x13565))
% 188.15/187.99 [1357]~E(x13571,x13572)+E(f816(x13573,x13574,x13575,x13571),f816(x13573,x13574,x13575,x13572))
% 188.15/187.99 [1358]~E(x13581,x13582)+E(f821(x13581,x13583,x13584),f821(x13582,x13583,x13584))
% 188.15/187.99 [1359]~E(x13591,x13592)+E(f821(x13593,x13591,x13594),f821(x13593,x13592,x13594))
% 188.15/187.99 [1360]~E(x13601,x13602)+E(f821(x13603,x13604,x13601),f821(x13603,x13604,x13602))
% 188.15/187.99 [1361]~E(x13611,x13612)+E(f128(x13611),f128(x13612))
% 188.15/187.99 [1362]~E(x13621,x13622)+E(f388(x13621,x13623),f388(x13622,x13623))
% 188.15/187.99 [1363]~E(x13631,x13632)+E(f388(x13633,x13631),f388(x13633,x13632))
% 188.15/187.99 [1364]~E(x13641,x13642)+E(f439(x13641,x13643,x13644,x13645),f439(x13642,x13643,x13644,x13645))
% 188.15/187.99 [1365]~E(x13651,x13652)+E(f439(x13653,x13651,x13654,x13655),f439(x13653,x13652,x13654,x13655))
% 188.15/187.99 [1366]~E(x13661,x13662)+E(f439(x13663,x13664,x13661,x13665),f439(x13663,x13664,x13662,x13665))
% 188.15/187.99 [1367]~E(x13671,x13672)+E(f439(x13673,x13674,x13675,x13671),f439(x13673,x13674,x13675,x13672))
% 188.15/187.99 [1368]~E(x13681,x13682)+E(f216(x13681,x13683),f216(x13682,x13683))
% 188.15/187.99 [1369]~E(x13691,x13692)+E(f216(x13693,x13691),f216(x13693,x13692))
% 188.15/187.99 [1370]~E(x13701,x13702)+E(f510(x13701,x13703,x13704,x13705,x13706,x13707,x13708),f510(x13702,x13703,x13704,x13705,x13706,x13707,x13708))
% 188.15/187.99 [1371]~E(x13711,x13712)+E(f510(x13713,x13711,x13714,x13715,x13716,x13717,x13718),f510(x13713,x13712,x13714,x13715,x13716,x13717,x13718))
% 188.15/187.99 [1372]~E(x13721,x13722)+E(f510(x13723,x13724,x13721,x13725,x13726,x13727,x13728),f510(x13723,x13724,x13722,x13725,x13726,x13727,x13728))
% 188.15/187.99 [1373]~E(x13731,x13732)+E(f510(x13733,x13734,x13735,x13731,x13736,x13737,x13738),f510(x13733,x13734,x13735,x13732,x13736,x13737,x13738))
% 188.15/187.99 [1374]~E(x13741,x13742)+E(f510(x13743,x13744,x13745,x13746,x13741,x13747,x13748),f510(x13743,x13744,x13745,x13746,x13742,x13747,x13748))
% 188.15/187.99 [1375]~E(x13751,x13752)+E(f510(x13753,x13754,x13755,x13756,x13757,x13751,x13758),f510(x13753,x13754,x13755,x13756,x13757,x13752,x13758))
% 188.15/187.99 [1376]~E(x13761,x13762)+E(f510(x13763,x13764,x13765,x13766,x13767,x13768,x13761),f510(x13763,x13764,x13765,x13766,x13767,x13768,x13762))
% 188.15/187.99 [1377]~E(x13771,x13772)+E(f250(x13771,x13773,x13774),f250(x13772,x13773,x13774))
% 188.15/187.99 [1378]~E(x13781,x13782)+E(f250(x13783,x13781,x13784),f250(x13783,x13782,x13784))
% 188.15/187.99 [1379]~E(x13791,x13792)+E(f250(x13793,x13794,x13791),f250(x13793,x13794,x13792))
% 188.15/187.99 [1380]~E(x13801,x13802)+E(f564(x13801,x13803,x13804),f564(x13802,x13803,x13804))
% 188.15/187.99 [1381]~E(x13811,x13812)+E(f564(x13813,x13811,x13814),f564(x13813,x13812,x13814))
% 188.15/187.99 [1382]~E(x13821,x13822)+E(f564(x13823,x13824,x13821),f564(x13823,x13824,x13822))
% 188.15/187.99 [1383]~E(x13831,x13832)+E(f629(x13831,x13833,x13834,x13835,x13836,x13837,x13838),f629(x13832,x13833,x13834,x13835,x13836,x13837,x13838))
% 188.15/187.99 [1384]~E(x13841,x13842)+E(f629(x13843,x13841,x13844,x13845,x13846,x13847,x13848),f629(x13843,x13842,x13844,x13845,x13846,x13847,x13848))
% 188.15/187.99 [1385]~E(x13851,x13852)+E(f629(x13853,x13854,x13851,x13855,x13856,x13857,x13858),f629(x13853,x13854,x13852,x13855,x13856,x13857,x13858))
% 188.15/187.99 [1386]~E(x13861,x13862)+E(f629(x13863,x13864,x13865,x13861,x13866,x13867,x13868),f629(x13863,x13864,x13865,x13862,x13866,x13867,x13868))
% 188.15/187.99 [1387]~E(x13871,x13872)+E(f629(x13873,x13874,x13875,x13876,x13871,x13877,x13878),f629(x13873,x13874,x13875,x13876,x13872,x13877,x13878))
% 188.15/187.99 [1388]~E(x13881,x13882)+E(f629(x13883,x13884,x13885,x13886,x13887,x13881,x13888),f629(x13883,x13884,x13885,x13886,x13887,x13882,x13888))
% 188.15/187.99 [1389]~E(x13891,x13892)+E(f629(x13893,x13894,x13895,x13896,x13897,x13898,x13891),f629(x13893,x13894,x13895,x13896,x13897,x13898,x13892))
% 188.15/187.99 [1390]~E(x13901,x13902)+E(f222(x13901,x13903),f222(x13902,x13903))
% 188.15/187.99 [1391]~E(x13911,x13912)+E(f222(x13913,x13911),f222(x13913,x13912))
% 188.15/187.99 [1392]~E(x13921,x13922)+E(f545(x13921,x13923),f545(x13922,x13923))
% 188.15/187.99 [1393]~E(x13931,x13932)+E(f545(x13933,x13931),f545(x13933,x13932))
% 188.15/187.99 [1394]~E(x13941,x13942)+E(f569(x13941,x13943,x13944),f569(x13942,x13943,x13944))
% 188.15/187.99 [1395]~E(x13951,x13952)+E(f569(x13953,x13951,x13954),f569(x13953,x13952,x13954))
% 188.15/187.99 [1396]~E(x13961,x13962)+E(f569(x13963,x13964,x13961),f569(x13963,x13964,x13962))
% 188.15/187.99 [1397]~E(x13971,x13972)+E(f315(x13971,x13973,x13974,x13975),f315(x13972,x13973,x13974,x13975))
% 188.15/187.99 [1398]~E(x13981,x13982)+E(f315(x13983,x13981,x13984,x13985),f315(x13983,x13982,x13984,x13985))
% 188.15/187.99 [1399]~E(x13991,x13992)+E(f315(x13993,x13994,x13991,x13995),f315(x13993,x13994,x13992,x13995))
% 188.15/187.99 [1400]~E(x14001,x14002)+E(f315(x14003,x14004,x14005,x14001),f315(x14003,x14004,x14005,x14002))
% 188.15/187.99 [1401]~E(x14011,x14012)+E(f775(x14011,x14013),f775(x14012,x14013))
% 188.15/187.99 [1402]~E(x14021,x14022)+E(f775(x14023,x14021),f775(x14023,x14022))
% 188.15/187.99 [1403]~E(x14031,x14032)+E(f484(x14031,x14033,x14034,x14035,x14036),f484(x14032,x14033,x14034,x14035,x14036))
% 188.15/187.99 [1404]~E(x14041,x14042)+E(f484(x14043,x14041,x14044,x14045,x14046),f484(x14043,x14042,x14044,x14045,x14046))
% 188.15/187.99 [1405]~E(x14051,x14052)+E(f484(x14053,x14054,x14051,x14055,x14056),f484(x14053,x14054,x14052,x14055,x14056))
% 188.15/187.99 [1406]~E(x14061,x14062)+E(f484(x14063,x14064,x14065,x14061,x14066),f484(x14063,x14064,x14065,x14062,x14066))
% 188.15/187.99 [1407]~E(x14071,x14072)+E(f484(x14073,x14074,x14075,x14076,x14071),f484(x14073,x14074,x14075,x14076,x14072))
% 188.15/187.99 [1408]~E(x14081,x14082)+E(f679(x14081,x14083,x14084,x14085,x14086,x14087,x14088,x14089),f679(x14082,x14083,x14084,x14085,x14086,x14087,x14088,x14089))
% 188.15/187.99 [1409]~E(x14091,x14092)+E(f679(x14093,x14091,x14094,x14095,x14096,x14097,x14098,x14099),f679(x14093,x14092,x14094,x14095,x14096,x14097,x14098,x14099))
% 188.15/187.99 [1410]~E(x14101,x14102)+E(f679(x14103,x14104,x14101,x14105,x14106,x14107,x14108,x14109),f679(x14103,x14104,x14102,x14105,x14106,x14107,x14108,x14109))
% 188.15/187.99 [1411]~E(x14111,x14112)+E(f679(x14113,x14114,x14115,x14111,x14116,x14117,x14118,x14119),f679(x14113,x14114,x14115,x14112,x14116,x14117,x14118,x14119))
% 188.15/187.99 [1412]~E(x14121,x14122)+E(f679(x14123,x14124,x14125,x14126,x14121,x14127,x14128,x14129),f679(x14123,x14124,x14125,x14126,x14122,x14127,x14128,x14129))
% 188.15/187.99 [1413]~E(x14131,x14132)+E(f679(x14133,x14134,x14135,x14136,x14137,x14131,x14138,x14139),f679(x14133,x14134,x14135,x14136,x14137,x14132,x14138,x14139))
% 188.15/187.99 [1414]~E(x14141,x14142)+E(f679(x14143,x14144,x14145,x14146,x14147,x14148,x14141,x14149),f679(x14143,x14144,x14145,x14146,x14147,x14148,x14142,x14149))
% 188.15/187.99 [1415]~E(x14151,x14152)+E(f679(x14153,x14154,x14155,x14156,x14157,x14158,x14159,x14151),f679(x14153,x14154,x14155,x14156,x14157,x14158,x14159,x14152))
% 188.15/187.99 [1416]~E(x14161,x14162)+E(f345(x14161,x14163),f345(x14162,x14163))
% 188.15/187.99 [1417]~E(x14171,x14172)+E(f345(x14173,x14171),f345(x14173,x14172))
% 188.15/187.99 [1418]~E(x14181,x14182)+E(f386(x14181,x14183),f386(x14182,x14183))
% 188.15/187.99 [1419]~E(x14191,x14192)+E(f386(x14193,x14191),f386(x14193,x14192))
% 188.15/187.99 [1420]~E(x14201,x14202)+E(f304(x14201,x14203),f304(x14202,x14203))
% 188.15/187.99 [1421]~E(x14211,x14212)+E(f304(x14213,x14211),f304(x14213,x14212))
% 188.15/187.99 [1422]~E(x14221,x14222)+E(f410(x14221,x14223,x14224,x14225),f410(x14222,x14223,x14224,x14225))
% 188.15/187.99 [1423]~E(x14231,x14232)+E(f410(x14233,x14231,x14234,x14235),f410(x14233,x14232,x14234,x14235))
% 188.15/187.99 [1424]~E(x14241,x14242)+E(f410(x14243,x14244,x14241,x14245),f410(x14243,x14244,x14242,x14245))
% 188.15/187.99 [1425]~E(x14251,x14252)+E(f410(x14253,x14254,x14255,x14251),f410(x14253,x14254,x14255,x14252))
% 188.15/187.99 [1426]~E(x14261,x14262)+E(f286(x14261,x14263,x14264),f286(x14262,x14263,x14264))
% 188.15/187.99 [1427]~E(x14271,x14272)+E(f286(x14273,x14271,x14274),f286(x14273,x14272,x14274))
% 188.15/187.99 [1428]~E(x14281,x14282)+E(f286(x14283,x14284,x14281),f286(x14283,x14284,x14282))
% 188.15/187.99 [1429]~E(x14291,x14292)+E(f231(x14291,x14293,x14294),f231(x14292,x14293,x14294))
% 188.15/187.99 [1430]~E(x14301,x14302)+E(f231(x14303,x14301,x14304),f231(x14303,x14302,x14304))
% 188.15/187.99 [1431]~E(x14311,x14312)+E(f231(x14313,x14314,x14311),f231(x14313,x14314,x14312))
% 188.15/187.99 [1432]~E(x14321,x14322)+E(f780(x14321,x14323,x14324,x14325,x14326,x14327),f780(x14322,x14323,x14324,x14325,x14326,x14327))
% 188.15/187.99 [1433]~E(x14331,x14332)+E(f780(x14333,x14331,x14334,x14335,x14336,x14337),f780(x14333,x14332,x14334,x14335,x14336,x14337))
% 188.15/187.99 [1434]~E(x14341,x14342)+E(f780(x14343,x14344,x14341,x14345,x14346,x14347),f780(x14343,x14344,x14342,x14345,x14346,x14347))
% 188.15/187.99 [1435]~E(x14351,x14352)+E(f780(x14353,x14354,x14355,x14351,x14356,x14357),f780(x14353,x14354,x14355,x14352,x14356,x14357))
% 188.15/187.99 [1436]~E(x14361,x14362)+E(f780(x14363,x14364,x14365,x14366,x14361,x14367),f780(x14363,x14364,x14365,x14366,x14362,x14367))
% 188.15/187.99 [1437]~E(x14371,x14372)+E(f780(x14373,x14374,x14375,x14376,x14377,x14371),f780(x14373,x14374,x14375,x14376,x14377,x14372))
% 188.15/187.99 [1438]~E(x14381,x14382)+E(f389(x14381,x14383),f389(x14382,x14383))
% 188.15/187.99 [1439]~E(x14391,x14392)+E(f389(x14393,x14391),f389(x14393,x14392))
% 188.15/187.99 [1440]~E(x14401,x14402)+E(f427(x14401),f427(x14402))
% 188.15/187.99 [1441]~E(x14411,x14412)+E(f815(x14411,x14413,x14414,x14415,x14416,x14417,x14418,x14419,x144110),f815(x14412,x14413,x14414,x14415,x14416,x14417,x14418,x14419,x144110))
% 188.15/187.99 [1442]~E(x14421,x14422)+E(f815(x14423,x14421,x14424,x14425,x14426,x14427,x14428,x14429,x144210),f815(x14423,x14422,x14424,x14425,x14426,x14427,x14428,x14429,x144210))
% 188.15/187.99 [1443]~E(x14431,x14432)+E(f815(x14433,x14434,x14431,x14435,x14436,x14437,x14438,x14439,x144310),f815(x14433,x14434,x14432,x14435,x14436,x14437,x14438,x14439,x144310))
% 188.15/187.99 [1444]~E(x14441,x14442)+E(f815(x14443,x14444,x14445,x14441,x14446,x14447,x14448,x14449,x144410),f815(x14443,x14444,x14445,x14442,x14446,x14447,x14448,x14449,x144410))
% 188.15/187.99 [1445]~E(x14451,x14452)+E(f815(x14453,x14454,x14455,x14456,x14451,x14457,x14458,x14459,x144510),f815(x14453,x14454,x14455,x14456,x14452,x14457,x14458,x14459,x144510))
% 188.15/187.99 [1446]~E(x14461,x14462)+E(f815(x14463,x14464,x14465,x14466,x14467,x14461,x14468,x14469,x144610),f815(x14463,x14464,x14465,x14466,x14467,x14462,x14468,x14469,x144610))
% 188.15/187.99 [1447]~E(x14471,x14472)+E(f815(x14473,x14474,x14475,x14476,x14477,x14478,x14471,x14479,x144710),f815(x14473,x14474,x14475,x14476,x14477,x14478,x14472,x14479,x144710))
% 188.15/187.99 [1448]~E(x14481,x14482)+E(f815(x14483,x14484,x14485,x14486,x14487,x14488,x14489,x14481,x144810),f815(x14483,x14484,x14485,x14486,x14487,x14488,x14489,x14482,x144810))
% 188.15/187.99 [1449]~E(x14491,x14492)+E(f815(x14493,x14494,x14495,x14496,x14497,x14498,x14499,x144910,x14491),f815(x14493,x14494,x14495,x14496,x14497,x14498,x14499,x144910,x14492))
% 188.15/187.99 [1450]~E(x14501,x14502)+E(f403(x14501,x14503,x14504,x14505),f403(x14502,x14503,x14504,x14505))
% 188.15/187.99 [1451]~E(x14511,x14512)+E(f403(x14513,x14511,x14514,x14515),f403(x14513,x14512,x14514,x14515))
% 188.15/187.99 [1452]~E(x14521,x14522)+E(f403(x14523,x14524,x14521,x14525),f403(x14523,x14524,x14522,x14525))
% 188.15/187.99 [1453]~E(x14531,x14532)+E(f403(x14533,x14534,x14535,x14531),f403(x14533,x14534,x14535,x14532))
% 188.15/187.99 [1454]~E(x14541,x14542)+E(f383(x14541),f383(x14542))
% 188.15/187.99 [1455]~E(x14551,x14552)+E(f253(x14551,x14553,x14554),f253(x14552,x14553,x14554))
% 188.15/187.99 [1456]~E(x14561,x14562)+E(f253(x14563,x14561,x14564),f253(x14563,x14562,x14564))
% 188.15/187.99 [1457]~E(x14571,x14572)+E(f253(x14573,x14574,x14571),f253(x14573,x14574,x14572))
% 188.15/187.99 [1458]~E(x14581,x14582)+E(f722(x14581,x14583,x14584,x14585),f722(x14582,x14583,x14584,x14585))
% 188.15/187.99 [1459]~E(x14591,x14592)+E(f722(x14593,x14591,x14594,x14595),f722(x14593,x14592,x14594,x14595))
% 188.15/187.99 [1460]~E(x14601,x14602)+E(f722(x14603,x14604,x14601,x14605),f722(x14603,x14604,x14602,x14605))
% 188.15/187.99 [1461]~E(x14611,x14612)+E(f722(x14613,x14614,x14615,x14611),f722(x14613,x14614,x14615,x14612))
% 188.15/187.99 [1462]~E(x14621,x14622)+E(f272(x14621,x14623,x14624,x14625),f272(x14622,x14623,x14624,x14625))
% 188.15/187.99 [1463]~E(x14631,x14632)+E(f272(x14633,x14631,x14634,x14635),f272(x14633,x14632,x14634,x14635))
% 188.15/187.99 [1464]~E(x14641,x14642)+E(f272(x14643,x14644,x14641,x14645),f272(x14643,x14644,x14642,x14645))
% 188.15/187.99 [1465]~E(x14651,x14652)+E(f272(x14653,x14654,x14655,x14651),f272(x14653,x14654,x14655,x14652))
% 188.15/187.99 [1466]~E(x14661,x14662)+E(f710(x14661,x14663,x14664),f710(x14662,x14663,x14664))
% 188.15/187.99 [1467]~E(x14671,x14672)+E(f710(x14673,x14671,x14674),f710(x14673,x14672,x14674))
% 188.15/187.99 [1468]~E(x14681,x14682)+E(f710(x14683,x14684,x14681),f710(x14683,x14684,x14682))
% 188.15/187.99 [1469]~E(x14691,x14692)+E(f805(x14691,x14693),f805(x14692,x14693))
% 188.15/187.99 [1470]~E(x14701,x14702)+E(f805(x14703,x14701),f805(x14703,x14702))
% 188.15/187.99 [1471]~E(x14711,x14712)+E(f499(x14711,x14713,x14714),f499(x14712,x14713,x14714))
% 188.15/187.99 [1472]~E(x14721,x14722)+E(f499(x14723,x14721,x14724),f499(x14723,x14722,x14724))
% 188.15/187.99 [1473]~E(x14731,x14732)+E(f499(x14733,x14734,x14731),f499(x14733,x14734,x14732))
% 188.15/187.99 [1474]~E(x14741,x14742)+E(f387(x14741,x14743),f387(x14742,x14743))
% 188.15/187.99 [1475]~E(x14751,x14752)+E(f387(x14753,x14751),f387(x14753,x14752))
% 188.15/187.99 [1476]~E(x14761,x14762)+E(f565(x14761,x14763,x14764),f565(x14762,x14763,x14764))
% 188.15/187.99 [1477]~E(x14771,x14772)+E(f565(x14773,x14771,x14774),f565(x14773,x14772,x14774))
% 188.15/187.99 [1478]~E(x14781,x14782)+E(f565(x14783,x14784,x14781),f565(x14783,x14784,x14782))
% 188.15/187.99 [1479]~E(x14791,x14792)+E(f450(x14791,x14793,x14794,x14795,x14796),f450(x14792,x14793,x14794,x14795,x14796))
% 188.15/187.99 [1480]~E(x14801,x14802)+E(f450(x14803,x14801,x14804,x14805,x14806),f450(x14803,x14802,x14804,x14805,x14806))
% 188.15/187.99 [1481]~E(x14811,x14812)+E(f450(x14813,x14814,x14811,x14815,x14816),f450(x14813,x14814,x14812,x14815,x14816))
% 188.15/187.99 [1482]~E(x14821,x14822)+E(f450(x14823,x14824,x14825,x14821,x14826),f450(x14823,x14824,x14825,x14822,x14826))
% 188.15/187.99 [1483]~E(x14831,x14832)+E(f450(x14833,x14834,x14835,x14836,x14831),f450(x14833,x14834,x14835,x14836,x14832))
% 188.15/187.99 [1484]~E(x14841,x14842)+E(f453(x14841,x14843,x14844,x14845,x14846),f453(x14842,x14843,x14844,x14845,x14846))
% 188.15/187.99 [1485]~E(x14851,x14852)+E(f453(x14853,x14851,x14854,x14855,x14856),f453(x14853,x14852,x14854,x14855,x14856))
% 188.15/187.99 [1486]~E(x14861,x14862)+E(f453(x14863,x14864,x14861,x14865,x14866),f453(x14863,x14864,x14862,x14865,x14866))
% 188.15/187.99 [1487]~E(x14871,x14872)+E(f453(x14873,x14874,x14875,x14871,x14876),f453(x14873,x14874,x14875,x14872,x14876))
% 188.15/187.99 [1488]~E(x14881,x14882)+E(f453(x14883,x14884,x14885,x14886,x14881),f453(x14883,x14884,x14885,x14886,x14882))
% 188.15/187.99 [1489]~E(x14891,x14892)+E(f817(x14891,x14893),f817(x14892,x14893))
% 188.15/187.99 [1490]~E(x14901,x14902)+E(f817(x14903,x14901),f817(x14903,x14902))
% 188.15/187.99 [1491]~E(x14911,x14912)+E(f840(x14911,x14913,x14914,x14915),f840(x14912,x14913,x14914,x14915))
% 188.15/187.99 [1492]~E(x14921,x14922)+E(f840(x14923,x14921,x14924,x14925),f840(x14923,x14922,x14924,x14925))
% 188.15/187.99 [1493]~E(x14931,x14932)+E(f840(x14933,x14934,x14931,x14935),f840(x14933,x14934,x14932,x14935))
% 188.15/187.99 [1494]~E(x14941,x14942)+E(f840(x14943,x14944,x14945,x14941),f840(x14943,x14944,x14945,x14942))
% 188.15/187.99 [1495]~E(x14951,x14952)+E(f289(x14951,x14953,x14954),f289(x14952,x14953,x14954))
% 188.15/187.99 [1496]~E(x14961,x14962)+E(f289(x14963,x14961,x14964),f289(x14963,x14962,x14964))
% 188.15/187.99 [1497]~E(x14971,x14972)+E(f289(x14973,x14974,x14971),f289(x14973,x14974,x14972))
% 188.15/187.99 [1498]~E(x14981,x14982)+E(f622(x14981,x14983,x14984),f622(x14982,x14983,x14984))
% 188.15/187.99 [1499]~E(x14991,x14992)+E(f622(x14993,x14991,x14994),f622(x14993,x14992,x14994))
% 188.15/187.99 [1500]~E(x15001,x15002)+E(f622(x15003,x15004,x15001),f622(x15003,x15004,x15002))
% 188.15/187.99 [1501]~E(x15011,x15012)+E(f356(x15011,x15013,x15014,x15015,x15016,x15017,x15018),f356(x15012,x15013,x15014,x15015,x15016,x15017,x15018))
% 188.15/187.99 [1502]~E(x15021,x15022)+E(f356(x15023,x15021,x15024,x15025,x15026,x15027,x15028),f356(x15023,x15022,x15024,x15025,x15026,x15027,x15028))
% 188.15/187.99 [1503]~E(x15031,x15032)+E(f356(x15033,x15034,x15031,x15035,x15036,x15037,x15038),f356(x15033,x15034,x15032,x15035,x15036,x15037,x15038))
% 188.15/187.99 [1504]~E(x15041,x15042)+E(f356(x15043,x15044,x15045,x15041,x15046,x15047,x15048),f356(x15043,x15044,x15045,x15042,x15046,x15047,x15048))
% 188.15/187.99 [1505]~E(x15051,x15052)+E(f356(x15053,x15054,x15055,x15056,x15051,x15057,x15058),f356(x15053,x15054,x15055,x15056,x15052,x15057,x15058))
% 188.15/187.99 [1506]~E(x15061,x15062)+E(f356(x15063,x15064,x15065,x15066,x15067,x15061,x15068),f356(x15063,x15064,x15065,x15066,x15067,x15062,x15068))
% 188.15/187.99 [1507]~E(x15071,x15072)+E(f356(x15073,x15074,x15075,x15076,x15077,x15078,x15071),f356(x15073,x15074,x15075,x15076,x15077,x15078,x15072))
% 188.15/187.99 [1508]~E(x15081,x15082)+E(f340(x15081,x15083,x15084),f340(x15082,x15083,x15084))
% 188.15/187.99 [1509]~E(x15091,x15092)+E(f340(x15093,x15091,x15094),f340(x15093,x15092,x15094))
% 188.15/187.99 [1510]~E(x15101,x15102)+E(f340(x15103,x15104,x15101),f340(x15103,x15104,x15102))
% 188.15/187.99 [1511]~E(x15111,x15112)+E(f807(x15111),f807(x15112))
% 188.15/187.99 [1512]~E(x15121,x15122)+E(f86(x15121),f86(x15122))
% 188.15/187.99 [1513]~E(x15131,x15132)+E(f740(x15131,x15133),f740(x15132,x15133))
% 188.15/187.99 [1514]~E(x15141,x15142)+E(f740(x15143,x15141),f740(x15143,x15142))
% 188.15/187.99 [1515]~E(x15151,x15152)+E(f717(x15151,x15153,x15154,x15155,x15156,x15157,x15158),f717(x15152,x15153,x15154,x15155,x15156,x15157,x15158))
% 188.15/187.99 [1516]~E(x15161,x15162)+E(f717(x15163,x15161,x15164,x15165,x15166,x15167,x15168),f717(x15163,x15162,x15164,x15165,x15166,x15167,x15168))
% 188.15/187.99 [1517]~E(x15171,x15172)+E(f717(x15173,x15174,x15171,x15175,x15176,x15177,x15178),f717(x15173,x15174,x15172,x15175,x15176,x15177,x15178))
% 188.15/187.99 [1518]~E(x15181,x15182)+E(f717(x15183,x15184,x15185,x15181,x15186,x15187,x15188),f717(x15183,x15184,x15185,x15182,x15186,x15187,x15188))
% 188.15/187.99 [1519]~E(x15191,x15192)+E(f717(x15193,x15194,x15195,x15196,x15191,x15197,x15198),f717(x15193,x15194,x15195,x15196,x15192,x15197,x15198))
% 188.15/187.99 [1520]~E(x15201,x15202)+E(f717(x15203,x15204,x15205,x15206,x15207,x15201,x15208),f717(x15203,x15204,x15205,x15206,x15207,x15202,x15208))
% 188.15/187.99 [1521]~E(x15211,x15212)+E(f717(x15213,x15214,x15215,x15216,x15217,x15218,x15211),f717(x15213,x15214,x15215,x15216,x15217,x15218,x15212))
% 188.15/187.99 [1522]~E(x15221,x15222)+E(f343(x15221,x15223),f343(x15222,x15223))
% 188.15/187.99 [1523]~E(x15231,x15232)+E(f343(x15233,x15231),f343(x15233,x15232))
% 188.15/187.99 [1524]~E(x15241,x15242)+E(f598(x15241,x15243,x15244),f598(x15242,x15243,x15244))
% 188.15/187.99 [1525]~E(x15251,x15252)+E(f598(x15253,x15251,x15254),f598(x15253,x15252,x15254))
% 188.15/187.99 [1526]~E(x15261,x15262)+E(f598(x15263,x15264,x15261),f598(x15263,x15264,x15262))
% 188.15/187.99 [1527]~E(x15271,x15272)+E(f845(x15271,x15273),f845(x15272,x15273))
% 188.15/187.99 [1528]~E(x15281,x15282)+E(f845(x15283,x15281),f845(x15283,x15282))
% 188.15/187.99 [1529]~E(x15291,x15292)+E(f275(x15291,x15293,x15294,x15295),f275(x15292,x15293,x15294,x15295))
% 188.15/187.99 [1530]~E(x15301,x15302)+E(f275(x15303,x15301,x15304,x15305),f275(x15303,x15302,x15304,x15305))
% 188.15/187.99 [1531]~E(x15311,x15312)+E(f275(x15313,x15314,x15311,x15315),f275(x15313,x15314,x15312,x15315))
% 188.15/187.99 [1532]~E(x15321,x15322)+E(f275(x15323,x15324,x15325,x15321),f275(x15323,x15324,x15325,x15322))
% 188.15/187.99 [1533]~E(x15331,x15332)+E(f334(x15331,x15333,x15334),f334(x15332,x15333,x15334))
% 188.15/187.99 [1534]~E(x15341,x15342)+E(f334(x15343,x15341,x15344),f334(x15343,x15342,x15344))
% 188.15/187.99 [1535]~E(x15351,x15352)+E(f334(x15353,x15354,x15351),f334(x15353,x15354,x15352))
% 188.15/187.99 [1536]~E(x15361,x15362)+E(f712(x15361,x15363,x15364,x15365,x15366),f712(x15362,x15363,x15364,x15365,x15366))
% 188.15/187.99 [1537]~E(x15371,x15372)+E(f712(x15373,x15371,x15374,x15375,x15376),f712(x15373,x15372,x15374,x15375,x15376))
% 188.15/187.99 [1538]~E(x15381,x15382)+E(f712(x15383,x15384,x15381,x15385,x15386),f712(x15383,x15384,x15382,x15385,x15386))
% 188.15/187.99 [1539]~E(x15391,x15392)+E(f712(x15393,x15394,x15395,x15391,x15396),f712(x15393,x15394,x15395,x15392,x15396))
% 188.15/187.99 [1540]~E(x15401,x15402)+E(f712(x15403,x15404,x15405,x15406,x15401),f712(x15403,x15404,x15405,x15406,x15402))
% 188.15/187.99 [1541]~E(x15411,x15412)+E(f853(x15411,x15413),f853(x15412,x15413))
% 188.15/187.99 [1542]~E(x15421,x15422)+E(f853(x15423,x15421),f853(x15423,x15422))
% 188.15/187.99 [1543]~E(x15431,x15432)+E(f124(x15431),f124(x15432))
% 188.15/187.99 [1544]~E(x15441,x15442)+E(f561(x15441,x15443,x15444,x15445),f561(x15442,x15443,x15444,x15445))
% 188.15/187.99 [1545]~E(x15451,x15452)+E(f561(x15453,x15451,x15454,x15455),f561(x15453,x15452,x15454,x15455))
% 188.15/187.99 [1546]~E(x15461,x15462)+E(f561(x15463,x15464,x15461,x15465),f561(x15463,x15464,x15462,x15465))
% 188.15/187.99 [1547]~E(x15471,x15472)+E(f561(x15473,x15474,x15475,x15471),f561(x15473,x15474,x15475,x15472))
% 188.15/187.99 [1548]~E(x15481,x15482)+E(f496(x15481,x15483,x15484,x15485),f496(x15482,x15483,x15484,x15485))
% 188.15/187.99 [1549]~E(x15491,x15492)+E(f496(x15493,x15491,x15494,x15495),f496(x15493,x15492,x15494,x15495))
% 188.15/187.99 [1550]~E(x15501,x15502)+E(f496(x15503,x15504,x15501,x15505),f496(x15503,x15504,x15502,x15505))
% 188.15/187.99 [1551]~E(x15511,x15512)+E(f496(x15513,x15514,x15515,x15511),f496(x15513,x15514,x15515,x15512))
% 188.15/187.99 [1552]~E(x15521,x15522)+E(f404(x15521,x15523,x15524,x15525),f404(x15522,x15523,x15524,x15525))
% 188.15/187.99 [1553]~E(x15531,x15532)+E(f404(x15533,x15531,x15534,x15535),f404(x15533,x15532,x15534,x15535))
% 188.15/187.99 [1554]~E(x15541,x15542)+E(f404(x15543,x15544,x15541,x15545),f404(x15543,x15544,x15542,x15545))
% 188.15/187.99 [1555]~E(x15551,x15552)+E(f404(x15553,x15554,x15555,x15551),f404(x15553,x15554,x15555,x15552))
% 188.15/187.99 [1556]~E(x15561,x15562)+E(f656(x15561,x15563,x15564,x15565,x15566),f656(x15562,x15563,x15564,x15565,x15566))
% 188.15/187.99 [1557]~E(x15571,x15572)+E(f656(x15573,x15571,x15574,x15575,x15576),f656(x15573,x15572,x15574,x15575,x15576))
% 188.15/187.99 [1558]~E(x15581,x15582)+E(f656(x15583,x15584,x15581,x15585,x15586),f656(x15583,x15584,x15582,x15585,x15586))
% 188.15/187.99 [1559]~E(x15591,x15592)+E(f656(x15593,x15594,x15595,x15591,x15596),f656(x15593,x15594,x15595,x15592,x15596))
% 188.15/187.99 [1560]~E(x15601,x15602)+E(f656(x15603,x15604,x15605,x15606,x15601),f656(x15603,x15604,x15605,x15606,x15602))
% 188.15/187.99 [1561]~E(x15611,x15612)+E(f779(x15611,x15613,x15614,x15615),f779(x15612,x15613,x15614,x15615))
% 188.15/187.99 [1562]~E(x15621,x15622)+E(f779(x15623,x15621,x15624,x15625),f779(x15623,x15622,x15624,x15625))
% 188.15/187.99 [1563]~E(x15631,x15632)+E(f779(x15633,x15634,x15631,x15635),f779(x15633,x15634,x15632,x15635))
% 188.15/187.99 [1564]~E(x15641,x15642)+E(f779(x15643,x15644,x15645,x15641),f779(x15643,x15644,x15645,x15642))
% 188.15/187.99 [1565]~E(x15651,x15652)+E(f746(x15651,x15653,x15654,x15655,x15656),f746(x15652,x15653,x15654,x15655,x15656))
% 188.15/187.99 [1566]~E(x15661,x15662)+E(f746(x15663,x15661,x15664,x15665,x15666),f746(x15663,x15662,x15664,x15665,x15666))
% 188.15/187.99 [1567]~E(x15671,x15672)+E(f746(x15673,x15674,x15671,x15675,x15676),f746(x15673,x15674,x15672,x15675,x15676))
% 188.15/187.99 [1568]~E(x15681,x15682)+E(f746(x15683,x15684,x15685,x15681,x15686),f746(x15683,x15684,x15685,x15682,x15686))
% 188.15/187.99 [1569]~E(x15691,x15692)+E(f746(x15693,x15694,x15695,x15696,x15691),f746(x15693,x15694,x15695,x15696,x15692))
% 188.15/187.99 [1570]~E(x15701,x15702)+E(f738(x15701,x15703),f738(x15702,x15703))
% 188.15/187.99 [1571]~E(x15711,x15712)+E(f738(x15713,x15711),f738(x15713,x15712))
% 188.15/187.99 [1572]~E(x15721,x15722)+E(f156(x15721,x15723,x15724,x15725),f156(x15722,x15723,x15724,x15725))
% 188.15/187.99 [1573]~E(x15731,x15732)+E(f156(x15733,x15731,x15734,x15735),f156(x15733,x15732,x15734,x15735))
% 188.15/187.99 [1574]~E(x15741,x15742)+E(f156(x15743,x15744,x15741,x15745),f156(x15743,x15744,x15742,x15745))
% 188.15/187.99 [1575]~E(x15751,x15752)+E(f156(x15753,x15754,x15755,x15751),f156(x15753,x15754,x15755,x15752))
% 188.15/187.99 [1576]~E(x15761,x15762)+E(f390(x15761,x15763,x15764,x15765),f390(x15762,x15763,x15764,x15765))
% 188.15/187.99 [1577]~E(x15771,x15772)+E(f390(x15773,x15771,x15774,x15775),f390(x15773,x15772,x15774,x15775))
% 188.15/187.99 [1578]~E(x15781,x15782)+E(f390(x15783,x15784,x15781,x15785),f390(x15783,x15784,x15782,x15785))
% 188.15/187.99 [1579]~E(x15791,x15792)+E(f390(x15793,x15794,x15795,x15791),f390(x15793,x15794,x15795,x15792))
% 188.15/187.99 [1580]~E(x15801,x15802)+E(f824(x15801,x15803),f824(x15802,x15803))
% 188.15/187.99 [1581]~E(x15811,x15812)+E(f824(x15813,x15811),f824(x15813,x15812))
% 188.15/187.99 [1582]~E(x15821,x15822)+E(f290(x15821,x15823,x15824,x15825),f290(x15822,x15823,x15824,x15825))
% 188.15/187.99 [1583]~E(x15831,x15832)+E(f290(x15833,x15831,x15834,x15835),f290(x15833,x15832,x15834,x15835))
% 188.15/187.99 [1584]~E(x15841,x15842)+E(f290(x15843,x15844,x15841,x15845),f290(x15843,x15844,x15842,x15845))
% 188.15/187.99 [1585]~E(x15851,x15852)+E(f290(x15853,x15854,x15855,x15851),f290(x15853,x15854,x15855,x15852))
% 188.15/187.99 [1586]~E(x15861,x15862)+E(f851(x15861,x15863,x15864,x15865,x15866,x15867),f851(x15862,x15863,x15864,x15865,x15866,x15867))
% 188.15/187.99 [1587]~E(x15871,x15872)+E(f851(x15873,x15871,x15874,x15875,x15876,x15877),f851(x15873,x15872,x15874,x15875,x15876,x15877))
% 188.15/187.99 [1588]~E(x15881,x15882)+E(f851(x15883,x15884,x15881,x15885,x15886,x15887),f851(x15883,x15884,x15882,x15885,x15886,x15887))
% 188.15/187.99 [1589]~E(x15891,x15892)+E(f851(x15893,x15894,x15895,x15891,x15896,x15897),f851(x15893,x15894,x15895,x15892,x15896,x15897))
% 188.15/187.99 [1590]~E(x15901,x15902)+E(f851(x15903,x15904,x15905,x15906,x15901,x15907),f851(x15903,x15904,x15905,x15906,x15902,x15907))
% 188.15/187.99 [1591]~E(x15911,x15912)+E(f851(x15913,x15914,x15915,x15916,x15917,x15911),f851(x15913,x15914,x15915,x15916,x15917,x15912))
% 188.15/187.99 [1592]~E(x15921,x15922)+E(f203(x15921),f203(x15922))
% 188.15/187.99 [1593]~E(x15931,x15932)+E(f528(x15931,x15933,x15934,x15935),f528(x15932,x15933,x15934,x15935))
% 188.15/187.99 [1594]~E(x15941,x15942)+E(f528(x15943,x15941,x15944,x15945),f528(x15943,x15942,x15944,x15945))
% 188.15/187.99 [1595]~E(x15951,x15952)+E(f528(x15953,x15954,x15951,x15955),f528(x15953,x15954,x15952,x15955))
% 188.15/187.99 [1596]~E(x15961,x15962)+E(f528(x15963,x15964,x15965,x15961),f528(x15963,x15964,x15965,x15962))
% 188.15/187.99 [1597]~E(x15971,x15972)+E(f117(x15971,x15973,x15974),f117(x15972,x15973,x15974))
% 188.15/187.99 [1598]~E(x15981,x15982)+E(f117(x15983,x15981,x15984),f117(x15983,x15982,x15984))
% 188.15/187.99 [1599]~E(x15991,x15992)+E(f117(x15993,x15994,x15991),f117(x15993,x15994,x15992))
% 188.15/187.99 [1600]~E(x16001,x16002)+E(f747(x16001,x16003,x16004,x16005,x16006),f747(x16002,x16003,x16004,x16005,x16006))
% 188.15/187.99 [1601]~E(x16011,x16012)+E(f747(x16013,x16011,x16014,x16015,x16016),f747(x16013,x16012,x16014,x16015,x16016))
% 188.15/187.99 [1602]~E(x16021,x16022)+E(f747(x16023,x16024,x16021,x16025,x16026),f747(x16023,x16024,x16022,x16025,x16026))
% 188.15/187.99 [1603]~E(x16031,x16032)+E(f747(x16033,x16034,x16035,x16031,x16036),f747(x16033,x16034,x16035,x16032,x16036))
% 188.15/187.99 [1604]~E(x16041,x16042)+E(f747(x16043,x16044,x16045,x16046,x16041),f747(x16043,x16044,x16045,x16046,x16042))
% 188.15/187.99 [1605]~E(x16051,x16052)+E(f777(x16051,x16053,x16054,x16055,x16056,x16057),f777(x16052,x16053,x16054,x16055,x16056,x16057))
% 188.15/187.99 [1606]~E(x16061,x16062)+E(f777(x16063,x16061,x16064,x16065,x16066,x16067),f777(x16063,x16062,x16064,x16065,x16066,x16067))
% 188.15/187.99 [1607]~E(x16071,x16072)+E(f777(x16073,x16074,x16071,x16075,x16076,x16077),f777(x16073,x16074,x16072,x16075,x16076,x16077))
% 188.15/187.99 [1608]~E(x16081,x16082)+E(f777(x16083,x16084,x16085,x16081,x16086,x16087),f777(x16083,x16084,x16085,x16082,x16086,x16087))
% 188.15/187.99 [1609]~E(x16091,x16092)+E(f777(x16093,x16094,x16095,x16096,x16091,x16097),f777(x16093,x16094,x16095,x16096,x16092,x16097))
% 188.15/187.99 [1610]~E(x16101,x16102)+E(f777(x16103,x16104,x16105,x16106,x16107,x16101),f777(x16103,x16104,x16105,x16106,x16107,x16102))
% 188.15/187.99 [1611]~E(x16111,x16112)+E(f608(x16111,x16113),f608(x16112,x16113))
% 188.15/187.99 [1612]~E(x16121,x16122)+E(f608(x16123,x16121),f608(x16123,x16122))
% 188.15/187.99 [1613]~E(x16131,x16132)+E(f456(x16131,x16133),f456(x16132,x16133))
% 188.15/187.99 [1614]~E(x16141,x16142)+E(f456(x16143,x16141),f456(x16143,x16142))
% 188.15/187.99 [1615]~E(x16151,x16152)+E(f444(x16151,x16153,x16154,x16155),f444(x16152,x16153,x16154,x16155))
% 188.15/187.99 [1616]~E(x16161,x16162)+E(f444(x16163,x16161,x16164,x16165),f444(x16163,x16162,x16164,x16165))
% 188.15/187.99 [1617]~E(x16171,x16172)+E(f444(x16173,x16174,x16171,x16175),f444(x16173,x16174,x16172,x16175))
% 188.15/187.99 [1618]~E(x16181,x16182)+E(f444(x16183,x16184,x16185,x16181),f444(x16183,x16184,x16185,x16182))
% 188.15/187.99 [1619]~E(x16191,x16192)+E(f428(x16191,x16193,x16194),f428(x16192,x16193,x16194))
% 188.15/187.99 [1620]~E(x16201,x16202)+E(f428(x16203,x16201,x16204),f428(x16203,x16202,x16204))
% 188.15/187.99 [1621]~E(x16211,x16212)+E(f428(x16213,x16214,x16211),f428(x16213,x16214,x16212))
% 188.15/187.99 [1622]~E(x16221,x16222)+E(f858(x16221,x16223,x16224,x16225,x16226,x16227),f858(x16222,x16223,x16224,x16225,x16226,x16227))
% 188.15/187.99 [1623]~E(x16231,x16232)+E(f858(x16233,x16231,x16234,x16235,x16236,x16237),f858(x16233,x16232,x16234,x16235,x16236,x16237))
% 188.15/187.99 [1624]~E(x16241,x16242)+E(f858(x16243,x16244,x16241,x16245,x16246,x16247),f858(x16243,x16244,x16242,x16245,x16246,x16247))
% 188.15/187.99 [1625]~E(x16251,x16252)+E(f858(x16253,x16254,x16255,x16251,x16256,x16257),f858(x16253,x16254,x16255,x16252,x16256,x16257))
% 188.15/187.99 [1626]~E(x16261,x16262)+E(f858(x16263,x16264,x16265,x16266,x16261,x16267),f858(x16263,x16264,x16265,x16266,x16262,x16267))
% 188.15/187.99 [1627]~E(x16271,x16272)+E(f858(x16273,x16274,x16275,x16276,x16277,x16271),f858(x16273,x16274,x16275,x16276,x16277,x16272))
% 188.15/187.99 [1628]~E(x16281,x16282)+E(f846(x16281,x16283),f846(x16282,x16283))
% 188.15/187.99 [1629]~E(x16291,x16292)+E(f846(x16293,x16291),f846(x16293,x16292))
% 188.15/187.99 [1630]~E(x16301,x16302)+E(f357(x16301,x16303,x16304,x16305),f357(x16302,x16303,x16304,x16305))
% 188.15/187.99 [1631]~E(x16311,x16312)+E(f357(x16313,x16311,x16314,x16315),f357(x16313,x16312,x16314,x16315))
% 188.15/187.99 [1632]~E(x16321,x16322)+E(f357(x16323,x16324,x16321,x16325),f357(x16323,x16324,x16322,x16325))
% 188.15/187.99 [1633]~E(x16331,x16332)+E(f357(x16333,x16334,x16335,x16331),f357(x16333,x16334,x16335,x16332))
% 188.15/187.99 [1634]~E(x16341,x16342)+E(f567(x16341,x16343,x16344,x16345,x16346),f567(x16342,x16343,x16344,x16345,x16346))
% 188.15/187.99 [1635]~E(x16351,x16352)+E(f567(x16353,x16351,x16354,x16355,x16356),f567(x16353,x16352,x16354,x16355,x16356))
% 188.15/187.99 [1636]~E(x16361,x16362)+E(f567(x16363,x16364,x16361,x16365,x16366),f567(x16363,x16364,x16362,x16365,x16366))
% 188.15/187.99 [1637]~E(x16371,x16372)+E(f567(x16373,x16374,x16375,x16371,x16376),f567(x16373,x16374,x16375,x16372,x16376))
% 188.15/187.99 [1638]~E(x16381,x16382)+E(f567(x16383,x16384,x16385,x16386,x16381),f567(x16383,x16384,x16385,x16386,x16382))
% 188.15/187.99 [1639]~E(x16391,x16392)+E(f615(x16391,x16393,x16394,x16395),f615(x16392,x16393,x16394,x16395))
% 188.15/187.99 [1640]~E(x16401,x16402)+E(f615(x16403,x16401,x16404,x16405),f615(x16403,x16402,x16404,x16405))
% 188.15/187.99 [1641]~E(x16411,x16412)+E(f615(x16413,x16414,x16411,x16415),f615(x16413,x16414,x16412,x16415))
% 188.15/187.99 [1642]~E(x16421,x16422)+E(f615(x16423,x16424,x16425,x16421),f615(x16423,x16424,x16425,x16422))
% 188.15/187.99 [1643]~E(x16431,x16432)+E(f595(x16431,x16433,x16434,x16435,x16436),f595(x16432,x16433,x16434,x16435,x16436))
% 188.15/187.99 [1644]~E(x16441,x16442)+E(f595(x16443,x16441,x16444,x16445,x16446),f595(x16443,x16442,x16444,x16445,x16446))
% 188.15/187.99 [1645]~E(x16451,x16452)+E(f595(x16453,x16454,x16451,x16455,x16456),f595(x16453,x16454,x16452,x16455,x16456))
% 188.15/187.99 [1646]~E(x16461,x16462)+E(f595(x16463,x16464,x16465,x16461,x16466),f595(x16463,x16464,x16465,x16462,x16466))
% 188.15/187.99 [1647]~E(x16471,x16472)+E(f595(x16473,x16474,x16475,x16476,x16471),f595(x16473,x16474,x16475,x16476,x16472))
% 188.15/187.99 [1648]~E(x16481,x16482)+E(f566(x16481,x16483,x16484),f566(x16482,x16483,x16484))
% 188.15/187.99 [1649]~E(x16491,x16492)+E(f566(x16493,x16491,x16494),f566(x16493,x16492,x16494))
% 188.15/187.99 [1650]~E(x16501,x16502)+E(f566(x16503,x16504,x16501),f566(x16503,x16504,x16502))
% 188.15/187.99 [1651]~E(x16511,x16512)+E(f790(x16511,x16513,x16514,x16515),f790(x16512,x16513,x16514,x16515))
% 188.15/187.99 [1652]~E(x16521,x16522)+E(f790(x16523,x16521,x16524,x16525),f790(x16523,x16522,x16524,x16525))
% 188.15/187.99 [1653]~E(x16531,x16532)+E(f790(x16533,x16534,x16531,x16535),f790(x16533,x16534,x16532,x16535))
% 188.15/187.99 [1654]~E(x16541,x16542)+E(f790(x16543,x16544,x16545,x16541),f790(x16543,x16544,x16545,x16542))
% 188.15/187.99 [1655]~E(x16551,x16552)+E(f582(x16551,x16553),f582(x16552,x16553))
% 188.15/187.99 [1656]~E(x16561,x16562)+E(f582(x16563,x16561),f582(x16563,x16562))
% 188.15/187.99 [1657]~E(x16571,x16572)+E(f449(x16571,x16573,x16574,x16575,x16576),f449(x16572,x16573,x16574,x16575,x16576))
% 188.15/187.99 [1658]~E(x16581,x16582)+E(f449(x16583,x16581,x16584,x16585,x16586),f449(x16583,x16582,x16584,x16585,x16586))
% 188.15/187.99 [1659]~E(x16591,x16592)+E(f449(x16593,x16594,x16591,x16595,x16596),f449(x16593,x16594,x16592,x16595,x16596))
% 188.15/187.99 [1660]~E(x16601,x16602)+E(f449(x16603,x16604,x16605,x16601,x16606),f449(x16603,x16604,x16605,x16602,x16606))
% 188.15/187.99 [1661]~E(x16611,x16612)+E(f449(x16613,x16614,x16615,x16616,x16611),f449(x16613,x16614,x16615,x16616,x16612))
% 188.15/187.99 [1662]~E(x16621,x16622)+E(f480(x16621,x16623,x16624,x16625,x16626),f480(x16622,x16623,x16624,x16625,x16626))
% 188.15/187.99 [1663]~E(x16631,x16632)+E(f480(x16633,x16631,x16634,x16635,x16636),f480(x16633,x16632,x16634,x16635,x16636))
% 188.15/187.99 [1664]~E(x16641,x16642)+E(f480(x16643,x16644,x16641,x16645,x16646),f480(x16643,x16644,x16642,x16645,x16646))
% 188.15/187.99 [1665]~E(x16651,x16652)+E(f480(x16653,x16654,x16655,x16651,x16656),f480(x16653,x16654,x16655,x16652,x16656))
% 188.15/187.99 [1666]~E(x16661,x16662)+E(f480(x16663,x16664,x16665,x16666,x16661),f480(x16663,x16664,x16665,x16666,x16662))
% 188.15/187.99 [1667]~E(x16671,x16672)+E(f848(x16671,x16673,x16674,x16675,x16676),f848(x16672,x16673,x16674,x16675,x16676))
% 188.15/187.99 [1668]~E(x16681,x16682)+E(f848(x16683,x16681,x16684,x16685,x16686),f848(x16683,x16682,x16684,x16685,x16686))
% 188.15/187.99 [1669]~E(x16691,x16692)+E(f848(x16693,x16694,x16691,x16695,x16696),f848(x16693,x16694,x16692,x16695,x16696))
% 188.15/187.99 [1670]~E(x16701,x16702)+E(f848(x16703,x16704,x16705,x16701,x16706),f848(x16703,x16704,x16705,x16702,x16706))
% 188.15/187.99 [1671]~E(x16711,x16712)+E(f848(x16713,x16714,x16715,x16716,x16711),f848(x16713,x16714,x16715,x16716,x16712))
% 188.15/187.99 [1672]~E(x16721,x16722)+E(f714(x16721,x16723,x16724,x16725,x16726),f714(x16722,x16723,x16724,x16725,x16726))
% 188.15/187.99 [1673]~E(x16731,x16732)+E(f714(x16733,x16731,x16734,x16735,x16736),f714(x16733,x16732,x16734,x16735,x16736))
% 188.15/187.99 [1674]~E(x16741,x16742)+E(f714(x16743,x16744,x16741,x16745,x16746),f714(x16743,x16744,x16742,x16745,x16746))
% 188.15/187.99 [1675]~E(x16751,x16752)+E(f714(x16753,x16754,x16755,x16751,x16756),f714(x16753,x16754,x16755,x16752,x16756))
% 188.15/187.99 [1676]~E(x16761,x16762)+E(f714(x16763,x16764,x16765,x16766,x16761),f714(x16763,x16764,x16765,x16766,x16762))
% 188.15/187.99 [1677]~E(x16771,x16772)+E(f833(x16771,x16773),f833(x16772,x16773))
% 188.15/187.99 [1678]~E(x16781,x16782)+E(f833(x16783,x16781),f833(x16783,x16782))
% 188.15/187.99 [1679]~E(x16791,x16792)+E(f751(x16791,x16793,x16794,x16795,x16796),f751(x16792,x16793,x16794,x16795,x16796))
% 188.15/187.99 [1680]~E(x16801,x16802)+E(f751(x16803,x16801,x16804,x16805,x16806),f751(x16803,x16802,x16804,x16805,x16806))
% 188.15/187.99 [1681]~E(x16811,x16812)+E(f751(x16813,x16814,x16811,x16815,x16816),f751(x16813,x16814,x16812,x16815,x16816))
% 188.15/187.99 [1682]~E(x16821,x16822)+E(f751(x16823,x16824,x16825,x16821,x16826),f751(x16823,x16824,x16825,x16822,x16826))
% 188.15/187.99 [1683]~E(x16831,x16832)+E(f751(x16833,x16834,x16835,x16836,x16831),f751(x16833,x16834,x16835,x16836,x16832))
% 188.15/187.99 [1684]~E(x16841,x16842)+E(f688(x16841,x16843),f688(x16842,x16843))
% 188.15/187.99 [1685]~E(x16851,x16852)+E(f688(x16853,x16851),f688(x16853,x16852))
% 188.15/187.99 [1686]~E(x16861,x16862)+E(f498(x16861,x16863,x16864),f498(x16862,x16863,x16864))
% 188.15/187.99 [1687]~E(x16871,x16872)+E(f498(x16873,x16871,x16874),f498(x16873,x16872,x16874))
% 188.15/187.99 [1688]~E(x16881,x16882)+E(f498(x16883,x16884,x16881),f498(x16883,x16884,x16882))
% 188.15/187.99 [1689]~E(x16891,x16892)+E(f669(x16891,x16893,x16894,x16895),f669(x16892,x16893,x16894,x16895))
% 188.15/187.99 [1690]~E(x16901,x16902)+E(f669(x16903,x16901,x16904,x16905),f669(x16903,x16902,x16904,x16905))
% 188.15/187.99 [1691]~E(x16911,x16912)+E(f669(x16913,x16914,x16911,x16915),f669(x16913,x16914,x16912,x16915))
% 188.15/187.99 [1692]~E(x16921,x16922)+E(f669(x16923,x16924,x16925,x16921),f669(x16923,x16924,x16925,x16922))
% 188.15/187.99 [1693]~E(x16931,x16932)+E(f466(x16931,x16933,x16934,x16935),f466(x16932,x16933,x16934,x16935))
% 188.15/187.99 [1694]~E(x16941,x16942)+E(f466(x16943,x16941,x16944,x16945),f466(x16943,x16942,x16944,x16945))
% 188.15/187.99 [1695]~E(x16951,x16952)+E(f466(x16953,x16954,x16951,x16955),f466(x16953,x16954,x16952,x16955))
% 188.15/187.99 [1696]~E(x16961,x16962)+E(f466(x16963,x16964,x16965,x16961),f466(x16963,x16964,x16965,x16962))
% 188.15/187.99 [1697]~E(x16971,x16972)+E(f434(x16971,x16973,x16974,x16975,x16976),f434(x16972,x16973,x16974,x16975,x16976))
% 188.15/187.99 [1698]~E(x16981,x16982)+E(f434(x16983,x16981,x16984,x16985,x16986),f434(x16983,x16982,x16984,x16985,x16986))
% 188.15/187.99 [1699]~E(x16991,x16992)+E(f434(x16993,x16994,x16991,x16995,x16996),f434(x16993,x16994,x16992,x16995,x16996))
% 188.15/187.99 [1700]~E(x17001,x17002)+E(f434(x17003,x17004,x17005,x17001,x17006),f434(x17003,x17004,x17005,x17002,x17006))
% 188.15/187.99 [1701]~E(x17011,x17012)+E(f434(x17013,x17014,x17015,x17016,x17011),f434(x17013,x17014,x17015,x17016,x17012))
% 188.15/187.99 [1702]~E(x17021,x17022)+E(f832(x17021,x17023,x17024),f832(x17022,x17023,x17024))
% 188.15/187.99 [1703]~E(x17031,x17032)+E(f832(x17033,x17031,x17034),f832(x17033,x17032,x17034))
% 188.15/187.99 [1704]~E(x17041,x17042)+E(f832(x17043,x17044,x17041),f832(x17043,x17044,x17042))
% 188.15/187.99 [1705]~E(x17051,x17052)+E(f609(x17051,x17053,x17054,x17055,x17056,x17057,x17058,x17059),f609(x17052,x17053,x17054,x17055,x17056,x17057,x17058,x17059))
% 188.15/187.99 [1706]~E(x17061,x17062)+E(f609(x17063,x17061,x17064,x17065,x17066,x17067,x17068,x17069),f609(x17063,x17062,x17064,x17065,x17066,x17067,x17068,x17069))
% 188.15/187.99 [1707]~E(x17071,x17072)+E(f609(x17073,x17074,x17071,x17075,x17076,x17077,x17078,x17079),f609(x17073,x17074,x17072,x17075,x17076,x17077,x17078,x17079))
% 188.15/187.99 [1708]~E(x17081,x17082)+E(f609(x17083,x17084,x17085,x17081,x17086,x17087,x17088,x17089),f609(x17083,x17084,x17085,x17082,x17086,x17087,x17088,x17089))
% 188.15/187.99 [1709]~E(x17091,x17092)+E(f609(x17093,x17094,x17095,x17096,x17091,x17097,x17098,x17099),f609(x17093,x17094,x17095,x17096,x17092,x17097,x17098,x17099))
% 188.15/187.99 [1710]~E(x17101,x17102)+E(f609(x17103,x17104,x17105,x17106,x17107,x17101,x17108,x17109),f609(x17103,x17104,x17105,x17106,x17107,x17102,x17108,x17109))
% 188.15/187.99 [1711]~E(x17111,x17112)+E(f609(x17113,x17114,x17115,x17116,x17117,x17118,x17111,x17119),f609(x17113,x17114,x17115,x17116,x17117,x17118,x17112,x17119))
% 188.15/187.99 [1712]~E(x17121,x17122)+E(f609(x17123,x17124,x17125,x17126,x17127,x17128,x17129,x17121),f609(x17123,x17124,x17125,x17126,x17127,x17128,x17129,x17122))
% 188.15/187.99 [1713]~E(x17131,x17132)+E(f654(x17131,x17133),f654(x17132,x17133))
% 188.15/187.99 [1714]~E(x17141,x17142)+E(f654(x17143,x17141),f654(x17143,x17142))
% 188.15/187.99 [1715]~E(x17151,x17152)+E(f649(x17151,x17153),f649(x17152,x17153))
% 188.15/187.99 [1716]~E(x17161,x17162)+E(f649(x17163,x17161),f649(x17163,x17162))
% 188.15/187.99 [1717]~E(x17171,x17172)+E(f288(x17171,x17173,x17174,x17175,x17176),f288(x17172,x17173,x17174,x17175,x17176))
% 188.15/187.99 [1718]~E(x17181,x17182)+E(f288(x17183,x17181,x17184,x17185,x17186),f288(x17183,x17182,x17184,x17185,x17186))
% 188.15/187.99 [1719]~E(x17191,x17192)+E(f288(x17193,x17194,x17191,x17195,x17196),f288(x17193,x17194,x17192,x17195,x17196))
% 188.15/187.99 [1720]~E(x17201,x17202)+E(f288(x17203,x17204,x17205,x17201,x17206),f288(x17203,x17204,x17205,x17202,x17206))
% 188.15/187.99 [1721]~E(x17211,x17212)+E(f288(x17213,x17214,x17215,x17216,x17211),f288(x17213,x17214,x17215,x17216,x17212))
% 188.15/187.99 [1722]~E(x17221,x17222)+E(f617(x17221,x17223,x17224,x17225,x17226,x17227),f617(x17222,x17223,x17224,x17225,x17226,x17227))
% 188.15/187.99 [1723]~E(x17231,x17232)+E(f617(x17233,x17231,x17234,x17235,x17236,x17237),f617(x17233,x17232,x17234,x17235,x17236,x17237))
% 188.15/187.99 [1724]~E(x17241,x17242)+E(f617(x17243,x17244,x17241,x17245,x17246,x17247),f617(x17243,x17244,x17242,x17245,x17246,x17247))
% 188.15/187.99 [1725]~E(x17251,x17252)+E(f617(x17253,x17254,x17255,x17251,x17256,x17257),f617(x17253,x17254,x17255,x17252,x17256,x17257))
% 188.15/187.99 [1726]~E(x17261,x17262)+E(f617(x17263,x17264,x17265,x17266,x17261,x17267),f617(x17263,x17264,x17265,x17266,x17262,x17267))
% 188.15/187.99 [1727]~E(x17271,x17272)+E(f617(x17273,x17274,x17275,x17276,x17277,x17271),f617(x17273,x17274,x17275,x17276,x17277,x17272))
% 188.15/187.99 [1728]~E(x17281,x17282)+E(f502(x17281,x17283,x17284,x17285,x17286),f502(x17282,x17283,x17284,x17285,x17286))
% 188.15/187.99 [1729]~E(x17291,x17292)+E(f502(x17293,x17291,x17294,x17295,x17296),f502(x17293,x17292,x17294,x17295,x17296))
% 188.15/187.99 [1730]~E(x17301,x17302)+E(f502(x17303,x17304,x17301,x17305,x17306),f502(x17303,x17304,x17302,x17305,x17306))
% 188.15/187.99 [1731]~E(x17311,x17312)+E(f502(x17313,x17314,x17315,x17311,x17316),f502(x17313,x17314,x17315,x17312,x17316))
% 188.15/187.99 [1732]~E(x17321,x17322)+E(f502(x17323,x17324,x17325,x17326,x17321),f502(x17323,x17324,x17325,x17326,x17322))
% 188.15/187.99 [1733]~E(x17331,x17332)+E(f728(x17331,x17333,x17334,x17335,x17336,x17337,x17338,x17339),f728(x17332,x17333,x17334,x17335,x17336,x17337,x17338,x17339))
% 188.15/187.99 [1734]~E(x17341,x17342)+E(f728(x17343,x17341,x17344,x17345,x17346,x17347,x17348,x17349),f728(x17343,x17342,x17344,x17345,x17346,x17347,x17348,x17349))
% 188.15/187.99 [1735]~E(x17351,x17352)+E(f728(x17353,x17354,x17351,x17355,x17356,x17357,x17358,x17359),f728(x17353,x17354,x17352,x17355,x17356,x17357,x17358,x17359))
% 188.15/187.99 [1736]~E(x17361,x17362)+E(f728(x17363,x17364,x17365,x17361,x17366,x17367,x17368,x17369),f728(x17363,x17364,x17365,x17362,x17366,x17367,x17368,x17369))
% 188.15/187.99 [1737]~E(x17371,x17372)+E(f728(x17373,x17374,x17375,x17376,x17371,x17377,x17378,x17379),f728(x17373,x17374,x17375,x17376,x17372,x17377,x17378,x17379))
% 188.15/187.99 [1738]~E(x17381,x17382)+E(f728(x17383,x17384,x17385,x17386,x17387,x17381,x17388,x17389),f728(x17383,x17384,x17385,x17386,x17387,x17382,x17388,x17389))
% 188.15/187.99 [1739]~E(x17391,x17392)+E(f728(x17393,x17394,x17395,x17396,x17397,x17398,x17391,x17399),f728(x17393,x17394,x17395,x17396,x17397,x17398,x17392,x17399))
% 188.15/187.99 [1740]~E(x17401,x17402)+E(f728(x17403,x17404,x17405,x17406,x17407,x17408,x17409,x17401),f728(x17403,x17404,x17405,x17406,x17407,x17408,x17409,x17402))
% 188.15/187.99 [1741]~E(x17411,x17412)+E(f533(x17411,x17413,x17414),f533(x17412,x17413,x17414))
% 188.15/187.99 [1742]~E(x17421,x17422)+E(f533(x17423,x17421,x17424),f533(x17423,x17422,x17424))
% 188.15/187.99 [1743]~E(x17431,x17432)+E(f533(x17433,x17434,x17431),f533(x17433,x17434,x17432))
% 188.15/187.99 [1744]~E(x17441,x17442)+E(f485(x17441,x17443,x17444),f485(x17442,x17443,x17444))
% 188.15/187.99 [1745]~E(x17451,x17452)+E(f485(x17453,x17451,x17454),f485(x17453,x17452,x17454))
% 188.15/187.99 [1746]~E(x17461,x17462)+E(f485(x17463,x17464,x17461),f485(x17463,x17464,x17462))
% 188.15/187.99 [1747]~E(x17471,x17472)+E(f538(x17471,x17473,x17474),f538(x17472,x17473,x17474))
% 188.15/187.99 [1748]~E(x17481,x17482)+E(f538(x17483,x17481,x17484),f538(x17483,x17482,x17484))
% 188.15/187.99 [1749]~E(x17491,x17492)+E(f538(x17493,x17494,x17491),f538(x17493,x17494,x17492))
% 188.15/187.99 [1750]~E(x17501,x17502)+E(f607(x17501,x17503),f607(x17502,x17503))
% 188.15/187.99 [1751]~E(x17511,x17512)+E(f607(x17513,x17511),f607(x17513,x17512))
% 188.15/187.99 [1752]~E(x17521,x17522)+E(f770(x17521,x17523,x17524,x17525),f770(x17522,x17523,x17524,x17525))
% 188.15/187.99 [1753]~E(x17531,x17532)+E(f770(x17533,x17531,x17534,x17535),f770(x17533,x17532,x17534,x17535))
% 188.15/187.99 [1754]~E(x17541,x17542)+E(f770(x17543,x17544,x17541,x17545),f770(x17543,x17544,x17542,x17545))
% 188.15/187.99 [1755]~E(x17551,x17552)+E(f770(x17553,x17554,x17555,x17551),f770(x17553,x17554,x17555,x17552))
% 188.15/187.99 [1756]~E(x17561,x17562)+E(f856(x17561,x17563,x17564),f856(x17562,x17563,x17564))
% 188.15/187.99 [1757]~E(x17571,x17572)+E(f856(x17573,x17571,x17574),f856(x17573,x17572,x17574))
% 188.15/187.99 [1758]~E(x17581,x17582)+E(f856(x17583,x17584,x17581),f856(x17583,x17584,x17582))
% 188.15/187.99 [1759]~E(x17591,x17592)+E(f359(x17591,x17593,x17594,x17595),f359(x17592,x17593,x17594,x17595))
% 188.15/187.99 [1760]~E(x17601,x17602)+E(f359(x17603,x17601,x17604,x17605),f359(x17603,x17602,x17604,x17605))
% 188.15/187.99 [1761]~E(x17611,x17612)+E(f359(x17613,x17614,x17611,x17615),f359(x17613,x17614,x17612,x17615))
% 188.15/187.99 [1762]~E(x17621,x17622)+E(f359(x17623,x17624,x17625,x17621),f359(x17623,x17624,x17625,x17622))
% 188.15/187.99 [1763]~E(x17631,x17632)+E(f252(x17631,x17633,x17634),f252(x17632,x17633,x17634))
% 188.15/187.99 [1764]~E(x17641,x17642)+E(f252(x17643,x17641,x17644),f252(x17643,x17642,x17644))
% 188.15/187.99 [1765]~E(x17651,x17652)+E(f252(x17653,x17654,x17651),f252(x17653,x17654,x17652))
% 188.15/187.99 [1766]~E(x17661,x17662)+E(f401(x17661,x17663,x17664,x17665),f401(x17662,x17663,x17664,x17665))
% 188.15/187.99 [1767]~E(x17671,x17672)+E(f401(x17673,x17671,x17674,x17675),f401(x17673,x17672,x17674,x17675))
% 188.15/187.99 [1768]~E(x17681,x17682)+E(f401(x17683,x17684,x17681,x17685),f401(x17683,x17684,x17682,x17685))
% 188.15/187.99 [1769]~E(x17691,x17692)+E(f401(x17693,x17694,x17695,x17691),f401(x17693,x17694,x17695,x17692))
% 188.15/187.99 [1770]~E(x17701,x17702)+E(f725(x17701,x17703,x17704),f725(x17702,x17703,x17704))
% 188.15/187.99 [1771]~E(x17711,x17712)+E(f725(x17713,x17711,x17714),f725(x17713,x17712,x17714))
% 188.15/187.99 [1772]~E(x17721,x17722)+E(f725(x17723,x17724,x17721),f725(x17723,x17724,x17722))
% 188.15/187.99 [1773]~E(x17731,x17732)+E(f503(x17731,x17733,x17734,x17735,x17736,x17737,x17738),f503(x17732,x17733,x17734,x17735,x17736,x17737,x17738))
% 188.15/187.99 [1774]~E(x17741,x17742)+E(f503(x17743,x17741,x17744,x17745,x17746,x17747,x17748),f503(x17743,x17742,x17744,x17745,x17746,x17747,x17748))
% 188.15/187.99 [1775]~E(x17751,x17752)+E(f503(x17753,x17754,x17751,x17755,x17756,x17757,x17758),f503(x17753,x17754,x17752,x17755,x17756,x17757,x17758))
% 188.15/187.99 [1776]~E(x17761,x17762)+E(f503(x17763,x17764,x17765,x17761,x17766,x17767,x17768),f503(x17763,x17764,x17765,x17762,x17766,x17767,x17768))
% 188.15/187.99 [1777]~E(x17771,x17772)+E(f503(x17773,x17774,x17775,x17776,x17771,x17777,x17778),f503(x17773,x17774,x17775,x17776,x17772,x17777,x17778))
% 188.15/187.99 [1778]~E(x17781,x17782)+E(f503(x17783,x17784,x17785,x17786,x17787,x17781,x17788),f503(x17783,x17784,x17785,x17786,x17787,x17782,x17788))
% 188.15/187.99 [1779]~E(x17791,x17792)+E(f503(x17793,x17794,x17795,x17796,x17797,x17798,x17791),f503(x17793,x17794,x17795,x17796,x17797,x17798,x17792))
% 188.15/187.99 [1780]~E(x17801,x17802)+E(f475(x17801,x17803,x17804),f475(x17802,x17803,x17804))
% 188.15/187.99 [1781]~E(x17811,x17812)+E(f475(x17813,x17811,x17814),f475(x17813,x17812,x17814))
% 188.15/187.99 [1782]~E(x17821,x17822)+E(f475(x17823,x17824,x17821),f475(x17823,x17824,x17822))
% 188.15/187.99 [1783]~E(x17831,x17832)+E(f464(x17831,x17833),f464(x17832,x17833))
% 188.15/187.99 [1784]~E(x17841,x17842)+E(f464(x17843,x17841),f464(x17843,x17842))
% 188.15/187.99 [1785]~E(x17851,x17852)+E(f402(x17851,x17853,x17854,x17855),f402(x17852,x17853,x17854,x17855))
% 188.15/187.99 [1786]~E(x17861,x17862)+E(f402(x17863,x17861,x17864,x17865),f402(x17863,x17862,x17864,x17865))
% 188.15/187.99 [1787]~E(x17871,x17872)+E(f402(x17873,x17874,x17871,x17875),f402(x17873,x17874,x17872,x17875))
% 188.15/187.99 [1788]~E(x17881,x17882)+E(f402(x17883,x17884,x17885,x17881),f402(x17883,x17884,x17885,x17882))
% 188.15/187.99 [1789]~E(x17891,x17892)+E(f384(x17891),f384(x17892))
% 188.15/187.99 [1790]~E(x17901,x17902)+E(f668(x17901,x17903,x17904,x17905,x17906),f668(x17902,x17903,x17904,x17905,x17906))
% 188.15/187.99 [1791]~E(x17911,x17912)+E(f668(x17913,x17911,x17914,x17915,x17916),f668(x17913,x17912,x17914,x17915,x17916))
% 188.15/187.99 [1792]~E(x17921,x17922)+E(f668(x17923,x17924,x17921,x17925,x17926),f668(x17923,x17924,x17922,x17925,x17926))
% 188.15/187.99 [1793]~E(x17931,x17932)+E(f668(x17933,x17934,x17935,x17931,x17936),f668(x17933,x17934,x17935,x17932,x17936))
% 188.15/187.99 [1794]~E(x17941,x17942)+E(f668(x17943,x17944,x17945,x17946,x17941),f668(x17943,x17944,x17945,x17946,x17942))
% 188.15/187.99 [1795]~E(x17951,x17952)+E(f541(x17951,x17953,x17954),f541(x17952,x17953,x17954))
% 188.15/187.99 [1796]~E(x17961,x17962)+E(f541(x17963,x17961,x17964),f541(x17963,x17962,x17964))
% 188.15/187.99 [1797]~E(x17971,x17972)+E(f541(x17973,x17974,x17971),f541(x17973,x17974,x17972))
% 188.15/187.99 [1798]~E(x17981,x17982)+E(f704(x17981,x17983,x17984,x17985,x17986),f704(x17982,x17983,x17984,x17985,x17986))
% 188.15/187.99 [1799]~E(x17991,x17992)+E(f704(x17993,x17991,x17994,x17995,x17996),f704(x17993,x17992,x17994,x17995,x17996))
% 188.15/187.99 [1800]~E(x18001,x18002)+E(f704(x18003,x18004,x18001,x18005,x18006),f704(x18003,x18004,x18002,x18005,x18006))
% 188.15/187.99 [1801]~E(x18011,x18012)+E(f704(x18013,x18014,x18015,x18011,x18016),f704(x18013,x18014,x18015,x18012,x18016))
% 188.15/187.99 [1802]~E(x18021,x18022)+E(f704(x18023,x18024,x18025,x18026,x18021),f704(x18023,x18024,x18025,x18026,x18022))
% 188.15/187.99 [1803]~E(x18031,x18032)+E(f413(x18031,x18033,x18034,x18035),f413(x18032,x18033,x18034,x18035))
% 188.15/187.99 [1804]~E(x18041,x18042)+E(f413(x18043,x18041,x18044,x18045),f413(x18043,x18042,x18044,x18045))
% 188.15/187.99 [1805]~E(x18051,x18052)+E(f413(x18053,x18054,x18051,x18055),f413(x18053,x18054,x18052,x18055))
% 188.15/187.99 [1806]~E(x18061,x18062)+E(f413(x18063,x18064,x18065,x18061),f413(x18063,x18064,x18065,x18062))
% 188.15/187.99 [1807]~E(x18071,x18072)+E(f489(x18071,x18073,x18074),f489(x18072,x18073,x18074))
% 188.15/187.99 [1808]~E(x18081,x18082)+E(f489(x18083,x18081,x18084),f489(x18083,x18082,x18084))
% 188.15/187.99 [1809]~E(x18091,x18092)+E(f489(x18093,x18094,x18091),f489(x18093,x18094,x18092))
% 188.15/187.99 [1810]~E(x18101,x18102)+E(f508(x18101,x18103,x18104),f508(x18102,x18103,x18104))
% 188.15/187.99 [1811]~E(x18111,x18112)+E(f508(x18113,x18111,x18114),f508(x18113,x18112,x18114))
% 188.15/187.99 [1812]~E(x18121,x18122)+E(f508(x18123,x18124,x18121),f508(x18123,x18124,x18122))
% 188.15/187.99 [1813]~E(x18131,x18132)+E(f405(x18131,x18133),f405(x18132,x18133))
% 188.15/187.99 [1814]~E(x18141,x18142)+E(f405(x18143,x18141),f405(x18143,x18142))
% 188.15/187.99 [1815]~E(x18151,x18152)+E(f348(x18151,x18153,x18154,x18155,x18156,x18157,x18158),f348(x18152,x18153,x18154,x18155,x18156,x18157,x18158))
% 188.15/187.99 [1816]~E(x18161,x18162)+E(f348(x18163,x18161,x18164,x18165,x18166,x18167,x18168),f348(x18163,x18162,x18164,x18165,x18166,x18167,x18168))
% 188.15/187.99 [1817]~E(x18171,x18172)+E(f348(x18173,x18174,x18171,x18175,x18176,x18177,x18178),f348(x18173,x18174,x18172,x18175,x18176,x18177,x18178))
% 188.15/187.99 [1818]~E(x18181,x18182)+E(f348(x18183,x18184,x18185,x18181,x18186,x18187,x18188),f348(x18183,x18184,x18185,x18182,x18186,x18187,x18188))
% 188.15/187.99 [1819]~E(x18191,x18192)+E(f348(x18193,x18194,x18195,x18196,x18191,x18197,x18198),f348(x18193,x18194,x18195,x18196,x18192,x18197,x18198))
% 188.15/187.99 [1820]~E(x18201,x18202)+E(f348(x18203,x18204,x18205,x18206,x18207,x18201,x18208),f348(x18203,x18204,x18205,x18206,x18207,x18202,x18208))
% 188.15/187.99 [1821]~E(x18211,x18212)+E(f348(x18213,x18214,x18215,x18216,x18217,x18218,x18211),f348(x18213,x18214,x18215,x18216,x18217,x18218,x18212))
% 188.15/187.99 [1822]~E(x18221,x18222)+E(f436(x18221,x18223,x18224,x18225,x18226),f436(x18222,x18223,x18224,x18225,x18226))
% 188.15/187.99 [1823]~E(x18231,x18232)+E(f436(x18233,x18231,x18234,x18235,x18236),f436(x18233,x18232,x18234,x18235,x18236))
% 188.15/187.99 [1824]~E(x18241,x18242)+E(f436(x18243,x18244,x18241,x18245,x18246),f436(x18243,x18244,x18242,x18245,x18246))
% 188.15/187.99 [1825]~E(x18251,x18252)+E(f436(x18253,x18254,x18255,x18251,x18256),f436(x18253,x18254,x18255,x18252,x18256))
% 188.15/187.99 [1826]~E(x18261,x18262)+E(f436(x18263,x18264,x18265,x18266,x18261),f436(x18263,x18264,x18265,x18266,x18262))
% 188.15/187.99 [1827]~E(x18271,x18272)+E(f516(x18271,x18273,x18274),f516(x18272,x18273,x18274))
% 188.15/187.99 [1828]~E(x18281,x18282)+E(f516(x18283,x18281,x18284),f516(x18283,x18282,x18284))
% 188.15/187.99 [1829]~E(x18291,x18292)+E(f516(x18293,x18294,x18291),f516(x18293,x18294,x18292))
% 188.15/187.99 [1830]~E(x18301,x18302)+E(f586(x18301,x18303,x18304),f586(x18302,x18303,x18304))
% 188.15/187.99 [1831]~E(x18311,x18312)+E(f586(x18313,x18311,x18314),f586(x18313,x18312,x18314))
% 188.15/187.99 [1832]~E(x18321,x18322)+E(f586(x18323,x18324,x18321),f586(x18323,x18324,x18322))
% 188.15/187.99 [1833]~E(x18331,x18332)+E(f774(x18331,x18333,x18334),f774(x18332,x18333,x18334))
% 188.15/187.99 [1834]~E(x18341,x18342)+E(f774(x18343,x18341,x18344),f774(x18343,x18342,x18344))
% 188.15/187.99 [1835]~E(x18351,x18352)+E(f774(x18353,x18354,x18351),f774(x18353,x18354,x18352))
% 188.15/187.99 [1836]~E(x18361,x18362)+E(f268(x18361),f268(x18362))
% 188.15/187.99 [1837]~E(x18371,x18372)+E(f820(x18371,x18373),f820(x18372,x18373))
% 188.15/187.99 [1838]~E(x18381,x18382)+E(f820(x18383,x18381),f820(x18383,x18382))
% 188.15/187.99 [1839]~E(x18391,x18392)+E(f136(x18391,x18393),f136(x18392,x18393))
% 188.15/187.99 [1840]~E(x18401,x18402)+E(f136(x18403,x18401),f136(x18403,x18402))
% 188.15/187.99 [1841]~E(x18411,x18412)+E(f619(x18411,x18413,x18414,x18415,x18416,x18417),f619(x18412,x18413,x18414,x18415,x18416,x18417))
% 188.15/187.99 [1842]~E(x18421,x18422)+E(f619(x18423,x18421,x18424,x18425,x18426,x18427),f619(x18423,x18422,x18424,x18425,x18426,x18427))
% 188.15/187.99 [1843]~E(x18431,x18432)+E(f619(x18433,x18434,x18431,x18435,x18436,x18437),f619(x18433,x18434,x18432,x18435,x18436,x18437))
% 188.15/187.99 [1844]~E(x18441,x18442)+E(f619(x18443,x18444,x18445,x18441,x18446,x18447),f619(x18443,x18444,x18445,x18442,x18446,x18447))
% 188.15/187.99 [1845]~E(x18451,x18452)+E(f619(x18453,x18454,x18455,x18456,x18451,x18457),f619(x18453,x18454,x18455,x18456,x18452,x18457))
% 188.15/187.99 [1846]~E(x18461,x18462)+E(f619(x18463,x18464,x18465,x18466,x18467,x18461),f619(x18463,x18464,x18465,x18466,x18467,x18462))
% 188.15/187.99 [1847]~E(x18471,x18472)+E(f133(x18471,x18473,x18474),f133(x18472,x18473,x18474))
% 188.15/187.99 [1848]~E(x18481,x18482)+E(f133(x18483,x18481,x18484),f133(x18483,x18482,x18484))
% 188.15/187.99 [1849]~E(x18491,x18492)+E(f133(x18493,x18494,x18491),f133(x18493,x18494,x18492))
% 188.15/187.99 [1850]~E(x18501,x18502)+E(f843(x18501,x18503,x18504,x18505),f843(x18502,x18503,x18504,x18505))
% 188.15/187.99 [1851]~E(x18511,x18512)+E(f843(x18513,x18511,x18514,x18515),f843(x18513,x18512,x18514,x18515))
% 188.15/187.99 [1852]~E(x18521,x18522)+E(f843(x18523,x18524,x18521,x18525),f843(x18523,x18524,x18522,x18525))
% 188.15/187.99 [1853]~E(x18531,x18532)+E(f843(x18533,x18534,x18535,x18531),f843(x18533,x18534,x18535,x18532))
% 188.15/187.99 [1854]~E(x18541,x18542)+E(f421(x18541),f421(x18542))
% 188.15/187.99 [1855]~E(x18551,x18552)+E(f825(x18551,x18553),f825(x18552,x18553))
% 188.15/187.99 [1856]~E(x18561,x18562)+E(f825(x18563,x18561),f825(x18563,x18562))
% 188.15/187.99 [1857]~E(x18571,x18572)+E(f500(x18571,x18573,x18574),f500(x18572,x18573,x18574))
% 188.15/187.99 [1858]~E(x18581,x18582)+E(f500(x18583,x18581,x18584),f500(x18583,x18582,x18584))
% 188.15/187.99 [1859]~E(x18591,x18592)+E(f500(x18593,x18594,x18591),f500(x18593,x18594,x18592))
% 188.15/187.99 [1860]~E(x18601,x18602)+E(f850(x18601,x18603,x18604,x18605,x18606),f850(x18602,x18603,x18604,x18605,x18606))
% 188.15/187.99 [1861]~E(x18611,x18612)+E(f850(x18613,x18611,x18614,x18615,x18616),f850(x18613,x18612,x18614,x18615,x18616))
% 188.15/187.99 [1862]~E(x18621,x18622)+E(f850(x18623,x18624,x18621,x18625,x18626),f850(x18623,x18624,x18622,x18625,x18626))
% 188.15/187.99 [1863]~E(x18631,x18632)+E(f850(x18633,x18634,x18635,x18631,x18636),f850(x18633,x18634,x18635,x18632,x18636))
% 188.15/187.99 [1864]~E(x18641,x18642)+E(f850(x18643,x18644,x18645,x18646,x18641),f850(x18643,x18644,x18645,x18646,x18642))
% 188.15/187.99 [1865]~E(x18651,x18652)+E(f445(x18651,x18653,x18654),f445(x18652,x18653,x18654))
% 188.15/187.99 [1866]~E(x18661,x18662)+E(f445(x18663,x18661,x18664),f445(x18663,x18662,x18664))
% 188.15/187.99 [1867]~E(x18671,x18672)+E(f445(x18673,x18674,x18671),f445(x18673,x18674,x18672))
% 188.15/187.99 [1868]~E(x18681,x18682)+E(f750(x18681,x18683,x18684,x18685,x18686),f750(x18682,x18683,x18684,x18685,x18686))
% 188.15/187.99 [1869]~E(x18691,x18692)+E(f750(x18693,x18691,x18694,x18695,x18696),f750(x18693,x18692,x18694,x18695,x18696))
% 188.15/187.99 [1870]~E(x18701,x18702)+E(f750(x18703,x18704,x18701,x18705,x18706),f750(x18703,x18704,x18702,x18705,x18706))
% 188.15/187.99 [1871]~E(x18711,x18712)+E(f750(x18713,x18714,x18715,x18711,x18716),f750(x18713,x18714,x18715,x18712,x18716))
% 188.15/187.99 [1872]~E(x18721,x18722)+E(f750(x18723,x18724,x18725,x18726,x18721),f750(x18723,x18724,x18725,x18726,x18722))
% 188.15/187.99 [1873]~E(x18731,x18732)+E(f378(x18731,x18733),f378(x18732,x18733))
% 188.15/187.99 [1874]~E(x18741,x18742)+E(f378(x18743,x18741),f378(x18743,x18742))
% 188.15/187.99 [1875]~E(x18751,x18752)+E(f769(x18751,x18753,x18754,x18755,x18756,x18757,x18758),f769(x18752,x18753,x18754,x18755,x18756,x18757,x18758))
% 188.15/187.99 [1876]~E(x18761,x18762)+E(f769(x18763,x18761,x18764,x18765,x18766,x18767,x18768),f769(x18763,x18762,x18764,x18765,x18766,x18767,x18768))
% 188.15/187.99 [1877]~E(x18771,x18772)+E(f769(x18773,x18774,x18771,x18775,x18776,x18777,x18778),f769(x18773,x18774,x18772,x18775,x18776,x18777,x18778))
% 188.15/187.99 [1878]~E(x18781,x18782)+E(f769(x18783,x18784,x18785,x18781,x18786,x18787,x18788),f769(x18783,x18784,x18785,x18782,x18786,x18787,x18788))
% 188.15/187.99 [1879]~E(x18791,x18792)+E(f769(x18793,x18794,x18795,x18796,x18791,x18797,x18798),f769(x18793,x18794,x18795,x18796,x18792,x18797,x18798))
% 188.15/187.99 [1880]~E(x18801,x18802)+E(f769(x18803,x18804,x18805,x18806,x18807,x18801,x18808),f769(x18803,x18804,x18805,x18806,x18807,x18802,x18808))
% 188.15/187.99 [1881]~E(x18811,x18812)+E(f769(x18813,x18814,x18815,x18816,x18817,x18818,x18811),f769(x18813,x18814,x18815,x18816,x18817,x18818,x18812))
% 188.15/187.99 [1882]~E(x18821,x18822)+E(f787(x18821,x18823,x18824,x18825),f787(x18822,x18823,x18824,x18825))
% 188.15/187.99 [1883]~E(x18831,x18832)+E(f787(x18833,x18831,x18834,x18835),f787(x18833,x18832,x18834,x18835))
% 188.15/187.99 [1884]~E(x18841,x18842)+E(f787(x18843,x18844,x18841,x18845),f787(x18843,x18844,x18842,x18845))
% 188.15/187.99 [1885]~E(x18851,x18852)+E(f787(x18853,x18854,x18855,x18851),f787(x18853,x18854,x18855,x18852))
% 188.15/187.99 [1886]~E(x18861,x18862)+E(f579(x18861,x18863,x18864,x18865,x18866),f579(x18862,x18863,x18864,x18865,x18866))
% 188.15/187.99 [1887]~E(x18871,x18872)+E(f579(x18873,x18871,x18874,x18875,x18876),f579(x18873,x18872,x18874,x18875,x18876))
% 188.15/187.99 [1888]~E(x18881,x18882)+E(f579(x18883,x18884,x18881,x18885,x18886),f579(x18883,x18884,x18882,x18885,x18886))
% 188.15/187.99 [1889]~E(x18891,x18892)+E(f579(x18893,x18894,x18895,x18891,x18896),f579(x18893,x18894,x18895,x18892,x18896))
% 188.15/187.99 [1890]~E(x18901,x18902)+E(f579(x18903,x18904,x18905,x18906,x18901),f579(x18903,x18904,x18905,x18906,x18902))
% 188.15/187.99 [1891]~E(x18911,x18912)+E(f702(x18911,x18913,x18914,x18915,x18916),f702(x18912,x18913,x18914,x18915,x18916))
% 188.15/187.99 [1892]~E(x18921,x18922)+E(f702(x18923,x18921,x18924,x18925,x18926),f702(x18923,x18922,x18924,x18925,x18926))
% 188.15/187.99 [1893]~E(x18931,x18932)+E(f702(x18933,x18934,x18931,x18935,x18936),f702(x18933,x18934,x18932,x18935,x18936))
% 188.15/187.99 [1894]~E(x18941,x18942)+E(f702(x18943,x18944,x18945,x18941,x18946),f702(x18943,x18944,x18945,x18942,x18946))
% 188.15/187.99 [1895]~E(x18951,x18952)+E(f702(x18953,x18954,x18955,x18956,x18951),f702(x18953,x18954,x18955,x18956,x18952))
% 188.15/187.99 [1896]~E(x18961,x18962)+E(f273(x18961,x18963,x18964),f273(x18962,x18963,x18964))
% 188.15/187.99 [1897]~E(x18971,x18972)+E(f273(x18973,x18971,x18974),f273(x18973,x18972,x18974))
% 188.15/187.99 [1898]~E(x18981,x18982)+E(f273(x18983,x18984,x18981),f273(x18983,x18984,x18982))
% 188.15/187.99 [1899]~E(x18991,x18992)+E(f672(x18991,x18993),f672(x18992,x18993))
% 188.15/187.99 [1900]~E(x19001,x19002)+E(f672(x19003,x19001),f672(x19003,x19002))
% 188.15/187.99 [1901]~E(x19011,x19012)+E(f729(x19011,x19013,x19014),f729(x19012,x19013,x19014))
% 188.15/187.99 [1902]~E(x19021,x19022)+E(f729(x19023,x19021,x19024),f729(x19023,x19022,x19024))
% 188.15/187.99 [1903]~E(x19031,x19032)+E(f729(x19033,x19034,x19031),f729(x19033,x19034,x19032))
% 188.15/187.99 [1904]~E(x19041,x19042)+E(f708(x19041,x19043,x19044),f708(x19042,x19043,x19044))
% 188.15/187.99 [1905]~E(x19051,x19052)+E(f708(x19053,x19051,x19054),f708(x19053,x19052,x19054))
% 188.15/187.99 [1906]~E(x19061,x19062)+E(f708(x19063,x19064,x19061),f708(x19063,x19064,x19062))
% 188.15/187.99 [1907]~E(x19071,x19072)+E(f317(x19071,x19073,x19074),f317(x19072,x19073,x19074))
% 188.15/187.99 [1908]~E(x19081,x19082)+E(f317(x19083,x19081,x19084),f317(x19083,x19082,x19084))
% 188.15/187.99 [1909]~E(x19091,x19092)+E(f317(x19093,x19094,x19091),f317(x19093,x19094,x19092))
% 188.15/187.99 [1910]~E(x19101,x19102)+E(f664(x19101,x19103,x19104,x19105),f664(x19102,x19103,x19104,x19105))
% 188.15/187.99 [1911]~E(x19111,x19112)+E(f664(x19113,x19111,x19114,x19115),f664(x19113,x19112,x19114,x19115))
% 188.15/187.99 [1912]~E(x19121,x19122)+E(f664(x19123,x19124,x19121,x19125),f664(x19123,x19124,x19122,x19125))
% 188.15/187.99 [1913]~E(x19131,x19132)+E(f664(x19133,x19134,x19135,x19131),f664(x19133,x19134,x19135,x19132))
% 188.15/187.99 [1914]~E(x19141,x19142)+E(f583(x19141,x19143,x19144),f583(x19142,x19143,x19144))
% 188.15/187.99 [1915]~E(x19151,x19152)+E(f583(x19153,x19151,x19154),f583(x19153,x19152,x19154))
% 188.15/187.99 [1916]~E(x19161,x19162)+E(f583(x19163,x19164,x19161),f583(x19163,x19164,x19162))
% 188.15/187.99 [1917]~E(x19171,x19172)+E(f662(x19171,x19173,x19174,x19175,x19176),f662(x19172,x19173,x19174,x19175,x19176))
% 188.15/187.99 [1918]~E(x19181,x19182)+E(f662(x19183,x19181,x19184,x19185,x19186),f662(x19183,x19182,x19184,x19185,x19186))
% 188.15/187.99 [1919]~E(x19191,x19192)+E(f662(x19193,x19194,x19191,x19195,x19196),f662(x19193,x19194,x19192,x19195,x19196))
% 188.15/187.99 [1920]~E(x19201,x19202)+E(f662(x19203,x19204,x19205,x19201,x19206),f662(x19203,x19204,x19205,x19202,x19206))
% 188.15/187.99 [1921]~E(x19211,x19212)+E(f662(x19213,x19214,x19215,x19216,x19211),f662(x19213,x19214,x19215,x19216,x19212))
% 188.15/187.99 [1922]~E(x19221,x19222)+E(f363(x19221,x19223,x19224,x19225,x19226),f363(x19222,x19223,x19224,x19225,x19226))
% 188.15/187.99 [1923]~E(x19231,x19232)+E(f363(x19233,x19231,x19234,x19235,x19236),f363(x19233,x19232,x19234,x19235,x19236))
% 188.15/187.99 [1924]~E(x19241,x19242)+E(f363(x19243,x19244,x19241,x19245,x19246),f363(x19243,x19244,x19242,x19245,x19246))
% 188.15/187.99 [1925]~E(x19251,x19252)+E(f363(x19253,x19254,x19255,x19251,x19256),f363(x19253,x19254,x19255,x19252,x19256))
% 188.15/187.99 [1926]~E(x19261,x19262)+E(f363(x19263,x19264,x19265,x19266,x19261),f363(x19263,x19264,x19265,x19266,x19262))
% 188.15/187.99 [1927]~E(x19271,x19272)+E(f330(x19271),f330(x19272))
% 188.15/187.99 [1928]~E(x19281,x19282)+E(f207(x19281,x19283,x19284,x19285),f207(x19282,x19283,x19284,x19285))
% 188.15/187.99 [1929]~E(x19291,x19292)+E(f207(x19293,x19291,x19294,x19295),f207(x19293,x19292,x19294,x19295))
% 188.15/187.99 [1930]~E(x19301,x19302)+E(f207(x19303,x19304,x19301,x19305),f207(x19303,x19304,x19302,x19305))
% 188.15/187.99 [1931]~E(x19311,x19312)+E(f207(x19313,x19314,x19315,x19311),f207(x19313,x19314,x19315,x19312))
% 188.15/187.99 [1932]~E(x19321,x19322)+E(f727(x19321,x19323,x19324,x19325,x19326,x19327,x19328,x19329),f727(x19322,x19323,x19324,x19325,x19326,x19327,x19328,x19329))
% 188.15/187.99 [1933]~E(x19331,x19332)+E(f727(x19333,x19331,x19334,x19335,x19336,x19337,x19338,x19339),f727(x19333,x19332,x19334,x19335,x19336,x19337,x19338,x19339))
% 188.15/187.99 [1934]~E(x19341,x19342)+E(f727(x19343,x19344,x19341,x19345,x19346,x19347,x19348,x19349),f727(x19343,x19344,x19342,x19345,x19346,x19347,x19348,x19349))
% 188.15/187.99 [1935]~E(x19351,x19352)+E(f727(x19353,x19354,x19355,x19351,x19356,x19357,x19358,x19359),f727(x19353,x19354,x19355,x19352,x19356,x19357,x19358,x19359))
% 188.15/187.99 [1936]~E(x19361,x19362)+E(f727(x19363,x19364,x19365,x19366,x19361,x19367,x19368,x19369),f727(x19363,x19364,x19365,x19366,x19362,x19367,x19368,x19369))
% 188.15/187.99 [1937]~E(x19371,x19372)+E(f727(x19373,x19374,x19375,x19376,x19377,x19371,x19378,x19379),f727(x19373,x19374,x19375,x19376,x19377,x19372,x19378,x19379))
% 188.15/187.99 [1938]~E(x19381,x19382)+E(f727(x19383,x19384,x19385,x19386,x19387,x19388,x19381,x19389),f727(x19383,x19384,x19385,x19386,x19387,x19388,x19382,x19389))
% 188.15/187.99 [1939]~E(x19391,x19392)+E(f727(x19393,x19394,x19395,x19396,x19397,x19398,x19399,x19391),f727(x19393,x19394,x19395,x19396,x19397,x19398,x19399,x19392))
% 188.15/187.99 [1940]~E(x19401,x19402)+E(f155(x19401,x19403),f155(x19402,x19403))
% 188.15/187.99 [1941]~E(x19411,x19412)+E(f155(x19413,x19411),f155(x19413,x19412))
% 188.15/187.99 [1942]~E(x19421,x19422)+E(f204(x19421),f204(x19422))
% 188.15/187.99 [1943]~E(x19431,x19432)+E(f349(x19431,x19433),f349(x19432,x19433))
% 188.15/187.99 [1944]~E(x19441,x19442)+E(f349(x19443,x19441),f349(x19443,x19442))
% 188.15/187.99 [1945]~E(x19451,x19452)+E(f424(x19451,x19453),f424(x19452,x19453))
% 188.15/187.99 [1946]~E(x19461,x19462)+E(f424(x19463,x19461),f424(x19463,x19462))
% 188.15/187.99 [1947]~E(x19471,x19472)+E(f367(x19471,x19473,x19474,x19475,x19476),f367(x19472,x19473,x19474,x19475,x19476))
% 188.15/187.99 [1948]~E(x19481,x19482)+E(f367(x19483,x19481,x19484,x19485,x19486),f367(x19483,x19482,x19484,x19485,x19486))
% 188.15/187.99 [1949]~E(x19491,x19492)+E(f367(x19493,x19494,x19491,x19495,x19496),f367(x19493,x19494,x19492,x19495,x19496))
% 188.15/187.99 [1950]~E(x19501,x19502)+E(f367(x19503,x19504,x19505,x19501,x19506),f367(x19503,x19504,x19505,x19502,x19506))
% 188.15/187.99 [1951]~E(x19511,x19512)+E(f367(x19513,x19514,x19515,x19516,x19511),f367(x19513,x19514,x19515,x19516,x19512))
% 188.15/187.99 [1952]~E(x19521,x19522)+E(f487(x19521,x19523,x19524),f487(x19522,x19523,x19524))
% 188.15/187.99 [1953]~E(x19531,x19532)+E(f487(x19533,x19531,x19534),f487(x19533,x19532,x19534))
% 188.15/187.99 [1954]~E(x19541,x19542)+E(f487(x19543,x19544,x19541),f487(x19543,x19544,x19542))
% 188.15/187.99 [1955]~E(x19551,x19552)+E(f665(x19551,x19553),f665(x19552,x19553))
% 188.15/187.99 [1956]~E(x19561,x19562)+E(f665(x19563,x19561),f665(x19563,x19562))
% 188.15/187.99 [1957]~E(x19571,x19572)+E(f352(x19571,x19573,x19574),f352(x19572,x19573,x19574))
% 188.15/187.99 [1958]~E(x19581,x19582)+E(f352(x19583,x19581,x19584),f352(x19583,x19582,x19584))
% 188.15/187.99 [1959]~E(x19591,x19592)+E(f352(x19593,x19594,x19591),f352(x19593,x19594,x19592))
% 188.15/187.99 [1960]~E(x19601,x19602)+E(f764(x19601,x19603,x19604,x19605),f764(x19602,x19603,x19604,x19605))
% 188.15/187.99 [1961]~E(x19611,x19612)+E(f764(x19613,x19611,x19614,x19615),f764(x19613,x19612,x19614,x19615))
% 188.15/187.99 [1962]~E(x19621,x19622)+E(f764(x19623,x19624,x19621,x19625),f764(x19623,x19624,x19622,x19625))
% 188.15/187.99 [1963]~E(x19631,x19632)+E(f764(x19633,x19634,x19635,x19631),f764(x19633,x19634,x19635,x19632))
% 188.15/187.99 [1964]~E(x19641,x19642)+E(f837(x19641,x19643,x19644,x19645),f837(x19642,x19643,x19644,x19645))
% 188.15/187.99 [1965]~E(x19651,x19652)+E(f837(x19653,x19651,x19654,x19655),f837(x19653,x19652,x19654,x19655))
% 188.15/187.99 [1966]~E(x19661,x19662)+E(f837(x19663,x19664,x19661,x19665),f837(x19663,x19664,x19662,x19665))
% 188.15/187.99 [1967]~E(x19671,x19672)+E(f837(x19673,x19674,x19675,x19671),f837(x19673,x19674,x19675,x19672))
% 188.15/187.99 [1968]~E(x19681,x19682)+E(f550(x19681,x19683,x19684),f550(x19682,x19683,x19684))
% 188.15/187.99 [1969]~E(x19691,x19692)+E(f550(x19693,x19691,x19694),f550(x19693,x19692,x19694))
% 188.15/187.99 [1970]~E(x19701,x19702)+E(f550(x19703,x19704,x19701),f550(x19703,x19704,x19702))
% 188.15/187.99 [1971]~E(x19711,x19712)+E(f432(x19711,x19713,x19714),f432(x19712,x19713,x19714))
% 188.15/187.99 [1972]~E(x19721,x19722)+E(f432(x19723,x19721,x19724),f432(x19723,x19722,x19724))
% 188.15/187.99 [1973]~E(x19731,x19732)+E(f432(x19733,x19734,x19731),f432(x19733,x19734,x19732))
% 188.15/187.99 [1974]~E(x19741,x19742)+E(f781(x19741,x19743,x19744,x19745,x19746,x19747),f781(x19742,x19743,x19744,x19745,x19746,x19747))
% 188.15/187.99 [1975]~E(x19751,x19752)+E(f781(x19753,x19751,x19754,x19755,x19756,x19757),f781(x19753,x19752,x19754,x19755,x19756,x19757))
% 188.15/187.99 [1976]~E(x19761,x19762)+E(f781(x19763,x19764,x19761,x19765,x19766,x19767),f781(x19763,x19764,x19762,x19765,x19766,x19767))
% 188.15/187.99 [1977]~E(x19771,x19772)+E(f781(x19773,x19774,x19775,x19771,x19776,x19777),f781(x19773,x19774,x19775,x19772,x19776,x19777))
% 188.15/187.99 [1978]~E(x19781,x19782)+E(f781(x19783,x19784,x19785,x19786,x19781,x19787),f781(x19783,x19784,x19785,x19786,x19782,x19787))
% 188.15/187.99 [1979]~E(x19791,x19792)+E(f781(x19793,x19794,x19795,x19796,x19797,x19791),f781(x19793,x19794,x19795,x19796,x19797,x19792))
% 188.15/187.99 [1980]~E(x19801,x19802)+E(f509(x19801,x19803,x19804,x19805),f509(x19802,x19803,x19804,x19805))
% 188.15/187.99 [1981]~E(x19811,x19812)+E(f509(x19813,x19811,x19814,x19815),f509(x19813,x19812,x19814,x19815))
% 188.15/187.99 [1982]~E(x19821,x19822)+E(f509(x19823,x19824,x19821,x19825),f509(x19823,x19824,x19822,x19825))
% 188.15/187.99 [1983]~E(x19831,x19832)+E(f509(x19833,x19834,x19835,x19831),f509(x19833,x19834,x19835,x19832))
% 188.15/187.99 [1984]~E(x19841,x19842)+E(f726(x19841,x19843),f726(x19842,x19843))
% 188.15/187.99 [1985]~E(x19851,x19852)+E(f726(x19853,x19851),f726(x19853,x19852))
% 188.15/187.99 [1986]~E(x19861,x19862)+E(f291(x19861,x19863,x19864,x19865,x19866),f291(x19862,x19863,x19864,x19865,x19866))
% 188.15/187.99 [1987]~E(x19871,x19872)+E(f291(x19873,x19871,x19874,x19875,x19876),f291(x19873,x19872,x19874,x19875,x19876))
% 188.15/187.99 [1988]~E(x19881,x19882)+E(f291(x19883,x19884,x19881,x19885,x19886),f291(x19883,x19884,x19882,x19885,x19886))
% 188.15/187.99 [1989]~E(x19891,x19892)+E(f291(x19893,x19894,x19895,x19891,x19896),f291(x19893,x19894,x19895,x19892,x19896))
% 188.15/187.99 [1990]~E(x19901,x19902)+E(f291(x19903,x19904,x19905,x19906,x19901),f291(x19903,x19904,x19905,x19906,x19902))
% 188.15/187.99 [1991]~E(x19911,x19912)+E(f526(x19911),f526(x19912))
% 188.15/187.99 [1992]~E(x19921,x19922)+E(f721(x19921,x19923,x19924,x19925,x19926),f721(x19922,x19923,x19924,x19925,x19926))
% 188.15/187.99 [1993]~E(x19931,x19932)+E(f721(x19933,x19931,x19934,x19935,x19936),f721(x19933,x19932,x19934,x19935,x19936))
% 188.15/187.99 [1994]~E(x19941,x19942)+E(f721(x19943,x19944,x19941,x19945,x19946),f721(x19943,x19944,x19942,x19945,x19946))
% 188.15/187.99 [1995]~E(x19951,x19952)+E(f721(x19953,x19954,x19955,x19951,x19956),f721(x19953,x19954,x19955,x19952,x19956))
% 188.15/187.99 [1996]~E(x19961,x19962)+E(f721(x19963,x19964,x19965,x19966,x19961),f721(x19963,x19964,x19965,x19966,x19962))
% 188.15/187.99 [1997]~E(x19971,x19972)+E(f677(x19971,x19973,x19974,x19975),f677(x19972,x19973,x19974,x19975))
% 188.15/187.99 [1998]~E(x19981,x19982)+E(f677(x19983,x19981,x19984,x19985),f677(x19983,x19982,x19984,x19985))
% 188.15/187.99 [1999]~E(x19991,x19992)+E(f677(x19993,x19994,x19991,x19995),f677(x19993,x19994,x19992,x19995))
% 188.15/187.99 [2000]~E(x20001,x20002)+E(f677(x20003,x20004,x20005,x20001),f677(x20003,x20004,x20005,x20002))
% 188.15/187.99 [2001]~E(x20011,x20012)+E(f205(x20011,x20013),f205(x20012,x20013))
% 188.15/187.99 [2002]~E(x20021,x20022)+E(f205(x20023,x20021),f205(x20023,x20022))
% 188.15/187.99 [2003]~E(x20031,x20032)+E(f749(x20031,x20033,x20034,x20035,x20036),f749(x20032,x20033,x20034,x20035,x20036))
% 188.15/187.99 [2004]~E(x20041,x20042)+E(f749(x20043,x20041,x20044,x20045,x20046),f749(x20043,x20042,x20044,x20045,x20046))
% 188.15/187.99 [2005]~E(x20051,x20052)+E(f749(x20053,x20054,x20051,x20055,x20056),f749(x20053,x20054,x20052,x20055,x20056))
% 188.15/187.99 [2006]~E(x20061,x20062)+E(f749(x20063,x20064,x20065,x20061,x20066),f749(x20063,x20064,x20065,x20062,x20066))
% 188.15/187.99 [2007]~E(x20071,x20072)+E(f749(x20073,x20074,x20075,x20076,x20071),f749(x20073,x20074,x20075,x20076,x20072))
% 188.15/187.99 [2008]~E(x20081,x20082)+E(f547(x20081,x20083),f547(x20082,x20083))
% 188.15/187.99 [2009]~E(x20091,x20092)+E(f547(x20093,x20091),f547(x20093,x20092))
% 188.15/187.99 [2010]~E(x20101,x20102)+E(f435(x20101,x20103,x20104,x20105,x20106),f435(x20102,x20103,x20104,x20105,x20106))
% 188.15/187.99 [2011]~E(x20111,x20112)+E(f435(x20113,x20111,x20114,x20115,x20116),f435(x20113,x20112,x20114,x20115,x20116))
% 188.15/187.99 [2012]~E(x20121,x20122)+E(f435(x20123,x20124,x20121,x20125,x20126),f435(x20123,x20124,x20122,x20125,x20126))
% 188.15/187.99 [2013]~E(x20131,x20132)+E(f435(x20133,x20134,x20135,x20131,x20136),f435(x20133,x20134,x20135,x20132,x20136))
% 188.15/187.99 [2014]~E(x20141,x20142)+E(f435(x20143,x20144,x20145,x20146,x20141),f435(x20143,x20144,x20145,x20146,x20142))
% 188.15/187.99 [2015]~E(x20151,x20152)+E(f847(x20151,x20153,x20154),f847(x20152,x20153,x20154))
% 188.15/187.99 [2016]~E(x20161,x20162)+E(f847(x20163,x20161,x20164),f847(x20163,x20162,x20164))
% 188.15/187.99 [2017]~E(x20171,x20172)+E(f847(x20173,x20174,x20171),f847(x20173,x20174,x20172))
% 188.15/187.99 [2018]~E(x20181,x20182)+E(f684(x20181,x20183),f684(x20182,x20183))
% 188.15/187.99 [2019]~E(x20191,x20192)+E(f684(x20193,x20191),f684(x20193,x20192))
% 188.15/187.99 [2020]~E(x20201,x20202)+E(f682(x20201,x20203,x20204),f682(x20202,x20203,x20204))
% 188.15/187.99 [2021]~E(x20211,x20212)+E(f682(x20213,x20211,x20214),f682(x20213,x20212,x20214))
% 188.15/187.99 [2022]~E(x20221,x20222)+E(f682(x20223,x20224,x20221),f682(x20223,x20224,x20222))
% 188.15/187.99 [2023]~E(x20231,x20232)+E(f463(x20231,x20233,x20234,x20235,x20236,x20237,x20238),f463(x20232,x20233,x20234,x20235,x20236,x20237,x20238))
% 188.15/187.99 [2024]~E(x20241,x20242)+E(f463(x20243,x20241,x20244,x20245,x20246,x20247,x20248),f463(x20243,x20242,x20244,x20245,x20246,x20247,x20248))
% 188.15/187.99 [2025]~E(x20251,x20252)+E(f463(x20253,x20254,x20251,x20255,x20256,x20257,x20258),f463(x20253,x20254,x20252,x20255,x20256,x20257,x20258))
% 188.15/187.99 [2026]~E(x20261,x20262)+E(f463(x20263,x20264,x20265,x20261,x20266,x20267,x20268),f463(x20263,x20264,x20265,x20262,x20266,x20267,x20268))
% 188.15/187.99 [2027]~E(x20271,x20272)+E(f463(x20273,x20274,x20275,x20276,x20271,x20277,x20278),f463(x20273,x20274,x20275,x20276,x20272,x20277,x20278))
% 188.15/187.99 [2028]~E(x20281,x20282)+E(f463(x20283,x20284,x20285,x20286,x20287,x20281,x20288),f463(x20283,x20284,x20285,x20286,x20287,x20282,x20288))
% 188.15/187.99 [2029]~E(x20291,x20292)+E(f463(x20293,x20294,x20295,x20296,x20297,x20298,x20291),f463(x20293,x20294,x20295,x20296,x20297,x20298,x20292))
% 188.15/187.99 [2030]~E(x20301,x20302)+E(f552(x20301,x20303,x20304,x20305,x20306),f552(x20302,x20303,x20304,x20305,x20306))
% 188.15/187.99 [2031]~E(x20311,x20312)+E(f552(x20313,x20311,x20314,x20315,x20316),f552(x20313,x20312,x20314,x20315,x20316))
% 188.15/187.99 [2032]~E(x20321,x20322)+E(f552(x20323,x20324,x20321,x20325,x20326),f552(x20323,x20324,x20322,x20325,x20326))
% 188.15/187.99 [2033]~E(x20331,x20332)+E(f552(x20333,x20334,x20335,x20331,x20336),f552(x20333,x20334,x20335,x20332,x20336))
% 188.15/187.99 [2034]~E(x20341,x20342)+E(f552(x20343,x20344,x20345,x20346,x20341),f552(x20343,x20344,x20345,x20346,x20342))
% 188.15/187.99 [2035]~E(x20351,x20352)+E(f394(x20351,x20353,x20354),f394(x20352,x20353,x20354))
% 188.15/187.99 [2036]~E(x20361,x20362)+E(f394(x20363,x20361,x20364),f394(x20363,x20362,x20364))
% 188.15/187.99 [2037]~E(x20371,x20372)+E(f394(x20373,x20374,x20371),f394(x20373,x20374,x20372))
% 188.15/187.99 [2038]~E(x20381,x20382)+E(f431(x20381,x20383,x20384),f431(x20382,x20383,x20384))
% 188.15/187.99 [2039]~E(x20391,x20392)+E(f431(x20393,x20391,x20394),f431(x20393,x20392,x20394))
% 188.15/187.99 [2040]~E(x20401,x20402)+E(f431(x20403,x20404,x20401),f431(x20403,x20404,x20402))
% 188.15/187.99 [2041]~E(x20411,x20412)+E(f240(x20411,x20413),f240(x20412,x20413))
% 188.15/187.99 [2042]~E(x20421,x20422)+E(f240(x20423,x20421),f240(x20423,x20422))
% 188.15/187.99 [2043]~E(x20431,x20432)+E(f646(x20431,x20433,x20434,x20435,x20436,x20437,x20438,x20439),f646(x20432,x20433,x20434,x20435,x20436,x20437,x20438,x20439))
% 188.15/187.99 [2044]~E(x20441,x20442)+E(f646(x20443,x20441,x20444,x20445,x20446,x20447,x20448,x20449),f646(x20443,x20442,x20444,x20445,x20446,x20447,x20448,x20449))
% 188.15/187.99 [2045]~E(x20451,x20452)+E(f646(x20453,x20454,x20451,x20455,x20456,x20457,x20458,x20459),f646(x20453,x20454,x20452,x20455,x20456,x20457,x20458,x20459))
% 188.15/187.99 [2046]~E(x20461,x20462)+E(f646(x20463,x20464,x20465,x20461,x20466,x20467,x20468,x20469),f646(x20463,x20464,x20465,x20462,x20466,x20467,x20468,x20469))
% 188.15/187.99 [2047]~E(x20471,x20472)+E(f646(x20473,x20474,x20475,x20476,x20471,x20477,x20478,x20479),f646(x20473,x20474,x20475,x20476,x20472,x20477,x20478,x20479))
% 188.15/187.99 [2048]~E(x20481,x20482)+E(f646(x20483,x20484,x20485,x20486,x20487,x20481,x20488,x20489),f646(x20483,x20484,x20485,x20486,x20487,x20482,x20488,x20489))
% 188.15/187.99 [2049]~E(x20491,x20492)+E(f646(x20493,x20494,x20495,x20496,x20497,x20498,x20491,x20499),f646(x20493,x20494,x20495,x20496,x20497,x20498,x20492,x20499))
% 188.15/187.99 [2050]~E(x20501,x20502)+E(f646(x20503,x20504,x20505,x20506,x20507,x20508,x20509,x20501),f646(x20503,x20504,x20505,x20506,x20507,x20508,x20509,x20502))
% 188.15/187.99 [2051]~E(x20511,x20512)+E(f785(x20511,x20513,x20514,x20515),f785(x20512,x20513,x20514,x20515))
% 188.15/187.99 [2052]~E(x20521,x20522)+E(f785(x20523,x20521,x20524,x20525),f785(x20523,x20522,x20524,x20525))
% 188.15/187.99 [2053]~E(x20531,x20532)+E(f785(x20533,x20534,x20531,x20535),f785(x20533,x20534,x20532,x20535))
% 188.15/187.99 [2054]~E(x20541,x20542)+E(f785(x20543,x20544,x20545,x20541),f785(x20543,x20544,x20545,x20542))
% 188.15/187.99 [2055]~E(x20551,x20552)+E(f715(x20551,x20553,x20554,x20555,x20556,x20557,x20558),f715(x20552,x20553,x20554,x20555,x20556,x20557,x20558))
% 188.15/187.99 [2056]~E(x20561,x20562)+E(f715(x20563,x20561,x20564,x20565,x20566,x20567,x20568),f715(x20563,x20562,x20564,x20565,x20566,x20567,x20568))
% 188.15/187.99 [2057]~E(x20571,x20572)+E(f715(x20573,x20574,x20571,x20575,x20576,x20577,x20578),f715(x20573,x20574,x20572,x20575,x20576,x20577,x20578))
% 188.15/187.99 [2058]~E(x20581,x20582)+E(f715(x20583,x20584,x20585,x20581,x20586,x20587,x20588),f715(x20583,x20584,x20585,x20582,x20586,x20587,x20588))
% 188.15/187.99 [2059]~E(x20591,x20592)+E(f715(x20593,x20594,x20595,x20596,x20591,x20597,x20598),f715(x20593,x20594,x20595,x20596,x20592,x20597,x20598))
% 188.15/187.99 [2060]~E(x20601,x20602)+E(f715(x20603,x20604,x20605,x20606,x20607,x20601,x20608),f715(x20603,x20604,x20605,x20606,x20607,x20602,x20608))
% 188.15/187.99 [2061]~E(x20611,x20612)+E(f715(x20613,x20614,x20615,x20616,x20617,x20618,x20611),f715(x20613,x20614,x20615,x20616,x20617,x20618,x20612))
% 188.15/187.99 [2062]~E(x20621,x20622)+E(f739(x20621,x20623,x20624),f739(x20622,x20623,x20624))
% 188.15/187.99 [2063]~E(x20631,x20632)+E(f739(x20633,x20631,x20634),f739(x20633,x20632,x20634))
% 188.15/187.99 [2064]~E(x20641,x20642)+E(f739(x20643,x20644,x20641),f739(x20643,x20644,x20642))
% 188.15/187.99 [2065]~E(x20651,x20652)+E(f706(x20651,x20653,x20654),f706(x20652,x20653,x20654))
% 188.15/187.99 [2066]~E(x20661,x20662)+E(f706(x20663,x20661,x20664),f706(x20663,x20662,x20664))
% 188.15/187.99 [2067]~E(x20671,x20672)+E(f706(x20673,x20674,x20671),f706(x20673,x20674,x20672))
% 188.15/187.99 [2068]~E(x20681,x20682)+E(f461(x20681,x20683,x20684,x20685),f461(x20682,x20683,x20684,x20685))
% 188.15/187.99 [2069]~E(x20691,x20692)+E(f461(x20693,x20691,x20694,x20695),f461(x20693,x20692,x20694,x20695))
% 188.15/187.99 [2070]~E(x20701,x20702)+E(f461(x20703,x20704,x20701,x20705),f461(x20703,x20704,x20702,x20705))
% 188.15/187.99 [2071]~E(x20711,x20712)+E(f461(x20713,x20714,x20715,x20711),f461(x20713,x20714,x20715,x20712))
% 188.15/187.99 [2072]~E(x20721,x20722)+E(f673(x20721,x20723),f673(x20722,x20723))
% 188.15/187.99 [2073]~E(x20731,x20732)+E(f673(x20733,x20731),f673(x20733,x20732))
% 188.15/187.99 [2074]~E(x20741,x20742)+E(f681(x20741),f681(x20742))
% 188.15/187.99 [2075]~E(x20751,x20752)+E(f836(x20751,x20753,x20754,x20755),f836(x20752,x20753,x20754,x20755))
% 188.15/187.99 [2076]~E(x20761,x20762)+E(f836(x20763,x20761,x20764,x20765),f836(x20763,x20762,x20764,x20765))
% 188.15/187.99 [2077]~E(x20771,x20772)+E(f836(x20773,x20774,x20771,x20775),f836(x20773,x20774,x20772,x20775))
% 188.15/187.99 [2078]~E(x20781,x20782)+E(f836(x20783,x20784,x20785,x20781),f836(x20783,x20784,x20785,x20782))
% 188.15/187.99 [2079]~E(x20791,x20792)+E(f786(x20791,x20793,x20794),f786(x20792,x20793,x20794))
% 188.15/187.99 [2080]~E(x20801,x20802)+E(f786(x20803,x20801,x20804),f786(x20803,x20802,x20804))
% 188.15/187.99 [2081]~E(x20811,x20812)+E(f786(x20813,x20814,x20811),f786(x20813,x20814,x20812))
% 188.15/187.99 [2082]~E(x20821,x20822)+E(f844(x20821,x20823,x20824,x20825,x20826,x20827),f844(x20822,x20823,x20824,x20825,x20826,x20827))
% 188.15/187.99 [2083]~E(x20831,x20832)+E(f844(x20833,x20831,x20834,x20835,x20836,x20837),f844(x20833,x20832,x20834,x20835,x20836,x20837))
% 188.15/187.99 [2084]~E(x20841,x20842)+E(f844(x20843,x20844,x20841,x20845,x20846,x20847),f844(x20843,x20844,x20842,x20845,x20846,x20847))
% 188.15/187.99 [2085]~E(x20851,x20852)+E(f844(x20853,x20854,x20855,x20851,x20856,x20857),f844(x20853,x20854,x20855,x20852,x20856,x20857))
% 188.15/187.99 [2086]~E(x20861,x20862)+E(f844(x20863,x20864,x20865,x20866,x20861,x20867),f844(x20863,x20864,x20865,x20866,x20862,x20867))
% 188.15/187.99 [2087]~E(x20871,x20872)+E(f844(x20873,x20874,x20875,x20876,x20877,x20871),f844(x20873,x20874,x20875,x20876,x20877,x20872))
% 188.15/187.99 [2088]~E(x20881,x20882)+E(f658(x20881,x20883,x20884,x20885,x20886),f658(x20882,x20883,x20884,x20885,x20886))
% 188.15/187.99 [2089]~E(x20891,x20892)+E(f658(x20893,x20891,x20894,x20895,x20896),f658(x20893,x20892,x20894,x20895,x20896))
% 188.15/187.99 [2090]~E(x20901,x20902)+E(f658(x20903,x20904,x20901,x20905,x20906),f658(x20903,x20904,x20902,x20905,x20906))
% 188.15/187.99 [2091]~E(x20911,x20912)+E(f658(x20913,x20914,x20915,x20911,x20916),f658(x20913,x20914,x20915,x20912,x20916))
% 188.15/187.99 [2092]~E(x20921,x20922)+E(f658(x20923,x20924,x20925,x20926,x20921),f658(x20923,x20924,x20925,x20926,x20922))
% 188.15/187.99 [2093]~E(x20931,x20932)+E(f441(x20931,x20933),f441(x20932,x20933))
% 188.15/187.99 [2094]~E(x20941,x20942)+E(f441(x20943,x20941),f441(x20943,x20942))
% 188.15/187.99 [2095]~E(x20951,x20952)+E(f804(x20951),f804(x20952))
% 188.15/187.99 [2096]~E(x20961,x20962)+E(f342(x20961,x20963),f342(x20962,x20963))
% 188.15/187.99 [2097]~E(x20971,x20972)+E(f342(x20973,x20971),f342(x20973,x20972))
% 188.15/187.99 [2098]~E(x20981,x20982)+E(f524(x20981,x20983,x20984),f524(x20982,x20983,x20984))
% 188.15/187.99 [2099]~E(x20991,x20992)+E(f524(x20993,x20991,x20994),f524(x20993,x20992,x20994))
% 188.15/187.99 [2100]~E(x21001,x21002)+E(f524(x21003,x21004,x21001),f524(x21003,x21004,x21002))
% 188.15/187.99 [2101]~E(x21011,x21012)+E(f792(x21011,x21013),f792(x21012,x21013))
% 188.15/187.99 [2102]~E(x21021,x21022)+E(f792(x21023,x21021),f792(x21023,x21022))
% 188.15/187.99 [2103]~E(x21031,x21032)+E(f819(x21031,x21033,x21034,x21035,x21036,x21037),f819(x21032,x21033,x21034,x21035,x21036,x21037))
% 188.15/187.99 [2104]~E(x21041,x21042)+E(f819(x21043,x21041,x21044,x21045,x21046,x21047),f819(x21043,x21042,x21044,x21045,x21046,x21047))
% 188.15/187.99 [2105]~E(x21051,x21052)+E(f819(x21053,x21054,x21051,x21055,x21056,x21057),f819(x21053,x21054,x21052,x21055,x21056,x21057))
% 188.15/187.99 [2106]~E(x21061,x21062)+E(f819(x21063,x21064,x21065,x21061,x21066,x21067),f819(x21063,x21064,x21065,x21062,x21066,x21067))
% 188.15/187.99 [2107]~E(x21071,x21072)+E(f819(x21073,x21074,x21075,x21076,x21071,x21077),f819(x21073,x21074,x21075,x21076,x21072,x21077))
% 188.15/187.99 [2108]~E(x21081,x21082)+E(f819(x21083,x21084,x21085,x21086,x21087,x21081),f819(x21083,x21084,x21085,x21086,x21087,x21082))
% 188.15/187.99 [2109]~E(x21091,x21092)+E(f223(x21091,x21093,x21094),f223(x21092,x21093,x21094))
% 188.15/187.99 [2110]~E(x21101,x21102)+E(f223(x21103,x21101,x21104),f223(x21103,x21102,x21104))
% 188.15/187.99 [2111]~E(x21111,x21112)+E(f223(x21113,x21114,x21111),f223(x21113,x21114,x21112))
% 188.15/187.99 [2112]~E(x21121,x21122)+E(f589(x21121,x21123,x21124,x21125),f589(x21122,x21123,x21124,x21125))
% 188.15/187.99 [2113]~E(x21131,x21132)+E(f589(x21133,x21131,x21134,x21135),f589(x21133,x21132,x21134,x21135))
% 188.15/187.99 [2114]~E(x21141,x21142)+E(f589(x21143,x21144,x21141,x21145),f589(x21143,x21144,x21142,x21145))
% 188.15/187.99 [2115]~E(x21151,x21152)+E(f589(x21153,x21154,x21155,x21151),f589(x21153,x21154,x21155,x21152))
% 188.15/187.99 [2116]~E(x21161,x21162)+E(f72(x21161,x21163),f72(x21162,x21163))
% 188.15/187.99 [2117]~E(x21171,x21172)+E(f72(x21173,x21171),f72(x21173,x21172))
% 188.15/187.99 [2118]~E(x21181,x21182)+E(f675(x21181,x21183,x21184,x21185),f675(x21182,x21183,x21184,x21185))
% 188.15/187.99 [2119]~E(x21191,x21192)+E(f675(x21193,x21191,x21194,x21195),f675(x21193,x21192,x21194,x21195))
% 188.15/187.99 [2120]~E(x21201,x21202)+E(f675(x21203,x21204,x21201,x21205),f675(x21203,x21204,x21202,x21205))
% 188.15/187.99 [2121]~E(x21211,x21212)+E(f675(x21213,x21214,x21215,x21211),f675(x21213,x21214,x21215,x21212))
% 188.15/187.99 [2122]~E(x21221,x21222)+E(f474(x21221,x21223,x21224,x21225,x21226),f474(x21222,x21223,x21224,x21225,x21226))
% 188.15/187.99 [2123]~E(x21231,x21232)+E(f474(x21233,x21231,x21234,x21235,x21236),f474(x21233,x21232,x21234,x21235,x21236))
% 188.15/187.99 [2124]~E(x21241,x21242)+E(f474(x21243,x21244,x21241,x21245,x21246),f474(x21243,x21244,x21242,x21245,x21246))
% 188.15/187.99 [2125]~E(x21251,x21252)+E(f474(x21253,x21254,x21255,x21251,x21256),f474(x21253,x21254,x21255,x21252,x21256))
% 188.15/187.99 [2126]~E(x21261,x21262)+E(f474(x21263,x21264,x21265,x21266,x21261),f474(x21263,x21264,x21265,x21266,x21262))
% 188.15/187.99 [2127]~E(x21271,x21272)+E(f358(x21271,x21273,x21274),f358(x21272,x21273,x21274))
% 188.15/187.99 [2128]~E(x21281,x21282)+E(f358(x21283,x21281,x21284),f358(x21283,x21282,x21284))
% 188.15/187.99 [2129]~E(x21291,x21292)+E(f358(x21293,x21294,x21291),f358(x21293,x21294,x21292))
% 188.15/187.99 [2130]~E(x21301,x21302)+E(f430(x21301,x21303,x21304,x21305),f430(x21302,x21303,x21304,x21305))
% 188.15/187.99 [2131]~E(x21311,x21312)+E(f430(x21313,x21311,x21314,x21315),f430(x21313,x21312,x21314,x21315))
% 188.15/187.99 [2132]~E(x21321,x21322)+E(f430(x21323,x21324,x21321,x21325),f430(x21323,x21324,x21322,x21325))
% 188.15/187.99 [2133]~E(x21331,x21332)+E(f430(x21333,x21334,x21335,x21331),f430(x21333,x21334,x21335,x21332))
% 188.15/187.99 [2134]~E(x21341,x21342)+E(f644(x21341,x21343,x21344),f644(x21342,x21343,x21344))
% 188.15/187.99 [2135]~E(x21351,x21352)+E(f644(x21353,x21351,x21354),f644(x21353,x21352,x21354))
% 188.15/187.99 [2136]~E(x21361,x21362)+E(f644(x21363,x21364,x21361),f644(x21363,x21364,x21362))
% 188.15/187.99 [2137]~E(x21371,x21372)+E(f425(x21371,x21373),f425(x21372,x21373))
% 188.15/187.99 [2138]~E(x21381,x21382)+E(f425(x21383,x21381),f425(x21383,x21382))
% 188.15/187.99 [2139]~E(x21391,x21392)+E(f849(x21391,x21393,x21394,x21395,x21396),f849(x21392,x21393,x21394,x21395,x21396))
% 188.15/187.99 [2140]~E(x21401,x21402)+E(f849(x21403,x21401,x21404,x21405,x21406),f849(x21403,x21402,x21404,x21405,x21406))
% 188.15/187.99 [2141]~E(x21411,x21412)+E(f849(x21413,x21414,x21411,x21415,x21416),f849(x21413,x21414,x21412,x21415,x21416))
% 188.15/187.99 [2142]~E(x21421,x21422)+E(f849(x21423,x21424,x21425,x21421,x21426),f849(x21423,x21424,x21425,x21422,x21426))
% 188.15/187.99 [2143]~E(x21431,x21432)+E(f849(x21433,x21434,x21435,x21436,x21431),f849(x21433,x21434,x21435,x21436,x21432))
% 188.15/187.99 [2144]~E(x21441,x21442)+E(f778(x21441,x21443,x21444,x21445),f778(x21442,x21443,x21444,x21445))
% 188.15/187.99 [2145]~E(x21451,x21452)+E(f778(x21453,x21451,x21454,x21455),f778(x21453,x21452,x21454,x21455))
% 188.15/187.99 [2146]~E(x21461,x21462)+E(f778(x21463,x21464,x21461,x21465),f778(x21463,x21464,x21462,x21465))
% 188.15/187.99 [2147]~E(x21471,x21472)+E(f778(x21473,x21474,x21475,x21471),f778(x21473,x21474,x21475,x21472))
% 188.15/187.99 [2148]~E(x21481,x21482)+E(f520(x21481,x21483,x21484,x21485),f520(x21482,x21483,x21484,x21485))
% 188.15/187.99 [2149]~E(x21491,x21492)+E(f520(x21493,x21491,x21494,x21495),f520(x21493,x21492,x21494,x21495))
% 188.15/187.99 [2150]~E(x21501,x21502)+E(f520(x21503,x21504,x21501,x21505),f520(x21503,x21504,x21502,x21505))
% 188.15/187.99 [2151]~E(x21511,x21512)+E(f520(x21513,x21514,x21515,x21511),f520(x21513,x21514,x21515,x21512))
% 188.15/187.99 [2152]~E(x21521,x21522)+E(f338(x21521,x21523,x21524),f338(x21522,x21523,x21524))
% 188.15/187.99 [2153]~E(x21531,x21532)+E(f338(x21533,x21531,x21534),f338(x21533,x21532,x21534))
% 188.15/187.99 [2154]~E(x21541,x21542)+E(f338(x21543,x21544,x21541),f338(x21543,x21544,x21542))
% 188.15/187.99 [2155]~E(x21551,x21552)+E(f705(x21551,x21553),f705(x21552,x21553))
% 188.15/187.99 [2156]~E(x21561,x21562)+E(f705(x21563,x21561),f705(x21563,x21562))
% 188.15/187.99 [2157]~E(x21571,x21572)+E(f195(x21571,x21573,x21574,x21575),f195(x21572,x21573,x21574,x21575))
% 188.15/187.99 [2158]~E(x21581,x21582)+E(f195(x21583,x21581,x21584,x21585),f195(x21583,x21582,x21584,x21585))
% 188.15/187.99 [2159]~E(x21591,x21592)+E(f195(x21593,x21594,x21591,x21595),f195(x21593,x21594,x21592,x21595))
% 188.15/187.99 [2160]~E(x21601,x21602)+E(f195(x21603,x21604,x21605,x21601),f195(x21603,x21604,x21605,x21602))
% 188.15/187.99 [2161]~E(x21611,x21612)+E(f534(x21611,x21613,x21614,x21615,x21616),f534(x21612,x21613,x21614,x21615,x21616))
% 188.15/187.99 [2162]~E(x21621,x21622)+E(f534(x21623,x21621,x21624,x21625,x21626),f534(x21623,x21622,x21624,x21625,x21626))
% 188.15/187.99 [2163]~E(x21631,x21632)+E(f534(x21633,x21634,x21631,x21635,x21636),f534(x21633,x21634,x21632,x21635,x21636))
% 188.15/187.99 [2164]~E(x21641,x21642)+E(f534(x21643,x21644,x21645,x21641,x21646),f534(x21643,x21644,x21645,x21642,x21646))
% 188.15/187.99 [2165]~E(x21651,x21652)+E(f534(x21653,x21654,x21655,x21656,x21651),f534(x21653,x21654,x21655,x21656,x21652))
% 188.15/187.99 [2166]~E(x21661,x21662)+E(f551(x21661,x21663,x21664,x21665,x21666),f551(x21662,x21663,x21664,x21665,x21666))
% 188.15/187.99 [2167]~E(x21671,x21672)+E(f551(x21673,x21671,x21674,x21675,x21676),f551(x21673,x21672,x21674,x21675,x21676))
% 188.15/187.99 [2168]~E(x21681,x21682)+E(f551(x21683,x21684,x21681,x21685,x21686),f551(x21683,x21684,x21682,x21685,x21686))
% 188.15/187.99 [2169]~E(x21691,x21692)+E(f551(x21693,x21694,x21695,x21691,x21696),f551(x21693,x21694,x21695,x21692,x21696))
% 188.15/187.99 [2170]~E(x21701,x21702)+E(f551(x21703,x21704,x21705,x21706,x21701),f551(x21703,x21704,x21705,x21706,x21702))
% 188.15/187.99 [2171]~E(x21711,x21712)+E(f233(x21711,x21713,x21714,x21715,x21716),f233(x21712,x21713,x21714,x21715,x21716))
% 188.15/187.99 [2172]~E(x21721,x21722)+E(f233(x21723,x21721,x21724,x21725,x21726),f233(x21723,x21722,x21724,x21725,x21726))
% 188.15/187.99 [2173]~E(x21731,x21732)+E(f233(x21733,x21734,x21731,x21735,x21736),f233(x21733,x21734,x21732,x21735,x21736))
% 188.15/187.99 [2174]~E(x21741,x21742)+E(f233(x21743,x21744,x21745,x21741,x21746),f233(x21743,x21744,x21745,x21742,x21746))
% 188.15/187.99 [2175]~E(x21751,x21752)+E(f233(x21753,x21754,x21755,x21756,x21751),f233(x21753,x21754,x21755,x21756,x21752))
% 188.15/187.99 [2176]~E(x21761,x21762)+E(f724(x21761,x21763,x21764),f724(x21762,x21763,x21764))
% 188.15/187.99 [2177]~E(x21771,x21772)+E(f724(x21773,x21771,x21774),f724(x21773,x21772,x21774))
% 188.15/187.99 [2178]~E(x21781,x21782)+E(f724(x21783,x21784,x21781),f724(x21783,x21784,x21782))
% 188.15/187.99 [2179]~E(x21791,x21792)+E(f590(x21791,x21793,x21794,x21795),f590(x21792,x21793,x21794,x21795))
% 188.15/187.99 [2180]~E(x21801,x21802)+E(f590(x21803,x21801,x21804,x21805),f590(x21803,x21802,x21804,x21805))
% 188.15/187.99 [2181]~E(x21811,x21812)+E(f590(x21813,x21814,x21811,x21815),f590(x21813,x21814,x21812,x21815))
% 188.15/187.99 [2182]~E(x21821,x21822)+E(f590(x21823,x21824,x21825,x21821),f590(x21823,x21824,x21825,x21822))
% 188.15/187.99 [2183]~E(x21831,x21832)+E(f635(x21831,x21833,x21834,x21835,x21836),f635(x21832,x21833,x21834,x21835,x21836))
% 188.15/187.99 [2184]~E(x21841,x21842)+E(f635(x21843,x21841,x21844,x21845,x21846),f635(x21843,x21842,x21844,x21845,x21846))
% 188.15/187.99 [2185]~E(x21851,x21852)+E(f635(x21853,x21854,x21851,x21855,x21856),f635(x21853,x21854,x21852,x21855,x21856))
% 188.15/187.99 [2186]~E(x21861,x21862)+E(f635(x21863,x21864,x21865,x21861,x21866),f635(x21863,x21864,x21865,x21862,x21866))
% 188.15/187.99 [2187]~E(x21871,x21872)+E(f635(x21873,x21874,x21875,x21876,x21871),f635(x21873,x21874,x21875,x21876,x21872))
% 188.15/187.99 [2188]~E(x21881,x21882)+E(f791(x21881,x21883,x21884),f791(x21882,x21883,x21884))
% 188.15/187.99 [2189]~E(x21891,x21892)+E(f791(x21893,x21891,x21894),f791(x21893,x21892,x21894))
% 188.15/187.99 [2190]~E(x21901,x21902)+E(f791(x21903,x21904,x21901),f791(x21903,x21904,x21902))
% 188.15/187.99 [2191]~E(x21911,x21912)+E(f507(x21911,x21913,x21914),f507(x21912,x21913,x21914))
% 188.15/187.99 [2192]~E(x21921,x21922)+E(f507(x21923,x21921,x21924),f507(x21923,x21922,x21924))
% 188.15/187.99 [2193]~E(x21931,x21932)+E(f507(x21933,x21934,x21931),f507(x21933,x21934,x21932))
% 188.15/187.99 [2194]~E(x21941,x21942)+E(f442(x21941,x21943),f442(x21942,x21943))
% 188.15/187.99 [2195]~E(x21951,x21952)+E(f442(x21953,x21951),f442(x21953,x21952))
% 188.15/187.99 [2196]~E(x21961,x21962)+E(f418(x21961,x21963,x21964,x21965),f418(x21962,x21963,x21964,x21965))
% 188.15/187.99 [2197]~E(x21971,x21972)+E(f418(x21973,x21971,x21974,x21975),f418(x21973,x21972,x21974,x21975))
% 188.15/187.99 [2198]~E(x21981,x21982)+E(f418(x21983,x21984,x21981,x21985),f418(x21983,x21984,x21982,x21985))
% 188.15/187.99 [2199]~E(x21991,x21992)+E(f418(x21993,x21994,x21995,x21991),f418(x21993,x21994,x21995,x21992))
% 188.15/187.99 [2200]~E(x22001,x22002)+E(f266(x22001,x22003,x22004,x22005,x22006),f266(x22002,x22003,x22004,x22005,x22006))
% 188.15/187.99 [2201]~E(x22011,x22012)+E(f266(x22013,x22011,x22014,x22015,x22016),f266(x22013,x22012,x22014,x22015,x22016))
% 188.15/187.99 [2202]~E(x22021,x22022)+E(f266(x22023,x22024,x22021,x22025,x22026),f266(x22023,x22024,x22022,x22025,x22026))
% 188.15/187.99 [2203]~E(x22031,x22032)+E(f266(x22033,x22034,x22035,x22031,x22036),f266(x22033,x22034,x22035,x22032,x22036))
% 188.15/187.99 [2204]~E(x22041,x22042)+E(f266(x22043,x22044,x22045,x22046,x22041),f266(x22043,x22044,x22045,x22046,x22042))
% 188.15/187.99 [2205]~E(x22051,x22052)+E(f452(x22051,x22053,x22054,x22055,x22056),f452(x22052,x22053,x22054,x22055,x22056))
% 188.15/187.99 [2206]~E(x22061,x22062)+E(f452(x22063,x22061,x22064,x22065,x22066),f452(x22063,x22062,x22064,x22065,x22066))
% 188.15/187.99 [2207]~E(x22071,x22072)+E(f452(x22073,x22074,x22071,x22075,x22076),f452(x22073,x22074,x22072,x22075,x22076))
% 188.15/187.99 [2208]~E(x22081,x22082)+E(f452(x22083,x22084,x22085,x22081,x22086),f452(x22083,x22084,x22085,x22082,x22086))
% 188.15/187.99 [2209]~E(x22091,x22092)+E(f452(x22093,x22094,x22095,x22096,x22091),f452(x22093,x22094,x22095,x22096,x22092))
% 188.15/187.99 [2210]~E(x22101,x22102)+E(f794(x22101,x22103,x22104,x22105),f794(x22102,x22103,x22104,x22105))
% 188.15/187.99 [2211]~E(x22111,x22112)+E(f794(x22113,x22111,x22114,x22115),f794(x22113,x22112,x22114,x22115))
% 188.15/187.99 [2212]~E(x22121,x22122)+E(f794(x22123,x22124,x22121,x22125),f794(x22123,x22124,x22122,x22125))
% 188.15/187.99 [2213]~E(x22131,x22132)+E(f794(x22133,x22134,x22135,x22131),f794(x22133,x22134,x22135,x22132))
% 188.15/187.99 [2214]~E(x22141,x22142)+E(f285(x22141,x22143,x22144),f285(x22142,x22143,x22144))
% 188.15/187.99 [2215]~E(x22151,x22152)+E(f285(x22153,x22151,x22154),f285(x22153,x22152,x22154))
% 188.15/187.99 [2216]~E(x22161,x22162)+E(f285(x22163,x22164,x22161),f285(x22163,x22164,x22162))
% 188.15/187.99 [2217]~E(x22171,x22172)+E(f574(x22171,x22173,x22174),f574(x22172,x22173,x22174))
% 188.15/187.99 [2218]~E(x22181,x22182)+E(f574(x22183,x22181,x22184),f574(x22183,x22182,x22184))
% 188.15/187.99 [2219]~E(x22191,x22192)+E(f574(x22193,x22194,x22191),f574(x22193,x22194,x22192))
% 188.15/187.99 [2220]~E(x22201,x22202)+E(f857(x22201,x22203,x22204),f857(x22202,x22203,x22204))
% 188.15/187.99 [2221]~E(x22211,x22212)+E(f857(x22213,x22211,x22214),f857(x22213,x22212,x22214))
% 188.15/187.99 [2222]~E(x22221,x22222)+E(f857(x22223,x22224,x22221),f857(x22223,x22224,x22222))
% 188.15/187.99 [2223]~E(x22231,x22232)+E(f21(x22231,x22233),f21(x22232,x22233))
% 188.15/187.99 [2224]~E(x22241,x22242)+E(f21(x22243,x22241),f21(x22243,x22242))
% 188.15/187.99 [2225]~E(x22251,x22252)+E(f695(x22251,x22253,x22254,x22255),f695(x22252,x22253,x22254,x22255))
% 188.15/187.99 [2226]~E(x22261,x22262)+E(f695(x22263,x22261,x22264,x22265),f695(x22263,x22262,x22264,x22265))
% 188.15/187.99 [2227]~E(x22271,x22272)+E(f695(x22273,x22274,x22271,x22275),f695(x22273,x22274,x22272,x22275))
% 188.15/187.99 [2228]~E(x22281,x22282)+E(f695(x22283,x22284,x22285,x22281),f695(x22283,x22284,x22285,x22282))
% 188.15/187.99 [2229]~E(x22291,x22292)+E(f174(x22291),f174(x22292))
% 188.15/187.99 [2230]~E(x22301,x22302)+E(f784(x22301,x22303,x22304),f784(x22302,x22303,x22304))
% 188.15/187.99 [2231]~E(x22311,x22312)+E(f784(x22313,x22311,x22314),f784(x22313,x22312,x22314))
% 188.15/187.99 [2232]~E(x22321,x22322)+E(f784(x22323,x22324,x22321),f784(x22323,x22324,x22322))
% 188.15/187.99 [2233]~E(x22331,x22332)+E(f194(x22331,x22333),f194(x22332,x22333))
% 188.15/187.99 [2234]~E(x22341,x22342)+E(f194(x22343,x22341),f194(x22343,x22342))
% 188.15/187.99 [2235]~E(x22351,x22352)+E(f239(x22351,x22353),f239(x22352,x22353))
% 188.15/187.99 [2236]~E(x22361,x22362)+E(f239(x22363,x22361),f239(x22363,x22362))
% 188.15/187.99 [2237]~E(x22371,x22372)+E(f788(x22371,x22373,x22374),f788(x22372,x22373,x22374))
% 188.15/187.99 [2238]~E(x22381,x22382)+E(f788(x22383,x22381,x22384),f788(x22383,x22382,x22384))
% 188.15/187.99 [2239]~E(x22391,x22392)+E(f788(x22393,x22394,x22391),f788(x22393,x22394,x22392))
% 188.15/187.99 [2240]~E(x22401,x22402)+E(f605(x22401,x22403,x22404,x22405),f605(x22402,x22403,x22404,x22405))
% 188.15/187.99 [2241]~E(x22411,x22412)+E(f605(x22413,x22411,x22414,x22415),f605(x22413,x22412,x22414,x22415))
% 188.15/187.99 [2242]~E(x22421,x22422)+E(f605(x22423,x22424,x22421,x22425),f605(x22423,x22424,x22422,x22425))
% 188.15/187.99 [2243]~E(x22431,x22432)+E(f605(x22433,x22434,x22435,x22431),f605(x22433,x22434,x22435,x22432))
% 188.15/187.99 [2244]~E(x22441,x22442)+E(f842(x22441,x22443,x22444),f842(x22442,x22443,x22444))
% 188.15/187.99 [2245]~E(x22451,x22452)+E(f842(x22453,x22451,x22454),f842(x22453,x22452,x22454))
% 188.15/187.99 [2246]~E(x22461,x22462)+E(f842(x22463,x22464,x22461),f842(x22463,x22464,x22462))
% 188.15/187.99 [2247]~E(x22471,x22472)+E(f374(x22471),f374(x22472))
% 188.15/187.99 [2248]~E(x22481,x22482)+E(f693(x22481,x22483,x22484),f693(x22482,x22483,x22484))
% 188.15/187.99 [2249]~E(x22491,x22492)+E(f693(x22493,x22491,x22494),f693(x22493,x22492,x22494))
% 188.15/187.99 [2250]~E(x22501,x22502)+E(f693(x22503,x22504,x22501),f693(x22503,x22504,x22502))
% 188.15/187.99 [2251]~E(x22511,x22512)+E(f168(x22511,x22513,x22514),f168(x22512,x22513,x22514))
% 188.15/187.99 [2252]~E(x22521,x22522)+E(f168(x22523,x22521,x22524),f168(x22523,x22522,x22524))
% 188.15/187.99 [2253]~E(x22531,x22532)+E(f168(x22533,x22534,x22531),f168(x22533,x22534,x22532))
% 188.15/187.99 [2254]~E(x22541,x22542)+E(f208(x22541,x22543,x22544,x22545),f208(x22542,x22543,x22544,x22545))
% 188.15/187.99 [2255]~E(x22551,x22552)+E(f208(x22553,x22551,x22554,x22555),f208(x22553,x22552,x22554,x22555))
% 188.15/187.99 [2256]~E(x22561,x22562)+E(f208(x22563,x22564,x22561,x22565),f208(x22563,x22564,x22562,x22565))
% 188.15/187.99 [2257]~E(x22571,x22572)+E(f208(x22573,x22574,x22575,x22571),f208(x22573,x22574,x22575,x22572))
% 188.15/187.99 [2258]~E(x22581,x22582)+E(f426(x22581),f426(x22582))
% 188.15/187.99 [2259]~E(x22591,x22592)+E(f610(x22591,x22593,x22594,x22595,x22596,x22597,x22598,x22599),f610(x22592,x22593,x22594,x22595,x22596,x22597,x22598,x22599))
% 188.15/187.99 [2260]~E(x22601,x22602)+E(f610(x22603,x22601,x22604,x22605,x22606,x22607,x22608,x22609),f610(x22603,x22602,x22604,x22605,x22606,x22607,x22608,x22609))
% 188.15/187.99 [2261]~E(x22611,x22612)+E(f610(x22613,x22614,x22611,x22615,x22616,x22617,x22618,x22619),f610(x22613,x22614,x22612,x22615,x22616,x22617,x22618,x22619))
% 188.15/187.99 [2262]~E(x22621,x22622)+E(f610(x22623,x22624,x22625,x22621,x22626,x22627,x22628,x22629),f610(x22623,x22624,x22625,x22622,x22626,x22627,x22628,x22629))
% 188.15/187.99 [2263]~E(x22631,x22632)+E(f610(x22633,x22634,x22635,x22636,x22631,x22637,x22638,x22639),f610(x22633,x22634,x22635,x22636,x22632,x22637,x22638,x22639))
% 188.15/187.99 [2264]~E(x22641,x22642)+E(f610(x22643,x22644,x22645,x22646,x22647,x22641,x22648,x22649),f610(x22643,x22644,x22645,x22646,x22647,x22642,x22648,x22649))
% 188.15/187.99 [2265]~E(x22651,x22652)+E(f610(x22653,x22654,x22655,x22656,x22657,x22658,x22651,x22659),f610(x22653,x22654,x22655,x22656,x22657,x22658,x22652,x22659))
% 188.15/187.99 [2266]~E(x22661,x22662)+E(f610(x22663,x22664,x22665,x22666,x22667,x22668,x22669,x22661),f610(x22663,x22664,x22665,x22666,x22667,x22668,x22669,x22662))
% 188.15/187.99 [2267]~E(x22671,x22672)+E(f631(x22671,x22673,x22674,x22675),f631(x22672,x22673,x22674,x22675))
% 188.15/187.99 [2268]~E(x22681,x22682)+E(f631(x22683,x22681,x22684,x22685),f631(x22683,x22682,x22684,x22685))
% 188.15/187.99 [2269]~E(x22691,x22692)+E(f631(x22693,x22694,x22691,x22695),f631(x22693,x22694,x22692,x22695))
% 188.15/187.99 [2270]~E(x22701,x22702)+E(f631(x22703,x22704,x22705,x22701),f631(x22703,x22704,x22705,x22702))
% 188.15/187.99 [2271]~E(x22711,x22712)+E(f696(x22711,x22713,x22714,x22715,x22716),f696(x22712,x22713,x22714,x22715,x22716))
% 188.15/187.99 [2272]~E(x22721,x22722)+E(f696(x22723,x22721,x22724,x22725,x22726),f696(x22723,x22722,x22724,x22725,x22726))
% 188.15/187.99 [2273]~E(x22731,x22732)+E(f696(x22733,x22734,x22731,x22735,x22736),f696(x22733,x22734,x22732,x22735,x22736))
% 188.15/187.99 [2274]~E(x22741,x22742)+E(f696(x22743,x22744,x22745,x22741,x22746),f696(x22743,x22744,x22745,x22742,x22746))
% 188.15/187.99 [2275]~E(x22751,x22752)+E(f696(x22753,x22754,x22755,x22756,x22751),f696(x22753,x22754,x22755,x22756,x22752))
% 188.15/187.99 [2276]~E(x22761,x22762)+E(f94(x22761,x22763,x22764,x22765),f94(x22762,x22763,x22764,x22765))
% 188.15/187.99 [2277]~E(x22771,x22772)+E(f94(x22773,x22771,x22774,x22775),f94(x22773,x22772,x22774,x22775))
% 188.15/187.99 [2278]~E(x22781,x22782)+E(f94(x22783,x22784,x22781,x22785),f94(x22783,x22784,x22782,x22785))
% 188.15/187.99 [2279]~E(x22791,x22792)+E(f94(x22793,x22794,x22795,x22791),f94(x22793,x22794,x22795,x22792))
% 188.15/187.99 [2280]~E(x22801,x22802)+E(f478(x22801,x22803,x22804,x22805,x22806),f478(x22802,x22803,x22804,x22805,x22806))
% 188.15/187.99 [2281]~E(x22811,x22812)+E(f478(x22813,x22811,x22814,x22815,x22816),f478(x22813,x22812,x22814,x22815,x22816))
% 188.15/187.99 [2282]~E(x22821,x22822)+E(f478(x22823,x22824,x22821,x22825,x22826),f478(x22823,x22824,x22822,x22825,x22826))
% 188.15/187.99 [2283]~E(x22831,x22832)+E(f478(x22833,x22834,x22835,x22831,x22836),f478(x22833,x22834,x22835,x22832,x22836))
% 188.15/187.99 [2284]~E(x22841,x22842)+E(f478(x22843,x22844,x22845,x22846,x22841),f478(x22843,x22844,x22845,x22846,x22842))
% 188.15/187.99 [2285]~E(x22851,x22852)+E(f756(x22851,x22853,x22854,x22855),f756(x22852,x22853,x22854,x22855))
% 188.15/187.99 [2286]~E(x22861,x22862)+E(f756(x22863,x22861,x22864,x22865),f756(x22863,x22862,x22864,x22865))
% 188.15/187.99 [2287]~E(x22871,x22872)+E(f756(x22873,x22874,x22871,x22875),f756(x22873,x22874,x22872,x22875))
% 188.15/187.99 [2288]~E(x22881,x22882)+E(f756(x22883,x22884,x22885,x22881),f756(x22883,x22884,x22885,x22882))
% 188.15/187.99 [2289]~E(x22891,x22892)+E(f753(x22891,x22893,x22894,x22895,x22896),f753(x22892,x22893,x22894,x22895,x22896))
% 188.15/187.99 [2290]~E(x22901,x22902)+E(f753(x22903,x22901,x22904,x22905,x22906),f753(x22903,x22902,x22904,x22905,x22906))
% 188.15/187.99 [2291]~E(x22911,x22912)+E(f753(x22913,x22914,x22911,x22915,x22916),f753(x22913,x22914,x22912,x22915,x22916))
% 188.15/187.99 [2292]~E(x22921,x22922)+E(f753(x22923,x22924,x22925,x22921,x22926),f753(x22923,x22924,x22925,x22922,x22926))
% 188.15/187.99 [2293]~E(x22931,x22932)+E(f753(x22933,x22934,x22935,x22936,x22931),f753(x22933,x22934,x22935,x22936,x22932))
% 188.15/187.99 [2294]~E(x22941,x22942)+E(f328(x22941),f328(x22942))
% 188.15/187.99 [2295]~E(x22951,x22952)+E(f575(x22951,x22953,x22954,x22955),f575(x22952,x22953,x22954,x22955))
% 188.15/187.99 [2296]~E(x22961,x22962)+E(f575(x22963,x22961,x22964,x22965),f575(x22963,x22962,x22964,x22965))
% 188.15/187.99 [2297]~E(x22971,x22972)+E(f575(x22973,x22974,x22971,x22975),f575(x22973,x22974,x22972,x22975))
% 188.15/187.99 [2298]~E(x22981,x22982)+E(f575(x22983,x22984,x22985,x22981),f575(x22983,x22984,x22985,x22982))
% 188.15/187.99 [2299]~E(x22991,x22992)+E(f415(x22991,x22993,x22994,x22995),f415(x22992,x22993,x22994,x22995))
% 188.15/187.99 [2300]~E(x23001,x23002)+E(f415(x23003,x23001,x23004,x23005),f415(x23003,x23002,x23004,x23005))
% 188.15/187.99 [2301]~E(x23011,x23012)+E(f415(x23013,x23014,x23011,x23015),f415(x23013,x23014,x23012,x23015))
% 188.15/187.99 [2302]~E(x23021,x23022)+E(f415(x23023,x23024,x23025,x23021),f415(x23023,x23024,x23025,x23022))
% 188.15/187.99 [2303]~E(x23031,x23032)+E(f651(x23031,x23033,x23034,x23035),f651(x23032,x23033,x23034,x23035))
% 188.15/187.99 [2304]~E(x23041,x23042)+E(f651(x23043,x23041,x23044,x23045),f651(x23043,x23042,x23044,x23045))
% 188.15/187.99 [2305]~E(x23051,x23052)+E(f651(x23053,x23054,x23051,x23055),f651(x23053,x23054,x23052,x23055))
% 188.15/187.99 [2306]~E(x23061,x23062)+E(f651(x23063,x23064,x23065,x23061),f651(x23063,x23064,x23065,x23062))
% 188.15/187.99 [2307]~E(x23071,x23072)+E(f723(x23071,x23073,x23074),f723(x23072,x23073,x23074))
% 188.15/187.99 [2308]~E(x23081,x23082)+E(f723(x23083,x23081,x23084),f723(x23083,x23082,x23084))
% 188.15/187.99 [2309]~E(x23091,x23092)+E(f723(x23093,x23094,x23091),f723(x23093,x23094,x23092))
% 188.15/187.99 [2310]~E(x23101,x23102)+E(f797(x23101,x23103),f797(x23102,x23103))
% 188.15/187.99 [2311]~E(x23111,x23112)+E(f797(x23113,x23111),f797(x23113,x23112))
% 188.15/187.99 [2312]~E(x23121,x23122)+E(f429(x23121,x23123,x23124),f429(x23122,x23123,x23124))
% 188.15/187.99 [2313]~E(x23131,x23132)+E(f429(x23133,x23131,x23134),f429(x23133,x23132,x23134))
% 188.15/187.99 [2314]~E(x23141,x23142)+E(f429(x23143,x23144,x23141),f429(x23143,x23144,x23142))
% 188.15/187.99 [2315]~E(x23151,x23152)+E(f813(x23151,x23153,x23154,x23155,x23156,x23157),f813(x23152,x23153,x23154,x23155,x23156,x23157))
% 188.15/187.99 [2316]~E(x23161,x23162)+E(f813(x23163,x23161,x23164,x23165,x23166,x23167),f813(x23163,x23162,x23164,x23165,x23166,x23167))
% 188.15/187.99 [2317]~E(x23171,x23172)+E(f813(x23173,x23174,x23171,x23175,x23176,x23177),f813(x23173,x23174,x23172,x23175,x23176,x23177))
% 188.15/187.99 [2318]~E(x23181,x23182)+E(f813(x23183,x23184,x23185,x23181,x23186,x23187),f813(x23183,x23184,x23185,x23182,x23186,x23187))
% 188.15/187.99 [2319]~E(x23191,x23192)+E(f813(x23193,x23194,x23195,x23196,x23191,x23197),f813(x23193,x23194,x23195,x23196,x23192,x23197))
% 188.15/187.99 [2320]~E(x23201,x23202)+E(f813(x23203,x23204,x23205,x23206,x23207,x23201),f813(x23203,x23204,x23205,x23206,x23207,x23202))
% 188.15/187.99 [2321]~E(x23211,x23212)+E(f408(x23211,x23213,x23214,x23215),f408(x23212,x23213,x23214,x23215))
% 188.15/187.99 [2322]~E(x23221,x23222)+E(f408(x23223,x23221,x23224,x23225),f408(x23223,x23222,x23224,x23225))
% 188.15/187.99 [2323]~E(x23231,x23232)+E(f408(x23233,x23234,x23231,x23235),f408(x23233,x23234,x23232,x23235))
% 188.15/187.99 [2324]~E(x23241,x23242)+E(f408(x23243,x23244,x23245,x23241),f408(x23243,x23244,x23245,x23242))
% 188.15/187.99 [2325]~E(x23251,x23252)+E(f601(x23251,x23253,x23254),f601(x23252,x23253,x23254))
% 188.15/187.99 [2326]~E(x23261,x23262)+E(f601(x23263,x23261,x23264),f601(x23263,x23262,x23264))
% 188.15/187.99 [2327]~E(x23271,x23272)+E(f601(x23273,x23274,x23271),f601(x23273,x23274,x23272))
% 188.15/187.99 [2328]~E(x23281,x23282)+E(f572(x23281,x23283,x23284,x23285,x23286),f572(x23282,x23283,x23284,x23285,x23286))
% 188.15/187.99 [2329]~E(x23291,x23292)+E(f572(x23293,x23291,x23294,x23295,x23296),f572(x23293,x23292,x23294,x23295,x23296))
% 188.15/187.99 [2330]~E(x23301,x23302)+E(f572(x23303,x23304,x23301,x23305,x23306),f572(x23303,x23304,x23302,x23305,x23306))
% 188.15/187.99 [2331]~E(x23311,x23312)+E(f572(x23313,x23314,x23315,x23311,x23316),f572(x23313,x23314,x23315,x23312,x23316))
% 188.15/187.99 [2332]~E(x23321,x23322)+E(f572(x23323,x23324,x23325,x23326,x23321),f572(x23323,x23324,x23325,x23326,x23322))
% 188.15/187.99 [2333]~E(x23331,x23332)+E(f339(x23331,x23333,x23334),f339(x23332,x23333,x23334))
% 188.15/187.99 [2334]~E(x23341,x23342)+E(f339(x23343,x23341,x23344),f339(x23343,x23342,x23344))
% 188.15/187.99 [2335]~E(x23351,x23352)+E(f339(x23353,x23354,x23351),f339(x23353,x23354,x23352))
% 188.15/187.99 [2336]~E(x23361,x23362)+E(f274(x23361,x23363),f274(x23362,x23363))
% 188.15/187.99 [2337]~E(x23371,x23372)+E(f274(x23373,x23371),f274(x23373,x23372))
% 188.15/187.99 [2338]~E(x23381,x23382)+E(f626(x23381,x23383,x23384,x23385),f626(x23382,x23383,x23384,x23385))
% 188.15/187.99 [2339]~E(x23391,x23392)+E(f626(x23393,x23391,x23394,x23395),f626(x23393,x23392,x23394,x23395))
% 188.15/187.99 [2340]~E(x23401,x23402)+E(f626(x23403,x23404,x23401,x23405),f626(x23403,x23404,x23402,x23405))
% 188.15/187.99 [2341]~E(x23411,x23412)+E(f626(x23413,x23414,x23415,x23411),f626(x23413,x23414,x23415,x23412))
% 188.15/187.99 [2342]~E(x23421,x23422)+E(f604(x23421,x23423,x23424),f604(x23422,x23423,x23424))
% 188.15/187.99 [2343]~E(x23431,x23432)+E(f604(x23433,x23431,x23434),f604(x23433,x23432,x23434))
% 188.15/187.99 [2344]~E(x23441,x23442)+E(f604(x23443,x23444,x23441),f604(x23443,x23444,x23442))
% 188.15/187.99 [2345]~E(x23451,x23452)+E(f830(x23451,x23453,x23454),f830(x23452,x23453,x23454))
% 188.15/187.99 [2346]~E(x23461,x23462)+E(f830(x23463,x23461,x23464),f830(x23463,x23462,x23464))
% 188.15/187.99 [2347]~E(x23471,x23472)+E(f830(x23473,x23474,x23471),f830(x23473,x23474,x23472))
% 188.15/187.99 [2348]~E(x23481,x23482)+E(f773(x23481,x23483,x23484),f773(x23482,x23483,x23484))
% 188.15/187.99 [2349]~E(x23491,x23492)+E(f773(x23493,x23491,x23494),f773(x23493,x23492,x23494))
% 188.15/187.99 [2350]~E(x23501,x23502)+E(f773(x23503,x23504,x23501),f773(x23503,x23504,x23502))
% 188.15/187.99 [2351]~E(x23511,x23512)+E(f347(x23511,x23513),f347(x23512,x23513))
% 188.15/187.99 [2352]~E(x23521,x23522)+E(f347(x23523,x23521),f347(x23523,x23522))
% 188.15/187.99 [2353]~E(x23531,x23532)+E(f667(x23531,x23533,x23534),f667(x23532,x23533,x23534))
% 188.15/187.99 [2354]~E(x23541,x23542)+E(f667(x23543,x23541,x23544),f667(x23543,x23542,x23544))
% 188.15/187.99 [2355]~E(x23551,x23552)+E(f667(x23553,x23554,x23551),f667(x23553,x23554,x23552))
% 188.15/187.99 [2356]~E(x23561,x23562)+E(f763(x23561,x23563,x23564),f763(x23562,x23563,x23564))
% 188.15/187.99 [2357]~E(x23571,x23572)+E(f763(x23573,x23571,x23574),f763(x23573,x23572,x23574))
% 188.15/187.99 [2358]~E(x23581,x23582)+E(f763(x23583,x23584,x23581),f763(x23583,x23584,x23582))
% 188.15/187.99 [2359]~E(x23591,x23592)+E(f93(x23591,x23593,x23594),f93(x23592,x23593,x23594))
% 188.15/187.99 [2360]~E(x23601,x23602)+E(f93(x23603,x23601,x23604),f93(x23603,x23602,x23604))
% 188.15/187.99 [2361]~E(x23611,x23612)+E(f93(x23613,x23614,x23611),f93(x23613,x23614,x23612))
% 188.15/187.99 [2362]~E(x23621,x23622)+E(f518(x23621,x23623),f518(x23622,x23623))
% 188.15/187.99 [2363]~E(x23631,x23632)+E(f518(x23633,x23631),f518(x23633,x23632))
% 188.15/187.99 [2364]~E(x23641,x23642)+E(f771(x23641,x23643,x23644),f771(x23642,x23643,x23644))
% 188.15/187.99 [2365]~E(x23651,x23652)+E(f771(x23653,x23651,x23654),f771(x23653,x23652,x23654))
% 188.15/187.99 [2366]~E(x23661,x23662)+E(f771(x23663,x23664,x23661),f771(x23663,x23664,x23662))
% 188.15/187.99 [2367]~E(x23671,x23672)+E(f139(x23671,x23673),f139(x23672,x23673))
% 188.15/187.99 [2368]~E(x23681,x23682)+E(f139(x23683,x23681),f139(x23683,x23682))
% 188.15/187.99 [2369]~E(x23691,x23692)+E(f465(x23691,x23693,x23694),f465(x23692,x23693,x23694))
% 188.15/187.99 [2370]~E(x23701,x23702)+E(f465(x23703,x23701,x23704),f465(x23703,x23702,x23704))
% 188.15/187.99 [2371]~E(x23711,x23712)+E(f465(x23713,x23714,x23711),f465(x23713,x23714,x23712))
% 188.15/187.99 [2372]~E(x23721,x23722)+E(f365(x23721,x23723,x23724,x23725,x23726,x23727,x23728),f365(x23722,x23723,x23724,x23725,x23726,x23727,x23728))
% 188.15/187.99 [2373]~E(x23731,x23732)+E(f365(x23733,x23731,x23734,x23735,x23736,x23737,x23738),f365(x23733,x23732,x23734,x23735,x23736,x23737,x23738))
% 188.15/187.99 [2374]~E(x23741,x23742)+E(f365(x23743,x23744,x23741,x23745,x23746,x23747,x23748),f365(x23743,x23744,x23742,x23745,x23746,x23747,x23748))
% 188.15/187.99 [2375]~E(x23751,x23752)+E(f365(x23753,x23754,x23755,x23751,x23756,x23757,x23758),f365(x23753,x23754,x23755,x23752,x23756,x23757,x23758))
% 188.15/187.99 [2376]~E(x23761,x23762)+E(f365(x23763,x23764,x23765,x23766,x23761,x23767,x23768),f365(x23763,x23764,x23765,x23766,x23762,x23767,x23768))
% 188.15/187.99 [2377]~E(x23771,x23772)+E(f365(x23773,x23774,x23775,x23776,x23777,x23771,x23778),f365(x23773,x23774,x23775,x23776,x23777,x23772,x23778))
% 188.15/187.99 [2378]~E(x23781,x23782)+E(f365(x23783,x23784,x23785,x23786,x23787,x23788,x23781),f365(x23783,x23784,x23785,x23786,x23787,x23788,x23782))
% 188.15/187.99 [2379]~E(x23791,x23792)+E(f265(x23791,x23793,x23794,x23795,x23796),f265(x23792,x23793,x23794,x23795,x23796))
% 188.15/187.99 [2380]~E(x23801,x23802)+E(f265(x23803,x23801,x23804,x23805,x23806),f265(x23803,x23802,x23804,x23805,x23806))
% 188.15/187.99 [2381]~E(x23811,x23812)+E(f265(x23813,x23814,x23811,x23815,x23816),f265(x23813,x23814,x23812,x23815,x23816))
% 188.15/187.99 [2382]~E(x23821,x23822)+E(f265(x23823,x23824,x23825,x23821,x23826),f265(x23823,x23824,x23825,x23822,x23826))
% 188.15/187.99 [2383]~E(x23831,x23832)+E(f265(x23833,x23834,x23835,x23836,x23831),f265(x23833,x23834,x23835,x23836,x23832))
% 188.15/187.99 [2384]~E(x23841,x23842)+E(f630(x23841,x23843,x23844),f630(x23842,x23843,x23844))
% 188.15/187.99 [2385]~E(x23851,x23852)+E(f630(x23853,x23851,x23854),f630(x23853,x23852,x23854))
% 188.15/187.99 [2386]~E(x23861,x23862)+E(f630(x23863,x23864,x23861),f630(x23863,x23864,x23862))
% 188.15/187.99 [2387]~E(x23871,x23872)+E(f270(x23871,x23873),f270(x23872,x23873))
% 188.15/187.99 [2388]~E(x23881,x23882)+E(f270(x23883,x23881),f270(x23883,x23882))
% 188.15/187.99 [2389]~E(x23891,x23892)+E(f827(x23891,x23893),f827(x23892,x23893))
% 188.15/187.99 [2390]~E(x23901,x23902)+E(f827(x23903,x23901),f827(x23903,x23902))
% 188.15/187.99 [2391]~E(x23911,x23912)+E(f614(x23911,x23913,x23914),f614(x23912,x23913,x23914))
% 188.15/187.99 [2392]~E(x23921,x23922)+E(f614(x23923,x23921,x23924),f614(x23923,x23922,x23924))
% 188.15/187.99 [2393]~E(x23931,x23932)+E(f614(x23933,x23934,x23931),f614(x23933,x23934,x23932))
% 188.15/187.99 [2394]~E(x23941,x23942)+E(f95(x23941,x23943,x23944,x23945),f95(x23942,x23943,x23944,x23945))
% 188.15/187.99 [2395]~E(x23951,x23952)+E(f95(x23953,x23951,x23954,x23955),f95(x23953,x23952,x23954,x23955))
% 188.15/187.99 [2396]~E(x23961,x23962)+E(f95(x23963,x23964,x23961,x23965),f95(x23963,x23964,x23962,x23965))
% 188.15/187.99 [2397]~E(x23971,x23972)+E(f95(x23973,x23974,x23975,x23971),f95(x23973,x23974,x23975,x23972))
% 188.15/187.99 [2398]~E(x23981,x23982)+E(f683(x23981,x23983),f683(x23982,x23983))
% 188.15/187.99 [2399]~E(x23991,x23992)+E(f683(x23993,x23991),f683(x23993,x23992))
% 188.15/187.99 [2400]~E(x24001,x24002)+E(f423(x24001),f423(x24002))
% 188.15/187.99 [2401]~E(x24011,x24012)+E(f650(x24011,x24013),f650(x24012,x24013))
% 188.15/187.99 [2402]~E(x24021,x24022)+E(f650(x24023,x24021),f650(x24023,x24022))
% 188.15/187.99 [2403]~E(x24031,x24032)+E(f486(x24031,x24033,x24034,x24035),f486(x24032,x24033,x24034,x24035))
% 188.15/187.99 [2404]~E(x24041,x24042)+E(f486(x24043,x24041,x24044,x24045),f486(x24043,x24042,x24044,x24045))
% 188.15/187.99 [2405]~E(x24051,x24052)+E(f486(x24053,x24054,x24051,x24055),f486(x24053,x24054,x24052,x24055))
% 188.15/187.99 [2406]~E(x24061,x24062)+E(f486(x24063,x24064,x24065,x24061),f486(x24063,x24064,x24065,x24062))
% 188.15/187.99 [2407]~E(x24071,x24072)+E(f307(x24071,x24073,x24074),f307(x24072,x24073,x24074))
% 188.15/187.99 [2408]~E(x24081,x24082)+E(f307(x24083,x24081,x24084),f307(x24083,x24082,x24084))
% 188.15/187.99 [2409]~E(x24091,x24092)+E(f307(x24093,x24094,x24091),f307(x24093,x24094,x24092))
% 188.15/187.99 [2410]~E(x24101,x24102)+E(f637(x24101,x24103,x24104,x24105),f637(x24102,x24103,x24104,x24105))
% 188.15/187.99 [2411]~E(x24111,x24112)+E(f637(x24113,x24111,x24114,x24115),f637(x24113,x24112,x24114,x24115))
% 188.15/187.99 [2412]~E(x24121,x24122)+E(f637(x24123,x24124,x24121,x24125),f637(x24123,x24124,x24122,x24125))
% 188.15/187.99 [2413]~E(x24131,x24132)+E(f637(x24133,x24134,x24135,x24131),f637(x24133,x24134,x24135,x24132))
% 188.15/187.99 [2414]~E(x24141,x24142)+E(f544(x24141,x24143,x24144,x24145),f544(x24142,x24143,x24144,x24145))
% 188.15/187.99 [2415]~E(x24151,x24152)+E(f544(x24153,x24151,x24154,x24155),f544(x24153,x24152,x24154,x24155))
% 188.15/187.99 [2416]~E(x24161,x24162)+E(f544(x24163,x24164,x24161,x24165),f544(x24163,x24164,x24162,x24165))
% 188.15/187.99 [2417]~E(x24171,x24172)+E(f544(x24173,x24174,x24175,x24171),f544(x24173,x24174,x24175,x24172))
% 188.15/187.99 [2418]~E(x24181,x24182)+E(f447(x24181,x24183,x24184,x24185,x24186),f447(x24182,x24183,x24184,x24185,x24186))
% 188.15/187.99 [2419]~E(x24191,x24192)+E(f447(x24193,x24191,x24194,x24195,x24196),f447(x24193,x24192,x24194,x24195,x24196))
% 188.15/187.99 [2420]~E(x24201,x24202)+E(f447(x24203,x24204,x24201,x24205,x24206),f447(x24203,x24204,x24202,x24205,x24206))
% 188.15/187.99 [2421]~E(x24211,x24212)+E(f447(x24213,x24214,x24215,x24211,x24216),f447(x24213,x24214,x24215,x24212,x24216))
% 188.15/187.99 [2422]~E(x24221,x24222)+E(f447(x24223,x24224,x24225,x24226,x24221),f447(x24223,x24224,x24225,x24226,x24222))
% 188.15/187.99 [2423]~E(x24231,x24232)+E(f448(x24231,x24233,x24234,x24235,x24236),f448(x24232,x24233,x24234,x24235,x24236))
% 188.15/187.99 [2424]~E(x24241,x24242)+E(f448(x24243,x24241,x24244,x24245,x24246),f448(x24243,x24242,x24244,x24245,x24246))
% 188.15/187.99 [2425]~E(x24251,x24252)+E(f448(x24253,x24254,x24251,x24255,x24256),f448(x24253,x24254,x24252,x24255,x24256))
% 188.15/187.99 [2426]~E(x24261,x24262)+E(f448(x24263,x24264,x24265,x24261,x24266),f448(x24263,x24264,x24265,x24262,x24266))
% 188.15/187.99 [2427]~E(x24271,x24272)+E(f448(x24273,x24274,x24275,x24276,x24271),f448(x24273,x24274,x24275,x24276,x24272))
% 188.15/187.99 [2428]~E(x24281,x24282)+E(f577(x24281,x24283,x24284,x24285,x24286),f577(x24282,x24283,x24284,x24285,x24286))
% 188.15/187.99 [2429]~E(x24291,x24292)+E(f577(x24293,x24291,x24294,x24295,x24296),f577(x24293,x24292,x24294,x24295,x24296))
% 188.15/187.99 [2430]~E(x24301,x24302)+E(f577(x24303,x24304,x24301,x24305,x24306),f577(x24303,x24304,x24302,x24305,x24306))
% 188.15/187.99 [2431]~E(x24311,x24312)+E(f577(x24313,x24314,x24315,x24311,x24316),f577(x24313,x24314,x24315,x24312,x24316))
% 188.15/187.99 [2432]~E(x24321,x24322)+E(f577(x24323,x24324,x24325,x24326,x24321),f577(x24323,x24324,x24325,x24326,x24322))
% 188.15/187.99 [2433]~E(x24331,x24332)+E(f306(x24331,x24333,x24334),f306(x24332,x24333,x24334))
% 188.15/187.99 [2434]~E(x24341,x24342)+E(f306(x24343,x24341,x24344),f306(x24343,x24342,x24344))
% 188.15/187.99 [2435]~E(x24351,x24352)+E(f306(x24353,x24354,x24351),f306(x24353,x24354,x24352))
% 188.15/187.99 [2436]~E(x24361,x24362)+E(f119(x24361,x24363,x24364,x24365),f119(x24362,x24363,x24364,x24365))
% 188.15/187.99 [2437]~E(x24371,x24372)+E(f119(x24373,x24371,x24374,x24375),f119(x24373,x24372,x24374,x24375))
% 188.15/187.99 [2438]~E(x24381,x24382)+E(f119(x24383,x24384,x24381,x24385),f119(x24383,x24384,x24382,x24385))
% 188.15/187.99 [2439]~E(x24391,x24392)+E(f119(x24393,x24394,x24395,x24391),f119(x24393,x24394,x24395,x24392))
% 188.15/187.99 [2440]~E(x24401,x24402)+E(f592(x24401,x24403,x24404,x24405),f592(x24402,x24403,x24404,x24405))
% 188.15/187.99 [2441]~E(x24411,x24412)+E(f592(x24413,x24411,x24414,x24415),f592(x24413,x24412,x24414,x24415))
% 188.15/187.99 [2442]~E(x24421,x24422)+E(f592(x24423,x24424,x24421,x24425),f592(x24423,x24424,x24422,x24425))
% 188.15/187.99 [2443]~E(x24431,x24432)+E(f592(x24433,x24434,x24435,x24431),f592(x24433,x24434,x24435,x24432))
% 188.15/187.99 [2444]~E(x24441,x24442)+E(f397(x24441,x24443,x24444,x24445),f397(x24442,x24443,x24444,x24445))
% 188.15/187.99 [2445]~E(x24451,x24452)+E(f397(x24453,x24451,x24454,x24455),f397(x24453,x24452,x24454,x24455))
% 188.15/187.99 [2446]~E(x24461,x24462)+E(f397(x24463,x24464,x24461,x24465),f397(x24463,x24464,x24462,x24465))
% 188.15/187.99 [2447]~E(x24471,x24472)+E(f397(x24473,x24474,x24475,x24471),f397(x24473,x24474,x24475,x24472))
% 188.15/187.99 [2448]~E(x24481,x24482)+E(f713(x24481,x24483,x24484,x24485,x24486),f713(x24482,x24483,x24484,x24485,x24486))
% 188.15/187.99 [2449]~E(x24491,x24492)+E(f713(x24493,x24491,x24494,x24495,x24496),f713(x24493,x24492,x24494,x24495,x24496))
% 188.15/187.99 [2450]~E(x24501,x24502)+E(f713(x24503,x24504,x24501,x24505,x24506),f713(x24503,x24504,x24502,x24505,x24506))
% 188.15/187.99 [2451]~E(x24511,x24512)+E(f713(x24513,x24514,x24515,x24511,x24516),f713(x24513,x24514,x24515,x24512,x24516))
% 188.15/187.99 [2452]~E(x24521,x24522)+E(f713(x24523,x24524,x24525,x24526,x24521),f713(x24523,x24524,x24525,x24526,x24522))
% 188.15/187.99 [2453]~E(x24531,x24532)+E(f472(x24531,x24533,x24534,x24535,x24536),f472(x24532,x24533,x24534,x24535,x24536))
% 188.15/187.99 [2454]~E(x24541,x24542)+E(f472(x24543,x24541,x24544,x24545,x24546),f472(x24543,x24542,x24544,x24545,x24546))
% 188.15/187.99 [2455]~E(x24551,x24552)+E(f472(x24553,x24554,x24551,x24555,x24556),f472(x24553,x24554,x24552,x24555,x24556))
% 188.15/187.99 [2456]~E(x24561,x24562)+E(f472(x24563,x24564,x24565,x24561,x24566),f472(x24563,x24564,x24565,x24562,x24566))
% 188.15/187.99 [2457]~E(x24571,x24572)+E(f472(x24573,x24574,x24575,x24576,x24571),f472(x24573,x24574,x24575,x24576,x24572))
% 188.15/187.99 [2458]~E(x24581,x24582)+E(f412(x24581,x24583,x24584,x24585),f412(x24582,x24583,x24584,x24585))
% 188.15/187.99 [2459]~E(x24591,x24592)+E(f412(x24593,x24591,x24594,x24595),f412(x24593,x24592,x24594,x24595))
% 188.15/187.99 [2460]~E(x24601,x24602)+E(f412(x24603,x24604,x24601,x24605),f412(x24603,x24604,x24602,x24605))
% 188.15/187.99 [2461]~E(x24611,x24612)+E(f412(x24613,x24614,x24615,x24611),f412(x24613,x24614,x24615,x24612))
% 188.15/187.99 [2462]~E(x24621,x24622)+E(f17(x24621,x24623,x24624,x24625),f17(x24622,x24623,x24624,x24625))
% 188.15/187.99 [2463]~E(x24631,x24632)+E(f17(x24633,x24631,x24634,x24635),f17(x24633,x24632,x24634,x24635))
% 188.15/187.99 [2464]~E(x24641,x24642)+E(f17(x24643,x24644,x24641,x24645),f17(x24643,x24644,x24642,x24645))
% 188.15/187.99 [2465]~E(x24651,x24652)+E(f17(x24653,x24654,x24655,x24651),f17(x24653,x24654,x24655,x24652))
% 188.15/187.99 [2466]~E(x24661,x24662)+E(f560(x24661,x24663,x24664,x24665,x24666),f560(x24662,x24663,x24664,x24665,x24666))
% 188.15/187.99 [2467]~E(x24671,x24672)+E(f560(x24673,x24671,x24674,x24675,x24676),f560(x24673,x24672,x24674,x24675,x24676))
% 188.15/187.99 [2468]~E(x24681,x24682)+E(f560(x24683,x24684,x24681,x24685,x24686),f560(x24683,x24684,x24682,x24685,x24686))
% 188.15/187.99 [2469]~E(x24691,x24692)+E(f560(x24693,x24694,x24695,x24691,x24696),f560(x24693,x24694,x24695,x24692,x24696))
% 188.15/187.99 [2470]~E(x24701,x24702)+E(f560(x24703,x24704,x24705,x24706,x24701),f560(x24703,x24704,x24705,x24706,x24702))
% 188.15/187.99 [2471]~E(x24711,x24712)+E(f283(x24711,x24713),f283(x24712,x24713))
% 188.15/187.99 [2472]~E(x24721,x24722)+E(f283(x24723,x24721),f283(x24723,x24722))
% 188.15/187.99 [2473]~E(x24731,x24732)+E(f828(x24731,x24733,x24734),f828(x24732,x24733,x24734))
% 188.15/187.99 [2474]~E(x24741,x24742)+E(f828(x24743,x24741,x24744),f828(x24743,x24742,x24744))
% 188.15/187.99 [2475]~E(x24751,x24752)+E(f828(x24753,x24754,x24751),f828(x24753,x24754,x24752))
% 188.15/187.99 [2476]~E(x24761,x24762)+E(f467(x24761,x24763),f467(x24762,x24763))
% 188.15/187.99 [2477]~E(x24771,x24772)+E(f467(x24773,x24771),f467(x24773,x24772))
% 188.15/187.99 [2478]~E(x24781,x24782)+E(f399(x24781,x24783,x24784,x24785),f399(x24782,x24783,x24784,x24785))
% 188.15/187.99 [2479]~E(x24791,x24792)+E(f399(x24793,x24791,x24794,x24795),f399(x24793,x24792,x24794,x24795))
% 188.15/187.99 [2480]~E(x24801,x24802)+E(f399(x24803,x24804,x24801,x24805),f399(x24803,x24804,x24802,x24805))
% 188.15/187.99 [2481]~E(x24811,x24812)+E(f399(x24813,x24814,x24815,x24811),f399(x24813,x24814,x24815,x24812))
% 188.15/187.99 [2482]~E(x24821,x24822)+E(f459(x24821,x24823,x24824),f459(x24822,x24823,x24824))
% 188.15/187.99 [2483]~E(x24831,x24832)+E(f459(x24833,x24831,x24834),f459(x24833,x24832,x24834))
% 188.15/187.99 [2484]~E(x24841,x24842)+E(f459(x24843,x24844,x24841),f459(x24843,x24844,x24842))
% 188.15/187.99 [2485]~E(x24851,x24852)+E(f327(x24851,x24853,x24854,x24855),f327(x24852,x24853,x24854,x24855))
% 188.15/187.99 [2486]~E(x24861,x24862)+E(f327(x24863,x24861,x24864,x24865),f327(x24863,x24862,x24864,x24865))
% 188.15/187.99 [2487]~E(x24871,x24872)+E(f327(x24873,x24874,x24871,x24875),f327(x24873,x24874,x24872,x24875))
% 188.15/187.99 [2488]~E(x24881,x24882)+E(f327(x24883,x24884,x24885,x24881),f327(x24883,x24884,x24885,x24882))
% 188.15/187.99 [2489]~E(x24891,x24892)+E(f562(x24891,x24893),f562(x24892,x24893))
% 188.15/187.99 [2490]~E(x24901,x24902)+E(f562(x24903,x24901),f562(x24903,x24902))
% 188.15/187.99 [2491]~E(x24911,x24912)+E(f391(x24911,x24913,x24914),f391(x24912,x24913,x24914))
% 188.15/187.99 [2492]~E(x24921,x24922)+E(f391(x24923,x24921,x24924),f391(x24923,x24922,x24924))
% 188.15/187.99 [2493]~E(x24931,x24932)+E(f391(x24933,x24934,x24931),f391(x24933,x24934,x24932))
% 188.15/187.99 [2494]~E(x24941,x24942)+E(f284(x24941,x24943,x24944),f284(x24942,x24943,x24944))
% 188.15/187.99 [2495]~E(x24951,x24952)+E(f284(x24953,x24951,x24954),f284(x24953,x24952,x24954))
% 188.15/187.99 [2496]~E(x24961,x24962)+E(f284(x24963,x24964,x24961),f284(x24963,x24964,x24962))
% 188.15/187.99 [2497]~E(x24971,x24972)+E(f659(x24971,x24973),f659(x24972,x24973))
% 188.15/187.99 [2498]~E(x24981,x24982)+E(f659(x24983,x24981),f659(x24983,x24982))
% 188.15/187.99 [2499]~E(x24991,x24992)+E(f563(x24991,x24993),f563(x24992,x24993))
% 188.15/187.99 [2500]~E(x25001,x25002)+E(f563(x25003,x25001),f563(x25003,x25002))
% 188.15/187.99 [2501]~E(x25011,x25012)+E(f422(x25011),f422(x25012))
% 188.15/187.99 [2502]~E(x25021,x25022)+E(f741(x25021,x25023,x25024),f741(x25022,x25023,x25024))
% 188.15/187.99 [2503]~E(x25031,x25032)+E(f741(x25033,x25031,x25034),f741(x25033,x25032,x25034))
% 188.15/187.99 [2504]~E(x25041,x25042)+E(f741(x25043,x25044,x25041),f741(x25043,x25044,x25042))
% 188.15/187.99 [2505]~E(x25051,x25052)+E(f818(x25051),f818(x25052))
% 188.15/187.99 [2506]~E(x25061,x25062)+E(f639(x25061,x25063,x25064,x25065,x25066),f639(x25062,x25063,x25064,x25065,x25066))
% 188.15/187.99 [2507]~E(x25071,x25072)+E(f639(x25073,x25071,x25074,x25075,x25076),f639(x25073,x25072,x25074,x25075,x25076))
% 188.15/187.99 [2508]~E(x25081,x25082)+E(f639(x25083,x25084,x25081,x25085,x25086),f639(x25083,x25084,x25082,x25085,x25086))
% 188.15/187.99 [2509]~E(x25091,x25092)+E(f639(x25093,x25094,x25095,x25091,x25096),f639(x25093,x25094,x25095,x25092,x25096))
% 188.15/187.99 [2510]~E(x25101,x25102)+E(f639(x25103,x25104,x25105,x25106,x25101),f639(x25103,x25104,x25105,x25106,x25102))
% 188.15/187.99 [2511]~E(x25111,x25112)+E(f692(x25111,x25113,x25114),f692(x25112,x25113,x25114))
% 188.15/187.99 [2512]~E(x25121,x25122)+E(f692(x25123,x25121,x25124),f692(x25123,x25122,x25124))
% 188.15/187.99 [2513]~E(x25131,x25132)+E(f692(x25133,x25134,x25131),f692(x25133,x25134,x25132))
% 188.15/187.99 [2514]~E(x25141,x25142)+E(f761(x25141,x25143,x25144),f761(x25142,x25143,x25144))
% 188.15/187.99 [2515]~E(x25151,x25152)+E(f761(x25153,x25151,x25154),f761(x25153,x25152,x25154))
% 188.15/187.99 [2516]~E(x25161,x25162)+E(f761(x25163,x25164,x25161),f761(x25163,x25164,x25162))
% 188.15/187.99 [2517]~E(x25171,x25172)+E(f720(x25171,x25173,x25174),f720(x25172,x25173,x25174))
% 188.15/187.99 [2518]~E(x25181,x25182)+E(f720(x25183,x25181,x25184),f720(x25183,x25182,x25184))
% 188.15/187.99 [2519]~E(x25191,x25192)+E(f720(x25193,x25194,x25191),f720(x25193,x25194,x25192))
% 188.15/187.99 [2520]~E(x25201,x25202)+E(f628(x25201,x25203,x25204,x25205),f628(x25202,x25203,x25204,x25205))
% 188.15/187.99 [2521]~E(x25211,x25212)+E(f628(x25213,x25211,x25214,x25215),f628(x25213,x25212,x25214,x25215))
% 188.15/187.99 [2522]~E(x25221,x25222)+E(f628(x25223,x25224,x25221,x25225),f628(x25223,x25224,x25222,x25225))
% 188.15/187.99 [2523]~E(x25231,x25232)+E(f628(x25233,x25234,x25235,x25231),f628(x25233,x25234,x25235,x25232))
% 188.15/187.99 [2524]~E(x25241,x25242)+E(f606(x25241,x25243,x25244),f606(x25242,x25243,x25244))
% 188.15/187.99 [2525]~E(x25251,x25252)+E(f606(x25253,x25251,x25254),f606(x25253,x25252,x25254))
% 188.15/187.99 [2526]~E(x25261,x25262)+E(f606(x25263,x25264,x25261),f606(x25263,x25264,x25262))
% 188.15/187.99 [2527]~E(x25271,x25272)+E(f535(x25271,x25273,x25274,x25275,x25276),f535(x25272,x25273,x25274,x25275,x25276))
% 188.15/187.99 [2528]~E(x25281,x25282)+E(f535(x25283,x25281,x25284,x25285,x25286),f535(x25283,x25282,x25284,x25285,x25286))
% 188.15/187.99 [2529]~E(x25291,x25292)+E(f535(x25293,x25294,x25291,x25295,x25296),f535(x25293,x25294,x25292,x25295,x25296))
% 188.15/187.99 [2530]~E(x25301,x25302)+E(f535(x25303,x25304,x25305,x25301,x25306),f535(x25303,x25304,x25305,x25302,x25306))
% 188.15/187.99 [2531]~E(x25311,x25312)+E(f535(x25313,x25314,x25315,x25316,x25311),f535(x25313,x25314,x25315,x25316,x25312))
% 188.15/187.99 [2532]~E(x25321,x25322)+E(f224(x25321,x25323,x25324,x25325),f224(x25322,x25323,x25324,x25325))
% 188.15/187.99 [2533]~E(x25331,x25332)+E(f224(x25333,x25331,x25334,x25335),f224(x25333,x25332,x25334,x25335))
% 188.15/187.99 [2534]~E(x25341,x25342)+E(f224(x25343,x25344,x25341,x25345),f224(x25343,x25344,x25342,x25345))
% 188.15/187.99 [2535]~E(x25351,x25352)+E(f224(x25353,x25354,x25355,x25351),f224(x25353,x25354,x25355,x25352))
% 188.15/187.99 [2536]~E(x25361,x25362)+E(f329(x25361),f329(x25362))
% 188.15/187.99 [2537]~E(x25371,x25372)+E(f730(x25371,x25373,x25374,x25375,x25376),f730(x25372,x25373,x25374,x25375,x25376))
% 188.15/187.99 [2538]~E(x25381,x25382)+E(f730(x25383,x25381,x25384,x25385,x25386),f730(x25383,x25382,x25384,x25385,x25386))
% 188.15/187.99 [2539]~E(x25391,x25392)+E(f730(x25393,x25394,x25391,x25395,x25396),f730(x25393,x25394,x25392,x25395,x25396))
% 188.15/187.99 [2540]~E(x25401,x25402)+E(f730(x25403,x25404,x25405,x25401,x25406),f730(x25403,x25404,x25405,x25402,x25406))
% 188.15/187.99 [2541]~E(x25411,x25412)+E(f730(x25413,x25414,x25415,x25416,x25411),f730(x25413,x25414,x25415,x25416,x25412))
% 188.15/187.99 [2542]~E(x25421,x25422)+E(f494(x25421,x25423,x25424),f494(x25422,x25423,x25424))
% 188.15/187.99 [2543]~E(x25431,x25432)+E(f494(x25433,x25431,x25434),f494(x25433,x25432,x25434))
% 188.15/187.99 [2544]~E(x25441,x25442)+E(f494(x25443,x25444,x25441),f494(x25443,x25444,x25442))
% 188.15/187.99 [2545]~E(x25451,x25452)+E(f578(x25451,x25453,x25454,x25455,x25456),f578(x25452,x25453,x25454,x25455,x25456))
% 188.15/187.99 [2546]~E(x25461,x25462)+E(f578(x25463,x25461,x25464,x25465,x25466),f578(x25463,x25462,x25464,x25465,x25466))
% 188.15/187.99 [2547]~E(x25471,x25472)+E(f578(x25473,x25474,x25471,x25475,x25476),f578(x25473,x25474,x25472,x25475,x25476))
% 188.15/187.99 [2548]~E(x25481,x25482)+E(f578(x25483,x25484,x25485,x25481,x25486),f578(x25483,x25484,x25485,x25482,x25486))
% 188.15/187.99 [2549]~E(x25491,x25492)+E(f578(x25493,x25494,x25495,x25496,x25491),f578(x25493,x25494,x25495,x25496,x25492))
% 188.15/187.99 [2550]~E(x25501,x25502)+E(f440(x25501,x25503),f440(x25502,x25503))
% 188.15/187.99 [2551]~E(x25511,x25512)+E(f440(x25513,x25511),f440(x25513,x25512))
% 188.15/187.99 [2552]~E(x25521,x25522)+E(f530(x25521),f530(x25522))
% 188.15/187.99 [2553]~E(x25531,x25532)+E(f829(x25531,x25533,x25534),f829(x25532,x25533,x25534))
% 188.15/187.99 [2554]~E(x25541,x25542)+E(f829(x25543,x25541,x25544),f829(x25543,x25542,x25544))
% 188.15/187.99 [2555]~E(x25551,x25552)+E(f829(x25553,x25554,x25551),f829(x25553,x25554,x25552))
% 188.15/187.99 [2556]~E(x25561,x25562)+E(f454(x25561,x25563,x25564,x25565),f454(x25562,x25563,x25564,x25565))
% 188.15/187.99 [2557]~E(x25571,x25572)+E(f454(x25573,x25571,x25574,x25575),f454(x25573,x25572,x25574,x25575))
% 188.15/187.99 [2558]~E(x25581,x25582)+E(f454(x25583,x25584,x25581,x25585),f454(x25583,x25584,x25582,x25585))
% 188.15/187.99 [2559]~E(x25591,x25592)+E(f454(x25593,x25594,x25595,x25591),f454(x25593,x25594,x25595,x25592))
% 188.15/187.99 [2560]~E(x25601,x25602)+E(f737(x25601,x25603,x25604),f737(x25602,x25603,x25604))
% 188.15/187.99 [2561]~E(x25611,x25612)+E(f737(x25613,x25611,x25614),f737(x25613,x25612,x25614))
% 188.15/187.99 [2562]~E(x25621,x25622)+E(f737(x25623,x25624,x25621),f737(x25623,x25624,x25622))
% 188.15/187.99 [2563]~E(x25631,x25632)+E(f663(x25631,x25633,x25634,x25635),f663(x25632,x25633,x25634,x25635))
% 188.15/187.99 [2564]~E(x25641,x25642)+E(f663(x25643,x25641,x25644,x25645),f663(x25643,x25642,x25644,x25645))
% 188.15/187.99 [2565]~E(x25651,x25652)+E(f663(x25653,x25654,x25651,x25655),f663(x25653,x25654,x25652,x25655))
% 188.15/187.99 [2566]~E(x25661,x25662)+E(f663(x25663,x25664,x25665,x25661),f663(x25663,x25664,x25665,x25662))
% 188.15/187.99 [2567]~E(x25671,x25672)+E(f587(x25671,x25673,x25674,x25675,x25676),f587(x25672,x25673,x25674,x25675,x25676))
% 188.15/187.99 [2568]~E(x25681,x25682)+E(f587(x25683,x25681,x25684,x25685,x25686),f587(x25683,x25682,x25684,x25685,x25686))
% 188.15/187.99 [2569]~E(x25691,x25692)+E(f587(x25693,x25694,x25691,x25695,x25696),f587(x25693,x25694,x25692,x25695,x25696))
% 188.15/187.99 [2570]~E(x25701,x25702)+E(f587(x25703,x25704,x25705,x25701,x25706),f587(x25703,x25704,x25705,x25702,x25706))
% 188.15/187.99 [2571]~E(x25711,x25712)+E(f587(x25713,x25714,x25715,x25716,x25711),f587(x25713,x25714,x25715,x25716,x25712))
% 188.15/187.99 [2572]~E(x25721,x25722)+E(f501(x25721,x25723,x25724),f501(x25722,x25723,x25724))
% 188.15/187.99 [2573]~E(x25731,x25732)+E(f501(x25733,x25731,x25734),f501(x25733,x25732,x25734))
% 188.15/187.99 [2574]~E(x25741,x25742)+E(f501(x25743,x25744,x25741),f501(x25743,x25744,x25742))
% 188.15/187.99 [2575]~E(x25751,x25752)+E(f596(x25751,x25753,x25754,x25755),f596(x25752,x25753,x25754,x25755))
% 188.15/187.99 [2576]~E(x25761,x25762)+E(f596(x25763,x25761,x25764,x25765),f596(x25763,x25762,x25764,x25765))
% 188.15/187.99 [2577]~E(x25771,x25772)+E(f596(x25773,x25774,x25771,x25775),f596(x25773,x25774,x25772,x25775))
% 188.15/187.99 [2578]~E(x25781,x25782)+E(f596(x25783,x25784,x25785,x25781),f596(x25783,x25784,x25785,x25782))
% 188.15/187.99 [2579]~E(x25791,x25792)+E(f462(x25791,x25793,x25794,x25795),f462(x25792,x25793,x25794,x25795))
% 188.15/187.99 [2580]~E(x25801,x25802)+E(f462(x25803,x25801,x25804,x25805),f462(x25803,x25802,x25804,x25805))
% 188.15/187.99 [2581]~E(x25811,x25812)+E(f462(x25813,x25814,x25811,x25815),f462(x25813,x25814,x25812,x25815))
% 188.15/187.99 [2582]~E(x25821,x25822)+E(f462(x25823,x25824,x25825,x25821),f462(x25823,x25824,x25825,x25822))
% 188.15/187.99 [2583]~E(x25831,x25832)+E(f599(x25831,x25833,x25834),f599(x25832,x25833,x25834))
% 188.15/187.99 [2584]~E(x25841,x25842)+E(f599(x25843,x25841,x25844),f599(x25843,x25842,x25844))
% 188.15/187.99 [2585]~E(x25851,x25852)+E(f599(x25853,x25854,x25851),f599(x25853,x25854,x25852))
% 188.15/187.99 [2586]~E(x25861,x25862)+E(f209(x25861,x25863,x25864,x25865,x25866,x25867,x25868),f209(x25862,x25863,x25864,x25865,x25866,x25867,x25868))
% 188.15/187.99 [2587]~E(x25871,x25872)+E(f209(x25873,x25871,x25874,x25875,x25876,x25877,x25878),f209(x25873,x25872,x25874,x25875,x25876,x25877,x25878))
% 188.15/187.99 [2588]~E(x25881,x25882)+E(f209(x25883,x25884,x25881,x25885,x25886,x25887,x25888),f209(x25883,x25884,x25882,x25885,x25886,x25887,x25888))
% 188.15/187.99 [2589]~E(x25891,x25892)+E(f209(x25893,x25894,x25895,x25891,x25896,x25897,x25898),f209(x25893,x25894,x25895,x25892,x25896,x25897,x25898))
% 188.15/187.99 [2590]~E(x25901,x25902)+E(f209(x25903,x25904,x25905,x25906,x25901,x25907,x25908),f209(x25903,x25904,x25905,x25906,x25902,x25907,x25908))
% 188.15/187.99 [2591]~E(x25911,x25912)+E(f209(x25913,x25914,x25915,x25916,x25917,x25911,x25918),f209(x25913,x25914,x25915,x25916,x25917,x25912,x25918))
% 188.15/187.99 [2592]~E(x25921,x25922)+E(f209(x25923,x25924,x25925,x25926,x25927,x25928,x25921),f209(x25923,x25924,x25925,x25926,x25927,x25928,x25922))
% 188.15/187.99 [2593]~E(x25931,x25932)+E(f660(x25931,x25933),f660(x25932,x25933))
% 188.15/187.99 [2594]~E(x25941,x25942)+E(f660(x25943,x25941),f660(x25943,x25942))
% 188.15/187.99 [2595]~E(x25951,x25952)+E(f852(x25951,x25953,x25954,x25955,x25956,x25957,x25958),f852(x25952,x25953,x25954,x25955,x25956,x25957,x25958))
% 188.15/187.99 [2596]~E(x25961,x25962)+E(f852(x25963,x25961,x25964,x25965,x25966,x25967,x25968),f852(x25963,x25962,x25964,x25965,x25966,x25967,x25968))
% 188.15/187.99 [2597]~E(x25971,x25972)+E(f852(x25973,x25974,x25971,x25975,x25976,x25977,x25978),f852(x25973,x25974,x25972,x25975,x25976,x25977,x25978))
% 188.15/187.99 [2598]~E(x25981,x25982)+E(f852(x25983,x25984,x25985,x25981,x25986,x25987,x25988),f852(x25983,x25984,x25985,x25982,x25986,x25987,x25988))
% 188.15/187.99 [2599]~E(x25991,x25992)+E(f852(x25993,x25994,x25995,x25996,x25991,x25997,x25998),f852(x25993,x25994,x25995,x25996,x25992,x25997,x25998))
% 188.15/187.99 [2600]~E(x26001,x26002)+E(f852(x26003,x26004,x26005,x26006,x26007,x26001,x26008),f852(x26003,x26004,x26005,x26006,x26007,x26002,x26008))
% 188.15/187.99 [2601]~E(x26011,x26012)+E(f852(x26013,x26014,x26015,x26016,x26017,x26018,x26011),f852(x26013,x26014,x26015,x26016,x26017,x26018,x26012))
% 188.15/187.99 [2602]~E(x26021,x26022)+E(f823(x26021,x26023,x26024),f823(x26022,x26023,x26024))
% 188.15/187.99 [2603]~E(x26031,x26032)+E(f823(x26033,x26031,x26034),f823(x26033,x26032,x26034))
% 188.15/187.99 [2604]~E(x26041,x26042)+E(f823(x26043,x26044,x26041),f823(x26043,x26044,x26042))
% 188.15/187.99 [2605]~E(x26051,x26052)+E(f691(x26051,x26053),f691(x26052,x26053))
% 188.15/187.99 [2606]~E(x26061,x26062)+E(f691(x26063,x26061),f691(x26063,x26062))
% 188.15/187.99 [2607]~E(x26071,x26072)+E(f680(x26071,x26073,x26074,x26075),f680(x26072,x26073,x26074,x26075))
% 188.15/187.99 [2608]~E(x26081,x26082)+E(f680(x26083,x26081,x26084,x26085),f680(x26083,x26082,x26084,x26085))
% 188.15/187.99 [2609]~E(x26091,x26092)+E(f680(x26093,x26094,x26091,x26095),f680(x26093,x26094,x26092,x26095))
% 188.15/187.99 [2610]~E(x26101,x26102)+E(f680(x26103,x26104,x26105,x26101),f680(x26103,x26104,x26105,x26102))
% 188.15/187.99 [2611]~E(x26111,x26112)+E(f703(x26111,x26113),f703(x26112,x26113))
% 188.15/187.99 [2612]~E(x26121,x26122)+E(f703(x26123,x26121),f703(x26123,x26122))
% 188.15/187.99 [2613]~E(x26131,x26132)+E(f468(x26131,x26133),f468(x26132,x26133))
% 188.15/187.99 [2614]~E(x26141,x26142)+E(f468(x26143,x26141),f468(x26143,x26142))
% 188.15/187.99 [2615]~P1(x26151)+P1(x26152)+~E(x26151,x26152)
% 188.15/187.99 [2616]~P101(x26161)+P101(x26162)+~E(x26161,x26162)
% 188.15/187.99 [2617]P26(x26172,x26173,x26174)+~E(x26171,x26172)+~P26(x26171,x26173,x26174)
% 188.15/187.99 [2618]P26(x26183,x26182,x26184)+~E(x26181,x26182)+~P26(x26183,x26181,x26184)
% 188.15/187.99 [2619]P26(x26193,x26194,x26192)+~E(x26191,x26192)+~P26(x26193,x26194,x26191)
% 188.15/187.99 [2620]~P2(x26201)+P2(x26202)+~E(x26201,x26202)
% 188.15/187.99 [2621]~P103(x26211)+P103(x26212)+~E(x26211,x26212)
% 188.15/187.99 [2622]P16(x26222,x26223)+~E(x26221,x26222)+~P16(x26221,x26223)
% 188.15/187.99 [2623]P16(x26233,x26232)+~E(x26231,x26232)+~P16(x26233,x26231)
% 188.15/187.99 [2624]~P3(x26241)+P3(x26242)+~E(x26241,x26242)
% 188.15/187.99 [2625]~P97(x26251)+P97(x26252)+~E(x26251,x26252)
% 188.15/187.99 [2626]~P116(x26261)+P116(x26262)+~E(x26261,x26262)
% 188.15/187.99 [2627]~P129(x26271)+P129(x26272)+~E(x26271,x26272)
% 188.15/187.99 [2628]~P4(x26281)+P4(x26282)+~E(x26281,x26282)
% 188.15/187.99 [2629]~P105(x26291)+P105(x26292)+~E(x26291,x26292)
% 188.15/187.99 [2630]P17(x26302,x26303,x26304)+~E(x26301,x26302)+~P17(x26301,x26303,x26304)
% 188.15/187.99 [2631]P17(x26313,x26312,x26314)+~E(x26311,x26312)+~P17(x26313,x26311,x26314)
% 188.15/187.99 [2632]P17(x26323,x26324,x26322)+~E(x26321,x26322)+~P17(x26323,x26324,x26321)
% 188.15/187.99 [2633]~P90(x26331)+P90(x26332)+~E(x26331,x26332)
% 188.15/187.99 [2634]~P102(x26341)+P102(x26342)+~E(x26341,x26342)
% 188.15/187.99 [2635]~P65(x26351)+P65(x26352)+~E(x26351,x26352)
% 188.15/187.99 [2636]~P6(x26361)+P6(x26362)+~E(x26361,x26362)
% 188.15/187.99 [2637]P143(x26372,x26373,x26374)+~E(x26371,x26372)+~P143(x26371,x26373,x26374)
% 188.15/187.99 [2638]P143(x26383,x26382,x26384)+~E(x26381,x26382)+~P143(x26383,x26381,x26384)
% 188.15/187.99 [2639]P143(x26393,x26394,x26392)+~E(x26391,x26392)+~P143(x26393,x26394,x26391)
% 188.15/187.99 [2640]~P98(x26401)+P98(x26402)+~E(x26401,x26402)
% 188.15/187.99 [2641]~P120(x26411)+P120(x26412)+~E(x26411,x26412)
% 188.15/187.99 [2642]~P39(x26421)+P39(x26422)+~E(x26421,x26422)
% 188.15/187.99 [2643]~P64(x26431)+P64(x26432)+~E(x26431,x26432)
% 188.15/187.99 [2644]~P91(x26441)+P91(x26442)+~E(x26441,x26442)
% 188.15/187.99 [2645]~P57(x26451)+P57(x26452)+~E(x26451,x26452)
% 188.15/187.99 [2646]~P104(x26461)+P104(x26462)+~E(x26461,x26462)
% 188.15/187.99 [2647]~P77(x26471)+P77(x26472)+~E(x26471,x26472)
% 188.15/187.99 [2648]P33(x26482,x26483,x26484,x26485)+~E(x26481,x26482)+~P33(x26481,x26483,x26484,x26485)
% 188.15/187.99 [2649]P33(x26493,x26492,x26494,x26495)+~E(x26491,x26492)+~P33(x26493,x26491,x26494,x26495)
% 188.15/187.99 [2650]P33(x26503,x26504,x26502,x26505)+~E(x26501,x26502)+~P33(x26503,x26504,x26501,x26505)
% 188.15/187.99 [2651]P33(x26513,x26514,x26515,x26512)+~E(x26511,x26512)+~P33(x26513,x26514,x26515,x26511)
% 188.15/187.99 [2652]~P82(x26521)+P82(x26522)+~E(x26521,x26522)
% 188.15/187.99 [2653]P27(x26532,x26533,x26534,x26535)+~E(x26531,x26532)+~P27(x26531,x26533,x26534,x26535)
% 188.15/187.99 [2654]P27(x26543,x26542,x26544,x26545)+~E(x26541,x26542)+~P27(x26543,x26541,x26544,x26545)
% 188.15/187.99 [2655]P27(x26553,x26554,x26552,x26555)+~E(x26551,x26552)+~P27(x26553,x26554,x26551,x26555)
% 188.15/187.99 [2656]P27(x26563,x26564,x26565,x26562)+~E(x26561,x26562)+~P27(x26563,x26564,x26565,x26561)
% 188.15/187.99 [2657]~P68(x26571)+P68(x26572)+~E(x26571,x26572)
% 188.15/187.99 [2658]P20(x26582,x26583,x26584)+~E(x26581,x26582)+~P20(x26581,x26583,x26584)
% 188.15/187.99 [2659]P20(x26593,x26592,x26594)+~E(x26591,x26592)+~P20(x26593,x26591,x26594)
% 188.15/187.99 [2660]P20(x26603,x26604,x26602)+~E(x26601,x26602)+~P20(x26603,x26604,x26601)
% 188.15/187.99 [2661]P38(x26612,x26613)+~E(x26611,x26612)+~P38(x26611,x26613)
% 188.15/187.99 [2662]P38(x26623,x26622)+~E(x26621,x26622)+~P38(x26623,x26621)
% 188.15/187.99 [2663]~P106(x26631)+P106(x26632)+~E(x26631,x26632)
% 188.15/187.99 [2664]~P95(x26641)+P95(x26642)+~E(x26641,x26642)
% 188.15/187.99 [2665]~P96(x26651)+P96(x26652)+~E(x26651,x26652)
% 188.15/187.99 [2666]P54(x26662,x26663)+~E(x26661,x26662)+~P54(x26661,x26663)
% 188.15/187.99 [2667]P54(x26673,x26672)+~E(x26671,x26672)+~P54(x26673,x26671)
% 188.15/187.99 [2668]P28(x26682,x26683,x26684,x26685,x26686)+~E(x26681,x26682)+~P28(x26681,x26683,x26684,x26685,x26686)
% 188.15/187.99 [2669]P28(x26693,x26692,x26694,x26695,x26696)+~E(x26691,x26692)+~P28(x26693,x26691,x26694,x26695,x26696)
% 188.15/187.99 [2670]P28(x26703,x26704,x26702,x26705,x26706)+~E(x26701,x26702)+~P28(x26703,x26704,x26701,x26705,x26706)
% 188.15/187.99 [2671]P28(x26713,x26714,x26715,x26712,x26716)+~E(x26711,x26712)+~P28(x26713,x26714,x26715,x26711,x26716)
% 188.15/187.99 [2672]P28(x26723,x26724,x26725,x26726,x26722)+~E(x26721,x26722)+~P28(x26723,x26724,x26725,x26726,x26721)
% 188.15/187.99 [2673]~P75(x26731)+P75(x26732)+~E(x26731,x26732)
% 188.15/187.99 [2674]~P5(x26741)+P5(x26742)+~E(x26741,x26742)
% 188.15/187.99 [2675]P9(x26752,x26753,x26754)+~E(x26751,x26752)+~P9(x26751,x26753,x26754)
% 188.15/187.99 [2676]P9(x26763,x26762,x26764)+~E(x26761,x26762)+~P9(x26763,x26761,x26764)
% 188.15/187.99 [2677]P9(x26773,x26774,x26772)+~E(x26771,x26772)+~P9(x26773,x26774,x26771)
% 188.15/187.99 [2678]~P79(x26781)+P79(x26782)+~E(x26781,x26782)
% 188.15/187.99 [2679]P35(x26792,x26793,x26794,x26795,x26796)+~E(x26791,x26792)+~P35(x26791,x26793,x26794,x26795,x26796)
% 188.15/187.99 [2680]P35(x26803,x26802,x26804,x26805,x26806)+~E(x26801,x26802)+~P35(x26803,x26801,x26804,x26805,x26806)
% 188.15/187.99 [2681]P35(x26813,x26814,x26812,x26815,x26816)+~E(x26811,x26812)+~P35(x26813,x26814,x26811,x26815,x26816)
% 188.15/187.99 [2682]P35(x26823,x26824,x26825,x26822,x26826)+~E(x26821,x26822)+~P35(x26823,x26824,x26825,x26821,x26826)
% 188.15/187.99 [2683]P35(x26833,x26834,x26835,x26836,x26832)+~E(x26831,x26832)+~P35(x26833,x26834,x26835,x26836,x26831)
% 188.15/187.99 [2684]~P87(x26841)+P87(x26842)+~E(x26841,x26842)
% 188.15/187.99 [2685]~P59(x26851)+P59(x26852)+~E(x26851,x26852)
% 188.15/187.99 [2686]~P60(x26861)+P60(x26862)+~E(x26861,x26862)
% 188.15/187.99 [2687]~P66(x26871)+P66(x26872)+~E(x26871,x26872)
% 188.15/187.99 [2688]~P134(x26881)+P134(x26882)+~E(x26881,x26882)
% 188.15/187.99 [2689]~P131(x26891)+P131(x26892)+~E(x26891,x26892)
% 188.15/187.99 [2690]~P107(x26901)+P107(x26902)+~E(x26901,x26902)
% 188.15/187.99 [2691]~P108(x26911)+P108(x26912)+~E(x26911,x26912)
% 188.15/187.99 [2692]~P93(x26921)+P93(x26922)+~E(x26921,x26922)
% 188.15/187.99 [2693]~P61(x26931)+P61(x26932)+~E(x26931,x26932)
% 188.15/187.99 [2694]P25(x26942,x26943,x26944,x26945,x26946,x26947)+~E(x26941,x26942)+~P25(x26941,x26943,x26944,x26945,x26946,x26947)
% 188.15/187.99 [2695]P25(x26953,x26952,x26954,x26955,x26956,x26957)+~E(x26951,x26952)+~P25(x26953,x26951,x26954,x26955,x26956,x26957)
% 188.15/187.99 [2696]P25(x26963,x26964,x26962,x26965,x26966,x26967)+~E(x26961,x26962)+~P25(x26963,x26964,x26961,x26965,x26966,x26967)
% 188.15/187.99 [2697]P25(x26973,x26974,x26975,x26972,x26976,x26977)+~E(x26971,x26972)+~P25(x26973,x26974,x26975,x26971,x26976,x26977)
% 188.15/187.99 [2698]P25(x26983,x26984,x26985,x26986,x26982,x26987)+~E(x26981,x26982)+~P25(x26983,x26984,x26985,x26986,x26981,x26987)
% 188.15/187.99 [2699]P25(x26993,x26994,x26995,x26996,x26997,x26992)+~E(x26991,x26992)+~P25(x26993,x26994,x26995,x26996,x26997,x26991)
% 188.15/187.99 [2700]P142(x27002,x27003,x27004)+~E(x27001,x27002)+~P142(x27001,x27003,x27004)
% 188.15/187.99 [2701]P142(x27013,x27012,x27014)+~E(x27011,x27012)+~P142(x27013,x27011,x27014)
% 188.15/187.99 [2702]P142(x27023,x27024,x27022)+~E(x27021,x27022)+~P142(x27023,x27024,x27021)
% 188.15/187.99 [2703]~P58(x27031)+P58(x27032)+~E(x27031,x27032)
% 188.15/187.99 [2704]~P72(x27041)+P72(x27042)+~E(x27041,x27042)
% 188.15/187.99 [2705]~P76(x27051)+P76(x27052)+~E(x27051,x27052)
% 188.15/187.99 [2706]P40(x27062,x27063,x27064)+~E(x27061,x27062)+~P40(x27061,x27063,x27064)
% 188.15/187.99 [2707]P40(x27073,x27072,x27074)+~E(x27071,x27072)+~P40(x27073,x27071,x27074)
% 188.15/187.99 [2708]P40(x27083,x27084,x27082)+~E(x27081,x27082)+~P40(x27083,x27084,x27081)
% 188.15/187.99 [2709]P8(x27092,x27093)+~E(x27091,x27092)+~P8(x27091,x27093)
% 188.15/187.99 [2710]P8(x27103,x27102)+~E(x27101,x27102)+~P8(x27103,x27101)
% 188.15/187.99 [2711]~P74(x27111)+P74(x27112)+~E(x27111,x27112)
% 188.15/187.99 [2712]~P125(x27121)+P125(x27122)+~E(x27121,x27122)
% 188.15/187.99 [2713]~P140(x27131)+P140(x27132)+~E(x27131,x27132)
% 188.15/187.99 [2714]~P119(x27141)+P119(x27142)+~E(x27141,x27142)
% 188.15/187.99 [2715]~P112(x27151)+P112(x27152)+~E(x27151,x27152)
% 188.15/187.99 [2716]~P7(x27161)+P7(x27162)+~E(x27161,x27162)
% 188.15/187.99 [2717]~P133(x27171)+P133(x27172)+~E(x27171,x27172)
% 188.15/187.99 [2718]~P109(x27181)+P109(x27182)+~E(x27181,x27182)
% 188.15/187.99 [2719]~P62(x27191)+P62(x27192)+~E(x27191,x27192)
% 188.15/187.99 [2720]P34(x27202,x27203,x27204)+~E(x27201,x27202)+~P34(x27201,x27203,x27204)
% 188.15/187.99 [2721]P34(x27213,x27212,x27214)+~E(x27211,x27212)+~P34(x27213,x27211,x27214)
% 188.15/187.99 [2722]P34(x27223,x27224,x27222)+~E(x27221,x27222)+~P34(x27223,x27224,x27221)
% 188.15/187.99 [2723]P52(x27232,x27233,x27234)+~E(x27231,x27232)+~P52(x27231,x27233,x27234)
% 188.15/187.99 [2724]P52(x27243,x27242,x27244)+~E(x27241,x27242)+~P52(x27243,x27241,x27244)
% 188.15/187.99 [2725]P52(x27253,x27254,x27252)+~E(x27251,x27252)+~P52(x27253,x27254,x27251)
% 188.15/187.99 [2726]~P135(x27261)+P135(x27262)+~E(x27261,x27262)
% 188.15/187.99 [2727]~P63(x27271)+P63(x27272)+~E(x27271,x27272)
% 188.15/187.99 [2728]~P67(x27281)+P67(x27282)+~E(x27281,x27282)
% 188.15/187.99 [2729]~P83(x27291)+P83(x27292)+~E(x27291,x27292)
% 188.15/187.99 [2730]~P114(x27301)+P114(x27302)+~E(x27301,x27302)
% 188.15/187.99 [2731]~P69(x27311)+P69(x27312)+~E(x27311,x27312)
% 188.15/187.99 [2732]~P81(x27321)+P81(x27322)+~E(x27321,x27322)
% 188.15/187.99 [2733]P29(x27332,x27333)+~E(x27331,x27332)+~P29(x27331,x27333)
% 188.15/187.99 [2734]P29(x27343,x27342)+~E(x27341,x27342)+~P29(x27343,x27341)
% 188.15/187.99 [2735]~P70(x27351)+P70(x27352)+~E(x27351,x27352)
% 188.15/187.99 [2736]P19(x27362,x27363,x27364)+~E(x27361,x27362)+~P19(x27361,x27363,x27364)
% 188.15/187.99 [2737]P19(x27373,x27372,x27374)+~E(x27371,x27372)+~P19(x27373,x27371,x27374)
% 188.15/187.99 [2738]P19(x27383,x27384,x27382)+~E(x27381,x27382)+~P19(x27383,x27384,x27381)
% 188.15/187.99 [2739]~P110(x27391)+P110(x27392)+~E(x27391,x27392)
% 188.15/187.99 [2740]~P80(x27401)+P80(x27402)+~E(x27401,x27402)
% 188.15/187.99 [2741]~P124(x27411)+P124(x27412)+~E(x27411,x27412)
% 188.15/187.99 [2742]~P122(x27421)+P122(x27422)+~E(x27421,x27422)
% 188.15/187.99 [2743]~P92(x27431)+P92(x27432)+~E(x27431,x27432)
% 188.15/187.99 [2744]P15(x27442,x27443,x27444,x27445,x27446,x27447)+~E(x27441,x27442)+~P15(x27441,x27443,x27444,x27445,x27446,x27447)
% 188.15/187.99 [2745]P15(x27453,x27452,x27454,x27455,x27456,x27457)+~E(x27451,x27452)+~P15(x27453,x27451,x27454,x27455,x27456,x27457)
% 188.15/187.99 [2746]P15(x27463,x27464,x27462,x27465,x27466,x27467)+~E(x27461,x27462)+~P15(x27463,x27464,x27461,x27465,x27466,x27467)
% 188.15/187.99 [2747]P15(x27473,x27474,x27475,x27472,x27476,x27477)+~E(x27471,x27472)+~P15(x27473,x27474,x27475,x27471,x27476,x27477)
% 188.15/187.99 [2748]P15(x27483,x27484,x27485,x27486,x27482,x27487)+~E(x27481,x27482)+~P15(x27483,x27484,x27485,x27486,x27481,x27487)
% 188.15/187.99 [2749]P15(x27493,x27494,x27495,x27496,x27497,x27492)+~E(x27491,x27492)+~P15(x27493,x27494,x27495,x27496,x27497,x27491)
% 188.15/187.99 [2750]~P139(x27501)+P139(x27502)+~E(x27501,x27502)
% 188.15/187.99 [2751]P51(x27512,x27513,x27514)+~E(x27511,x27512)+~P51(x27511,x27513,x27514)
% 188.15/187.99 [2752]P51(x27523,x27522,x27524)+~E(x27521,x27522)+~P51(x27523,x27521,x27524)
% 188.15/187.99 [2753]P51(x27533,x27534,x27532)+~E(x27531,x27532)+~P51(x27533,x27534,x27531)
% 188.15/187.99 [2754]P18(x27542,x27543,x27544)+~E(x27541,x27542)+~P18(x27541,x27543,x27544)
% 188.15/187.99 [2755]P18(x27553,x27552,x27554)+~E(x27551,x27552)+~P18(x27553,x27551,x27554)
% 188.15/187.99 [2756]P18(x27563,x27564,x27562)+~E(x27561,x27562)+~P18(x27563,x27564,x27561)
% 188.15/187.99 [2757]P13(x27572,x27573,x27574)+~E(x27571,x27572)+~P13(x27571,x27573,x27574)
% 188.15/187.99 [2758]P13(x27583,x27582,x27584)+~E(x27581,x27582)+~P13(x27583,x27581,x27584)
% 188.15/187.99 [2759]P13(x27593,x27594,x27592)+~E(x27591,x27592)+~P13(x27593,x27594,x27591)
% 188.15/187.99 [2760]~P113(x27601)+P113(x27602)+~E(x27601,x27602)
% 188.15/187.99 [2761]~P84(x27611)+P84(x27612)+~E(x27611,x27612)
% 188.15/187.99 [2762]P32(x27622,x27623,x27624)+~E(x27621,x27622)+~P32(x27621,x27623,x27624)
% 188.15/187.99 [2763]P32(x27633,x27632,x27634)+~E(x27631,x27632)+~P32(x27633,x27631,x27634)
% 188.15/187.99 [2764]P32(x27643,x27644,x27642)+~E(x27641,x27642)+~P32(x27643,x27644,x27641)
% 188.15/187.99 [2765]~P136(x27651)+P136(x27652)+~E(x27651,x27652)
% 188.15/187.99 [2766]~P115(x27661)+P115(x27662)+~E(x27661,x27662)
% 188.15/187.99 [2767]~P123(x27671)+P123(x27672)+~E(x27671,x27672)
% 188.15/187.99 [2768]P42(x27682,x27683)+~E(x27681,x27682)+~P42(x27681,x27683)
% 188.15/187.99 [2769]P42(x27693,x27692)+~E(x27691,x27692)+~P42(x27693,x27691)
% 188.15/187.99 [2770]~P73(x27701)+P73(x27702)+~E(x27701,x27702)
% 188.15/187.99 [2771]P56(x27712,x27713)+~E(x27711,x27712)+~P56(x27711,x27713)
% 188.15/187.99 [2772]P56(x27723,x27722)+~E(x27721,x27722)+~P56(x27723,x27721)
% 188.15/187.99 [2773]P11(x27732,x27733,x27734,x27735,x27736)+~E(x27731,x27732)+~P11(x27731,x27733,x27734,x27735,x27736)
% 188.15/187.99 [2774]P11(x27743,x27742,x27744,x27745,x27746)+~E(x27741,x27742)+~P11(x27743,x27741,x27744,x27745,x27746)
% 188.15/187.99 [2775]P11(x27753,x27754,x27752,x27755,x27756)+~E(x27751,x27752)+~P11(x27753,x27754,x27751,x27755,x27756)
% 188.15/187.99 [2776]P11(x27763,x27764,x27765,x27762,x27766)+~E(x27761,x27762)+~P11(x27763,x27764,x27765,x27761,x27766)
% 188.15/187.99 [2777]P11(x27773,x27774,x27775,x27776,x27772)+~E(x27771,x27772)+~P11(x27773,x27774,x27775,x27776,x27771)
% 188.15/187.99 [2778]~P88(x27781)+P88(x27782)+~E(x27781,x27782)
% 188.15/187.99 [2779]P30(x27792,x27793)+~E(x27791,x27792)+~P30(x27791,x27793)
% 188.15/187.99 [2780]P30(x27803,x27802)+~E(x27801,x27802)+~P30(x27803,x27801)
% 188.15/187.99 [2781]P50(x27812,x27813,x27814,x27815)+~E(x27811,x27812)+~P50(x27811,x27813,x27814,x27815)
% 188.15/187.99 [2782]P50(x27823,x27822,x27824,x27825)+~E(x27821,x27822)+~P50(x27823,x27821,x27824,x27825)
% 188.15/187.99 [2783]P50(x27833,x27834,x27832,x27835)+~E(x27831,x27832)+~P50(x27833,x27834,x27831,x27835)
% 188.15/187.99 [2784]P50(x27843,x27844,x27845,x27842)+~E(x27841,x27842)+~P50(x27843,x27844,x27845,x27841)
% 188.15/187.99 [2785]~P78(x27851)+P78(x27852)+~E(x27851,x27852)
% 188.15/187.99 [2786]P53(x27862,x27863,x27864,x27865,x27866)+~E(x27861,x27862)+~P53(x27861,x27863,x27864,x27865,x27866)
% 188.15/187.99 [2787]P53(x27873,x27872,x27874,x27875,x27876)+~E(x27871,x27872)+~P53(x27873,x27871,x27874,x27875,x27876)
% 188.15/187.99 [2788]P53(x27883,x27884,x27882,x27885,x27886)+~E(x27881,x27882)+~P53(x27883,x27884,x27881,x27885,x27886)
% 188.15/187.99 [2789]P53(x27893,x27894,x27895,x27892,x27896)+~E(x27891,x27892)+~P53(x27893,x27894,x27895,x27891,x27896)
% 188.15/187.99 [2790]P53(x27903,x27904,x27905,x27906,x27902)+~E(x27901,x27902)+~P53(x27903,x27904,x27905,x27906,x27901)
% 188.15/187.99 [2791]P24(x27912,x27913,x27914,x27915,x27916,x27917)+~E(x27911,x27912)+~P24(x27911,x27913,x27914,x27915,x27916,x27917)
% 188.15/187.99 [2792]P24(x27923,x27922,x27924,x27925,x27926,x27927)+~E(x27921,x27922)+~P24(x27923,x27921,x27924,x27925,x27926,x27927)
% 188.15/187.99 [2793]P24(x27933,x27934,x27932,x27935,x27936,x27937)+~E(x27931,x27932)+~P24(x27933,x27934,x27931,x27935,x27936,x27937)
% 188.15/187.99 [2794]P24(x27943,x27944,x27945,x27942,x27946,x27947)+~E(x27941,x27942)+~P24(x27943,x27944,x27945,x27941,x27946,x27947)
% 188.15/187.99 [2795]P24(x27953,x27954,x27955,x27956,x27952,x27957)+~E(x27951,x27952)+~P24(x27953,x27954,x27955,x27956,x27951,x27957)
% 188.15/187.99 [2796]P24(x27963,x27964,x27965,x27966,x27967,x27962)+~E(x27961,x27962)+~P24(x27963,x27964,x27965,x27966,x27967,x27961)
% 188.15/187.99 [2797]P36(x27972,x27973,x27974)+~E(x27971,x27972)+~P36(x27971,x27973,x27974)
% 188.15/187.99 [2798]P36(x27983,x27982,x27984)+~E(x27981,x27982)+~P36(x27983,x27981,x27984)
% 188.15/187.99 [2799]P36(x27993,x27994,x27992)+~E(x27991,x27992)+~P36(x27993,x27994,x27991)
% 188.15/187.99 [2800]~P89(x28001)+P89(x28002)+~E(x28001,x28002)
% 188.15/187.99 [2801]P21(x28012,x28013,x28014,x28015)+~E(x28011,x28012)+~P21(x28011,x28013,x28014,x28015)
% 188.15/187.99 [2802]P21(x28023,x28022,x28024,x28025)+~E(x28021,x28022)+~P21(x28023,x28021,x28024,x28025)
% 188.15/187.99 [2803]P21(x28033,x28034,x28032,x28035)+~E(x28031,x28032)+~P21(x28033,x28034,x28031,x28035)
% 188.15/187.99 [2804]P21(x28043,x28044,x28045,x28042)+~E(x28041,x28042)+~P21(x28043,x28044,x28045,x28041)
% 188.15/187.99 [2805]P47(x28052,x28053,x28054)+~E(x28051,x28052)+~P47(x28051,x28053,x28054)
% 188.15/187.99 [2806]P47(x28063,x28062,x28064)+~E(x28061,x28062)+~P47(x28063,x28061,x28064)
% 188.15/187.99 [2807]P47(x28073,x28074,x28072)+~E(x28071,x28072)+~P47(x28073,x28074,x28071)
% 188.15/187.99 [2808]P22(x28082,x28083,x28084,x28085)+~E(x28081,x28082)+~P22(x28081,x28083,x28084,x28085)
% 188.15/187.99 [2809]P22(x28093,x28092,x28094,x28095)+~E(x28091,x28092)+~P22(x28093,x28091,x28094,x28095)
% 188.15/187.99 [2810]P22(x28103,x28104,x28102,x28105)+~E(x28101,x28102)+~P22(x28103,x28104,x28101,x28105)
% 188.15/187.99 [2811]P22(x28113,x28114,x28115,x28112)+~E(x28111,x28112)+~P22(x28113,x28114,x28115,x28111)
% 188.15/187.99 [2812]~P86(x28121)+P86(x28122)+~E(x28121,x28122)
% 188.15/187.99 [2813]~P111(x28131)+P111(x28132)+~E(x28131,x28132)
% 188.15/187.99 [2814]~P137(x28141)+P137(x28142)+~E(x28141,x28142)
% 188.15/187.99 [2815]~P45(x28151)+P45(x28152)+~E(x28151,x28152)
% 188.15/187.99 [2816]~P37(x28161)+P37(x28162)+~E(x28161,x28162)
% 188.15/187.99 [2817]P12(x28172,x28173,x28174)+~E(x28171,x28172)+~P12(x28171,x28173,x28174)
% 188.15/187.99 [2818]P12(x28183,x28182,x28184)+~E(x28181,x28182)+~P12(x28183,x28181,x28184)
% 188.15/187.99 [2819]P12(x28193,x28194,x28192)+~E(x28191,x28192)+~P12(x28193,x28194,x28191)
% 188.15/187.99 [2820]~P138(x28201)+P138(x28202)+~E(x28201,x28202)
% 188.15/188.00 [2821]P14(x28212,x28213,x28214,x28215)+~E(x28211,x28212)+~P14(x28211,x28213,x28214,x28215)
% 188.15/188.00 [2822]P14(x28223,x28222,x28224,x28225)+~E(x28221,x28222)+~P14(x28223,x28221,x28224,x28225)
% 188.15/188.00 [2823]P14(x28233,x28234,x28232,x28235)+~E(x28231,x28232)+~P14(x28233,x28234,x28231,x28235)
% 188.15/188.00 [2824]P14(x28243,x28244,x28245,x28242)+~E(x28241,x28242)+~P14(x28243,x28244,x28245,x28241)
% 188.15/188.00 [2825]~P71(x28251)+P71(x28252)+~E(x28251,x28252)
% 188.15/188.00 [2826]~P130(x28261)+P130(x28262)+~E(x28261,x28262)
% 188.15/188.00 [2827]~P121(x28271)+P121(x28272)+~E(x28271,x28272)
% 188.15/188.00 [2828]P55(x28282,x28283,x28284,x28285)+~E(x28281,x28282)+~P55(x28281,x28283,x28284,x28285)
% 188.15/188.00 [2829]P55(x28293,x28292,x28294,x28295)+~E(x28291,x28292)+~P55(x28293,x28291,x28294,x28295)
% 188.15/188.00 [2830]P55(x28303,x28304,x28302,x28305)+~E(x28301,x28302)+~P55(x28303,x28304,x28301,x28305)
% 188.15/188.00 [2831]P55(x28313,x28314,x28315,x28312)+~E(x28311,x28312)+~P55(x28313,x28314,x28315,x28311)
% 188.15/188.00 [2832]P43(x28322,x28323,x28324,x28325,x28326,x28327)+~E(x28321,x28322)+~P43(x28321,x28323,x28324,x28325,x28326,x28327)
% 188.15/188.00 [2833]P43(x28333,x28332,x28334,x28335,x28336,x28337)+~E(x28331,x28332)+~P43(x28333,x28331,x28334,x28335,x28336,x28337)
% 188.15/188.00 [2834]P43(x28343,x28344,x28342,x28345,x28346,x28347)+~E(x28341,x28342)+~P43(x28343,x28344,x28341,x28345,x28346,x28347)
% 188.15/188.00 [2835]P43(x28353,x28354,x28355,x28352,x28356,x28357)+~E(x28351,x28352)+~P43(x28353,x28354,x28355,x28351,x28356,x28357)
% 188.15/188.00 [2836]P43(x28363,x28364,x28365,x28366,x28362,x28367)+~E(x28361,x28362)+~P43(x28363,x28364,x28365,x28366,x28361,x28367)
% 188.15/188.00 [2837]P43(x28373,x28374,x28375,x28376,x28377,x28372)+~E(x28371,x28372)+~P43(x28373,x28374,x28375,x28376,x28377,x28371)
% 188.15/188.00 [2838]~P94(x28381)+P94(x28382)+~E(x28381,x28382)
% 188.15/188.00 [2839]P23(x28392,x28393,x28394,x28395,x28396)+~E(x28391,x28392)+~P23(x28391,x28393,x28394,x28395,x28396)
% 188.15/188.00 [2840]P23(x28403,x28402,x28404,x28405,x28406)+~E(x28401,x28402)+~P23(x28403,x28401,x28404,x28405,x28406)
% 188.15/188.00 [2841]P23(x28413,x28414,x28412,x28415,x28416)+~E(x28411,x28412)+~P23(x28413,x28414,x28411,x28415,x28416)
% 188.15/188.00 [2842]P23(x28423,x28424,x28425,x28422,x28426)+~E(x28421,x28422)+~P23(x28423,x28424,x28425,x28421,x28426)
% 188.15/188.00 [2843]P23(x28433,x28434,x28435,x28436,x28432)+~E(x28431,x28432)+~P23(x28433,x28434,x28435,x28436,x28431)
% 188.15/188.00 [2844]P44(x28442,x28443)+~E(x28441,x28442)+~P44(x28441,x28443)
% 188.15/188.00 [2845]P44(x28453,x28452)+~E(x28451,x28452)+~P44(x28453,x28451)
% 188.15/188.00 [2846]~P100(x28461)+P100(x28462)+~E(x28461,x28462)
% 188.15/188.00 [2847]P46(x28472,x28473)+~E(x28471,x28472)+~P46(x28471,x28473)
% 188.15/188.00 [2848]P46(x28483,x28482)+~E(x28481,x28482)+~P46(x28483,x28481)
% 188.15/188.00 [2849]~P118(x28491)+P118(x28492)+~E(x28491,x28492)
% 188.15/188.00 [2850]~P141(x28501)+P141(x28502)+~E(x28501,x28502)
% 188.15/188.00 [2851]~P132(x28511)+P132(x28512)+~E(x28511,x28512)
% 188.15/188.00 [2852]~P126(x28521)+P126(x28522)+~E(x28521,x28522)
% 188.15/188.00 [2853]P31(x28532,x28533,x28534)+~E(x28531,x28532)+~P31(x28531,x28533,x28534)
% 188.15/188.00 [2854]P31(x28543,x28542,x28544)+~E(x28541,x28542)+~P31(x28543,x28541,x28544)
% 188.15/188.00 [2855]P31(x28553,x28554,x28552)+~E(x28551,x28552)+~P31(x28553,x28554,x28551)
% 188.15/188.00 [2856]~P117(x28561)+P117(x28562)+~E(x28561,x28562)
% 188.15/188.00 [2857]~P99(x28571)+P99(x28572)+~E(x28571,x28572)
% 188.15/188.00 [2858]P48(x28582,x28583,x28584)+~E(x28581,x28582)+~P48(x28581,x28583,x28584)
% 188.15/188.00 [2859]P48(x28593,x28592,x28594)+~E(x28591,x28592)+~P48(x28593,x28591,x28594)
% 188.15/188.00 [2860]P48(x28603,x28604,x28602)+~E(x28601,x28602)+~P48(x28603,x28604,x28601)
% 188.15/188.00 [2861]~P127(x28611)+P127(x28612)+~E(x28611,x28612)
% 188.15/188.00 [2862]P49(x28622,x28623)+~E(x28621,x28622)+~P49(x28621,x28623)
% 188.15/188.00 [2863]P49(x28633,x28632)+~E(x28631,x28632)+~P49(x28633,x28631)
% 188.15/188.00 [2864]~P85(x28641)+P85(x28642)+~E(x28641,x28642)
% 188.15/188.00 [2865]~P128(x28651)+P128(x28652)+~E(x28651,x28652)
% 188.15/188.00 [2866]P41(x28662,x28663,x28664,x28665)+~E(x28661,x28662)+~P41(x28661,x28663,x28664,x28665)
% 188.15/188.00 [2867]P41(x28673,x28672,x28674,x28675)+~E(x28671,x28672)+~P41(x28673,x28671,x28674,x28675)
% 188.15/188.00 [2868]P41(x28683,x28684,x28682,x28685)+~E(x28681,x28682)+~P41(x28683,x28684,x28681,x28685)
% 188.15/188.00 [2869]P41(x28693,x28694,x28695,x28692)+~E(x28691,x28692)+~P41(x28693,x28694,x28695,x28691)
% 188.15/188.00 [2870]P10(x28702,x28703,x28704)+~E(x28701,x28702)+~P10(x28701,x28703,x28704)
% 188.15/188.00 [2871]P10(x28713,x28712,x28714)+~E(x28711,x28712)+~P10(x28713,x28711,x28714)
% 188.15/188.00 [2872]P10(x28723,x28724,x28722)+~E(x28721,x28722)+~P10(x28723,x28724,x28721)
% 188.15/188.00
% 188.15/188.00 %-------------------------------------------
% 188.20/188.04 cnf(10166,plain,
% 188.20/188.04 (E(f31(x101661,x101662,x101663,x101664,x101665,x101666,x101667,x101668,x101669,a24),x101662)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(10169,plain,
% 188.20/188.04 (~E(f323(a112,x101691),x101691)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(10172,plain,
% 188.20/188.04 (E(f31(x101721,x101722,x101723,x101724,x101725,x101726,x101727,x101728,x101729,a24),x101722)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(10179,plain,
% 188.20/188.04 (~E(f323(a112,x101791),x101791)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(10186,plain,
% 188.20/188.04 (E(f31(x101861,x101862,x101863,x101864,x101865,x101866,x101867,x101868,x101869,a24),x101862)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(10193,plain,
% 188.20/188.04 (~E(f323(a112,x101931),x101931)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(10198,plain,
% 188.20/188.04 (~P101(f323(f60(x101981,x101982,f188(f872(x101981,a860))),x101983))),
% 188.20/188.04 inference(rename_variables,[],[4560])).
% 188.20/188.04 cnf(10201,plain,
% 188.20/188.04 (~P101(f323(f60(x102011,x102012,f188(f872(x102011,a860))),x102013))),
% 188.20/188.04 inference(rename_variables,[],[4560])).
% 188.20/188.04 cnf(10204,plain,
% 188.20/188.04 (~E(f323(a112,x102041),x102041)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(10207,plain,
% 188.20/188.04 (~E(f323(a112,x102071),x102071)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(10210,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x102101),f2(a865)))),
% 188.20/188.04 inference(rename_variables,[],[4540])).
% 188.20/188.04 cnf(10213,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x102131),f2(a865)))),
% 188.20/188.04 inference(rename_variables,[],[4540])).
% 188.20/188.04 cnf(10226,plain,
% 188.20/188.04 (~P101(f323(f188(f872(x102261,a860)),x102262))),
% 188.20/188.04 inference(scs_inference,[],[4459,10166,10172,4473,10169,10179,10193,10204,3114,3173,3123,3265,4540,10210,4537,4495,4543,3256,4527,4560,10198,4564,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033])).
% 188.20/188.04 cnf(10230,plain,
% 188.20/188.04 (~P101(f323(f323(f237(a865),f323(a112,x102301)),x102301))),
% 188.20/188.04 inference(rename_variables,[],[4545])).
% 188.20/188.04 cnf(10233,plain,
% 188.20/188.04 (~E(f323(f323(f144(x102331),x102332),x102333),x102333)),
% 188.20/188.04 inference(rename_variables,[],[4500])).
% 188.20/188.04 cnf(10239,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x102391),f2(a865)))),
% 188.20/188.04 inference(rename_variables,[],[4540])).
% 188.20/188.04 cnf(10242,plain,
% 188.20/188.04 (E(f31(x102421,x102422,x102423,x102424,x102425,x102426,x102427,x102428,x102429,a24),x102422)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(10245,plain,
% 188.20/188.04 (E(f31(x102451,x102452,x102453,x102454,x102455,x102456,x102457,x102458,x102459,a24),x102452)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(10252,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),f323(f323(f78(a865),x102521),x102522)),x102522))),
% 188.20/188.04 inference(rename_variables,[],[4562])).
% 188.20/188.04 cnf(10255,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),f323(f323(f78(a865),x102551),x102552)),x102552))),
% 188.20/188.04 inference(rename_variables,[],[4562])).
% 188.20/188.04 cnf(10262,plain,
% 188.20/188.04 (~E(x102621,f323(a112,x102621))),
% 188.20/188.04 inference(scs_inference,[],[4459,10166,10172,10186,10242,4473,10169,10179,10193,10204,3114,3173,3140,3123,4500,3349,3265,4540,10210,10213,4537,4495,4545,4115,4543,3256,4527,4560,10198,4564,4562,10252,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165])).
% 188.20/188.04 cnf(10276,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x102761),x102761))),
% 188.20/188.04 inference(rename_variables,[],[4536])).
% 188.20/188.04 cnf(10279,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),f42(a865,x102791,x102792)),x102791))),
% 188.20/188.04 inference(rename_variables,[],[3738])).
% 188.20/188.04 cnf(10300,plain,
% 188.20/188.04 (E(f323(f35(a865),f323(f244(a865),x103001)),x103001)),
% 188.20/188.04 inference(rename_variables,[],[3171])).
% 188.20/188.04 cnf(10308,plain,
% 188.20/188.04 (~E(f323(a112,x103081),x103081)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(10311,plain,
% 188.20/188.04 (~E(f323(a112,x103111),x103111)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(10314,plain,
% 188.20/188.04 (~E(f323(a112,x103141),x103141)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(10316,plain,
% 188.20/188.04 (P101(f323(a193,a97))),
% 188.20/188.04 inference(scs_inference,[],[4459,10166,10172,10186,10242,4473,10169,10179,10193,10204,10207,10308,10311,3114,3173,3140,3123,3208,4500,3171,4569,3191,3349,3265,4540,10210,10213,3872,3284,4537,4495,4536,10276,3375,3801,3738,4545,10230,4115,4543,4526,3256,4527,4531,4560,10198,4564,4562,10252,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305])).
% 188.20/188.04 cnf(10319,plain,
% 188.20/188.04 (P101(f323(f323(f238(a865),x103191),f323(a112,x103191)))),
% 188.20/188.04 inference(rename_variables,[],[3349])).
% 188.20/188.04 cnf(10328,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x103281),x103281))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(10335,plain,
% 188.20/188.04 (E(f31(x103351,x103352,x103353,x103354,x103355,x103356,x103357,x103358,x103359,a24),x103352)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(10338,plain,
% 188.20/188.04 (E(f31(x103381,x103382,x103383,x103384,x103385,x103386,x103387,x103388,x103389,a24),x103382)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(10357,plain,
% 188.20/188.04 (P101(f323(f323(f237(a1),x103571),x103571))),
% 188.20/188.04 inference(rename_variables,[],[3282])).
% 188.20/188.04 cnf(10366,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x103661),x103661))),
% 188.20/188.04 inference(rename_variables,[],[4536])).
% 188.20/188.04 cnf(10371,plain,
% 188.20/188.04 (~E(f323(f323(f323(f70(x103711,f869(x103712)),x103713),x103714),f323(f230(x103712),x103715)),f323(f16(f869(x103712),x103711),f200(x103712)))),
% 188.20/188.04 inference(rename_variables,[],[4557])).
% 188.20/188.04 cnf(10375,plain,
% 188.20/188.04 (E(f323(f323(f78(a865),x103751),f805(x103751,x103751)),x103751)),
% 188.20/188.04 inference(scs_inference,[],[4459,10166,10172,10186,10242,10245,10335,4473,10169,10179,10193,10204,10207,10308,10311,3114,3173,3140,3123,3208,4557,4500,3171,4071,4569,3191,3349,10319,3265,4540,10210,10213,3720,3872,3311,3284,4537,4495,4024,3281,10328,3282,3283,4536,10276,3375,3801,3738,10279,4545,10230,4115,4543,4526,3256,4527,4531,4560,10198,4564,3761,4562,10252,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449])).
% 188.20/188.04 cnf(10398,plain,
% 188.20/188.04 (~E(f323(f323(f144(x103981),x103982),x103983),x103983)),
% 188.20/188.04 inference(rename_variables,[],[4500])).
% 188.20/188.04 cnf(10401,plain,
% 188.20/188.04 (~E(f323(a112,x104011),f2(a865))),
% 188.20/188.04 inference(rename_variables,[],[4485])).
% 188.20/188.04 cnf(10412,plain,
% 188.20/188.04 (P101(f323(f323(f237(a1),x104121),x104121))),
% 188.20/188.04 inference(rename_variables,[],[3282])).
% 188.20/188.04 cnf(10417,plain,
% 188.20/188.04 (~E(f323(a112,x104171),x104171)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(10424,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x104241),x104241))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(10437,plain,
% 188.20/188.04 (P101(f323(f323(f238(a865),x104371),f323(a112,x104371)))),
% 188.20/188.04 inference(rename_variables,[],[3349])).
% 188.20/188.04 cnf(10458,plain,
% 188.20/188.04 (~P101(f323(f60(x104581,x104582,f188(f872(x104581,a860))),x104583))),
% 188.20/188.04 inference(rename_variables,[],[4560])).
% 188.20/188.04 cnf(10477,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x104771),x104771))),
% 188.20/188.04 inference(rename_variables,[],[4536])).
% 188.20/188.04 cnf(10492,plain,
% 188.20/188.04 (~E(f323(a112,x104921),f2(a865))),
% 188.20/188.04 inference(rename_variables,[],[4485])).
% 188.20/188.04 cnf(10498,plain,
% 188.20/188.04 (P101(f323(f323(f238(a865),f2(a865)),f323(a104,f76(a1))))),
% 188.20/188.04 inference(scs_inference,[],[4459,10166,10172,10186,10242,10245,10335,4473,10169,10179,10193,10204,10207,10308,10311,10314,4485,10401,3114,3173,3140,3123,3753,3208,4557,4500,10233,3171,4071,4569,3191,3645,3349,10319,10437,3265,4540,10210,10213,10239,4552,3720,3872,3309,3311,3284,4537,4495,4024,3281,10328,10424,3282,10357,3283,4536,10276,10366,3375,3801,3738,10279,4545,10230,4115,4543,4526,3256,3260,4528,4527,4531,4560,10198,10201,4564,3761,4562,10252,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868])).
% 188.20/188.04 cnf(10501,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x105011),x105011))),
% 188.20/188.04 inference(rename_variables,[],[4536])).
% 188.20/188.04 cnf(10506,plain,
% 188.20/188.04 (P101(f323(f323(f238(a865),x105061),f323(a112,x105061)))),
% 188.20/188.04 inference(rename_variables,[],[3349])).
% 188.20/188.04 cnf(10509,plain,
% 188.20/188.04 (~P101(f323(f60(x105091,x105092,f188(f872(x105091,a860))),x105093))),
% 188.20/188.04 inference(rename_variables,[],[4560])).
% 188.20/188.04 cnf(10512,plain,
% 188.20/188.04 (~P101(f323(f60(x105121,x105122,f188(f872(x105121,a860))),x105123))),
% 188.20/188.04 inference(rename_variables,[],[4560])).
% 188.20/188.04 cnf(10517,plain,
% 188.20/188.04 (~P101(f323(f60(x105171,x105172,f188(f872(x105171,a860))),x105173))),
% 188.20/188.04 inference(rename_variables,[],[4560])).
% 188.20/188.04 cnf(10528,plain,
% 188.20/188.04 (~E(f323(a112,x105281),x105281)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(10553,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x105531),x105531))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(10556,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x105561),f323(f323(f79(a865),x105561),x105561)))),
% 188.20/188.04 inference(rename_variables,[],[3548])).
% 188.20/188.04 cnf(10559,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x105591),f323(f323(f79(a865),x105591),x105591)))),
% 188.20/188.04 inference(rename_variables,[],[3548])).
% 188.20/188.04 cnf(10562,plain,
% 188.20/188.04 (P101(f323(f323(f238(a865),x105621),f323(a112,f323(f323(f78(a865),x105622),x105621))))),
% 188.20/188.04 inference(rename_variables,[],[3731])).
% 188.20/188.04 cnf(10567,plain,
% 188.20/188.04 (P101(f323(f323(f238(a865),x105671),f323(a112,x105671)))),
% 188.20/188.04 inference(rename_variables,[],[3349])).
% 188.20/188.04 cnf(10570,plain,
% 188.20/188.04 (P101(f323(f323(f238(a865),x105701),f323(a112,x105701)))),
% 188.20/188.04 inference(rename_variables,[],[3349])).
% 188.20/188.04 cnf(10573,plain,
% 188.20/188.04 (P101(f323(f323(f325(x105731),x105732),f246(f872(x105731,a860))))),
% 188.20/188.04 inference(rename_variables,[],[3439])).
% 188.20/188.04 cnf(10590,plain,
% 188.20/188.04 (~P101(f323(f323(f237(a865),f323(a112,x105901)),x105901))),
% 188.20/188.04 inference(rename_variables,[],[4545])).
% 188.20/188.04 cnf(10593,plain,
% 188.20/188.04 (~P101(f323(f323(f237(a865),f323(a112,x105931)),x105931))),
% 188.20/188.04 inference(rename_variables,[],[4545])).
% 188.20/188.04 cnf(10596,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),f323(f323(f78(a865),x105961),x105962)),x105962))),
% 188.20/188.04 inference(rename_variables,[],[4562])).
% 188.20/188.04 cnf(10599,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),f323(f323(f78(a865),x105991),x105992)),x105992))),
% 188.20/188.04 inference(rename_variables,[],[4562])).
% 188.20/188.04 cnf(10602,plain,
% 188.20/188.04 (P101(f323(f246(f872(x106021,a860)),x106022))),
% 188.20/188.04 inference(rename_variables,[],[3343])).
% 188.20/188.04 cnf(10605,plain,
% 188.20/188.04 (E(f323(f35(a865),f323(f244(a865),x106051)),x106051)),
% 188.20/188.04 inference(rename_variables,[],[3171])).
% 188.20/188.04 cnf(10608,plain,
% 188.20/188.04 (P101(f323(f323(f238(a865),x106081),f323(a112,x106081)))),
% 188.20/188.04 inference(rename_variables,[],[3349])).
% 188.20/188.04 cnf(10615,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x106151),x106151))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(10620,plain,
% 188.20/188.04 (P101(f323(f323(f237(a1),x106201),x106201))),
% 188.20/188.04 inference(rename_variables,[],[3282])).
% 188.20/188.04 cnf(10629,plain,
% 188.20/188.04 (E(f31(x106291,x106292,x106293,x106294,x106295,x106296,x106297,x106298,x106299,a24),x106292)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(10632,plain,
% 188.20/188.04 (P101(f323(f246(f872(x106321,a860)),x106322))),
% 188.20/188.04 inference(rename_variables,[],[3343])).
% 188.20/188.04 cnf(10635,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),f2(a865)),x106351))),
% 188.20/188.04 inference(rename_variables,[],[3303])).
% 188.20/188.04 cnf(10638,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x106381,a860)),f188(f872(x106381,a860))),x106382))),
% 188.20/188.04 inference(rename_variables,[],[3729])).
% 188.20/188.04 cnf(10641,plain,
% 188.20/188.04 (P101(f323(f246(f872(x106411,a860)),x106412))),
% 188.20/188.04 inference(rename_variables,[],[3343])).
% 188.20/188.04 cnf(10643,plain,
% 188.20/188.04 (~P101(f323(f323(f237(a865),f323(f323(f79(a865),f323(a112,x106431)),f323(a112,x106431))),x106431))),
% 188.20/188.04 inference(scs_inference,[],[4459,10166,10172,10186,10242,10245,10335,10338,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,4485,10401,3114,3173,3140,3123,3753,3208,4557,4500,10233,3171,10300,4071,4569,3191,3645,3585,3349,10319,10437,10506,10567,10570,3733,3265,4540,10210,10213,10239,4552,3720,3492,3872,3309,3311,3284,4537,4495,4024,3281,10328,10424,10553,3282,10357,10412,3283,4536,10276,10366,10477,3439,3343,10602,10632,3375,3801,3738,10279,4545,10230,10590,3303,4115,4543,4526,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,4567,3729,3548,10556,10559,4564,3761,4562,10252,10255,10596,3731,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287])).
% 188.20/188.04 cnf(10644,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x106441),f323(f323(f79(a865),x106441),x106441)))),
% 188.20/188.04 inference(rename_variables,[],[3548])).
% 188.20/188.04 cnf(10648,plain,
% 188.20/188.04 (E(f323(f162(x106481),f31(x106482,f323(f323(f121(x106481),f323(f162(x106481),x106483)),f323(f323(f144(x106481),x106484),f113(x106481))),x106485,x106486,x106487,x106488,x106489,x1064810,x1064811,a24)),f323(f323(f144(x106481),x106484),x106483))),
% 188.20/188.04 inference(scs_inference,[],[4459,10166,10172,10186,10242,10245,10335,10338,10629,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,4485,10401,3114,3173,3140,3123,3753,3208,4557,4500,10233,3171,10300,4071,4569,3191,3645,3585,3349,10319,10437,10506,10567,10570,3733,3265,4540,10210,10213,10239,4552,3720,3492,3872,3309,3311,3284,4537,4495,4024,3281,10328,10424,10553,3282,10357,10412,3283,4536,10276,10366,10477,3439,3343,10602,10632,3375,3801,3738,10279,4545,10230,10590,3303,4115,4543,4526,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,4567,3729,3548,10556,10559,4564,3761,4562,10252,10255,10596,3731,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326])).
% 188.20/188.04 cnf(10649,plain,
% 188.20/188.04 (E(f31(x106491,x106492,x106493,x106494,x106495,x106496,x106497,x106498,x106499,a24),x106492)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(10653,plain,
% 188.20/188.04 (~P101(f323(f323(f237(a865),f323(a112,f323(a112,f323(f323(f78(a865),x106531),x106532)))),f323(a112,x106532)))),
% 188.20/188.04 inference(scs_inference,[],[4459,10166,10172,10186,10242,10245,10335,10338,10629,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,4485,10401,3114,3173,3140,3123,3753,3208,4557,4500,10233,3171,10300,4071,4569,3191,3645,3585,3349,10319,10437,10506,10567,10570,10608,3733,3265,4540,10210,10213,10239,4552,3720,3492,3872,3309,3311,3284,4537,4495,4024,3281,10328,10424,10553,3282,10357,10412,3283,4536,10276,10366,10477,3439,3343,10602,10632,3375,3801,3738,10279,4545,10230,10590,3303,4115,4543,4526,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,4567,3729,3548,10556,10559,4564,3761,4562,10252,10255,10596,3731,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329])).
% 188.20/188.04 cnf(10686,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x106861),x106861))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(10697,plain,
% 188.20/188.04 (~P101(f323(f323(f188(f872(x106971,f872(x106972,a860))),x106973),x106974))),
% 188.20/188.04 inference(rename_variables,[],[4565])).
% 188.20/188.04 cnf(10706,plain,
% 188.20/188.04 (P101(f323(f323(f238(a865),x107061),f323(a112,x107061)))),
% 188.20/188.04 inference(rename_variables,[],[3349])).
% 188.20/188.04 cnf(10708,plain,
% 188.20/188.04 (P101(f323(f323(f238(a1),f323(f323(f22(a1),x107081),f76(a1))),x107081))),
% 188.20/188.04 inference(scs_inference,[],[3240,4459,10166,10172,10186,10242,10245,10335,10338,10629,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,4485,10401,3114,3173,3140,3123,3753,3208,4557,4500,10233,3171,10300,4071,3924,4569,3191,3645,3585,3349,10319,10437,10506,10567,10570,10608,3733,3265,4540,10210,10213,10239,4552,3720,3492,3872,3309,3311,3284,4537,4495,4024,3281,10328,10424,10553,10615,10686,3282,10357,10412,10620,3283,4536,10276,10366,10477,3439,4548,3343,10602,10632,3375,3801,3738,10279,4545,10230,10590,10593,3303,4115,4543,4526,4529,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,4567,3729,3548,10556,10559,4564,4565,3761,4562,10252,10255,10596,3731,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588])).
% 188.20/188.04 cnf(10709,plain,
% 188.20/188.04 (P101(f323(f323(f237(a1),x107091),x107091))),
% 188.20/188.04 inference(rename_variables,[],[3282])).
% 188.20/188.04 cnf(10714,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x107141),f2(a865)))),
% 188.20/188.04 inference(rename_variables,[],[4540])).
% 188.20/188.04 cnf(10727,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x107271),f2(a865)))),
% 188.20/188.04 inference(rename_variables,[],[4540])).
% 188.20/188.04 cnf(10730,plain,
% 188.20/188.04 (~P101(f323(f323(f238(f872(x107301,a860)),x107302),f188(f872(x107301,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4558])).
% 188.20/188.04 cnf(10733,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x107331),x107331))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(10736,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x107361),x107361))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(10750,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x107501),f323(f323(f22(a865),x107501),x107502)))),
% 188.20/188.04 inference(scs_inference,[],[3240,4459,10166,10172,10186,10242,10245,10335,10338,10629,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,4485,10401,3114,3173,3140,3123,3753,3208,4557,4500,10233,3171,10300,4071,3924,4569,3191,3645,3585,3349,10319,10437,10506,10567,10570,10608,3733,3265,4540,10210,10213,10239,10714,4552,3720,3492,3872,3309,3311,3284,4537,4495,4035,4024,4558,3281,10328,10424,10553,10615,10686,10733,10736,3282,10357,10412,10620,3283,4536,10276,10366,10477,10501,3439,4548,3343,10602,10632,3375,3801,3738,10279,4545,10230,10590,10593,3303,4115,4543,4526,4529,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,4567,3729,3548,10556,10559,4564,4565,3761,4562,10252,10255,10596,3731,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749])).
% 188.20/188.04 cnf(10751,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x107511),x107511))),
% 188.20/188.04 inference(rename_variables,[],[4536])).
% 188.20/188.04 cnf(10760,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x107601),x107602),f188(f872(x107601,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(10769,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x107691),x107691))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(10772,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x107721,a860)),f323(f302(x107722,x107721,x107723),f323(f303(x107722,x107721,x107723),x107724))),x107724))),
% 188.20/188.04 inference(rename_variables,[],[4174])).
% 188.20/188.04 cnf(10779,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x107791,a860)),f323(f166(x107791),f323(f129(x107791,x107792),x107793))),f323(f166(x107791),x107793)))),
% 188.20/188.04 inference(rename_variables,[],[3934])).
% 188.20/188.04 cnf(10782,plain,
% 188.20/188.04 (E(f323(f302(x107821,x107821,f5(x107821)),x107822),x107822)),
% 188.20/188.04 inference(rename_variables,[],[3339])).
% 188.20/188.04 cnf(10787,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),f2(a865)),x107871))),
% 188.20/188.04 inference(rename_variables,[],[3303])).
% 188.20/188.04 cnf(10790,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x107901),x107901))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(10793,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x107931),x107931))),
% 188.20/188.04 inference(rename_variables,[],[4536])).
% 188.20/188.04 cnf(10796,plain,
% 188.20/188.04 (~P101(f323(f323(f188(f872(x107961,f872(x107962,a860))),x107963),x107964))),
% 188.20/188.04 inference(rename_variables,[],[4565])).
% 188.20/188.04 cnf(10803,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x108031),x108031))),
% 188.20/188.04 inference(rename_variables,[],[4536])).
% 188.20/188.04 cnf(10814,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x108141),f323(f323(f79(a865),x108141),x108141)))),
% 188.20/188.04 inference(rename_variables,[],[3548])).
% 188.20/188.04 cnf(10820,plain,
% 188.20/188.04 (P101(f323(f323(f238(a865),x108201),f323(a112,f323(f323(f78(a865),x108202),x108201))))),
% 188.20/188.04 inference(rename_variables,[],[3731])).
% 188.20/188.04 cnf(10827,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x108271),x108271))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(10830,plain,
% 188.20/188.04 (P101(f323(f323(f237(a1),x108301),x108301))),
% 188.20/188.04 inference(rename_variables,[],[3282])).
% 188.20/188.04 cnf(10833,plain,
% 188.20/188.04 (~E(f323(a112,x108331),x108331)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(10838,plain,
% 188.20/188.04 (P101(f323(f323(f325(x108381),x108382),f246(f872(x108381,a860))))),
% 188.20/188.04 inference(rename_variables,[],[3439])).
% 188.20/188.04 cnf(10843,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x108431),f2(a865)))),
% 188.20/188.04 inference(rename_variables,[],[4540])).
% 188.20/188.04 cnf(10858,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),f2(a865)),x108581))),
% 188.20/188.04 inference(rename_variables,[],[3303])).
% 188.20/188.04 cnf(10865,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x108651),x108651))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(10874,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x108741),x108742),f188(f872(x108741,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(10882,plain,
% 188.20/188.04 (P101(f323(f323(f325(x108821),x108822),f246(f872(x108821,a860))))),
% 188.20/188.04 inference(rename_variables,[],[3439])).
% 188.20/188.04 cnf(10885,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(f866(x108851),f866(x108851))),f323(f323(f258(f866(x108851),f866(x108851)),x108852),f113(x108851))),f138(x108851,x108853)))),
% 188.20/188.04 inference(rename_variables,[],[4569])).
% 188.20/188.04 cnf(10891,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(x108911,x108911)),x108912),f255(x108911,f188(f872(x108911,a860)))))),
% 188.20/188.04 inference(scs_inference,[],[3240,4459,10166,10172,10186,10242,10245,10335,10338,10629,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,4485,10401,3114,3173,3140,3123,3753,3339,3208,4557,4500,10233,3171,10300,4071,3924,4569,3191,3483,3645,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,3733,3265,4540,10210,10213,10239,10714,10727,4552,3720,3492,3872,3309,3311,3284,4537,4495,4035,3934,10779,3646,4024,4558,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,3282,10357,10412,10620,10709,3283,4536,10276,10366,10477,10501,10751,10793,3439,10573,10838,4548,10760,10874,3343,10602,10632,3375,3801,3738,10279,4545,10230,10590,10593,3303,10635,10787,4115,4543,3809,4526,4529,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,4567,3729,3548,10556,10559,10644,10814,4564,4565,10697,4174,3761,4562,10252,10255,10596,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869])).
% 188.20/188.04 cnf(10892,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x108921),x108922),f188(f872(x108921,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(10894,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x108941),x108942),f323(f303(x108941,x108943,x108944),f188(f872(x108943,a860)))))),
% 188.20/188.04 inference(scs_inference,[],[3240,4459,10166,10172,10186,10242,10245,10335,10338,10629,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,4485,10401,3114,3173,3140,3123,3753,3339,3208,4557,4500,10233,3171,10300,4071,3924,4569,3191,3483,3645,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,3733,3265,4540,10210,10213,10239,10714,10727,4552,3720,3492,3872,3309,3311,3284,4537,4495,4035,3934,10779,3646,4024,4558,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,3282,10357,10412,10620,10709,3283,4536,10276,10366,10477,10501,10751,10793,3439,10573,10838,4548,10760,10874,10892,3343,10602,10632,3375,3801,3738,10279,4545,10230,10590,10593,3303,10635,10787,4115,4543,3809,4526,4529,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,4567,3729,3548,10556,10559,10644,10814,4564,4565,10697,4174,3761,4562,10252,10255,10596,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904])).
% 188.20/188.04 cnf(10895,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x108951),x108952),f188(f872(x108951,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(10898,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x108981,a860)),x108982),f323(f323(f301(x108981),x108983),x108982)))),
% 188.20/188.04 inference(rename_variables,[],[3727])).
% 188.20/188.04 cnf(10901,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x109011),x109011))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(10904,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x109041,a860)),x109042),f323(f323(f301(x109041),x109043),x109042)))),
% 188.20/188.04 inference(rename_variables,[],[3727])).
% 188.20/188.04 cnf(10907,plain,
% 188.20/188.04 (E(f323(f302(x109071,x109071,f5(x109071)),x109072),x109072)),
% 188.20/188.04 inference(rename_variables,[],[3339])).
% 188.20/188.04 cnf(10910,plain,
% 188.20/188.04 (E(f31(x109101,x109102,x109103,x109104,x109105,x109106,x109107,x109108,x109109,a24),x109102)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(10913,plain,
% 188.20/188.04 (E(f31(x109131,x109132,x109133,x109134,x109135,x109136,x109137,x109138,x109139,a24),x109132)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(10926,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x109261,a860)),x109262),f323(f323(f301(x109261),x109263),x109262)))),
% 188.20/188.04 inference(rename_variables,[],[3727])).
% 188.20/188.04 cnf(10939,plain,
% 188.20/188.04 (~E(f323(a112,x109391),f2(a865))),
% 188.20/188.04 inference(rename_variables,[],[4485])).
% 188.20/188.04 cnf(10942,plain,
% 188.20/188.04 (~P101(f323(f60(x109421,x109422,f188(f872(x109421,a860))),x109423))),
% 188.20/188.04 inference(rename_variables,[],[4560])).
% 188.20/188.04 cnf(10946,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(a865,a865)),f323(f323(f258(a865,a865),f323(a112,x109461)),x109461)),f299(a865,a313)))),
% 188.20/188.04 inference(scs_inference,[],[3240,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,4485,10401,10492,3114,3173,3140,3123,3753,3339,10782,3208,4557,4500,10233,3171,10300,4071,3924,4569,3191,3483,3645,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,3733,3265,4540,10210,10213,10239,10714,10727,4552,3720,3492,3872,3309,3311,3284,4537,4495,4035,3934,10779,3646,4024,4558,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,3282,10357,10412,10620,10709,3283,4536,10276,10366,10477,10501,10751,10793,3439,10573,10838,10882,4548,10760,10874,10892,3343,10602,10632,3375,3801,3738,10279,4545,10230,10590,10593,3303,10635,10787,4115,4543,3809,4526,4529,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,10517,4567,3889,3727,10898,10904,3729,3548,10556,10559,10644,10814,4564,4565,10697,4174,3761,4562,10252,10255,10596,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332])).
% 188.20/188.04 cnf(10955,plain,
% 188.20/188.04 (P101(f323(f323(f238(a865),x109551),f323(a112,x109551)))),
% 188.20/188.04 inference(rename_variables,[],[3349])).
% 188.20/188.04 cnf(10965,plain,
% 188.20/188.04 (~E(f323(f302(x109651,f872(x109651,a860),x109652),x109653),f323(f300(x109651),x109653))),
% 188.20/188.04 inference(rename_variables,[],[4546])).
% 188.20/188.04 cnf(10968,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x109681),x109682),f188(f872(x109681,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(10971,plain,
% 188.20/188.04 (P101(f323(f323(f325(f871(x109711,x109711)),f323(f323(f258(x109711,x109711),x109712),x109712)),f299(x109711,x109713)))),
% 188.20/188.04 inference(rename_variables,[],[3924])).
% 188.20/188.04 cnf(10974,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x109741,a860)),x109742),f246(f872(x109741,a860))))),
% 188.20/188.04 inference(rename_variables,[],[3663])).
% 188.20/188.04 cnf(10977,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x109771,a860)),f323(f166(x109771),f164(x109771,x109772,x109773))),f323(f166(x109771),x109773)))),
% 188.20/188.04 inference(rename_variables,[],[3987])).
% 188.20/188.04 cnf(10993,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x109931,a860)),f188(f872(x109931,a860))),x109932))),
% 188.20/188.04 inference(rename_variables,[],[3729])).
% 188.20/188.04 cnf(11004,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(f866(x110041),f866(x110041))),f323(f323(f258(f866(x110041),f866(x110041)),x110042),f113(x110041))),f140(x110041,x110043)))),
% 188.20/188.04 inference(rename_variables,[],[4570])).
% 188.20/188.04 cnf(11015,plain,
% 188.20/188.04 (~E(f323(a112,x110151),x110151)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(11018,plain,
% 188.20/188.04 (~E(f323(a112,x110181),x110181)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(11023,plain,
% 188.20/188.04 (~E(f323(a112,x110231),f2(a865))),
% 188.20/188.04 inference(rename_variables,[],[4485])).
% 188.20/188.04 cnf(11028,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x110281,a860)),x110282),x110282))),
% 188.20/188.04 inference(rename_variables,[],[3581])).
% 188.20/188.04 cnf(11035,plain,
% 188.20/188.04 (~E(f323(a112,x110351),x110351)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(11038,plain,
% 188.20/188.04 (~E(f323(a112,x110381),x110381)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(11043,plain,
% 188.20/188.04 (P27(x110431,x110431,f5(x110431),x110432)),
% 188.20/188.04 inference(rename_variables,[],[3522])).
% 188.20/188.04 cnf(11048,plain,
% 188.20/188.04 (~E(f323(f302(x110481,f872(x110481,a860),x110482),x110483),f323(f300(x110481),x110483))),
% 188.20/188.04 inference(rename_variables,[],[4546])).
% 188.20/188.04 cnf(11053,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x110531,a860)),x110532),f246(f872(x110531,a860))))),
% 188.20/188.04 inference(rename_variables,[],[3663])).
% 188.20/188.04 cnf(11069,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x110691),x110692),f188(f872(x110691,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11072,plain,
% 188.20/188.04 (~P101(f323(f323(f237(a865),f323(a112,x110721)),x110721))),
% 188.20/188.04 inference(rename_variables,[],[4545])).
% 188.20/188.04 cnf(11077,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x110771),x110772),f188(f872(x110771,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11090,plain,
% 188.20/188.04 (~P101(f323(f323(f237(a865),f323(a112,x110901)),x110901))),
% 188.20/188.04 inference(rename_variables,[],[4545])).
% 188.20/188.04 cnf(11093,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x110931),x110932),f188(f872(x110931,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11105,plain,
% 188.20/188.04 (E(f323(x111051,f841(f323(x111051,x111052),f323(f230(x111053),x111052),x111051,x111054,x111053)),f323(x111051,x111052))),
% 188.20/188.04 inference(scs_inference,[],[3240,3522,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,4485,10401,10492,10939,3740,3114,3173,3140,3123,3753,3339,10782,3208,3385,4557,3922,4500,10233,4546,10965,3386,3171,10300,4071,3924,10971,4569,10885,4570,3191,3483,3645,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,10955,3733,3265,4540,10210,10213,10239,10714,10727,10843,4552,3720,3492,3872,3309,3311,3284,4537,4495,4035,3934,10779,3987,3646,4024,3663,10974,4558,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,3282,10357,10412,10620,10709,3283,4536,10276,10366,10477,10501,10751,10793,3439,10573,10838,10882,4548,10760,10874,10892,10895,10968,11069,11077,3343,10602,10632,3375,3801,3738,10279,4545,10230,10590,10593,11072,3303,10635,10787,4115,4543,3809,4526,4529,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,10517,4567,3889,3727,10898,10904,3581,3729,10638,3548,10556,10559,10644,10814,4564,4565,10697,4174,3761,4562,10252,10255,10596,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870])).
% 188.20/188.04 cnf(11114,plain,
% 188.20/188.04 (P101(f323(f323(f325(f871(x111141,x111141)),f323(f323(f258(x111141,x111141),x111142),x111142)),f299(x111141,x111143)))),
% 188.20/188.04 inference(rename_variables,[],[3924])).
% 188.20/188.04 cnf(11119,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(f866(x111191),f866(x111191))),f323(f323(f258(f866(x111191),f866(x111191)),x111192),f113(x111191))),f138(x111191,x111193)))),
% 188.20/188.04 inference(rename_variables,[],[4569])).
% 188.20/188.04 cnf(11122,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(f866(x111221),f866(x111221))),f323(f323(f258(f866(x111221),f866(x111221)),x111222),f113(x111221))),f140(x111221,x111223)))),
% 188.20/188.04 inference(rename_variables,[],[4570])).
% 188.20/188.04 cnf(11125,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(f866(x111251),f866(x111251))),f323(f323(f258(f866(x111251),f866(x111251)),x111252),f113(x111251))),f150(x111251,x111253)))),
% 188.20/188.04 inference(rename_variables,[],[4571])).
% 188.20/188.04 cnf(11130,plain,
% 188.20/188.04 (~P101(f323(f323(f238(f872(x111301,a860)),x111302),f188(f872(x111301,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4558])).
% 188.20/188.04 cnf(11132,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x111321),x111322),f323(f302(x111323,x111321,x111324),f188(f872(x111323,a860)))))),
% 188.20/188.04 inference(scs_inference,[],[3240,3522,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,4485,10401,10492,10939,3740,3114,3173,3140,3123,3753,3339,10782,3208,3385,4557,3922,4500,10233,4546,10965,3386,3171,10300,4071,3924,10971,4569,10885,11119,4570,11004,4571,3191,3483,3645,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,10955,3733,3265,4540,10210,10213,10239,10714,10727,10843,4552,3720,3492,3872,3309,3311,3284,4537,4495,4035,3934,10779,3987,3646,4024,3663,10974,4558,10730,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,3282,10357,10412,10620,10709,3283,4536,10276,10366,10477,10501,10751,10793,3439,10573,10838,10882,4548,10760,10874,10892,10895,10968,11069,11077,11093,3343,10602,10632,3375,3801,3738,10279,4545,10230,10590,10593,11072,3303,10635,10787,4115,4543,3809,4526,4529,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,10517,4567,3889,3727,10898,10904,3581,3729,10638,3548,10556,10559,10644,10814,4564,4565,10697,4174,3761,4562,10252,10255,10596,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034])).
% 188.20/188.04 cnf(11133,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x111331),x111332),f188(f872(x111331,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11139,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x111391,a860)),x111392),f323(f323(f110(f872(x111391,a860)),x111393),f246(f872(x111391,a860)))))),
% 188.20/188.04 inference(scs_inference,[],[3240,3522,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,4485,10401,10492,10939,3740,3114,3173,3140,3123,3753,3339,10782,3208,3385,4557,3922,4500,10233,4546,10965,3386,3171,10300,4071,3924,10971,4569,10885,11119,4570,11004,4571,3191,3483,3645,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,10955,3733,3265,4540,10210,10213,10239,10714,10727,10843,4552,3720,3492,3872,3309,3311,3284,4537,4495,4035,3934,10779,3987,3646,4024,3663,10974,11053,4558,10730,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,3282,10357,10412,10620,10709,3283,4536,10276,10366,10477,10501,10751,10793,3439,10573,10838,10882,4548,10760,10874,10892,10895,10968,11069,11077,11093,3343,10602,10632,3375,3801,3738,10279,4545,10230,10590,10593,11072,3303,10635,10787,4115,4543,3809,4526,4529,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,10517,4567,3889,3727,10898,10904,3581,3729,10638,3548,10556,10559,10644,10814,4564,4565,10697,4174,3761,4562,10252,10255,10596,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065])).
% 188.20/188.04 cnf(11140,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x111401,a860)),x111402),f246(f872(x111401,a860))))),
% 188.20/188.04 inference(rename_variables,[],[3663])).
% 188.20/188.04 cnf(11151,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x111511),x111512),f188(f872(x111511,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11154,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(x111541,x111541)),f323(f323(f258(x111541,x111541),x111542),x111543)),f146(x111541,f113(f872(x111541,a865)))))),
% 188.20/188.04 inference(rename_variables,[],[4567])).
% 188.20/188.04 cnf(11157,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x111571,a860)),x111572),x111572))),
% 188.20/188.04 inference(rename_variables,[],[3581])).
% 188.20/188.04 cnf(11160,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x111601),x111602),f188(f872(x111601,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11162,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x111621,a860)),f323(f277(x111622,x111621,f188(f872(f871(x111622,x111621),a860))),x111623)),x111624))),
% 188.20/188.04 inference(scs_inference,[],[3240,3522,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,4485,10401,10492,10939,3740,3114,3173,3140,3123,3753,3339,10782,3208,3385,4557,3922,4500,10233,4546,10965,3386,3171,10300,4071,3924,10971,4569,10885,11119,4570,11004,4571,3191,3483,3645,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,10955,3733,3265,4540,10210,10213,10239,10714,10727,10843,4552,3720,3492,3872,3309,3311,3284,4537,4495,4035,3934,10779,3987,3646,4024,3663,10974,11053,4558,10730,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,3282,10357,10412,10620,10709,3283,4536,10276,10366,10477,10501,10751,10793,3439,10573,10838,10882,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,3343,10602,10632,3375,3801,3738,10279,4545,10230,10590,10593,11072,3303,10635,10787,4115,4543,3809,4526,4529,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,10517,4567,3889,3727,10898,10904,3581,11028,3729,10638,10993,3548,10556,10559,10644,10814,4564,4565,10697,4174,3761,4562,10252,10255,10596,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235])).
% 188.20/188.04 cnf(11163,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x111631,a860)),f188(f872(x111631,a860))),x111632))),
% 188.20/188.04 inference(rename_variables,[],[3729])).
% 188.20/188.04 cnf(11166,plain,
% 188.20/188.04 (P101(f323(f323(f325(f871(x111661,x111661)),f323(f323(f258(x111661,x111661),x111662),x111662)),f299(x111661,x111663)))),
% 188.20/188.04 inference(rename_variables,[],[3924])).
% 188.20/188.04 cnf(11177,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(f866(x111771),f866(x111771))),f323(f323(f258(f866(x111771),f866(x111771)),x111772),f113(x111771))),f150(x111771,x111773)))),
% 188.20/188.04 inference(rename_variables,[],[4571])).
% 188.20/188.04 cnf(11180,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(f866(x111801),f866(x111801))),f323(f323(f258(f866(x111801),f866(x111801)),f113(x111801)),x111802)),f138(x111801,x111803)))),
% 188.20/188.04 inference(rename_variables,[],[4572])).
% 188.20/188.04 cnf(11185,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(f872(x111851,a860),f872(x111851,a860))),f323(f323(f258(f872(x111851,a860),f872(x111851,a860)),x111852),f188(f872(x111851,a860)))),f298(x111851)))),
% 188.20/188.04 inference(scs_inference,[],[3240,3522,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,4485,10401,10492,10939,3740,3114,3173,3140,3123,3753,3339,10782,3208,3385,4557,3922,4500,10233,4546,10965,3386,3171,10300,4071,3924,10971,11114,4569,10885,11119,4570,11004,4571,11125,4572,4573,3191,3483,3645,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,10955,3733,3265,4540,10210,10213,10239,10714,10727,10843,4552,3720,3492,3872,3309,3311,3284,4537,4495,4035,3934,10779,3987,3646,4024,3663,10974,11053,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,3282,10357,10412,10620,10709,3283,4536,10276,10366,10477,10501,10751,10793,3439,10573,10838,10882,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,3343,10602,10632,3375,3801,3738,10279,4545,10230,10590,10593,11072,3303,10635,10787,4115,4543,3809,4526,4529,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,10517,4567,3889,3727,10898,10904,3581,11028,3729,10638,10993,3548,10556,10559,10644,10814,4564,4565,10697,4174,3761,4562,10252,10255,10596,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392])).
% 188.20/188.04 cnf(11188,plain,
% 188.20/188.04 (P101(f323(f323(f325(x111881),x111882),f246(f872(x111881,a860))))),
% 188.20/188.04 inference(rename_variables,[],[3439])).
% 188.20/188.04 cnf(11193,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x111931,a860)),f188(f872(x111931,a860))),x111932))),
% 188.20/188.04 inference(rename_variables,[],[3729])).
% 188.20/188.04 cnf(11196,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x111961),x111962),f188(f872(x111961,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11199,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x111991,a860)),x111992),f246(f872(x111991,a860))))),
% 188.20/188.04 inference(rename_variables,[],[3663])).
% 188.20/188.04 cnf(11204,plain,
% 188.20/188.04 (P101(f323(f323(f237(f872(x112041,a860)),f188(f872(x112041,a860))),x112042))),
% 188.20/188.04 inference(rename_variables,[],[3729])).
% 188.20/188.04 cnf(11217,plain,
% 188.20/188.04 (P101(f323(f246(f872(x112171,a860)),x112172))),
% 188.20/188.04 inference(rename_variables,[],[3343])).
% 188.20/188.04 cnf(11225,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(f866(x112251),f866(x112251))),f323(f323(f258(f866(x112251),f866(x112251)),x112252),f113(x112251))),f138(x112251,x112253)))),
% 188.20/188.04 inference(rename_variables,[],[4569])).
% 188.20/188.04 cnf(11228,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(f866(x112281),f866(x112281))),f323(f323(f258(f866(x112281),f866(x112281)),x112282),f113(x112281))),f140(x112281,x112283)))),
% 188.20/188.04 inference(rename_variables,[],[4570])).
% 188.20/188.04 cnf(11231,plain,
% 188.20/188.04 (~E(f323(f323(f144(x112311),x112312),x112313),x112313)),
% 188.20/188.04 inference(rename_variables,[],[4500])).
% 188.20/188.04 cnf(11234,plain,
% 188.20/188.04 (~E(f323(a112,x112341),x112341)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(11237,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x112371),x112372),f188(f872(x112371,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11242,plain,
% 188.20/188.04 (P101(f323(f323(f325(f871(f866(x112421),f866(x112421))),f323(f323(f258(f866(x112421),f866(x112421)),x112422),x112422)),f151(x112421,f299(x112421,x112423))))),
% 188.20/188.04 inference(rename_variables,[],[4065])).
% 188.20/188.04 cnf(11247,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(f866(x112471),f866(x112471))),f323(f323(f258(f866(x112471),f866(x112471)),x112472),f113(x112471))),f138(x112471,x112473)))),
% 188.20/188.04 inference(rename_variables,[],[4569])).
% 188.20/188.04 cnf(11251,plain,
% 188.20/188.04 (E(f323(f323(f144(x112511),f579(f299(x112511,x112512),f323(f323(f144(x112511),x112513),x112514),x112514,x112513,x112511)),f580(f299(x112511,x112512),f323(f323(f144(x112511),x112513),x112514),x112514,x112513,x112511)),f323(f323(f144(x112511),x112513),x112514))),
% 188.20/188.04 inference(scs_inference,[],[3240,3522,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,4485,10401,10492,10939,3740,3114,3173,3140,3123,3753,3339,10782,3208,3385,4557,3922,4500,10233,10398,4546,10965,3386,3171,10300,4071,3924,10971,11114,4569,10885,11119,11225,4570,11004,11122,4571,11125,4572,11180,4573,3191,3483,3645,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,10955,3733,3265,4540,10210,10213,10239,10714,10727,10843,4552,3720,3492,3872,3309,3311,3284,4537,4495,4065,11242,4035,3934,10779,3987,3646,4024,3663,10974,11053,11140,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,3282,10357,10412,10620,10709,3283,4536,10276,10366,10477,10501,10751,10793,3439,10573,10838,10882,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,3343,10602,10632,10641,3375,3801,3738,10279,4545,10230,10590,10593,11072,3303,10635,10787,4115,4543,3809,4526,4529,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,10517,4567,3889,3727,10898,10904,3581,11028,3729,10638,10993,11163,11193,3548,10556,10559,10644,10814,4564,4565,10697,4174,4076,3761,4562,10252,10255,10596,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694])).
% 188.20/188.04 cnf(11256,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x112561),x112562),f178(x112563,x112561,f182(x112563,x112561,x112564,f188(f872(x112563,a860))))))),
% 188.20/188.04 inference(scs_inference,[],[3240,3522,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,4485,10401,10492,10939,3740,3114,3173,3140,3123,3753,3339,10782,3208,3385,4557,3922,4500,10233,10398,4546,10965,3386,3171,10300,4071,3924,10971,11114,4569,10885,11119,11225,4570,11004,11122,4571,11125,4572,11180,4573,3191,3483,3645,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,10955,3733,3265,4540,10210,10213,10239,10714,10727,10843,4552,3720,3492,3872,3309,3311,3284,4537,4495,4065,11242,4035,3934,10779,3987,3646,4024,3663,10974,11053,11140,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,3282,10357,10412,10620,10709,3283,4536,10276,10366,10477,10501,10751,10793,3439,10573,10838,10882,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,3343,10602,10632,10641,3375,3801,3738,10279,4545,10230,10590,10593,11072,3303,10635,10787,4115,4543,3809,4526,4529,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,10517,4567,3889,3727,10898,10904,3581,11028,3729,10638,10993,11163,11193,3548,10556,10559,10644,10814,4564,4565,10697,4174,4076,3761,4562,10252,10255,10596,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717])).
% 188.20/188.04 cnf(11257,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x112571),x112572),f188(f872(x112571,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11260,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x112601),x112602),f188(f872(x112601,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11263,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x112631),x112632),f188(f872(x112631,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11266,plain,
% 188.20/188.04 (P101(f323(f323(f325(x112661),x112662),f246(f872(x112661,a860))))),
% 188.20/188.04 inference(rename_variables,[],[3439])).
% 188.20/188.04 cnf(11269,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x112691),f2(a865)))),
% 188.20/188.04 inference(rename_variables,[],[4540])).
% 188.20/188.04 cnf(11274,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(x112741,x112741)),f323(f323(f258(x112741,x112741),x112742),x112743)),f146(x112741,f113(f872(x112741,a865)))))),
% 188.20/188.04 inference(rename_variables,[],[4567])).
% 188.20/188.04 cnf(11277,plain,
% 188.20/188.04 (~E(f323(f302(x112771,f872(x112771,a860),x112772),x112773),f323(f300(x112771),x112773))),
% 188.20/188.04 inference(rename_variables,[],[4546])).
% 188.20/188.04 cnf(11280,plain,
% 188.20/188.04 (~E(f323(f302(x112801,f872(x112801,a860),x112802),x112803),f323(f300(x112801),x112803))),
% 188.20/188.04 inference(rename_variables,[],[4546])).
% 188.20/188.04 cnf(11285,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(f866(x112851),f866(x112851))),f323(f323(f258(f866(x112851),f866(x112851)),x112852),f113(x112851))),f138(x112851,x112853)))),
% 188.20/188.04 inference(rename_variables,[],[4569])).
% 188.20/188.04 cnf(11291,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(f866(x112911),f866(x112911))),f323(f323(f258(f866(x112911),f866(x112911)),x112912),f113(x112911))),f138(x112911,x112913)))),
% 188.20/188.04 inference(rename_variables,[],[4569])).
% 188.20/188.04 cnf(11294,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x112941),x112942),f188(f872(x112941,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11298,plain,
% 188.20/188.04 (P101(f323(f323(f325(f871(x112981,x112982)),f323(f323(f258(x112981,x112982),f323(x112983,x112984)),f323(x112985,x112984))),f323(f302(f871(x112986,x112986),f871(x112981,x112982),f263(x112986,x112981,x112986,x112982,x112983,x112985)),f299(x112986,x112987))))),
% 188.20/188.04 inference(scs_inference,[],[3240,3522,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,4485,10401,10492,10939,3740,3114,3173,3140,3123,3753,3339,10782,3208,3385,4557,3922,4500,10233,10398,4546,10965,11048,11277,3386,3171,10300,4071,3924,10971,11114,11166,4569,10885,11119,11225,11247,11285,4570,11004,11122,11228,4571,11125,4572,11180,4573,3191,3483,3645,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,10955,3733,3265,4540,10210,10213,10239,10714,10727,10843,4552,3720,3492,3872,3309,3311,3284,4537,4495,4065,11242,4035,3934,10779,3987,3646,4024,3663,10974,11053,11140,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,3282,10357,10412,10620,10709,3283,4536,10276,10366,10477,10501,10751,10793,3439,10573,10838,10882,11188,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,3343,10602,10632,10641,3375,3801,3738,10279,4545,10230,10590,10593,11072,3303,10635,10787,4115,4543,3809,4526,4529,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,10517,4567,11154,3889,3727,10898,10904,3581,11028,3729,10638,10993,11163,11193,3548,10556,10559,10644,10814,4564,4565,10697,4174,4076,3761,4562,10252,10255,10596,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014])).
% 188.20/188.04 cnf(11301,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x113011),x113012),f188(f872(x113011,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11304,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x113041),x113042),f188(f872(x113041,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11307,plain,
% 188.20/188.04 (P101(f323(f323(f325(x113071),f323(x113072,x113073)),f323(f302(x113074,x113071,x113072),f246(f872(x113074,a860)))))),
% 188.20/188.04 inference(rename_variables,[],[3889])).
% 188.20/188.04 cnf(11310,plain,
% 188.20/188.04 (~P101(f323(f323(f325(f871(x113101,x113101)),f323(f323(f258(x113101,x113101),x113102),x113103)),f146(x113101,f113(f872(x113101,a865)))))),
% 188.20/188.04 inference(rename_variables,[],[4567])).
% 188.20/188.04 cnf(11319,plain,
% 188.20/188.04 (E(f31(x113191,x113192,x113193,x113194,x113195,x113196,x113197,x113198,x113199,a24),x113192)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11322,plain,
% 188.20/188.04 (E(f31(x113221,x113222,x113223,x113224,x113225,x113226,x113227,x113228,x113229,a24),x113222)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11325,plain,
% 188.20/188.04 (~E(f323(a112,x113251),x113251)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(11332,plain,
% 188.20/188.04 (~E(f323(a112,x113321),x113321)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(11337,plain,
% 188.20/188.04 (E(f31(x113371,x113372,x113373,x113374,x113375,x113376,x113377,x113378,x113379,a24),x113372)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11340,plain,
% 188.20/188.04 (E(f31(x113401,x113402,x113403,x113404,x113405,x113406,x113407,x113408,x113409,a24),x113402)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11346,plain,
% 188.20/188.04 (~E(f323(a112,x113461),x113461)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(11353,plain,
% 188.20/188.04 (~E(f323(f323(f78(a1),x113531),x113531),a97)),
% 188.20/188.04 inference(rename_variables,[],[4498])).
% 188.20/188.04 cnf(11362,plain,
% 188.20/188.04 (E(f323(f323(f22(a865),f2(a865)),x113621),f2(a865))),
% 188.20/188.04 inference(rename_variables,[],[3192])).
% 188.20/188.04 cnf(11365,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x113651),f2(a865)))),
% 188.20/188.04 inference(rename_variables,[],[4540])).
% 188.20/188.04 cnf(11372,plain,
% 188.20/188.04 (E(f323(f323(f78(a1),f323(f323(f79(a1),x113721),f323(f323(f36(a1),x113722),x113721))),f42(a1,x113722,x113721)),x113722)),
% 188.20/188.04 inference(rename_variables,[],[3835])).
% 188.20/188.04 cnf(11384,plain,
% 188.20/188.04 (E(f31(x113841,x113842,x113843,x113844,x113845,x113846,x113847,x113848,x113849,a24),x113842)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11391,plain,
% 188.20/188.04 (E(f31(x113911,x113912,x113913,x113914,x113915,x113916,x113917,x113918,x113919,a24),x113912)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11394,plain,
% 188.20/188.04 (E(f31(x113941,x113942,x113943,x113944,x113945,x113946,x113947,x113948,x113949,a24),x113942)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11397,plain,
% 188.20/188.04 (E(f31(x113971,x113972,x113973,x113974,x113975,x113976,x113977,x113978,x113979,a24),x113972)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11400,plain,
% 188.20/188.04 (E(f31(x114001,x114002,x114003,x114004,x114005,x114006,x114007,x114008,x114009,a24),x114002)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11403,plain,
% 188.20/188.04 (~E(f323(a112,x114031),x114031)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(11406,plain,
% 188.20/188.04 (~E(f323(a112,x114061),x114061)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(11410,plain,
% 188.20/188.04 (E(f31(x114101,x114102,x114103,x114104,x114105,x114106,x114107,x114108,x114109,a24),x114102)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11433,plain,
% 188.20/188.04 (~P101(f323(f60(x114331,x114332,f188(f872(x114331,a860))),x114333))),
% 188.20/188.04 inference(rename_variables,[],[4560])).
% 188.20/188.04 cnf(11436,plain,
% 188.20/188.04 (~P101(f323(f323(f188(f872(x114361,f872(x114362,a860))),x114363),x114364))),
% 188.20/188.04 inference(rename_variables,[],[4565])).
% 188.20/188.04 cnf(11439,plain,
% 188.20/188.04 (P101(f323(f323(f325(x114391),x114392),f246(f872(x114391,a860))))),
% 188.20/188.04 inference(rename_variables,[],[3439])).
% 188.20/188.04 cnf(11447,plain,
% 188.20/188.04 (E(f31(x114471,x114472,x114473,x114474,x114475,x114476,x114477,x114478,x114479,a24),x114472)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11452,plain,
% 188.20/188.04 (~E(f323(a112,x114521),x114521)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(11455,plain,
% 188.20/188.04 (P101(f323(f323(f237(a1),x114551),x114551))),
% 188.20/188.04 inference(rename_variables,[],[3282])).
% 188.20/188.04 cnf(11462,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x114621),x114621))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(11463,plain,
% 188.20/188.04 (E(f31(x114631,x114632,x114633,x114634,x114635,x114636,x114637,x114638,x114639,a24),x114632)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11468,plain,
% 188.20/188.04 (~P101(f323(f323(f188(f872(x114681,f872(x114682,a860))),x114683),x114684))),
% 188.20/188.04 inference(rename_variables,[],[4565])).
% 188.20/188.04 cnf(11479,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),f323(f323(f78(a865),x114791),x114792)),x114792))),
% 188.20/188.04 inference(rename_variables,[],[4562])).
% 188.20/188.04 cnf(11482,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a1),f323(f100(a1),x114821)),f2(a1)))),
% 188.20/188.04 inference(rename_variables,[],[4552])).
% 188.20/188.04 cnf(11493,plain,
% 188.20/188.04 (E(f31(x114931,x114932,x114933,x114934,x114935,x114936,x114937,x114938,x114939,a24),x114932)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11496,plain,
% 188.20/188.04 (E(f31(x114961,x114962,x114963,x114964,x114965,x114966,x114967,x114968,x114969,a24),x114962)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11500,plain,
% 188.20/188.04 (~E(f323(f323(f101(a865),f323(a112,x115001)),x115001),f323(a112,x115001))),
% 188.20/188.04 inference(scs_inference,[],[3240,3522,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,4485,10401,10492,10939,2880,2884,2892,2895,2897,2905,2906,2914,2918,2919,2926,2929,2946,2947,2951,2982,2985,3021,3030,3035,3056,3072,4471,3740,3114,3835,11372,3173,3140,4186,3123,3753,3339,10782,3208,3385,4557,3922,4500,10233,10398,4546,10965,11048,11277,11280,3386,3170,3171,10300,10605,3094,3192,11362,4071,3924,10971,11114,11166,4569,10885,11119,11225,11247,11285,11291,4570,11004,11122,11228,4571,11125,4572,11180,4573,3191,3483,3645,4498,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,10955,3733,3265,4540,10210,10213,10239,10714,10727,10843,11269,11365,4552,3720,3492,3872,3309,3311,3284,4537,4495,3476,4553,4065,11242,3607,4035,3934,10779,3987,3646,4024,3663,10974,11053,11140,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,3282,10357,10412,10620,10709,10830,3283,4536,10276,10366,10477,10501,10751,10793,3439,10573,10838,10882,11188,11266,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,3343,10602,10632,10641,3375,3801,3738,10279,4545,10230,10590,10593,11072,11090,3303,10635,10787,4115,4543,3809,4526,4529,3256,3260,4528,4527,4531,4560,10198,10201,10458,10509,10512,10517,10942,4567,11154,11274,3889,3727,10898,10904,3581,11028,3729,10638,10993,11163,11193,3548,10556,10559,10644,10814,4564,4554,4565,10697,10796,11436,4174,4076,3761,4562,10252,10255,10596,10599,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351])).
% 188.20/188.04 cnf(11507,plain,
% 188.20/188.04 (E(f31(x115071,x115072,x115073,x115074,x115075,x115076,x115077,x115078,x115079,a24),x115072)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11512,plain,
% 188.20/188.04 (E(f31(x115121,x115122,x115123,x115124,x115125,x115126,x115127,x115128,x115129,a24),x115122)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11515,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a1),f323(f100(a1),x115151)),f2(a1)))),
% 188.20/188.04 inference(rename_variables,[],[4552])).
% 188.20/188.04 cnf(11518,plain,
% 188.20/188.04 (E(f31(x115181,x115182,x115183,x115184,x115185,x115186,x115187,x115188,x115189,a24),x115182)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11521,plain,
% 188.20/188.04 (~E(f323(a112,x115211),x115211)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(11524,plain,
% 188.20/188.04 (P101(f323(f323(f237(a1),x115241),x115241))),
% 188.20/188.04 inference(rename_variables,[],[3282])).
% 188.20/188.04 cnf(11531,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x115311),x115311))),
% 188.20/188.04 inference(rename_variables,[],[4536])).
% 188.20/188.04 cnf(11552,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a1),f323(f100(a1),x115521)),f2(a1)))),
% 188.20/188.04 inference(rename_variables,[],[4552])).
% 188.20/188.04 cnf(11567,plain,
% 188.20/188.04 (~P101(f323(f323(f237(a865),f323(a112,x115671)),x115671))),
% 188.20/188.04 inference(rename_variables,[],[4545])).
% 188.20/188.04 cnf(11568,plain,
% 188.20/188.04 (~E(f323(a112,x115681),x115681)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(11578,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),f323(f323(f78(a865),x115781),x115782)),x115781))),
% 188.20/188.04 inference(rename_variables,[],[4563])).
% 188.20/188.04 cnf(11581,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a1),f323(f100(a1),x115811)),f2(a1)))),
% 188.20/188.04 inference(rename_variables,[],[4552])).
% 188.20/188.04 cnf(11584,plain,
% 188.20/188.04 (~E(f323(a112,x115841),x115841)),
% 188.20/188.04 inference(rename_variables,[],[4473])).
% 188.20/188.04 cnf(11597,plain,
% 188.20/188.04 (P101(f323(f323(f325(x115971),x115972),f323(f323(f301(x115971),x115972),x115973)))),
% 188.20/188.04 inference(rename_variables,[],[3597])).
% 188.20/188.04 cnf(11598,plain,
% 188.20/188.04 (~P101(f323(f323(f237(a1),f2(a1)),f323(f77(a1),f323(f100(a1),f323(a112,x115981)))))),
% 188.20/188.04 inference(rename_variables,[],[4564])).
% 188.20/188.04 cnf(11601,plain,
% 188.20/188.04 (P101(f323(f323(f238(a865),f323(f323(f22(a865),x116011),x116012)),f323(a112,x116011)))),
% 188.20/188.04 inference(rename_variables,[],[3733])).
% 188.20/188.04 cnf(11604,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),f42(a865,x116041,x116042)),x116041))),
% 188.20/188.04 inference(rename_variables,[],[3738])).
% 188.20/188.04 cnf(11610,plain,
% 188.20/188.04 (E(f31(x116101,x116102,x116103,x116104,x116105,x116106,x116107,x116108,x116109,a24),x116102)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11613,plain,
% 188.20/188.04 (E(f31(x116131,x116132,x116133,x116134,x116135,x116136,x116137,x116138,x116139,a24),x116132)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11616,plain,
% 188.20/188.04 (E(f31(x116161,x116162,x116163,x116164,x116165,x116166,x116167,x116168,x116169,a24),x116162)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11619,plain,
% 188.20/188.04 (E(f31(x116191,x116192,x116193,x116194,x116195,x116196,x116197,x116198,x116199,a24),x116192)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11622,plain,
% 188.20/188.04 (~P101(f323(f323(f237(a865),f323(a112,x116221)),x116221))),
% 188.20/188.04 inference(rename_variables,[],[4545])).
% 188.20/188.04 cnf(11623,plain,
% 188.20/188.04 (E(f31(x116231,x116232,x116233,x116234,x116235,x116236,x116237,x116238,x116239,a24),x116232)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11632,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x116321),x116321))),
% 188.20/188.04 inference(rename_variables,[],[4536])).
% 188.20/188.04 cnf(11633,plain,
% 188.20/188.04 (E(f31(x116331,x116332,x116333,x116334,x116335,x116336,x116337,x116338,x116339,a24),x116332)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.04 cnf(11636,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),f42(a865,x116361,x116362)),x116361))),
% 188.20/188.04 inference(rename_variables,[],[3738])).
% 188.20/188.04 cnf(11637,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),f2(a865)),x116371))),
% 188.20/188.04 inference(rename_variables,[],[3303])).
% 188.20/188.04 cnf(11654,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x116541),x116541))),
% 188.20/188.04 inference(rename_variables,[],[4536])).
% 188.20/188.04 cnf(11657,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x116571),x116571))),
% 188.20/188.04 inference(rename_variables,[],[4536])).
% 188.20/188.04 cnf(11660,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x116601),x116601))),
% 188.20/188.04 inference(rename_variables,[],[4536])).
% 188.20/188.04 cnf(11663,plain,
% 188.20/188.04 (P101(f323(f323(f325(x116631),f323(x116632,x116633)),f323(f302(x116634,x116631,x116632),f246(f872(x116634,a860)))))),
% 188.20/188.04 inference(rename_variables,[],[3889])).
% 188.20/188.04 cnf(11664,plain,
% 188.20/188.04 (~P101(f323(f323(f237(a865),f323(a112,x116641)),x116641))),
% 188.20/188.04 inference(rename_variables,[],[4545])).
% 188.20/188.04 cnf(11667,plain,
% 188.20/188.04 (P101(f323(f323(f325(x116671),f323(x116672,x116673)),f323(f302(x116674,x116671,x116672),f246(f872(x116674,a860)))))),
% 188.20/188.04 inference(rename_variables,[],[3889])).
% 188.20/188.04 cnf(11668,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),f323(f323(f78(a865),x116681),x116682)),x116682))),
% 188.20/188.04 inference(rename_variables,[],[4562])).
% 188.20/188.04 cnf(11673,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),f323(f323(f78(a865),x116731),x116732)),x116731))),
% 188.20/188.04 inference(rename_variables,[],[4563])).
% 188.20/188.04 cnf(11676,plain,
% 188.20/188.04 (~P101(f323(f323(f238(a865),x116761),x116761))),
% 188.20/188.04 inference(rename_variables,[],[4536])).
% 188.20/188.04 cnf(11679,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x116791),x116791))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(11685,plain,
% 188.20/188.04 (~P36(x116851,x116852,f113(x116851))),
% 188.20/188.04 inference(rename_variables,[],[4509])).
% 188.20/188.04 cnf(11688,plain,
% 188.20/188.04 (P101(f323(f323(f325(x116881),x116882),f246(f872(x116881,a860))))),
% 188.20/188.04 inference(rename_variables,[],[3439])).
% 188.20/188.04 cnf(11689,plain,
% 188.20/188.04 (~P101(f323(f323(f237(a865),f323(a112,x116891)),x116891))),
% 188.20/188.04 inference(rename_variables,[],[4545])).
% 188.20/188.04 cnf(11692,plain,
% 188.20/188.04 (~P101(f323(f60(x116921,x116922,f188(f872(x116921,a860))),x116923))),
% 188.20/188.04 inference(rename_variables,[],[4560])).
% 188.20/188.04 cnf(11705,plain,
% 188.20/188.04 (~P101(f323(f323(f325(x117051),x117052),f188(f872(x117051,a860))))),
% 188.20/188.04 inference(rename_variables,[],[4548])).
% 188.20/188.04 cnf(11708,plain,
% 188.20/188.04 (E(f323(f323(f16(x117081,x117082),x117083),x117084),x117083)),
% 188.20/188.04 inference(rename_variables,[],[3272])).
% 188.20/188.04 cnf(11711,plain,
% 188.20/188.04 (E(f323(f323(f16(x117111,x117112),x117113),x117114),x117113)),
% 188.20/188.04 inference(rename_variables,[],[3272])).
% 188.20/188.04 cnf(11723,plain,
% 188.20/188.04 (P101(f323(f323(f238(a865),f2(a865)),f323(a112,x117231)))),
% 188.20/188.04 inference(rename_variables,[],[3361])).
% 188.20/188.04 cnf(11726,plain,
% 188.20/188.04 (P101(f323(f323(f237(a865),x117261),x117261))),
% 188.20/188.04 inference(rename_variables,[],[3281])).
% 188.20/188.04 cnf(11727,plain,
% 188.20/188.04 (E(f31(x117271,x117272,x117273,x117274,x117275,x117276,x117277,x117278,x117279,a24),x117272)),
% 188.20/188.04 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(11730,plain,
% 188.20/188.05 (P101(f323(f323(f325(x117301),f323(x117302,x117303)),f323(f302(x117304,x117301,x117302),f246(f872(x117304,a860)))))),
% 188.20/188.05 inference(rename_variables,[],[3889])).
% 188.20/188.05 cnf(11733,plain,
% 188.20/188.05 (P101(f323(f59(x117331),f323(f166(x117331),x117332)))),
% 188.20/188.05 inference(rename_variables,[],[3322])).
% 188.20/188.05 cnf(11736,plain,
% 188.20/188.05 (P101(f323(f59(x117361),f323(f166(x117361),x117362)))),
% 188.20/188.05 inference(rename_variables,[],[3322])).
% 188.20/188.05 cnf(11739,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),f323(f77(a1),f323(f100(a1),x117391))),f323(f100(a1),x117392)))),
% 188.20/188.05 inference(rename_variables,[],[3762])).
% 188.20/188.05 cnf(11742,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x117421),x117422),f188(f872(x117421,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(11758,plain,
% 188.20/188.05 (~P101(f323(f323(f325(a865),x117581),f323(f244(a865),f2(a865))))),
% 188.20/188.05 inference(scs_inference,[],[3240,3522,4508,4509,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,4485,10401,10492,10939,2880,2884,2885,2891,2892,2895,2896,2897,2898,2901,2905,2906,2914,2918,2919,2926,2929,2946,2947,2951,2982,2985,3021,3030,3033,3035,3036,3056,3072,4471,3850,3323,3740,3114,3835,11372,3173,3140,3135,4186,3123,3124,3753,3339,10782,3208,3385,4557,3922,4500,10233,10398,3272,11708,4546,10965,11048,11277,11280,3386,3170,3171,10300,10605,3444,3094,3192,11362,4071,3924,10971,11114,11166,4569,10885,11119,11225,11247,11285,11291,4570,11004,11122,11228,4571,11125,4572,11180,4573,3191,3483,3645,4357,4358,4498,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,10955,3733,11601,3265,3361,4540,10210,10213,10239,10714,10727,10843,11269,11365,4552,11482,11515,11552,3720,3492,3872,3309,3311,3284,4537,4495,3476,4553,4065,11242,3607,3322,11733,4035,3934,10779,3987,3646,4024,3663,10974,11053,11140,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,3282,10357,10412,10620,10709,10830,11455,3283,3357,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,3439,10573,10838,10882,11188,11266,11439,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,3343,10602,10632,10641,3381,3375,3801,3738,10279,11604,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,3303,10635,10787,10858,3762,4115,4543,3809,4526,4529,3256,3260,4528,4527,4531,3597,4560,10198,10201,10458,10509,10512,10517,10942,11433,4567,11154,11274,4001,3889,11307,11663,11667,3727,10898,10904,3581,11028,3729,10638,10993,11163,11193,3548,10556,10559,10644,10814,4564,11598,4554,4565,10697,10796,11436,4174,4076,3761,3707,4562,10252,10255,10596,10599,11479,4563,11578,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114])).
% 188.20/188.05 cnf(11761,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x117611),x117611))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(11762,plain,
% 188.20/188.05 (E(f31(x117621,x117622,x117623,x117624,x117625,x117626,x117627,x117628,x117629,a24),x117622)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(11765,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x117651),x117651))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(11774,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x117741),x117741))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(11777,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x117771),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(11782,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x117821),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(11789,plain,
% 188.20/188.05 (P101(f323(f246(f872(x117891,a860)),x117892))),
% 188.20/188.05 inference(rename_variables,[],[3343])).
% 188.20/188.05 cnf(11794,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),f2(a865)),x117941))),
% 188.20/188.05 inference(rename_variables,[],[3303])).
% 188.20/188.05 cnf(11795,plain,
% 188.20/188.05 (~P101(f323(f323(f237(a865),f323(a112,x117951)),x117951))),
% 188.20/188.05 inference(rename_variables,[],[4545])).
% 188.20/188.05 cnf(11798,plain,
% 188.20/188.05 (~P101(f323(f60(x117981,x117982,f188(f872(x117981,a860))),x117983))),
% 188.20/188.05 inference(rename_variables,[],[4560])).
% 188.20/188.05 cnf(11804,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x118041),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(11805,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),x118051),f323(a112,x118051)))),
% 188.20/188.05 inference(rename_variables,[],[3349])).
% 188.20/188.05 cnf(11824,plain,
% 188.20/188.05 (~P101(f323(f323(f237(a865),f323(a112,x118241)),x118241))),
% 188.20/188.05 inference(rename_variables,[],[4545])).
% 188.20/188.05 cnf(11827,plain,
% 188.20/188.05 (~P101(f323(f323(f237(a865),f323(a112,x118271)),x118271))),
% 188.20/188.05 inference(rename_variables,[],[4545])).
% 188.20/188.05 cnf(11830,plain,
% 188.20/188.05 (~P101(f323(f323(f237(a865),f323(a112,x118301)),x118301))),
% 188.20/188.05 inference(rename_variables,[],[4545])).
% 188.20/188.05 cnf(11833,plain,
% 188.20/188.05 (~P101(f323(f323(f237(a865),f323(a112,x118331)),x118331))),
% 188.20/188.05 inference(rename_variables,[],[4545])).
% 188.20/188.05 cnf(11836,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x118361),x118361))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(11839,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x118391),x118391))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(11842,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x118421),x118421))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(11845,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x118451),x118451))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(11862,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x118621),x118621))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(11865,plain,
% 188.20/188.05 (P27(a865,a865,a112,x118651)),
% 188.20/188.05 inference(rename_variables,[],[3491])).
% 188.20/188.05 cnf(11867,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x118671),f323(f73(a1),x118671)))),
% 188.20/188.05 inference(scs_inference,[],[3240,3522,4508,4509,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,11727,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,3491,4485,10401,10492,10939,2880,2884,2885,2891,2892,2895,2896,2897,2898,2901,2905,2906,2913,2914,2918,2919,2926,2929,2938,2946,2947,2951,2982,2985,3021,3030,3033,3035,3036,3044,3056,3072,4471,3850,3323,3740,3114,3835,11372,3173,3140,3135,4186,3123,3124,3753,3339,10782,3208,3385,4557,3922,4500,10233,10398,3272,11708,4546,10965,11048,11277,11280,3386,3170,3171,10300,10605,3444,3094,3192,11362,4071,3924,10971,11114,11166,4569,10885,11119,11225,11247,11285,11291,4570,11004,11122,11228,4571,11125,4572,11180,4573,3191,3483,3645,4357,4358,4498,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,10955,11805,3733,11601,3265,3361,4540,10210,10213,10239,10714,10727,10843,11269,11365,11777,11782,4552,11482,11515,11552,11581,3720,3492,3872,3309,3311,3284,4537,4495,3476,4553,4065,11242,3607,3322,11733,4035,3934,10779,3987,3646,4024,3663,10974,11053,11140,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,11726,3282,10357,10412,10620,10709,10830,11455,11524,11761,11765,11774,3283,3357,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,11676,11836,11839,11842,3439,10573,10838,10882,11188,11266,11439,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,3343,10602,10632,10641,11217,3381,3375,3801,3738,10279,11604,11636,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,11795,11824,11827,11830,3303,10635,10787,10858,11637,3762,4115,4543,3809,4526,4529,3256,3260,4528,4527,4531,3597,4560,10198,10201,10458,10509,10512,10517,10942,11433,11692,11798,4567,11154,11274,4001,3889,11307,11663,11667,3727,10898,10904,3581,11028,3729,10638,10993,11163,11193,3548,10556,10559,10644,10814,4564,11598,4554,4565,10697,10796,11436,4174,4076,3761,3707,4562,10252,10255,10596,10599,11479,4563,11578,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114,6147,6163,6216,6251,6253,6274,6275,6280,6284,6285,6288,6294,6303,6318,6338,6339,6342,6345,6354,6369,6390,6395,6397,6412,6413,6416,6417,6419,6421,6422,6423,6425,6427,6429,6434,6435,6437,6438,6444,6446,6488,6493,6508])).
% 188.20/188.05 cnf(11868,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x118681),x118681))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(11879,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x118791),x118791))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(11882,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(f871(f866(x118821),f866(x118821)),a860)),f151(x118821,x118822)),f299(f866(x118821),f150(x118821,x118822))))),
% 188.20/188.05 inference(rename_variables,[],[3992])).
% 188.20/188.05 cnf(11889,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),x118891),f323(a112,x118891)))),
% 188.20/188.05 inference(rename_variables,[],[3349])).
% 188.20/188.05 cnf(11892,plain,
% 188.20/188.05 (P101(f323(f323(f325(f872(x118921,a860)),x118922),f323(f300(x118921),x118922)))),
% 188.20/188.05 inference(rename_variables,[],[3646])).
% 188.20/188.05 cnf(11893,plain,
% 188.20/188.05 (~E(f323(a112,x118931),x118931)),
% 188.20/188.05 inference(rename_variables,[],[4473])).
% 188.20/188.05 cnf(11898,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x118981),x118981))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(11903,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x119031),x119031))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(11914,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x119141,a860)),x119142),f323(f323(f301(x119141),x119143),x119142)))),
% 188.20/188.05 inference(rename_variables,[],[3727])).
% 188.20/188.05 cnf(11917,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x119171),x119171))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(11918,plain,
% 188.20/188.05 (~E(f323(a112,x119181),x119181)),
% 188.20/188.05 inference(rename_variables,[],[4473])).
% 188.20/188.05 cnf(11929,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x119291),x119291))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(11930,plain,
% 188.20/188.05 (~E(f323(a112,x119301),x119301)),
% 188.20/188.05 inference(rename_variables,[],[4473])).
% 188.20/188.05 cnf(11933,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x119331),x119331))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(11936,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x119361),x119361))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(11939,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x119391),x119391))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(11942,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x119421),x119421))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(11945,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x119451),x119451))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(11948,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x119481),x119481))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(11951,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x119511),x119511))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(11952,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),x119521),f323(a112,x119521)))),
% 188.20/188.05 inference(rename_variables,[],[3349])).
% 188.20/188.05 cnf(11959,plain,
% 188.20/188.05 (~E(f323(a112,x119591),x119591)),
% 188.20/188.05 inference(rename_variables,[],[4473])).
% 188.20/188.05 cnf(11964,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x119641),x119641))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(11965,plain,
% 188.20/188.05 (~E(f323(a112,x119651),x119651)),
% 188.20/188.05 inference(rename_variables,[],[4473])).
% 188.20/188.05 cnf(11968,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x119681),x119681))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(11985,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x119851),x119851))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(11990,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),f2(a865)),x119901))),
% 188.20/188.05 inference(rename_variables,[],[3303])).
% 188.20/188.05 cnf(12007,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x120071),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(12010,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x120101),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(12013,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x120131),x120132),f188(f872(x120131,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12016,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x120161),x120162),f188(f872(x120161,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12018,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x120181),f323(f323(f101(a865),x120182),x120181)))),
% 188.20/188.05 inference(scs_inference,[],[3240,3522,4508,4509,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,11727,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,11584,11893,11918,11930,11959,3491,4485,10401,10492,10939,2880,2884,2885,2891,2892,2895,2896,2897,2898,2901,2905,2906,2913,2914,2918,2919,2926,2929,2938,2946,2947,2951,2982,2985,3021,3030,3033,3035,3036,3044,3056,3072,4471,3850,3323,3223,3740,3984,3114,3835,11372,3173,3140,3135,4186,3123,3124,3753,3339,10782,3208,3385,4557,3922,4500,10233,10398,3272,11708,4546,10965,11048,11277,11280,3386,3170,3171,10300,10605,3444,3094,3192,11362,4071,3924,10971,11114,11166,4569,10885,11119,11225,11247,11285,11291,4570,11004,11122,11228,4571,11125,4572,11180,4573,3191,3483,3645,4357,4358,4498,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,10955,11805,11889,3733,11601,3265,3361,4540,10210,10213,10239,10714,10727,10843,11269,11365,11777,11782,11804,12007,4552,11482,11515,11552,11581,3720,3492,3872,3309,3311,3284,4537,4495,3476,4553,4065,11242,3607,3322,11733,4035,3992,3934,10779,3987,3646,4024,3663,10974,11053,11140,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,11726,11862,11917,11933,11936,11939,11942,3282,10357,10412,10620,10709,10830,11455,11524,11761,11765,11774,11868,11879,11898,11903,11945,11968,3283,3357,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,11676,11836,11839,11842,11845,11929,11948,11951,11964,3439,10573,10838,10882,11188,11266,11439,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,11742,12013,3343,10602,10632,10641,11217,3381,3375,3801,3738,10279,11604,11636,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,11795,11824,11827,11830,11833,3303,10635,10787,10858,11637,11794,3762,4115,4543,3773,3809,4526,4529,3256,3260,4528,4527,4531,3780,3597,4560,10198,10201,10458,10509,10512,10517,10942,11433,11692,11798,4567,11154,11274,4001,3889,11307,11663,11667,3727,10898,10904,10926,3581,11028,3729,10638,10993,11163,11193,3548,10556,10559,10644,10814,4564,11598,4554,4565,10697,10796,11436,4174,4076,3761,3707,4562,10252,10255,10596,10599,11479,4563,11578,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114,6147,6163,6216,6251,6253,6274,6275,6280,6284,6285,6288,6294,6303,6318,6338,6339,6342,6345,6354,6369,6390,6395,6397,6412,6413,6416,6417,6419,6421,6422,6423,6425,6427,6429,6434,6435,6437,6438,6444,6446,6488,6493,6508,6510,6511,6512,6546,6551,6553,6558,6559,6567,6571,6583,6607,6608,6610,6611,6622,6628,6645,6648,6667,6699,6700,6701,6706,6720,6739,6741,6743,6745,6750,6756,6758,6773,6778,6781,6817,6818,6819,6833,6834,6836,6837,6855,6857,6871,6897,6919,6930,6932,6934,6936,6937,6938,6971,6972,6977,6978,6985])).
% 188.20/188.05 cnf(12019,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x120191),x120191))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(12021,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x120211),f323(f323(f101(a865),x120211),x120212)))),
% 188.20/188.05 inference(scs_inference,[],[3240,3522,4508,4509,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,11727,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,11584,11893,11918,11930,11959,3491,4485,10401,10492,10939,2880,2884,2885,2891,2892,2895,2896,2897,2898,2901,2905,2906,2913,2914,2918,2919,2926,2929,2938,2946,2947,2951,2982,2985,3021,3030,3033,3035,3036,3044,3056,3072,4471,3850,3323,3223,3740,3984,3114,3835,11372,3173,3140,3135,4186,3123,3124,3753,3339,10782,3208,3385,4557,3922,4500,10233,10398,3272,11708,4546,10965,11048,11277,11280,3386,3170,3171,10300,10605,3444,3094,3192,11362,4071,3924,10971,11114,11166,4569,10885,11119,11225,11247,11285,11291,4570,11004,11122,11228,4571,11125,4572,11180,4573,3191,3483,3645,4357,4358,4498,3585,3797,3349,10319,10437,10506,10567,10570,10608,10706,10955,11805,11889,3733,11601,3265,3361,4540,10210,10213,10239,10714,10727,10843,11269,11365,11777,11782,11804,12007,4552,11482,11515,11552,11581,3720,3492,3872,3309,3311,3284,4537,4495,3476,4553,4065,11242,3607,3322,11733,4035,3992,3934,10779,3987,3646,4024,3663,10974,11053,11140,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,11726,11862,11917,11933,11936,11939,11942,3282,10357,10412,10620,10709,10830,11455,11524,11761,11765,11774,11868,11879,11898,11903,11945,11968,3283,3357,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,11676,11836,11839,11842,11845,11929,11948,11951,11964,12019,3439,10573,10838,10882,11188,11266,11439,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,11742,12013,3343,10602,10632,10641,11217,3381,3375,3801,3738,10279,11604,11636,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,11795,11824,11827,11830,11833,3303,10635,10787,10858,11637,11794,3762,4115,4543,3773,3809,4526,4529,3256,3260,4528,4527,4531,3780,3597,4560,10198,10201,10458,10509,10512,10517,10942,11433,11692,11798,4567,11154,11274,4001,3889,11307,11663,11667,3727,10898,10904,10926,3581,11028,3729,10638,10993,11163,11193,3548,10556,10559,10644,10814,4564,11598,4554,4565,10697,10796,11436,4174,4076,3761,3707,4562,10252,10255,10596,10599,11479,4563,11578,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114,6147,6163,6216,6251,6253,6274,6275,6280,6284,6285,6288,6294,6303,6318,6338,6339,6342,6345,6354,6369,6390,6395,6397,6412,6413,6416,6417,6419,6421,6422,6423,6425,6427,6429,6434,6435,6437,6438,6444,6446,6488,6493,6508,6510,6511,6512,6546,6551,6553,6558,6559,6567,6571,6583,6607,6608,6610,6611,6622,6628,6645,6648,6667,6699,6700,6701,6706,6720,6739,6741,6743,6745,6750,6756,6758,6773,6778,6781,6817,6818,6819,6833,6834,6836,6837,6855,6857,6871,6897,6919,6930,6932,6934,6936,6937,6938,6971,6972,6977,6978,6985,6986])).
% 188.20/188.05 cnf(12022,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x120221),x120221))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(12025,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x120251),x120251))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(12028,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x120281),x120281))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(12031,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),x120311),f323(a112,x120311)))),
% 188.20/188.05 inference(rename_variables,[],[3349])).
% 188.20/188.05 cnf(12038,plain,
% 188.20/188.05 (P101(f323(f323(f325(f872(x120381,a860)),x120382),f323(f300(x120381),x120382)))),
% 188.20/188.05 inference(rename_variables,[],[3646])).
% 188.20/188.05 cnf(12043,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x120431,a860)),x120432),f323(f323(f301(x120431),x120433),x120432)))),
% 188.20/188.05 inference(rename_variables,[],[3727])).
% 188.20/188.05 cnf(12050,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x120501),x120502),f188(f872(x120501,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12059,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x120591,a860)),x120592),f246(f872(x120591,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3663])).
% 188.20/188.05 cnf(12060,plain,
% 188.20/188.05 (~E(f323(a112,x120601),x120601)),
% 188.20/188.05 inference(rename_variables,[],[4473])).
% 188.20/188.05 cnf(12063,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x120631,a860)),f323(f166(x120631),f323(f129(x120631,x120632),x120633))),f323(f166(x120631),x120633)))),
% 188.20/188.05 inference(rename_variables,[],[3934])).
% 188.20/188.05 cnf(12069,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),x120691),f323(a112,x120691)))),
% 188.20/188.05 inference(rename_variables,[],[3349])).
% 188.20/188.05 cnf(12077,plain,
% 188.20/188.05 (~P101(f323(f323(f325(f871(x120771,x120771)),x120772),f146(x120771,f113(f872(x120771,a865)))))),
% 188.20/188.05 inference(scs_inference,[],[3240,3522,4508,4509,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,11727,11762,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,11584,11893,11918,11930,11959,11965,3491,4485,10401,10492,10939,2880,2884,2885,2891,2892,2895,2896,2897,2898,2900,2901,2905,2906,2913,2914,2918,2919,2926,2929,2938,2946,2947,2951,2982,2985,3021,3030,3033,3035,3036,3044,3056,3072,4471,3850,3323,3223,3740,3984,3114,3835,11372,3173,3140,3135,4186,3123,3124,3753,3339,10782,3208,3385,4557,3922,4500,10233,10398,3272,11708,4546,10965,11048,11277,11280,3386,3170,3171,10300,10605,3444,3094,3192,11362,4071,3924,10971,11114,11166,4569,10885,11119,11225,11247,11285,11291,4570,11004,11122,11228,4571,11125,4572,11180,4573,3191,3483,3645,4357,4358,4498,3585,3797,3470,3722,3349,10319,10437,10506,10567,10570,10608,10706,10955,11805,11889,11952,12031,3733,11601,3265,3361,3547,4540,10210,10213,10239,10714,10727,10843,11269,11365,11777,11782,11804,12007,4552,11482,11515,11552,11581,3720,3492,3872,3309,3311,3284,4537,4495,3476,4553,4065,11242,3607,3322,11733,4035,3992,3934,10779,3987,3646,11892,4024,3663,10974,11053,11140,11199,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,11726,11862,11917,11933,11936,11939,11942,3282,10357,10412,10620,10709,10830,11455,11524,11761,11765,11774,11868,11879,11898,11903,11945,11968,3283,3357,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,11676,11836,11839,11842,11845,11929,11948,11951,11964,12019,12022,12025,3439,10573,10838,10882,11188,11266,11439,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,11742,12013,12016,3343,10602,10632,10641,11217,3381,3375,3801,3738,10279,11604,11636,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,11795,11824,11827,11830,11833,3303,10635,10787,10858,11637,11794,3762,4115,4543,3773,3809,4526,4529,3256,3260,4528,4527,4531,3780,3597,4560,10198,10201,10458,10509,10512,10517,10942,11433,11692,11798,4567,11154,11274,4001,3889,11307,11663,11667,3727,10898,10904,10926,11914,3581,11028,3729,10638,10993,11163,11193,3548,10556,10559,10644,10814,4564,11598,4554,4565,10697,10796,11436,4174,4076,3761,3707,4562,10252,10255,10596,10599,11479,4563,11578,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114,6147,6163,6216,6251,6253,6274,6275,6280,6284,6285,6288,6294,6303,6318,6338,6339,6342,6345,6354,6369,6390,6395,6397,6412,6413,6416,6417,6419,6421,6422,6423,6425,6427,6429,6434,6435,6437,6438,6444,6446,6488,6493,6508,6510,6511,6512,6546,6551,6553,6558,6559,6567,6571,6583,6607,6608,6610,6611,6622,6628,6645,6648,6667,6699,6700,6701,6706,6720,6739,6741,6743,6745,6750,6756,6758,6773,6778,6781,6817,6818,6819,6833,6834,6836,6837,6855,6857,6871,6897,6919,6930,6932,6934,6936,6937,6938,6971,6972,6977,6978,6985,6986,6988,6990,7009,7018,7019,7031,7041,7080,7090,7094,7101,7112,7118,7120,7126,7135,7148,7165,7183,7185,7202])).
% 188.20/188.05 cnf(12078,plain,
% 188.20/188.05 (E(f31(x120781,x120782,x120783,x120784,x120785,x120786,x120787,x120788,x120789,a24),x120782)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12089,plain,
% 188.20/188.05 (~P101(f323(f323(f237(a865),f323(a112,x120891)),x120891))),
% 188.20/188.05 inference(rename_variables,[],[4545])).
% 188.20/188.05 cnf(12090,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x120901),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(12093,plain,
% 188.20/188.05 (P101(f323(f59(x120931),f188(f872(x120931,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3357])).
% 188.20/188.05 cnf(12094,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x120941),x120942),f188(f872(x120941,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12099,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x120991),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(12100,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x121001),x121001))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(12105,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x121051,a860)),f323(f166(x121051),f164(x121051,x121052,x121053))),f323(f166(x121051),x121053)))),
% 188.20/188.05 inference(rename_variables,[],[3987])).
% 188.20/188.05 cnf(12108,plain,
% 188.20/188.05 (P27(x121081,x121081,f5(x121081),x121082)),
% 188.20/188.05 inference(rename_variables,[],[3522])).
% 188.20/188.05 cnf(12113,plain,
% 188.20/188.05 (P101(f323(f323(f325(f872(x121131,a860)),x121132),f323(f300(x121131),x121132)))),
% 188.20/188.05 inference(rename_variables,[],[3646])).
% 188.20/188.05 cnf(12120,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x121201),x121201))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12123,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x121231),x121232),f188(f872(x121231,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12126,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x121261,a860)),x121262),f323(f323(f301(x121261),x121263),x121262)))),
% 188.20/188.05 inference(rename_variables,[],[3727])).
% 188.20/188.05 cnf(12127,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x121271,a860)),x121272),f246(f872(x121271,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3663])).
% 188.20/188.05 cnf(12134,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x121341),x121341))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12137,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x121371),x121371))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12140,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x121401),x121401))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12143,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x121431),x121431))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12146,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),x121461),f323(a112,x121461)))),
% 188.20/188.05 inference(rename_variables,[],[3349])).
% 188.20/188.05 cnf(12149,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),x121491),f323(a112,x121491)))),
% 188.20/188.05 inference(rename_variables,[],[3349])).
% 188.20/188.05 cnf(12152,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x121521,a860)),x121522),x121522))),
% 188.20/188.05 inference(rename_variables,[],[3581])).
% 188.20/188.05 cnf(12154,plain,
% 188.20/188.05 (~P101(f323(f323(f237(a1),f323(f323(f22(a1),a81),a97)),f2(a1)))),
% 188.20/188.05 inference(scs_inference,[],[3240,3522,11043,4508,4509,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,11727,11762,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,11584,11893,11918,11930,11959,11965,3491,4485,10401,10492,10939,2880,2884,2885,2891,2892,2895,2896,2897,2898,2900,2901,2904,2905,2906,2913,2914,2918,2919,2926,2929,2938,2946,2947,2951,2982,2985,3021,3030,3033,3035,3036,3044,3056,3072,4471,3850,3323,3223,3740,3984,3114,3835,11372,3173,3140,3135,4186,3123,3124,3753,3339,10782,3208,3385,4557,3922,4500,10233,10398,3272,11708,4546,10965,11048,11277,11280,3386,3170,3171,10300,10605,3444,3094,3192,11362,4071,3924,10971,11114,11166,4569,10885,11119,11225,11247,11285,11291,4570,11004,11122,11228,4571,11125,4572,11180,4573,3191,3483,3645,4357,4358,4498,3585,3797,3470,3722,3349,10319,10437,10506,10567,10570,10608,10706,10955,11805,11889,11952,12031,12069,12146,3733,11601,3265,3361,3547,4540,10210,10213,10239,10714,10727,10843,11269,11365,11777,11782,11804,12007,12010,12090,4552,11482,11515,11552,11581,3720,3492,3872,3309,3311,3284,4537,4495,3476,4553,4065,11242,3607,3322,11733,11736,4035,3992,3934,10779,3987,10977,3646,11892,12038,4024,3663,10974,11053,11140,11199,12059,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,11726,11862,11917,11933,11936,11939,11942,12120,12134,12137,12140,3282,10357,10412,10620,10709,10830,11455,11524,11761,11765,11774,11868,11879,11898,11903,11945,11968,3283,3357,12093,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,11676,11836,11839,11842,11845,11929,11948,11951,11964,12019,12022,12025,12028,3439,10573,10838,10882,11188,11266,11439,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,11742,12013,12016,12050,12094,3343,10602,10632,10641,11217,3381,3375,3801,3738,10279,11604,11636,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,11795,11824,11827,11830,11833,3303,10635,10787,10858,11637,11794,3762,4115,4543,3773,3809,4526,4529,3256,3260,4528,4527,4531,3780,3597,4560,10198,10201,10458,10509,10512,10517,10942,11433,11692,11798,4567,11154,11274,4001,3889,11307,11663,11667,3727,10898,10904,10926,11914,12043,3581,11028,11157,3729,10638,10993,11163,11193,3548,10556,10559,10644,10814,4564,11598,4554,4565,10697,10796,11436,4174,4076,3761,3707,4562,10252,10255,10596,10599,11479,4563,11578,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114,6147,6163,6216,6251,6253,6274,6275,6280,6284,6285,6288,6294,6303,6318,6338,6339,6342,6345,6354,6369,6390,6395,6397,6412,6413,6416,6417,6419,6421,6422,6423,6425,6427,6429,6434,6435,6437,6438,6444,6446,6488,6493,6508,6510,6511,6512,6546,6551,6553,6558,6559,6567,6571,6583,6607,6608,6610,6611,6622,6628,6645,6648,6667,6699,6700,6701,6706,6720,6739,6741,6743,6745,6750,6756,6758,6773,6778,6781,6817,6818,6819,6833,6834,6836,6837,6855,6857,6871,6897,6919,6930,6932,6934,6936,6937,6938,6971,6972,6977,6978,6985,6986,6988,6990,7009,7018,7019,7031,7041,7080,7090,7094,7101,7112,7118,7120,7126,7135,7148,7165,7183,7185,7202,7251,7252,7253,7255,7257,7261,7266,7289,7331,7363,7378,7395,7427,7430,7455,7479,7496,7499,7500,7510,7529,7531,7533,7535,7536,7537,7562,7588])).
% 188.20/188.05 cnf(12159,plain,
% 188.20/188.05 (P101(f323(f323(f325(f872(x121591,a860)),x121592),f323(f300(x121591),x121592)))),
% 188.20/188.05 inference(rename_variables,[],[3646])).
% 188.20/188.05 cnf(12168,plain,
% 188.20/188.05 (~E(f323(a112,x121681),x121681)),
% 188.20/188.05 inference(rename_variables,[],[4473])).
% 188.20/188.05 cnf(12169,plain,
% 188.20/188.05 (E(f323(f302(x121691,x121691,f5(x121691)),x121692),x121692)),
% 188.20/188.05 inference(rename_variables,[],[3339])).
% 188.20/188.05 cnf(12172,plain,
% 188.20/188.05 (P33(x121721,x121722,f113(x121721),f113(x121721))),
% 188.20/188.05 inference(rename_variables,[],[3531])).
% 188.20/188.05 cnf(12175,plain,
% 188.20/188.05 (~E(f323(a112,x121751),x121751)),
% 188.20/188.05 inference(rename_variables,[],[4473])).
% 188.20/188.05 cnf(12178,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x121781,a860)),f323(f166(x121781),f164(x121781,x121782,x121783))),f323(f166(x121781),x121783)))),
% 188.20/188.05 inference(rename_variables,[],[3987])).
% 188.20/188.05 cnf(12179,plain,
% 188.20/188.05 (P101(f323(f59(x121791),f323(f166(x121791),x121792)))),
% 188.20/188.05 inference(rename_variables,[],[3322])).
% 188.20/188.05 cnf(12190,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x121901),x121901))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(12193,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x121931),x121931))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(12198,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),f2(a865)),x121981))),
% 188.20/188.05 inference(rename_variables,[],[3303])).
% 188.20/188.05 cnf(12205,plain,
% 188.20/188.05 (P16(a865,f323(f162(a865),f323(f323(f147(f866(x122051),a865),f189(f866(x122051))),f173(x122051,x122052))))),
% 188.20/188.05 inference(rename_variables,[],[3845])).
% 188.20/188.05 cnf(12208,plain,
% 188.20/188.05 (P27(x122081,x122081,f5(x122081),x122082)),
% 188.20/188.05 inference(rename_variables,[],[3522])).
% 188.20/188.05 cnf(12211,plain,
% 188.20/188.05 (P27(x122111,x122111,f5(x122111),x122112)),
% 188.20/188.05 inference(rename_variables,[],[3522])).
% 188.20/188.05 cnf(12214,plain,
% 188.20/188.05 (P101(f323(f323(f325(f866(x122141)),f113(x122141)),f154(x122141,x122142)))),
% 188.20/188.05 inference(rename_variables,[],[3483])).
% 188.20/188.05 cnf(12217,plain,
% 188.20/188.05 (~P101(f323(f323(f188(f872(x122171,f872(x122172,a860))),x122173),x122174))),
% 188.20/188.05 inference(rename_variables,[],[4565])).
% 188.20/188.05 cnf(12222,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x122221),x122221))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12223,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),f2(a865)),x122231))),
% 188.20/188.05 inference(rename_variables,[],[3303])).
% 188.20/188.05 cnf(12226,plain,
% 188.20/188.05 (~P101(f323(f323(f188(f872(x122261,f872(x122262,a860))),x122263),x122264))),
% 188.20/188.05 inference(rename_variables,[],[4565])).
% 188.20/188.05 cnf(12229,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(f871(f866(x122291),f866(x122291)),a860)),f151(x122291,x122292)),f299(f866(x122291),f150(x122291,x122292))))),
% 188.20/188.05 inference(rename_variables,[],[3992])).
% 188.20/188.05 cnf(12235,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x122351,a860)),f323(f166(x122351),f164(x122351,x122352,x122353))),f323(f166(x122351),x122353)))),
% 188.20/188.05 inference(rename_variables,[],[3987])).
% 188.20/188.05 cnf(12236,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x122361,a860)),f323(f166(x122361),f323(f129(x122361,x122362),x122363))),f323(f166(x122361),x122363)))),
% 188.20/188.05 inference(rename_variables,[],[3934])).
% 188.20/188.05 cnf(12239,plain,
% 188.20/188.05 (~P101(f323(f323(f238(f872(x122391,a860)),x122392),f188(f872(x122391,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4558])).
% 188.20/188.05 cnf(12242,plain,
% 188.20/188.05 (P27(x122421,f869(x122421),f230(x122421),x122422)),
% 188.20/188.05 inference(rename_variables,[],[3532])).
% 188.20/188.05 cnf(12247,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x122471,a860)),f323(f302(x122472,x122471,x122473),f323(f303(x122472,x122471,x122473),x122474))),x122474))),
% 188.20/188.05 inference(rename_variables,[],[4174])).
% 188.20/188.05 cnf(12250,plain,
% 188.20/188.05 (P101(f323(f59(f869(x122501)),f323(f302(x122502,f869(x122501),f323(f179(x122502,x122501),x122503)),f246(f872(x122502,a860)))))),
% 188.20/188.05 inference(rename_variables,[],[4001])).
% 188.20/188.05 cnf(12255,plain,
% 188.20/188.05 (P101(f323(f323(f325(f866(x122551)),f113(x122551)),f154(x122551,x122552)))),
% 188.20/188.05 inference(rename_variables,[],[3483])).
% 188.20/188.05 cnf(12258,plain,
% 188.20/188.05 (~P101(f323(f323(f325(f871(f866(x122581),f866(x122581))),f323(f323(f258(f866(x122581),f866(x122581)),x122582),f113(x122581))),f138(x122581,x122583)))),
% 188.20/188.05 inference(rename_variables,[],[4569])).
% 188.20/188.05 cnf(12261,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x122611),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(12263,plain,
% 188.20/188.05 (~P101(f323(f59(x122631),f246(f872(x122631,a860))))),
% 188.20/188.05 inference(scs_inference,[],[3240,3522,11043,12108,12208,3531,3532,3250,4508,4509,3149,4489,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,11727,11762,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,11584,11893,11918,11930,11959,11965,12060,12168,3491,4485,10401,10492,10939,2880,2884,2885,2891,2892,2895,2896,2897,2898,2900,2901,2904,2905,2906,2913,2914,2918,2919,2926,2929,2938,2946,2947,2951,2957,2982,2985,3021,3030,3033,3035,3036,3044,3056,3072,4471,3850,3323,3223,3740,3984,3114,3835,11372,3173,3140,3135,4186,3123,3124,3753,3155,3339,10782,10907,3208,3385,4557,3922,4500,10233,10398,3272,11708,4546,10965,11048,11277,11280,3386,3170,3171,10300,10605,3444,3094,3192,11362,4071,3924,10971,11114,11166,4569,10885,11119,11225,11247,11285,11291,4570,11004,11122,11228,4571,11125,4572,11180,4573,3191,3483,12214,12255,3645,4357,4358,4498,3585,3797,3845,3470,3722,3349,10319,10437,10506,10567,10570,10608,10706,10955,11805,11889,11952,12031,12069,12146,3733,11601,3265,3361,3547,4540,10210,10213,10239,10714,10727,10843,11269,11365,11777,11782,11804,12007,12010,12090,12099,4552,11482,11515,11552,11581,3720,3492,3872,3309,3311,3284,4537,4495,3476,4553,4065,11242,3607,3322,11733,11736,4035,3992,11882,12229,3934,10779,12063,3987,10977,12105,12178,3646,11892,12038,12113,12159,4024,3663,10974,11053,11140,11199,12059,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,11726,11862,11917,11933,11936,11939,11942,12120,12134,12137,12140,12143,3282,10357,10412,10620,10709,10830,11455,11524,11761,11765,11774,11868,11879,11898,11903,11945,11968,3283,3357,12093,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,11676,11836,11839,11842,11845,11929,11948,11951,11964,12019,12022,12025,12028,12100,12190,3439,10573,10838,10882,11188,11266,11439,11688,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,11742,12013,12016,12050,12094,3343,10602,10632,10641,11217,3381,3375,3801,3738,10279,11604,11636,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,11795,11824,11827,11830,11833,12089,3303,10635,10787,10858,11637,11794,11990,12198,3762,4115,4543,3773,3809,4526,4529,3256,3260,4528,4527,4531,3780,3597,4560,10198,10201,10458,10509,10512,10517,10942,11433,11692,11798,4567,11154,11274,4001,3889,11307,11663,11667,3727,10898,10904,10926,11914,12043,3581,11028,11157,12152,3729,10638,10993,11163,11193,3548,10556,10559,10644,10814,4564,11598,4554,4565,10697,10796,11436,11468,12217,4174,10772,4076,3761,3707,4562,10252,10255,10596,10599,11479,4563,11578,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114,6147,6163,6216,6251,6253,6274,6275,6280,6284,6285,6288,6294,6303,6318,6338,6339,6342,6345,6354,6369,6390,6395,6397,6412,6413,6416,6417,6419,6421,6422,6423,6425,6427,6429,6434,6435,6437,6438,6444,6446,6488,6493,6508,6510,6511,6512,6546,6551,6553,6558,6559,6567,6571,6583,6607,6608,6610,6611,6622,6628,6645,6648,6667,6699,6700,6701,6706,6720,6739,6741,6743,6745,6750,6756,6758,6773,6778,6781,6817,6818,6819,6833,6834,6836,6837,6855,6857,6871,6897,6919,6930,6932,6934,6936,6937,6938,6971,6972,6977,6978,6985,6986,6988,6990,7009,7018,7019,7031,7041,7080,7090,7094,7101,7112,7118,7120,7126,7135,7148,7165,7183,7185,7202,7251,7252,7253,7255,7257,7261,7266,7289,7331,7363,7378,7395,7427,7430,7455,7479,7496,7499,7500,7510,7529,7531,7533,7535,7536,7537,7562,7588,7589,7621,7623,7624,7625,7630,7652,7661,7671,7676,7682,7684,7690,7702,7703,7705,7728,7734,7755,7822,7823,7824,7872,7880,7881,7906,7907,7924,7925,7982,7983,8012,8039,8049,8051,8060,8072,8102,8108,8115])).
% 188.20/188.05 cnf(12264,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x122641,a860)),x122642),x122642))),
% 188.20/188.05 inference(rename_variables,[],[3581])).
% 188.20/188.05 cnf(12267,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x122671),x122672),f188(f872(x122671,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12270,plain,
% 188.20/188.05 (~P101(f323(f323(f188(f872(x122701,f872(x122702,a860))),x122703),x122704))),
% 188.20/188.05 inference(rename_variables,[],[4565])).
% 188.20/188.05 cnf(12273,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x122731,a860)),f323(f302(x122732,x122731,x122733),f323(f303(x122732,x122731,x122733),x122734))),x122734))),
% 188.20/188.05 inference(rename_variables,[],[4174])).
% 188.20/188.05 cnf(12274,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x122741,a860)),x122742),x122742))),
% 188.20/188.05 inference(rename_variables,[],[3581])).
% 188.20/188.05 cnf(12279,plain,
% 188.20/188.05 (E(f31(x122791,x122792,x122793,x122794,x122795,x122796,x122797,x122798,x122799,a24),x122792)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12282,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x122821,a860)),f323(f166(x122821),f164(x122821,x122822,x122823))),f323(f166(x122821),x122823)))),
% 188.20/188.05 inference(rename_variables,[],[3987])).
% 188.20/188.05 cnf(12283,plain,
% 188.20/188.05 (P101(f323(f59(x122831),f323(f166(x122831),x122832)))),
% 188.20/188.05 inference(rename_variables,[],[3322])).
% 188.20/188.05 cnf(12286,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x122861),x122861))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12289,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x122891),x122891))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(12292,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x122921),x122921))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(12303,plain,
% 188.20/188.05 (P27(x123031,x123031,f5(x123031),x123032)),
% 188.20/188.05 inference(rename_variables,[],[3522])).
% 188.20/188.05 cnf(12311,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x123111),x123112),f188(f872(x123111,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12314,plain,
% 188.20/188.05 (P101(f323(f323(f325(f871(x123141,x123141)),f323(f323(f258(x123141,x123141),x123142),x123142)),f299(x123141,x123143)))),
% 188.20/188.05 inference(rename_variables,[],[3924])).
% 188.20/188.05 cnf(12317,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x123171),x123172),f188(f872(x123171,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12320,plain,
% 188.20/188.05 (P101(f323(f323(f325(f871(x123201,x123201)),f323(f323(f258(x123201,x123201),x123202),x123202)),f299(x123201,x123203)))),
% 188.20/188.05 inference(rename_variables,[],[3924])).
% 188.20/188.05 cnf(12330,plain,
% 188.20/188.05 (~E(f323(f323(f144(x123301),x123302),x123303),x123303)),
% 188.20/188.05 inference(rename_variables,[],[4500])).
% 188.20/188.05 cnf(12337,plain,
% 188.20/188.05 (P101(f323(f323(f325(x123371),x123372),f246(f872(x123371,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3439])).
% 188.20/188.05 cnf(12338,plain,
% 188.20/188.05 (~E(f323(a112,x123381),x123381)),
% 188.20/188.05 inference(rename_variables,[],[4473])).
% 188.20/188.05 cnf(12341,plain,
% 188.20/188.05 (P101(f323(f323(f325(f866(x123411)),f113(x123411)),f154(x123411,x123412)))),
% 188.20/188.05 inference(rename_variables,[],[3483])).
% 188.20/188.05 cnf(12342,plain,
% 188.20/188.05 (~E(f323(f323(f144(x123421),x123422),x123423),f113(x123421))),
% 188.20/188.05 inference(rename_variables,[],[4507])).
% 188.20/188.05 cnf(12345,plain,
% 188.20/188.05 (P27(x123451,x123451,f5(x123451),x123452)),
% 188.20/188.05 inference(rename_variables,[],[3522])).
% 188.20/188.05 cnf(12348,plain,
% 188.20/188.05 (P101(f323(f323(f325(x123481),f323(x123482,x123483)),f323(f302(x123484,x123481,x123482),f246(f872(x123484,a860)))))),
% 188.20/188.05 inference(rename_variables,[],[3889])).
% 188.20/188.05 cnf(12349,plain,
% 188.20/188.05 (P27(x123491,x123491,f5(x123491),x123492)),
% 188.20/188.05 inference(rename_variables,[],[3522])).
% 188.20/188.05 cnf(12352,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x123521,a860)),f188(f872(x123521,a860))),x123522))),
% 188.20/188.05 inference(rename_variables,[],[3729])).
% 188.20/188.05 cnf(12353,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x123531,a860)),x123532),x123532))),
% 188.20/188.05 inference(rename_variables,[],[3581])).
% 188.20/188.05 cnf(12356,plain,
% 188.20/188.05 (P101(f323(f323(f325(x123561),f323(x123562,x123563)),f323(f302(x123564,x123561,x123562),f246(f872(x123564,a860)))))),
% 188.20/188.05 inference(rename_variables,[],[3889])).
% 188.20/188.05 cnf(12357,plain,
% 188.20/188.05 (P27(x123571,x123571,f5(x123571),x123572)),
% 188.20/188.05 inference(rename_variables,[],[3522])).
% 188.20/188.05 cnf(12360,plain,
% 188.20/188.05 (P101(f323(f323(f325(f871(f866(x123601),f866(x123601))),f323(f323(f258(f866(x123601),f866(x123601)),f113(x123601)),f113(x123601))),f151(x123601,x123602)))),
% 188.20/188.05 inference(rename_variables,[],[4071])).
% 188.20/188.05 cnf(12363,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x123631),x123631))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(12364,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x123641),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(12370,plain,
% 188.20/188.05 (E(f323(f323(f121(x123701),x123702),f113(x123701)),x123702)),
% 188.20/188.05 inference(rename_variables,[],[3209])).
% 188.20/188.05 cnf(12371,plain,
% 188.20/188.05 (~E(f323(f323(f144(x123711),x123712),x123713),x123713)),
% 188.20/188.05 inference(rename_variables,[],[4500])).
% 188.20/188.05 cnf(12374,plain,
% 188.20/188.05 (E(f323(f323(f121(x123741),x123742),f113(x123741)),x123742)),
% 188.20/188.05 inference(rename_variables,[],[3209])).
% 188.20/188.05 cnf(12375,plain,
% 188.20/188.05 (~E(f323(f323(f144(x123751),x123752),x123753),x123753)),
% 188.20/188.05 inference(rename_variables,[],[4500])).
% 188.20/188.05 cnf(12378,plain,
% 188.20/188.05 (E(f323(f323(f121(x123781),x123782),f113(x123781)),x123782)),
% 188.20/188.05 inference(rename_variables,[],[3209])).
% 188.20/188.05 cnf(12385,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x123851,a860)),f323(f166(x123851),f323(f129(x123851,x123852),x123853))),f323(f166(x123851),x123853)))),
% 188.20/188.05 inference(rename_variables,[],[3934])).
% 188.20/188.05 cnf(12386,plain,
% 188.20/188.05 (E(f323(f302(x123861,x123861,f5(x123861)),x123862),x123862)),
% 188.20/188.05 inference(rename_variables,[],[3339])).
% 188.20/188.05 cnf(12391,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x123911,a860)),x123912),f246(f872(x123911,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3663])).
% 188.20/188.05 cnf(12395,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x123951),x123951))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(12396,plain,
% 188.20/188.05 (~E(f323(a112,x123961),x123961)),
% 188.20/188.05 inference(rename_variables,[],[4473])).
% 188.20/188.05 cnf(12399,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x123991,a860)),f188(f872(x123991,a860))),x123992))),
% 188.20/188.05 inference(rename_variables,[],[3729])).
% 188.20/188.05 cnf(12402,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x124021),x124021))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12405,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x124051,a860)),x124052),x124052))),
% 188.20/188.05 inference(rename_variables,[],[3581])).
% 188.20/188.05 cnf(12410,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x124101,a860)),x124102),f323(f323(f301(x124101),x124103),x124102)))),
% 188.20/188.05 inference(rename_variables,[],[3727])).
% 188.20/188.05 cnf(12413,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x124131,a860)),x124132),x124132))),
% 188.20/188.05 inference(rename_variables,[],[3581])).
% 188.20/188.05 cnf(12414,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x124141),x124142),f188(f872(x124141,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12417,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x124171),x124172),f188(f872(x124171,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12426,plain,
% 188.20/188.05 (P27(x124261,x124261,f5(x124261),x124262)),
% 188.20/188.05 inference(rename_variables,[],[3522])).
% 188.20/188.05 cnf(12429,plain,
% 188.20/188.05 (E(f323(f189(f866(x124291)),f323(f161(x124291),x124292)),f323(f189(f866(x124291)),x124292))),
% 188.20/188.05 inference(rename_variables,[],[3294])).
% 188.20/188.05 cnf(12432,plain,
% 188.20/188.05 (P28(x124321,x124321,f32(x124321),x124322,x124322)),
% 188.20/188.05 inference(rename_variables,[],[3949])).
% 188.20/188.05 cnf(12435,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x124351),x124351))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(12436,plain,
% 188.20/188.05 (P101(f323(f246(f872(x124361,a860)),x124362))),
% 188.20/188.05 inference(rename_variables,[],[3343])).
% 188.20/188.05 cnf(12439,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x124391),x124392),f188(f872(x124391,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12442,plain,
% 188.20/188.05 (P101(f323(f323(f325(x124421),f323(x124422,x124423)),f323(f302(x124424,x124421,x124422),f246(f872(x124424,a860)))))),
% 188.20/188.05 inference(rename_variables,[],[3889])).
% 188.20/188.05 cnf(12443,plain,
% 188.20/188.05 (P101(f323(f323(f325(f871(x124431,x124431)),f323(f323(f258(x124431,x124431),x124432),x124432)),f299(x124431,x124433)))),
% 188.20/188.05 inference(rename_variables,[],[3924])).
% 188.20/188.05 cnf(12446,plain,
% 188.20/188.05 (P101(f323(f323(f325(f871(x124461,x124461)),f323(f323(f258(x124461,x124461),x124462),x124462)),f299(x124461,x124463)))),
% 188.20/188.05 inference(rename_variables,[],[3924])).
% 188.20/188.05 cnf(12449,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x124491),x124491))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12450,plain,
% 188.20/188.05 (P101(f323(f246(f872(x124501,a860)),x124502))),
% 188.20/188.05 inference(rename_variables,[],[3343])).
% 188.20/188.05 cnf(12453,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x124531,a860)),x124532),f246(f872(x124531,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3663])).
% 188.20/188.05 cnf(12454,plain,
% 188.20/188.05 (P28(x124541,x124541,f32(x124541),x124542,x124542)),
% 188.20/188.05 inference(rename_variables,[],[3949])).
% 188.20/188.05 cnf(12457,plain,
% 188.20/188.05 (P101(f323(f59(x124571),f323(f166(x124571),x124572)))),
% 188.20/188.05 inference(rename_variables,[],[3322])).
% 188.20/188.05 cnf(12464,plain,
% 188.20/188.05 (P101(f323(f323(f325(f871(x124641,x124641)),f323(f323(f258(x124641,x124641),x124642),x124642)),f323(f323(f280(x124641,x124641,x124641),f299(x124641,x124643)),f299(x124641,f299(x124641,x124643)))))),
% 188.20/188.05 inference(scs_inference,[],[3240,3949,12432,3522,11043,12108,12208,12211,12303,12345,12349,12357,3531,3532,3250,4508,4509,3149,4489,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,11727,11762,12078,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,11584,11893,11918,11930,11959,11965,12060,12168,12175,12338,3338,3491,11865,4485,10401,10492,10939,2880,2884,2885,2891,2892,2895,2896,2897,2898,2900,2901,2904,2905,2906,2913,2914,2918,2919,2924,2926,2929,2938,2946,2947,2951,2957,2982,2985,3021,3030,3033,3035,3036,3044,3056,3072,4471,3850,3323,3209,12370,12374,12378,3223,3740,3984,3114,4487,3835,11372,3173,3140,3602,3135,4186,3123,3124,3753,3155,3294,3339,10782,10907,12169,12386,3207,3208,3385,4557,3922,4500,10233,10398,11231,12330,12371,4507,12342,3272,11708,4546,10965,11048,11277,11280,3386,3170,3171,10300,10605,3444,3094,3192,11362,4071,12360,3924,10971,11114,11166,12314,12320,12443,12446,4569,10885,11119,11225,11247,11285,11291,12258,4570,11004,11122,11228,4571,11125,4572,11180,4573,3191,3483,12214,12255,12341,3645,4357,4358,4498,11353,3585,3797,3845,3470,3722,3349,10319,10437,10506,10567,10570,10608,10706,10955,11805,11889,11952,12031,12069,12146,12149,3733,11601,3265,3361,3547,4540,10210,10213,10239,10714,10727,10843,11269,11365,11777,11782,11804,12007,12010,12090,12099,12261,4552,11482,11515,11552,11581,3720,3492,3872,3309,3311,3284,4537,4495,3672,3476,4553,4065,11242,3607,3322,11733,11736,12179,12283,4035,3992,11882,12229,3934,10779,12063,12236,3987,10977,12105,12178,12235,12282,3646,11892,12038,12113,12159,4024,3663,10974,11053,11140,11199,12059,12127,12391,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,11726,11862,11917,11933,11936,11939,11942,12120,12134,12137,12140,12143,12222,12286,12402,3282,10357,10412,10620,10709,10830,11455,11524,11761,11765,11774,11868,11879,11898,11903,11945,11968,3283,3357,12093,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,11676,11836,11839,11842,11845,11929,11948,11951,11964,12019,12022,12025,12028,12100,12190,12193,12289,12292,12363,12395,3439,10573,10838,10882,11188,11266,11439,11688,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,11742,12013,12016,12050,12094,12123,12267,12311,12317,12414,12417,3343,10602,10632,10641,11217,11789,12436,3381,3375,3801,3738,10279,11604,11636,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,11795,11824,11827,11830,11833,12089,3303,10635,10787,10858,11637,11794,11990,12198,3762,4115,4543,3773,3809,4526,4529,3256,3260,4528,4527,4531,3780,3597,4560,10198,10201,10458,10509,10512,10517,10942,11433,11692,11798,4567,11154,11274,11310,4001,3889,11307,11663,11667,11730,12348,12356,3727,10898,10904,10926,11914,12043,12126,3581,11028,11157,12152,12264,12274,12353,12405,3729,10638,10993,11163,11193,11204,12352,3548,10556,10559,10644,10814,4564,11598,4554,4565,10697,10796,11436,11468,12217,12226,4174,10772,12247,4076,3761,3707,4562,10252,10255,10596,10599,11479,4563,11578,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114,6147,6163,6216,6251,6253,6274,6275,6280,6284,6285,6288,6294,6303,6318,6338,6339,6342,6345,6354,6369,6390,6395,6397,6412,6413,6416,6417,6419,6421,6422,6423,6425,6427,6429,6434,6435,6437,6438,6444,6446,6488,6493,6508,6510,6511,6512,6546,6551,6553,6558,6559,6567,6571,6583,6607,6608,6610,6611,6622,6628,6645,6648,6667,6699,6700,6701,6706,6720,6739,6741,6743,6745,6750,6756,6758,6773,6778,6781,6817,6818,6819,6833,6834,6836,6837,6855,6857,6871,6897,6919,6930,6932,6934,6936,6937,6938,6971,6972,6977,6978,6985,6986,6988,6990,7009,7018,7019,7031,7041,7080,7090,7094,7101,7112,7118,7120,7126,7135,7148,7165,7183,7185,7202,7251,7252,7253,7255,7257,7261,7266,7289,7331,7363,7378,7395,7427,7430,7455,7479,7496,7499,7500,7510,7529,7531,7533,7535,7536,7537,7562,7588,7589,7621,7623,7624,7625,7630,7652,7661,7671,7676,7682,7684,7690,7702,7703,7705,7728,7734,7755,7822,7823,7824,7872,7880,7881,7906,7907,7924,7925,7982,7983,8012,8039,8049,8051,8060,8072,8102,8108,8115,8128,8147,8152,8174,8218,8248,8262,8281,8284,8314,8340,8399,8400,8403,8404,8468,8502,8503,8504,8505,8532,8565,8594,8603,8604,8646,8667,8713,8728,8775,8778,8793,8800,8836,8884,8885,8901,8902,9031,9037,9041,9062,9072,9095,9097,9100,9104,9106,9107,9118,9119,9139,9146,9159,9168,9205,9223,9276,9277,9284,9323,9346,9351,9386,9394])).
% 188.20/188.05 cnf(12467,plain,
% 188.20/188.05 (~P101(f323(f323(f188(f872(x124671,f872(x124672,a860))),x124673),x124674))),
% 188.20/188.05 inference(rename_variables,[],[4565])).
% 188.20/188.05 cnf(12470,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x124701,a860)),x124702),f246(f872(x124701,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3663])).
% 188.20/188.05 cnf(12473,plain,
% 188.20/188.05 (P101(f323(f323(f325(f871(x124731,x124731)),f323(f323(f258(x124731,x124731),x124732),x124732)),f299(x124731,x124733)))),
% 188.20/188.05 inference(rename_variables,[],[3924])).
% 188.20/188.05 cnf(12476,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),f323(f323(f78(a865),x124761),x124762)),x124762))),
% 188.20/188.05 inference(rename_variables,[],[4562])).
% 188.20/188.05 cnf(12477,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),x124771),f323(a112,x124771)))),
% 188.20/188.05 inference(rename_variables,[],[3349])).
% 188.20/188.05 cnf(12480,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x124801,a860)),f323(f166(x124801),f323(f129(x124801,x124802),x124803))),f323(f166(x124801),x124803)))),
% 188.20/188.05 inference(rename_variables,[],[3934])).
% 188.20/188.05 cnf(12483,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x124831,a860)),x124832),f246(f872(x124831,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3663])).
% 188.20/188.05 cnf(12486,plain,
% 188.20/188.05 (E(f31(x124861,x124862,x124863,x124864,x124865,x124866,x124867,x124868,x124869,a24),x124862)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12497,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x124971),x124972),f188(f872(x124971,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12498,plain,
% 188.20/188.05 (P101(f323(f323(f325(f871(f866(x124981),f866(x124981))),f323(f323(f258(f866(x124981),f866(x124981)),f113(x124981)),f113(x124981))),f151(x124981,x124982)))),
% 188.20/188.05 inference(rename_variables,[],[4071])).
% 188.20/188.05 cnf(12503,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x125031),x125032),f188(f872(x125031,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12506,plain,
% 188.20/188.05 (P32(x125061,x125062,f113(x125061))),
% 188.20/188.05 inference(rename_variables,[],[3214])).
% 188.20/188.05 cnf(12509,plain,
% 188.20/188.05 (E(f323(f189(f866(x125091)),f323(f161(x125091),x125092)),f323(f189(f866(x125091)),x125092))),
% 188.20/188.05 inference(rename_variables,[],[3294])).
% 188.20/188.05 cnf(12512,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x125121),x125122),f188(f872(x125121,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12518,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x125181),x125181))),
% 188.20/188.05 inference(rename_variables,[],[4536])).
% 188.20/188.05 cnf(12521,plain,
% 188.20/188.05 (P101(f323(f323(f325(x125211),x125212),f246(f872(x125211,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3439])).
% 188.20/188.05 cnf(12524,plain,
% 188.20/188.05 (~P101(f323(f323(f188(f872(x125241,f872(x125242,a860))),x125243),x125244))),
% 188.20/188.05 inference(rename_variables,[],[4565])).
% 188.20/188.05 cnf(12528,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x125281,a860)),x125282),x125282))),
% 188.20/188.05 inference(rename_variables,[],[3581])).
% 188.20/188.05 cnf(12531,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x125311),x125312),f188(f872(x125311,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12534,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),f2(a1)),f323(f323(f248(a1),f323(f73(a1),x125341)),x125342)))),
% 188.20/188.05 inference(rename_variables,[],[3761])).
% 188.20/188.05 cnf(12537,plain,
% 188.20/188.05 (E(f31(x125371,x125372,x125373,x125374,x125375,x125376,x125377,x125378,x125379,a24),x125372)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12539,plain,
% 188.20/188.05 (E(f31(x125391,x125392,x125393,x125394,x125395,x125396,x125397,x125398,x125399,a24),x125392)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12541,plain,
% 188.20/188.05 (P26(x125411,x125412,f188(f872(f864(x125411),a860)))),
% 188.20/188.05 inference(rename_variables,[],[3337])).
% 188.20/188.05 cnf(12543,plain,
% 188.20/188.05 (P26(x125431,f323(f323(f301(f864(x125431)),x125432),f188(f872(f864(x125431),a860))),f323(f323(f301(f864(x125431)),x125432),f188(f872(f864(x125431),a860))))),
% 188.20/188.05 inference(rename_variables,[],[3823])).
% 188.20/188.05 cnf(12549,plain,
% 188.20/188.05 (E(f31(x125491,x125492,x125493,x125494,x125495,x125496,x125497,x125498,x125499,a24),x125492)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12551,plain,
% 188.20/188.05 (P17(x125511,f872(x125511,a860),f301(x125511))),
% 188.20/188.05 inference(rename_variables,[],[3253])).
% 188.20/188.05 cnf(12555,plain,
% 188.20/188.05 (E(f31(x125551,x125552,x125553,x125554,x125555,x125556,x125557,x125558,x125559,a24),x125552)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12560,plain,
% 188.20/188.05 (E(f31(x125601,x125602,x125603,x125604,x125605,x125606,x125607,x125608,x125609,a24),x125602)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12562,plain,
% 188.20/188.05 (P33(x125621,x125622,f113(x125621),f113(x125621))),
% 188.20/188.05 inference(rename_variables,[],[3531])).
% 188.20/188.05 cnf(12564,plain,
% 188.20/188.05 (P33(x125641,x125642,f113(x125641),f113(x125641))),
% 188.20/188.05 inference(rename_variables,[],[3531])).
% 188.20/188.05 cnf(12568,plain,
% 188.20/188.05 (P27(x125681,x125681,f5(x125681),x125682)),
% 188.20/188.05 inference(rename_variables,[],[3522])).
% 188.20/188.05 cnf(12570,plain,
% 188.20/188.05 (P27(x125701,x125701,f5(x125701),x125702)),
% 188.20/188.05 inference(rename_variables,[],[3522])).
% 188.20/188.05 cnf(12576,plain,
% 188.20/188.05 (P38(x125761,f146(x125761,x125762))),
% 188.20/188.05 inference(rename_variables,[],[3149])).
% 188.20/188.05 cnf(12580,plain,
% 188.20/188.05 (E(f31(x125801,x125802,x125803,x125804,x125805,x125806,x125807,x125808,x125809,a24),x125802)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12582,plain,
% 188.20/188.05 (P28(x125821,x125821,f32(x125821),x125822,x125822)),
% 188.20/188.05 inference(rename_variables,[],[3949])).
% 188.20/188.05 cnf(12584,plain,
% 188.20/188.05 (P28(x125841,x125841,f32(x125841),x125842,x125842)),
% 188.20/188.05 inference(rename_variables,[],[3949])).
% 188.20/188.05 cnf(12586,plain,
% 188.20/188.05 (P28(x125861,x125861,f32(x125861),x125862,x125862)),
% 188.20/188.05 inference(rename_variables,[],[3949])).
% 188.20/188.05 cnf(12590,plain,
% 188.20/188.05 (E(f31(x125901,x125902,x125903,x125904,x125905,x125906,x125907,x125908,x125909,a24),x125902)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12593,plain,
% 188.20/188.05 (E(f188(f872(f871(x125931,x125931),a860)),f255(x125931,f188(f872(x125931,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3352])).
% 188.20/188.05 cnf(12599,plain,
% 188.20/188.05 (E(f31(x125991,x125992,x125993,x125994,x125995,x125996,x125997,x125998,x125999,a24),x125992)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12601,plain,
% 188.20/188.05 (E(f31(x126011,x126012,x126013,x126014,x126015,x126016,x126017,x126018,x126019,a24),x126012)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12603,plain,
% 188.20/188.05 (E(f31(x126031,x126032,x126033,x126034,x126035,x126036,x126037,x126038,x126039,a24),x126032)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12608,plain,
% 188.20/188.05 (P40(x126081,x126082,f255(x126081,x126082))),
% 188.20/188.05 inference(rename_variables,[],[3249])).
% 188.20/188.05 cnf(12610,plain,
% 188.20/188.05 (P40(x126101,x126102,f255(x126101,x126102))),
% 188.20/188.05 inference(rename_variables,[],[3249])).
% 188.20/188.05 cnf(12616,plain,
% 188.20/188.05 (E(f31(x126161,x126162,x126163,x126164,x126165,x126166,x126167,x126168,x126169,a24),x126162)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12618,plain,
% 188.20/188.05 (P52(x126181,f188(f872(x126181,a860)),x126182)),
% 188.20/188.05 inference(rename_variables,[],[3301])).
% 188.20/188.05 cnf(12622,plain,
% 188.20/188.05 (P51(x126221,x126221,f255(x126221,x126222))),
% 188.20/188.05 inference(rename_variables,[],[3250])).
% 188.20/188.05 cnf(12633,plain,
% 188.20/188.05 (E(f31(x126331,x126332,x126333,x126334,x126335,x126336,x126337,x126338,x126339,a24),x126332)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12647,plain,
% 188.20/188.05 (E(f31(x126471,x126472,x126473,x126474,x126475,x126476,x126477,x126478,x126479,a24),x126472)),
% 188.20/188.05 inference(rename_variables,[],[4459])).
% 188.20/188.05 cnf(12650,plain,
% 188.20/188.05 (P43(x126501,x126502,x126503,x126504,f188(f872(x126501,a860)),x126504)),
% 188.20/188.05 inference(rename_variables,[],[4239])).
% 188.20/188.05 cnf(12653,plain,
% 188.20/188.05 (P43(x126531,x126532,x126533,x126534,f188(f872(x126531,a860)),x126534)),
% 188.20/188.05 inference(rename_variables,[],[4239])).
% 188.20/188.05 cnf(12659,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),f2(a865)),f323(a112,x126591)))),
% 188.20/188.05 inference(rename_variables,[],[3361])).
% 188.20/188.05 cnf(12660,plain,
% 188.20/188.05 (~E(f323(a112,x126601),x126601)),
% 188.20/188.05 inference(rename_variables,[],[4473])).
% 188.20/188.05 cnf(12666,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),x126661),f323(a112,x126661)))),
% 188.20/188.05 inference(rename_variables,[],[3349])).
% 188.20/188.05 cnf(12671,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x126711),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(12680,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a1),f323(f100(a1),x126801)),f323(f77(a1),f323(f100(a1),x126802))))),
% 188.20/188.05 inference(rename_variables,[],[4559])).
% 188.20/188.05 cnf(12690,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x126901),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(12693,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x126931),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(12696,plain,
% 188.20/188.05 (P101(f323(f59(a865),f296(a865,x126961,x126962)))),
% 188.20/188.05 inference(rename_variables,[],[3494])).
% 188.20/188.05 cnf(12699,plain,
% 188.20/188.05 (P101(f323(f59(a865),f296(a865,x126991,x126992)))),
% 188.20/188.05 inference(rename_variables,[],[3494])).
% 188.20/188.05 cnf(12702,plain,
% 188.20/188.05 (P101(f323(f59(a865),f296(a865,x127021,x127022)))),
% 188.20/188.05 inference(rename_variables,[],[3494])).
% 188.20/188.05 cnf(12705,plain,
% 188.20/188.05 (P101(f323(f59(a865),f296(a865,x127051,x127052)))),
% 188.20/188.05 inference(rename_variables,[],[3494])).
% 188.20/188.05 cnf(12712,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),f323(f77(a1),f323(f100(a1),x127121))),f323(f100(a1),x127122)))),
% 188.20/188.05 inference(rename_variables,[],[3762])).
% 188.20/188.05 cnf(12714,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),f2(a1))))),
% 188.20/188.05 inference(scs_inference,[],[3240,3949,12432,12454,12582,12584,3522,11043,12108,12208,12211,12303,12345,12349,12357,12426,12568,3531,12172,12562,12564,3532,12242,3249,12608,12610,3250,12622,3214,12506,4508,4509,11685,4239,12650,12653,3253,12551,3093,3149,12576,4489,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,11727,11762,12078,12279,12486,12537,12539,12549,12555,12560,12580,12590,12599,12601,12603,12616,12633,12647,3583,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,11584,11893,11918,11930,11959,11965,12060,12168,12175,12338,12396,3338,3301,12618,3491,11865,4485,10401,10492,10939,2880,2884,2885,2891,2892,2895,2896,2897,2898,2900,2901,2904,2905,2906,2913,2914,2918,2919,2920,2924,2926,2929,2938,2946,2947,2951,2957,2982,2985,3021,3023,3030,3033,3035,3036,3044,3056,4470,3072,3148,4471,3620,3850,3263,3323,3209,12370,12374,12378,3223,3740,3984,3114,4487,3835,11372,3337,12541,3173,3140,3602,3135,3241,3957,3661,4444,4186,3823,3123,3124,3097,3103,3753,3155,3294,12429,12509,3339,10782,10907,12169,12386,3207,3208,3385,4557,10371,3922,4500,10233,10398,11231,12330,12371,4507,12342,3272,11708,4546,10965,11048,11277,11280,3362,3386,3608,3352,12593,3170,3171,10300,10605,3444,3162,3094,3192,11362,4071,12360,12498,3924,10971,11114,11166,12314,12320,12443,12446,12473,4569,10885,11119,11225,11247,11285,11291,12258,4570,11004,11122,11228,4571,11125,4572,11180,4573,3191,3483,12214,12255,12341,3645,4357,4358,4498,11353,3585,3797,3845,3470,3722,3349,10319,10437,10506,10567,10570,10608,10706,10955,11805,11889,11952,12031,12069,12146,12149,12477,3733,11601,3265,3361,11723,3547,4540,10210,10213,10239,10714,10727,10843,11269,11365,11777,11782,11804,12007,12010,12090,12099,12261,12364,12671,12690,4552,11482,11515,11552,11581,3720,3492,3494,12696,12699,12702,3872,3309,3311,3284,4537,4495,3672,4209,3993,3476,4553,4065,11242,3607,3322,11733,11736,12179,12283,4035,3992,11882,12229,3934,10779,12063,12236,12385,3987,10977,12105,12178,12235,12282,3646,11892,12038,12113,12159,4024,3663,10974,11053,11140,11199,12059,12127,12391,12453,12470,12483,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,11726,11862,11917,11933,11936,11939,11942,12120,12134,12137,12140,12143,12222,12286,12402,3282,10357,10412,10620,10709,10830,11455,11524,11761,11765,11774,11868,11879,11898,11903,11945,11968,3283,3357,12093,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,11676,11836,11839,11842,11845,11929,11948,11951,11964,12019,12022,12025,12028,12100,12190,12193,12289,12292,12363,12395,12435,3439,10573,10838,10882,11188,11266,11439,11688,12337,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,11742,12013,12016,12050,12094,12123,12267,12311,12317,12414,12417,12439,12497,12503,12512,3343,10602,10632,10641,11217,11789,12436,3381,3375,3801,3738,10279,11604,11636,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,11795,11824,11827,11830,11833,12089,3303,10635,10787,10858,11637,11794,11990,12198,3762,11739,4115,4543,3773,3809,4526,4529,4530,3256,3260,4528,4527,4531,3780,3597,4215,4560,10198,10201,10458,10509,10512,10517,10942,11433,11692,11798,4567,11154,11274,11310,4001,3889,11307,11663,11667,11730,12348,12356,3727,10898,10904,10926,11914,12043,12126,3581,11028,11157,12152,12264,12274,12353,12405,12413,4069,3729,10638,10993,11163,11193,11204,12352,3548,10556,10559,10644,10814,3550,4564,11598,4554,4559,12680,4565,10697,10796,11436,11468,12217,12226,12270,12467,4174,10772,12247,4076,3761,3707,3708,4562,10252,10255,10596,10599,11479,11668,4563,11578,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114,6147,6163,6216,6251,6253,6274,6275,6280,6284,6285,6288,6294,6303,6318,6338,6339,6342,6345,6354,6369,6390,6395,6397,6412,6413,6416,6417,6419,6421,6422,6423,6425,6427,6429,6434,6435,6437,6438,6444,6446,6488,6493,6508,6510,6511,6512,6546,6551,6553,6558,6559,6567,6571,6583,6607,6608,6610,6611,6622,6628,6645,6648,6667,6699,6700,6701,6706,6720,6739,6741,6743,6745,6750,6756,6758,6773,6778,6781,6817,6818,6819,6833,6834,6836,6837,6855,6857,6871,6897,6919,6930,6932,6934,6936,6937,6938,6971,6972,6977,6978,6985,6986,6988,6990,7009,7018,7019,7031,7041,7080,7090,7094,7101,7112,7118,7120,7126,7135,7148,7165,7183,7185,7202,7251,7252,7253,7255,7257,7261,7266,7289,7331,7363,7378,7395,7427,7430,7455,7479,7496,7499,7500,7510,7529,7531,7533,7535,7536,7537,7562,7588,7589,7621,7623,7624,7625,7630,7652,7661,7671,7676,7682,7684,7690,7702,7703,7705,7728,7734,7755,7822,7823,7824,7872,7880,7881,7906,7907,7924,7925,7982,7983,8012,8039,8049,8051,8060,8072,8102,8108,8115,8128,8147,8152,8174,8218,8248,8262,8281,8284,8314,8340,8399,8400,8403,8404,8468,8502,8503,8504,8505,8532,8565,8594,8603,8604,8646,8667,8713,8728,8775,8778,8793,8800,8836,8884,8885,8901,8902,9031,9037,9041,9062,9072,9095,9097,9100,9104,9106,9107,9118,9119,9139,9146,9159,9168,9205,9223,9276,9277,9284,9323,9346,9351,9386,9394,9397,9400,9401,9414,9431,9440,9455,9464,9465,9467,9469,9497,9621,9667,9668,9710,9755,9870,9927,9991,10064,10077,10082,3,2616,2617,2618,2619,2623,2626,2630,2632,2636,2637,2638,2639,2642,2648,2650,2651,2653,2654,2655,2656,2661,2662,2663,2668,2669,2670,2671,2672,2673,2675,2677,2679,2680,2682,2683,2685,2686,2693,2700,2701,2702,2706,2707,2708,2710,2716,2723,2724,2751,2752,2753,2762,2763,2764,2768,2769,2771,2780,2783,2784,2788,2789,2797,2798,2799,2821,2823,2832,2835,2836,2837,2847,2848,5213,5272,5370,5456,5457,5458,5533,5630,5661,5695,5711,5713,5719,5780,5781,5782,5783,5789,5822,5949,5983])).
% 188.20/188.05 cnf(12717,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x127171),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(12718,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x127181),x127181))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12725,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),x127251),f323(a112,x127251)))),
% 188.20/188.05 inference(rename_variables,[],[3349])).
% 188.20/188.05 cnf(12730,plain,
% 188.20/188.05 (P101(f323(f323(f325(x127301),f323(x127302,x127303)),f323(f302(x127304,x127301,x127302),f246(f872(x127304,a860)))))),
% 188.20/188.05 inference(rename_variables,[],[3889])).
% 188.20/188.05 cnf(12731,plain,
% 188.20/188.05 (~E(f323(a112,x127311),f2(a865))),
% 188.20/188.05 inference(rename_variables,[],[4485])).
% 188.20/188.05 cnf(12733,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a1),f2(a1)),f323(f103(a1),f2(a1))))),
% 188.20/188.05 inference(scs_inference,[],[3240,3949,12432,12454,12582,12584,3522,11043,12108,12208,12211,12303,12345,12349,12357,12426,12568,3531,12172,12562,12564,3532,12242,3249,12608,12610,3250,12622,3214,12506,4508,4509,11685,4239,12650,12653,3253,12551,3093,3149,12576,4489,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,11727,11762,12078,12279,12486,12537,12539,12549,12555,12560,12580,12590,12599,12601,12603,12616,12633,12647,3583,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,11584,11893,11918,11930,11959,11965,12060,12168,12175,12338,12396,3338,3301,12618,3491,11865,4485,10401,10492,10939,11023,2880,2884,2885,2891,2892,2895,2896,2897,2898,2900,2901,2904,2905,2906,2913,2914,2918,2919,2920,2924,2926,2929,2938,2946,2947,2951,2957,2982,2985,3021,3023,3030,3033,3035,3036,3044,3056,4470,3072,3148,4471,3620,3850,3263,3323,3209,12370,12374,12378,3223,3740,3984,3114,4487,3835,11372,3337,12541,3173,3140,3602,3135,3241,3957,3661,4444,4186,3823,3123,3124,3097,3103,3753,3155,3294,12429,12509,3339,10782,10907,12169,12386,3207,3208,3385,4557,10371,3922,4500,10233,10398,11231,12330,12371,4507,12342,3272,11708,4546,10965,11048,11277,11280,3362,3386,3608,3352,12593,3170,3171,10300,10605,3444,3162,3094,3192,11362,4071,12360,12498,3924,10971,11114,11166,12314,12320,12443,12446,12473,4569,10885,11119,11225,11247,11285,11291,12258,4570,11004,11122,11228,4571,11125,4572,11180,4573,3191,3483,12214,12255,12341,3645,4357,4358,4498,11353,3585,3623,3797,3845,3470,3722,3349,10319,10437,10506,10567,10570,10608,10706,10955,11805,11889,11952,12031,12069,12146,12149,12477,12666,3733,11601,3265,3361,11723,3547,4540,10210,10213,10239,10714,10727,10843,11269,11365,11777,11782,11804,12007,12010,12090,12099,12261,12364,12671,12690,12693,4552,11482,11515,11552,11581,3720,3492,3494,12696,12699,12702,3872,3309,3311,3284,4537,3169,4495,3672,4209,3993,3476,4553,4065,11242,3607,3322,11733,11736,12179,12283,4035,3992,11882,12229,3934,10779,12063,12236,12385,3987,10977,12105,12178,12235,12282,3646,11892,12038,12113,12159,4024,3663,10974,11053,11140,11199,12059,12127,12391,12453,12470,12483,4558,10730,11130,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,11726,11862,11917,11933,11936,11939,11942,12120,12134,12137,12140,12143,12222,12286,12402,12449,3282,10357,10412,10620,10709,10830,11455,11524,11761,11765,11774,11868,11879,11898,11903,11945,11968,3283,3357,12093,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,11676,11836,11839,11842,11845,11929,11948,11951,11964,12019,12022,12025,12028,12100,12190,12193,12289,12292,12363,12395,12435,3439,10573,10838,10882,11188,11266,11439,11688,12337,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,11742,12013,12016,12050,12094,12123,12267,12311,12317,12414,12417,12439,12497,12503,12512,3343,10602,10632,10641,11217,11789,12436,3381,3375,3801,3738,10279,11604,11636,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,11795,11824,11827,11830,11833,12089,3303,10635,10787,10858,11637,11794,11990,12198,3762,11739,4115,3498,4543,3773,3809,4526,4529,4530,3256,3260,4528,4527,4531,3780,3597,4215,4560,10198,10201,10458,10509,10512,10517,10942,11433,11692,11798,4567,11154,11274,11310,4001,12250,3889,11307,11663,11667,11730,12348,12356,12442,3727,10898,10904,10926,11914,12043,12126,3581,11028,11157,12152,12264,12274,12353,12405,12413,4069,3729,10638,10993,11163,11193,11204,12352,3548,10556,10559,10644,10814,3550,4564,11598,4554,4559,12680,4565,10697,10796,11436,11468,12217,12226,12270,12467,4174,10772,12247,4076,3761,3707,3708,4562,10252,10255,10596,10599,11479,11668,4563,11578,3731,10562,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114,6147,6163,6216,6251,6253,6274,6275,6280,6284,6285,6288,6294,6303,6318,6338,6339,6342,6345,6354,6369,6390,6395,6397,6412,6413,6416,6417,6419,6421,6422,6423,6425,6427,6429,6434,6435,6437,6438,6444,6446,6488,6493,6508,6510,6511,6512,6546,6551,6553,6558,6559,6567,6571,6583,6607,6608,6610,6611,6622,6628,6645,6648,6667,6699,6700,6701,6706,6720,6739,6741,6743,6745,6750,6756,6758,6773,6778,6781,6817,6818,6819,6833,6834,6836,6837,6855,6857,6871,6897,6919,6930,6932,6934,6936,6937,6938,6971,6972,6977,6978,6985,6986,6988,6990,7009,7018,7019,7031,7041,7080,7090,7094,7101,7112,7118,7120,7126,7135,7148,7165,7183,7185,7202,7251,7252,7253,7255,7257,7261,7266,7289,7331,7363,7378,7395,7427,7430,7455,7479,7496,7499,7500,7510,7529,7531,7533,7535,7536,7537,7562,7588,7589,7621,7623,7624,7625,7630,7652,7661,7671,7676,7682,7684,7690,7702,7703,7705,7728,7734,7755,7822,7823,7824,7872,7880,7881,7906,7907,7924,7925,7982,7983,8012,8039,8049,8051,8060,8072,8102,8108,8115,8128,8147,8152,8174,8218,8248,8262,8281,8284,8314,8340,8399,8400,8403,8404,8468,8502,8503,8504,8505,8532,8565,8594,8603,8604,8646,8667,8713,8728,8775,8778,8793,8800,8836,8884,8885,8901,8902,9031,9037,9041,9062,9072,9095,9097,9100,9104,9106,9107,9118,9119,9139,9146,9159,9168,9205,9223,9276,9277,9284,9323,9346,9351,9386,9394,9397,9400,9401,9414,9431,9440,9455,9464,9465,9467,9469,9497,9621,9667,9668,9710,9755,9870,9927,9991,10064,10077,10082,3,2616,2617,2618,2619,2623,2626,2630,2632,2636,2637,2638,2639,2642,2648,2650,2651,2653,2654,2655,2656,2661,2662,2663,2668,2669,2670,2671,2672,2673,2675,2677,2679,2680,2682,2683,2685,2686,2693,2700,2701,2702,2706,2707,2708,2710,2716,2723,2724,2751,2752,2753,2762,2763,2764,2768,2769,2771,2780,2783,2784,2788,2789,2797,2798,2799,2821,2823,2832,2835,2836,2837,2847,2848,5213,5272,5370,5456,5457,5458,5533,5630,5661,5695,5711,5713,5719,5780,5781,5782,5783,5789,5822,5949,5983,5992,6015,6052,6087,6092,6232])).
% 188.20/188.05 cnf(12736,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x127361),x127361))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(12739,plain,
% 188.20/188.05 (P101(f323(f59(a865),f296(a865,x127391,x127392)))),
% 188.20/188.05 inference(rename_variables,[],[3494])).
% 188.20/188.05 cnf(12742,plain,
% 188.20/188.05 (P101(f323(f59(a865),f296(a865,x127421,x127422)))),
% 188.20/188.05 inference(rename_variables,[],[3494])).
% 188.20/188.05 cnf(12745,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x127451),x127451))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12746,plain,
% 188.20/188.05 (~E(f323(a112,x127461),f2(a865))),
% 188.20/188.05 inference(rename_variables,[],[4485])).
% 188.20/188.05 cnf(12763,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),f42(a865,x127631,x127632)),x127631))),
% 188.20/188.05 inference(rename_variables,[],[3738])).
% 188.20/188.05 cnf(12768,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),x127681),f323(a112,x127681)))),
% 188.20/188.05 inference(rename_variables,[],[3349])).
% 188.20/188.05 cnf(12771,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),x127711),f323(a112,x127711)))),
% 188.20/188.05 inference(rename_variables,[],[3349])).
% 188.20/188.05 cnf(12772,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x127721),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(12781,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a1),f323(f100(a1),x127811)),f2(a1)))),
% 188.20/188.05 inference(rename_variables,[],[4552])).
% 188.20/188.05 cnf(12782,plain,
% 188.20/188.05 (P101(f323(f246(f872(x127821,a860)),x127822))),
% 188.20/188.05 inference(rename_variables,[],[3343])).
% 188.20/188.05 cnf(12785,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a1),f323(f100(a1),x127851)),f2(a1)))),
% 188.20/188.05 inference(rename_variables,[],[4552])).
% 188.20/188.05 cnf(12786,plain,
% 188.20/188.05 (P101(f323(f246(f872(x127861,a860)),x127862))),
% 188.20/188.05 inference(rename_variables,[],[3343])).
% 188.20/188.05 cnf(12789,plain,
% 188.20/188.05 (P101(f323(f246(f872(x127891,a860)),x127892))),
% 188.20/188.05 inference(rename_variables,[],[3343])).
% 188.20/188.05 cnf(12800,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x128001),x128002),f188(f872(x128001,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12801,plain,
% 188.20/188.05 (P101(f323(f59(x128011),f188(f872(x128011,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3357])).
% 188.20/188.05 cnf(12810,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),f2(a865)),x128101))),
% 188.20/188.05 inference(rename_variables,[],[3303])).
% 188.20/188.05 cnf(12813,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),x128131),f323(a112,x128131)))),
% 188.20/188.05 inference(rename_variables,[],[3349])).
% 188.20/188.05 cnf(12814,plain,
% 188.20/188.05 (~E(f323(a112,x128141),x128141)),
% 188.20/188.05 inference(rename_variables,[],[4473])).
% 188.20/188.05 cnf(12817,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x128171),x128172),f188(f872(x128171,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12820,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x128201),x128202),f188(f872(x128201,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12823,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x128231),x128231))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12831,plain,
% 188.20/188.05 (P101(f323(f323(f238(a865),x128311),f323(a112,x128311)))),
% 188.20/188.05 inference(rename_variables,[],[3349])).
% 188.20/188.05 cnf(12834,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x128341),x128341))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12839,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x128391),x128391))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12842,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x128421),x128421))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12845,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x128451),x128451))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12848,plain,
% 188.20/188.05 (E(f323(f323(f22(f872(x128481,a860)),f188(f872(x128481,a860))),x128482),f188(f872(x128481,a860)))),
% 188.20/188.05 inference(rename_variables,[],[3553])).
% 188.20/188.05 cnf(12849,plain,
% 188.20/188.05 (P101(f323(f59(x128491),f188(f872(x128491,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3357])).
% 188.20/188.05 cnf(12852,plain,
% 188.20/188.05 (E(f323(f323(f22(f872(x128521,a860)),f188(f872(x128521,a860))),x128522),f188(f872(x128521,a860)))),
% 188.20/188.05 inference(rename_variables,[],[3553])).
% 188.20/188.05 cnf(12853,plain,
% 188.20/188.05 (P101(f323(f59(x128531),f188(f872(x128531,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3357])).
% 188.20/188.05 cnf(12856,plain,
% 188.20/188.05 (E(f323(f323(f22(f872(x128561,a860)),f188(f872(x128561,a860))),x128562),f188(f872(x128561,a860)))),
% 188.20/188.05 inference(rename_variables,[],[3553])).
% 188.20/188.05 cnf(12857,plain,
% 188.20/188.05 (P101(f323(f59(x128571),f188(f872(x128571,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3357])).
% 188.20/188.05 cnf(12860,plain,
% 188.20/188.05 (E(f323(f323(f22(f872(x128601,a860)),f188(f872(x128601,a860))),x128602),f188(f872(x128601,a860)))),
% 188.20/188.05 inference(rename_variables,[],[3553])).
% 188.20/188.05 cnf(12861,plain,
% 188.20/188.05 (P101(f323(f59(x128611),f188(f872(x128611,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3357])).
% 188.20/188.05 cnf(12865,plain,
% 188.20/188.05 (E(f323(f254(x128651,x128651),f255(x128651,x128652)),x128652)),
% 188.20/188.05 inference(rename_variables,[],[3238])).
% 188.20/188.05 cnf(12870,plain,
% 188.20/188.05 (E(f323(f323(f22(f872(x128701,a860)),f188(f872(x128701,a860))),x128702),f188(f872(x128701,a860)))),
% 188.20/188.05 inference(rename_variables,[],[3553])).
% 188.20/188.05 cnf(12871,plain,
% 188.20/188.05 (P101(f323(f59(x128711),f188(f872(x128711,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3357])).
% 188.20/188.05 cnf(12875,plain,
% 188.20/188.05 (P101(f323(f59(x128751),f188(f872(x128751,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3357])).
% 188.20/188.05 cnf(12878,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x128781),x128781))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12882,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x128821),x128821))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(12891,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x128911),x128911))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12902,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x129021),x129021))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12905,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x129051),x129051))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(12912,plain,
% 188.20/188.05 (~P101(f323(f323(f325(x129121),x129122),f188(f872(x129121,a860))))),
% 188.20/188.05 inference(rename_variables,[],[4548])).
% 188.20/188.05 cnf(12923,plain,
% 188.20/188.05 (P101(f323(f323(f325(x129231),x129232),f246(f872(x129231,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3439])).
% 188.20/188.05 cnf(12924,plain,
% 188.20/188.05 (E(f323(f232(f869(x129241),x129242,f200(x129241),f323(f16(f869(x129241),x129242),f200(x129241))),f323(x129243,x129244)),f200(x129241))),
% 188.20/188.05 inference(rename_variables,[],[3863])).
% 188.20/188.05 cnf(12930,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x129301,a860)),x129302),f246(f872(x129301,a860))))),
% 188.20/188.05 inference(rename_variables,[],[3663])).
% 188.20/188.05 cnf(12933,plain,
% 188.20/188.05 (P101(f323(f323(f237(f872(x129331,a860)),x129332),x129332))),
% 188.20/188.05 inference(rename_variables,[],[3581])).
% 188.20/188.05 cnf(12939,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x129391),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(12940,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x129401),x129401))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(12944,plain,
% 188.20/188.05 (~P101(f323(f323(f238(a865),x129441),f2(a865)))),
% 188.20/188.05 inference(rename_variables,[],[4540])).
% 188.20/188.05 cnf(12945,plain,
% 188.20/188.05 (P101(f323(f323(f237(a1),x129451),x129451))),
% 188.20/188.05 inference(rename_variables,[],[3282])).
% 188.20/188.05 cnf(12950,plain,
% 188.20/188.05 (P101(f323(f323(f237(a865),x129501),x129501))),
% 188.20/188.05 inference(rename_variables,[],[3281])).
% 188.20/188.05 cnf(12951,plain,
% 188.21/188.05 (P101(f323(f59(a865),f294(a865,x129511,x129512)))),
% 188.21/188.05 inference(rename_variables,[],[3492])).
% 188.21/188.05 cnf(12958,plain,
% 188.21/188.05 (E(f323(f323(f16(x129581,x129582),x129583),x129584),x129583)),
% 188.21/188.05 inference(rename_variables,[],[3272])).
% 188.21/188.05 cnf(12961,plain,
% 188.21/188.05 (P101(f323(f323(f237(f872(x129611,a860)),f323(f166(x129611),f164(x129611,x129612,x129613))),f323(f166(x129611),x129613)))),
% 188.21/188.05 inference(rename_variables,[],[3987])).
% 188.21/188.05 cnf(12965,plain,
% 188.21/188.05 (~P101(f323(f323(f238(a865),x129651),f2(a865)))),
% 188.21/188.05 inference(rename_variables,[],[4540])).
% 188.21/188.05 cnf(12966,plain,
% 188.21/188.05 (P101(f323(f323(f237(a1),x129661),x129661))),
% 188.21/188.05 inference(rename_variables,[],[3282])).
% 188.21/188.05 cnf(12970,plain,
% 188.21/188.05 (~P101(f323(f323(f238(a865),x129701),f2(a865)))),
% 188.21/188.05 inference(rename_variables,[],[4540])).
% 188.21/188.05 cnf(12971,plain,
% 188.21/188.05 (P101(f323(f323(f237(a1),x129711),x129711))),
% 188.21/188.05 inference(rename_variables,[],[3282])).
% 188.21/188.05 cnf(12976,plain,
% 188.21/188.05 (P101(f323(f323(f237(a865),x129761),x129761))),
% 188.21/188.05 inference(rename_variables,[],[3281])).
% 188.21/188.05 cnf(12979,plain,
% 188.21/188.05 (P101(f323(f323(f237(a865),x129791),x129791))),
% 188.21/188.05 inference(rename_variables,[],[3281])).
% 188.21/188.05 cnf(12982,plain,
% 188.21/188.05 (~P101(f323(f323(f237(a865),f323(a112,x129821)),x129821))),
% 188.21/188.05 inference(rename_variables,[],[4545])).
% 188.21/188.05 cnf(12988,plain,
% 188.21/188.05 (P101(f323(f323(f325(x129881),f323(x129882,x129883)),f323(f302(x129884,x129881,x129882),f246(f872(x129884,a860)))))),
% 188.21/188.05 inference(rename_variables,[],[3889])).
% 188.21/188.05 cnf(12989,plain,
% 188.21/188.05 (P27(x129891,x129891,f5(x129891),x129892)),
% 188.21/188.05 inference(rename_variables,[],[3522])).
% 188.21/188.05 cnf(12994,plain,
% 188.21/188.05 (P101(f323(f323(f237(f872(x129941,a860)),x129942),f246(f872(x129941,a860))))),
% 188.21/188.05 inference(rename_variables,[],[3663])).
% 188.21/188.05 cnf(12995,plain,
% 188.21/188.05 (P27(x129951,x129951,f5(x129951),x129952)),
% 188.21/188.05 inference(rename_variables,[],[3522])).
% 188.21/188.05 cnf(12999,plain,
% 188.21/188.05 (P101(f323(f323(f237(f872(x129991,a860)),x129992),f246(f872(x129991,a860))))),
% 188.21/188.05 inference(rename_variables,[],[3663])).
% 188.21/188.05 cnf(13000,plain,
% 188.21/188.05 (P27(x130001,x130001,f5(x130001),x130002)),
% 188.21/188.05 inference(rename_variables,[],[3522])).
% 188.21/188.05 cnf(13004,plain,
% 188.21/188.05 (P27(x130041,x130041,f5(x130041),x130042)),
% 188.21/188.05 inference(rename_variables,[],[3522])).
% 188.21/188.05 cnf(13007,plain,
% 188.21/188.05 (~P101(f323(f323(f238(f872(x130071,a860)),x130072),f188(f872(x130071,a860))))),
% 188.21/188.05 inference(rename_variables,[],[4558])).
% 188.21/188.05 cnf(13010,plain,
% 188.21/188.05 (P27(x130101,x130101,f5(x130101),x130102)),
% 188.21/188.05 inference(rename_variables,[],[3522])).
% 188.21/188.05 cnf(13013,plain,
% 188.21/188.05 (P27(x130131,x130131,f5(x130131),x130132)),
% 188.21/188.05 inference(rename_variables,[],[3522])).
% 188.21/188.05 cnf(13019,plain,
% 188.21/188.05 (P101(f323(f323(f237(f872(x130191,a860)),x130192),f246(f872(x130191,a860))))),
% 188.21/188.05 inference(rename_variables,[],[3663])).
% 188.21/188.05 cnf(13024,plain,
% 188.21/188.05 (P101(f323(f323(f237(f872(x130241,a860)),f188(f872(x130241,a860))),x130242))),
% 188.21/188.05 inference(rename_variables,[],[3729])).
% 188.21/188.05 cnf(13028,plain,
% 188.21/188.05 (E(f323(f254(x130281,x130281),f255(x130281,x130282)),x130282)),
% 188.21/188.05 inference(rename_variables,[],[3238])).
% 188.21/188.05 cnf(13032,plain,
% 188.21/188.05 (~P101(f323(f323(f325(x130321),x130322),f188(f872(x130321,a860))))),
% 188.21/188.05 inference(rename_variables,[],[4548])).
% 188.21/188.05 cnf(13036,plain,
% 188.21/188.05 (P101(f323(f323(f325(x130361),f323(x130362,x130363)),f323(f302(x130364,x130361,x130362),f246(f872(x130364,a860)))))),
% 188.21/188.05 inference(rename_variables,[],[3889])).
% 188.21/188.05 cnf(13037,plain,
% 188.21/188.05 (P27(x130371,x130371,f5(x130371),x130372)),
% 188.21/188.05 inference(rename_variables,[],[3522])).
% 188.21/188.05 cnf(13040,plain,
% 188.21/188.05 (P101(f323(f323(f237(f872(x130401,a860)),x130402),f246(f872(x130401,a860))))),
% 188.21/188.05 inference(rename_variables,[],[3663])).
% 188.21/188.05 cnf(13044,plain,
% 188.21/188.05 (P101(f323(f323(f325(x130441),x130442),f246(f872(x130441,a860))))),
% 188.21/188.05 inference(rename_variables,[],[3439])).
% 188.21/188.05 cnf(13048,plain,
% 188.21/188.05 (E(f323(f323(f16(x130481,x130482),x130483),x130484),x130483)),
% 188.21/188.05 inference(rename_variables,[],[3272])).
% 188.21/188.05 cnf(13051,plain,
% 188.21/188.05 (~P101(f323(f323(f325(x130511),x130512),f188(f872(x130511,a860))))),
% 188.21/188.05 inference(rename_variables,[],[4548])).
% 188.21/188.05 cnf(13054,plain,
% 188.21/188.05 (~P101(f323(f323(f325(x130541),x130542),f188(f872(x130541,a860))))),
% 188.21/188.05 inference(rename_variables,[],[4548])).
% 188.21/188.05 cnf(13058,plain,
% 188.21/188.05 (P101(f323(f323(f237(a865),x130581),x130581))),
% 188.21/188.05 inference(rename_variables,[],[3281])).
% 188.21/188.05 cnf(13063,plain,
% 188.21/188.05 (E(f323(f323(f16(x130631,x130632),x130633),x130634),x130633)),
% 188.21/188.05 inference(rename_variables,[],[3272])).
% 188.21/188.05 cnf(13066,plain,
% 188.21/188.05 (P101(f323(f323(f238(a865),x130661),f323(a112,x130661)))),
% 188.21/188.05 inference(rename_variables,[],[3349])).
% 188.21/188.05 cnf(13067,plain,
% 188.21/188.05 (~E(f323(a112,x130671),x130671)),
% 188.21/188.05 inference(rename_variables,[],[4473])).
% 188.21/188.05 cnf(13070,plain,
% 188.21/188.05 (P101(f323(f323(f238(a865),x130701),f323(a112,f323(f323(f78(a865),x130702),x130701))))),
% 188.21/188.05 inference(rename_variables,[],[3731])).
% 188.21/188.05 cnf(13071,plain,
% 188.21/188.05 (P101(f323(f323(f238(a865),x130711),f323(a112,x130711)))),
% 188.21/188.05 inference(rename_variables,[],[3349])).
% 188.21/188.05 cnf(13080,plain,
% 188.21/188.05 (P101(f323(f323(f237(a1),f2(a1)),f323(f100(a1),x130801)))),
% 188.21/188.05 inference(rename_variables,[],[3381])).
% 188.21/188.05 cnf(13083,plain,
% 188.21/188.05 (P101(f323(f323(f237(a865),f2(a865)),x130831))),
% 188.21/188.05 inference(rename_variables,[],[3303])).
% 188.21/188.05 cnf(13087,plain,
% 188.21/188.05 (~E(f323(a112,x130871),f2(a865))),
% 188.21/188.05 inference(rename_variables,[],[4485])).
% 188.21/188.05 cnf(13090,plain,
% 188.21/188.05 (P101(f323(f323(f237(a1),x130901),x130901))),
% 188.21/188.05 inference(rename_variables,[],[3282])).
% 188.21/188.05 cnf(13100,plain,
% 188.21/188.05 (~P101(f323(f323(f325(x131001),x131002),f188(f872(x131001,a860))))),
% 188.21/188.05 inference(rename_variables,[],[4548])).
% 188.21/188.05 cnf(13103,plain,
% 188.21/188.05 (P101(f323(f59(a865),f296(a865,x131031,x131032)))),
% 188.21/188.05 inference(rename_variables,[],[3494])).
% 188.21/188.05 cnf(13104,plain,
% 188.21/188.05 (E(f323(f323(f236(a865),f323(a112,x131041)),f323(a112,x131042)),f323(a112,f323(f323(f236(a865),x131041),x131042)))),
% 188.21/188.05 inference(rename_variables,[],[3457])).
% 188.21/188.05 cnf(13107,plain,
% 188.21/188.05 (P101(f323(f59(a865),f296(a865,x131071,x131072)))),
% 188.21/188.05 inference(rename_variables,[],[3494])).
% 188.21/188.05 cnf(13108,plain,
% 188.21/188.05 (E(f323(f323(f235(a865),f323(a112,x131081)),f323(a112,x131082)),f323(a112,f323(f323(f235(a865),x131081),x131082)))),
% 188.21/188.05 inference(rename_variables,[],[3456])).
% 188.21/188.05 cnf(13111,plain,
% 188.21/188.05 (P101(f323(f59(a865),f296(a865,x131111,x131112)))),
% 188.21/188.05 inference(rename_variables,[],[3494])).
% 188.21/188.05 cnf(13119,plain,
% 188.21/188.05 (P101(f323(f323(f237(f872(x131191,a860)),f323(f166(x131191),f323(f129(x131191,x131192),x131193))),f323(f166(x131191),x131193)))),
% 188.21/188.05 inference(rename_variables,[],[3934])).
% 188.21/188.05 cnf(13120,plain,
% 188.21/188.05 (E(f323(f323(f16(x131201,x131202),x131203),x131204),x131203)),
% 188.21/188.05 inference(rename_variables,[],[3272])).
% 188.21/188.05 cnf(13123,plain,
% 188.21/188.05 (P101(f323(f323(f237(f872(x131231,a860)),f323(f166(x131231),f323(f323(f169(x131231),x131232),x131233))),f323(f166(x131231),x131233)))),
% 188.21/188.05 inference(rename_variables,[],[3981])).
% 188.21/188.05 cnf(13124,plain,
% 188.21/188.05 (E(f323(f323(f16(x131241,x131242),x131243),x131244),x131243)),
% 188.21/188.05 inference(rename_variables,[],[3272])).
% 188.21/188.05 cnf(13128,plain,
% 188.21/188.05 (E(f323(f323(f16(x131281,x131282),x131283),x131284),x131283)),
% 188.21/188.05 inference(rename_variables,[],[3272])).
% 188.21/188.05 cnf(13141,plain,
% 188.21/188.05 (P101(f323(f323(f237(a1),f2(a1)),f323(f100(a1),x131411)))),
% 188.21/188.05 inference(rename_variables,[],[3381])).
% 188.21/188.05 cnf(13146,plain,
% 188.21/188.05 (P27(x131461,x131461,f5(x131461),x131462)),
% 188.21/188.05 inference(rename_variables,[],[3522])).
% 188.21/188.05 cnf(13149,plain,
% 188.21/188.05 (~P101(f323(f323(f325(x131491),x131492),f188(f872(x131491,a860))))),
% 188.21/188.05 inference(rename_variables,[],[4548])).
% 188.21/188.05 cnf(13152,plain,
% 188.21/188.05 (~P101(f323(f323(f325(x131521),x131522),f188(f872(x131521,a860))))),
% 188.21/188.05 inference(rename_variables,[],[4548])).
% 188.21/188.05 cnf(13153,plain,
% 188.21/188.05 (E(f323(f254(x131531,x131531),f255(x131531,x131532)),x131532)),
% 188.21/188.05 inference(rename_variables,[],[3238])).
% 188.21/188.05 cnf(13154,plain,
% 188.21/188.05 (P27(x131541,x131541,f5(x131541),x131542)),
% 188.21/188.05 inference(rename_variables,[],[3522])).
% 188.21/188.05 cnf(13158,plain,
% 188.21/188.05 (E(f323(f254(x131581,x131581),f255(x131581,x131582)),x131582)),
% 188.21/188.05 inference(rename_variables,[],[3238])).
% 188.21/188.05 cnf(13165,plain,
% 188.21/188.05 (P101(f323(f323(f238(f872(a1,a860)),f294(a1,f2(a1),f2(a1))),f294(a1,f323(f77(a1),f323(f100(a1),f323(a112,x131651))),f2(a1))))),
% 188.21/188.05 inference(scs_inference,[],[3240,3949,12432,12454,12582,12584,12586,3522,11043,12108,12208,12211,12303,12345,12349,12357,12426,12568,12570,12989,12995,13000,13004,13010,13013,13037,13146,13154,3531,12172,12562,12564,3532,12242,3249,12608,12610,3250,12622,3214,12506,4508,4509,11685,4239,12650,12653,3253,12551,3093,3149,12576,4489,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,11727,11762,12078,12279,12486,12537,12539,12549,12555,12560,12580,12590,12599,12601,12603,12616,12633,12647,3583,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,11584,11893,11918,11930,11959,11965,12060,12168,12175,12338,12396,12660,12814,13067,3338,3301,12618,3491,11865,4485,10401,10492,10939,11023,12731,12746,2879,2880,2884,2885,2891,2892,2895,2896,2897,2898,2900,2901,2904,2905,2906,2913,2914,2918,2919,2920,2921,2924,2926,2929,2938,2943,2946,2947,2951,2957,2963,2982,2985,2986,2996,2998,2999,3001,3002,3011,3021,3023,3030,3033,3034,3035,3036,3044,3045,3056,4470,3072,3148,4471,3620,3850,3263,3323,3238,12865,13028,13153,3863,12924,3209,12370,12374,12378,3223,3740,3984,3114,3115,4487,3835,11372,3337,12541,3173,3140,3602,3135,3241,3957,3661,4444,4186,3823,12543,3123,3124,3097,3103,3753,3155,3294,12429,12509,3339,10782,10907,12169,12386,3207,3208,3385,4557,10371,3922,4500,10233,10398,11231,12330,12371,12375,4507,12342,3272,11708,11711,12958,13048,13063,13120,13124,13128,4546,10965,11048,11277,11280,3362,3269,3386,3608,3378,3352,12593,3170,3171,10300,10605,4534,3444,3162,3094,3277,3192,11362,4071,12360,12498,3924,10971,11114,11166,12314,12320,12443,12446,12473,4569,10885,11119,11225,11247,11285,11291,12258,4570,11004,11122,11228,4571,11125,11177,4572,11180,4573,3191,3483,12214,12255,12341,3645,4357,4358,4498,11353,3585,3623,3797,3553,12848,12852,12856,12860,12870,3845,12205,3470,3722,3349,10319,10437,10506,10567,10570,10608,10706,10955,11805,11889,11952,12031,12069,12146,12149,12477,12666,12725,12768,12771,12813,12831,13066,3733,11601,3265,3361,11723,3547,4540,10210,10213,10239,10714,10727,10843,11269,11365,11777,11782,11804,12007,12010,12090,12099,12261,12364,12671,12690,12693,12717,12772,12939,12944,12965,4552,11482,11515,11552,11581,12781,12785,3720,3492,12951,3494,12696,12699,12702,12705,12739,12742,13103,13107,13111,3495,3872,3456,13108,3457,13104,3309,3311,3284,4537,3169,4495,3672,4209,3993,3476,4553,4065,11242,3607,3322,11733,11736,12179,12283,12457,4035,3992,11882,12229,3934,10779,12063,12236,12385,12480,13119,3981,13123,3987,10977,12105,12178,12235,12282,12961,3646,11892,12038,12113,12159,4024,3663,10974,11053,11140,11199,12059,12127,12391,12453,12470,12483,12930,12994,12999,13019,13040,4558,10730,11130,12239,13007,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,11726,11862,11917,11933,11936,11939,11942,12120,12134,12137,12140,12143,12222,12286,12402,12449,12718,12745,12823,12834,12839,12842,12845,12878,12891,12902,12950,12976,12979,13058,3282,10357,10412,10620,10709,10830,11455,11524,11761,11765,11774,11868,11879,11898,11903,11945,11968,11985,12736,12882,12905,12940,12945,12966,12971,13090,3283,3357,12093,12801,12849,12853,12857,12861,12871,12875,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,11676,11836,11839,11842,11845,11929,11948,11951,11964,12019,12022,12025,12028,12100,12190,12193,12289,12292,12363,12395,12435,12518,3439,10573,10838,10882,11188,11266,11439,11688,12337,12521,12923,13044,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,11742,12013,12016,12050,12094,12123,12267,12311,12317,12414,12417,12439,12497,12503,12512,12531,12800,12817,12820,12912,13032,13051,13054,13100,13149,13152,3343,10602,10632,10641,11217,11789,12436,12450,12782,12786,12789,3381,13080,3375,3801,3738,10279,11604,11636,12763,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,11795,11824,11827,11830,11833,12089,12982,3303,10635,10787,10858,11637,11794,11990,12198,12223,12810,3762,11739,12712,4115,3498,4543,3773,3809,4526,4529,4530,3256,3260,4528,4527,4531,4292,3780,3597,11597,4215,4560,10198,10201,10458,10509,10512,10517,10942,11433,11692,11798,4567,11154,11274,11310,4001,12250,3889,11307,11663,11667,11730,12348,12356,12442,12730,12988,13036,3727,10898,10904,10926,11914,12043,12126,12410,3581,11028,11157,12152,12264,12274,12353,12405,12413,12528,12933,4069,3729,10638,10993,11163,11193,11204,12352,12399,13024,3548,10556,10559,10644,10814,3550,4564,11598,4554,4559,12680,4565,10697,10796,11436,11468,12217,12226,12270,12467,12524,4174,10772,12247,12273,4076,3761,12534,3707,3708,4562,10252,10255,10596,10599,11479,11668,12476,4563,11578,11673,3731,10562,10820,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114,6147,6163,6216,6251,6253,6274,6275,6280,6284,6285,6288,6294,6303,6318,6338,6339,6342,6345,6354,6369,6390,6395,6397,6412,6413,6416,6417,6419,6421,6422,6423,6425,6427,6429,6434,6435,6437,6438,6444,6446,6488,6493,6508,6510,6511,6512,6546,6551,6553,6558,6559,6567,6571,6583,6607,6608,6610,6611,6622,6628,6645,6648,6667,6699,6700,6701,6706,6720,6739,6741,6743,6745,6750,6756,6758,6773,6778,6781,6817,6818,6819,6833,6834,6836,6837,6855,6857,6871,6897,6919,6930,6932,6934,6936,6937,6938,6971,6972,6977,6978,6985,6986,6988,6990,7009,7018,7019,7031,7041,7080,7090,7094,7101,7112,7118,7120,7126,7135,7148,7165,7183,7185,7202,7251,7252,7253,7255,7257,7261,7266,7289,7331,7363,7378,7395,7427,7430,7455,7479,7496,7499,7500,7510,7529,7531,7533,7535,7536,7537,7562,7588,7589,7621,7623,7624,7625,7630,7652,7661,7671,7676,7682,7684,7690,7702,7703,7705,7728,7734,7755,7822,7823,7824,7872,7880,7881,7906,7907,7924,7925,7982,7983,8012,8039,8049,8051,8060,8072,8102,8108,8115,8128,8147,8152,8174,8218,8248,8262,8281,8284,8314,8340,8399,8400,8403,8404,8468,8502,8503,8504,8505,8532,8565,8594,8603,8604,8646,8667,8713,8728,8775,8778,8793,8800,8836,8884,8885,8901,8902,9031,9037,9041,9062,9072,9095,9097,9100,9104,9106,9107,9118,9119,9139,9146,9159,9168,9205,9223,9276,9277,9284,9323,9346,9351,9386,9394,9397,9400,9401,9414,9431,9440,9455,9464,9465,9467,9469,9497,9621,9667,9668,9710,9755,9870,9927,9991,10064,10077,10082,3,2616,2617,2618,2619,2623,2626,2630,2632,2636,2637,2638,2639,2642,2648,2650,2651,2653,2654,2655,2656,2661,2662,2663,2668,2669,2670,2671,2672,2673,2675,2677,2679,2680,2682,2683,2685,2686,2693,2700,2701,2702,2706,2707,2708,2710,2716,2723,2724,2751,2752,2753,2762,2763,2764,2768,2769,2771,2780,2783,2784,2788,2789,2797,2798,2799,2821,2823,2832,2835,2836,2837,2847,2848,5213,5272,5370,5456,5457,5458,5533,5630,5661,5695,5711,5713,5719,5780,5781,5782,5783,5789,5822,5949,5983,5992,6015,6052,6087,6092,6232,6237,6272,6273,6293,6296,6298,6305,6306,6307,6308,6309,6310,6311,6312,6391,6458,6459,6545,6578,6579,6619,6620,6757,6772,6845,6846,6852,6872,6895,6903,6905,6952,6975,6976,6994,6995,7030,7074,7075,7172,7233,7234,7235,7236,7250,7283,7336,7337,7346,7353,7354,7366,7398,7399,7400,7401,7543,7544,7546,7548,7554,7555,7763,7769,7770,7780,7819,7820,7901,7941,7995,8017,8018,8088,8189,8258,8259,8263,8299,8362,8363,8427,8445,8446,8447,8448,8598,8854,8855,8927,8941,8994,8995,9115,9150,9177,9206,9247,9438,9562,9704,9896,9952,9954,10087,6010,6374,6375,6461,6481,6482,6894,7110,8245,8517,8553,8769,8952,8953,9022,9023,9295,9296,9297,9298,9499,9775,9789,10073,10128,10129,6443,8353,8354])).
% 188.21/188.05 cnf(13172,plain,
% 188.21/188.05 (P101(f323(f323(f237(a865),f2(a865)),x131721))),
% 188.21/188.05 inference(rename_variables,[],[3303])).
% 188.21/188.05 cnf(13173,plain,
% 188.21/188.05 (P101(f323(f323(f238(a865),f2(a865)),f323(a112,x131731)))),
% 188.21/188.05 inference(rename_variables,[],[3361])).
% 188.21/188.05 cnf(13174,plain,
% 188.21/188.05 (E(f323(f254(x131741,x131741),f255(x131741,x131742)),x131742)),
% 188.21/188.05 inference(rename_variables,[],[3238])).
% 188.21/188.05 cnf(13242,plain,
% 188.21/188.05 (~P101(f323(f323(f238(a1),f2(a1)),f2(a1)))),
% 188.21/188.05 inference(scs_inference,[],[3240,3949,12432,12454,12582,12584,12586,3522,11043,12108,12208,12211,12303,12345,12349,12357,12426,12568,12570,12989,12995,13000,13004,13010,13013,13037,13146,13154,3531,12172,12562,12564,3532,12242,3249,12608,12610,3250,12622,3214,12506,4508,4509,11685,4239,12650,12653,3253,12551,3093,3149,12576,4489,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,11727,11762,12078,12279,12486,12537,12539,12549,12555,12560,12580,12590,12599,12601,12603,12616,12633,12647,3583,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,11584,11893,11918,11930,11959,11965,12060,12168,12175,12338,12396,12660,12814,13067,3338,3301,12618,3491,11865,4485,10401,10492,10939,11023,12731,12746,13087,2879,2880,2884,2885,2891,2892,2895,2896,2897,2898,2900,2901,2904,2905,2906,2913,2914,2918,2919,2920,2921,2924,2926,2929,2938,2943,2946,2947,2951,2957,2961,2963,2982,2983,2985,2986,2996,2998,2999,3001,3002,3011,3021,3023,3030,3033,3034,3035,3036,3044,3045,3056,4470,3072,3148,4471,3620,3850,3263,3323,3238,12865,13028,13153,13158,13174,3863,12924,3209,12370,12374,12378,3223,3740,3984,3114,3115,4487,3835,11372,3337,12541,3173,3140,3602,3135,3241,3957,3661,4444,4186,3823,12543,3123,3124,3097,3103,3753,3155,3294,12429,12509,3339,10782,10907,12169,12386,3207,3208,3385,4557,10371,3922,4500,10233,10398,11231,12330,12371,12375,4507,12342,3272,11708,11711,12958,13048,13063,13120,13124,13128,4546,10965,11048,11277,11280,3362,3269,3386,3608,3378,3352,12593,3170,3171,10300,10605,4534,3444,3162,3094,3277,3192,11362,4071,12360,12498,3924,10971,11114,11166,12314,12320,12443,12446,12473,4569,10885,11119,11225,11247,11285,11291,12258,4570,11004,11122,11228,4571,11125,11177,4572,11180,4573,3191,3483,12214,12255,12341,3645,4357,4358,3467,4498,11353,3585,3623,3797,3553,12848,12852,12856,12860,12870,3845,12205,3470,3722,3349,10319,10437,10506,10567,10570,10608,10706,10955,11805,11889,11952,12031,12069,12146,12149,12477,12666,12725,12768,12771,12813,12831,13066,13071,3733,11601,3265,3361,11723,12659,13173,3547,4540,10210,10213,10239,10714,10727,10843,11269,11365,11777,11782,11804,12007,12010,12090,12099,12261,12364,12671,12690,12693,12717,12772,12939,12944,12965,12970,4552,11482,11515,11552,11581,12781,12785,3720,3492,12951,3494,12696,12699,12702,12705,12739,12742,13103,13107,13111,3495,3872,3456,13108,3457,13104,3309,3311,3284,4537,3169,4495,3672,4209,3993,3476,4553,4065,11242,3607,3322,11733,11736,12179,12283,12457,4035,3992,11882,12229,3934,10779,12063,12236,12385,12480,13119,3981,13123,3987,10977,12105,12178,12235,12282,12961,3988,3646,11892,12038,12113,12159,4024,3663,10974,11053,11140,11199,12059,12127,12391,12453,12470,12483,12930,12994,12999,13019,13040,4558,10730,11130,12239,13007,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,11726,11862,11917,11933,11936,11939,11942,12120,12134,12137,12140,12143,12222,12286,12402,12449,12718,12745,12823,12834,12839,12842,12845,12878,12891,12902,12950,12976,12979,13058,3282,10357,10412,10620,10709,10830,11455,11524,11761,11765,11774,11868,11879,11898,11903,11945,11968,11985,12736,12882,12905,12940,12945,12966,12971,13090,3283,3357,12093,12801,12849,12853,12857,12861,12871,12875,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,11676,11836,11839,11842,11845,11929,11948,11951,11964,12019,12022,12025,12028,12100,12190,12193,12289,12292,12363,12395,12435,12518,3439,10573,10838,10882,11188,11266,11439,11688,12337,12521,12923,13044,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,11742,12013,12016,12050,12094,12123,12267,12311,12317,12414,12417,12439,12497,12503,12512,12531,12800,12817,12820,12912,13032,13051,13054,13100,13149,13152,3343,10602,10632,10641,11217,11789,12436,12450,12782,12786,12789,3381,13080,13141,3375,3801,3738,10279,11604,11636,12763,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,11795,11824,11827,11830,11833,12089,12982,3303,10635,10787,10858,11637,11794,11990,12198,12223,12810,13083,13172,3762,11739,12712,4115,3498,4543,3773,3809,4526,4529,4530,3256,3260,4528,4527,4531,4292,3780,3597,11597,4215,4560,10198,10201,10458,10509,10512,10517,10942,11433,11692,11798,4567,11154,11274,11310,4001,12250,3889,11307,11663,11667,11730,12348,12356,12442,12730,12988,13036,3727,10898,10904,10926,11914,12043,12126,12410,3581,11028,11157,12152,12264,12274,12353,12405,12413,12528,12933,4069,3729,10638,10993,11163,11193,11204,12352,12399,13024,3548,10556,10559,10644,10814,3550,4564,11598,4554,4559,12680,4565,10697,10796,11436,11468,12217,12226,12270,12467,12524,4174,10772,12247,12273,4076,3761,12534,3707,3708,4562,10252,10255,10596,10599,11479,11668,12476,4563,11578,11673,3731,10562,10820,13070,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114,6147,6163,6216,6251,6253,6274,6275,6280,6284,6285,6288,6294,6303,6318,6338,6339,6342,6345,6354,6369,6390,6395,6397,6412,6413,6416,6417,6419,6421,6422,6423,6425,6427,6429,6434,6435,6437,6438,6444,6446,6488,6493,6508,6510,6511,6512,6546,6551,6553,6558,6559,6567,6571,6583,6607,6608,6610,6611,6622,6628,6645,6648,6667,6699,6700,6701,6706,6720,6739,6741,6743,6745,6750,6756,6758,6773,6778,6781,6817,6818,6819,6833,6834,6836,6837,6855,6857,6871,6897,6919,6930,6932,6934,6936,6937,6938,6971,6972,6977,6978,6985,6986,6988,6990,7009,7018,7019,7031,7041,7080,7090,7094,7101,7112,7118,7120,7126,7135,7148,7165,7183,7185,7202,7251,7252,7253,7255,7257,7261,7266,7289,7331,7363,7378,7395,7427,7430,7455,7479,7496,7499,7500,7510,7529,7531,7533,7535,7536,7537,7562,7588,7589,7621,7623,7624,7625,7630,7652,7661,7671,7676,7682,7684,7690,7702,7703,7705,7728,7734,7755,7822,7823,7824,7872,7880,7881,7906,7907,7924,7925,7982,7983,8012,8039,8049,8051,8060,8072,8102,8108,8115,8128,8147,8152,8174,8218,8248,8262,8281,8284,8314,8340,8399,8400,8403,8404,8468,8502,8503,8504,8505,8532,8565,8594,8603,8604,8646,8667,8713,8728,8775,8778,8793,8800,8836,8884,8885,8901,8902,9031,9037,9041,9062,9072,9095,9097,9100,9104,9106,9107,9118,9119,9139,9146,9159,9168,9205,9223,9276,9277,9284,9323,9346,9351,9386,9394,9397,9400,9401,9414,9431,9440,9455,9464,9465,9467,9469,9497,9621,9667,9668,9710,9755,9870,9927,9991,10064,10077,10082,3,2616,2617,2618,2619,2623,2626,2630,2632,2636,2637,2638,2639,2642,2648,2650,2651,2653,2654,2655,2656,2661,2662,2663,2668,2669,2670,2671,2672,2673,2675,2677,2679,2680,2682,2683,2685,2686,2693,2700,2701,2702,2706,2707,2708,2710,2716,2723,2724,2751,2752,2753,2762,2763,2764,2768,2769,2771,2780,2783,2784,2788,2789,2797,2798,2799,2821,2823,2832,2835,2836,2837,2847,2848,5213,5272,5370,5456,5457,5458,5533,5630,5661,5695,5711,5713,5719,5780,5781,5782,5783,5789,5822,5949,5983,5992,6015,6052,6087,6092,6232,6237,6272,6273,6293,6296,6298,6305,6306,6307,6308,6309,6310,6311,6312,6391,6458,6459,6545,6578,6579,6619,6620,6757,6772,6845,6846,6852,6872,6895,6903,6905,6952,6975,6976,6994,6995,7030,7074,7075,7172,7233,7234,7235,7236,7250,7283,7336,7337,7346,7353,7354,7366,7398,7399,7400,7401,7543,7544,7546,7548,7554,7555,7763,7769,7770,7780,7819,7820,7901,7941,7995,8017,8018,8088,8189,8258,8259,8263,8299,8362,8363,8427,8445,8446,8447,8448,8598,8854,8855,8927,8941,8994,8995,9115,9150,9177,9206,9247,9438,9562,9704,9896,9952,9954,10087,6010,6374,6375,6461,6481,6482,6894,7110,8245,8517,8553,8769,8952,8953,9022,9023,9295,9296,9297,9298,9499,9775,9789,10073,10128,10129,6443,8353,8354,8820,8837,9776,10127,4651,4652,4653,4709,4717,4854,4870,4871,4898,4899,4930,4985,5045,5173,5208,5211,5216,5217,5243,5317,5338,5472,5538,5539,5540,5657])).
% 188.21/188.05 cnf(13254,plain,
% 188.21/188.05 (~P101(f323(f323(f238(a865),f323(a112,f323(f323(f78(a865),x132541),x132542))),f323(a112,x132541)))),
% 188.21/188.05 inference(scs_inference,[],[3240,3949,12432,12454,12582,12584,12586,3522,11043,12108,12208,12211,12303,12345,12349,12357,12426,12568,12570,12989,12995,13000,13004,13010,13013,13037,13146,13154,3531,12172,12562,12564,3532,12242,3249,12608,12610,3250,12622,3214,12506,4508,4509,11685,4239,12650,12653,3253,12551,3093,3149,12576,4489,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,11727,11762,12078,12279,12486,12537,12539,12549,12555,12560,12580,12590,12599,12601,12603,12616,12633,12647,3583,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,11584,11893,11918,11930,11959,11965,12060,12168,12175,12338,12396,12660,12814,13067,3338,3301,12618,3491,11865,4485,10401,10492,10939,11023,12731,12746,13087,2879,2880,2884,2885,2891,2892,2895,2896,2897,2898,2900,2901,2904,2905,2906,2913,2914,2918,2919,2920,2921,2924,2926,2929,2938,2943,2946,2947,2951,2957,2961,2963,2982,2983,2985,2986,2996,2998,2999,3001,3002,3011,3021,3023,3030,3033,3034,3035,3036,3044,3045,3056,4470,3072,3148,4471,3620,3850,3263,3323,3238,12865,13028,13153,13158,13174,3863,12924,3209,12370,12374,12378,3223,3740,3984,3114,3115,4487,3835,11372,3337,12541,3173,3140,3602,3135,3241,3957,3661,4444,4186,3823,12543,3123,3124,3097,3103,3753,3155,3294,12429,12509,3339,10782,10907,12169,12386,3207,3208,3385,4557,10371,3922,4500,10233,10398,11231,12330,12371,12375,4507,12342,3272,11708,11711,12958,13048,13063,13120,13124,13128,4546,10965,11048,11277,11280,3362,3269,3386,3608,3378,3352,12593,3170,3171,10300,10605,4534,3444,3162,3094,3277,3192,11362,4071,12360,12498,3924,10971,11114,11166,12314,12320,12443,12446,12473,4569,10885,11119,11225,11247,11285,11291,12258,4570,11004,11122,11228,4571,11125,11177,4572,11180,4573,3191,3483,12214,12255,12341,3645,4357,4358,3467,4498,11353,3585,3623,3797,3553,12848,12852,12856,12860,12870,3845,12205,3470,3722,3349,10319,10437,10506,10567,10570,10608,10706,10955,11805,11889,11952,12031,12069,12146,12149,12477,12666,12725,12768,12771,12813,12831,13066,13071,3733,11601,3265,3361,11723,12659,13173,3547,4540,10210,10213,10239,10714,10727,10843,11269,11365,11777,11782,11804,12007,12010,12090,12099,12261,12364,12671,12690,12693,12717,12772,12939,12944,12965,12970,4552,11482,11515,11552,11581,12781,12785,3720,3492,12951,3494,12696,12699,12702,12705,12739,12742,13103,13107,13111,3495,3872,3456,13108,3457,13104,3309,3311,3284,4537,3169,4495,3672,4209,3993,3476,4553,4065,11242,3607,3322,11733,11736,12179,12283,12457,4035,3992,11882,12229,3934,10779,12063,12236,12385,12480,13119,3981,13123,3987,10977,12105,12178,12235,12282,12961,3988,3646,11892,12038,12113,12159,4024,3663,10974,11053,11140,11199,12059,12127,12391,12453,12470,12483,12930,12994,12999,13019,13040,4558,10730,11130,12239,13007,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,11726,11862,11917,11933,11936,11939,11942,12120,12134,12137,12140,12143,12222,12286,12402,12449,12718,12745,12823,12834,12839,12842,12845,12878,12891,12902,12950,12976,12979,13058,3282,10357,10412,10620,10709,10830,11455,11524,11761,11765,11774,11868,11879,11898,11903,11945,11968,11985,12736,12882,12905,12940,12945,12966,12971,13090,3283,3357,12093,12801,12849,12853,12857,12861,12871,12875,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,11676,11836,11839,11842,11845,11929,11948,11951,11964,12019,12022,12025,12028,12100,12190,12193,12289,12292,12363,12395,12435,12518,3439,10573,10838,10882,11188,11266,11439,11688,12337,12521,12923,13044,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,11742,12013,12016,12050,12094,12123,12267,12311,12317,12414,12417,12439,12497,12503,12512,12531,12800,12817,12820,12912,13032,13051,13054,13100,13149,13152,3343,10602,10632,10641,11217,11789,12436,12450,12782,12786,12789,3381,13080,13141,3375,3801,3738,10279,11604,11636,12763,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,11795,11824,11827,11830,11833,12089,12982,3303,10635,10787,10858,11637,11794,11990,12198,12223,12810,13083,13172,3762,11739,12712,4115,3498,4543,3773,3809,4526,4529,4530,3256,3260,4528,4527,4531,4292,3780,3597,11597,4215,4560,10198,10201,10458,10509,10512,10517,10942,11433,11692,11798,4567,11154,11274,11310,4001,12250,3889,11307,11663,11667,11730,12348,12356,12442,12730,12988,13036,3727,10898,10904,10926,11914,12043,12126,12410,3581,11028,11157,12152,12264,12274,12353,12405,12413,12528,12933,4069,3729,10638,10993,11163,11193,11204,12352,12399,13024,3548,10556,10559,10644,10814,3550,4564,11598,4554,4559,12680,4565,10697,10796,11436,11468,12217,12226,12270,12467,12524,4174,10772,12247,12273,4076,3761,12534,3707,3708,4562,10252,10255,10596,10599,11479,11668,12476,4563,11578,11673,3731,10562,10820,13070,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114,6147,6163,6216,6251,6253,6274,6275,6280,6284,6285,6288,6294,6303,6318,6338,6339,6342,6345,6354,6369,6390,6395,6397,6412,6413,6416,6417,6419,6421,6422,6423,6425,6427,6429,6434,6435,6437,6438,6444,6446,6488,6493,6508,6510,6511,6512,6546,6551,6553,6558,6559,6567,6571,6583,6607,6608,6610,6611,6622,6628,6645,6648,6667,6699,6700,6701,6706,6720,6739,6741,6743,6745,6750,6756,6758,6773,6778,6781,6817,6818,6819,6833,6834,6836,6837,6855,6857,6871,6897,6919,6930,6932,6934,6936,6937,6938,6971,6972,6977,6978,6985,6986,6988,6990,7009,7018,7019,7031,7041,7080,7090,7094,7101,7112,7118,7120,7126,7135,7148,7165,7183,7185,7202,7251,7252,7253,7255,7257,7261,7266,7289,7331,7363,7378,7395,7427,7430,7455,7479,7496,7499,7500,7510,7529,7531,7533,7535,7536,7537,7562,7588,7589,7621,7623,7624,7625,7630,7652,7661,7671,7676,7682,7684,7690,7702,7703,7705,7728,7734,7755,7822,7823,7824,7872,7880,7881,7906,7907,7924,7925,7982,7983,8012,8039,8049,8051,8060,8072,8102,8108,8115,8128,8147,8152,8174,8218,8248,8262,8281,8284,8314,8340,8399,8400,8403,8404,8468,8502,8503,8504,8505,8532,8565,8594,8603,8604,8646,8667,8713,8728,8775,8778,8793,8800,8836,8884,8885,8901,8902,9031,9037,9041,9062,9072,9095,9097,9100,9104,9106,9107,9118,9119,9139,9146,9159,9168,9205,9223,9276,9277,9284,9323,9346,9351,9386,9394,9397,9400,9401,9414,9431,9440,9455,9464,9465,9467,9469,9497,9621,9667,9668,9710,9755,9870,9927,9991,10064,10077,10082,3,2616,2617,2618,2619,2623,2626,2630,2632,2636,2637,2638,2639,2642,2648,2650,2651,2653,2654,2655,2656,2661,2662,2663,2668,2669,2670,2671,2672,2673,2675,2677,2679,2680,2682,2683,2685,2686,2693,2700,2701,2702,2706,2707,2708,2710,2716,2723,2724,2751,2752,2753,2762,2763,2764,2768,2769,2771,2780,2783,2784,2788,2789,2797,2798,2799,2821,2823,2832,2835,2836,2837,2847,2848,5213,5272,5370,5456,5457,5458,5533,5630,5661,5695,5711,5713,5719,5780,5781,5782,5783,5789,5822,5949,5983,5992,6015,6052,6087,6092,6232,6237,6272,6273,6293,6296,6298,6305,6306,6307,6308,6309,6310,6311,6312,6391,6458,6459,6545,6578,6579,6619,6620,6757,6772,6845,6846,6852,6872,6895,6903,6905,6952,6975,6976,6994,6995,7030,7074,7075,7172,7233,7234,7235,7236,7250,7283,7336,7337,7346,7353,7354,7366,7398,7399,7400,7401,7543,7544,7546,7548,7554,7555,7763,7769,7770,7780,7819,7820,7901,7941,7995,8017,8018,8088,8189,8258,8259,8263,8299,8362,8363,8427,8445,8446,8447,8448,8598,8854,8855,8927,8941,8994,8995,9115,9150,9177,9206,9247,9438,9562,9704,9896,9952,9954,10087,6010,6374,6375,6461,6481,6482,6894,7110,8245,8517,8553,8769,8952,8953,9022,9023,9295,9296,9297,9298,9499,9775,9789,10073,10128,10129,6443,8353,8354,8820,8837,9776,10127,4651,4652,4653,4709,4717,4854,4870,4871,4898,4899,4930,4985,5045,5173,5208,5211,5216,5217,5243,5317,5338,5472,5538,5539,5540,5657,5658,5684,5688,5746,5748,5835])).
% 188.21/188.05 cnf(13258,plain,
% 188.21/188.05 (~E(f323(f182(x132581,f872(x132582,a860),x132583,f188(f872(x132581,a860))),x132584),f323(f230(f872(x132582,a860)),f323(f323(f39(f31(x132585,a865,x132586,x132587,x132588,x132589,x1325810,x1325811,x1325812,a24),f872(x132582,a860)),x1325813),a112)))),
% 188.21/188.05 inference(scs_inference,[],[3240,3949,12432,12454,12582,12584,12586,3522,11043,12108,12208,12211,12303,12345,12349,12357,12426,12568,12570,12989,12995,13000,13004,13010,13013,13037,13146,13154,3531,12172,12562,12564,3532,12242,3249,12608,12610,3250,12622,3214,12506,4508,4509,11685,4239,12650,12653,3253,12551,3093,3149,12576,4489,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,11727,11762,12078,12279,12486,12537,12539,12549,12555,12560,12580,12590,12599,12601,12603,12616,12633,12647,3583,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,11584,11893,11918,11930,11959,11965,12060,12168,12175,12338,12396,12660,12814,13067,3338,3301,12618,3491,11865,4485,10401,10492,10939,11023,12731,12746,13087,2879,2880,2884,2885,2891,2892,2895,2896,2897,2898,2900,2901,2904,2905,2906,2913,2914,2918,2919,2920,2921,2924,2926,2929,2938,2943,2946,2947,2951,2957,2961,2963,2982,2983,2985,2986,2996,2998,2999,3001,3002,3011,3021,3023,3030,3033,3034,3035,3036,3044,3045,3056,4470,3072,3148,4471,3620,3850,3263,3323,3238,12865,13028,13153,13158,13174,3863,12924,3209,12370,12374,12378,3223,3740,3984,3114,3115,4487,3835,11372,3337,12541,3173,3140,3602,3135,3241,3957,3661,4444,4186,3823,12543,3123,3124,3097,3103,3753,3155,3294,12429,12509,3339,10782,10907,12169,12386,3207,3208,3385,4557,10371,3922,4500,10233,10398,11231,12330,12371,12375,4507,12342,3272,11708,11711,12958,13048,13063,13120,13124,13128,4546,10965,11048,11277,11280,3362,3269,3386,3608,3378,3352,12593,3170,3171,10300,10605,4534,3444,3162,3094,3277,3192,11362,4071,12360,12498,3924,10971,11114,11166,12314,12320,12443,12446,12473,4569,10885,11119,11225,11247,11285,11291,12258,4570,11004,11122,11228,4571,11125,11177,4572,11180,4573,3191,3483,12214,12255,12341,3645,4357,4358,3467,4498,11353,3585,3623,3797,3553,12848,12852,12856,12860,12870,3845,12205,3470,3722,3349,10319,10437,10506,10567,10570,10608,10706,10955,11805,11889,11952,12031,12069,12146,12149,12477,12666,12725,12768,12771,12813,12831,13066,13071,3733,11601,3265,3361,11723,12659,13173,3547,4540,10210,10213,10239,10714,10727,10843,11269,11365,11777,11782,11804,12007,12010,12090,12099,12261,12364,12671,12690,12693,12717,12772,12939,12944,12965,12970,4552,11482,11515,11552,11581,12781,12785,3720,3492,12951,3494,12696,12699,12702,12705,12739,12742,13103,13107,13111,3495,3872,3456,13108,3457,13104,3309,3311,3284,4537,3169,4495,3672,4209,3993,3476,4553,4065,11242,3607,3322,11733,11736,12179,12283,12457,4035,3992,11882,12229,3934,10779,12063,12236,12385,12480,13119,3981,13123,3987,10977,12105,12178,12235,12282,12961,3988,3646,11892,12038,12113,12159,4024,3663,10974,11053,11140,11199,12059,12127,12391,12453,12470,12483,12930,12994,12999,13019,13040,4558,10730,11130,12239,13007,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,11726,11862,11917,11933,11936,11939,11942,12120,12134,12137,12140,12143,12222,12286,12402,12449,12718,12745,12823,12834,12839,12842,12845,12878,12891,12902,12950,12976,12979,13058,3282,10357,10412,10620,10709,10830,11455,11524,11761,11765,11774,11868,11879,11898,11903,11945,11968,11985,12736,12882,12905,12940,12945,12966,12971,13090,3283,3357,12093,12801,12849,12853,12857,12861,12871,12875,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,11676,11836,11839,11842,11845,11929,11948,11951,11964,12019,12022,12025,12028,12100,12190,12193,12289,12292,12363,12395,12435,12518,3439,10573,10838,10882,11188,11266,11439,11688,12337,12521,12923,13044,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,11742,12013,12016,12050,12094,12123,12267,12311,12317,12414,12417,12439,12497,12503,12512,12531,12800,12817,12820,12912,13032,13051,13054,13100,13149,13152,3343,10602,10632,10641,11217,11789,12436,12450,12782,12786,12789,3381,13080,13141,3375,3801,3738,10279,11604,11636,12763,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,11795,11824,11827,11830,11833,12089,12982,3303,10635,10787,10858,11637,11794,11990,12198,12223,12810,13083,13172,3762,11739,12712,4115,3498,4543,3773,3809,4526,4529,4530,3256,3260,4528,4527,4531,4292,3780,3597,11597,4215,4560,10198,10201,10458,10509,10512,10517,10942,11433,11692,11798,4567,11154,11274,11310,4001,12250,3889,11307,11663,11667,11730,12348,12356,12442,12730,12988,13036,3727,10898,10904,10926,11914,12043,12126,12410,3581,11028,11157,12152,12264,12274,12353,12405,12413,12528,12933,4069,3729,10638,10993,11163,11193,11204,12352,12399,13024,3548,10556,10559,10644,10814,3550,4564,11598,4554,4559,12680,4565,10697,10796,11436,11468,12217,12226,12270,12467,12524,4174,10772,12247,12273,4076,3761,12534,3707,3708,4562,10252,10255,10596,10599,11479,11668,12476,4563,11578,11673,3731,10562,10820,13070,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114,6147,6163,6216,6251,6253,6274,6275,6280,6284,6285,6288,6294,6303,6318,6338,6339,6342,6345,6354,6369,6390,6395,6397,6412,6413,6416,6417,6419,6421,6422,6423,6425,6427,6429,6434,6435,6437,6438,6444,6446,6488,6493,6508,6510,6511,6512,6546,6551,6553,6558,6559,6567,6571,6583,6607,6608,6610,6611,6622,6628,6645,6648,6667,6699,6700,6701,6706,6720,6739,6741,6743,6745,6750,6756,6758,6773,6778,6781,6817,6818,6819,6833,6834,6836,6837,6855,6857,6871,6897,6919,6930,6932,6934,6936,6937,6938,6971,6972,6977,6978,6985,6986,6988,6990,7009,7018,7019,7031,7041,7080,7090,7094,7101,7112,7118,7120,7126,7135,7148,7165,7183,7185,7202,7251,7252,7253,7255,7257,7261,7266,7289,7331,7363,7378,7395,7427,7430,7455,7479,7496,7499,7500,7510,7529,7531,7533,7535,7536,7537,7562,7588,7589,7621,7623,7624,7625,7630,7652,7661,7671,7676,7682,7684,7690,7702,7703,7705,7728,7734,7755,7822,7823,7824,7872,7880,7881,7906,7907,7924,7925,7982,7983,8012,8039,8049,8051,8060,8072,8102,8108,8115,8128,8147,8152,8174,8218,8248,8262,8281,8284,8314,8340,8399,8400,8403,8404,8468,8502,8503,8504,8505,8532,8565,8594,8603,8604,8646,8667,8713,8728,8775,8778,8793,8800,8836,8884,8885,8901,8902,9031,9037,9041,9062,9072,9095,9097,9100,9104,9106,9107,9118,9119,9139,9146,9159,9168,9205,9223,9276,9277,9284,9323,9346,9351,9386,9394,9397,9400,9401,9414,9431,9440,9455,9464,9465,9467,9469,9497,9621,9667,9668,9710,9755,9870,9927,9991,10064,10077,10082,3,2616,2617,2618,2619,2623,2626,2630,2632,2636,2637,2638,2639,2642,2648,2650,2651,2653,2654,2655,2656,2661,2662,2663,2668,2669,2670,2671,2672,2673,2675,2677,2679,2680,2682,2683,2685,2686,2693,2700,2701,2702,2706,2707,2708,2710,2716,2723,2724,2751,2752,2753,2762,2763,2764,2768,2769,2771,2780,2783,2784,2788,2789,2797,2798,2799,2821,2823,2832,2835,2836,2837,2847,2848,5213,5272,5370,5456,5457,5458,5533,5630,5661,5695,5711,5713,5719,5780,5781,5782,5783,5789,5822,5949,5983,5992,6015,6052,6087,6092,6232,6237,6272,6273,6293,6296,6298,6305,6306,6307,6308,6309,6310,6311,6312,6391,6458,6459,6545,6578,6579,6619,6620,6757,6772,6845,6846,6852,6872,6895,6903,6905,6952,6975,6976,6994,6995,7030,7074,7075,7172,7233,7234,7235,7236,7250,7283,7336,7337,7346,7353,7354,7366,7398,7399,7400,7401,7543,7544,7546,7548,7554,7555,7763,7769,7770,7780,7819,7820,7901,7941,7995,8017,8018,8088,8189,8258,8259,8263,8299,8362,8363,8427,8445,8446,8447,8448,8598,8854,8855,8927,8941,8994,8995,9115,9150,9177,9206,9247,9438,9562,9704,9896,9952,9954,10087,6010,6374,6375,6461,6481,6482,6894,7110,8245,8517,8553,8769,8952,8953,9022,9023,9295,9296,9297,9298,9499,9775,9789,10073,10128,10129,6443,8353,8354,8820,8837,9776,10127,4651,4652,4653,4709,4717,4854,4870,4871,4898,4899,4930,4985,5045,5173,5208,5211,5216,5217,5243,5317,5338,5472,5538,5539,5540,5657,5658,5684,5688,5746,5748,5835,5911,6033])).
% 188.21/188.05 cnf(13274,plain,
% 188.21/188.05 (~P101(f323(f323(f238(a865),f2(a865)),f31(x132741,f2(a865),x132742,x132743,x132744,x132745,x132746,x132747,x132748,a24)))),
% 188.21/188.06 inference(scs_inference,[],[3240,3949,12432,12454,12582,12584,12586,3522,11043,12108,12208,12211,12303,12345,12349,12357,12426,12568,12570,12989,12995,13000,13004,13010,13013,13037,13146,13154,3531,12172,12562,12564,3532,12242,3249,12608,12610,3250,12622,3214,12506,4508,4509,11685,4239,12650,12653,3253,12551,3093,3149,12576,4489,4459,10166,10172,10186,10242,10245,10335,10338,10629,10649,10910,10913,11319,11322,11337,11340,11384,11391,11394,11397,11400,11410,11447,11463,11493,11496,11507,11512,11518,11610,11613,11616,11619,11623,11633,11727,11762,12078,12279,12486,12537,12539,12549,12555,12560,12580,12590,12599,12601,12603,12616,12633,12647,3583,4473,10169,10179,10193,10204,10207,10308,10311,10314,10417,10528,10833,11015,11018,11035,11038,11234,11325,11332,11346,11403,11406,11452,11521,11568,11584,11893,11918,11930,11959,11965,12060,12168,12175,12338,12396,12660,12814,13067,3338,3301,12618,3491,11865,4485,10401,10492,10939,11023,12731,12746,13087,2879,2880,2884,2885,2891,2892,2895,2896,2897,2898,2900,2901,2904,2905,2906,2913,2914,2918,2919,2920,2921,2924,2926,2929,2938,2943,2946,2947,2951,2957,2961,2963,2982,2983,2985,2986,2996,2998,2999,3001,3002,3011,3021,3023,3030,3033,3034,3035,3036,3044,3045,3056,4470,3072,3148,4471,3620,3850,3263,3323,3238,12865,13028,13153,13158,13174,3863,12924,3209,12370,12374,12378,3223,3740,3984,3114,3115,4487,3835,11372,3337,12541,3173,3140,3602,3135,3241,3957,3661,4444,4186,3823,12543,3123,3124,3097,3103,3753,3155,3294,12429,12509,3339,10782,10907,12169,12386,3207,3208,3385,4557,10371,3922,4500,10233,10398,11231,12330,12371,12375,4507,12342,3272,11708,11711,12958,13048,13063,13120,13124,13128,4546,10965,11048,11277,11280,3362,3269,3386,3608,3378,3352,12593,3170,3171,10300,10605,4534,3444,3162,3094,3277,3192,11362,4071,12360,12498,3924,10971,11114,11166,12314,12320,12443,12446,12473,4569,10885,11119,11225,11247,11285,11291,12258,4570,11004,11122,11228,4571,11125,11177,4572,11180,4573,3191,3483,12214,12255,12341,3645,4357,4358,3467,4498,11353,3585,3623,3797,3553,12848,12852,12856,12860,12870,3845,12205,3470,3722,3349,10319,10437,10506,10567,10570,10608,10706,10955,11805,11889,11952,12031,12069,12146,12149,12477,12666,12725,12768,12771,12813,12831,13066,13071,3733,11601,3265,3361,11723,12659,13173,3547,4540,10210,10213,10239,10714,10727,10843,11269,11365,11777,11782,11804,12007,12010,12090,12099,12261,12364,12671,12690,12693,12717,12772,12939,12944,12965,12970,4552,11482,11515,11552,11581,12781,12785,3720,3492,12951,3494,12696,12699,12702,12705,12739,12742,13103,13107,13111,3495,3872,3456,13108,3457,13104,3309,3311,3284,4537,3169,4495,3672,4209,3993,3476,4553,4065,11242,3607,3322,11733,11736,12179,12283,12457,4035,3992,11882,12229,3934,10779,12063,12236,12385,12480,13119,3981,13123,3987,10977,12105,12178,12235,12282,12961,3988,3646,11892,12038,12113,12159,4024,3663,10974,11053,11140,11199,12059,12127,12391,12453,12470,12483,12930,12994,12999,13019,13040,4558,10730,11130,12239,13007,3281,10328,10424,10553,10615,10686,10733,10736,10769,10790,10827,10865,10901,11462,11679,11726,11862,11917,11933,11936,11939,11942,12120,12134,12137,12140,12143,12222,12286,12402,12449,12718,12745,12823,12834,12839,12842,12845,12878,12891,12902,12950,12976,12979,13058,3282,10357,10412,10620,10709,10830,11455,11524,11761,11765,11774,11868,11879,11898,11903,11945,11968,11985,12736,12882,12905,12940,12945,12966,12971,13090,3283,3357,12093,12801,12849,12853,12857,12861,12871,12875,4536,10276,10366,10477,10501,10751,10793,10803,11531,11632,11654,11657,11660,11676,11836,11839,11842,11845,11929,11948,11951,11964,12019,12022,12025,12028,12100,12190,12193,12289,12292,12363,12395,12435,12518,3439,10573,10838,10882,11188,11266,11439,11688,12337,12521,12923,13044,4548,10760,10874,10892,10895,10968,11069,11077,11093,11133,11151,11160,11196,11237,11257,11260,11263,11294,11301,11304,11705,11742,12013,12016,12050,12094,12123,12267,12311,12317,12414,12417,12439,12497,12503,12512,12531,12800,12817,12820,12912,13032,13051,13054,13100,13149,13152,3343,10602,10632,10641,11217,11789,12436,12450,12782,12786,12789,3381,13080,13141,3375,3801,3738,10279,11604,11636,12763,4545,10230,10590,10593,11072,11090,11567,11622,11664,11689,11795,11824,11827,11830,11833,12089,12982,3303,10635,10787,10858,11637,11794,11990,12198,12223,12810,13083,13172,3762,11739,12712,4115,3498,4543,3773,3809,4526,4529,4530,3256,3260,4528,4527,4531,4292,3780,3597,11597,4215,4560,10198,10201,10458,10509,10512,10517,10942,11433,11692,11798,4567,11154,11274,11310,4001,12250,3889,11307,11663,11667,11730,12348,12356,12442,12730,12988,13036,3727,10898,10904,10926,11914,12043,12126,12410,3581,11028,11157,12152,12264,12274,12353,12405,12413,12528,12933,4069,3729,10638,10993,11163,11193,11204,12352,12399,13024,3548,10556,10559,10644,10814,3550,4564,11598,4554,4559,12680,4565,10697,10796,11436,11468,12217,12226,12270,12467,12524,4174,10772,12247,12273,4076,3761,12534,3707,3708,4562,10252,10255,10596,10599,11479,11668,12476,4563,11578,11673,3731,10562,10820,13070,4008,4583,4609,4657,4659,4691,4708,4715,4716,4752,4757,4787,4793,4876,4900,4901,4916,4938,4963,4964,4986,4987,5000,5004,5027,5033,5049,5052,5053,5054,5059,5060,5082,5107,5108,5118,5123,5129,5165,5166,5174,5184,5188,5190,5199,5201,5207,5210,5224,5231,5234,5235,5236,5240,5275,5288,5296,5298,5299,5303,5304,5305,5313,5316,5320,5321,5322,5329,5333,5334,5335,5343,5347,5348,5349,5354,5367,5376,5388,5390,5398,5399,5403,5407,5432,5438,5448,5449,5464,5476,5498,5504,5520,5521,5524,5543,5551,5552,5557,5558,5568,5570,5582,5586,5595,5596,5598,5613,5618,5628,5629,5641,5648,5662,5666,5669,5675,5676,5677,5680,5685,5721,5722,5725,5727,5730,5731,5732,5734,5736,5738,5743,5750,5765,5779,5784,5785,5798,5799,5804,5808,5810,5815,5856,5868,5877,5881,5890,5894,5895,5903,5916,5922,5940,5943,5952,5977,5991,6016,6036,6037,6040,6054,6056,6058,6060,6073,6074,6077,6079,6082,6083,6095,6101,6102,6103,6105,6107,6144,6145,6152,6158,6162,6198,6200,6202,6204,6213,6215,6217,6223,6225,6230,6233,6241,6248,6249,6250,6255,6277,6278,6279,6281,6287,6292,6326,6327,6329,6330,6331,6333,6334,6335,6336,6344,6376,6377,6378,6387,6407,6408,6428,6430,6441,6442,6448,6478,6480,6494,6498,6532,6534,6535,6588,6612,6654,6674,6683,6684,6685,6686,6704,6705,6711,6724,6727,6729,6731,6732,6733,6735,6749,6760,6762,6763,6776,6780,6831,6842,6844,6864,6865,6899,6911,6942,6974,7028,7056,7111,7132,7141,7144,7199,7207,7265,7267,7282,7292,7293,7294,7310,7316,7318,7367,7377,7380,7396,7446,7448,7451,7494,7495,7513,7580,7599,7622,7645,7660,7674,7685,7694,7695,7722,7725,7727,7736,7772,7783,7808,7869,7904,7936,7975,7991,7993,8009,8010,8081,8133,8151,8175,8181,8196,8221,8222,8260,8261,8278,8321,8323,8325,8332,8346,8350,8366,8388,8396,8398,8409,8414,8418,8438,8452,8453,8470,8471,8476,8477,8478,8479,8480,8498,8499,8500,8509,8522,8525,8537,8542,8544,8546,8547,8555,8562,8570,8573,8590,8591,8601,8602,8610,8630,8643,8647,8668,8690,8691,8694,8695,8701,8710,8711,8734,8746,8756,8757,8758,8759,8761,8784,8785,8796,8839,8845,8850,8852,8863,8868,8870,8872,8873,8878,8888,8960,8991,8992,8993,9008,9026,9034,9035,9064,9065,9108,9132,9169,9182,9183,9184,9193,9219,9235,9238,9242,9263,9264,9292,9354,9390,9391,9392,9415,9416,9435,9456,9462,9475,9498,9520,9529,9530,9531,9532,9547,9549,9554,9586,9587,9593,9594,9638,9639,9672,9681,9691,9693,9694,9703,9717,9720,9748,9781,9783,9787,9843,9884,9885,9887,9897,9898,9918,9923,9964,10014,10085,10086,10140,10154,2,8,9,8599,4596,4597,4615,4646,4647,4649,4675,4683,4684,4695,4744,4746,4778,4792,4821,4917,4918,4932,4951,5007,5008,5011,5012,5014,5016,5017,5026,5029,5030,5038,5050,5051,5057,5077,5078,5095,5100,5101,5102,5103,5106,5114,5117,5124,5180,5186,5187,5193,5221,5232,5238,5254,5273,5274,5281,5282,5283,5292,5302,5309,5311,5312,5318,5325,5326,5339,5340,5341,5342,5344,5345,5350,5351,5352,5353,5384,5385,5386,5394,5395,5396,5397,5440,5445,5447,5483,5485,5486,5488,5489,5491,5492,5494,5503,5508,5510,5511,5512,5513,5514,5515,5522,5532,5535,5546,5562,5563,5566,5576,5578,5579,5580,5605,5615,5631,5632,5642,5643,5645,5647,5652,5687,5692,5694,5752,5786,5787,5791,5797,5800,5801,5802,5803,5809,5820,5821,5823,5824,5832,5853,5882,5898,5901,5902,5904,5913,5930,5934,5937,5938,5939,5954,5964,5965,5993,5994,5998,6018,6021,6025,6044,6049,6050,6075,6078,6086,6094,6100,6104,6111,6112,6113,6114,6147,6163,6216,6251,6253,6274,6275,6280,6284,6285,6288,6294,6303,6318,6338,6339,6342,6345,6354,6369,6390,6395,6397,6412,6413,6416,6417,6419,6421,6422,6423,6425,6427,6429,6434,6435,6437,6438,6444,6446,6488,6493,6508,6510,6511,6512,6546,6551,6553,6558,6559,6567,6571,6583,6607,6608,6610,6611,6622,6628,6645,6648,6667,6699,6700,6701,6706,6720,6739,6741,6743,6745,6750,6756,6758,6773,6778,6781,6817,6818,6819,6833,6834,6836,6837,6855,6857,6871,6897,6919,6930,6932,6934,6936,6937,6938,6971,6972,6977,6978,6985,6986,6988,6990,7009,7018,7019,7031,7041,7080,7090,7094,7101,7112,7118,7120,7126,7135,7148,7165,7183,7185,7202,7251,7252,7253,7255,7257,7261,7266,7289,7331,7363,7378,7395,7427,7430,7455,7479,7496,7499,7500,7510,7529,7531,7533,7535,7536,7537,7562,7588,7589,7621,7623,7624,7625,7630,7652,7661,7671,7676,7682,7684,7690,7702,7703,7705,7728,7734,7755,7822,7823,7824,7872,7880,7881,7906,7907,7924,7925,7982,7983,8012,8039,8049,8051,8060,8072,8102,8108,8115,8128,8147,8152,8174,8218,8248,8262,8281,8284,8314,8340,8399,8400,8403,8404,8468,8502,8503,8504,8505,8532,8565,8594,8603,8604,8646,8667,8713,8728,8775,8778,8793,8800,8836,8884,8885,8901,8902,9031,9037,9041,9062,9072,9095,9097,9100,9104,9106,9107,9118,9119,9139,9146,9159,9168,9205,9223,9276,9277,9284,9323,9346,9351,9386,9394,9397,9400,9401,9414,9431,9440,9455,9464,9465,9467,9469,9497,9621,9667,9668,9710,9755,9870,9927,9991,10064,10077,10082,3,2616,2617,2618,2619,2623,2626,2630,2632,2636,2637,2638,2639,2642,2648,2650,2651,2653,2654,2655,2656,2661,2662,2663,2668,2669,2670,2671,2672,2673,2675,2677,2679,2680,2682,2683,2685,2686,2693,2700,2701,2702,2706,2707,2708,2710,2716,2723,2724,2751,2752,2753,2762,2763,2764,2768,2769,2771,2780,2783,2784,2788,2789,2797,2798,2799,2821,2823,2832,2835,2836,2837,2847,2848,5213,5272,5370,5456,5457,5458,5533,5630,5661,5695,5711,5713,5719,5780,5781,5782,5783,5789,5822,5949,5983,5992,6015,6052,6087,6092,6232,6237,6272,6273,6293,6296,6298,6305,6306,6307,6308,6309,6310,6311,6312,6391,6458,6459,6545,6578,6579,6619,6620,6757,6772,6845,6846,6852,6872,6895,6903,6905,6952,6975,6976,6994,6995,7030,7074,7075,7172,7233,7234,7235,7236,7250,7283,7336,7337,7346,7353,7354,7366,7398,7399,7400,7401,7543,7544,7546,7548,7554,7555,7763,7769,7770,7780,7819,7820,7901,7941,7995,8017,8018,8088,8189,8258,8259,8263,8299,8362,8363,8427,8445,8446,8447,8448,8598,8854,8855,8927,8941,8994,8995,9115,9150,9177,9206,9247,9438,9562,9704,9896,9952,9954,10087,6010,6374,6375,6461,6481,6482,6894,7110,8245,8517,8553,8769,8952,8953,9022,9023,9295,9296,9297,9298,9499,9775,9789,10073,10128,10129,6443,8353,8354,8820,8837,9776,10127,4651,4652,4653,4709,4717,4854,4870,4871,4898,4899,4930,4985,5045,5173,5208,5211,5216,5217,5243,5317,5338,5472,5538,5539,5540,5657,5658,5684,5688,5746,5748,5835,5911,6033,6059,6219,6337,6491,6692,6693,6906,6947])).
% 188.21/188.06 cnf(13417,plain,
% 188.21/188.06 (~P101(f323(f323(f325(a865),x134171),f323(f244(a865),f2(a865))))),
% 188.21/188.06 inference(rename_variables,[],[11758])).
% 188.21/188.06 cnf(13425,plain,
% 188.21/188.06 (~E(f323(f323(f144(x134251),x134252),x134253),x134253)),
% 188.21/188.06 inference(rename_variables,[],[4500])).
% 188.21/188.06 cnf(13430,plain,
% 188.21/188.06 (P101(f323(f323(f237(a865),f2(a865)),x134301))),
% 188.21/188.06 inference(rename_variables,[],[3303])).
% 188.21/188.06 cnf(13433,plain,
% 188.21/188.06 (P101(f323(f323(f237(a865),x134331),f323(f323(f79(a865),x134331),x134331)))),
% 188.21/188.06 inference(rename_variables,[],[3548])).
% 188.21/188.06 cnf(13438,plain,
% 188.21/188.06 (~E(x134381,f323(a112,x134381))),
% 188.21/188.06 inference(rename_variables,[],[10262])).
% 188.21/188.06 cnf(13444,plain,
% 188.21/188.06 (~P101(f323(f323(f325(x134441),x134442),f188(f872(x134441,a860))))),
% 188.21/188.06 inference(rename_variables,[],[4548])).
% 188.21/188.06 cnf(13452,plain,
% 188.21/188.06 (~E(f323(f323(f101(a865),f323(a112,x134521)),x134521),f323(a112,x134521))),
% 188.21/188.06 inference(rename_variables,[],[11500])).
% 188.21/188.06 cnf(13455,plain,
% 188.21/188.06 (P101(f323(f323(f237(a865),x134551),f323(f323(f78(a865),x134551),x134552)))),
% 188.21/188.06 inference(rename_variables,[],[3550])).
% 188.21/188.06 cnf(13458,plain,
% 188.21/188.06 (P101(f323(f323(f237(f872(x134581,a860)),x134582),f323(f323(f110(f872(x134581,a860)),x134583),f246(f872(x134581,a860)))))),
% 188.21/188.06 inference(rename_variables,[],[11139])).
% 188.21/188.06 cnf(13468,plain,
% 188.21/188.06 (E(f323(f302(x134681,x134681,f32(x134681)),x134682),x134682)),
% 188.21/188.06 inference(rename_variables,[],[3340])).
% 188.21/188.06 cnf(13483,plain,
% 188.21/188.06 (P101(f323(f323(f237(f872(x134831,a860)),f323(f166(x134831),f164(x134831,x134832,x134833))),f323(f166(x134831),x134833)))),
% 188.21/188.06 inference(rename_variables,[],[3987])).
% 188.21/188.06 cnf(13488,plain,
% 188.21/188.06 (~E(f323(f323(f144(x134881),x134882),x134883),x134883)),
% 188.21/188.06 inference(rename_variables,[],[4500])).
% 188.21/188.06 cnf(13493,plain,
% 188.21/188.06 (E(f323(f323(f121(x134931),f113(x134931)),x134932),x134932)),
% 188.21/188.06 inference(rename_variables,[],[3233])).
% 188.21/188.06 cnf(13503,plain,
% 188.21/188.06 (~P101(f323(f323(f325(a865),x135031),f323(f244(a865),f2(a865))))),
% 188.21/188.06 inference(rename_variables,[],[11758])).
% 188.21/188.06 cnf(13531,plain,
% 188.21/188.06 (~P101(f323(f323(f325(f871(f866(x135311),f866(x135311))),f323(f323(f258(f866(x135311),f866(x135311)),x135312),f113(x135311))),f140(x135311,x135313)))),
% 188.21/188.06 inference(rename_variables,[],[4570])).
% 188.21/188.06 cnf(13536,plain,
% 188.21/188.06 (P101(f323(f323(f237(a1),x135361),x135361))),
% 188.21/188.06 inference(rename_variables,[],[3282])).
% 188.21/188.06 cnf(13541,plain,
% 188.21/188.06 (~P101(f323(f323(f188(f872(x135411,f872(x135412,a860))),x135413),x135414))),
% 188.21/188.06 inference(rename_variables,[],[4565])).
% 188.21/188.06 cnf(13553,plain,
% 188.21/188.06 (~P101(f323(f323(f325(x135531),x135532),f323(f303(x135531,x135533,x135534),f188(f872(x135533,a860)))))),
% 188.21/188.06 inference(rename_variables,[],[10894])).
% 188.21/188.06 cnf(13556,plain,
% 188.21/188.06 (P101(f323(f323(f325(x135561),f323(x135562,x135563)),f323(f302(x135564,x135561,x135562),f246(f872(x135564,a860)))))),
% 188.21/188.06 inference(rename_variables,[],[3889])).
% 188.21/188.06 cnf(13559,plain,
% 188.21/188.06 (~P101(f323(f323(f325(x135591),x135592),f188(f872(x135591,a860))))),
% 188.21/188.06 inference(rename_variables,[],[4548])).
% 188.21/188.06 cnf(13567,plain,
% 188.21/188.06 (~P101(f323(f323(f188(f872(x135671,f872(x135672,a860))),x135673),x135674))),
% 188.21/188.06 inference(rename_variables,[],[4565])).
% 188.21/188.06 cnf(13570,plain,
% 188.21/188.06 (~P101(f323(f323(f188(f872(x135701,f872(x135702,a860))),x135703),x135704))),
% 188.21/188.06 inference(rename_variables,[],[4565])).
% 188.21/188.06 cnf(13575,plain,
% 188.21/188.06 (~P101(f323(f323(f325(x135751),x135752),f188(f872(x135751,a860))))),
% 188.21/188.06 inference(rename_variables,[],[4548])).
% 188.21/188.06 cnf(13583,plain,
% 188.21/188.06 (P101(f323(f323(f237(a865),x135831),f323(f323(f79(a865),x135831),x135831)))),
% 188.21/188.06 inference(rename_variables,[],[3548])).
% 188.21/188.06 cnf(13598,plain,
% 188.21/188.06 (P101(f323(f323(f237(f872(x135981,a860)),f323(f166(x135981),f164(x135981,x135982,x135983))),f323(f166(x135981),x135983)))),
% 188.21/188.06 inference(rename_variables,[],[3987])).
% 188.21/188.06 cnf(13601,plain,
% 188.21/188.06 (~P101(f323(f323(f325(f871(x136011,x136011)),x136012),f255(x136011,f188(f872(x136011,a860)))))),
% 188.21/188.06 inference(rename_variables,[],[10891])).
% 188.21/188.06 cnf(13610,plain,
% 188.21/188.06 (~E(f323(f230(x136101),x136102),f200(x136101))),
% 188.21/188.06 inference(rename_variables,[],[4487])).
% 188.21/188.06 cnf(13628,plain,
% 188.21/188.06 (E(f323(x136281,f841(f323(x136281,x136282),f323(f230(x136283),x136282),x136281,x136284,x136283)),f323(x136281,x136282))),
% 188.21/188.06 inference(rename_variables,[],[11105])).
% 188.21/188.06 cnf(13637,plain,
% 188.21/188.06 (P101(f323(f323(f237(a1),x136371),x136371))),
% 188.21/188.06 inference(rename_variables,[],[3282])).
% 188.21/188.06 cnf(13654,plain,
% 188.21/188.06 (P101(f323(f323(f325(x136541),f323(x136542,x136543)),f323(f302(x136544,x136541,x136542),f246(f872(x136544,a860)))))),
% 188.21/188.06 inference(rename_variables,[],[3889])).
% 188.21/188.06 cnf(13673,plain,
% 188.21/188.06 (~P101(f323(f323(f325(a865),x136731),f323(f244(a865),f2(a865))))),
% 188.21/188.06 inference(rename_variables,[],[11758])).
% 188.21/188.06 cnf(13683,plain,
% 188.21/188.06 (P101(f323(f323(f237(f872(x136831,a860)),f323(f166(x136831),f164(x136831,x136832,x136833))),f323(f166(x136831),x136833)))),
% 188.21/188.06 inference(rename_variables,[],[3987])).
% 188.21/188.06 cnf(13728,plain,
% 188.21/188.06 (~P101(f323(f323(f325(x137281),x137282),f188(f872(x137281,a860))))),
% 188.21/188.06 inference(rename_variables,[],[4548])).
% 188.21/188.06 cnf(13780,plain,
% 188.21/188.06 (~P101(f323(f323(f325(a865),x137801),f323(f244(a865),f2(a865))))),
% 188.21/188.06 inference(rename_variables,[],[11758])).
% 188.21/188.06 cnf(13800,plain,
% 188.21/188.06 ($false),
% 188.21/188.06 inference(scs_inference,[],[3309,3311,3872,4071,4564,4526,3260,4569,3924,3357,4528,3375,3733,3889,13556,13654,4548,13444,13559,13575,13728,3987,13483,13598,13683,3381,3072,4485,4487,13610,4500,13425,13488,4498,3265,3361,4065,3934,3282,13536,13637,3738,3303,13430,3727,3581,3548,13433,13583,3550,13455,3731,3238,3124,3233,13493,4570,13531,4573,4559,4565,13541,13567,13570,4562,4563,11500,13452,10262,13438,13258,10316,11298,10498,11867,12714,13165,12464,11139,13458,10708,4298,3648,11162,11105,13628,10375,11251,10648,3340,13468,3314,11185,10946,13254,10653,13242,12154,13274,12263,10226,12733,11758,13417,13503,13673,13780,10891,13601,12077,10894,13553,11132,10643,10750,12018,12021,11256,2927,8,2,5388,9531,6204,6692,5662,9593,8602,6249,6281,6711,7783,8647,4985,8992,6158,8756,9884,7293,7991,6831,8414,6378,7993,9549,5317,8544,6255,6760,8366,6535,8546,5027,5676,5677,6780,9132,8758,5504,5798,7282,9594,4854,5472,8845,8453,6906,4716,8222,9691,5173,5586,6162,5895,5367,6073,6145,9462,9183,7451,9898,6693,5520,8323,4901,5738,9918,4659,5298,6724,6683,6685,8991,7660,8610,8525,5540,7116,4752,4986,5558,7310,7722,9219,5894,5449,5675,4652,5190,9008,5940,6230,6763,5568,5730,7318,7975,4930,9238,8710,5054,8690,5322,7367,5217,8570,8734,6329,6200,6102,8590,5216,6033,6074,8888,9923,7396,6082,5398,5743,8151,4876,5165,5403,6037,5174,5570,5810,8221,8509,9184,9964,7808,4787,6942,6292,6428,6612,6899,5316,5033,6107,6749,8081,6279,5303,6704,8477,4583,9498,8759,9639,6735,8478,10086,4715,5464,6335,9520,4691]),
% 188.21/188.06 ['proof']).
% 188.21/188.06 % SZS output end Proof
% 188.21/188.06 % Total time :168.870000s
%------------------------------------------------------------------------------