TSTP Solution File: SWW342+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW342+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n004.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 : Fri Sep 1 00:13:53 EDT 2023
% Result : Theorem 21.40s 21.35s
% Output : CNFRefutation 21.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW342+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 22:57:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 21.05/21.18 %-------------------------------------------
% 21.05/21.18 % File :CSE---1.6
% 21.05/21.18 % Problem :theBenchmark
% 21.05/21.18 % Transform :cnf
% 21.05/21.18 % Format :tptp:raw
% 21.05/21.19 % Command :java -jar mcs_scs.jar %d %s
% 21.05/21.19
% 21.05/21.19 % Result :Theorem 17.650000s
% 21.05/21.19 % Output :CNFRefutation 17.650000s
% 21.05/21.19 %-------------------------------------------
% 21.05/21.19 %------------------------------------------------------------------------------
% 21.05/21.19 % File : SWW342+1 : TPTP v8.1.2. Released v5.2.0.
% 21.05/21.19 % Domain : Software Verification
% 21.05/21.19 % Problem : Hoare's Logic with Procedures 435202, 5000 axioms selected
% 21.05/21.19 % Version : Especial.
% 21.05/21.19 % English :
% 21.05/21.19
% 21.05/21.19 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 21.05/21.19 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 21.05/21.19 % Source : [Bla11]
% 21.05/21.19 % Names : hoare_435202.5000.p [Bla11]
% 21.05/21.19
% 21.05/21.19 % Status : Theorem
% 21.05/21.19 % Rating : 0.39 v8.1.0, 0.36 v7.5.0, 0.38 v7.4.0, 0.37 v7.3.0, 0.38 v7.2.0, 0.34 v7.1.0, 0.43 v7.0.0, 0.50 v6.3.0, 0.54 v6.2.0, 0.68 v6.1.0, 0.73 v6.0.0, 0.61 v5.5.0, 0.74 v5.4.0, 0.75 v5.3.0, 0.81 v5.2.0
% 21.05/21.19 % Syntax : Number of formulae : 5206 (1702 unt; 0 def)
% 21.05/21.19 % Number of atoms : 12599 (4533 equ)
% 21.05/21.19 % Maximal formula atoms : 13 ( 2 avg)
% 21.05/21.19 % Number of connectives : 8488 (1095 ~; 158 |; 712 &)
% 21.05/21.19 % ( 879 <=>;5644 =>; 0 <=; 0 <~>)
% 21.05/21.19 % Maximal formula depth : 22 ( 6 avg)
% 21.05/21.19 % Maximal term depth : 19 ( 2 avg)
% 21.05/21.19 % Number of predicates : 141 ( 140 usr; 1 prp; 0-7 aty)
% 21.05/21.19 % Number of functors : 394 ( 394 usr; 62 con; 0-10 aty)
% 21.05/21.19 % Number of variables : 16804 (16671 !; 133 ?)
% 21.05/21.19 % SPC : FOF_THM_RFO_SEQ
% 21.05/21.19
% 21.05/21.19 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 21.05/21.19 % 2011-03-01 12:12:38
% 21.05/21.19 %------------------------------------------------------------------------------
% 21.05/21.19 %----Relevant facts (4983)
% 21.05/21.19 fof(fact_ext,axiom,
% 21.05/21.19 ! [V_g_2,V_f_2] :
% 21.05/21.19 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 21.05/21.19 => V_f_2 = V_g_2 ) ).
% 21.05/21.19
% 21.05/21.19 fof(fact_evaln_OSkip,axiom,
% 21.05/21.19 ! [V_n,V_s] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s) ).
% 21.05/21.19
% 21.05/21.19 fof(fact_evaln__elim__cases_I1_J,axiom,
% 21.05/21.19 ! [V_t,V_n,V_s] :
% 21.05/21.19 ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t)
% 21.05/21.19 => V_t = V_s ) ).
% 21.05/21.19
% 21.05/21.19 fof(fact_evaln_Oequations_I1_J,axiom,
% 21.05/21.19 ! [V_a2,V_a1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_a1,V_a2,V_a1) ).
% 21.05/21.19
% 21.05/21.19 fof(fact_triple__valid__def2,axiom,
% 21.05/21.19 ! [V_Q_2,V_c_2,V_P_2,V_n_2,T_b] :
% 21.05/21.19 ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2))
% 21.05/21.19 <=> ! [B_Z,B_s] :
% 21.05/21.19 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 21.05/21.19 => ! [B_s_H] :
% 21.05/21.19 ( c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H)
% 21.05/21.19 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ).
% 21.05/21.19
% 21.05/21.19 fof(fact_triple__valid__Suc,axiom,
% 21.05/21.19 ! [V_t,V_n,T_a] :
% 21.05/21.19 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
% 21.05/21.19 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ).
% 21.05/21.19
% 21.05/21.19 fof(fact_com_Osimps_I64_J,axiom,
% 21.05/21.19 ! [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 ).
% 21.05/21.20
% 21.05/21.20 fof(fact_com_Orecs_I1_J,axiom,
% 21.05/21.20 ! [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__rec(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 ).
% 21.05/21.20
% 21.05/21.20 fof(fact_hoare__valids__def,axiom,
% 21.05/21.20 ! [V_tsa_2,V_Ga_2,T_b] :
% 21.05/21.20 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_tsa_2)
% 21.05/21.20 <=> ! [B_n] :
% 21.05/21.20 ( ! [B_x] :
% 21.05/21.20 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2))
% 21.05/21.20 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) )
% 21.05/21.20 => ! [B_x] :
% 21.05/21.20 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 21.05/21.20 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_evaln_OSemi,axiom,
% 21.05/21.20 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
% 21.05/21.20 ( c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1)
% 21.05/21.20 => ( c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2)
% 21.05/21.20 => c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_evaln_OIfFalse,axiom,
% 21.05/21.20 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] :
% 21.05/21.20 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 21.05/21.20 => ( c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_s1_2)
% 21.05/21.20 => c_Natural_Oevaln(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2),V_s_2,V_n_2,V_s1_2) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_evaln_OIfTrue,axiom,
% 21.05/21.20 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] :
% 21.05/21.20 ( hBOOL(hAPP(V_b_2,V_s_2))
% 21.05/21.20 => ( c_Natural_Oevaln(V_c0_2,V_s_2,V_n_2,V_s1_2)
% 21.05/21.20 => c_Natural_Oevaln(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2),V_s_2,V_n_2,V_s1_2) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_evaln__elim__cases_I5_J,axiom,
% 21.05/21.20 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 21.05/21.20 ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2),V_s_2,V_n_2,V_t_2)
% 21.05/21.20 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 21.05/21.20 => ~ c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_t_2) )
% 21.05/21.20 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 21.05/21.20 => ~ c_Natural_Oevaln(V_c2_2,V_s_2,V_n_2,V_t_2) ) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_WTs__elim__cases_I5_J,axiom,
% 21.05/21.20 ! [V_c2_2,V_c1_2,V_b_2] :
% 21.05/21.20 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)))
% 21.05/21.20 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 21.05/21.20 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_WTs__elim__cases_I4_J,axiom,
% 21.05/21.20 ! [V_c2,V_c1] :
% 21.05/21.20 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2)))
% 21.05/21.20 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 21.05/21.20 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_com_Osimps_I44_J,axiom,
% 21.05/21.20 ! [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) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_com_Osimps_I45_J,axiom,
% 21.05/21.20 ! [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) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_WT_Oequations_I4_J,axiom,
% 21.05/21.20 ! [V_a2_2,V_a1_2] :
% 21.05/21.20 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2)))
% 21.05/21.20 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 21.05/21.20 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_WT_Oequations_I5_J,axiom,
% 21.05/21.20 ! [V_a2_2,V_a1_2,V_a3_2] :
% 21.05/21.20 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2)))
% 21.05/21.20 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 21.05/21.20 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_com_Osimps_I3_J,axiom,
% 21.05/21.20 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 21.05/21.20 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 21.05/21.20 <=> ( V_com1_2 = V_com1_H_2
% 21.05/21.20 & V_com2_2 = V_com2_H_2 ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_com_Osimps_I4_J,axiom,
% 21.05/21.20 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 21.05/21.20 ( 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)
% 21.05/21.20 <=> ( V_fun_2 = V_fun_H_2
% 21.05/21.20 & V_com1_2 = V_com1_H_2
% 21.05/21.20 & V_com2_2 = V_com2_H_2 ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_triple_Oinject,axiom,
% 21.05/21.20 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
% 21.05/21.20 ( 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)
% 21.05/21.20 <=> ( V_fun1_2 = V_fun1_H_2
% 21.05/21.20 & V_com_2 = V_com_H_2
% 21.05/21.20 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_com_Osimps_I67_J,axiom,
% 21.05/21.20 ! [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) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_com_Orecs_I4_J,axiom,
% 21.05/21.20 ! [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__rec(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(hAPP(hAPP(V_f4_2,V_com1_2),V_com2_2),c_Com_Ocom_Ocom__rec(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,V_com1_2)),c_Com_Ocom_Ocom__rec(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,V_com2_2)) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_com_Osimps_I68_J,axiom,
% 21.05/21.20 ! [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) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_com_Orecs_I5_J,axiom,
% 21.05/21.20 ! [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__rec(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(hAPP(hAPP(V_f5_2,V_fun_2),V_com1_2),V_com2_2),c_Com_Ocom_Ocom__rec(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,V_com1_2)),c_Com_Ocom_Ocom__rec(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,V_com2_2)) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_WT_OSemi,axiom,
% 21.05/21.20 ! [V_c1,V_c0] :
% 21.05/21.20 ( hBOOL(hAPP(c_Com_OWT,V_c0))
% 21.05/21.20 => ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 21.05/21.20 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_WT_OIf,axiom,
% 21.05/21.20 ! [V_b_2,V_c1_2,V_c0_2] :
% 21.05/21.20 ( hBOOL(hAPP(c_Com_OWT,V_c0_2))
% 21.05/21.20 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 21.05/21.20 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_triples__valid__Suc,axiom,
% 21.05/21.20 ! [V_n_2,V_tsa_2,T_b] :
% 21.05/21.20 ( ! [B_x] :
% 21.05/21.20 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 21.05/21.20 => c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),B_x) )
% 21.05/21.20 => ! [B_x] :
% 21.05/21.20 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 21.05/21.20 => c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_evaln__Suc,axiom,
% 21.05/21.20 ! [V_s_H,V_n,V_s,V_c] :
% 21.05/21.20 ( c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
% 21.05/21.20 => c_Natural_Oevaln(V_c,V_s,hAPP(c_Nat_OSuc,V_n),V_s_H) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_evaln_Oequations_I6_J,axiom,
% 21.05/21.20 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
% 21.05/21.20 ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_a1_2,V_a6_2,V_a3_2),V_a2_2,V_a4_2,V_a5_2)
% 21.05/21.20 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 21.05/21.20 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) )
% 21.05/21.20 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 21.05/21.20 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_evaln_Oequations_I5_J,axiom,
% 21.05/21.20 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
% 21.05/21.20 ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a6_2),V_a2_2,V_a4_2,V_a5_2)
% 21.05/21.20 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 21.05/21.20 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) )
% 21.05/21.20 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 21.05/21.20 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_evaln_Oequations_I4_J,axiom,
% 21.05/21.20 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
% 21.05/21.20 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_a1_2,V_a5_2),V_a2_2,V_a3_2,V_a6_2)
% 21.05/21.20 <=> ? [B_s1] :
% 21.05/21.20 ( c_Natural_Oevaln(V_a1_2,V_a2_2,V_a3_2,B_s1)
% 21.05/21.20 & c_Natural_Oevaln(V_a5_2,B_s1,V_a3_2,V_a6_2) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_WT_Oequations_I1_J,axiom,
% 21.05/21.20 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_WT_OSkip,axiom,
% 21.05/21.20 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_com_Osimps_I15_J,axiom,
% 21.05/21.20 ! [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 ).
% 21.05/21.20
% 21.05/21.20 fof(fact_com_Osimps_I14_J,axiom,
% 21.05/21.20 ! [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) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_com_Osimps_I13_J,axiom,
% 21.05/21.20 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 21.05/21.20
% 21.05/21.20 fof(fact_com_Osimps_I12_J,axiom,
% 21.05/21.20 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_triple_Orecs,axiom,
% 21.05/21.20 ! [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) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_triple_Osimps_I2_J,axiom,
% 21.05/21.20 ! [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) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_evaln__elim__cases_I4_J,axiom,
% 21.05/21.20 ! [V_t,V_n,V_s,V_c2,V_c1] :
% 21.05/21.20 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c1,V_c2),V_s,V_n,V_t)
% 21.05/21.20 => ~ ! [B_s1] :
% 21.05/21.20 ( c_Natural_Oevaln(V_c1,V_s,V_n,B_s1)
% 21.05/21.20 => ~ c_Natural_Oevaln(V_c2,B_s1,V_n,V_t) ) ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_n__not__Suc__n,axiom,
% 21.05/21.20 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_Suc__n__not__n,axiom,
% 21.05/21.20 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 21.05/21.20
% 21.05/21.20 fof(fact_nat_Oinject,axiom,
% 21.05/21.20 ! [V_nat_H_2,V_nat_2] :
% 21.05/21.20 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 21.05/21.20 <=> V_nat_2 = V_nat_H_2 ) ).
% 21.05/21.20
% 21.05/21.20 fof(fact_Suc__inject,axiom,
% 21.05/21.20 ! [V_y,V_x] :
% 21.05/21.20 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 21.05/21.20 => V_x = V_y ) ).
% 21.05/21.20
% 21.13/21.20 fof(fact_WTs__elim__cases_I3_J,axiom,
% 21.13/21.20 ! [V_c_2,V_a_2,V_Y_2] :
% 21.13/21.20 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)))
% 21.13/21.20 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ).
% 21.13/21.20
% 21.13/21.20 fof(fact_com_Osimps_I71_J,axiom,
% 21.13/21.20 ! [V_fun_2,V_pname_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_OCall(V_vname_2,V_pname_2,V_fun_2)) = hAPP(hAPP(hAPP(V_f8_2,V_vname_2),V_pname_2),V_fun_2) ).
% 21.13/21.20
% 21.13/21.20 fof(fact_com_Osimps_I66_J,axiom,
% 21.13/21.20 ! [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) ).
% 21.13/21.20
% 21.13/21.20 fof(fact_com_Osimps_I32_J,axiom,
% 21.13/21.20 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 21.13/21.20
% 21.13/21.20 fof(fact_com_Osimps_I22_J,axiom,
% 21.13/21.20 ! [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) ).
% 21.13/21.20
% 21.13/21.20 fof(fact_com_Osimps_I33_J,axiom,
% 21.13/21.20 ! [V_fun_2,V_vname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 21.13/21.20
% 21.13/21.20 fof(fact_com_Osimps_I23_J,axiom,
% 21.13/21.20 ! [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) ).
% 21.13/21.20
% 21.13/21.20 fof(fact_com_Osimps_I43_J,axiom,
% 21.13/21.20 ! [V_com_2,V_fun_2,V_loc_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 21.13/21.20
% 21.13/21.20 fof(fact_com_Osimps_I42_J,axiom,
% 21.13/21.20 ! [V_fun_H_2,V_pname_H_2,V_vname_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_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 21.13/21.20
% 21.13/21.20 fof(fact_com_Osimps_I1_J,axiom,
% 21.13/21.20 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] :
% 21.13/21.20 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2)
% 21.13/21.20 <=> ( V_vname_2 = V_vname_H_2
% 21.13/21.20 & V_fun_2 = V_fun_H_2 ) ) ).
% 21.13/21.20
% 21.13/21.20 fof(fact_com_Osimps_I7_J,axiom,
% 21.13/21.20 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] :
% 21.13/21.20 ( c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2) = c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2)
% 21.13/21.20 <=> ( V_vname_2 = V_vname_H_2
% 21.13/21.20 & V_pname_2 = V_pname_H_2
% 21.13/21.20 & V_fun_2 = V_fun_H_2 ) ) ).
% 21.13/21.20
% 21.13/21.20 fof(fact_com_Osimps_I2_J,axiom,
% 21.13/21.20 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 21.13/21.20 ( 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)
% 21.13/21.20 <=> ( V_loc_2 = V_loc_H_2
% 21.13/21.20 & V_fun_2 = V_fun_H_2
% 21.13/21.20 & V_com_2 = V_com_H_2 ) ) ).
% 21.13/21.20
% 21.13/21.20 fof(fact_WT_Oequations_I2_J,axiom,
% 21.13/21.20 ! [V_a2_2,V_a1_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_a1_2,V_a2_2))) ).
% 21.13/21.20
% 21.13/21.20 fof(fact_WT_OAssign,axiom,
% 21.13/21.20 ! [V_a_2,V_X_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_X_2,V_a_2))) ).
% 21.13/21.20
% 21.13/21.20 fof(fact_WT_OLocal,axiom,
% 21.13/21.20 ! [V_a_2,V_Y_2,V_c_2] :
% 21.13/21.21 ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 21.13/21.21 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_WT_Oequations_I3_J,axiom,
% 21.13/21.21 ! [V_a1_2,V_a3_2,V_a2_2] :
% 21.13/21.21 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
% 21.13/21.21 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I27_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I26_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I36_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I37_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I56_J,axiom,
% 21.13/21.21 ! [V_fun_H_2,V_pname_H_2,V_vname_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_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I57_J,axiom,
% 21.13/21.21 ! [V_com2_2,V_com1_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I25_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I24_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I8_J,axiom,
% 21.13/21.21 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I9_J,axiom,
% 21.13/21.21 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I34_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I51_J,axiom,
% 21.13/21.21 ! [V_com2_2,V_com1_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I35_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I50_J,axiom,
% 21.13/21.21 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I20_J,axiom,
% 21.13/21.21 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I10_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I21_J,axiom,
% 21.13/21.21 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I11_J,axiom,
% 21.13/21.21 ! [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 ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Orecs_I2_J,axiom,
% 21.13/21.21 ! [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__rec(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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Orecs_I3_J,axiom,
% 21.13/21.21 ! [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__rec(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(hAPP(V_f3_2,V_loc_2),V_fun_2),V_com_2),c_Com_Ocom_Ocom__rec(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,V_com_2)) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Orecs_I8_J,axiom,
% 21.13/21.21 ! [V_fun_2,V_pname_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__rec(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_OCall(V_vname_2,V_pname_2,V_fun_2)) = hAPP(hAPP(hAPP(V_f8_2,V_vname_2),V_pname_2),V_fun_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I65_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evaln_OAssign,axiom,
% 21.13/21.21 ! [V_n_2,V_s_2,V_a_2,V_X_2] : c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2))) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evaln__elim__cases_I2_J,axiom,
% 21.13/21.21 ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] :
% 21.13/21.21 ( c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,V_t_2)
% 21.13/21.21 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_WTs__elim__cases_I8_J,axiom,
% 21.13/21.21 ! [V_a_2,V_P_2,V_X_2] :
% 21.13/21.21 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)))
% 21.13/21.21 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2))) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 21.13/21.21 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 21.13/21.21 ( class_Rings_Osemiring__1(T_b)
% 21.13/21.21 => 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)) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evaln_Oequations_I2_J,axiom,
% 21.13/21.21 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : c_Natural_Oevaln(c_Com_Ocom_OAss(V_a1_2,V_a2_2),V_a3_2,V_a4_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2))) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_WT_OCall,axiom,
% 21.13/21.21 ! [V_a_2,V_X_2,V_pn_2] :
% 21.13/21.21 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2)))
% 21.13/21.21 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_WT_Oequations_I8_J,axiom,
% 21.13/21.21 ! [V_a3_2,V_a1_2,V_a2_2] :
% 21.13/21.21 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2)))
% 21.13/21.21 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_nat__case__Suc,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_nat__rec__Suc,axiom,
% 21.13/21.21 ! [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)) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_WTs__elim__cases_I6_J,axiom,
% 21.13/21.21 ! [V_c_2,V_b_2] :
% 21.13/21.21 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2)))
% 21.13/21.21 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I69_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evaln_OWhileFalse,axiom,
% 21.13/21.21 ! [V_n_2,V_c_2,V_s_2,V_b_2] :
% 21.13/21.21 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 21.13/21.21 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_s_2) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evaln_OWhileTrue,axiom,
% 21.13/21.21 ! [V_s2_2,V_s1_2,V_n_2,V_c_2,V_s0_2,V_b_2] :
% 21.13/21.21 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 21.13/21.21 => ( c_Natural_Oevaln(V_c_2,V_s0_2,V_n_2,V_s1_2)
% 21.13/21.21 => ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s1_2,V_n_2,V_s2_2)
% 21.13/21.21 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s0_2,V_n_2,V_s2_2) ) ) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I5_J,axiom,
% 21.13/21.21 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 21.13/21.21 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 21.13/21.21 <=> ( V_fun_2 = V_fun_H_2
% 21.13/21.21 & V_com_2 = V_com_H_2 ) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I6_J,axiom,
% 21.13/21.21 ! [V_pname_H_2,V_pname_2] :
% 21.13/21.21 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
% 21.13/21.21 <=> V_pname_2 = V_pname_H_2 ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I58_J,axiom,
% 21.13/21.21 ! [V_pname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I59_J,axiom,
% 21.13/21.21 ! [V_com_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evaln_Oequations_I8_J,axiom,
% 21.13/21.21 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 21.13/21.21 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a6_2)
% 21.13/21.21 <=> ( ( V_a6_2 = V_a2_2
% 21.13/21.21 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 21.13/21.21 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 21.13/21.21 & ? [B_s1] :
% 21.13/21.21 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1)
% 21.13/21.21 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a6_2) ) ) ) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evaln_Oequations_I7_J,axiom,
% 21.13/21.21 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 21.13/21.21 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a2_2)
% 21.13/21.21 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 21.13/21.21 => ? [B_s1] :
% 21.13/21.21 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1)
% 21.13/21.21 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a2_2) ) ) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I55_J,axiom,
% 21.13/21.21 ! [V_com2_2,V_com1_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I54_J,axiom,
% 21.13/21.21 ! [V_pname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I30_J,axiom,
% 21.13/21.21 ! [V_pname_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I31_J,axiom,
% 21.13/21.21 ! [V_fun_2,V_vname_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_WT_Oequations_I6_J,axiom,
% 21.13/21.21 ! [V_a1_2,V_a2_2] :
% 21.13/21.21 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2)))
% 21.13/21.21 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_While,axiom,
% 21.13/21.21 ! [V_b_2,V_c_2] :
% 21.13/21.21 ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 21.13/21.21 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I49_J,axiom,
% 21.13/21.21 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I48_J,axiom,
% 21.13/21.21 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I40_J,axiom,
% 21.13/21.21 ! [V_pname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I63_J,axiom,
% 21.13/21.21 ! [V_pname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != hAPP(c_Com_Ocom_OBODY,V_pname_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I41_J,axiom,
% 21.13/21.21 ! [V_com_2,V_fun_2,V_loc_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I62_J,axiom,
% 21.13/21.21 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_pname_2] : hAPP(c_Com_Ocom_OBODY,V_pname_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I19_J,axiom,
% 21.13/21.21 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I18_J,axiom,
% 21.13/21.21 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I53_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I52_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I29_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I28_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I46_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I47_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I38_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I61_J,axiom,
% 21.13/21.21 ! [V_com_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I39_J,axiom,
% 21.13/21.21 ! [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) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I60_J,axiom,
% 21.13/21.21 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I17_J,axiom,
% 21.13/21.21 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I16_J,axiom,
% 21.13/21.21 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Orecs_I7_J,axiom,
% 21.13/21.21 ! [V_pname_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__rec(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,hAPP(c_Com_Ocom_OBODY,V_pname_2)) = hAPP(V_f7_2,V_pname_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Orecs_I6_J,axiom,
% 21.13/21.21 ! [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__rec(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(hAPP(V_f6_2,V_fun_2),V_com_2),c_Com_Ocom_Ocom__rec(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,V_com_2)) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com_Osimps_I70_J,axiom,
% 21.13/21.21 ! [V_pname_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,hAPP(c_Com_Ocom_OBODY,V_pname_2)) = hAPP(V_f7_2,V_pname_2) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_Body__triple__valid__0,axiom,
% 21.13/21.21 ! [V_Q_2,V_pn_2,V_P_2,T_b] : c_Hoare__Mirabelle_Otriple__valid(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_Body__triple__valid__Suc,axiom,
% 21.13/21.21 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_b] :
% 21.13/21.21 ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2))
% 21.13/21.21 <=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_def__nat__rec__Suc,axiom,
% 21.13/21.21 ! [V_n_2,V_h_2,V_c_2,T_b,V_f_2] :
% 21.13/21.21 ( ! [B_n] : hAPP(V_f_2,B_n) = hAPP(c_Nat_Onat_Onat__rec(T_b,V_c_2,V_h_2),B_n)
% 21.13/21.21 => hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_h_2,V_n_2),hAPP(V_f_2,V_n_2)) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc__elim__cases_I2_J,axiom,
% 21.13/21.21 ! [V_t_2,V_s_2,V_a_2,V_X_2] :
% 21.13/21.21 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2))
% 21.13/21.21 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc_OAssign,axiom,
% 21.13/21.21 ! [V_s_2,V_a_2,V_X_2] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)))) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evaln__WHILE__case,axiom,
% 21.13/21.21 ! [V_t_2,V_n_2,V_s_2,V_c_2,V_b_2] :
% 21.13/21.21 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_t_2)
% 21.13/21.21 => ( ( V_t_2 = V_s_2
% 21.13/21.21 => hBOOL(hAPP(V_b_2,V_s_2)) )
% 21.13/21.21 => ~ ( hBOOL(hAPP(V_b_2,V_s_2))
% 21.13/21.21 => ! [B_s1] :
% 21.13/21.21 ( c_Natural_Oevaln(V_c_2,V_s_2,V_n_2,B_s1)
% 21.13/21.21 => ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),B_s1,V_n_2,V_t_2) ) ) ) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evaln_OBody,axiom,
% 21.13/21.21 ! [V_s1,V_n,V_s0,V_pn] :
% 21.13/21.21 ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1)
% 21.13/21.21 => c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,hAPP(c_Nat_OSuc,V_n),V_s1) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc_Oequations_I2_J,axiom,
% 21.13/21.21 ! [V_a3_2,V_a2_2,V_a1_2] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_a1_2,V_a2_2)),V_a3_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2)))) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evaln_OLocal,axiom,
% 21.13/21.21 ! [V_s1_2,V_n_2,V_a_2,V_Y_2,V_s0_2,V_c_2] :
% 21.13/21.21 ( c_Natural_Oevaln(V_c_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s0_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s0_2)),V_n_2,V_s1_2)
% 21.13/21.21 => c_Natural_Oevaln(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2),V_s0_2,V_n_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s1_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s0_2),V_Y_2))) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evaln_Oequations_I9_J,axiom,
% 21.13/21.21 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
% 21.13/21.21 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),V_a2_2,hAPP(c_Nat_OSuc,V_a3_2),V_a4_2)
% 21.13/21.21 <=> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2)),V_a2_2,V_a3_2,V_a4_2) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evaln_Oequations_I3_J,axiom,
% 21.13/21.21 ! [V_a6_2,V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] :
% 21.13/21.21 ( c_Natural_Oevaln(c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2),V_a2_2,V_a5_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)))
% 21.13/21.21 <=> ? [B_s1] :
% 21.13/21.21 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2))
% 21.13/21.21 & c_Natural_Oevaln(V_a1_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2)),V_a5_2,B_s1) ) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc_OWhileFalse,axiom,
% 21.13/21.21 ! [V_c_2,V_s_2,V_b_2] :
% 21.13/21.21 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 21.13/21.21 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_s_2)) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc_OWhileTrue,axiom,
% 21.13/21.21 ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] :
% 21.13/21.21 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 21.13/21.21 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s0_2),V_s1_2))
% 21.13/21.21 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2))
% 21.13/21.21 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_s2_2)) ) ) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc__elim__cases_I5_J,axiom,
% 21.13/21.21 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 21.13/21.21 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_t_2))
% 21.13/21.21 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 21.13/21.21 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) )
% 21.13/21.21 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 21.13/21.21 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc_OIfTrue,axiom,
% 21.13/21.21 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] :
% 21.13/21.21 ( hBOOL(hAPP(V_b_2,V_s_2))
% 21.13/21.21 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2))
% 21.13/21.21 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc_OIfFalse,axiom,
% 21.13/21.21 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
% 21.13/21.21 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 21.13/21.21 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2))
% 21.13/21.21 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc_OSemi,axiom,
% 21.13/21.21 ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
% 21.13/21.21 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1))
% 21.13/21.21 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2))
% 21.13/21.21 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc_OSkip,axiom,
% 21.13/21.21 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc__elim__cases_I1_J,axiom,
% 21.13/21.21 ! [V_t,V_s] :
% 21.13/21.21 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t))
% 21.13/21.21 => V_t = V_s ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc__elim__cases_I6_J,axiom,
% 21.13/21.21 ! [V_s1,V_s,V_P] :
% 21.13/21.21 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1))
% 21.13/21.21 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc_OBody,axiom,
% 21.13/21.21 ! [V_s1,V_s0,V_pn] :
% 21.13/21.21 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1))
% 21.13/21.21 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc_OLocal,axiom,
% 21.13/21.21 ! [V_s1_2,V_a_2,V_Y_2,V_s0_2,V_c_2] :
% 21.13/21.21 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s0_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s0_2))),V_s1_2))
% 21.13/21.21 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)),V_s0_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s1_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s0_2),V_Y_2)))) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_vname_Osimps_I2_J,axiom,
% 21.13/21.21 ! [V_loc_H_2,V_loc_2] :
% 21.13/21.21 ( c_Com_Ovname_OLoc(V_loc_2) = c_Com_Ovname_OLoc(V_loc_H_2)
% 21.13/21.21 <=> V_loc_2 = V_loc_H_2 ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_com__det,axiom,
% 21.13/21.21 ! [V_u,V_t,V_s,V_c] :
% 21.13/21.21 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 21.13/21.21 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
% 21.13/21.21 => V_u = V_t ) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc_Oequations_I9_J,axiom,
% 21.13/21.21 ! [V_a3_2,V_a2_2,V_a1_2] :
% 21.13/21.21 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
% 21.13/21.21 <=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2)) ) ).
% 21.13/21.21
% 21.13/21.21 fof(fact_evalc_Oequations_I3_J,axiom,
% 21.13/21.21 ! [V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] :
% 21.13/21.21 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2))))
% 21.13/21.21 <=> ? [B_s1] :
% 21.13/21.21 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2))
% 21.13/21.22 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2))),B_s1)) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_Suc__neq__Zero,axiom,
% 21.13/21.22 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_Zero__neq__Suc,axiom,
% 21.13/21.22 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat_Osimps_I3_J,axiom,
% 21.13/21.22 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_Suc__not__Zero,axiom,
% 21.13/21.22 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat_Osimps_I2_J,axiom,
% 21.13/21.22 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_Zero__not__Suc,axiom,
% 21.13/21.22 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_eval__eq,axiom,
% 21.13/21.22 ! [V_t_2,V_s_2,V_c_2] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),V_t_2))
% 21.13/21.22 <=> ? [B_n] : c_Natural_Oevaln(V_c_2,V_s_2,B_n,V_t_2) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evaln__evalc,axiom,
% 21.13/21.22 ! [V_t,V_n,V_s,V_c] :
% 21.13/21.22 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t)
% 21.13/21.22 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evalc_Oequations_I7_J,axiom,
% 21.13/21.22 ! [V_a2_2,V_a3_2,V_a1_2] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2))
% 21.13/21.22 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 21.13/21.22 => ? [B_s1] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 21.13/21.22 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evalc_Oequations_I8_J,axiom,
% 21.13/21.22 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2))
% 21.13/21.22 <=> ( ( V_a5_2 = V_a2_2
% 21.13/21.22 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 21.13/21.22 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 21.13/21.22 & ? [B_s1] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 21.13/21.22 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evalc_Oequations_I6_J,axiom,
% 21.13/21.22 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a5_2,V_a3_2)),V_a2_2),V_a4_2))
% 21.13/21.22 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 21.13/21.22 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) )
% 21.13/21.22 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 21.13/21.22 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evalc_Oequations_I5_J,axiom,
% 21.13/21.22 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2))
% 21.13/21.22 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 21.13/21.22 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) )
% 21.13/21.22 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 21.13/21.22 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evalc_Oequations_I4_J,axiom,
% 21.13/21.22 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2))
% 21.13/21.22 <=> ? [B_s1] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1))
% 21.13/21.22 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evalc_Oequations_I1_J,axiom,
% 21.13/21.22 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat__case__0,axiom,
% 21.13/21.22 ! [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 ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat__rec__0,axiom,
% 21.13/21.22 ! [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 ).
% 21.13/21.22
% 21.13/21.22 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 21.13/21.22 ! [V_i_2,V_inc_2,T_b] :
% 21.13/21.22 ( class_Rings_Osemiring__1(T_b)
% 21.13/21.22 => 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 ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_triple_Osize_I1_J,axiom,
% 21.13/21.22 ! [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) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_vname_Osize_I2_J,axiom,
% 21.13/21.22 ! [V_loc] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_triple_Osize_I2_J,axiom,
% 21.13/21.22 ! [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) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evaln__elim__cases_I6_J,axiom,
% 21.13/21.22 ! [V_s1,V_n,V_s,V_P] :
% 21.13/21.22 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1)
% 21.13/21.22 => ~ ! [B_n] :
% 21.13/21.22 ( V_n = hAPP(c_Nat_OSuc,B_n)
% 21.13/21.22 => ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evalc__elim__cases_I3_J,axiom,
% 21.13/21.22 ! [V_t_2,V_s_2,V_c_2,V_a_2,V_Y_2] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)),V_s_2),V_t_2))
% 21.13/21.22 => ~ ! [B_s1] :
% 21.13/21.22 ( V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s_2),V_Y_2))
% 21.13/21.22 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s_2))),B_s1)) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evaln__elim__cases_I3_J,axiom,
% 21.13/21.22 ! [V_t_2,V_n_2,V_s_2,V_c_2,V_a_2,V_Y_2] :
% 21.13/21.22 ( c_Natural_Oevaln(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2),V_s_2,V_n_2,V_t_2)
% 21.13/21.22 => ~ ! [B_s1] :
% 21.13/21.22 ( V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s_2),V_Y_2))
% 21.13/21.22 => ~ c_Natural_Oevaln(V_c_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s_2)),V_n_2,B_s1) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_vname_Osize_I4_J,axiom,
% 21.13/21.22 ! [V_loc] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_vname_Orecs_I2_J,axiom,
% 21.13/21.22 ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_vname_Osimps_I6_J,axiom,
% 21.13/21.22 ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evalc__elim__cases_I4_J,axiom,
% 21.13/21.22 ! [V_t,V_s,V_c2,V_c1] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t))
% 21.13/21.22 => ~ ! [B_s1] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1))
% 21.13/21.22 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I1_J,axiom,
% 21.13/21.22 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I7_J,axiom,
% 21.13/21.22 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I2_J,axiom,
% 21.13/21.22 ! [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) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I8_J,axiom,
% 21.13/21.22 ! [V_fun_2,V_pname_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_vname_Osize_I3_J,axiom,
% 21.13/21.22 ! [V_glb] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_vname_Osize_I1_J,axiom,
% 21.13/21.22 ! [V_glb] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I4_J,axiom,
% 21.13/21.22 ! [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))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I3_J,axiom,
% 21.13/21.22 ! [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))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I5_J,axiom,
% 21.13/21.22 ! [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))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I6_J,axiom,
% 21.13/21.22 ! [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))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_vname_Osimps_I5_J,axiom,
% 21.13/21.22 ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_vname_Orecs_I1_J,axiom,
% 21.13/21.22 ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I9_J,axiom,
% 21.13/21.22 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I16_J,axiom,
% 21.13/21.22 ! [V_fun_2,V_pname_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I10_J,axiom,
% 21.13/21.22 ! [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) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat__add__commute,axiom,
% 21.13/21.22 ! [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) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat__add__left__commute,axiom,
% 21.13/21.22 ! [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)) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat__add__assoc,axiom,
% 21.13/21.22 ! [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)) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat__add__left__cancel,axiom,
% 21.13/21.22 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.22 ( 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)
% 21.13/21.22 <=> V_m_2 = V_n_2 ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat__add__right__cancel,axiom,
% 21.13/21.22 ! [V_n_2,V_k_2,V_m_2] :
% 21.13/21.22 ( 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)
% 21.13/21.22 <=> V_m_2 = V_n_2 ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_vname_Osimps_I1_J,axiom,
% 21.13/21.22 ! [V_glb_H_2,V_glb_2] :
% 21.13/21.22 ( c_Com_Ovname_OGlb(V_glb_2) = c_Com_Ovname_OGlb(V_glb_H_2)
% 21.13/21.22 <=> V_glb_2 = V_glb_H_2 ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_plus__nat_Oadd__0,axiom,
% 21.13/21.22 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 21.13/21.22
% 21.13/21.22 fof(fact_Nat_Oadd__0__right,axiom,
% 21.13/21.22 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__is__0,axiom,
% 21.13/21.22 ! [V_n_2,V_m_2] :
% 21.13/21.22 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.22 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.22 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__eq__self__zero,axiom,
% 21.13/21.22 ! [V_n,V_m] :
% 21.13/21.22 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 21.13/21.22 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__Suc__shift,axiom,
% 21.13/21.22 ! [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)) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__Suc,axiom,
% 21.13/21.22 ! [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)) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__Suc__right,axiom,
% 21.13/21.22 ! [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)) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I14_J,axiom,
% 21.13/21.22 ! [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))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I13_J,axiom,
% 21.13/21.22 ! [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))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I11_J,axiom,
% 21.13/21.22 ! [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))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I12_J,axiom,
% 21.13/21.22 ! [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))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_one__is__add,axiom,
% 21.13/21.22 ! [V_n_2,V_m_2] :
% 21.13/21.22 ( 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)
% 21.13/21.22 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 21.13/21.22 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 21.13/21.22 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.22 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__is__1,axiom,
% 21.13/21.22 ! [V_n_2,V_m_2] :
% 21.13/21.22 ( 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))
% 21.13/21.22 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 21.13/21.22 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 21.13/21.22 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.22 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_vname_Osimps_I3_J,axiom,
% 21.13/21.22 ! [V_loc_H,V_glb] : c_Com_Ovname_OGlb(V_glb) != c_Com_Ovname_OLoc(V_loc_H) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_vname_Osimps_I4_J,axiom,
% 21.13/21.22 ! [V_glb,V_loc_H] : c_Com_Ovname_OLoc(V_loc_H) != c_Com_Ovname_OGlb(V_glb) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_com_Osize_I15_J,axiom,
% 21.13/21.22 ! [V_pname] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_double__eq__0__iff,axiom,
% 21.13/21.22 ! [V_a_2,T_b] :
% 21.13/21.22 ( class_Groups_Olinordered__ab__group__add(T_b)
% 21.13/21.22 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.22 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__0__iff,axiom,
% 21.13/21.22 ! [V_a_2,V_b_2,T_b] :
% 21.13/21.22 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 21.13/21.22 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 21.13/21.22 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add_Ocomm__neutral,axiom,
% 21.13/21.22 ! [V_a,T_a] :
% 21.13/21.22 ( class_Groups_Ocomm__monoid__add(T_a)
% 21.13/21.22 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 21.13/21.22 ! [V_a,T_a] :
% 21.13/21.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.22 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__0__right,axiom,
% 21.13/21.22 ! [V_a,T_a] :
% 21.13/21.22 ( class_Groups_Omonoid__add(T_a)
% 21.13/21.22 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_double__zero__sym,axiom,
% 21.13/21.22 ! [V_a_2,T_b] :
% 21.13/21.22 ( class_Groups_Olinordered__ab__group__add(T_b)
% 21.13/21.22 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 21.13/21.22 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__0,axiom,
% 21.13/21.22 ! [V_a,T_a] :
% 21.13/21.22 ( class_Groups_Ocomm__monoid__add(T_a)
% 21.13/21.22 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 21.13/21.22 ! [V_a,T_a] :
% 21.13/21.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.22 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__0__left,axiom,
% 21.13/21.22 ! [V_a,T_a] :
% 21.13/21.22 ( class_Groups_Omonoid__add(T_a)
% 21.13/21.22 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat_Osize_I2_J,axiom,
% 21.13/21.22 ! [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))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat_Osize_I4_J,axiom,
% 21.13/21.22 ! [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))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat__size,axiom,
% 21.13/21.22 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat_Osize_I3_J,axiom,
% 21.13/21.22 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) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat_Osize_I1_J,axiom,
% 21.13/21.22 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_zero__reorient,axiom,
% 21.13/21.22 ! [V_x_2,T_b] :
% 21.13/21.22 ( class_Groups_Ozero(T_b)
% 21.13/21.22 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 21.13/21.22 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 21.13/21.22 ! [V_c,V_a,T_a] :
% 21.13/21.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.22 => 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) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 21.13/21.22 ! [V_d,V_c,V_a,T_a] :
% 21.13/21.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.22 => 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)) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 21.13/21.22 ! [V_d,V_c,V_a,T_a] :
% 21.13/21.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.22 => 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) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 21.13/21.22 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.22 => 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)) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 21.13/21.22 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.22 ( class_Groups_Oab__semigroup__add(T_a)
% 21.13/21.22 => 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)) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 21.13/21.22 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.22 => 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) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__left__cancel,axiom,
% 21.13/21.22 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 21.13/21.22 ( class_Groups_Ocancel__semigroup__add(T_b)
% 21.13/21.22 => ( 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_c_2)
% 21.13/21.22 <=> V_b_2 = V_c_2 ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__right__cancel,axiom,
% 21.13/21.22 ! [V_c_2,V_a_2,V_b_2,T_b] :
% 21.13/21.22 ( class_Groups_Ocancel__semigroup__add(T_b)
% 21.13/21.22 => ( 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_c_2),V_a_2)
% 21.13/21.22 <=> V_b_2 = V_c_2 ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 21.13/21.22 ! [V_d,V_c,V_b,V_a,T_a] :
% 21.13/21.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.22 => 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)) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__left__imp__eq,axiom,
% 21.13/21.22 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.22 ( class_Groups_Ocancel__semigroup__add(T_a)
% 21.13/21.22 => ( 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)
% 21.13/21.22 => V_b = V_c ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__imp__eq,axiom,
% 21.13/21.22 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.22 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 21.13/21.22 => ( 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)
% 21.13/21.22 => V_b = V_c ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__right__imp__eq,axiom,
% 21.13/21.22 ! [V_c,V_a,V_b,T_a] :
% 21.13/21.22 ( class_Groups_Ocancel__semigroup__add(T_a)
% 21.13/21.22 => ( 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)
% 21.13/21.22 => V_b = V_c ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_bool_Osize_I1_J,axiom,
% 21.13/21.22 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_bool_Osize_I2_J,axiom,
% 21.13/21.22 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_bool_Osize_I3_J,axiom,
% 21.13/21.22 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_bool_Osize_I4_J,axiom,
% 21.13/21.22 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_WT_OBody,axiom,
% 21.13/21.22 ! [V_pn] :
% 21.13/21.22 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)
% 21.13/21.22 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_WT_Oequations_I7_J,axiom,
% 21.13/21.22 ! [V_a_2] :
% 21.13/21.22 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
% 21.13/21.22 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evalc_OCall,axiom,
% 21.13/21.22 ! [V_X_2,V_s1_2,V_a_2,V_s0_2,V_pn_2] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s0_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s0_2))),V_s1_2))
% 21.13/21.22 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2)),V_s0_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s1_2),hAPP(c_Natural_Ogetlocs,V_s0_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,V_s1_2),c_Com_ORes)))) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evaln_OCall,axiom,
% 21.13/21.22 ! [V_X_2,V_s1_2,V_n_2,V_a_2,V_s0_2,V_pn_2] :
% 21.13/21.22 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s0_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s0_2)),V_n_2,V_s1_2)
% 21.13/21.22 => c_Natural_Oevaln(c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2),V_s0_2,V_n_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s1_2),hAPP(c_Natural_Ogetlocs,V_s0_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,V_s1_2),c_Com_ORes))) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_def__nat__rec__0,axiom,
% 21.13/21.22 ! [V_h_2,V_c_2,T_b,V_f_2] :
% 21.13/21.22 ( ! [B_n] : hAPP(V_f_2,B_n) = hAPP(c_Nat_Onat_Onat__rec(T_b,V_c_2,V_h_2),B_n)
% 21.13/21.22 => hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_c_2 ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evalc_Oequations_I10_J,axiom,
% 21.13/21.22 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a5_2] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_a5_2,V_a1_2,V_a3_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a4_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a4_2),c_Com_ORes))))
% 21.13/21.22 <=> ? [B_s1] :
% 21.13/21.22 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a4_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a4_2),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes))
% 21.13/21.22 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a2_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a3_2,V_a2_2))),B_s1)) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evaln_Oequations_I10_J,axiom,
% 21.13/21.22 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a6_2] :
% 21.13/21.22 ( c_Natural_Oevaln(c_Com_Ocom_OCall(V_a6_2,V_a1_2,V_a3_2),V_a2_2,V_a4_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a5_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a5_2),c_Com_ORes)))
% 21.13/21.22 <=> ? [B_s1] :
% 21.13/21.22 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a5_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a5_2),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes))
% 21.13/21.22 & c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a2_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a3_2,V_a2_2)),V_a4_2,B_s1) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evalc__elim__cases_I7_J,axiom,
% 21.13/21.22 ! [V_s1_2,V_s_2,V_a_2,V_P_2,V_X_2] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)),V_s_2),V_s1_2))
% 21.13/21.22 => ~ ! [B_s1] :
% 21.13/21.22 ( V_s1_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_s_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes))
% 21.13/21.22 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s_2))),B_s1)) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evaln__elim__cases_I7_J,axiom,
% 21.13/21.22 ! [V_s1_2,V_n_2,V_s_2,V_a_2,V_P_2,V_X_2] :
% 21.13/21.22 ( c_Natural_Oevaln(c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2),V_s_2,V_n_2,V_s1_2)
% 21.13/21.22 => ~ ! [B_s1] :
% 21.13/21.22 ( V_s1_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_s_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes))
% 21.13/21.22 => ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s_2)),V_n_2,B_s1) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_WT__bodiesD,axiom,
% 21.13/21.22 ! [V_b,V_pn] :
% 21.13/21.22 ( c_Com_OWT__bodies
% 21.13/21.22 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
% 21.13/21.22 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_option_Osize_I2_J,axiom,
% 21.13/21.22 ! [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))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_option_Osize_I1_J,axiom,
% 21.13/21.22 ! [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) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_WTs__elim__cases_I7_J,axiom,
% 21.13/21.22 ! [V_P] :
% 21.13/21.22 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P)))
% 21.13/21.22 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_the_Osimps,axiom,
% 21.13/21.22 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 21.13/21.22
% 21.13/21.22 fof(fact_not__None__eq,axiom,
% 21.13/21.22 ! [T_b,V_x_2] :
% 21.13/21.22 ( V_x_2 != c_Option_Ooption_ONone(T_b)
% 21.13/21.22 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_not__Some__eq,axiom,
% 21.13/21.22 ! [T_b,V_x_2] :
% 21.13/21.22 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y)
% 21.13/21.22 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_option_Osimps_I3_J,axiom,
% 21.13/21.22 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_option_Osimps_I2_J,axiom,
% 21.13/21.22 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_option_Oinject,axiom,
% 21.13/21.22 ! [V_a_H_2,V_a_2,T_b] :
% 21.13/21.22 ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2)
% 21.13/21.22 <=> V_a_2 = V_a_H_2 ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_option_Osize_I4_J,axiom,
% 21.13/21.22 ! [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) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_option_Osize_I3_J,axiom,
% 21.13/21.22 ! [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) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_option_Orecs_I2_J,axiom,
% 21.13/21.22 ! [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) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_option_Osimps_I5_J,axiom,
% 21.13/21.22 ! [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) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_option_Orecs_I1_J,axiom,
% 21.13/21.22 ! [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 ).
% 21.13/21.22
% 21.13/21.22 fof(fact_option_Osimps_I4_J,axiom,
% 21.13/21.22 ! [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 ).
% 21.13/21.22
% 21.13/21.22 fof(fact_is__none__code_I2_J,axiom,
% 21.13/21.22 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_is__none__code_I1_J,axiom,
% 21.13/21.22 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_is__none__def,axiom,
% 21.13/21.22 ! [V_x_2,T_b] :
% 21.13/21.22 ( c_Option_Ois__none(T_b,V_x_2)
% 21.13/21.22 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evalc__WHILE__case,axiom,
% 21.13/21.22 ! [V_t_2,V_s_2,V_c_2,V_b_2] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_t_2))
% 21.13/21.22 => ( ( V_t_2 = V_s_2
% 21.13/21.22 => hBOOL(hAPP(V_b_2,V_s_2)) )
% 21.13/21.22 => ~ ( hBOOL(hAPP(V_b_2,V_s_2))
% 21.13/21.22 => ! [B_s1] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),B_s1))
% 21.13/21.22 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),B_s1),V_t_2)) ) ) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_pair__box_Osize_I1_J,axiom,
% 21.13/21.22 ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_pair__box_Oinject,axiom,
% 21.13/21.22 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 21.13/21.22 ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2)
% 21.13/21.22 <=> ( V_a_2 = V_a_H_2
% 21.13/21.22 & V_b_2 = V_b_H_2 ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_pair__box_Osize_I2_J,axiom,
% 21.13/21.22 ! [V_b,V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_pair__box_Osimps_I2_J,axiom,
% 21.13/21.22 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_pair__box_Orecs,axiom,
% 21.13/21.22 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_evalc__evaln,axiom,
% 21.13/21.22 ! [V_t,V_s,V_c] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 21.13/21.22 => ? [B_n] : c_Natural_Oevaln(V_c,V_s,B_n,V_t) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_sum_Osize_I1_J,axiom,
% 21.13/21.22 ! [V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Sum__Type_Osum_Osum__size(T_b,T_c,V_fa_2,V_fb_2,hAPP(c_Sum__Type_OInl(T_b,T_c),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))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_sum_Osize_I2_J,axiom,
% 21.13/21.22 ! [V_b_2,V_fb_2,V_fa_2,T_c,T_b] : c_Sum__Type_Osum_Osum__size(T_b,T_c,V_fa_2,V_fb_2,hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fb_2,V_b_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_option_Oexhaust,axiom,
% 21.13/21.22 ! [T_a,V_y] :
% 21.13/21.22 ( V_y != c_Option_Ooption_ONone(T_a)
% 21.13/21.22 => ~ ! [B_a] : V_y != hAPP(c_Option_Ooption_OSome(T_a),B_a) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_zero__less__Suc,axiom,
% 21.13/21.22 ! [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))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_not0__implies__Suc,axiom,
% 21.13/21.22 ! [V_n] :
% 21.13/21.22 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.22 => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat__induct,axiom,
% 21.13/21.22 ! [V_n_2,V_P_2] :
% 21.13/21.22 ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 21.13/21.22 => ( ! [B_n] :
% 21.13/21.22 ( hBOOL(hAPP(V_P_2,B_n))
% 21.13/21.22 => hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_n))) )
% 21.13/21.22 => hBOOL(hAPP(V_P_2,V_n_2)) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_zero__induct,axiom,
% 21.13/21.22 ! [V_k_2,V_P_2] :
% 21.13/21.22 ( hBOOL(hAPP(V_P_2,V_k_2))
% 21.13/21.22 => ( ! [B_n] :
% 21.13/21.22 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_n)))
% 21.13/21.22 => hBOOL(hAPP(V_P_2,B_n)) )
% 21.13/21.22 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_less__zeroE,axiom,
% 21.13/21.22 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_lessI,axiom,
% 21.13/21.22 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_Suc__mono,axiom,
% 21.13/21.22 ! [V_n,V_m] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat__less__cases,axiom,
% 21.13/21.22 ! [V_P_2,V_n_2,V_m_2] :
% 21.13/21.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 21.13/21.22 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 21.13/21.22 => ( ( V_m_2 = V_n_2
% 21.13/21.22 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 21.13/21.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 21.13/21.22 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 21.13/21.22 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_less__not__refl3,axiom,
% 21.13/21.22 ! [V_t,V_s] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 21.13/21.22 => V_s != V_t ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_less__not__refl2,axiom,
% 21.13/21.22 ! [V_m,V_n] :
% 21.13/21.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 21.13/21.22 => V_m != V_n ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_less__irrefl__nat,axiom,
% 21.13/21.22 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_linorder__neqE__nat,axiom,
% 21.13/21.22 ! [V_y,V_x] :
% 21.13/21.22 ( V_x != V_y
% 21.13/21.22 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 21.13/21.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_nat__neq__iff,axiom,
% 21.13/21.22 ! [V_n_2,V_m_2] :
% 21.13/21.22 ( V_m_2 != V_n_2
% 21.13/21.22 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 21.13/21.22 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_less__not__refl,axiom,
% 21.13/21.22 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__less__cancel__right,axiom,
% 21.13/21.22 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 21.13/21.22 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 21.13/21.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
% 21.13/21.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__less__cancel__left,axiom,
% 21.13/21.22 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 21.13/21.22 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 21.13/21.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
% 21.13/21.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__strict__right__mono,axiom,
% 21.13/21.22 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.22 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 21.13/21.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.22 => 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))) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__strict__left__mono,axiom,
% 21.13/21.22 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.22 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 21.13/21.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.22 => 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))) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__strict__mono,axiom,
% 21.13/21.22 ! [V_d,V_c,V_b,V_a,T_a] :
% 21.13/21.22 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 21.13/21.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 21.13/21.22 => 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))) ) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__less__imp__less__right,axiom,
% 21.13/21.22 ! [V_b,V_c,V_a,T_a] :
% 21.13/21.22 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 21.13/21.22 => ( 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)))
% 21.13/21.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_add__less__imp__less__left,axiom,
% 21.13/21.22 ! [V_b,V_a,V_c,T_a] :
% 21.13/21.22 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 21.13/21.22 => ( 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)))
% 21.13/21.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 21.13/21.22
% 21.13/21.22 fof(fact_gr0I,axiom,
% 21.13/21.22 ! [V_n] :
% 21.13/21.23 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_gr__implies__not0,axiom,
% 21.13/21.23 ! [V_n,V_m] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.23 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__nat__zero__code,axiom,
% 21.13/21.23 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_neq0__conv,axiom,
% 21.13/21.23 ! [V_n_2] :
% 21.13/21.23 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_not__less0,axiom,
% 21.13/21.23 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_not__less__eq,axiom,
% 21.13/21.23 ! [V_n_2,V_m_2] :
% 21.13/21.23 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__Suc__eq,axiom,
% 21.13/21.23 ! [V_n_2,V_m_2] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 21.13/21.23 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 21.13/21.23 | V_m_2 = V_n_2 ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Suc__less__eq,axiom,
% 21.13/21.23 ! [V_n_2,V_m_2] :
% 21.13/21.23 ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_not__less__less__Suc__eq,axiom,
% 21.13/21.23 ! [V_m_2,V_n_2] :
% 21.13/21.23 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 21.13/21.23 <=> V_n_2 = V_m_2 ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__antisym,axiom,
% 21.13/21.23 ! [V_m,V_n] :
% 21.13/21.23 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 21.13/21.23 => V_m = V_n ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__SucI,axiom,
% 21.13/21.23 ! [V_n,V_m] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Suc__lessI,axiom,
% 21.13/21.23 ! [V_n,V_m] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.23 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 21.13/21.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__trans__Suc,axiom,
% 21.13/21.23 ! [V_k,V_j,V_i] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 21.13/21.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__SucE,axiom,
% 21.13/21.23 ! [V_n,V_m] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 21.13/21.23 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.23 => V_m = V_n ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Suc__lessD,axiom,
% 21.13/21.23 ! [V_n,V_m] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 21.13/21.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Suc__less__SucD,axiom,
% 21.13/21.23 ! [V_n,V_m] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 21.13/21.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_add__lessD1,axiom,
% 21.13/21.23 ! [V_k,V_j,V_i] :
% 21.13/21.23 ( 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))
% 21.13/21.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__add__eq__less,axiom,
% 21.13/21.23 ! [V_n,V_m,V_l,V_k] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 21.13/21.23 => ( 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)
% 21.13/21.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_add__less__mono,axiom,
% 21.13/21.23 ! [V_l,V_k,V_j,V_i] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 21.13/21.23 => 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))) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_add__less__mono1,axiom,
% 21.13/21.23 ! [V_k,V_j,V_i] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 21.13/21.23 => 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))) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_trans__less__add2,axiom,
% 21.13/21.23 ! [V_m,V_j,V_i] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 21.13/21.23 => 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))) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_trans__less__add1,axiom,
% 21.13/21.23 ! [V_m,V_j,V_i] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 21.13/21.23 => 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))) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_nat__add__left__cancel__less,axiom,
% 21.13/21.23 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.23 ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_not__add__less2,axiom,
% 21.13/21.23 ! [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)) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_not__add__less1,axiom,
% 21.13/21.23 ! [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)) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_add__neg__neg,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.23 => 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))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_add__pos__pos,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.23 => 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))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 21.13/21.23 ! [V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Olinordered__ab__group__add(T_b)
% 21.13/21.23 => ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_even__less__0__iff,axiom,
% 21.13/21.23 ! [V_a_2,T_b] :
% 21.13/21.23 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.23 => ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 21.13/21.23 ! [V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Olinordered__ab__group__add(T_b)
% 21.13/21.23 => ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__Suc__eq__0__disj,axiom,
% 21.13/21.23 ! [V_n_2,V_m_2] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 21.13/21.23 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.23 | ? [B_j] :
% 21.13/21.23 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 21.13/21.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__Suc0,axiom,
% 21.13/21.23 ! [V_n_2] :
% 21.13/21.23 ( 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))))
% 21.13/21.23 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_gr0__conv__Suc,axiom,
% 21.13/21.23 ! [V_n_2] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 21.13/21.23 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_add__gr__0,axiom,
% 21.13/21.23 ! [V_n_2,V_m_2] :
% 21.13/21.23 ( 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)))
% 21.13/21.23 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 21.13/21.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__iff__Suc__add,axiom,
% 21.13/21.23 ! [V_n_2,V_m_2] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 21.13/21.23 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__add__Suc2,axiom,
% 21.13/21.23 ! [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)))) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__add__Suc1,axiom,
% 21.13/21.23 ! [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)))) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_pos__add__strict,axiom,
% 21.13/21.23 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 21.13/21.23 => 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))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Inl__not__Inr,axiom,
% 21.13/21.23 ! [V_b,V_a,T_b,T_a] : hAPP(c_Sum__Type_OInl(T_a,T_b),V_a) != hAPP(c_Sum__Type_OInr(T_b,T_a),V_b) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_sum_Osimps_I3_J,axiom,
% 21.13/21.23 ! [V_b_H,V_a,T_b,T_a] : hAPP(c_Sum__Type_OInl(T_a,T_b),V_a) != hAPP(c_Sum__Type_OInr(T_b,T_a),V_b_H) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Inr__not__Inl,axiom,
% 21.13/21.23 ! [V_a,V_b,T_a,T_b] : hAPP(c_Sum__Type_OInr(T_b,T_a),V_b) != hAPP(c_Sum__Type_OInl(T_a,T_b),V_a) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_sum_Osimps_I4_J,axiom,
% 21.13/21.23 ! [V_a_1,V_b_H_1,T_a_1,T_b_1] : hAPP(c_Sum__Type_OInr(T_b_1,T_a_1),V_b_H_1) != hAPP(c_Sum__Type_OInl(T_a_1,T_b_1),V_a_1) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_sum_Osize_I3_J,axiom,
% 21.13/21.23 ! [V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_sum(T_a,T_b)),hAPP(c_Sum__Type_OInl(T_a,T_b),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_sum_Osize_I4_J,axiom,
% 21.13/21.23 ! [V_b,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_sum(T_a,T_b)),hAPP(c_Sum__Type_OInr(T_b,T_a),V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_termination__basic__simps_I1_J,axiom,
% 21.13/21.23 ! [V_z,V_y,V_x] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 21.13/21.23 => 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))) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_termination__basic__simps_I2_J,axiom,
% 21.13/21.23 ! [V_y,V_z,V_x] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 21.13/21.23 => 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))) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__nat__0__less__iff,axiom,
% 21.13/21.23 ! [V_n_2,T_b] :
% 21.13/21.23 ( class_Rings_Olinordered__semidom(T_b)
% 21.13/21.23 => ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__nat__eq__iff,axiom,
% 21.13/21.23 ! [V_n_2,V_m_2,T_b] :
% 21.13/21.23 ( class_Nat_Osemiring__char__0(T_b)
% 21.13/21.23 => ( 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)
% 21.13/21.23 <=> V_m_2 = V_n_2 ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zless__iff__Suc__zadd,axiom,
% 21.13/21.23 ! [V_z_2,V_w_2] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 21.13/21.23 <=> ? [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))) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zless__int,axiom,
% 21.13/21.23 ! [V_n_2,V_m_2] :
% 21.13/21.23 ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zero__less__int__conv,axiom,
% 21.13/21.23 ! [V_n_2] :
% 21.13/21.23 ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_int__0,axiom,
% 21.13/21.23 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) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_int__eq__0__conv,axiom,
% 21.13/21.23 ! [V_n_2] :
% 21.13/21.23 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.23 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zadd__int,axiom,
% 21.13/21.23 ! [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)) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zadd__int__left,axiom,
% 21.13/21.23 ! [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) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__nat__less__0__iff,axiom,
% 21.13/21.23 ! [V_m,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.23 => ~ 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))) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__nat__0,axiom,
% 21.13/21.23 ! [T_a] :
% 21.13/21.23 ( class_Rings_Osemiring__1(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__nat__less__iff,axiom,
% 21.13/21.23 ! [V_n_2,V_m_2,T_b] :
% 21.13/21.23 ( class_Rings_Olinordered__semidom(T_b)
% 21.13/21.23 => ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__imp__of__nat__less,axiom,
% 21.13/21.23 ! [V_n,V_m,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.23 => 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))) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__nat__less__imp__less,axiom,
% 21.13/21.23 ! [V_n,V_m,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.23 => ( 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)))
% 21.13/21.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__nat__add,axiom,
% 21.13/21.23 ! [V_n,V_m,T_a] :
% 21.13/21.23 ( class_Rings_Osemiring__1(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_linorder__neqE__linordered__idom,axiom,
% 21.13/21.23 ! [V_y,V_x,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.23 => ( V_x != V_y
% 21.13/21.23 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Inr__inject,axiom,
% 21.13/21.23 ! [V_y,V_x,T_a,T_b] :
% 21.13/21.23 ( hAPP(c_Sum__Type_OInr(T_b,T_a),V_x) = hAPP(c_Sum__Type_OInr(T_b,T_a),V_y)
% 21.13/21.23 => V_x = V_y ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_sum_Osimps_I2_J,axiom,
% 21.13/21.23 ! [V_b_H_2,V_b_2,T_b,T_c] :
% 21.13/21.23 ( hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_2) = hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_H_2)
% 21.13/21.23 <=> V_b_2 = V_b_H_2 ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Inl__inject,axiom,
% 21.13/21.23 ! [V_y,V_x,T_b,T_a] :
% 21.13/21.23 ( hAPP(c_Sum__Type_OInl(T_a,T_b),V_x) = hAPP(c_Sum__Type_OInl(T_a,T_b),V_y)
% 21.13/21.23 => V_x = V_y ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_sum_Osimps_I1_J,axiom,
% 21.13/21.23 ! [V_a_H_2,V_a_2,T_c,T_b] :
% 21.13/21.23 ( hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_2) = hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_H_2)
% 21.13/21.23 <=> V_a_2 = V_a_H_2 ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Projl_Osimps,axiom,
% 21.13/21.23 ! [V_x,T_b,T_a] : c_Sum__Type_OProjl(T_a,T_b,hAPP(c_Sum__Type_OInl(T_a,T_b),V_x)) = V_x ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Projr_Osimps,axiom,
% 21.13/21.23 ! [V_x,T_b,T_a] : c_Sum__Type_OProjr(T_a,T_b,hAPP(c_Sum__Type_OInr(T_b,T_a),V_x)) = V_x ).
% 21.13/21.23
% 21.13/21.23 fof(fact_sum_Orecs_I1_J,axiom,
% 21.13/21.23 ! [V_a_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : c_Sum__Type_Osum_Osum__rec(T_c,T_b,T_d,V_f1_2,V_f2_2,hAPP(c_Sum__Type_OInl(T_c,T_d),V_a_2)) = hAPP(V_f1_2,V_a_2) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_sum_Orecs_I2_J,axiom,
% 21.13/21.23 ! [V_b_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : c_Sum__Type_Osum_Osum__rec(T_c,T_b,T_d,V_f1_2,V_f2_2,hAPP(c_Sum__Type_OInr(T_d,T_c),V_b_2)) = hAPP(V_f2_2,V_b_2) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Suml_Osimps,axiom,
% 21.13/21.23 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_OSuml(T_c,T_b,T_d,V_f_2),hAPP(c_Sum__Type_OInl(T_c,T_d),V_x_2)) = hAPP(V_f_2,V_x_2) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Sumr_Osimps,axiom,
% 21.13/21.23 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_OSumr(T_c,T_b,T_d,V_f_2),hAPP(c_Sum__Type_OInr(T_c,T_d),V_x_2)) = hAPP(V_f_2,V_x_2) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__imp__Suc__add,axiom,
% 21.13/21.23 ! [V_n,V_m] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.23 => ? [B_k] : V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),B_k)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__imp__add__positive,axiom,
% 21.13/21.23 ! [V_j,V_i] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 21.13/21.23 => ? [B_k] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_k))
% 21.13/21.23 & hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),B_k) = V_j ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_gr0__implies__Suc,axiom,
% 21.13/21.23 ! [V_n] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.23 => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_lift__Suc__mono__less,axiom,
% 21.13/21.23 ! [V_n_H_2,V_n_2,V_f_2,T_b] :
% 21.13/21.23 ( class_Orderings_Oorder(T_b)
% 21.13/21.23 => ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_n_H_2))
% 21.13/21.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_n_H_2))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zless__linear,axiom,
% 21.13/21.23 ! [V_y,V_x] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 21.13/21.23 | V_x = V_y
% 21.13/21.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_int__less__0__conv,axiom,
% 21.13/21.23 ! [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))) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zadd__strict__right__mono,axiom,
% 21.13/21.23 ! [V_k,V_j,V_i] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 21.13/21.23 => 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))) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_int__int__eq,axiom,
% 21.13/21.23 ! [V_n_2,V_m_2] :
% 21.13/21.23 ( 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)
% 21.13/21.23 <=> V_m_2 = V_n_2 ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zadd__0__right,axiom,
% 21.13/21.23 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zadd__0,axiom,
% 21.13/21.23 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zadd__commute,axiom,
% 21.13/21.23 ! [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) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zadd__left__commute,axiom,
% 21.13/21.23 ! [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)) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zadd__assoc,axiom,
% 21.13/21.23 ! [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)) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Suml__inject,axiom,
% 21.13/21.23 ! [V_g_2,V_f_2,T_c,T_d,T_b] :
% 21.13/21.23 ( c_Sum__Type_OSuml(T_b,T_d,T_c,V_f_2) = c_Sum__Type_OSuml(T_b,T_d,T_c,V_g_2)
% 21.13/21.23 => V_f_2 = V_g_2 ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Sumr__inject,axiom,
% 21.13/21.23 ! [V_g_2,V_f_2,T_b,T_d,T_c] :
% 21.13/21.23 ( c_Sum__Type_OSumr(T_c,T_d,T_b,V_f_2) = c_Sum__Type_OSumr(T_c,T_d,T_b,V_g_2)
% 21.13/21.23 => V_f_2 = V_g_2 ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 21.13/21.23 ! [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)) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 21.13/21.23 ! [V_y_2,V_x_2] :
% 21.13/21.23 ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 21.13/21.23 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)) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zero__less__imp__eq__int,axiom,
% 21.13/21.23 ! [V_k] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 21.13/21.23 => ? [B_n] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 21.13/21.23 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__int__0__less__iff,axiom,
% 21.13/21.23 ! [V_z_2,T_b] :
% 21.13/21.23 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.23 => ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__int__less__0__iff,axiom,
% 21.13/21.23 ! [V_z_2,T_b] :
% 21.13/21.23 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.23 => ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zmult__zless__mono2__lemma,axiom,
% 21.13/21.23 ! [V_k,V_j,V_i] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 21.13/21.23 => 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))) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_negative__zless__0,axiom,
% 21.13/21.23 ! [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))) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_split__nat,axiom,
% 21.13/21.23 ! [V_i_2,V_P_2] :
% 21.13/21.23 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 21.13/21.23 <=> ( ! [B_n] :
% 21.13/21.23 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 21.13/21.23 => hBOOL(hAPP(V_P_2,B_n)) )
% 21.13/21.23 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.23 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zero__less__nat__eq,axiom,
% 21.13/21.23 ! [V_z_2] :
% 21.13/21.23 ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_negative__zless,axiom,
% 21.13/21.23 ! [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))) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_minus__minus,axiom,
% 21.13/21.23 ! [V_a,T_a] :
% 21.13/21.23 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.23 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zminus__zminus,axiom,
% 21.13/21.23 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__int__minus,axiom,
% 21.13/21.23 ! [V_z,T_a] :
% 21.13/21.23 ( class_Rings_Oring__1(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__int__mult,axiom,
% 21.13/21.23 ! [V_z,V_w,T_a] :
% 21.13/21.23 ( class_Rings_Oring__1(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zmult__commute,axiom,
% 21.13/21.23 ! [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) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_equation__minus__iff,axiom,
% 21.13/21.23 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Ogroup__add(T_b)
% 21.13/21.23 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 21.13/21.23 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 21.13/21.23 ! [V_ry,V_rx,V_lx,T_a] :
% 21.13/21.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 21.13/21.23 ! [V_ry,V_rx,V_lx,T_a] :
% 21.13/21.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zmult__zminus,axiom,
% 21.13/21.23 ! [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)) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_minus__equation__iff,axiom,
% 21.13/21.23 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Ogroup__add(T_b)
% 21.13/21.23 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 21.13/21.23 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__int__eq__iff,axiom,
% 21.13/21.23 ! [V_z_2,V_w_2,T_b] :
% 21.13/21.23 ( class_Int_Oring__char__0(T_b)
% 21.13/21.23 => ( 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)
% 21.13/21.23 <=> V_w_2 = V_z_2 ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_neg__equal__iff__equal,axiom,
% 21.13/21.23 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Ogroup__add(T_b)
% 21.13/21.23 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 21.13/21.23 <=> V_a_2 = V_b_2 ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 21.13/21.23 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.23 ( class_Groups_Oab__semigroup__mult(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 21.13/21.23 ! [V_rx,V_ly,V_lx,T_a] :
% 21.13/21.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zmult__assoc,axiom,
% 21.13/21.23 ! [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)) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 21.13/21.23 ! [V_rx,V_ly,V_lx,T_a] :
% 21.13/21.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 21.13/21.23 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 21.13/21.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.23 => 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))) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 21.13/21.23 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 21.13/21.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 21.13/21.23 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 21.13/21.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_minus__mult__right,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Oring(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_minus__mult__left,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Oring(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_minus__mult__commute,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Oring(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_minus__mult__minus,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Oring(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_square__eq__iff,axiom,
% 21.13/21.23 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.23 ( class_Rings_Oidom(T_b)
% 21.13/21.23 => ( 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)
% 21.13/21.23 <=> ( V_a_2 = V_b_2
% 21.13/21.23 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__nat__mult,axiom,
% 21.13/21.23 ! [V_n,V_m,T_a] :
% 21.13/21.23 ( class_Rings_Osemiring__1(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__int__of__nat,axiom,
% 21.13/21.23 ! [V_k,T_a] :
% 21.13/21.23 ( class_Rings_Oring__1(T_a)
% 21.13/21.23 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.23 => 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)))) )
% 21.13/21.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.23 => 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)) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_nat__zminus__int,axiom,
% 21.13/21.23 ! [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) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_neg__equal__zero,axiom,
% 21.13/21.23 ! [V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Olinordered__ab__group__add(T_b)
% 21.13/21.23 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 21.13/21.23 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_neg__equal__0__iff__equal,axiom,
% 21.13/21.23 ! [V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Ogroup__add(T_b)
% 21.13/21.23 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.23 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_equal__neg__zero,axiom,
% 21.13/21.23 ! [V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Olinordered__ab__group__add(T_b)
% 21.13/21.23 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 21.13/21.23 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_neg__0__equal__iff__equal,axiom,
% 21.13/21.23 ! [V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Ogroup__add(T_b)
% 21.13/21.23 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 21.13/21.23 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_minus__zero,axiom,
% 21.13/21.23 ! [T_a] :
% 21.13/21.23 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.23 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__minus__iff,axiom,
% 21.13/21.23 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_minus__less__iff,axiom,
% 21.13/21.23 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_neg__less__iff__less,axiom,
% 21.13/21.23 ! [V_a_2,V_b_2,T_b] :
% 21.13/21.23 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.13/21.23 => ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_minus__add__cancel,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.23 => 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 ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_add__minus__cancel,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.23 => 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 ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_minus__add,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_minus__add__distrib,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Groups_Oab__group__add(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_divisors__zero,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Ono__zero__divisors(T_a)
% 21.13/21.23 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.23 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.23 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_no__zero__divisors,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Ono__zero__divisors(T_a)
% 21.13/21.23 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.23 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.23 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__eq__0__iff,axiom,
% 21.13/21.23 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.23 ( class_Rings_Oring__no__zero__divisors(T_b)
% 21.13/21.23 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.23 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.23 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__zero__right,axiom,
% 21.13/21.23 ! [V_a,T_a] :
% 21.13/21.23 ( class_Rings_Omult__zero(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__zero__left,axiom,
% 21.13/21.23 ! [V_a,T_a] :
% 21.13/21.23 ( class_Rings_Omult__zero(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 21.13/21.23 ! [V_a,T_a] :
% 21.13/21.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 21.13/21.23 ! [V_a,T_a] :
% 21.13/21.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zminus__0,axiom,
% 21.13/21.23 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) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_nat__int,axiom,
% 21.13/21.23 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 21.13/21.23
% 21.13/21.23 fof(fact_combine__common__factor,axiom,
% 21.13/21.23 ! [V_c,V_b,V_e,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Osemiring(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__semiring__class_Odistrib,axiom,
% 21.13/21.23 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Ocomm__semiring(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_crossproduct__eq,axiom,
% 21.13/21.23 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 21.13/21.23 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 21.13/21.23 => ( 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))
% 21.13/21.23 <=> ( V_w_2 = V_x_2
% 21.13/21.23 | V_y_2 = V_z_2 ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 21.13/21.23 ! [V_b,V_m,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 21.13/21.23 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_crossproduct__noteq,axiom,
% 21.13/21.23 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.13/21.23 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 21.13/21.23 => ( ( V_a_2 != V_b_2
% 21.13/21.23 & V_c_2 != V_d_2 )
% 21.13/21.23 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_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_c_2)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 21.13/21.23 ! [V_z,V_y,V_x,T_a] :
% 21.13/21.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zminus__zadd__distrib,axiom,
% 21.13/21.23 ! [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)) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zadd__zmult__distrib,axiom,
% 21.13/21.23 ! [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)) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zadd__zmult__distrib2,axiom,
% 21.13/21.23 ! [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)) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 21.13/21.23 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__int__int__eq,axiom,
% 21.13/21.23 ! [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) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_less__minus__self__iff,axiom,
% 21.13/21.23 ! [V_a_2,T_b] :
% 21.13/21.23 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_neg__less__nonneg,axiom,
% 21.13/21.23 ! [V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Olinordered__ab__group__add(T_b)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_neg__less__0__iff__less,axiom,
% 21.13/21.23 ! [V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.13/21.23 => ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_neg__0__less__iff__less,axiom,
% 21.13/21.23 ! [V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.13/21.23 => ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_right__minus,axiom,
% 21.13/21.23 ! [V_a,T_a] :
% 21.13/21.23 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 21.13/21.23 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.23 ( class_Groups_Ogroup__add(T_b)
% 21.13/21.23 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 21.13/21.23 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_left__minus,axiom,
% 21.13/21.23 ! [V_a,T_a] :
% 21.13/21.23 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_ab__left__minus,axiom,
% 21.13/21.23 ! [V_a,T_a] :
% 21.13/21.23 ( class_Groups_Oab__group__add(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_minus__unique,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.23 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.23 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_nat__0,axiom,
% 21.13/21.23 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__strict__left__mono__neg,axiom,
% 21.13/21.23 ! [V_c,V_a,V_b,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__ring__strict(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.23 => 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))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__strict__right__mono__neg,axiom,
% 21.13/21.23 ! [V_c,V_a,V_b,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__ring__strict(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.23 => 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))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_comm__mult__strict__left__mono,axiom,
% 21.13/21.23 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.23 => 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))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__strict__left__mono,axiom,
% 21.13/21.23 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.23 => 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))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__strict__right__mono,axiom,
% 21.13/21.23 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.23 => 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))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__neg__neg,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__ring__strict(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.23 => 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))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__neg__pos,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.23 => 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))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__less__cancel__left__neg,axiom,
% 21.13/21.23 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 21.13/21.23 ( class_Rings_Olinordered__ring__strict(T_b)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zero__less__mult__pos2,axiom,
% 21.13/21.23 ! [V_a,V_b,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.23 => ( 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)))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zero__less__mult__pos,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.23 => ( 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)))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__pos__neg2,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.23 => 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))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__pos__neg,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.23 => 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))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__pos__pos,axiom,
% 21.13/21.23 ! [V_b,V_a,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.23 => 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))) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__less__cancel__left__pos,axiom,
% 21.13/21.23 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 21.13/21.23 ( class_Rings_Olinordered__ring__strict(T_b)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__less__cancel__left__disj,axiom,
% 21.13/21.23 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 21.13/21.23 ( class_Rings_Olinordered__ring__strict(T_b)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 21.13/21.23 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 21.13/21.23 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_mult__less__cancel__right__disj,axiom,
% 21.13/21.23 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 21.13/21.23 ( class_Rings_Olinordered__ring__strict(T_b)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
% 21.13/21.23 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 21.13/21.23 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_not__square__less__zero,axiom,
% 21.13/21.23 ! [V_a,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__ring(T_a)
% 21.13/21.23 => ~ 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))) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_sum__squares__eq__zero__iff,axiom,
% 21.13/21.23 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.23 ( class_Rings_Olinordered__ring__strict(T_b)
% 21.13/21.23 => ( 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)
% 21.13/21.23 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.23 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_add__scale__eq__noteq,axiom,
% 21.13/21.23 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 21.13/21.23 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 21.13/21.23 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.23 => ( ( V_a = V_b
% 21.13/21.23 & V_c != V_d )
% 21.13/21.23 => 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)) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zadd__zminus__inverse2,axiom,
% 21.13/21.23 ! [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) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_negative__eq__positive,axiom,
% 21.13/21.23 ! [V_m_2,V_n_2] :
% 21.13/21.23 ( 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)
% 21.13/21.23 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.23 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_not__int__zless__negative,axiom,
% 21.13/21.23 ! [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)))) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zmult__zless__mono2,axiom,
% 21.13/21.23 ! [V_k,V_j,V_i] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 21.13/21.23 => 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))) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__int__eq__0__iff,axiom,
% 21.13/21.23 ! [V_z_2,T_b] :
% 21.13/21.23 ( class_Int_Oring__char__0(T_b)
% 21.13/21.23 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.23 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__int__0__eq__iff,axiom,
% 21.13/21.23 ! [V_z_2,T_b] :
% 21.13/21.23 ( class_Int_Oring__char__0(T_b)
% 21.13/21.23 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 21.13/21.23 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__int__0,axiom,
% 21.13/21.23 ! [T_a] :
% 21.13/21.23 ( class_Rings_Oring__1(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__int__less__iff,axiom,
% 21.13/21.23 ! [V_z_2,V_w_2,T_b] :
% 21.13/21.23 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.23 => ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__int__add,axiom,
% 21.13/21.23 ! [V_z,V_w,T_a] :
% 21.13/21.23 ( class_Rings_Oring__1(T_a)
% 21.13/21.23 => 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__int__of__nat__eq,axiom,
% 21.13/21.23 ! [V_n,T_a] :
% 21.13/21.23 ( class_Rings_Oring__1(T_a)
% 21.13/21.23 => 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) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_nat__mono__iff,axiom,
% 21.13/21.23 ! [V_w_2,V_z_2] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 21.13/21.23 => ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zless__nat__conj,axiom,
% 21.13/21.23 ! [V_z_2,V_w_2] :
% 21.13/21.23 ( 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)))
% 21.13/21.23 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 21.13/21.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_zless__nat__eq__int__zless,axiom,
% 21.13/21.23 ! [V_z_2,V_m_2] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 21.13/21.23 <=> 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)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_sum__squares__gt__zero__iff,axiom,
% 21.13/21.23 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.23 ( class_Rings_Olinordered__ring__strict(T_b)
% 21.13/21.23 => ( 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))))
% 21.13/21.23 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.23 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_not__sum__squares__lt__zero,axiom,
% 21.13/21.23 ! [V_y,V_x,T_a] :
% 21.13/21.23 ( class_Rings_Olinordered__ring(T_a)
% 21.13/21.23 => ~ 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))) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 21.13/21.23 ! [V_y_2,V_x_2] :
% 21.13/21.23 ( 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)
% 21.13/21.23 <=> V_x_2 = V_y_2 ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_nat__aux__def,axiom,
% 21.13/21.23 ! [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) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_negD,axiom,
% 21.13/21.23 ! [V_x] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.23 => ? [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))) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_nat__less__iff,axiom,
% 21.13/21.23 ! [V_m_2,V_w_2] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 21.13/21.23 <=> 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))) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_one__less__nat__eq,axiom,
% 21.13/21.23 ! [V_z_2] :
% 21.13/21.23 ( 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)))
% 21.13/21.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_of__nat__nat,axiom,
% 21.13/21.23 ! [V_z,T_a] :
% 21.13/21.23 ( class_Rings_Oring__1(T_a)
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 21.13/21.23 => 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) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_not__zle__0__negative,axiom,
% 21.13/21.23 ! [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))))) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 21.13/21.23 ! [V_y,V_x] :
% 21.13/21.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 21.13/21.23 => 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)) ) ) ).
% 21.13/21.23
% 21.13/21.23 fof(fact_nat__add__distrib,axiom,
% 21.13/21.24 ! [V_z_H,V_z] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 21.13/21.24 => 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)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__eq__iff2,axiom,
% 21.13/21.24 ! [V_w_2,V_m_2] :
% 21.13/21.24 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 21.13/21.24 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 21.13/21.24 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 21.13/21.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 21.13/21.24 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__eq__iff,axiom,
% 21.13/21.24 ! [V_m_2,V_w_2] :
% 21.13/21.24 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 21.13/21.24 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 21.13/21.24 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 21.13/21.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 21.13/21.24 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_negative__zle,axiom,
% 21.13/21.24 ! [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))) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 21.13/21.24 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))) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__mult__commute,axiom,
% 21.13/21.24 ! [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) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__mult__assoc,axiom,
% 21.13/21.24 ! [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)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zle__antisym,axiom,
% 21.13/21.24 ! [V_w,V_z] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 21.13/21.24 => V_z = V_w ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zle__trans,axiom,
% 21.13/21.24 ! [V_k,V_j,V_i] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zle__linear,axiom,
% 21.13/21.24 ! [V_w,V_z] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 21.13/21.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_one__reorient,axiom,
% 21.13/21.24 ! [V_x_2,T_b] :
% 21.13/21.24 ( class_Groups_Oone(T_b)
% 21.13/21.24 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 21.13/21.24 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zle__refl,axiom,
% 21.13/21.24 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_not__one__le__zero,axiom,
% 21.13/21.24 ! [T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.24 => ~ 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zero__le__one,axiom,
% 21.13/21.24 ! [T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.24 => 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_of__nat__1,axiom,
% 21.13/21.24 ! [T_a] :
% 21.13/21.24 ( class_Rings_Osemiring__1(T_a)
% 21.13/21.24 => 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) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_of__nat__le__iff,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2,T_b] :
% 21.13/21.24 ( class_Rings_Olinordered__semidom(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_of__int__le__iff,axiom,
% 21.13/21.24 ! [V_z_2,V_w_2,T_b] :
% 21.13/21.24 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_of__int__1,axiom,
% 21.13/21.24 ! [T_a] :
% 21.13/21.24 ( class_Rings_Oring__1(T_a)
% 21.13/21.24 => 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) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__right__le__one__le,axiom,
% 21.13/21.24 ! [V_y,V_x,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 21.13/21.24 => 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)) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__left__le__one__le,axiom,
% 21.13/21.24 ! [V_y,V_x,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 21.13/21.24 => 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)) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_int__one__le__iff__zero__less,axiom,
% 21.13/21.24 ! [V_z_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zle__add1__eq__le,axiom,
% 21.13/21.24 ! [V_z_2,V_w_2] :
% 21.13/21.24 ( 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))))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add1__zle__eq,axiom,
% 21.13/21.24 ! [V_z_2,V_w_2] :
% 21.13/21.24 ( 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))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zless__imp__add1__zle,axiom,
% 21.13/21.24 ! [V_z,V_w] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 21.13/21.24 => 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)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_one__neq__zero,axiom,
% 21.13/21.24 ! [T_a] :
% 21.13/21.24 ( class_Rings_Ozero__neq__one(T_a)
% 21.13/21.24 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zero__neq__one,axiom,
% 21.13/21.24 ! [T_a] :
% 21.13/21.24 ( class_Rings_Ozero__neq__one(T_a)
% 21.13/21.24 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult_Ocomm__neutral,axiom,
% 21.13/21.24 ! [V_a,T_a] :
% 21.13/21.24 ( class_Groups_Ocomm__monoid__mult(T_a)
% 21.13/21.24 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 21.13/21.24 ! [V_a,T_a] :
% 21.13/21.24 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.24 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__1__right,axiom,
% 21.13/21.24 ! [V_a,T_a] :
% 21.13/21.24 ( class_Groups_Omonoid__mult(T_a)
% 21.13/21.24 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__1,axiom,
% 21.13/21.24 ! [V_a,T_a] :
% 21.13/21.24 ( class_Groups_Ocomm__monoid__mult(T_a)
% 21.13/21.24 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 21.13/21.24 ! [V_a,T_a] :
% 21.13/21.24 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.24 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__1__left,axiom,
% 21.13/21.24 ! [V_a,T_a] :
% 21.13/21.24 ( class_Groups_Omonoid__mult(T_a)
% 21.13/21.24 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__le__cancel__right,axiom,
% 21.13/21.24 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 21.13/21.24 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__le__cancel__left,axiom,
% 21.13/21.24 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 21.13/21.24 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__right__mono,axiom,
% 21.13/21.24 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__left__mono,axiom,
% 21.13/21.24 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__mono,axiom,
% 21.13/21.24 ! [V_d,V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__le__imp__le__right,axiom,
% 21.13/21.24 ! [V_b,V_c,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__le__imp__le__left,axiom,
% 21.13/21.24 ! [V_b,V_a,V_c,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__cancel2,axiom,
% 21.13/21.24 ! [V_n_2,V_k_2,V_m_2] :
% 21.13/21.24 ( 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)
% 21.13/21.24 <=> ( V_m_2 = V_n_2
% 21.13/21.24 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__cancel1,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.24 ( 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)
% 21.13/21.24 <=> ( V_m_2 = V_n_2
% 21.13/21.24 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__is__0,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.24 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.24 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__0__right,axiom,
% 21.13/21.24 ! [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) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__0,axiom,
% 21.13/21.24 ! [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) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Suc__mult__cancel1,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.24 ( 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)
% 21.13/21.24 <=> V_m_2 = V_n_2 ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__imp__neg__le,axiom,
% 21.13/21.24 ! [V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__ab__group__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_neg__le__iff__le,axiom,
% 21.13/21.24 ! [V_a_2,V_b_2,T_b] :
% 21.13/21.24 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_minus__le__iff,axiom,
% 21.13/21.24 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.24 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.13/21.24 => ( 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))
% 21.13/21.24 <=> 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)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__minus__iff,axiom,
% 21.13/21.24 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.24 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__mult__distrib,axiom,
% 21.13/21.24 ! [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)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__mult__distrib2,axiom,
% 21.13/21.24 ! [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)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 21.13/21.24 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))) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_int__0__neq__1,axiom,
% 21.13/21.24 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zless__le,axiom,
% 21.13/21.24 ! [V_w_2,V_z_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 21.13/21.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 21.13/21.24 & V_z_2 != V_w_2 ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zadd__left__mono,axiom,
% 21.13/21.24 ! [V_k,V_j,V_i] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 21.13/21.24 => 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zmult__1__right,axiom,
% 21.13/21.24 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zmult__1,axiom,
% 21.13/21.24 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 21.13/21.24
% 21.13/21.24 fof(fact_convex__bound__le,axiom,
% 21.13/21.24 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semiring__1(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 21.13/21.24 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 21.13/21.24 => 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)) ) ) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__imp__0__less,axiom,
% 21.13/21.24 ! [V_z] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 21.13/21.24 => 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 21.13/21.24 ! [V_y,V_x] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 21.13/21.24 => 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)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__mult__distrib,axiom,
% 21.13/21.24 ! [V_z_H,V_z] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 21.13/21.24 => 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)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_of__int__0__le__iff,axiom,
% 21.13/21.24 ! [V_z_2,T_b] :
% 21.13/21.24 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_of__int__le__0__iff,axiom,
% 21.13/21.24 ! [V_z_2,T_b] :
% 21.13/21.24 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_convex__bound__lt,axiom,
% 21.13/21.24 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 21.13/21.24 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 21.13/21.24 => 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)) ) ) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 21.13/21.24 ! [V_z] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 21.13/21.24 => 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)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_not__one__less__zero,axiom,
% 21.13/21.24 ! [T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.24 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zero__less__one,axiom,
% 21.13/21.24 ! [T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__mult__distrib__neg,axiom,
% 21.13/21.24 ! [V_z_H,V_z] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.24 => 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_less__add__one,axiom,
% 21.13/21.24 ! [V_a,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.24 => 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)))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_less__1__mult,axiom,
% 21.13/21.24 ! [V_n,V_m,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 21.13/21.24 ! [V_m,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.24 => 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) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 21.13/21.24 ! [V_a,V_m,T_a] :
% 21.13/21.24 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.24 => 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) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 21.13/21.24 ! [V_m,T_a] :
% 21.13/21.24 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.24 => 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) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__nonpos__nonpos,axiom,
% 21.13/21.24 ! [V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__increasing2,axiom,
% 21.13/21.24 ! [V_a,V_b,V_c,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__increasing,axiom,
% 21.13/21.24 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__nonneg__eq__0__iff,axiom,
% 21.13/21.24 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.24 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 21.13/21.24 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.24 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.24 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__nonneg__nonneg,axiom,
% 21.13/21.24 ! [V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 21.13/21.24 ! [V_a_2,T_b] :
% 21.13/21.24 ( class_Groups_Olinordered__ab__group__add(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 21.13/21.24 ! [V_a_2,T_b] :
% 21.13/21.24 ( class_Groups_Olinordered__ab__group__add(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zero__le__square,axiom,
% 21.13/21.24 ! [V_a,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__ring(T_a)
% 21.13/21.24 => 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zero__le__mult__iff,axiom,
% 21.13/21.24 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.24 ( class_Rings_Olinordered__ring__strict(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 21.13/21.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 21.13/21.24 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__le__0__iff,axiom,
% 21.13/21.24 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.24 ( class_Rings_Olinordered__ring__strict(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 21.13/21.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 21.13/21.24 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__nonneg__nonneg,axiom,
% 21.13/21.24 ! [V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Oordered__cancel__semiring(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__nonneg__nonpos,axiom,
% 21.13/21.24 ! [V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Oordered__cancel__semiring(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__nonneg__nonpos2,axiom,
% 21.13/21.24 ! [V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Oordered__cancel__semiring(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__nonpos__nonneg,axiom,
% 21.13/21.24 ! [V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Oordered__cancel__semiring(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__nonpos__nonpos,axiom,
% 21.13/21.24 ! [V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Oordered__ring(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__right__mono,axiom,
% 21.13/21.24 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Oordered__semiring(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__left__mono,axiom,
% 21.13/21.24 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Oordered__semiring(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_comm__mult__left__mono,axiom,
% 21.13/21.24 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Oordered__comm__semiring(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__right__mono__neg,axiom,
% 21.13/21.24 ! [V_c,V_a,V_b,T_a] :
% 21.13/21.24 ( class_Rings_Oordered__ring(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__left__mono__neg,axiom,
% 21.13/21.24 ! [V_c,V_a,V_b,T_a] :
% 21.13/21.24 ( class_Rings_Oordered__ring(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__mono_H,axiom,
% 21.13/21.24 ! [V_d,V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Oordered__semiring(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => 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))) ) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__mono,axiom,
% 21.13/21.24 ! [V_d,V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Oordered__semiring(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => 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))) ) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_split__mult__pos__le,axiom,
% 21.13/21.24 ! [V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Oordered__ring(T_a)
% 21.13/21.24 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 21.13/21.24 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_split__mult__neg__le,axiom,
% 21.13/21.24 ! [V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Oordered__cancel__semiring(T_a)
% 21.13/21.24 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 21.13/21.24 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__le__less__mono,axiom,
% 21.13/21.24 ! [V_d,V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__less__le__mono,axiom,
% 21.13/21.24 ! [V_d,V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_square__eq__1__iff,axiom,
% 21.13/21.24 ! [V_x_2,T_b] :
% 21.13/21.24 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 21.13/21.24 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 21.13/21.24 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 21.13/21.24 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 21.13/21.24 ! [V_x,T_a] :
% 21.13/21.24 ( class_Rings_Ocomm__ring__1(T_a)
% 21.13/21.24 => 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) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_minus__le__self__iff,axiom,
% 21.13/21.24 ! [V_a_2,T_b] :
% 21.13/21.24 ( class_Groups_Olinordered__ab__group__add(T_b)
% 21.13/21.24 => ( 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))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_neg__le__0__iff__le,axiom,
% 21.13/21.24 ! [V_a_2,T_b] :
% 21.13/21.24 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__minus__self__iff,axiom,
% 21.13/21.24 ! [V_a_2,T_b] :
% 21.13/21.24 ( class_Groups_Olinordered__ab__group__add(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_neg__0__le__iff__le,axiom,
% 21.13/21.24 ! [V_a_2,T_b] :
% 21.13/21.24 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__eq__1__iff,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( 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))
% 21.13/21.24 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 21.13/21.24 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_of__nat__0__le__iff,axiom,
% 21.13/21.24 ! [V_n,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.24 => 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zero__le__imp__of__nat,axiom,
% 21.13/21.24 ! [V_m,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.24 => 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__less__mono2,axiom,
% 21.13/21.24 ! [V_k,V_j,V_i] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__less__mono1,axiom,
% 21.13/21.24 ! [V_k,V_j,V_i] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__less__cancel2,axiom,
% 21.13/21.24 ! [V_n_2,V_k_2,V_m_2] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 21.13/21.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__less__cancel1,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 21.13/21.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__0__less__mult__iff,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 21.13/21.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Suc__mult__less__cancel1,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__Suc,axiom,
% 21.13/21.24 ! [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)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__Suc__right,axiom,
% 21.13/21.24 ! [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)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 21.13/21.24 ! [V_y,V_x] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_int__0__less__1,axiom,
% 21.13/21.24 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))) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zero__zle__int,axiom,
% 21.13/21.24 ! [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))) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 21.13/21.24 ! [V_P_2] :
% 21.13/21.24 ( ! [B_x] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 21.13/21.24 => hBOOL(hAPP(V_P_2,B_x)) )
% 21.13/21.24 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 21.13/21.24 ! [V_P_2] :
% 21.13/21.24 ( ? [B_x] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 21.13/21.24 & hBOOL(hAPP(V_P_2,B_x)) )
% 21.13/21.24 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 21.13/21.24 ! [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))) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_eq__nat__nat__iff,axiom,
% 21.13/21.24 ! [V_z_H_2,V_z_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 21.13/21.24 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 21.13/21.24 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 21.13/21.24 ! [V_y_2,V_x_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 21.13/21.24 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 21.13/21.24 <=> V_x_2 = V_y_2 ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_all__nat,axiom,
% 21.13/21.24 ! [V_P_2] :
% 21.13/21.24 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 21.13/21.24 <=> ! [B_x] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 21.13/21.24 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_ex__nat,axiom,
% 21.13/21.24 ! [V_P_2] :
% 21.13/21.24 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 21.13/21.24 <=> ? [B_x] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 21.13/21.24 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zadd__zless__mono,axiom,
% 21.13/21.24 ! [V_z,V_z_H,V_w,V_w_H] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 21.13/21.24 ! [V_y,V_x] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_odd__nonzero,axiom,
% 21.13/21.24 ! [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) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_int__mult,axiom,
% 21.13/21.24 ! [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)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zmult__int,axiom,
% 21.13/21.24 ! [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)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 21.13/21.24 ! [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)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zless__add1__eq,axiom,
% 21.13/21.24 ! [V_z_2,V_w_2] :
% 21.13/21.24 ( 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))))
% 21.13/21.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 21.13/21.24 | V_w_2 = V_z_2 ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zle__iff__zadd,axiom,
% 21.13/21.24 ! [V_z_2,V_w_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 21.13/21.24 <=> ? [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)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zero__less__two,axiom,
% 21.13/21.24 ! [T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.24 => 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)))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__nonpos__neg,axiom,
% 21.13/21.24 ! [V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__neg__nonpos,axiom,
% 21.13/21.24 ! [V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__strict__increasing2,axiom,
% 21.13/21.24 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__strict__increasing,axiom,
% 21.13/21.24 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__nonneg__pos,axiom,
% 21.13/21.24 ! [V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__pos__nonneg,axiom,
% 21.13/21.24 ! [V_b,V_a,T_a] :
% 21.13/21.24 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.24 => 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))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__le__cancel__left__pos,axiom,
% 21.13/21.24 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 21.13/21.24 ( class_Rings_Olinordered__ring__strict(T_b)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__le__cancel__left__neg,axiom,
% 21.13/21.24 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 21.13/21.24 ( class_Rings_Olinordered__ring__strict(T_b)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__strict__mono,axiom,
% 21.13/21.24 ! [V_d,V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => 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))) ) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__strict__mono_H,axiom,
% 21.13/21.24 ! [V_d,V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => 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))) ) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__less__le__imp__less,axiom,
% 21.13/21.24 ! [V_d,V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => 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))) ) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__le__less__imp__less,axiom,
% 21.13/21.24 ! [V_d,V_c,V_b,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => 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))) ) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__right__less__imp__less,axiom,
% 21.13/21.24 ! [V_b,V_c,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semiring(T_a)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__less__imp__less__right,axiom,
% 21.13/21.24 ! [V_b,V_c,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__left__less__imp__less,axiom,
% 21.13/21.24 ! [V_b,V_a,V_c,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semiring(T_a)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__less__imp__less__left,axiom,
% 21.13/21.24 ! [V_b,V_a,V_c,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__right__le__imp__le,axiom,
% 21.13/21.24 ! [V_b,V_c,V_a,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__left__le__imp__le,axiom,
% 21.13/21.24 ! [V_b,V_a,V_c,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_sum__squares__ge__zero,axiom,
% 21.13/21.24 ! [V_y,V_x,T_a] :
% 21.13/21.24 ( class_Rings_Olinordered__ring(T_a)
% 21.13/21.24 => 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)))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_sum__squares__le__zero__iff,axiom,
% 21.13/21.24 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.24 ( class_Rings_Olinordered__ring__strict(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.24 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_of__nat__Suc,axiom,
% 21.13/21.24 ! [V_m,T_a] :
% 21.13/21.24 ( class_Rings_Osemiring__1(T_a)
% 21.13/21.24 => 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)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_n__less__m__mult__n,axiom,
% 21.13/21.24 ! [V_m,V_n] :
% 21.13/21.24 ( 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))
% 21.13/21.24 => ( 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))
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_n__less__n__mult__m,axiom,
% 21.13/21.24 ! [V_m,V_n] :
% 21.13/21.24 ( 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))
% 21.13/21.24 => ( 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))
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_one__less__mult,axiom,
% 21.13/21.24 ! [V_m,V_n] :
% 21.13/21.24 ( 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))
% 21.13/21.24 => ( 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))
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_int__le__0__conv,axiom,
% 21.13/21.24 ! [V_n_2] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__0__iff,axiom,
% 21.13/21.24 ! [V_i_2] :
% 21.13/21.24 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__le__0,axiom,
% 21.13/21.24 ! [V_z] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.24 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_int__Suc0__eq__1,axiom,
% 21.13/21.24 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) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__1,axiom,
% 21.13/21.24 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_odd__less__0,axiom,
% 21.13/21.24 ! [V_z_2] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__0__le,axiom,
% 21.13/21.24 ! [V_z] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 21.13/21.24 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_int__eq__iff,axiom,
% 21.13/21.24 ! [V_z_2,V_m_2] :
% 21.13/21.24 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 21.13/21.24 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 21.13/21.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_int__nat__eq,axiom,
% 21.13/21.24 ! [V_z] :
% 21.13/21.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 21.13/21.24 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 21.13/21.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 21.13/21.24 => 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) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_pos__zmult__eq__1__iff,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 21.13/21.24 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 21.13/21.24 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 21.13/21.24 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_int__Suc,axiom,
% 21.13/21.24 ! [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)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_int__zle__neg,axiom,
% 21.13/21.24 ! [V_m_2,V_n_2] :
% 21.13/21.24 ( 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))))
% 21.13/21.24 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.24 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_negative__zle__0,axiom,
% 21.13/21.24 ! [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))) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__less__eq__zless,axiom,
% 21.13/21.24 ! [V_z_2,V_w_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 21.13/21.24 ! [V_y_2,V_x_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_self__quotient__aux1,axiom,
% 21.13/21.24 ! [V_q,V_r,V_a] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.13/21.24 => ( 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))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_self__quotient__aux2,axiom,
% 21.13/21.24 ! [V_q,V_r,V_a] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.13/21.24 => ( 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))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 21.13/21.24 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 21.13/21.24 ( 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)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_unique__quotient__lemma__neg,axiom,
% 21.13/21.24 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zdiv__mono2__lemma,axiom,
% 21.13/21.24 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 21.13/21.24 ( 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)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_unique__quotient__lemma,axiom,
% 21.13/21.24 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_q__neg__lemma,axiom,
% 21.13/21.24 ! [V_r_H,V_q_H,V_b_H] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_q__pos__lemma,axiom,
% 21.13/21.24 ! [V_r_H,V_q_H,V_b_H] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__mult__eq__cancel1,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 21.13/21.24 => ( 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)
% 21.13/21.24 <=> V_m_2 = V_n_2 ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le0,axiom,
% 21.13/21.24 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__antisym,axiom,
% 21.13/21.24 ! [V_n,V_m] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 21.13/21.24 => V_m = V_n ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__trans,axiom,
% 21.13/21.24 ! [V_k,V_j,V_i] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_eq__imp__le,axiom,
% 21.13/21.24 ! [V_n,V_m] :
% 21.13/21.24 ( V_m = V_n
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__le__linear,axiom,
% 21.13/21.24 ! [V_n,V_m] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 21.13/21.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__refl,axiom,
% 21.13/21.24 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 21.13/21.24 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__0__eq,axiom,
% 21.13/21.24 ! [V_n_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 21.13/21.24 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Suc__leD,axiom,
% 21.13/21.24 ! [V_n,V_m] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__SucE,axiom,
% 21.13/21.24 ! [V_n,V_m] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 21.13/21.24 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 21.13/21.24 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__SucI,axiom,
% 21.13/21.24 ! [V_n,V_m] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Suc__le__mono,axiom,
% 21.13/21.24 ! [V_m_2,V_n_2] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__Suc__eq,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 21.13/21.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.13/21.24 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_not__less__eq__eq,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Suc__n__not__le__n,axiom,
% 21.13/21.24 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_termination__basic__simps_I5_J,axiom,
% 21.13/21.24 ! [V_y,V_x] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__less__le,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 21.13/21.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.13/21.24 & V_m_2 != V_n_2 ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__eq__less__or__eq,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.13/21.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 21.13/21.24 | V_m_2 = V_n_2 ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_less__imp__le__nat,axiom,
% 21.13/21.24 ! [V_n,V_m] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__neq__implies__less,axiom,
% 21.13/21.24 ! [V_n,V_m] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 21.13/21.24 => ( V_m != V_n
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_less__or__eq__imp__le,axiom,
% 21.13/21.24 ! [V_n,V_m] :
% 21.13/21.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.24 | V_m = V_n )
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_termination__basic__simps_I4_J,axiom,
% 21.13/21.24 ! [V_y,V_z,V_x] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 21.13/21.24 => 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_termination__basic__simps_I3_J,axiom,
% 21.13/21.24 ! [V_z,V_y,V_x] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 21.13/21.24 => 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__add2,axiom,
% 21.13/21.24 ! [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))) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__add1,axiom,
% 21.13/21.24 ! [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))) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__iff__add,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.13/21.24 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__add__left__cancel__le,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_trans__le__add1,axiom,
% 21.13/21.24 ! [V_m,V_j,V_i] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.13/21.24 => 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_trans__le__add2,axiom,
% 21.13/21.24 ! [V_m,V_j,V_i] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.13/21.24 => 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__le__mono1,axiom,
% 21.13/21.24 ! [V_k,V_j,V_i] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.13/21.24 => 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__le__mono,axiom,
% 21.13/21.24 ! [V_l,V_k,V_j,V_i] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__leD2,axiom,
% 21.13/21.24 ! [V_n,V_k,V_m] :
% 21.13/21.24 ( 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))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__leD1,axiom,
% 21.13/21.24 ! [V_n,V_k,V_m] :
% 21.13/21.24 ( 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))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_add__leE,axiom,
% 21.13/21.24 ! [V_n,V_k,V_m] :
% 21.13/21.24 ( 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))
% 21.13/21.24 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 21.13/21.24 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__le__mono,axiom,
% 21.13/21.24 ! [V_l,V_k,V_j,V_i] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__le__mono2,axiom,
% 21.13/21.24 ! [V_k,V_j,V_i] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.13/21.24 => 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__le__mono1,axiom,
% 21.13/21.24 ! [V_k,V_j,V_i] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.13/21.24 => 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))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__cube,axiom,
% 21.13/21.24 ! [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)))) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__square,axiom,
% 21.13/21.24 ! [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))) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__mult__eq__1__iff,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 21.13/21.24 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 21.13/21.24 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__mult__1__right,axiom,
% 21.13/21.24 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__1__eq__mult__iff,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 21.13/21.24 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 21.13/21.24 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__mult__1,axiom,
% 21.13/21.24 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 21.13/21.24
% 21.13/21.24 fof(fact_evaln__nonstrict,axiom,
% 21.13/21.24 ! [V_m,V_t,V_n,V_s,V_c] :
% 21.13/21.24 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 21.13/21.24 => c_Natural_Oevaln(V_c,V_s,V_m,V_t) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__mult__le__cancel1,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_One__nat__def,axiom,
% 21.13/21.24 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_less__eq__Suc__le,axiom,
% 21.13/21.24 ! [V_m_2,V_n_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_less__Suc__eq__le,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Suc__le__eq,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__imp__less__Suc,axiom,
% 21.13/21.24 ! [V_n,V_m] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Suc__leI,axiom,
% 21.13/21.24 ! [V_n,V_m] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_le__less__Suc__eq,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 21.13/21.24 <=> V_n_2 = V_m_2 ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Suc__le__lessD,axiom,
% 21.13/21.24 ! [V_n,V_m] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Suc__eq__plus1__left,axiom,
% 21.13/21.24 ! [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) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Suc__eq__plus1,axiom,
% 21.13/21.24 ! [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)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__eq__self__implies__10,axiom,
% 21.13/21.24 ! [V_n,V_m] :
% 21.13/21.24 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 21.13/21.24 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 21.13/21.24 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_Suc__mult__le__cancel1,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 21.13/21.24 ! [V_y_2,V_x_2] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_zle__int,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 21.13/21.24 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)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_int__1,axiom,
% 21.13/21.24 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) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 21.13/21.24 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_one__le__mult__iff,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 <=> ( 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))
% 21.13/21.24 & 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)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__le__cancel1,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_mult__le__cancel2,axiom,
% 21.13/21.24 ! [V_n_2,V_k_2,V_m_2] :
% 21.13/21.24 ( 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)))
% 21.13/21.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 21.13/21.24 ! [V_y_2,V_x_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__le__eq__zle,axiom,
% 21.13/21.24 ! [V_z_2,V_w_2] :
% 21.13/21.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 21.13/21.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.24 ( 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)
% 21.13/21.24 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.24 | V_m_2 = V_n_2 ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_left__add__mult__distrib,axiom,
% 21.13/21.24 ! [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) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_nat__mult__less__cancel1,axiom,
% 21.13/21.24 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_transfer__morphism__nat__int,axiom,
% 21.13/21.24 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))) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_order__refl,axiom,
% 21.13/21.24 ! [V_x,T_a] :
% 21.13/21.24 ( class_Orderings_Opreorder(T_a)
% 21.13/21.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_compl__mono,axiom,
% 21.13/21.24 ! [V_y,V_x,T_a] :
% 21.13/21.24 ( class_Lattices_Oboolean__algebra(T_a)
% 21.13/21.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.13/21.24 => 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))) ) ) ).
% 21.13/21.24
% 21.13/21.24 fof(fact_compl__le__compl__iff,axiom,
% 21.13/21.24 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.24 ( class_Lattices_Oboolean__algebra(T_b)
% 21.13/21.24 => ( 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)))
% 21.13/21.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_xt1_I8_J,axiom,
% 21.13/21.25 ! [V_z,V_x,V_y,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__le__less__trans,axiom,
% 21.13/21.25 ! [V_z,V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Opreorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_xt1_I7_J,axiom,
% 21.13/21.25 ! [V_z,V_x,V_y,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__less__le__trans,axiom,
% 21.13/21.25 ! [V_z,V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Opreorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_xt1_I11_J,axiom,
% 21.13/21.25 ! [V_a,V_b,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 21.13/21.25 => ( V_a != V_b
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__fun__def,axiom,
% 21.13/21.25 ! [V_g_2,V_f_2,T_b,T_c] :
% 21.13/21.25 ( class_Orderings_Oord(T_c)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 21.13/21.25 <=> ! [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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_linorder__linear,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.13/21.25 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__eq__iff,axiom,
% 21.13/21.25 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.25 ( class_Orderings_Oorder(T_b)
% 21.13/21.25 => ( V_x_2 = V_y_2
% 21.13/21.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.13/21.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__eq__refl,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Opreorder(T_a)
% 21.13/21.25 => ( V_x = V_y
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__funD,axiom,
% 21.13/21.25 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 21.13/21.25 ( class_Orderings_Oord(T_c)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__antisym__conv,axiom,
% 21.13/21.25 ! [V_x_2,V_y_2,T_b] :
% 21.13/21.25 ( class_Orderings_Oorder(T_b)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.13/21.25 <=> V_x_2 = V_y_2 ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_ord__eq__le__trans,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Orderings_Oord(T_a)
% 21.13/21.25 => ( V_a = V_b
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_xt1_I3_J,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( V_a = V_b
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_ord__le__eq__trans,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Orderings_Oord(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.25 => ( V_b = V_c
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_xt1_I4_J,axiom,
% 21.13/21.25 ! [V_c,V_a,V_b,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 21.13/21.25 => ( V_b = V_c
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__antisym,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 21.13/21.25 => V_x = V_y ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__trans,axiom,
% 21.13/21.25 ! [V_z,V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Opreorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_xt1_I5_J,axiom,
% 21.13/21.25 ! [V_x,V_y,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.13/21.25 => V_x = V_y ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_xt1_I6_J,axiom,
% 21.13/21.25 ! [V_z,V_x,V_y,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__funE,axiom,
% 21.13/21.25 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 21.13/21.25 ( class_Orderings_Oord(T_c)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_linorder__le__cases,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_a)
% 21.13/21.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__less__irrefl,axiom,
% 21.13/21.25 ! [V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Opreorder(T_a)
% 21.13/21.25 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_linorder__neq__iff,axiom,
% 21.13/21.25 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_b)
% 21.13/21.25 => ( V_x_2 != V_y_2
% 21.13/21.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 21.13/21.25 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_not__less__iff__gr__or__eq,axiom,
% 21.13/21.25 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_b)
% 21.13/21.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 21.13/21.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 21.13/21.25 | V_x_2 = V_y_2 ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_linorder__less__linear,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.25 | V_x = V_y
% 21.13/21.25 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_linorder__antisym__conv3,axiom,
% 21.13/21.25 ! [V_x_2,V_y_2,T_b] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_b)
% 21.13/21.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 21.13/21.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 21.13/21.25 <=> V_x_2 = V_y_2 ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_linorder__neqE,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_a)
% 21.13/21.25 => ( V_x != V_y
% 21.13/21.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_less__imp__neq,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.25 => V_x != V_y ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__less__not__sym,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Opreorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.25 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__less__imp__not__less,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Opreorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.25 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__less__imp__not__eq,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.25 => V_x != V_y ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__less__imp__not__eq2,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.25 => V_y != V_x ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__less__asym_H,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Orderings_Opreorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.25 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_xt1_I9_J,axiom,
% 21.13/21.25 ! [V_a,V_b,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 21.13/21.25 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_ord__eq__less__trans,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Orderings_Oord(T_a)
% 21.13/21.25 => ( V_a = V_b
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_xt1_I1_J,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( V_a = V_b
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_ord__less__eq__trans,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Orderings_Oord(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.25 => ( V_b = V_c
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_xt1_I2_J,axiom,
% 21.13/21.25 ! [V_c,V_a,V_b,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 21.13/21.25 => ( V_b = V_c
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__less__trans,axiom,
% 21.13/21.25 ! [V_z,V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Opreorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_xt1_I10_J,axiom,
% 21.13/21.25 ! [V_z,V_x,V_y,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__less__asym,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Opreorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.25 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_linorder__cases,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_a)
% 21.13/21.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.25 => ( V_x != V_y
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_times_Oidem,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 21.13/21.25 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mult__idem,axiom,
% 21.13/21.25 ! [V_x,T_a] :
% 21.13/21.25 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 21.13/21.25 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mult__left__idem,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_double__compl,axiom,
% 21.13/21.25 ! [V_x,T_a] :
% 21.13/21.25 ( class_Lattices_Oboolean__algebra(T_a)
% 21.13/21.25 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_uminus__apply,axiom,
% 21.13/21.25 ! [V_x_2,V_A_2,T_c,T_b] :
% 21.13/21.25 ( class_Groups_Ouminus(T_b)
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_compl__eq__compl__iff,axiom,
% 21.13/21.25 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.25 ( class_Lattices_Oboolean__algebra(T_b)
% 21.13/21.25 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 21.13/21.25 <=> V_x_2 = V_y_2 ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_linorder__not__less,axiom,
% 21.13/21.25 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_b)
% 21.13/21.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_linorder__not__le,axiom,
% 21.13/21.25 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_b)
% 21.13/21.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_linorder__le__less__linear,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.13/21.25 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__less__le,axiom,
% 21.13/21.25 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.25 ( class_Orderings_Oorder(T_b)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 21.13/21.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.13/21.25 & V_x_2 != V_y_2 ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_less__le__not__le,axiom,
% 21.13/21.25 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.25 ( class_Orderings_Opreorder(T_b)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 21.13/21.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.13/21.25 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__le__less,axiom,
% 21.13/21.25 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.25 ( class_Orderings_Oorder(T_b)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.13/21.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 21.13/21.25 | V_x_2 = V_y_2 ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_leI,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_a)
% 21.13/21.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_not__leE,axiom,
% 21.13/21.25 ! [V_x,V_y,T_a] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_a)
% 21.13/21.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_linorder__antisym__conv1,axiom,
% 21.13/21.25 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_b)
% 21.13/21.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.13/21.25 <=> V_x_2 = V_y_2 ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__neq__le__trans,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( V_a != V_b
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_xt1_I12_J,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( V_a != V_b
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_leD,axiom,
% 21.13/21.25 ! [V_x,V_y,T_a] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 21.13/21.25 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__less__imp__le,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Opreorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_linorder__antisym__conv2,axiom,
% 21.13/21.25 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.25 ( class_Orderings_Olinorder(T_b)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.13/21.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 21.13/21.25 <=> V_x_2 = V_y_2 ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__le__imp__less__or__eq,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.25 | V_x = V_y ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_order__le__neq__trans,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Orderings_Oorder(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.25 => ( V_a != V_b
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_ex__least__nat__less,axiom,
% 21.13/21.25 ! [V_n_2,V_P_2] :
% 21.13/21.25 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 21.13/21.25 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 21.13/21.25 => ? [B_k] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 21.13/21.25 & ! [B_i] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 21.13/21.25 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 21.13/21.25 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_sgn__if,axiom,
% 21.13/21.25 ! [V_x,T_a] :
% 21.13/21.25 ( class_Groups_Osgn__if(T_a)
% 21.13/21.25 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.25 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 21.13/21.25 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.25 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 21.13/21.25 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 21.13/21.25 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 21.13/21.25 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_sgn__neg,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.25 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_sgn__1__neg,axiom,
% 21.13/21.25 ! [V_a_2,T_b] :
% 21.13/21.25 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.25 => ( 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))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zsgn__def,axiom,
% 21.13/21.25 ! [V_i] :
% 21.13/21.25 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 21.13/21.25 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 21.13/21.25 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 21.13/21.25 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 21.13/21.25 => 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)) ) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_divmod__int__rel__mod__eq,axiom,
% 21.13/21.25 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 21.13/21.25 ( 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)
% 21.13/21.25 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 21.13/21.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 21.13/21.25 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 21.13/21.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 21.13/21.25 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmult2__lemma__aux2,axiom,
% 21.13/21.25 ! [V_q,V_r,V_b,V_c] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => 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))) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmult2__lemma__aux1,axiom,
% 21.13/21.25 ! [V_q,V_r,V_b,V_c] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => 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))) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_less__fun__def,axiom,
% 21.13/21.25 ! [V_g_2,V_f_2,T_b,T_c] :
% 21.13/21.25 ( class_Orderings_Oord(T_c)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 21.13/21.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 21.13/21.25 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_sgn__sgn,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mod__trivial,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__0,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__by__0,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__self,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__add__self2,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__add__self1,axiom,
% 21.13/21.25 ! [V_a,V_b,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__add__right__eq,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__add__left__eq,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__add__eq,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__simps_I2_J,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__simps_I1_J,axiom,
% 21.13/21.25 ! [V_b,V_c,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__add__cong,axiom,
% 21.13/21.25 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 21.13/21.25 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 21.13/21.25 => 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) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult__right__eq,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult__left__eq,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult__eq,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult__mult1,axiom,
% 21.13/21.25 ! [V_b,V_a,V_c,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult__mult2,axiom,
% 21.13/21.25 ! [V_b,V_c,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__simps_I4_J,axiom,
% 21.13/21.25 ! [V_b,V_c,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult__cong,axiom,
% 21.13/21.25 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 21.13/21.25 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 21.13/21.25 => 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) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__minus__eq,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Oring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__minus__cong,axiom,
% 21.13/21.25 ! [V_a_H,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Oring__div(T_a)
% 21.13/21.25 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 21.13/21.25 => 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) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__self,axiom,
% 21.13/21.25 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__zero,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__simps_I3_J,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__zmult1__eq,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zminus__zmod,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__zminus__zminus,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__zminus2,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_sgn__0__0,axiom,
% 21.13/21.25 ! [V_a_2,T_b] :
% 21.13/21.25 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.25 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.25 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_sgn0,axiom,
% 21.13/21.25 ! [T_a] :
% 21.13/21.25 ( class_Groups_Osgn__if(T_a)
% 21.13/21.25 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_sgn__times,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult__self2__is__0,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult__self1__is__0,axiom,
% 21.13/21.25 ! [V_a,V_b,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult__self2,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult__self1,axiom,
% 21.13/21.25 ! [V_b,V_c,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__by__1,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__le__nonneg__dividend,axiom,
% 21.13/21.25 ! [V_k,V_m] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 21.13/21.25 ! [V_y,V_x] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_neg__mod__bound,axiom,
% 21.13/21.25 ! [V_a,V_b] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => 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))) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_pos__mod__bound,axiom,
% 21.13/21.25 ! [V_a,V_b] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__eq__0__iff,axiom,
% 21.13/21.25 ! [V_d_2,V_m_2] :
% 21.13/21.25 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__zminus2__not__zero,axiom,
% 21.13/21.25 ! [V_l,V_k] :
% 21.13/21.25 ( 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)
% 21.13/21.25 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__zminus1__not__zero,axiom,
% 21.13/21.25 ! [V_l,V_k] :
% 21.13/21.25 ( 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)
% 21.13/21.25 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__neg__neg__trivial,axiom,
% 21.13/21.25 ! [V_b,V_a] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 21.13/21.25 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_neg__mod__conj,axiom,
% 21.13/21.25 ! [V_a,V_b] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => ( 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)))
% 21.13/21.25 & 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_neg__mod__sign,axiom,
% 21.13/21.25 ! [V_a,V_b] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => 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))) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__pos__pos__trivial,axiom,
% 21.13/21.25 ! [V_b,V_a] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 21.13/21.25 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_pos__mod__conj,axiom,
% 21.13/21.25 ! [V_a,V_b] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.13/21.25 => ( 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)))
% 21.13/21.25 & 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_pos__mod__sign,axiom,
% 21.13/21.25 ! [V_a,V_b] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.13/21.25 => 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))) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_sgn__less,axiom,
% 21.13/21.25 ! [V_a_2,T_b] :
% 21.13/21.25 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.25 => ( 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)))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_sgn__greater,axiom,
% 21.13/21.25 ! [V_a_2,T_b] :
% 21.13/21.25 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.25 => ( 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)))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__pos__neg__trivial,axiom,
% 21.13/21.25 ! [V_b,V_a] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.13/21.25 => ( 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)))
% 21.13/21.25 => 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) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_sgn__pos,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.25 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_sgn__1__pos,axiom,
% 21.13/21.25 ! [V_a_2,T_b] :
% 21.13/21.25 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.25 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_split__zmod,axiom,
% 21.13/21.25 ! [V_k_2,V_n_2,V_P_2] :
% 21.13/21.25 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 21.13/21.25 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 21.13/21.25 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 21.13/21.25 => ! [B_i,B_j] :
% 21.13/21.25 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 21.13/21.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 21.13/21.25 & 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) )
% 21.13/21.25 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 21.13/21.25 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => ! [B_i,B_j] :
% 21.13/21.25 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 21.13/21.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 & 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) )
% 21.13/21.25 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmult2__lemma__aux3,axiom,
% 21.13/21.25 ! [V_q,V_b,V_r,V_c] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 21.13/21.25 => 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))) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmult2__lemma__aux4,axiom,
% 21.13/21.25 ! [V_q,V_b,V_r,V_c] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 21.13/21.25 => 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))) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_z3mod__def,axiom,
% 21.13/21.25 ! [V_k,V_l] :
% 21.13/21.25 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 21.13/21.25 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 21.13/21.25 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_split__neg__lemma,axiom,
% 21.13/21.25 ! [V_n_2,V_P_2,V_k_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 21.13/21.25 <=> ! [B_i,B_j] :
% 21.13/21.25 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 21.13/21.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 & 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) )
% 21.13/21.25 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_split__pos__lemma,axiom,
% 21.13/21.25 ! [V_n_2,V_P_2,V_k_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 21.13/21.25 <=> ! [B_i,B_j] :
% 21.13/21.25 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 21.13/21.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 21.13/21.25 & 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) )
% 21.13/21.25 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__zmult2__eq,axiom,
% 21.13/21.25 ! [V_b,V_a,V_c] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 21.13/21.25 ! [V_y,V_x] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_split__zdiv,axiom,
% 21.13/21.25 ! [V_k_2,V_n_2,V_P_2] :
% 21.13/21.25 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 21.13/21.25 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 21.13/21.25 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 21.13/21.25 => ! [B_i] :
% 21.13/21.25 ( ? [B_j] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 21.13/21.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 21.13/21.25 & 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) )
% 21.13/21.25 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 21.13/21.25 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => ! [B_i] :
% 21.13/21.25 ( ? [B_j] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 21.13/21.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 & 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) )
% 21.13/21.25 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_divmod__int__rel__div__eq,axiom,
% 21.13/21.25 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 21.13/21.25 ( 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)
% 21.13/21.25 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 21.13/21.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 21.13/21.25 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 21.13/21.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 21.13/21.25 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_split__div_H,axiom,
% 21.13/21.25 ! [V_n_2,V_m_2,V_P_2] :
% 21.13/21.25 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 21.13/21.25 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.25 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 21.13/21.25 | ? [B_q] :
% 21.13/21.25 ( 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))
% 21.13/21.25 & 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))))
% 21.13/21.25 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__add1__eq,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__int,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult2__eq,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__mult1__eq,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__le__mono,axiom,
% 21.13/21.25 ! [V_k,V_n,V_m] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 21.13/21.25 => 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))) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__le__dividend,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__zero,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__mult2__eq,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__less,axiom,
% 21.13/21.25 ! [V_n,V_m] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.25 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__less__eq__dividend,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult__distrib,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult__distrib2,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__zminus2,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__zminus__zminus,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__0,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__by__0,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__by__1,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_nat__div__distrib,axiom,
% 21.13/21.25 ! [V_y,V_x] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 21.13/21.25 ! [V_y,V_x] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__1,axiom,
% 21.13/21.25 ! [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 ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__less,axiom,
% 21.13/21.25 ! [V_n,V_m] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.25 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_nat__mult__div__cancel__disj,axiom,
% 21.13/21.25 ! [V_n,V_m,V_k] :
% 21.13/21.25 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.25 => 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) )
% 21.13/21.25 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.25 => 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) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__Suc,axiom,
% 21.13/21.25 ! [V_n,V_m] :
% 21.13/21.25 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 21.13/21.25 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 21.13/21.25 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__1,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 21.13/21.25 ! [V_y,V_x] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__less__divisor,axiom,
% 21.13/21.25 ! [V_m,V_n] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 21.13/21.25 ! [V_a_2,V_b_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 21.13/21.25 => ( 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)))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 21.13/21.25 ! [V_a_2,V_b_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => ( 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)))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__neg__pos__less0,axiom,
% 21.13/21.25 ! [V_b,V_a] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__self,axiom,
% 21.13/21.25 ! [V_a] :
% 21.13/21.25 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__eq__0__iff,axiom,
% 21.13/21.25 ! [V_d_2,V_m_2] :
% 21.13/21.25 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.25 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_DIVISION__BY__ZERO,axiom,
% 21.13/21.25 ! [V_a] :
% 21.13/21.25 ( 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)
% 21.13/21.25 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__zdiv__trivial,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult__self3,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__zadd1__eq,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__int,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__mult__mult1,axiom,
% 21.13/21.25 ! [V_b,V_a,V_c,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.25 => 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) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__mult__mult2,axiom,
% 21.13/21.25 ! [V_b,V_a,V_c,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.25 => 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) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__mult__self1__is__id,axiom,
% 21.13/21.25 ! [V_a,V_b,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.25 => 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 ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__mult__self2__is__id,axiom,
% 21.13/21.25 ! [V_a,V_b,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.25 => 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 ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__mult__mult1__if,axiom,
% 21.13/21.25 ! [V_b,V_a,V_c,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.25 => 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) )
% 21.13/21.25 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.25 => 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) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__self,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.25 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__div__trivial,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__le__mono2,axiom,
% 21.13/21.25 ! [V_k,V_n,V_m] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__mult__self__is__m,axiom,
% 21.13/21.25 ! [V_m,V_n] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.25 => 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 ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__mult__self1__is__m,axiom,
% 21.13/21.25 ! [V_m,V_n] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.25 => 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 ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_nat__mult__div__cancel1,axiom,
% 21.13/21.25 ! [V_n,V_m,V_k] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__less__dividend,axiom,
% 21.13/21.25 ! [V_m,V_n] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__eq__0__iff,axiom,
% 21.13/21.25 ! [V_k_2,V_i_2] :
% 21.13/21.25 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 21.13/21.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 21.13/21.25 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 21.13/21.25 ! [V_a_2,V_b_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 21.13/21.25 => ( 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)))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 21.13/21.25 ! [V_i_2,V_k_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 21.13/21.25 => ( 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)))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 21.13/21.25 ! [V_b_2,V_a_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 21.13/21.25 => ( 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)))
% 21.13/21.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 21.13/21.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__mono2,axiom,
% 21.13/21.25 ! [V_b,V_b_H,V_a] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 21.13/21.25 => 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))) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__nonneg__neg__le0,axiom,
% 21.13/21.25 ! [V_b,V_a] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__pos__pos__trivial,axiom,
% 21.13/21.25 ! [V_b,V_a] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 21.13/21.25 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 21.13/21.25 ! [V_a_2,V_b_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => ( 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)))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__nonpos__pos__le0,axiom,
% 21.13/21.25 ! [V_b,V_a] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__mono2__neg,axiom,
% 21.13/21.25 ! [V_b,V_b_H,V_a] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 21.13/21.25 => 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))) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__neg__neg__trivial,axiom,
% 21.13/21.25 ! [V_b,V_a] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 21.13/21.25 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__mono1,axiom,
% 21.13/21.25 ! [V_b,V_a_H,V_a] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__mono1__neg,axiom,
% 21.13/21.25 ! [V_b,V_a_H,V_a] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__le__divisor,axiom,
% 21.13/21.25 ! [V_m,V_n] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_int__div__less__self,axiom,
% 21.13/21.25 ! [V_k,V_x] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__zmult2__eq,axiom,
% 21.13/21.25 ! [V_b,V_a,V_c] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__mult__self4,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__zmod__equality2,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__zmod__equality,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__zmult1__eq,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zmod__zdiv__equality,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__mult__self1,axiom,
% 21.13/21.25 ! [V_c,V_a,V_b,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__mult__self2,axiom,
% 21.13/21.25 ! [V_c,V_a,V_b,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__add__self1,axiom,
% 21.13/21.25 ! [V_a,V_b,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__add__self2,axiom,
% 21.13/21.25 ! [V_a,V_b,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__mod__equality,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__mod__equality2,axiom,
% 21.13/21.25 ! [V_c,V_a,V_b,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__div__equality,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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 ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__div__equality2,axiom,
% 21.13/21.25 ! [V_a,V_b,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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 ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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 ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_split__div,axiom,
% 21.13/21.25 ! [V_k_2,V_n_2,V_P_2] :
% 21.13/21.25 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 21.13/21.25 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.25 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 21.13/21.25 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.25 => ! [B_i,B_j] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 21.13/21.25 => ( 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)
% 21.13/21.25 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__lemma,axiom,
% 21.13/21.25 ! [V_q,V_b,V_r,V_c] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_split__mod,axiom,
% 21.13/21.25 ! [V_k_2,V_n_2,V_P_2] :
% 21.13/21.25 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 21.13/21.25 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.25 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 21.13/21.25 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.25 => ! [B_i,B_j] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 21.13/21.25 => ( 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)
% 21.13/21.25 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Suc__times__mod__eq,axiom,
% 21.13/21.25 ! [V_m,V_k] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_nat__mod__distrib,axiom,
% 21.13/21.25 ! [V_y,V_x] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 21.13/21.25 ! [V_y,V_x] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_split__div__lemma,axiom,
% 21.13/21.25 ! [V_m_2,V_q_2,V_n_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 21.13/21.25 => ( ( 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))
% 21.13/21.25 & 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)))) )
% 21.13/21.25 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_z3div__def,axiom,
% 21.13/21.25 ! [V_k,V_l] :
% 21.13/21.25 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 21.13/21.25 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 21.13/21.25 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__zminus2__eq__if,axiom,
% 21.13/21.25 ! [V_a,V_b] :
% 21.13/21.25 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 => 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)) )
% 21.13/21.25 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 => 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)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiv__zminus1__eq__if,axiom,
% 21.13/21.25 ! [V_a,V_b] :
% 21.13/21.25 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 => 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)) )
% 21.13/21.25 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.25 => 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)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__div__geq,axiom,
% 21.13/21.25 ! [V_m,V_n] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__div__decomp,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Osemiring__div(T_a)
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 21.13/21.25 ! [V_y,V_x] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_incr__mult__lemma,axiom,
% 21.13/21.25 ! [V_k_2,V_P_2,V_d_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 21.13/21.25 => ( ! [B_x] :
% 21.13/21.25 ( hBOOL(hAPP(V_P_2,B_x))
% 21.13/21.25 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 21.13/21.25 => ! [B_x] :
% 21.13/21.25 ( hBOOL(hAPP(V_P_2,B_x))
% 21.13/21.25 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_field__le__mult__one__interval,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 21.13/21.25 => ( ! [B_z] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 21.13/21.25 => 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)) ) )
% 21.13/21.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_minus__apply,axiom,
% 21.13/21.25 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 21.13/21.25 ( class_Groups_Ominus(T_b)
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_of__int__diff,axiom,
% 21.13/21.25 ! [V_z,V_w,T_a] :
% 21.13/21.25 ( class_Rings_Oring__1(T_a)
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__eq__diff__eq,axiom,
% 21.13/21.25 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.13/21.25 ( class_Groups_Oab__group__add(T_b)
% 21.13/21.25 => ( 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_c_2),V_d_2)
% 21.13/21.25 => ( V_a_2 = V_b_2
% 21.13/21.25 <=> V_c_2 = V_d_2 ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__commute,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_of__nat__diff,axiom,
% 21.13/21.25 ! [V_m,V_n,T_a] :
% 21.13/21.25 ( class_Rings_Oring__1(T_a)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiff__int,axiom,
% 21.13/21.25 ! [V_m,V_n] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__eq__diff__less__eq,axiom,
% 21.13/21.25 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.13/21.25 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.13/21.25 => ( 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_c_2),V_d_2)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_right__minus__eq,axiom,
% 21.13/21.25 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.25 ( class_Groups_Ogroup__add(T_b)
% 21.13/21.25 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.25 <=> V_a_2 = V_b_2 ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_eq__iff__diff__eq__0,axiom,
% 21.13/21.25 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.25 ( class_Groups_Oab__group__add(T_b)
% 21.13/21.25 => ( V_a_2 = V_b_2
% 21.13/21.25 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__self,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.25 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__0__right,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.25 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__eq__diff__less,axiom,
% 21.13/21.25 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.13/21.25 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.13/21.25 => ( 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_c_2),V_d_2)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_add__diff__cancel,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.25 => 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 ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__add__cancel,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.25 => 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 ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_minus__diff__eq,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Groups_Oab__group__add(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__diff__right__eq,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Oring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__diff__left__eq,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Oring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__diff__eq,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Oring__div(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__diff__cong,axiom,
% 21.13/21.25 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 21.13/21.25 ( class_Divides_Oring__div(T_a)
% 21.13/21.25 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 21.13/21.25 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 21.13/21.25 => 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) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__0__eq__0,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_minus__nat_Odiff__0,axiom,
% 21.13/21.25 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__self__eq__0,axiom,
% 21.13/21.25 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diffs0__imp__equal,axiom,
% 21.13/21.25 ! [V_n,V_m] :
% 21.13/21.25 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.25 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.25 => V_m = V_n ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Suc__diff__diff,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__Suc__Suc,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_less__imp__diff__less,axiom,
% 21.13/21.25 ! [V_n,V_k,V_j] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__less__mono2,axiom,
% 21.13/21.25 ! [V_l,V_n,V_m] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__if,axiom,
% 21.13/21.25 ! [V_n,V_m] :
% 21.13/21.25 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.25 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 21.13/21.25 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.25 => 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) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mod__geq,axiom,
% 21.13/21.25 ! [V_n,V_m] :
% 21.13/21.25 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__add__inverse2,axiom,
% 21.13/21.25 ! [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 ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__add__inverse,axiom,
% 21.13/21.25 ! [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 ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__diff__left,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__cancel,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__cancel2,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__diff__iff,axiom,
% 21.13/21.25 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 21.13/21.25 => ( 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)))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Nat_Odiff__diff__eq,axiom,
% 21.13/21.25 ! [V_n,V_m,V_k] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 21.13/21.25 => 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) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_eq__diff__iff,axiom,
% 21.13/21.25 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 21.13/21.25 => ( 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)
% 21.13/21.25 <=> V_m_2 = V_n_2 ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__diff__cancel,axiom,
% 21.13/21.25 ! [V_n,V_i] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 21.13/21.25 => 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 ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__le__mono,axiom,
% 21.13/21.25 ! [V_l,V_n,V_m] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 21.13/21.25 => 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))) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__le__mono2,axiom,
% 21.13/21.25 ! [V_l,V_n,V_m] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 21.13/21.25 => 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))) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__le__self,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__mod__geq,axiom,
% 21.13/21.25 ! [V_m,V_n] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiff__zmult__distrib2,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiff__zmult__distrib,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__mult__distrib,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__mult__distrib2,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiff__zmod__right,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiff__zmod__left,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_nat__diff__distrib,axiom,
% 21.13/21.25 ! [V_z,V_z_H] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zdiff__int__split,axiom,
% 21.13/21.25 ! [V_y_2,V_x_2,V_P_2] :
% 21.13/21.25 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
% 21.13/21.25 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 21.13/21.25 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) )
% 21.13/21.25 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 21.13/21.25 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__iff__diff__le__0,axiom,
% 21.13/21.25 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.25 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 21.13/21.25 <=> 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_less__iff__diff__less__0,axiom,
% 21.13/21.25 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.25 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 21.13/21.25 <=> 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_eq__add__iff1,axiom,
% 21.13/21.25 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 21.13/21.25 ( class_Rings_Oring(T_b)
% 21.13/21.25 => ( 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_c_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)
% 21.13/21.25 <=> 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_c_2) = V_d_2 ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_eq__add__iff2,axiom,
% 21.13/21.25 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 21.13/21.25 ( class_Rings_Oring(T_b)
% 21.13/21.25 => ( 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_c_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)
% 21.13/21.25 <=> V_c_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) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__0,axiom,
% 21.13/21.25 ! [V_a,T_a] :
% 21.13/21.25 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__def,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_ab__diff__minus,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Groups_Oab__group__add(T_a)
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 21.13/21.25 ! [V_y,V_x,T_a] :
% 21.13/21.25 ( class_Rings_Ocomm__ring__1(T_a)
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__minus__eq__add,axiom,
% 21.13/21.25 ! [V_b,V_a,T_a] :
% 21.13/21.25 ( class_Groups_Ogroup__add(T_a)
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_less__bin__lemma,axiom,
% 21.13/21.25 ! [V_l_2,V_k_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 21.13/21.25 <=> 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))) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_zero__less__diff,axiom,
% 21.13/21.25 ! [V_m_2,V_n_2] :
% 21.13/21.25 ( 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)))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__less,axiom,
% 21.13/21.25 ! [V_m,V_n] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 21.13/21.25 => 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__less__Suc,axiom,
% 21.13/21.25 ! [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))) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__add__0,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__is__0__eq_H,axiom,
% 21.13/21.25 ! [V_n,V_m] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 21.13/21.25 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__is__0__eq,axiom,
% 21.13/21.25 ! [V_n_2,V_m_2] :
% 21.13/21.25 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_less__diff__conv,axiom,
% 21.13/21.25 ! [V_k_2,V_j_2,V_i_2] :
% 21.13/21.25 ( 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)))
% 21.13/21.25 <=> 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_add__diff__inverse,axiom,
% 21.13/21.25 ! [V_n,V_m] :
% 21.13/21.25 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.25 => 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 ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Suc__diff__le,axiom,
% 21.13/21.25 ! [V_m,V_n] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_less__diff__iff,axiom,
% 21.13/21.25 ! [V_n_2,V_m_2,V_k_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 21.13/21.25 => ( 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)))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__less__mono,axiom,
% 21.13/21.25 ! [V_c,V_b,V_a] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 21.13/21.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 21.13/21.25 => 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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__diff__right,axiom,
% 21.13/21.25 ! [V_i,V_j,V_k] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__diff__conv,axiom,
% 21.13/21.25 ! [V_i_2,V_k_2,V_j_2] :
% 21.13/21.25 ( 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))
% 21.13/21.25 <=> 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))) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__add__diff,axiom,
% 21.13/21.25 ! [V_m,V_n,V_k] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 21.13/21.25 => 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))) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__add__diff__inverse,axiom,
% 21.13/21.25 ! [V_m,V_n] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 21.13/21.25 => 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 ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_add__diff__assoc,axiom,
% 21.13/21.25 ! [V_i,V_j,V_k] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__diff__conv2,axiom,
% 21.13/21.25 ! [V_i_2,V_j_2,V_k_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 21.13/21.25 => ( 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)))
% 21.13/21.25 <=> 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)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__add__diff__inverse2,axiom,
% 21.13/21.25 ! [V_m,V_n] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 21.13/21.25 => 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 ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__imp__diff__is__add,axiom,
% 21.13/21.25 ! [V_k_2,V_j_2,V_i_2] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 21.13/21.25 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 21.13/21.25 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__add__assoc,axiom,
% 21.13/21.25 ! [V_i,V_j,V_k] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_add__diff__assoc2,axiom,
% 21.13/21.25 ! [V_i,V_j,V_k] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__add__assoc2,axiom,
% 21.13/21.25 ! [V_i,V_j,V_k] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 21.13/21.25 => 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) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__int__def,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__int__def__symmetric,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 21.13/21.25 ! [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) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__Suc__1,axiom,
% 21.13/21.25 ! [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 ).
% 21.13/21.25
% 21.13/21.25 fof(fact_div__mod__equality_H,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_mult__div__cancel,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Divides_Omod__div__equality_H,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_tsub__eq,axiom,
% 21.13/21.25 ! [V_x,V_y] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 21.13/21.25 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 21.13/21.25 ! [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)) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__add__iff1,axiom,
% 21.13/21.25 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 21.13/21.25 ( class_Rings_Oordered__ring(T_b)
% 21.13/21.25 => ( 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_c_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)))
% 21.13/21.25 <=> 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_c_2)),V_d_2)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_le__add__iff2,axiom,
% 21.13/21.25 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 21.13/21.25 ( class_Rings_Oordered__ring(T_b)
% 21.13/21.25 => ( 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_c_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)))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_less__add__iff1,axiom,
% 21.13/21.25 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 21.13/21.25 ( class_Rings_Oordered__ring(T_b)
% 21.13/21.25 => ( 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_c_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)))
% 21.13/21.25 <=> 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_c_2)),V_d_2)) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_less__add__iff2,axiom,
% 21.13/21.25 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 21.13/21.25 ( class_Rings_Oordered__ring(T_b)
% 21.13/21.25 => ( 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_c_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)))
% 21.13/21.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_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))) ) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_diff__Suc__less,axiom,
% 21.13/21.25 ! [V_i,V_n] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.25 => 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)) ) ).
% 21.13/21.25
% 21.13/21.25 fof(fact_Suc__pred,axiom,
% 21.13/21.25 ! [V_n] :
% 21.13/21.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.25 => 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 ) ).
% 21.13/21.25
% 21.13/21.26 fof(fact_nat__diff__split,axiom,
% 21.13/21.26 ! [V_b_2,V_a_2,V_P_2] :
% 21.13/21.26 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 21.13/21.26 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 21.13/21.26 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 21.13/21.26 & ! [B_d] :
% 21.13/21.26 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 21.13/21.26 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__diff__split__asm,axiom,
% 21.13/21.26 ! [V_b_2,V_a_2,V_P_2] :
% 21.13/21.26 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 21.13/21.26 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 21.13/21.26 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 21.13/21.26 | ? [B_d] :
% 21.13/21.26 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 21.13/21.26 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zle__diff1__eq,axiom,
% 21.13/21.26 ! [V_z_2,V_w_2] :
% 21.13/21.26 ( 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))))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_diff__Suc__diff__eq2,axiom,
% 21.13/21.26 ! [V_m,V_j,V_k] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_diff__Suc__diff__eq1,axiom,
% 21.13/21.26 ! [V_m,V_j,V_k] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__le__add__iff1,axiom,
% 21.13/21.26 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__diff__add__eq1,axiom,
% 21.13/21.26 ! [V_n,V_m,V_u,V_i,V_j] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__eq__add__iff1,axiom,
% 21.13/21.26 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 21.13/21.26 => ( 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)
% 21.13/21.26 <=> 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 ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__le__add__iff2,axiom,
% 21.13/21.26 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> 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))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__diff__add__eq2,axiom,
% 21.13/21.26 ! [V_n,V_m,V_u,V_j,V_i] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__eq__add__iff2,axiom,
% 21.13/21.26 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 21.13/21.26 => ( 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)
% 21.13/21.26 <=> 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) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zmod__zminus2__eq__if,axiom,
% 21.13/21.26 ! [V_b,V_a] :
% 21.13/21.26 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.26 => 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) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zmod__zminus1__eq__if,axiom,
% 21.13/21.26 ! [V_b,V_a] :
% 21.13/21.26 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.26 => 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zmod__zdiv__equality_H,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zmult__div__cancel,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_tsub__def,axiom,
% 21.13/21.26 ! [V_x,V_y] :
% 21.13/21.26 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 21.13/21.26 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 21.13/21.26 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Suc__diff__1,axiom,
% 21.13/21.26 ! [V_n] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.26 => 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 ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Suc__pred_H,axiom,
% 21.13/21.26 ! [V_n] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__less__add__iff1,axiom,
% 21.13/21.26 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__less__add__iff2,axiom,
% 21.13/21.26 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> 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))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__eq__if,axiom,
% 21.13/21.26 ! [V_n,V_m] :
% 21.13/21.26 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.26 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 21.13/21.26 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.26 => 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_div__if,axiom,
% 21.13/21.26 ! [V_m,V_n] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.26 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.26 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.26 => 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)) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_div__geq,axiom,
% 21.13/21.26 ! [V_m,V_n] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.26 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.13/21.26 => 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_mult__eq__if,axiom,
% 21.13/21.26 ! [V_n,V_m] :
% 21.13/21.26 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.26 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 21.13/21.26 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.26 => 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_int__power__div__base,axiom,
% 21.13/21.26 ! [V_k,V_m] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 21.13/21.26 => 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)))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_decr__mult__lemma,axiom,
% 21.13/21.26 ! [V_k_2,V_P_2,V_d_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 21.13/21.26 => ( ! [B_x] :
% 21.13/21.26 ( hBOOL(hAPP(V_P_2,B_x))
% 21.13/21.26 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 21.13/21.26 => ! [B_x] :
% 21.13/21.26 ( hBOOL(hAPP(V_P_2,B_x))
% 21.13/21.26 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_incr__lemma,axiom,
% 21.13/21.26 ! [V_x,V_z,V_d] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 21.13/21.26 => 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)))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_decr__lemma,axiom,
% 21.13/21.26 ! [V_z,V_x,V_d] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__mod__eq__lemma,axiom,
% 21.13/21.26 ! [V_y,V_n,V_x] :
% 21.13/21.26 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 21.13/21.26 => ? [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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_mod__induct__0,axiom,
% 21.13/21.26 ! [V_i_2,V_P_2,V_p_2] :
% 21.13/21.26 ( ! [B_i] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 21.13/21.26 => ( hBOOL(hAPP(V_P_2,B_i))
% 21.13/21.26 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 21.13/21.26 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 21.13/21.26 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_expand__Suc,axiom,
% 21.13/21.26 ! [V_v] :
% 21.13/21.26 ( 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)))
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_eq__number__of,axiom,
% 21.13/21.26 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 & class_Int_Oring__char__0(T_b) )
% 21.13/21.26 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 21.13/21.26 <=> V_x_2 = V_y_2 ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_number__of__reorient,axiom,
% 21.13/21.26 ! [V_x_2,V_w_2,T_b] :
% 21.13/21.26 ( class_Int_Onumber(T_b)
% 21.13/21.26 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 21.13/21.26 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__idempotent,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_of__int__number__of__eq,axiom,
% 21.13/21.26 ! [V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_of__int__power,axiom,
% 21.13/21.26 ! [V_n,V_z,T_a] :
% 21.13/21.26 ( class_Rings_Oring__1(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zero__le__zpower__abs,axiom,
% 21.13/21.26 ! [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))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__le__D1,axiom,
% 21.13/21.26 ! [V_b,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 21.13/21.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__ge__self,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__zero,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__eq__0,axiom,
% 21.13/21.26 ! [V_a_2,T_b] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 21.13/21.26 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.26 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__add__abs,axiom,
% 21.13/21.26 ! [V_b,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__mult__self,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__mult,axiom,
% 21.13/21.26 ! [V_b,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__minus__commute,axiom,
% 21.13/21.26 ! [V_b,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__one,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.26 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__minus__cancel,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 21.13/21.26 ! [V_q,V_y,V_x,T_a] :
% 21.13/21.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__of__nat,axiom,
% 21.13/21.26 ! [V_n,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__int__eq,axiom,
% 21.13/21.26 ! [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) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 21.13/21.26 ! [V_q,V_p,V_x,T_a] :
% 21.13/21.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zpower__zpower,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 21.13/21.26 ! [V_x,T_a] :
% 21.13/21.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.26 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zpower__zmod,axiom,
% 21.13/21.26 ! [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) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_of__nat__number__of__lemma,axiom,
% 21.13/21.26 ! [V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => ( ( 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)))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ 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)))
% 21.13/21.26 => 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) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_number__of__eq,axiom,
% 21.13/21.26 ! [V_k,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__number__of,axiom,
% 21.13/21.26 ! [V_x,T_a] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 & class_Rings_Olinordered__idom(T_a) )
% 21.13/21.26 => ( ( 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)))
% 21.13/21.26 => 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)) )
% 21.13/21.26 & ( ~ 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)))
% 21.13/21.26 => 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) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zero__less__zpower__abs__iff,axiom,
% 21.13/21.26 ! [V_n_2,V_x_2] :
% 21.13/21.26 ( 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)))
% 21.13/21.26 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.13/21.26 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__of__nonneg,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.26 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__le__zero__iff,axiom,
% 21.13/21.26 ! [V_a_2,T_b] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__ge__zero,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__not__less__zero,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => ~ 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zero__less__abs__iff,axiom,
% 21.13/21.26 ! [V_a_2,T_b] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__of__pos,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.26 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__triangle__ineq,axiom,
% 21.13/21.26 ! [V_b,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => 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)))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__mult__less,axiom,
% 21.13/21.26 ! [V_d,V_b,V_c,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 21.13/21.26 => 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))) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__triangle__ineq3,axiom,
% 21.13/21.26 ! [V_b,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => 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)))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__triangle__ineq2,axiom,
% 21.13/21.26 ! [V_b,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => 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)))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__triangle__ineq2__sym,axiom,
% 21.13/21.26 ! [V_b,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => 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)))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__ge__minus__self,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__le__iff,axiom,
% 21.13/21.26 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 21.13/21.26 => ( 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))
% 21.13/21.26 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 21.13/21.26 & 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)) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__leI,axiom,
% 21.13/21.26 ! [V_b,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 21.13/21.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__le__D2,axiom,
% 21.13/21.26 ! [V_b,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 21.13/21.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__less__iff,axiom,
% 21.13/21.26 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.26 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 21.13/21.26 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 21.13/21.26 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_le__number__of__eq__not__less,axiom,
% 21.13/21.26 ! [V_w_2,V_v_2,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber(T_b)
% 21.13/21.26 & class_Orderings_Olinorder(T_b) )
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> ~ 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))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_left__distrib__number__of,axiom,
% 21.13/21.26 ! [V_v,V_b,V_a,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber(T_b)
% 21.13/21.26 & class_Rings_Osemiring(T_b) )
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_right__distrib__number__of,axiom,
% 21.13/21.26 ! [V_c,V_b,V_v,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber(T_b)
% 21.13/21.26 & class_Rings_Osemiring(T_b) )
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 21.13/21.26 ! [V_q,V_x,T_a] :
% 21.13/21.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 21.13/21.26 ! [V_q,V_x,T_a] :
% 21.13/21.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 21.13/21.26 ! [V_q,V_x,T_a] :
% 21.13/21.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_left__diff__distrib__number__of,axiom,
% 21.13/21.26 ! [V_v,V_b,V_a,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber(T_b)
% 21.13/21.26 & class_Rings_Oring(T_b) )
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_right__diff__distrib__number__of,axiom,
% 21.13/21.26 ! [V_c,V_b,V_v,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber(T_b)
% 21.13/21.26 & class_Rings_Oring(T_b) )
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_le__number__of,axiom,
% 21.13/21.26 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 & class_Rings_Olinordered__idom(T_b) )
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 21.13/21.26 ! [V_x,T_a] :
% 21.13/21.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 21.13/21.26 ! [V_q,V_p,V_x,T_a] :
% 21.13/21.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_less__number__of,axiom,
% 21.13/21.26 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 & class_Rings_Olinordered__idom(T_b) )
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_number__of__add,axiom,
% 21.13/21.26 ! [V_w,V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__number__of__eq,axiom,
% 21.13/21.26 ! [V_w,V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__number__of__left,axiom,
% 21.13/21.26 ! [V_z,V_w,V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 21.13/21.26 ! [V_n,V_x] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_mult__number__of__left,axiom,
% 21.13/21.26 ! [V_z,V_w,V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_arith__simps_I32_J,axiom,
% 21.13/21.26 ! [V_w,V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_number__of__mult,axiom,
% 21.13/21.26 ! [V_w,V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__zmult__eq__1,axiom,
% 21.13/21.26 ! [V_n,V_m] :
% 21.13/21.26 ( 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)
% 21.13/21.26 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_number__of__diff,axiom,
% 21.13/21.26 ! [V_w,V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zpower__zadd__distrib,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_number__of__minus,axiom,
% 21.13/21.26 ! [V_w,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_arith__simps_I30_J,axiom,
% 21.13/21.26 ! [V_w,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__sgn,axiom,
% 21.13/21.26 ! [V_k,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_mult__sgn__abs,axiom,
% 21.13/21.26 ! [V_x,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.26 => 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 ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__mult__pos,axiom,
% 21.13/21.26 ! [V_y,V_x,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 21.13/21.26 => 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__eq__mult,axiom,
% 21.13/21.26 ! [V_b,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Oordered__ring__abs(T_a)
% 21.13/21.26 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.26 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 21.13/21.26 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.26 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 21.13/21.26 => 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__diff__triangle__ineq,axiom,
% 21.13/21.26 ! [V_d,V_c,V_b,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => 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))))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__triangle__ineq4,axiom,
% 21.13/21.26 ! [V_b,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => 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)))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__of__nonpos,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.26 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__minus__le__zero,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__if,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oabs__if(T_a)
% 21.13/21.26 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.26 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.26 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__of__neg,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.26 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zabs__less__one__iff,axiom,
% 21.13/21.26 ! [V_z_2] :
% 21.13/21.26 ( 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)))
% 21.13/21.26 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__number__of__diff1,axiom,
% 21.13/21.26 ! [V_c,V_w,V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zabs__def,axiom,
% 21.13/21.26 ! [V_i] :
% 21.13/21.26 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.26 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.26 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_minus__number__of__mult,axiom,
% 21.13/21.26 ! [V_z,V_w,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__abs__mult__distrib,axiom,
% 21.13/21.26 ! [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))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_diff__number__of__eq,axiom,
% 21.13/21.26 ! [V_w,V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__number__of__diff2,axiom,
% 21.13/21.26 ! [V_w,V_c,V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__strict__mono,axiom,
% 21.13/21.26 ! [V_n,V_b,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.26 => 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))) ) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_one__less__power,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.26 => 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))) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__le__imp__le__exp,axiom,
% 21.13/21.26 ! [V_n,V_m,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 21.13/21.26 => ( 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)))
% 21.13/21.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__increasing__iff,axiom,
% 21.13/21.26 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_b)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__decreasing,axiom,
% 21.13/21.26 ! [V_a,V_N,V_n,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 21.13/21.26 => 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))) ) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__strict__decreasing,axiom,
% 21.13/21.26 ! [V_a,V_N,V_n,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 21.13/21.26 => 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))) ) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__Suc__less__one,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 21.13/21.26 => 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))) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_number__of__is__id,axiom,
% 21.13/21.26 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 21.13/21.26
% 21.13/21.26 fof(fact_less__eq__number__of__int__code,axiom,
% 21.13/21.26 ! [V_l_2,V_k_2] :
% 21.13/21.26 ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_less__number__of__int__code,axiom,
% 21.13/21.26 ! [V_l_2,V_k_2] :
% 21.13/21.26 ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_plus__numeral__code_I9_J,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_times__numeral__code_I5_J,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_minus__numeral__code_I5_J,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__Suc__0,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 21.13/21.26 ! [V_m_2,V_x_2] :
% 21.13/21.26 ( 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))
% 21.13/21.26 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.26 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__power__less__imp__less,axiom,
% 21.13/21.26 ! [V_n,V_m,V_i] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 21.13/21.26 => ( 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)))
% 21.13/21.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__zero__less__power__iff,axiom,
% 21.13/21.26 ! [V_n_2,V_x_2] :
% 21.13/21.26 ( 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)))
% 21.13/21.26 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 21.13/21.26 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_int__number__of__def,axiom,
% 21.13/21.26 ! [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) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__one__le__power,axiom,
% 21.13/21.26 ! [V_n,V_i] :
% 21.13/21.26 ( 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))
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__number__of,axiom,
% 21.13/21.26 ! [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) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__number__of__def,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_int__power,axiom,
% 21.13/21.26 ! [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) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zpower__int,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_minus__numeral__code_I6_J,axiom,
% 21.13/21.26 ! [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))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__eq__if,axiom,
% 21.13/21.26 ! [V_p,V_m] :
% 21.13/21.26 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.26 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 21.13/21.26 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.26 => 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)))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_int__eq__iff__number__of,axiom,
% 21.13/21.26 ! [V_v_2,V_m_2] :
% 21.13/21.26 ( 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)
% 21.13/21.26 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 21.13/21.26 & 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))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__power__eq,axiom,
% 21.13/21.26 ! [V_n,V_z] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 21.13/21.26 ! [V_n,V_x] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_field__power__not__zero,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 21.13/21.26 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.26 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__commutes,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Omonoid__mult(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__mult__distrib,axiom,
% 21.13/21.26 ! [V_n,V_b,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Ocomm__monoid__mult(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__one,axiom,
% 21.13/21.26 ! [V_n,T_a] :
% 21.13/21.26 ( class_Groups_Omonoid__mult(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_of__nat__power,axiom,
% 21.13/21.26 ! [V_n,V_m,T_a] :
% 21.13/21.26 ( class_Rings_Osemiring__1(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__mult,axiom,
% 21.13/21.26 ! [V_n,V_m,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Omonoid__mult(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_one__div__nat__number__of,axiom,
% 21.13/21.26 ! [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))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__abs,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__one__right,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Groups_Omonoid__mult(T_a)
% 21.13/21.26 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zero__le__power,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.26 => 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))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__mono,axiom,
% 21.13/21.26 ! [V_n,V_b,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.26 => 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))) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zero__less__power,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.26 => 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))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__eq__0__iff,axiom,
% 21.13/21.26 ! [V_n_2,V_a_2,T_b] :
% 21.13/21.26 ( ( class_Power_Opower(T_b)
% 21.13/21.26 & class_Rings_Omult__zero(T_b)
% 21.13/21.26 & class_Rings_Ono__zero__divisors(T_b)
% 21.13/21.26 & class_Rings_Ozero__neq__one(T_b) )
% 21.13/21.26 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.26 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.26 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_one__le__power,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 21.13/21.26 => 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))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__0__Suc,axiom,
% 21.13/21.26 ! [V_n,T_a] :
% 21.13/21.26 ( ( class_Power_Opower(T_a)
% 21.13/21.26 & class_Rings_Osemiring__0(T_a) )
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__inject__exp,axiom,
% 21.13/21.26 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_b)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 21.13/21.26 => ( 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)
% 21.13/21.26 <=> V_m_2 = V_n_2 ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__Suc,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Power_Opower(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__Suc2,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Omonoid__mult(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__0,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Power_Opower(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__add,axiom,
% 21.13/21.26 ! [V_n,V_m,V_a,T_a] :
% 21.13/21.26 ( class_Groups_Omonoid__mult(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__power__minus,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__less__imp__less__base,axiom,
% 21.13/21.26 ! [V_b,V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( 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)))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__le__imp__le__base,axiom,
% 21.13/21.26 ! [V_b,V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( 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))))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__inject__base,axiom,
% 21.13/21.26 ! [V_b,V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( 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))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.26 => V_a = V_b ) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__gt1__lemma,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 21.13/21.26 => 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)))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__less__power__Suc,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 21.13/21.26 => 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)))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__0__left,axiom,
% 21.13/21.26 ! [V_n,T_a] :
% 21.13/21.26 ( ( class_Power_Opower(T_a)
% 21.13/21.26 & class_Rings_Osemiring__0(T_a) )
% 21.13/21.26 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.26 => 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) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__gt1,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 21.13/21.26 => 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)))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__strict__increasing,axiom,
% 21.13/21.26 ! [V_a,V_N,V_n,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 21.13/21.26 => 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))) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__less__imp__less__exp,axiom,
% 21.13/21.26 ! [V_n,V_m,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 21.13/21.26 => ( 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)))
% 21.13/21.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__strict__increasing__iff,axiom,
% 21.13/21.26 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_b)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zero__le__power__abs,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__increasing,axiom,
% 21.13/21.26 ! [V_a,V_N,V_n,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 21.13/21.26 => 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))) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__minus,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Oring__1(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__Suc__less,axiom,
% 21.13/21.26 ! [V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 21.13/21.26 => 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))) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__eq__imp__eq__base,axiom,
% 21.13/21.26 ! [V_b,V_n,V_a,T_a] :
% 21.13/21.26 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.26 => ( 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)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.26 => V_a = V_b ) ) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_one__mod__nat__number__of,axiom,
% 21.13/21.26 ! [V_v_H] :
% 21.13/21.26 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 21.13/21.26 => 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)) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 21.13/21.26 => 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))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__power__power,axiom,
% 21.13/21.26 ! [T_b] :
% 21.13/21.26 ( class_Power_Opower(T_b)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_div__nat__number__of,axiom,
% 21.13/21.26 ! [V_v_H,V_v] :
% 21.13/21.26 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_mod__nat__number__of,axiom,
% 21.13/21.26 ! [V_v_H,V_v] :
% 21.13/21.26 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 21.13/21.26 => 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))) ) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 21.13/21.26 ! [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)))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__nat__number__of,axiom,
% 21.13/21.26 ! [V_n,V_v] :
% 21.13/21.26 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power__nat__number__of__number__of,axiom,
% 21.13/21.26 ! [V_w,V_v] :
% 21.13/21.26 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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)) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_not__neg__0,axiom,
% 21.13/21.26 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_not__neg__int,axiom,
% 21.13/21.26 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_not__neg__1,axiom,
% 21.13/21.26 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_not__neg__eq__ge__0,axiom,
% 21.13/21.26 ! [V_x_2] :
% 21.13/21.26 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_neg__def,axiom,
% 21.13/21.26 ! [V_Z_2] :
% 21.13/21.26 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_neg__nat,axiom,
% 21.13/21.26 ! [V_z] :
% 21.13/21.26 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 21.13/21.26 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_not__neg__nat,axiom,
% 21.13/21.26 ! [V_z] :
% 21.13/21.26 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 21.13/21.26 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power_Opower_Opower__0,axiom,
% 21.13/21.26 ! [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 ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power_Opower_Opower__Suc,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_neg__imp__number__of__eq__0,axiom,
% 21.13/21.26 ! [V_v] :
% 21.13/21.26 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_neg__zminus__int,axiom,
% 21.13/21.26 ! [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))))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_eq__nat__number__of,axiom,
% 21.13/21.26 ! [V_v_H_2,V_v_2] :
% 21.13/21.26 ( 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)
% 21.13/21.26 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 21.13/21.26 => 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))) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 21.13/21.26 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 21.13/21.26 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 21.13/21.26 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__number__of__add__left,axiom,
% 21.13/21.26 ! [V_k,V_v_H,V_v] :
% 21.13/21.26 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 21.13/21.26 => 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) ) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_int__nat__number__of,axiom,
% 21.13/21.26 ! [V_v] :
% 21.13/21.26 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_of__nat__number__of__eq,axiom,
% 21.13/21.26 ! [V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Suc__nat__number__of__add,axiom,
% 21.13/21.26 ! [V_n,V_v] :
% 21.13/21.26 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Suc__nat__number__of,axiom,
% 21.13/21.26 ! [V_v] :
% 21.13/21.26 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 21.13/21.26 => 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zmod__minus1,axiom,
% 21.13/21.26 ! [V_b] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_div__pos__neg__trivial,axiom,
% 21.13/21.26 ! [V_b,V_a] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.13/21.26 => ( 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)))
% 21.13/21.26 => 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) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_int__val__lemma,axiom,
% 21.13/21.26 ! [V_k_2,V_f_2,V_n_2] :
% 21.13/21.26 ( ! [B_i] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 21.13/21.26 => 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))) )
% 21.13/21.26 => ( 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))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 21.13/21.26 => ? [B_i] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 21.13/21.26 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat0__intermed__int__val,axiom,
% 21.13/21.26 ! [V_k_2,V_f_2,V_n_2] :
% 21.13/21.26 ( ! [B_i] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 21.13/21.26 => 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))) )
% 21.13/21.26 => ( 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))
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 21.13/21.26 => ? [B_i] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 21.13/21.26 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_diff__bin__simps_I2_J,axiom,
% 21.13/21.26 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I24_J,axiom,
% 21.13/21.26 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I7_J,axiom,
% 21.13/21.26 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_bin__less__0__simps_I2_J,axiom,
% 21.13/21.26 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Int_OMin__def,axiom,
% 21.13/21.26 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_mult__Min,axiom,
% 21.13/21.26 ! [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) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_neg__number__of__Min,axiom,
% 21.13/21.26 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_mult__minus1__right,axiom,
% 21.13/21.26 ! [V_z,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_mult__minus1,axiom,
% 21.13/21.26 ! [V_z,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_number__of__Min,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_arith__simps_I31_J,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__minus__one,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 & class_Rings_Olinordered__idom(T_a) )
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zmod__minus1__right,axiom,
% 21.13/21.26 ! [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) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 21.13/21.26 ! [V_n,V_m] :
% 21.13/21.26 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 21.13/21.26 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 21.13/21.26 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zmult__eq__1__iff,axiom,
% 21.13/21.26 ! [V_n_2,V_m_2] :
% 21.13/21.26 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 21.13/21.26 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 21.13/21.26 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 21.13/21.26 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 21.13/21.26 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_of__int__m1,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zdiv__minus1__right,axiom,
% 21.13/21.26 ! [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) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_succ__def,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_abs__power__minus__one,axiom,
% 21.13/21.26 ! [V_n,T_a] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 & class_Rings_Olinordered__idom(T_a) )
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_div__eq__minus1,axiom,
% 21.13/21.26 ! [V_b] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_number__of__succ,axiom,
% 21.13/21.26 ! [V_k,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__gcd_Osimps,axiom,
% 21.13/21.26 ! [V_x,V_y] :
% 21.13/21.26 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.26 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 21.13/21.26 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.26 => 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 21.13/21.26 ! [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)))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__1__add__number__of,axiom,
% 21.13/21.26 ! [V_v] :
% 21.13/21.26 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 21.13/21.26 => 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__number__of__add__1,axiom,
% 21.13/21.26 ! [V_v] :
% 21.13/21.26 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 21.13/21.26 => 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_eq__number__of__eq,axiom,
% 21.13/21.26 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 21.13/21.26 <=> 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)))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_neg__number__of__pred__iff__0,axiom,
% 21.13/21.26 ! [V_v_2] :
% 21.13/21.26 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 21.13/21.26 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__number__of__mult__left,axiom,
% 21.13/21.26 ! [V_k,V_v_H,V_v] :
% 21.13/21.26 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 21.13/21.26 => 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) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_mult__nat__number__of,axiom,
% 21.13/21.26 ! [V_v_H,V_v] :
% 21.13/21.26 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 21.13/21.26 => 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_pred__Pls,axiom,
% 21.13/21.26 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 21.13/21.26
% 21.13/21.26 fof(fact_iszero__Numeral0,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Pls__def,axiom,
% 21.13/21.26 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I19_J,axiom,
% 21.13/21.26 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I2_J,axiom,
% 21.13/21.26 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__Pls,axiom,
% 21.13/21.26 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__Pls__right,axiom,
% 21.13/21.26 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 21.13/21.26
% 21.13/21.26 fof(fact_mult__Pls,axiom,
% 21.13/21.26 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 21.13/21.26
% 21.13/21.26 fof(fact_diff__bin__simps_I1_J,axiom,
% 21.13/21.26 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 21.13/21.26
% 21.13/21.26 fof(fact_minus__Pls,axiom,
% 21.13/21.26 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I37_J,axiom,
% 21.13/21.26 c_Int_OPls != c_Int_OMin ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I40_J,axiom,
% 21.13/21.26 c_Int_OMin != c_Int_OPls ).
% 21.13/21.26
% 21.13/21.26 fof(fact_succ__pred,axiom,
% 21.13/21.26 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 21.13/21.26
% 21.13/21.26 fof(fact_iszero__0,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( class_Rings_Osemiring__1(T_a)
% 21.13/21.26 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_iszero__def,axiom,
% 21.13/21.26 ! [V_z_2,T_b] :
% 21.13/21.26 ( class_Rings_Osemiring__1(T_b)
% 21.13/21.26 => ( c_Int_Oiszero(T_b,V_z_2)
% 21.13/21.26 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_not__iszero__1,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( class_Rings_Osemiring__1(T_a)
% 21.13/21.26 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_number__of__Pls,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_semiring__norm_I112_J,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__numeral__0,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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 ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__numeral__0__right,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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 ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_bin__less__0__simps_I1_J,axiom,
% 21.13/21.26 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__number__of__Pls,axiom,
% 21.13/21.26 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_semiring__norm_I113_J,axiom,
% 21.13/21.26 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zero__is__num__zero,axiom,
% 21.13/21.26 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Suc__diff__number__of,axiom,
% 21.13/21.26 ! [V_m,V_v] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I23_J,axiom,
% 21.13/21.26 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I20_J,axiom,
% 21.13/21.26 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I3_J,axiom,
% 21.13/21.26 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I6_J,axiom,
% 21.13/21.26 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_eq__number__of__Pls__Min,axiom,
% 21.13/21.26 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) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_not__neg__number__of__Pls,axiom,
% 21.13/21.26 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_eq__special_I1_J,axiom,
% 21.13/21.26 ! [V_y_2,T_b] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 21.13/21.26 <=> 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)))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_eq__special_I3_J,axiom,
% 21.13/21.26 ! [V_x_2,T_b] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.26 <=> 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)))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_succ__Min,axiom,
% 21.13/21.26 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 21.13/21.26
% 21.13/21.26 fof(fact_le__iff__pred__less,axiom,
% 21.13/21.26 ! [V_l_2,V_k_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_pred__def,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__Min__right,axiom,
% 21.13/21.26 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__Min,axiom,
% 21.13/21.26 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__number__of__diff__1,axiom,
% 21.13/21.26 ! [V_v] :
% 21.13/21.26 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 21.13/21.26 => 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_eq__0__number__of,axiom,
% 21.13/21.26 ! [V_v_2] :
% 21.13/21.26 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_eq__number__of__0,axiom,
% 21.13/21.26 ! [V_v_2] :
% 21.13/21.26 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_number__of2,axiom,
% 21.13/21.26 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))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_less__nat__number__of,axiom,
% 21.13/21.26 ! [V_v_H_2,V_v_2] :
% 21.13/21.26 ( 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)))
% 21.13/21.26 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 21.13/21.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 21.13/21.26 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_le__nat__number__of,axiom,
% 21.13/21.26 ! [V_v_H_2,V_v_2] :
% 21.13/21.26 ( 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)))
% 21.13/21.26 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 21.13/21.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nonzero__number__of__Min,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_le__special_I3_J,axiom,
% 21.13/21.26 ! [V_x_2,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 & class_Rings_Olinordered__idom(T_b) )
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_le__special_I1_J,axiom,
% 21.13/21.26 ! [V_y_2,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 & class_Rings_Olinordered__idom(T_b) )
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_less__special_I1_J,axiom,
% 21.13/21.26 ! [V_y_2,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 & class_Rings_Olinordered__idom(T_b) )
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_less__special_I3_J,axiom,
% 21.13/21.26 ! [V_x_2,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 & class_Rings_Olinordered__idom(T_b) )
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_less__0__number__of,axiom,
% 21.13/21.26 ! [V_v_2] :
% 21.13/21.26 ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__nat__number__of,axiom,
% 21.13/21.26 ! [V_v_H,V_v] :
% 21.13/21.26 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 21.13/21.26 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 21.13/21.26 => 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) )
% 21.13/21.26 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 21.13/21.26 => 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)) ) ) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_number__of__pred,axiom,
% 21.13/21.26 ! [V_w,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_eq__special_I4_J,axiom,
% 21.13/21.26 ! [V_x_2,T_b] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 21.13/21.26 <=> 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))))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_eq__special_I2_J,axiom,
% 21.13/21.26 ! [V_y_2,T_b] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 21.13/21.26 <=> 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)))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_diff__special_I1_J,axiom,
% 21.13/21.26 ! [V_w,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_diff__special_I2_J,axiom,
% 21.13/21.26 ! [V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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)))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Suc__div__eq__add3__div,axiom,
% 21.13/21.26 ! [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) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I51_J,axiom,
% 21.13/21.26 ! [V_l_2,V_k_2] :
% 21.13/21.26 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 21.13/21.26 <=> V_k_2 = V_l_2 ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I34_J,axiom,
% 21.13/21.26 ! [V_l_2,V_k_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_less__eq__int__code_I16_J,axiom,
% 21.13/21.26 ! [V_k2_2,V_k1_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I17_J,axiom,
% 21.13/21.26 ! [V_l_2,V_k_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_less__int__code_I16_J,axiom,
% 21.13/21.26 ! [V_k2_2,V_k1_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I39_J,axiom,
% 21.13/21.26 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I46_J,axiom,
% 21.13/21.26 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Bit1__Min,axiom,
% 21.13/21.26 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I43_J,axiom,
% 21.13/21.26 ! [V_l_2] :
% 21.13/21.26 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 21.13/21.26 <=> c_Int_OMin = V_l_2 ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I47_J,axiom,
% 21.13/21.26 ! [V_k_2] :
% 21.13/21.26 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 21.13/21.26 <=> V_k_2 = c_Int_OMin ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_bin__less__0__simps_I4_J,axiom,
% 21.13/21.26 ! [V_w_2] :
% 21.13/21.26 ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I22_J,axiom,
% 21.13/21.26 ! [V_k_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I12_J,axiom,
% 21.13/21.26 ! [V_k_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Bit1__def,axiom,
% 21.13/21.26 ! [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) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I30_J,axiom,
% 21.13/21.26 ! [V_k_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I26_J,axiom,
% 21.13/21.26 ! [V_k_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I9_J,axiom,
% 21.13/21.26 ! [V_k_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I13_J,axiom,
% 21.13/21.26 ! [V_k_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_neg__number__of__Bit1,axiom,
% 21.13/21.26 ! [V_w_2] :
% 21.13/21.26 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 21.13/21.26 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_minus__Bit1,axiom,
% 21.13/21.26 ! [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))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_iszero__number__of__Bit1,axiom,
% 21.13/21.26 ! [V_w,T_a] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 & class_Int_Oring__char__0(T_a) )
% 21.13/21.26 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_succ__Pls,axiom,
% 21.13/21.26 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_number__of__Bit1,axiom,
% 21.13/21.26 ! [V_w,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_mult__numeral__1__right,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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 ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_mult__numeral__1,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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 ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_numeral__1__eq__1,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_semiring__norm_I110_J,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I29_J,axiom,
% 21.13/21.26 ! [V_k_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I5_J,axiom,
% 21.13/21.26 ! [V_k_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_one__is__num__one,axiom,
% 21.13/21.26 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Numeral1__eq1__nat,axiom,
% 21.13/21.26 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_nat__numeral__1__eq__1,axiom,
% 21.13/21.26 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_diff__bin__simps_I4_J,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_minus__Min,axiom,
% 21.13/21.26 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_not__iszero__Numeral1,axiom,
% 21.13/21.26 ! [T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_numeral__1__eq__Suc__0,axiom,
% 21.13/21.26 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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_numeral__3__eq__3,axiom,
% 21.13/21.26 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)))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_power3__eq__cube,axiom,
% 21.13/21.26 ! [V_a,T_a] :
% 21.13/21.26 ( class_Groups_Omonoid__mult(T_a)
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 21.13/21.26 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))))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Suc3__eq__add__3,axiom,
% 21.13/21.26 ! [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) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 21.13/21.26 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)))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 21.13/21.26 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)))) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_le__special_I2_J,axiom,
% 21.13/21.26 ! [V_y_2,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 & class_Rings_Olinordered__idom(T_b) )
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_le__special_I4_J,axiom,
% 21.13/21.26 ! [V_x_2,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 & class_Rings_Olinordered__idom(T_b) )
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_less__special_I4_J,axiom,
% 21.13/21.26 ! [V_x_2,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 & class_Rings_Olinordered__idom(T_b) )
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_less__special_I2_J,axiom,
% 21.13/21.26 ! [V_y_2,T_b] :
% 21.13/21.26 ( ( class_Int_Onumber__ring(T_b)
% 21.13/21.26 & class_Rings_Olinordered__idom(T_b) )
% 21.13/21.26 => ( 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)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__special_I2_J,axiom,
% 21.13/21.26 ! [V_w,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__special_I3_J,axiom,
% 21.13/21.26 ! [V_v,T_a] :
% 21.13/21.26 ( class_Int_Onumber__ring(T_a)
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 21.13/21.26 ! [V_m,V_n] :
% 21.13/21.26 ( 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))
% 21.13/21.26 => 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)))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 21.13/21.26 ! [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) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_div__Suc__eq__div__add3,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_zmod__number__of__Bit1,axiom,
% 21.13/21.26 ! [V_v,V_w] :
% 21.13/21.26 ( ( 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)))
% 21.13/21.26 => 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)) )
% 21.13/21.26 & ( ~ 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)))
% 21.13/21.26 => 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)) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_neg__zmod__mult__2,axiom,
% 21.13/21.26 ! [V_b,V_a] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.26 => 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)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_pos__zdiv__mult__2,axiom,
% 21.13/21.26 ! [V_b,V_a] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_neg__zdiv__mult__2,axiom,
% 21.13/21.26 ! [V_b,V_a] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.13/21.26 => 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) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_pos__zmod__mult__2,axiom,
% 21.13/21.26 ! [V_b,V_a] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.13/21.26 => 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))) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_of__nat__double,axiom,
% 21.13/21.26 ! [V_x,T_a] :
% 21.13/21.26 ( class_Rings_Osemiring__1(T_a)
% 21.13/21.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 21.13/21.26 => 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))) ) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I48_J,axiom,
% 21.13/21.26 ! [V_l_2,V_k_2] :
% 21.13/21.26 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 21.13/21.26 <=> V_k_2 = V_l_2 ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_less__eq__int__code_I13_J,axiom,
% 21.13/21.26 ! [V_k2_2,V_k1_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I31_J,axiom,
% 21.13/21.26 ! [V_l_2,V_k_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_less__int__code_I13_J,axiom,
% 21.13/21.26 ! [V_k2_2,V_k1_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I14_J,axiom,
% 21.13/21.26 ! [V_l_2,V_k_2] :
% 21.13/21.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 21.13/21.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I44_J,axiom,
% 21.13/21.26 ! [V_k_2] :
% 21.13/21.26 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 21.13/21.26 <=> V_k_2 = c_Int_OPls ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I38_J,axiom,
% 21.13/21.26 ! [V_l_2] :
% 21.13/21.26 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 21.13/21.26 <=> c_Int_OPls = V_l_2 ) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Bit0__Pls,axiom,
% 21.13/21.26 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I50_J,axiom,
% 21.13/21.26 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_rel__simps_I49_J,axiom,
% 21.13/21.26 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_Bit0__def,axiom,
% 21.13/21.26 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_add__Bit0__Bit0,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.26 fof(fact_mult__Bit0,axiom,
% 21.13/21.26 ! [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)) ).
% 21.13/21.26
% 21.13/21.27 fof(fact_diff__bin__simps_I7_J,axiom,
% 21.13/21.27 ! [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)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_minus__Bit0,axiom,
% 21.13/21.27 ! [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)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_rel__simps_I45_J,axiom,
% 21.13/21.27 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 21.13/21.27
% 21.13/21.27 fof(fact_rel__simps_I42_J,axiom,
% 21.13/21.27 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_bin__less__0__simps_I3_J,axiom,
% 21.13/21.27 ! [V_w_2] :
% 21.13/21.27 ( 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)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_rel__simps_I21_J,axiom,
% 21.13/21.27 ! [V_k_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_rel__simps_I27_J,axiom,
% 21.13/21.27 ! [V_k_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_rel__simps_I32_J,axiom,
% 21.13/21.27 ! [V_l_2,V_k_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_less__eq__int__code_I14_J,axiom,
% 21.13/21.27 ! [V_k2_2,V_k1_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_rel__simps_I10_J,axiom,
% 21.13/21.27 ! [V_k_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_rel__simps_I4_J,axiom,
% 21.13/21.27 ! [V_k_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_less__int__code_I15_J,axiom,
% 21.13/21.27 ! [V_k2_2,V_k1_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_rel__simps_I16_J,axiom,
% 21.13/21.27 ! [V_l_2,V_k_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_add__Bit1__Bit0,axiom,
% 21.13/21.27 ! [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)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_add__Bit0__Bit1,axiom,
% 21.13/21.27 ! [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)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_diff__bin__simps_I3_J,axiom,
% 21.13/21.27 ! [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)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_diff__bin__simps_I10_J,axiom,
% 21.13/21.27 ! [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)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_diff__bin__simps_I9_J,axiom,
% 21.13/21.27 ! [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)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_rel__simps_I28_J,axiom,
% 21.13/21.27 ! [V_k_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_rel__simps_I8_J,axiom,
% 21.13/21.27 ! [V_k_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_zdiv__number__of__Bit0,axiom,
% 21.13/21.27 ! [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)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_neg__number__of__Bit0,axiom,
% 21.13/21.27 ! [V_w_2] :
% 21.13/21.27 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 21.13/21.27 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_pred__Bit1,axiom,
% 21.13/21.27 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_pred__Bit0,axiom,
% 21.13/21.27 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_pred__Min,axiom,
% 21.13/21.27 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_iszero__number__of__Bit0,axiom,
% 21.13/21.27 ! [V_w_2,T_b] :
% 21.13/21.27 ( ( class_Int_Onumber__ring(T_b)
% 21.13/21.27 & class_Int_Oring__char__0(T_b) )
% 21.13/21.27 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 21.13/21.27 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_succ__Bit0,axiom,
% 21.13/21.27 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_succ__Bit1,axiom,
% 21.13/21.27 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_number__of__Bit0,axiom,
% 21.13/21.27 ! [V_w,T_a] :
% 21.13/21.27 ( class_Int_Onumber__ring(T_a)
% 21.13/21.27 => 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)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_rel__simps_I15_J,axiom,
% 21.13/21.27 ! [V_l_2,V_k_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_less__int__code_I14_J,axiom,
% 21.13/21.27 ! [V_k2_2,V_k1_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_rel__simps_I33_J,axiom,
% 21.13/21.27 ! [V_l_2,V_k_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_less__eq__int__code_I15_J,axiom,
% 21.13/21.27 ! [V_k2_2,V_k1_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_mult__Bit1,axiom,
% 21.13/21.27 ! [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) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_rel__simps_I25_J,axiom,
% 21.13/21.27 ! [V_k_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_rel__simps_I11_J,axiom,
% 21.13/21.27 ! [V_k_2] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_diff__bin__simps_I6_J,axiom,
% 21.13/21.27 ! [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)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_diff__bin__simps_I5_J,axiom,
% 21.13/21.27 ! [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)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_diff__bin__simps_I8_J,axiom,
% 21.13/21.27 ! [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)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_add__Bit1__Bit1,axiom,
% 21.13/21.27 ! [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))) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_double__number__of__Bit0,axiom,
% 21.13/21.27 ! [V_w,T_a] :
% 21.13/21.27 ( class_Int_Onumber__ring(T_a)
% 21.13/21.27 => 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)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_number__of1,axiom,
% 21.13/21.27 ! [V_n] :
% 21.13/21.27 ( 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)))
% 21.13/21.27 => ( 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))))
% 21.13/21.27 & 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)))) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_mult__2__right,axiom,
% 21.13/21.27 ! [V_z,T_a] :
% 21.13/21.27 ( class_Int_Onumber__ring(T_a)
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_mult__2,axiom,
% 21.13/21.27 ! [V_z,T_a] :
% 21.13/21.27 ( class_Int_Onumber__ring(T_a)
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_one__add__one__is__two,axiom,
% 21.13/21.27 ! [T_a] :
% 21.13/21.27 ( class_Int_Onumber__ring(T_a)
% 21.13/21.27 => 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))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_zero__power2,axiom,
% 21.13/21.27 ! [T_a] :
% 21.13/21.27 ( class_Rings_Osemiring__1(T_a)
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_zero__eq__power2,axiom,
% 21.13/21.27 ! [V_a_2,T_b] :
% 21.13/21.27 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 21.13/21.27 => ( 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)
% 21.13/21.27 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_numeral__2__eq__2,axiom,
% 21.13/21.27 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))) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_semiring__norm_I115_J,axiom,
% 21.13/21.27 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))) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power2__eq__square,axiom,
% 21.13/21.27 ! [V_a,T_a] :
% 21.13/21.27 ( class_Groups_Omonoid__mult(T_a)
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 21.13/21.27 ! [V_x,T_a] :
% 21.13/21.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.27 => 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)))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 21.13/21.27 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))))) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_add__2__eq__Suc,axiom,
% 21.13/21.27 ! [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)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_add__2__eq__Suc_H,axiom,
% 21.13/21.27 ! [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)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_one__power2,axiom,
% 21.13/21.27 ! [T_a] :
% 21.13/21.27 ( class_Rings_Osemiring__1(T_a)
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power2__minus,axiom,
% 21.13/21.27 ! [V_a,T_a] :
% 21.13/21.27 ( class_Rings_Oring__1(T_a)
% 21.13/21.27 => 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)))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_nat__mult__2__right,axiom,
% 21.13/21.27 ! [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) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_nat__mult__2,axiom,
% 21.13/21.27 ! [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) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power__even__eq,axiom,
% 21.13/21.27 ! [V_n,V_a,T_a] :
% 21.13/21.27 ( class_Groups_Omonoid__mult(T_a)
% 21.13/21.27 => 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)))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 21.13/21.27 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)))) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 21.13/21.27 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)))) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power2__abs,axiom,
% 21.13/21.27 ! [V_a,T_a] :
% 21.13/21.27 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.27 => 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)))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_abs__power2,axiom,
% 21.13/21.27 ! [V_a,T_a] :
% 21.13/21.27 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.27 => 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)))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_nat__1__add__1,axiom,
% 21.13/21.27 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))) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_mod2__Suc__Suc,axiom,
% 21.13/21.27 ! [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)))) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_div2__Suc__Suc,axiom,
% 21.13/21.27 ! [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))))) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_zmod__number__of__Bit0,axiom,
% 21.13/21.27 ! [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))) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_add__self__div__2,axiom,
% 21.13/21.27 ! [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 ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power2__eq__imp__eq,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.27 => ( 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))))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 21.13/21.27 => V_x = V_y ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power2__le__imp__le,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.27 => ( 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))))))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 21.13/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_zero__le__power2,axiom,
% 21.13/21.27 ! [V_a,T_a] :
% 21.13/21.27 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.27 => 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)))))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_zero__less__power2,axiom,
% 21.13/21.27 ! [V_a_2,T_b] :
% 21.13/21.27 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.27 => ( 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))))))
% 21.13/21.27 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power2__less__0,axiom,
% 21.13/21.27 ! [V_a,T_a] :
% 21.13/21.27 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.27 => ~ 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))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_sum__power2__eq__zero__iff,axiom,
% 21.13/21.27 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.27 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.27 => ( 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)
% 21.13/21.27 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power2__eq__square__number__of,axiom,
% 21.13/21.27 ! [V_w,T_b] :
% 21.13/21.27 ( ( class_Groups_Omonoid__mult(T_b)
% 21.13/21.27 & class_Int_Onumber(T_b) )
% 21.13/21.27 => 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)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_less__2__cases,axiom,
% 21.13/21.27 ! [V_n] :
% 21.13/21.27 ( 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)))))
% 21.13/21.27 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.13/21.27 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_nat__2,axiom,
% 21.13/21.27 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))) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power2__eq__1__iff,axiom,
% 21.13/21.27 ! [V_a_2,T_b] :
% 21.13/21.27 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 21.13/21.27 => ( 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)
% 21.13/21.27 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 21.13/21.27 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 21.13/21.27 ! [V_n,V_x,T_a] :
% 21.13/21.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.27 => 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)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power__minus__even,axiom,
% 21.13/21.27 ! [V_n,V_a,T_a] :
% 21.13/21.27 ( class_Rings_Oring__1(T_a)
% 21.13/21.27 => 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)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power2__less__imp__less,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Rings_Olinordered__semidom(T_a)
% 21.13/21.27 => ( 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))))))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 21.13/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_sum__power2__ge__zero,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.27 => 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))))))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_sum__power2__le__zero__iff,axiom,
% 21.13/21.27 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.27 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.27 => ( 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)))
% 21.13/21.27 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_not__sum__power2__lt__zero,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.27 => ~ 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))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_sum__power2__gt__zero__iff,axiom,
% 21.13/21.27 ! [V_y_2,V_x_2,T_b] :
% 21.13/21.27 ( class_Rings_Olinordered__idom(T_b)
% 21.13/21.27 => ( 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)))))))
% 21.13/21.27 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power2__sum,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Int_Onumber__ring(T_a)
% 21.13/21.27 => 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)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_zero__le__even__power_H,axiom,
% 21.13/21.27 ! [V_n,V_a,T_a] :
% 21.13/21.27 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.27 => 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)))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power__odd__eq,axiom,
% 21.13/21.27 ! [V_n,V_a,T_a] :
% 21.13/21.27 ( class_Groups_Omonoid__mult(T_a)
% 21.13/21.27 => 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))))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 21.13/21.27 ! [V_n,V_x,T_a] :
% 21.13/21.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.13/21.27 => 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))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power__minus1__even,axiom,
% 21.13/21.27 ! [V_n,T_a] :
% 21.13/21.27 ( class_Rings_Oring__1(T_a)
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_zdiv__number__of__Bit1,axiom,
% 21.13/21.27 ! [V_v,V_w] :
% 21.13/21.27 ( ( 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)))
% 21.13/21.27 => 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)) )
% 21.13/21.27 & ( ~ 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)))
% 21.13/21.27 => 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)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_mod2__gr__0,axiom,
% 21.13/21.27 ! [V_m_2] :
% 21.13/21.27 ( 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))))))
% 21.13/21.27 <=> 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_div__2__gt__zero,axiom,
% 21.13/21.27 ! [V_n] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 21.13/21.27 => 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)))))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power2__diff,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Int_Onumber__ring(T_a)
% 21.13/21.27 => 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)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 21.13/21.27 ! [V_n,V_a,T_a] :
% 21.13/21.27 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.27 => ( 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)))))
% 21.13/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_odd__power__less__zero,axiom,
% 21.13/21.27 ! [V_n,V_a,T_a] :
% 21.13/21.27 ( class_Rings_Olinordered__idom(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.27 => 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))) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power__minus1__odd,axiom,
% 21.13/21.27 ! [V_n,T_a] :
% 21.13/21.27 ( class_Rings_Oring__1(T_a)
% 21.13/21.27 => 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)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power__m1__even,axiom,
% 21.13/21.27 ! [V_n,T_a] :
% 21.13/21.27 ( class_Int_Onumber__ring(T_a)
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power__m1__odd,axiom,
% 21.13/21.27 ! [V_n,T_a] :
% 21.13/21.27 ( class_Int_Onumber__ring(T_a)
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 21.13/21.27 ! [V_n] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.13/21.27 => 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)))))) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_int__of__code,axiom,
% 21.13/21.27 ! [V_k] :
% 21.13/21.27 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 21.13/21.27 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 21.13/21.27 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 21.13/21.27 => ( ( 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)
% 21.13/21.27 => 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)))))) )
% 21.13/21.27 & ( 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)
% 21.13/21.27 => 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)) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_one__code__numeral__code,axiom,
% 21.13/21.27 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)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_half__gt__zero__iff,axiom,
% 21.13/21.27 ! [V_r_2,T_b] :
% 21.13/21.27 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.13/21.27 & class_Int_Onumber__ring(T_b) )
% 21.13/21.27 => ( 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))))))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_half__gt__zero,axiom,
% 21.13/21.27 ! [V_r,T_a] :
% 21.13/21.27 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 21.13/21.27 & class_Int_Onumber__ring(T_a) )
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 21.13/21.27 => 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)))))) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 21.13/21.27 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_nat__intermed__int__val,axiom,
% 21.13/21.27 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 21.13/21.27 ( ! [B_i] :
% 21.13/21.27 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 21.13/21.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 21.13/21.27 => 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))) )
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 21.13/21.27 => ? [B_i] :
% 21.13/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 21.13/21.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 21.13/21.27 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_code__numeral__zero__minus__one,axiom,
% 21.13/21.27 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) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__zero,axiom,
% 21.13/21.27 ! [V_a,T_a] :
% 21.13/21.27 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__zero__left,axiom,
% 21.13/21.27 ! [V_a,T_a] :
% 21.13/21.27 ( class_Rings_Odivision__ring(T_a)
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_add__divide__distrib,axiom,
% 21.13/21.27 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.27 ( class_Rings_Odivision__ring(T_a)
% 21.13/21.27 => 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)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_times__divide__times__eq,axiom,
% 21.13/21.27 ! [V_w,V_z,V_y,V_x,T_a] :
% 21.13/21.27 ( class_Fields_Ofield__inverse__zero(T_a)
% 21.13/21.27 => 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)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_times__divide__eq__right,axiom,
% 21.13/21.27 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.27 ( class_Rings_Odivision__ring(T_a)
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_diff__divide__distrib,axiom,
% 21.13/21.27 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.27 ( class_Rings_Odivision__ring(T_a)
% 21.13/21.27 => 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)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__1,axiom,
% 21.13/21.27 ! [V_a,T_a] :
% 21.13/21.27 ( class_Rings_Odivision__ring(T_a)
% 21.13/21.27 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_minus__divide__divide,axiom,
% 21.13/21.27 ! [V_b,V_a,T_a] :
% 21.13/21.27 ( class_Fields_Ofield__inverse__zero(T_a)
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_minus__divide__right,axiom,
% 21.13/21.27 ! [V_b,V_a,T_a] :
% 21.13/21.27 ( class_Fields_Ofield__inverse__zero(T_a)
% 21.13/21.27 => 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)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_minus__divide__left,axiom,
% 21.13/21.27 ! [V_b,V_a,T_a] :
% 21.13/21.27 ( class_Rings_Odivision__ring(T_a)
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power__divide,axiom,
% 21.13/21.27 ! [V_n,V_b,V_a,T_a] :
% 21.13/21.27 ( class_Fields_Ofield__inverse__zero(T_a)
% 21.13/21.27 => 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)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_abs__divide,axiom,
% 21.13/21.27 ! [V_b,V_a,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 21.13/21.27 => 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)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 21.13/21.27 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 21.13/21.27 ! [V_y,V_x] :
% 21.13/21.27 ( c_Nat__Transfer_Ois__nat(V_x)
% 21.13/21.27 => ( c_Nat__Transfer_Ois__nat(V_y)
% 21.13/21.27 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 21.13/21.27 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 21.13/21.27 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 21.13/21.27 ! [V_y,V_x] :
% 21.13/21.27 ( c_Nat__Transfer_Ois__nat(V_x)
% 21.13/21.27 => ( c_Nat__Transfer_Ois__nat(V_y)
% 21.13/21.27 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 21.13/21.27 ! [V_y,V_x] :
% 21.13/21.27 ( c_Nat__Transfer_Ois__nat(V_x)
% 21.13/21.27 => ( c_Nat__Transfer_Ois__nat(V_y)
% 21.13/21.27 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 21.13/21.27 ! [V_y,V_x] :
% 21.13/21.27 ( c_Nat__Transfer_Ois__nat(V_x)
% 21.13/21.27 => ( c_Nat__Transfer_Ois__nat(V_y)
% 21.13/21.27 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 21.13/21.27 ! [V_n,V_x] :
% 21.13/21.27 ( c_Nat__Transfer_Ois__nat(V_x)
% 21.13/21.27 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_zero__le__divide__iff,axiom,
% 21.13/21.27 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.13/21.27 => ( 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)))
% 21.13/21.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 21.13/21.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 21.13/21.27 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__le__0__iff,axiom,
% 21.13/21.27 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.13/21.27 => ( 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)))
% 21.13/21.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 21.13/21.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 21.13/21.27 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__right__mono,axiom,
% 21.13/21.27 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.27 => 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))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__right__mono__neg,axiom,
% 21.13/21.27 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.27 => 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))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__strict__right__mono__neg,axiom,
% 21.13/21.27 ! [V_c,V_a,V_b,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.27 => 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))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__strict__right__mono,axiom,
% 21.13/21.27 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.27 => 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))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__neg__neg,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.27 => 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))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__neg__pos,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 21.13/21.27 => 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))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__pos__neg,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.27 => 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))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__pos__pos,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 21.13/21.27 => 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))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__less__0__iff,axiom,
% 21.13/21.27 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.13/21.27 => ( 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)))
% 21.13/21.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 21.13/21.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 21.13/21.27 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_zero__less__divide__iff,axiom,
% 21.13/21.27 ! [V_b_2,V_a_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.13/21.27 => ( 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)))
% 21.13/21.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 21.13/21.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 21.13/21.27 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_eq__divide__eq,axiom,
% 21.13/21.27 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 21.13/21.27 ( class_Fields_Ofield__inverse__zero(T_b)
% 21.13/21.27 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 21.13/21.27 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 )
% 21.13/21.27 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__eq__eq,axiom,
% 21.13/21.27 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 21.13/21.27 ( class_Fields_Ofield__inverse__zero(T_b)
% 21.13/21.27 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 21.13/21.27 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
% 21.13/21.27 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_mult__divide__mult__cancel__right,axiom,
% 21.13/21.27 ! [V_b,V_a,V_c,T_a] :
% 21.13/21.27 ( class_Fields_Ofield__inverse__zero(T_a)
% 21.13/21.27 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => 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) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_mult__divide__mult__cancel__left,axiom,
% 21.13/21.27 ! [V_b,V_a,V_c,T_a] :
% 21.13/21.27 ( class_Fields_Ofield__inverse__zero(T_a)
% 21.13/21.27 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => 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) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_frac__eq__eq,axiom,
% 21.13/21.27 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 21.13/21.27 ( class_Fields_Ofield(T_b)
% 21.13/21.27 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => ( 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)
% 21.13/21.27 <=> 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) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_eq__divide__imp,axiom,
% 21.13/21.27 ! [V_b,V_a,V_c,T_a] :
% 21.13/21.27 ( class_Rings_Odivision__ring(T_a)
% 21.13/21.27 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 21.13/21.27 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__eq__imp,axiom,
% 21.13/21.27 ! [V_a,V_b,V_c,T_a] :
% 21.13/21.27 ( class_Rings_Odivision__ring(T_a)
% 21.13/21.27 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 21.13/21.27 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_nonzero__divide__eq__eq,axiom,
% 21.13/21.27 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 21.13/21.27 ( class_Rings_Odivision__ring(T_b)
% 21.13/21.27 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 21.13/21.27 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_nonzero__eq__divide__eq,axiom,
% 21.13/21.27 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 21.13/21.27 ( class_Rings_Odivision__ring(T_b)
% 21.13/21.27 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 21.13/21.27 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_right__inverse__eq,axiom,
% 21.13/21.27 ! [V_a_2,V_b_2,T_b] :
% 21.13/21.27 ( class_Rings_Odivision__ring(T_b)
% 21.13/21.27 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 21.13/21.27 <=> V_a_2 = V_b_2 ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__self,axiom,
% 21.13/21.27 ! [V_a,T_a] :
% 21.13/21.27 ( class_Rings_Odivision__ring(T_a)
% 21.13/21.27 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__self__if,axiom,
% 21.13/21.27 ! [V_a,T_a] :
% 21.13/21.27 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 21.13/21.27 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 21.13/21.27 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_nonzero__minus__divide__divide,axiom,
% 21.13/21.27 ! [V_a,V_b,T_a] :
% 21.13/21.27 ( class_Rings_Odivision__ring(T_a)
% 21.13/21.27 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => 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) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_nonzero__minus__divide__right,axiom,
% 21.13/21.27 ! [V_a,V_b,T_a] :
% 21.13/21.27 ( class_Rings_Odivision__ring(T_a)
% 21.13/21.27 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => 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)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_nonzero__power__divide,axiom,
% 21.13/21.27 ! [V_n,V_a,V_b,T_a] :
% 21.13/21.27 ( class_Fields_Ofield(T_a)
% 21.13/21.27 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => 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)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_nonzero__abs__divide,axiom,
% 21.13/21.27 ! [V_a,V_b,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => 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)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_power__one__over,axiom,
% 21.13/21.27 ! [V_n,V_a,T_a] :
% 21.13/21.27 ( class_Fields_Ofield__inverse__zero(T_a)
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 21.13/21.27 ! [V_y,V_x] :
% 21.13/21.27 ( c_Nat__Transfer_Ois__nat(V_x)
% 21.13/21.27 => ( c_Nat__Transfer_Ois__nat(V_y)
% 21.13/21.27 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__nonpos__neg,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.27 => 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))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__nonpos__pos,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 21.13/21.27 => 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))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_frac__le,axiom,
% 21.13/21.27 ! [V_z,V_w,V_y,V_x,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 21.13/21.27 => 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))) ) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_frac__less,axiom,
% 21.13/21.27 ! [V_z,V_w,V_y,V_x,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 21.13/21.27 => 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))) ) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_frac__less2,axiom,
% 21.13/21.27 ! [V_z,V_w,V_y,V_x,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 21.13/21.27 => 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))) ) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__nonneg__neg,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.27 => 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))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__nonneg__pos,axiom,
% 21.13/21.27 ! [V_y,V_x,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 21.13/21.27 => 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))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__strict__left__mono__neg,axiom,
% 21.13/21.27 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.27 => ( 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)))
% 21.13/21.27 => 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))) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__strict__left__mono,axiom,
% 21.13/21.27 ! [V_c,V_a,V_b,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.27 => ( 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)))
% 21.13/21.27 => 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))) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_neg__divide__less__eq,axiom,
% 21.13/21.27 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_b)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_neg__less__divide__eq,axiom,
% 21.13/21.27 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_b)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 => ( 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_c_2)))
% 21.13/21.27 <=> 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_c_2))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_mult__imp__less__div__pos,axiom,
% 21.13/21.27 ! [V_x,V_z,V_y,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 21.13/21.27 => ( 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))
% 21.13/21.27 => 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))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_mult__imp__div__pos__less,axiom,
% 21.13/21.27 ! [V_z,V_x,V_y,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 21.13/21.27 => ( 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)))
% 21.13/21.27 => 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)) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_pos__divide__less__eq,axiom,
% 21.13/21.27 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_b)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 21.13/21.27 <=> 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_c_2))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_pos__less__divide__eq,axiom,
% 21.13/21.27 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_b)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.27 => ( 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_c_2)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__less__eq,axiom,
% 21.13/21.27 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 21.13/21.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.27 => 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_c_2))) )
% 21.13/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.27 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 21.13/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_less__divide__eq,axiom,
% 21.13/21.27 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.13/21.27 => ( 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_c_2)))
% 21.13/21.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 21.13/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.27 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 => 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_c_2))) )
% 21.13/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_is__nat__def,axiom,
% 21.13/21.27 ! [V_x_2] :
% 21.13/21.27 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_add__num__frac,axiom,
% 21.13/21.27 ! [V_x,V_z,V_y,T_a] :
% 21.13/21.27 ( class_Fields_Ofield__inverse__zero(T_a)
% 21.13/21.27 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => 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) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_add__divide__eq__iff,axiom,
% 21.13/21.27 ! [V_y,V_x,V_z,T_a] :
% 21.13/21.27 ( class_Fields_Ofield(T_a)
% 21.13/21.27 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => 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) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_add__frac__num,axiom,
% 21.13/21.27 ! [V_z,V_x,V_y,T_a] :
% 21.13/21.27 ( class_Fields_Ofield__inverse__zero(T_a)
% 21.13/21.27 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => 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) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__add__eq__iff,axiom,
% 21.13/21.27 ! [V_y,V_x,V_z,T_a] :
% 21.13/21.27 ( class_Fields_Ofield(T_a)
% 21.13/21.27 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => 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) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_add__frac__eq,axiom,
% 21.13/21.27 ! [V_w,V_x,V_z,V_y,T_a] :
% 21.13/21.27 ( class_Fields_Ofield(T_a)
% 21.13/21.27 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => 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)) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_diff__frac__eq,axiom,
% 21.13/21.27 ! [V_w,V_x,V_z,V_y,T_a] :
% 21.13/21.27 ( class_Fields_Ofield(T_a)
% 21.13/21.27 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => 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)) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__diff__eq__iff,axiom,
% 21.13/21.27 ! [V_y,V_x,V_z,T_a] :
% 21.13/21.27 ( class_Fields_Ofield(T_a)
% 21.13/21.27 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => 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) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_diff__divide__eq__iff,axiom,
% 21.13/21.27 ! [V_y,V_x,V_z,T_a] :
% 21.13/21.27 ( class_Fields_Ofield(T_a)
% 21.13/21.27 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 21.13/21.27 => 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) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_eq__divide__eq__number__of1,axiom,
% 21.13/21.27 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 21.13/21.27 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 21.13/21.27 & class_Int_Onumber(T_b) )
% 21.13/21.27 => ( 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))
% 21.13/21.27 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => 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 )
% 21.13/21.27 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_eq__divide__eq__number__of,axiom,
% 21.13/21.27 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 21.13/21.27 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 21.13/21.27 & class_Int_Onumber(T_b) )
% 21.13/21.27 => ( 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_c_2)
% 21.13/21.27 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2 )
% 21.13/21.27 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__eq__eq__number__of,axiom,
% 21.13/21.27 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 21.13/21.27 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 21.13/21.27 & class_Int_Onumber(T_b) )
% 21.13/21.27 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
% 21.13/21.27 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => 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_c_2) )
% 21.13/21.27 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__eq__eq__number__of1,axiom,
% 21.13/21.27 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 21.13/21.27 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 21.13/21.27 & class_Int_Onumber(T_b) )
% 21.13/21.27 => ( 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
% 21.13/21.27 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => 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)) )
% 21.13/21.27 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 21.13/21.27 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_gt__half__sum,axiom,
% 21.13/21.27 ! [V_b,V_a,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.27 => 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)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_less__half__sum,axiom,
% 21.13/21.27 ! [V_b,V_a,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 21.13/21.27 => 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))))) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__Numeral0,axiom,
% 21.13/21.27 ! [V_x,T_a] :
% 21.13/21.27 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 21.13/21.27 & class_Int_Onumber__ring(T_a) )
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_abs__div__pos,axiom,
% 21.13/21.27 ! [V_x,V_y,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 21.13/21.27 => 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)) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__numeral__1,axiom,
% 21.13/21.27 ! [V_a,T_a] :
% 21.13/21.27 ( ( class_Fields_Ofield(T_a)
% 21.13/21.27 & class_Int_Onumber__ring(T_a) )
% 21.13/21.27 => 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 ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__Numeral1,axiom,
% 21.13/21.27 ! [V_x,T_a] :
% 21.13/21.27 ( ( class_Fields_Ofield(T_a)
% 21.13/21.27 & class_Int_Onumber__ring(T_a) )
% 21.13/21.27 => 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 ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__minus1,axiom,
% 21.13/21.27 ! [V_x,T_a] :
% 21.13/21.27 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 21.13/21.27 & class_Int_Onumber__ring(T_a) )
% 21.13/21.27 => 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) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_zero__code__numeral__code,axiom,
% 21.13/21.27 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) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_le__divide__eq,axiom,
% 21.13/21.27 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.13/21.27 => ( 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_c_2)))
% 21.13/21.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 21.13/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.27 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 => 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_c_2))) )
% 21.13/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__le__eq,axiom,
% 21.13/21.27 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 21.13/21.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.27 => 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_c_2))) )
% 21.13/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.27 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 21.13/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_pos__le__divide__eq,axiom,
% 21.13/21.27 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_b)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.27 => ( 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_c_2)))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_pos__divide__le__eq,axiom,
% 21.13/21.27 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_b)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 21.13/21.27 <=> 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_c_2))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_mult__imp__div__pos__le,axiom,
% 21.13/21.27 ! [V_z,V_x,V_y,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 21.13/21.27 => ( 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)))
% 21.13/21.27 => 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)) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_mult__imp__le__div__pos,axiom,
% 21.13/21.27 ! [V_x,V_z,V_y,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 21.13/21.27 => ( 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))
% 21.13/21.27 => 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))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_neg__le__divide__eq,axiom,
% 21.13/21.27 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_b)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 => ( 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_c_2)))
% 21.13/21.27 <=> 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_c_2))) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_neg__divide__le__eq,axiom,
% 21.13/21.27 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_b)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 21.13/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__left__mono,axiom,
% 21.13/21.27 ! [V_c,V_a,V_b,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 21.13/21.27 => ( 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)))
% 21.13/21.27 => 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))) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__left__mono__neg,axiom,
% 21.13/21.27 ! [V_c,V_b,V_a,T_a] :
% 21.13/21.27 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 21.13/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 21.13/21.27 => ( 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)))
% 21.13/21.27 => 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))) ) ) ) ) ).
% 21.13/21.27
% 21.13/21.27 fof(fact_divide__less__eq__number__of1,axiom,
% 21.13/21.27 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 21.13/21.27 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.13/21.27 & class_Int_Onumber(T_b) )
% 21.13/21.27 => ( 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))
% 21.13/21.27 <=> ( ( 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)))
% 21.13/21.27 => 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)))) )
% 21.13/21.27 & ( ~ 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)))
% 21.13/21.27 => ( ( 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)))
% 21.13/21.27 => 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)) )
% 21.13/21.27 & ( ~ 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)))
% 21.13/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divide__less__eq__number__of,axiom,
% 21.40/21.27 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 21.40/21.27 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.40/21.27 & class_Int_Onumber(T_b) )
% 21.40/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 21.40/21.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.40/21.27 => 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_c_2))) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.40/21.27 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.40/21.27 => 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_c_2)),V_b_2)) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.40/21.27 => 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))) ) ) ) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_less__divide__eq__number__of,axiom,
% 21.40/21.27 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 21.40/21.27 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.40/21.27 & class_Int_Onumber(T_b) )
% 21.40/21.27 => ( 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_c_2)))
% 21.40/21.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.40/21.27 => 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_c_2)),V_b_2)) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.40/21.27 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.40/21.27 => 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_c_2))) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.40/21.27 => 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))) ) ) ) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_less__divide__eq__number__of1,axiom,
% 21.40/21.27 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 21.40/21.27 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.40/21.27 & class_Int_Onumber(T_b) )
% 21.40/21.27 => ( 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))))
% 21.40/21.27 <=> ( ( 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)))
% 21.40/21.27 => 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)) )
% 21.40/21.27 & ( ~ 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)))
% 21.40/21.27 => ( ( 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)))
% 21.40/21.27 => 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)))) )
% 21.40/21.27 & ( ~ 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)))
% 21.40/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_power__diff,axiom,
% 21.40/21.27 ! [V_m,V_n,V_a,T_a] :
% 21.40/21.27 ( class_Fields_Ofield(T_a)
% 21.40/21.27 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 21.40/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 21.40/21.27 => 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)) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_minus1__divide,axiom,
% 21.40/21.27 ! [V_x,T_a] :
% 21.40/21.27 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 21.40/21.27 & class_Int_Onumber__ring(T_a) )
% 21.40/21.27 => 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)) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 21.40/21.27 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_le__divide__eq__number__of1,axiom,
% 21.40/21.27 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 21.40/21.27 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.40/21.27 & class_Int_Onumber(T_b) )
% 21.40/21.27 => ( 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))))
% 21.40/21.27 <=> ( ( 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)))
% 21.40/21.27 => 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)) )
% 21.40/21.27 & ( ~ 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)))
% 21.40/21.27 => ( ( 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)))
% 21.40/21.27 => 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)))) )
% 21.40/21.27 & ( ~ 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)))
% 21.40/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_le__divide__eq__number__of,axiom,
% 21.40/21.27 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 21.40/21.27 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.40/21.27 & class_Int_Onumber(T_b) )
% 21.40/21.27 => ( 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_c_2)))
% 21.40/21.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.40/21.27 => 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_c_2)),V_b_2)) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.40/21.27 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.40/21.27 => 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_c_2))) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.40/21.27 => 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))) ) ) ) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divide__le__eq__number__of,axiom,
% 21.40/21.27 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 21.40/21.27 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.40/21.27 & class_Int_Onumber(T_b) )
% 21.40/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 21.40/21.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.40/21.27 => 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_c_2))) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 21.40/21.27 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.40/21.27 => 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_c_2)),V_b_2)) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 21.40/21.27 => 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))) ) ) ) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divide__le__eq__number__of1,axiom,
% 21.40/21.27 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 21.40/21.27 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 21.40/21.27 & class_Int_Onumber(T_b) )
% 21.40/21.27 => ( 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))
% 21.40/21.27 <=> ( ( 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)))
% 21.40/21.27 => 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)))) )
% 21.40/21.27 & ( ~ 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)))
% 21.40/21.27 => ( ( 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)))
% 21.40/21.27 => 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)) )
% 21.40/21.27 & ( ~ 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)))
% 21.40/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_nat__of__aux__code,axiom,
% 21.40/21.27 ! [V_n,V_i] :
% 21.40/21.27 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 21.40/21.27 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 21.40/21.27 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 21.40/21.27 => 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)) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_code__numeral_Osize_I1_J,axiom,
% 21.40/21.27 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) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_code__numeral_Osize_I3_J,axiom,
% 21.40/21.27 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) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 21.40/21.27 ! [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 ).
% 21.40/21.27
% 21.40/21.27 fof(fact_log_Osimps,axiom,
% 21.40/21.27 ! [V_i,V_b] :
% 21.40/21.27 ( ( ( 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)))
% 21.40/21.27 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 21.40/21.27 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 21.40/21.27 & ( ~ ( 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)))
% 21.40/21.27 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 21.40/21.27 => 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))) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_field__le__epsilon,axiom,
% 21.40/21.27 ! [V_y,V_x,T_a] :
% 21.40/21.27 ( class_Fields_Olinordered__field(T_a)
% 21.40/21.27 => ( ! [B_e] :
% 21.40/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 21.40/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) )
% 21.40/21.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_minus__shift__def,axiom,
% 21.40/21.27 ! [V_r,V_l,V_k] :
% 21.40/21.27 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 21.40/21.27 => 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) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 21.40/21.27 => 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) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_inc__shift__def,axiom,
% 21.40/21.27 ! [V_k,V_v] :
% 21.40/21.27 ( ( V_v = V_k
% 21.40/21.27 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 21.40/21.27 & ( V_v != V_k
% 21.40/21.27 => 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)) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_code__numeral_Osize_I4_J,axiom,
% 21.40/21.27 ! [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))) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_code__numeral_Osize_I2_J,axiom,
% 21.40/21.27 ! [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))) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_minus__code__numeral__code,axiom,
% 21.40/21.27 ! [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) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_code__numeral_Oinject,axiom,
% 21.40/21.27 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 21.40/21.27 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 21.40/21.27 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 21.40/21.27 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 21.40/21.27 ! [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) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 21.40/21.27 ! [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) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_Suc__code__numeral__minus__one,axiom,
% 21.40/21.27 ! [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 ).
% 21.40/21.27
% 21.40/21.27 fof(fact_subtract__code__numeral__def,axiom,
% 21.40/21.27 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 21.40/21.27 ! [V_w] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 => ( ( 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))))
% 21.40/21.27 => 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))) )
% 21.40/21.27 & ( ~ 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))))
% 21.40/21.27 => 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)))) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_diff__nat__number__of,axiom,
% 21.40/21.27 ! [V_v_2,V_v_H_2] :
% 21.40/21.27 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 21.40/21.27 => 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) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 21.40/21.27 => 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)) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 21.40/21.27 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divmod__nat__step,axiom,
% 21.40/21.27 ! [V_m,V_n] :
% 21.40/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.40/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 21.40/21.27 => 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)) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_code__numeral__not__eq__zero,axiom,
% 21.40/21.27 ! [V_i_2] :
% 21.40/21.27 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 21.40/21.27 <=> 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)) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 21.40/21.27 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 21.40/21.27 ! [V_m_2,V_n_2] :
% 21.40/21.27 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 21.40/21.27 <=> V_n_2 = V_m_2 ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divmod__nat__zero,axiom,
% 21.40/21.27 ! [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) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_fun__Compl__def,axiom,
% 21.40/21.27 ! [V_x_2,V_A_2,T_c,T_b] :
% 21.40/21.27 ( class_Groups_Ouminus(T_b)
% 21.40/21.27 => 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)) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_fun__diff__def,axiom,
% 21.40/21.27 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.27 ( class_Groups_Ominus(T_b)
% 21.40/21.27 => 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)) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 21.40/21.27 ! [V_n_2,V_m_2] :
% 21.40/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 21.40/21.27 <=> 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)) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divmod__nat__base,axiom,
% 21.40/21.27 ! [V_n,V_m] :
% 21.40/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.40/21.27 => 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) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_less__eq__Suc__le__raw,axiom,
% 21.40/21.27 ! [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)) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_diff__Suc,axiom,
% 21.40/21.27 ! [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)) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_nat__number__of__Bit0,axiom,
% 21.40/21.27 ! [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))) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_times__code__numeral__code,axiom,
% 21.40/21.27 ! [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)) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divmod__nat__div__mod,axiom,
% 21.40/21.27 ! [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)) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_power__number__of__even,axiom,
% 21.40/21.27 ! [V_w_2,V_z_2,T_b] :
% 21.40/21.27 ( class_Int_Onumber__ring(T_b)
% 21.40/21.27 => 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))) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_zpower__number__of__even,axiom,
% 21.40/21.27 ! [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))) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_power__number__of__even__number__of,axiom,
% 21.40/21.27 ! [V_w_2,V_v_2,T_b] :
% 21.40/21.27 ( class_Int_Onumber__ring(T_b)
% 21.40/21.27 => 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))) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_diff__nat__eq__if,axiom,
% 21.40/21.27 ! [V_z_2,V_z_H_2] :
% 21.40/21.27 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 21.40/21.27 => 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) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 21.40/21.27 => 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)) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_negDivAlg__div__mod,axiom,
% 21.40/21.27 ! [V_l,V_k] :
% 21.40/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 21.40/21.27 => 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)) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_negDivAlg__minus1,axiom,
% 21.40/21.27 ! [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))) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 21.40/21.27 ! [V_n_2,T_b] :
% 21.40/21.27 ( class_Rings_Osemiring__1(T_b)
% 21.40/21.27 => 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)) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_adjust__eq,axiom,
% 21.40/21.27 ! [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))) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_zero__code__numeral__def,axiom,
% 21.40/21.27 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_one__code__numeral__def,axiom,
% 21.40/21.27 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_less__code__numeral__code,axiom,
% 21.40/21.27 ! [V_m_2,V_n_2] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_Suc__eq__number__of,axiom,
% 21.40/21.27 ! [V_v_2,V_n_2] :
% 21.40/21.27 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 21.40/21.27 <=> 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))))) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_eq__number__of__Suc,axiom,
% 21.40/21.27 ! [V_n_2,V_v_2] :
% 21.40/21.27 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 21.40/21.27 <=> 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))))) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_nat__case__number__of,axiom,
% 21.40/21.27 ! [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))) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_nat__rec__number__of,axiom,
% 21.40/21.27 ! [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)))) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_plus__code__numeral__code,axiom,
% 21.40/21.27 ! [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)) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_less__eq__code__numeral__code,axiom,
% 21.40/21.27 ! [V_m_2,V_n_2] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_nat__number__of__Bit1,axiom,
% 21.40/21.27 ! [V_w_2] :
% 21.40/21.27 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 21.40/21.27 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 21.40/21.27 => 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)))) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_less__Suc__number__of,axiom,
% 21.40/21.27 ! [V_v_2,V_n_2] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 <=> 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))))) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_less__number__of__Suc,axiom,
% 21.40/21.27 ! [V_n_2,V_v_2] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 <=> 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)))) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_le__number__of__Suc,axiom,
% 21.40/21.27 ! [V_n_2,V_v_2] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 <=> 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)))) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_le__Suc__number__of,axiom,
% 21.40/21.27 ! [V_v_2,V_n_2] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 <=> 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))))) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_subtract__code__numeral__code,axiom,
% 21.40/21.27 ! [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)) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_nat__case__add__eq__if,axiom,
% 21.40/21.27 ! [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)))) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_nat__rec__add__eq__if,axiom,
% 21.40/21.27 ! [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))))) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_power__number__of__odd,axiom,
% 21.40/21.27 ! [V_z_2,V_w_2,T_b] :
% 21.40/21.27 ( class_Int_Onumber__ring(T_b)
% 21.40/21.27 => ( ( 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)))
% 21.40/21.27 => 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))) )
% 21.40/21.27 & ( ~ 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)))
% 21.40/21.27 => 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) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_zpower__number__of__odd,axiom,
% 21.40/21.27 ! [V_z_2,V_w_2] :
% 21.40/21.27 ( ( 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)))
% 21.40/21.27 => 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))) )
% 21.40/21.27 & ( ~ 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)))
% 21.40/21.27 => 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) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_negDivAlg_Osimps,axiom,
% 21.40/21.27 ! [V_b,V_a] :
% 21.40/21.27 ( ( ( 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)))
% 21.40/21.27 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 21.40/21.27 => 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)) )
% 21.40/21.27 & ( ~ ( 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)))
% 21.40/21.27 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 21.40/21.27 => 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))) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_power__number__of__odd__number__of,axiom,
% 21.40/21.27 ! [V_v_2,V_w_2,T_b] :
% 21.40/21.27 ( class_Int_Onumber__ring(T_b)
% 21.40/21.27 => ( ( 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)))
% 21.40/21.27 => 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))) )
% 21.40/21.27 & ( ~ 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)))
% 21.40/21.27 => 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) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 21.40/21.27 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ).
% 21.40/21.27
% 21.40/21.27 fof(fact_negDivAlg__eqn__number__of,axiom,
% 21.40/21.27 ! [V_w,V_v] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 => ( ( 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))))
% 21.40/21.27 => 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))) )
% 21.40/21.27 & ( ~ 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))))
% 21.40/21.27 => 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)))) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_negDivAlg__eqn,axiom,
% 21.40/21.27 ! [V_a,V_b] :
% 21.40/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.40/21.27 => ( ( 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)))
% 21.40/21.27 => 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)) )
% 21.40/21.27 & ( ~ 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)))
% 21.40/21.27 => 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))) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_norm__frac_Osimps,axiom,
% 21.40/21.27 ! [V_a_2,V_b_2] :
% 21.40/21.27 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.27 => 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)) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.27 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.27 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 21.40/21.27 => 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)) )
% 21.40/21.27 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.27 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 21.40/21.27 => 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))) ) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 21.40/21.27 ! [V_w] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 => ( ( 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)))
% 21.40/21.27 => 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)) )
% 21.40/21.27 & ( ~ 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)))
% 21.40/21.27 => 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)))) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_posDivAlg_Osimps,axiom,
% 21.40/21.27 ! [V_b,V_a] :
% 21.40/21.27 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 21.40/21.27 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 21.40/21.27 => 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) )
% 21.40/21.27 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 21.40/21.27 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 21.40/21.27 => 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))) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_adjust__def,axiom,
% 21.40/21.27 ! [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))))))) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_posDivAlg__eqn__number__of,axiom,
% 21.40/21.27 ! [V_w,V_v] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 => ( ( 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)))
% 21.40/21.27 => 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)) )
% 21.40/21.27 & ( ~ 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)))
% 21.40/21.27 => 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)))) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_posDivAlg__0,axiom,
% 21.40/21.27 ! [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)) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_posDivAlg__div__mod,axiom,
% 21.40/21.27 ! [V_l,V_k] :
% 21.40/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 21.40/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 21.40/21.27 => 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)) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_posDivAlg__eqn,axiom,
% 21.40/21.27 ! [V_a,V_b] :
% 21.40/21.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.40/21.27 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 21.40/21.27 => 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) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 21.40/21.27 => 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))) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_of__int__num,axiom,
% 21.40/21.27 ! [V_k_2,T_b] :
% 21.40/21.27 ( class_Rings_Oring__1(T_b)
% 21.40/21.27 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.27 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 21.40/21.27 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.27 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.27 => 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))) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.27 => 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))))) ) ) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_MGT__def,axiom,
% 21.40/21.27 ! [V_c_2] : c_Hoare__Mirabelle_OMGT(V_c_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_c_2),c_Natural_Oevalc(V_c_2)) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 21.40/21.27 ! [V_a,V_r,V_q,V_c,V_b] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 21.40/21.27 => 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)))) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 21.40/21.27 ! [V_c,V_r,V_q,V_b,V_a] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 21.40/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 21.40/21.27 => 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)))) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_negDivAlg_Opsimps,axiom,
% 21.40/21.27 ! [V_b_2,V_a_2] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 => ( ( ( 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)))
% 21.40/21.27 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 21.40/21.27 => 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)) )
% 21.40/21.27 & ( ~ ( 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)))
% 21.40/21.27 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 21.40/21.27 => 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))) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divmod__nat__rel__unique,axiom,
% 21.40/21.27 ! [V_qr_H,V_qr,V_n,V_m] :
% 21.40/21.27 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 21.40/21.27 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 21.40/21.27 => V_qr = V_qr_H ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_accp__downward,axiom,
% 21.40/21.27 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 21.40/21.27 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 21.40/21.27 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 21.40/21.27 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_accp_Oequations,axiom,
% 21.40/21.27 ! [V_a_2,V_r_2,T_b] :
% 21.40/21.27 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 21.40/21.27 <=> ! [B_x] :
% 21.40/21.27 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 21.40/21.27 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_accp_Osimps,axiom,
% 21.40/21.27 ! [V_a_2,V_r_2,T_b] :
% 21.40/21.27 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 21.40/21.27 <=> ! [B_x] :
% 21.40/21.27 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 21.40/21.27 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_accp__subset,axiom,
% 21.40/21.27 ! [V_R2_2,V_R1_2,T_b] :
% 21.40/21.27 ( 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))
% 21.40/21.27 => 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))) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divmod__nat__eq,axiom,
% 21.40/21.27 ! [V_qr,V_n,V_m] :
% 21.40/21.27 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 21.40/21.27 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 21.40/21.27 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_mod__eq,axiom,
% 21.40/21.27 ! [V_r,V_q,V_n,V_m] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_div__eq,axiom,
% 21.40/21.27 ! [V_r,V_q,V_n,V_m] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divmod__nat__rel,axiom,
% 21.40/21.27 ! [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)))) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divmod__int__mod__div,axiom,
% 21.40/21.27 ! [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)) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 21.40/21.27 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 => ( 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)))
% 21.40/21.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 21.40/21.27 => 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)))) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_posDivAlg_Opsimps,axiom,
% 21.40/21.27 ! [V_b_2,V_a_2] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 21.40/21.27 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 21.40/21.27 => 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) )
% 21.40/21.27 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 21.40/21.27 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 21.40/21.27 => 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))) ) ) ) ).
% 21.40/21.27
% 21.40/21.27 fof(fact_norm__frac_Opsimps,axiom,
% 21.40/21.27 ! [V_b_2,V_a_2] :
% 21.40/21.27 ( 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)))
% 21.40/21.27 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.27 => 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)) )
% 21.40/21.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.28 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 21.40/21.28 => 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)) )
% 21.40/21.28 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 21.40/21.28 => 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))) ) ) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Nitpick_OFrac__def,axiom,
% 21.40/21.28 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)))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_divmod__int__def,axiom,
% 21.40/21.28 ! [V_b,V_a] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.40/21.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.40/21.28 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 21.40/21.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.40/21.28 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => 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)) )
% 21.40/21.28 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => 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))) ) ) ) ) )
% 21.40/21.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.40/21.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.40/21.28 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 21.40/21.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.40/21.28 => 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))) ) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_negDivAlg_Opinduct,axiom,
% 21.40/21.28 ! [V_P_2,V_a1_2,V_a0_2] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( ! [B_a,B_b] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( ( ~ ( 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)))
% 21.40/21.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_negateSnd__eq,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_splitI,axiom,
% 21.40/21.28 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 21.40/21.28 => 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))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_prod__caseI,axiom,
% 21.40/21.28 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 21.40/21.28 => 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))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_posDivAlg_Opinduct,axiom,
% 21.40/21.28 ! [V_P_2,V_a1_2,V_a0_2] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( ! [B_a,B_b] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 21.40/21.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_nat__gcd_Opsimps,axiom,
% 21.40/21.28 ! [V_y_2,V_x_2] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.28 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 21.40/21.28 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.28 => 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)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_divmod__int__pdivmod,axiom,
% 21.40/21.28 ! [V_l_2,V_k_2] :
% 21.40/21.28 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => 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)) )
% 21.40/21.28 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => 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) )
% 21.40/21.28 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => 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)))) ) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_apsnd__conv,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_split__paired__All,axiom,
% 21.40/21.28 ! [T_c,T_b,V_P_2] :
% 21.40/21.28 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 21.40/21.28 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Pair__eq,axiom,
% 21.40/21.28 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 21.40/21.28 ( 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)
% 21.40/21.28 <=> ( V_a_2 = V_a_H_2
% 21.40/21.28 & V_b_2 = V_b_H_2 ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Pair__inject,axiom,
% 21.40/21.28 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 21.40/21.28 ( 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)
% 21.40/21.28 => ~ ( V_a = V_a_H
% 21.40/21.28 => V_b != V_b_H ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_negateSnd__def,axiom,
% 21.40/21.28 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_split__weak__cong,axiom,
% 21.40/21.28 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 21.40/21.28 ( V_p_2 = V_q_2
% 21.40/21.28 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_prod_Osimps_I2_J,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_split__conv,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_splitD,axiom,
% 21.40/21.28 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_split__eta,axiom,
% 21.40/21.28 ! [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 ).
% 21.40/21.28
% 21.40/21.28 fof(fact_split__twice,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_pdivmod__def,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_pdivmod__posDivAlg,axiom,
% 21.40/21.28 ! [V_k,V_l] :
% 21.40/21.28 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => 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)) )
% 21.40/21.28 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => 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)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_divmod__int__code,axiom,
% 21.40/21.28 ! [V_l_2,V_k_2] :
% 21.40/21.28 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => 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)) )
% 21.40/21.28 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => 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) )
% 21.40/21.28 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => 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)))) ) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_div__mod__code__numeral__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_zmult2__lemma,axiom,
% 21.40/21.28 ! [V_c,V_r,V_q,V_b,V_a] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 21.40/21.28 => 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)))) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_mod__pos__neg__1__number__of,axiom,
% 21.40/21.28 ! [V_w] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => 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))))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_divmod__int__rel__def,axiom,
% 21.40/21.28 ! [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))))))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_norm__frac_Opinduct,axiom,
% 21.40/21.28 ! [V_P_2,V_a1_2,V_a0_2] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( ! [B_a,B_b] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_splitD_H,axiom,
% 21.40/21.28 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 21.40/21.28 ( 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_c_2))
% 21.40/21.28 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_snd__conv,axiom,
% 21.40/21.28 ! [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 ).
% 21.40/21.28
% 21.40/21.28 fof(fact_snd__eqD,axiom,
% 21.40/21.28 ! [V_a,V_y,V_x,T_a,T_b] :
% 21.40/21.28 ( 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
% 21.40/21.28 => V_y = V_a ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_apsnd__eq__conv,axiom,
% 21.40/21.28 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 21.40/21.28 ( 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)
% 21.40/21.28 <=> 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_snd__apsnd,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_snd__def,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_mod__int__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_divmod__int__rel__0,axiom,
% 21.40/21.28 ! [V_b] :
% 21.40/21.28 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => 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)))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_self__remainder,axiom,
% 21.40/21.28 ! [V_r,V_q,V_a] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_unique__quotient,axiom,
% 21.40/21.28 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( 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)))
% 21.40/21.28 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => V_q = V_q_H ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_unique__remainder,axiom,
% 21.40/21.28 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( 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)))
% 21.40/21.28 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => V_r = V_r_H ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_divmod__int__rel__neg,axiom,
% 21.40/21.28 ! [V_qr,V_b,V_a] :
% 21.40/21.28 ( 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))
% 21.40/21.28 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_divmod__int__correct,axiom,
% 21.40/21.28 ! [V_a,V_b] :
% 21.40/21.28 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_self__quotient,axiom,
% 21.40/21.28 ! [V_r,V_q,V_a] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_divmod__int__rel__mod,axiom,
% 21.40/21.28 ! [V_r,V_q,V_b,V_a] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_divmod__int__rel__div,axiom,
% 21.40/21.28 ! [V_r,V_q,V_b,V_a] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_negDivAlg__correct,axiom,
% 21.40/21.28 ! [V_b,V_a] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.40/21.28 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_mod__neg__pos,axiom,
% 21.40/21.28 ! [V_b,V_a] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.40/21.28 => 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)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_divmod__int__rel__div__mod,axiom,
% 21.40/21.28 ! [V_a,V_b] :
% 21.40/21.28 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => 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)))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_posDivAlg__correct,axiom,
% 21.40/21.28 ! [V_b,V_a] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.40/21.28 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_mod__pos__pos,axiom,
% 21.40/21.28 ! [V_b,V_a] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.40/21.28 => 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)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_mod__pos__pos__1__number__of,axiom,
% 21.40/21.28 ! [V_w] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => 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))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_zadd1__lemma,axiom,
% 21.40/21.28 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( 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)))
% 21.40/21.28 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => 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)))) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_zminus1__lemma,axiom,
% 21.40/21.28 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => 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))))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_mod__pos__neg,axiom,
% 21.40/21.28 ! [V_b,V_a] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.28 => 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)))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_divmod__nat__if,axiom,
% 21.40/21.28 ! [V_m_2,V_n_2] :
% 21.40/21.28 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 21.40/21.28 => 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) )
% 21.40/21.28 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 21.40/21.28 => 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)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_divmod__int__relI,axiom,
% 21.40/21.28 ! [V_r,V_q,V_b,V_a] :
% 21.40/21.28 ( 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)
% 21.40/21.28 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 21.40/21.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 21.40/21.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 21.40/21.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 21.40/21.28 => 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))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_mod__neg__neg,axiom,
% 21.40/21.28 ! [V_b,V_a] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.28 => 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)))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_zmult1__lemma,axiom,
% 21.40/21.28 ! [V_a,V_r,V_q,V_c,V_b] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.28 => 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)))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_equalityI,axiom,
% 21.40/21.28 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.28 => V_A_2 = V_B_2 ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_div__pos__neg__1__number__of,axiom,
% 21.40/21.28 ! [V_w] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => 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))))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_nat__gcd_Opinduct,axiom,
% 21.40/21.28 ! [V_P_2,V_a1_2,V_a0_2] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( ! [B_x,B_y] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_div__neg__neg,axiom,
% 21.40/21.28 ! [V_b,V_a] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.28 => 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)))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__number__of__Suc,axiom,
% 21.40/21.28 ! [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)))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf__le1,axiom,
% 21.40/21.28 ! [V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf__le2,axiom,
% 21.40/21.28 ! [V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Ole__iff__inf,axiom,
% 21.40/21.28 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_b)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.40/21.28 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Ole__inf__iff,axiom,
% 21.40/21.28 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_b)
% 21.40/21.28 => ( 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)))
% 21.40/21.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.40/21.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__le__iff__disj,axiom,
% 21.40/21.28 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_b)
% 21.40/21.28 => ( 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))
% 21.40/21.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 21.40/21.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Ole__infI1,axiom,
% 21.40/21.28 ! [V_b,V_x,V_a,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 21.40/21.28 => 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)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Ole__infI2,axiom,
% 21.40/21.28 ! [V_a,V_x,V_b,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 21.40/21.28 => 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)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf__absorb1,axiom,
% 21.40/21.28 ! [V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.40/21.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf__absorb2,axiom,
% 21.40/21.28 ! [V_x,V_y,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 21.40/21.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Ole__infI,axiom,
% 21.40/21.28 ! [V_b,V_a,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 21.40/21.28 => 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))) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf__greatest,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 21.40/21.28 => 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))) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf__mono,axiom,
% 21.40/21.28 ! [V_d,V_b,V_c,V_a,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 21.40/21.28 => 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))) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Ole__infE,axiom,
% 21.40/21.28 ! [V_b,V_a,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( 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)))
% 21.40/21.28 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 21.40/21.28 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__0L,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__0R,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__add__distrib__left,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.28 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__diff__distrib__left,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.28 ( class_Groups_Oordered__ab__group__add(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf__assoc,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf_Oassoc,axiom,
% 21.40/21.28 ! [V_c,V_b,V_a,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf__left__commute,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 21.40/21.28 ! [V_c,V_a,V_b,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf__left__idem,axiom,
% 21.40/21.28 ! [V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 21.40/21.28 ! [V_b,V_a,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf__commute,axiom,
% 21.40/21.28 ! [V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf_Ocommute,axiom,
% 21.40/21.28 ! [V_b,V_a,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf_Oidem,axiom,
% 21.40/21.28 ! [V_a,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__less__iff__conj,axiom,
% 21.40/21.28 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_b)
% 21.40/21.28 => ( 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)))
% 21.40/21.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 21.40/21.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__less__iff__disj,axiom,
% 21.40/21.28 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_b)
% 21.40/21.28 => ( 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))
% 21.40/21.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 21.40/21.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oless__infI1,axiom,
% 21.40/21.28 ! [V_b,V_x,V_a,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 21.40/21.28 => 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)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oless__infI2,axiom,
% 21.40/21.28 ! [V_a,V_x,V_b,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 21.40/21.28 => 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)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__Suc__Suc,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__diff,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_fst__eqD,axiom,
% 21.40/21.28 ! [V_a,V_y,V_x,T_b,T_a] :
% 21.40/21.28 ( 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
% 21.40/21.28 => V_x = V_a ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_fst__conv,axiom,
% 21.40/21.28 ! [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 ).
% 21.40/21.28
% 21.40/21.28 fof(fact_prod__eqI,axiom,
% 21.40/21.28 ! [V_q,V_p,T_b,T_a] :
% 21.40/21.28 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 21.40/21.28 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 21.40/21.28 => V_p = V_q ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Pair__fst__snd__eq,axiom,
% 21.40/21.28 ! [T_c,T_b,V_t_2,V_s_2] :
% 21.40/21.28 ( V_s_2 = V_t_2
% 21.40/21.28 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 21.40/21.28 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_fst__apsnd,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_fst__def,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__number__of,axiom,
% 21.40/21.28 ! [V_v,V_u,T_b] :
% 21.40/21.28 ( ( class_Int_Onumber(T_b)
% 21.40/21.28 & class_Orderings_Oord(T_b) )
% 21.40/21.28 => ( ( 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)))
% 21.40/21.28 => 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) )
% 21.40/21.28 & ( ~ 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)))
% 21.40/21.28 => 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) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_surjective__pairing,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_pair__collapse,axiom,
% 21.40/21.28 ! [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 ).
% 21.40/21.28
% 21.40/21.28 fof(fact_prod__case__beta,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_div__int__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_mod__nat__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_split__beta,axiom,
% 21.40/21.28 ! [V_z_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_split__comp__eq,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_split__def,axiom,
% 21.40/21.28 ! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Diff__subset,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Diff__mono,axiom,
% 21.40/21.28 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 21.40/21.28 => 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))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_double__diff,axiom,
% 21.40/21.28 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 21.40/21.28 => 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 ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_psubset__eq,axiom,
% 21.40/21.28 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.28 & V_A_2 != V_B_2 ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_subset__iff__psubset__eq,axiom,
% 21.40/21.28 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.28 | V_A_2 = V_B_2 ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_psubset__imp__subset,axiom,
% 21.40/21.28 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_psubset__subset__trans,axiom,
% 21.40/21.28 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_subset__psubset__trans,axiom,
% 21.40/21.28 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Compl__anti__mono,axiom,
% 21.40/21.28 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.28 => 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))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Compl__subset__Compl__iff,axiom,
% 21.40/21.28 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_subset__refl,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_set__eq__subset,axiom,
% 21.40/21.28 ! [T_b,V_B_2,V_A_2] :
% 21.40/21.28 ( V_A_2 = V_B_2
% 21.40/21.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_equalityD1,axiom,
% 21.40/21.28 ! [T_b,V_B_2,V_A_2] :
% 21.40/21.28 ( V_A_2 = V_B_2
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_equalityD2,axiom,
% 21.40/21.28 ! [T_b,V_B_2,V_A_2] :
% 21.40/21.28 ( V_A_2 = V_B_2
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_subset__trans,axiom,
% 21.40/21.28 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_equalityE,axiom,
% 21.40/21.28 ! [T_b,V_B_2,V_A_2] :
% 21.40/21.28 ( V_A_2 = V_B_2
% 21.40/21.28 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.28 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__Suc1,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__Suc2,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_div__neg__pos,axiom,
% 21.40/21.28 ! [V_b,V_a] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.40/21.28 => 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)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_div__pos__pos,axiom,
% 21.40/21.28 ! [V_b,V_a] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 21.40/21.28 => 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)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_div__pos__pos__1__number__of,axiom,
% 21.40/21.28 ! [V_w] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => 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))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_div__pos__neg,axiom,
% 21.40/21.28 ! [V_b,V_a] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 21.40/21.28 => 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)))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__Suc__number__of,axiom,
% 21.40/21.28 ! [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)))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_prod__size__simp,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_conjI__realizer,axiom,
% 21.40/21.28 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 21.40/21.28 ( hBOOL(hAPP(V_P_2,V_p_2))
% 21.40/21.28 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 21.40/21.28 => ( hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
% 21.40/21.28 & hBOOL(hAPP(V_Q_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)))) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_exI__realizer,axiom,
% 21.40/21.28 ! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__ord__min,axiom,
% 21.40/21.28 ! [T_b] :
% 21.40/21.28 ( class_Orderings_Oord(T_b)
% 21.40/21.28 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_prod_Orecs,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Compl__eq__Compl__iff,axiom,
% 21.40/21.28 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.28 ( 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)
% 21.40/21.28 <=> V_A_2 = V_B_2 ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_double__complement,axiom,
% 21.40/21.28 ! [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 ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Diff__idemp,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_psubset__trans,axiom,
% 21.40/21.28 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_div__nat__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_divmod__nat__rel__def,axiom,
% 21.40/21.28 ! [V_qr_2,V_n_2,V_m_2] :
% 21.40/21.28 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 21.40/21.28 <=> ( 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))
% 21.40/21.28 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.28 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 21.40/21.28 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 21.40/21.28 => ( 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)))
% 21.40/21.28 & 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)) ) )
% 21.40/21.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 21.40/21.28 => ( 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)))
% 21.40/21.28 & 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))) ) ) ) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_range,axiom,
% 21.40/21.28 ! [V_s,V_k] :
% 21.40/21.28 ( 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))
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_max__number__of__Suc,axiom,
% 21.40/21.28 ! [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)))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_max__Suc__number__of,axiom,
% 21.40/21.28 ! [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)))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_apsnd__apfst,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 21.40/21.28 ! [V_x,V_z,V_y,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 21.40/21.28 ! [V_x,V_z,V_y,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 21.40/21.28 ! [V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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 ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup__inf__absorb,axiom,
% 21.40/21.28 ! [V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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 ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oless__supI2,axiom,
% 21.40/21.28 ! [V_a,V_b,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 21.40/21.28 => 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))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Oless__supI1,axiom,
% 21.40/21.28 ! [V_b,V_a,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 21.40/21.28 => 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))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_max__less__iff__conj,axiom,
% 21.40/21.28 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_b)
% 21.40/21.28 => ( 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))
% 21.40/21.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 21.40/21.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_less__max__iff__disj,axiom,
% 21.40/21.28 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_b)
% 21.40/21.28 => ( 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)))
% 21.40/21.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 21.40/21.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_max__diff__distrib__left,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.28 ( class_Groups_Oordered__ab__group__add(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_le__maxI1,axiom,
% 21.40/21.28 ! [V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_le__maxI2,axiom,
% 21.40/21.28 ! [V_x,V_y,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Ole__iff__sup,axiom,
% 21.40/21.28 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_b)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.40/21.28 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_le__max__iff__disj,axiom,
% 21.40/21.28 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_b)
% 21.40/21.28 => ( 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)))
% 21.40/21.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 21.40/21.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Ole__sup__iff,axiom,
% 21.40/21.28 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_b)
% 21.40/21.28 => ( 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))
% 21.40/21.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 21.40/21.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Ole__supI1,axiom,
% 21.40/21.28 ! [V_b,V_a,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 21.40/21.28 => 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))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Ole__supI2,axiom,
% 21.40/21.28 ! [V_a,V_b,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 21.40/21.28 => 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))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup__absorb2,axiom,
% 21.40/21.28 ! [V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.40/21.28 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup__absorb1,axiom,
% 21.40/21.28 ! [V_x,V_y,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 21.40/21.28 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Ole__supI,axiom,
% 21.40/21.28 ! [V_b,V_x,V_a,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 21.40/21.28 => 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)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup__least,axiom,
% 21.40/21.28 ! [V_z,V_x,V_y,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 21.40/21.28 => 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)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup__mono,axiom,
% 21.40/21.28 ! [V_d,V_b,V_c,V_a,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 21.40/21.28 => 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))) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Ole__supE,axiom,
% 21.40/21.28 ! [V_x,V_b,V_a,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => ( 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))
% 21.40/21.28 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 21.40/21.28 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_max__0L,axiom,
% 21.40/21.28 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 21.40/21.28
% 21.40/21.28 fof(fact_max__0R,axiom,
% 21.40/21.28 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 21.40/21.28
% 21.40/21.28 fof(fact_max__Suc__Suc,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_max__add__distrib__left,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.28 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup__assoc,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup_Oassoc,axiom,
% 21.40/21.28 ! [V_c,V_b,V_a,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup__left__commute,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 21.40/21.28 ! [V_c,V_a,V_b,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup__left__idem,axiom,
% 21.40/21.28 ! [V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 21.40/21.28 ! [V_b,V_a,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup__commute,axiom,
% 21.40/21.28 ! [V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup_Ocommute,axiom,
% 21.40/21.28 ! [V_b,V_a,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Osup_Oidem,axiom,
% 21.40/21.28 ! [V_a,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_apfst__conv,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_apfst__eq__conv,axiom,
% 21.40/21.28 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 21.40/21.28 ( 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)
% 21.40/21.28 <=> 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_fst__apfst,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_snd__apfst,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_max__number__of,axiom,
% 21.40/21.28 ! [V_v,V_u,T_b] :
% 21.40/21.28 ( ( class_Int_Onumber(T_b)
% 21.40/21.28 & class_Orderings_Oord(T_b) )
% 21.40/21.28 => ( ( 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)))
% 21.40/21.28 => 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) )
% 21.40/21.28 & ( ~ 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)))
% 21.40/21.28 => 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) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Odistrib__sup__le,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_min__max_Odistrib__inf__le,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => 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)))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_minus__max__eq__min,axiom,
% 21.40/21.28 ! [V_y,V_x,T_a] :
% 21.40/21.28 ( class_Groups_Olinordered__ab__group__add(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_minus__min__eq__max,axiom,
% 21.40/21.28 ! [V_y,V_x,T_a] :
% 21.40/21.28 ( class_Groups_Olinordered__ab__group__add(T_a)
% 21.40/21.28 => 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)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_nat__minus__add__max,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_apsnd__apfst__commute,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_max__Suc1,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_max__Suc2,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_apfst__apsnd,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dual__min,axiom,
% 21.40/21.28 ! [T_b] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_b)
% 21.40/21.28 => 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) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_max__ord__max,axiom,
% 21.40/21.28 ! [T_b] :
% 21.40/21.28 ( class_Orderings_Oord(T_b)
% 21.40/21.28 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_code__numeral__decr,axiom,
% 21.40/21.28 ! [V_k] :
% 21.40/21.28 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 21.40/21.28 => 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))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_pos__not__random__dseq__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 21.40/21.28 ! [V_l_2,V_k_2] :
% 21.40/21.28 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 21.40/21.28 <=> V_k_2 = V_l_2 ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_code__numeral_Onat__of__inject,axiom,
% 21.40/21.28 ! [V_y_2,V_x_2] :
% 21.40/21.28 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 21.40/21.28 <=> V_x_2 = V_y_2 ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_nat__of__of__nat,axiom,
% 21.40/21.28 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 21.40/21.28
% 21.40/21.28 fof(fact_of__nat__nat__of,axiom,
% 21.40/21.28 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 21.40/21.28
% 21.40/21.28 fof(fact_nat__of__inverse,axiom,
% 21.40/21.28 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 21.40/21.28
% 21.40/21.28 fof(fact_less__code__numeral__def,axiom,
% 21.40/21.28 ! [V_m_2,V_n_2] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 21.40/21.28 <=> 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))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_nat__of__number,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_less__eq__code__numeral__def,axiom,
% 21.40/21.28 ! [V_m_2,V_n_2] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 21.40/21.28 <=> 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))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_nat__of__code,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_nat__of__aux__def,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Min_Oidem,axiom,
% 21.40/21.28 ! [V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Max_Oidem,axiom,
% 21.40/21.28 ! [V_x,T_a] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_a)
% 21.40/21.28 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dual__max,axiom,
% 21.40/21.28 ! [T_b] :
% 21.40/21.28 ( class_Orderings_Olinorder(T_b)
% 21.40/21.28 => 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) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Suc__code__numeral__def,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_minus__code__numeral__def,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_plus__code__numeral__def,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_div__code__numeral__def,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_times__code__numeral__def,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_mod__code__numeral__def,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Nitpick_Oone__frac__def,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Nitpick_Ofrac__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_surjective__sum,axiom,
% 21.40/21.28 ! [V_f_2,T_c,T_d,T_b] : c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,hAPP(hAPP(c_COMBB(tc_sum(T_b,T_c),T_d,T_b),V_f_2),c_Sum__Type_OInl(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_sum(T_b,T_c),T_d,T_c),V_f_2),c_Sum__Type_OInr(T_c,T_b))) = V_f_2 ).
% 21.40/21.28
% 21.40/21.28 fof(fact_iterate_Osimps,axiom,
% 21.40/21.28 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 21.40/21.28 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 21.40/21.28 => 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) )
% 21.40/21.28 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 21.40/21.28 => 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)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_scomp__scomp,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_sum__case__KK,axiom,
% 21.40/21.28 ! [V_x_2,V_a_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_a_2),hAPP(c_COMBK(T_b,T_d),V_a_2)),V_x_2) = V_a_2 ).
% 21.40/21.28
% 21.40/21.28 fof(fact_sum__case__inject,axiom,
% 21.40/21.28 ! [V_g2_2,V_g1_2,V_f2_2,V_f1_2,T_c,T_d,T_b] :
% 21.40/21.28 ( c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f1_2,V_f2_2) = c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_g1_2,V_g2_2)
% 21.40/21.28 => ~ ( V_f1_2 = V_g1_2
% 21.40/21.28 => V_f2_2 != V_g2_2 ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_sum__case__weak__cong,axiom,
% 21.40/21.28 ! [V_g_2,V_f_2,T_c,T_d,T_b,V_t_2,V_s_2] :
% 21.40/21.28 ( V_s_2 = V_t_2
% 21.40/21.28 => hAPP(c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f_2,V_g_2),V_s_2) = hAPP(c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f_2,V_g_2),V_t_2) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_scomp__Pair,axiom,
% 21.40/21.28 ! [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 ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Pair__scomp,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_scomp__apply,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_sum_Osimps_I6_J,axiom,
% 21.40/21.28 ! [V_b_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,V_f1_2,V_f2_2),hAPP(c_Sum__Type_OInr(T_d,T_c),V_b_2)) = hAPP(V_f2_2,V_b_2) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_sum_Osimps_I5_J,axiom,
% 21.40/21.28 ! [V_a_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,V_f1_2,V_f2_2),hAPP(c_Sum__Type_OInl(T_c,T_d),V_a_2)) = hAPP(V_f1_2,V_a_2) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_scomp__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_scomp__unfold,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_internal__split__def,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_transfer__morphism__int__nat,axiom,
% 21.40/21.28 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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 21.40/21.28 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 21.40/21.28 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 21.40/21.28 => 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) )
% 21.40/21.28 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 21.40/21.28 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = 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)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 21.40/21.28 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 21.40/21.28 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 21.40/21.28 => 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) )
% 21.40/21.28 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 21.40/21.28 => 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)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_internal__split__conv,axiom,
% 21.40/21.28 ! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Nitpick_Oof__frac__def,axiom,
% 21.40/21.28 ! [V_q,T_a,T_b] :
% 21.40/21.28 ( ( class_Rings_Oinverse(T_b)
% 21.40/21.28 & class_Rings_Oring__1(T_b) )
% 21.40/21.28 => 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))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Nitpick_Oless__frac__def,axiom,
% 21.40/21.28 ! [V_r_2,V_q_2,T_b] :
% 21.40/21.28 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 21.40/21.28 <=> 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))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 21.40/21.28 ! [V_r_2,V_q_2,T_b] :
% 21.40/21.28 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 21.40/21.28 <=> 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))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 21.40/21.28 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_pos__empty__def,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_neg__bind__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 21.40/21.28 ! [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) = 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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_rev__predicate2D,axiom,
% 21.40/21.28 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_predicate2D,axiom,
% 21.40/21.28 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 21.40/21.28 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_rev__predicate1D,axiom,
% 21.40/21.28 ! [V_Q_2,T_b,V_x_2,V_P_2] :
% 21.40/21.28 ( hBOOL(hAPP(V_P_2,V_x_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 21.40/21.28 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_predicate1D,axiom,
% 21.40/21.28 ! [V_x_2,V_Q_2,V_P_2,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 21.40/21.28 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 21.40/21.28 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_pos__bind__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_The__split,axiom,
% 21.40/21.28 ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Random_Osimps,axiom,
% 21.40/21.28 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
% 21.40/21.28 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) )
% 21.40/21.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
% 21.40/21.28 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_exE__realizer,axiom,
% 21.40/21.28 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2)))
% 21.40/21.28 => ( ! [B_x,B_y] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(V_P_2,B_y),B_x))
% 21.40/21.28 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 21.40/21.28 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_beyond__def,axiom,
% 21.40/21.28 ! [V_l,V_k] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 21.40/21.28 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 21.40/21.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 21.40/21.28 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_beyond__zero,axiom,
% 21.40/21.28 ! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_split__paired__The,axiom,
% 21.40/21.28 ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_P_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_The__split__eq,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_divmod__nat__def,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Random__Sequence_Oempty__def,axiom,
% 21.40/21.28 ! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Random__Sequence_Osingle__def,axiom,
% 21.40/21.28 ! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_the__eq__trivial,axiom,
% 21.40/21.28 ! [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 ).
% 21.40/21.28
% 21.40/21.28 fof(fact_the__sym__eq__trivial,axiom,
% 21.40/21.28 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 21.40/21.28
% 21.40/21.28 fof(fact_curry__def,axiom,
% 21.40/21.28 ! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_curryI,axiom,
% 21.40/21.28 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 21.40/21.28 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_curryE,axiom,
% 21.40/21.28 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 21.40/21.28 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_curryD,axiom,
% 21.40/21.28 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 21.40/21.28 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_curry__conv,axiom,
% 21.40/21.28 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_curry__split,axiom,
% 21.40/21.28 ! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2 ).
% 21.40/21.28
% 21.40/21.28 fof(fact_split__curry,axiom,
% 21.40/21.28 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2 ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Powp__def,axiom,
% 21.40/21.28 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 21.40/21.28 <=> ! [B_x] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 21.40/21.28 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_power__dvd__imp__le,axiom,
% 21.40/21.28 ! [V_n,V_m,V_i] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_hoare__derivs_OCall,axiom,
% 21.40/21.28 ! [V_a_2,V_X_2,V_s_H_2,V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_b] :
% 21.40/21.28 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Q_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)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),hAPP(c_Natural_Ogetlocs,V_s_H_2)))),V_X_2)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Oloc,tc_Nat_Onat),c_Natural_Ogetlocs),c_Com_ORes))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 21.40/21.28 => 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_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,V_s_H_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),c_Natural_Onewlocs))),c_Com_Ovname_OLoc(c_Com_OArg))),V_a_2)))),c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__mult__cancel2,axiom,
% 21.40/21.28 ! [V_n_2,V_m_2] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2)),V_m_2))
% 21.40/21.28 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__mult__cancel1,axiom,
% 21.40/21.28 ! [V_n_2,V_m_2] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_m_2))
% 21.40/21.28 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oorder__refl,axiom,
% 21.40/21.28 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__0__right,axiom,
% 21.40/21.28 ! [V_a,T_a] :
% 21.40/21.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_empty__subsetI,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__1__left,axiom,
% 21.40/21.28 ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_ball__empty,axiom,
% 21.40/21.28 ! [V_P_2,T_b,B_x] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 21.40/21.28 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_hoare__derivs_Oequations_I8_J,axiom,
% 21.40/21.28 ! [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)))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Ass,axiom,
% 21.40/21.28 ! [V_a_2,V_X_2,V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_X_2)),V_a_2))),c_Com_Ocom_OAss(V_X_2,V_a_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_subset__singletonD,axiom,
% 21.40/21.28 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.28 ( 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)))))
% 21.40/21.28 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.28 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_empty__not__insert,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_insert__not__empty,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_insert__absorb2,axiom,
% 21.40/21.28 ! [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) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_insert__commute,axiom,
% 21.40/21.28 ! [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)) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_doubleton__eq__iff,axiom,
% 21.40/21.28 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.28 ( 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_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 21.40/21.28 <=> ( ( V_a_2 = V_c_2
% 21.40/21.28 & V_b_2 = V_d_2 )
% 21.40/21.28 | ( V_a_2 = V_d_2
% 21.40/21.28 & V_b_2 = V_c_2 ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_insert__code,axiom,
% 21.40/21.28 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 21.40/21.28 <=> ( V_y_2 = V_x_2
% 21.40/21.28 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_singleton__inject,axiom,
% 21.40/21.28 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.28 ( 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)))
% 21.40/21.28 => V_a_2 = V_b_2 ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__if__abs__eq,axiom,
% 21.40/21.28 ! [V_k,V_l,T_a] :
% 21.40/21.28 ( class_Rings_Olinordered__idom(T_a)
% 21.40/21.28 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_abs__dvd__iff,axiom,
% 21.40/21.28 ! [V_k_2,V_m_2,T_b] :
% 21.40/21.28 ( class_Rings_Olinordered__idom(T_b)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
% 21.40/21.28 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__abs__iff,axiom,
% 21.40/21.28 ! [V_k_2,V_m_2,T_b] :
% 21.40/21.28 ( class_Rings_Olinordered__idom(T_b)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
% 21.40/21.28 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_Comp,axiom,
% 21.40/21.28 ! [V_R_2,V_d_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_b] :
% 21.40/21.28 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 21.40/21.28 => ( 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_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 21.40/21.28 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 21.40/21.28 ! [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)))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_hoare__derivs_OSkip,axiom,
% 21.40/21.28 ! [V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OSKIP),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__0__left,axiom,
% 21.40/21.28 ! [V_a,T_a] :
% 21.40/21.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 21.40/21.28 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__add,axiom,
% 21.40/21.28 ! [V_c,V_b,V_a,T_a] :
% 21.40/21.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_one__dvd,axiom,
% 21.40/21.28 ! [V_a,T_a] :
% 21.40/21.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_bot__apply,axiom,
% 21.40/21.28 ! [V_x_2,T_c,T_b] :
% 21.40/21.28 ( class_Orderings_Obot(T_b)
% 21.40/21.28 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_derivs__insertD,axiom,
% 21.40/21.28 ! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
% 21.40/21.28 ( 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_tsa_2))
% 21.40/21.28 => ( 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))))
% 21.40/21.28 & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_hoare__derivs_Oinsert,axiom,
% 21.40/21.28 ! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
% 21.40/21.28 ( 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))))
% 21.40/21.28 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
% 21.40/21.28 => 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_tsa_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_cut,axiom,
% 21.40/21.28 ! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
% 21.40/21.28 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2)
% 21.40/21.28 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
% 21.40/21.28 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_empty,axiom,
% 21.40/21.28 ! [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))) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oeq__iff,axiom,
% 21.40/21.28 ! [V_y_2,V_x_2] :
% 21.40/21.28 ( V_x_2 = V_y_2
% 21.40/21.28 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 21.40/21.28 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Ole__less,axiom,
% 21.40/21.28 ! [V_y_2,V_x_2] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 21.40/21.28 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 21.40/21.28 | V_x_2 = V_y_2 ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oless__le,axiom,
% 21.40/21.28 ! [V_y_2,V_x_2] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 21.40/21.28 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 21.40/21.28 & V_x_2 != V_y_2 ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oneq__le__trans,axiom,
% 21.40/21.28 ! [V_b,V_a] :
% 21.40/21.28 ( V_a != V_b
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oeq__refl,axiom,
% 21.40/21.28 ! [V_y,V_x] :
% 21.40/21.28 ( V_x = V_y
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oantisym__conv,axiom,
% 21.40/21.28 ! [V_x_2,V_y_2] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 21.40/21.28 <=> V_x_2 = V_y_2 ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 21.40/21.28 ! [V_y,V_x] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 21.40/21.28 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 21.40/21.28 | V_x = V_y ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Ole__neq__trans,axiom,
% 21.40/21.28 ! [V_b,V_a] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 21.40/21.28 => ( V_a != V_b
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 21.40/21.28 ! [V_c,V_b,V_a] :
% 21.40/21.28 ( V_a = V_b
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 21.40/21.28 ! [V_c,V_b,V_a] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 21.40/21.28 => ( V_b = V_c
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__antisym,axiom,
% 21.40/21.28 ! [V_n,V_m] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
% 21.40/21.28 => V_m = V_n ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oantisym,axiom,
% 21.40/21.28 ! [V_y,V_x] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 21.40/21.28 => V_x = V_y ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oorder__trans,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oord__eq__less__trans,axiom,
% 21.40/21.28 ! [V_c,V_b,V_a] :
% 21.40/21.28 ( V_a = V_b
% 21.40/21.28 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) )
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Ole__less__trans,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x] :
% 21.40/21.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 21.40/21.28 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oless__imp__neq,axiom,
% 21.40/21.28 ! [V_y,V_x] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 21.40/21.28 => V_x != V_y ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oless__not__sym,axiom,
% 21.40/21.28 ! [V_y,V_x] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 21.40/21.28 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oless__imp__le,axiom,
% 21.40/21.28 ! [V_y,V_x] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oless__imp__not__less,axiom,
% 21.40/21.28 ! [V_y,V_x] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 21.40/21.28 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oless__imp__not__eq,axiom,
% 21.40/21.28 ! [V_y,V_x] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 21.40/21.28 => V_x != V_y ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oless__imp__not__eq2,axiom,
% 21.40/21.28 ! [V_y,V_x] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 21.40/21.28 => V_y != V_x ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oord__less__eq__trans,axiom,
% 21.40/21.28 ! [V_c,V_b,V_a] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 21.40/21.28 => ( V_b = V_c
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oless__le__trans,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oless__asym_H,axiom,
% 21.40/21.28 ! [V_b,V_a] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 21.40/21.28 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oless__trans,axiom,
% 21.40/21.28 ! [V_z,V_y,V_x] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 21.40/21.28 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd_Oless__asym,axiom,
% 21.40/21.28 ! [V_y,V_x] :
% 21.40/21.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 21.40/21.28 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 21.40/21.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__refl,axiom,
% 21.40/21.28 ! [V_a,T_a] :
% 21.40/21.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__trans,axiom,
% 21.40/21.28 ! [V_c,V_b,V_a,T_a] :
% 21.40/21.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_div__dvd__div,axiom,
% 21.40/21.28 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.28 ( class_Divides_Osemiring__div(T_b)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2)))
% 21.40/21.28 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__power__same,axiom,
% 21.40/21.28 ! [V_n,V_y,V_x,T_a] :
% 21.40/21.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__mod__imp__dvd,axiom,
% 21.40/21.28 ! [V_n,V_m,V_k,T_a] :
% 21.40/21.28 ( class_Divides_Osemiring__div(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__mod,axiom,
% 21.40/21.28 ! [V_n,V_m,V_k,T_a] :
% 21.40/21.28 ( class_Divides_Osemiring__div(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 21.40/21.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_mod__mod__cancel,axiom,
% 21.40/21.28 ! [V_a,V_b,V_c,T_a] :
% 21.40/21.28 ( class_Divides_Osemiring__div(T_a)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 21.40/21.28 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__mod__iff,axiom,
% 21.40/21.28 ! [V_m_2,V_n_2,V_k_2,T_b] :
% 21.40/21.28 ( class_Divides_Osemiring__div(T_b)
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
% 21.40/21.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))
% 21.40/21.28 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ).
% 21.40/21.28
% 21.40/21.28 fof(fact_dvd__triv__left,axiom,
% 21.40/21.28 ! [V_b,V_a,T_a] :
% 21.40/21.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__triv__right,axiom,
% 21.40/21.29 ! [V_b,V_a,T_a] :
% 21.40/21.29 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__mult2,axiom,
% 21.40/21.29 ! [V_c,V_b,V_a,T_a] :
% 21.40/21.29 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__mult,axiom,
% 21.40/21.29 ! [V_b,V_c,V_a,T_a] :
% 21.40/21.29 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_mult__dvd__mono,axiom,
% 21.40/21.29 ! [V_d,V_c,V_b,V_a,T_a] :
% 21.40/21.29 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvdI,axiom,
% 21.40/21.29 ! [V_k,V_b,V_a,T_a] :
% 21.40/21.29 ( class_Rings_Odvd(T_a)
% 21.40/21.29 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__mult__left,axiom,
% 21.40/21.29 ! [V_c,V_b,V_a,T_a] :
% 21.40/21.29 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__mult__right,axiom,
% 21.40/21.29 ! [V_c,V_b,V_a,T_a] :
% 21.40/21.29 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_asm,axiom,
% 21.40/21.29 ! [V_Ga_2,V_tsa_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_Ga_2))
% 21.40/21.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_weaken,axiom,
% 21.40/21.29 ! [V_tsa_2,V_ts_H_2,V_Ga_2,T_b] :
% 21.40/21.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
% 21.40/21.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_thin,axiom,
% 21.40/21.29 ! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
% 21.40/21.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2)
% 21.40/21.29 => ( 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))
% 21.40/21.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__diff__nat,axiom,
% 21.40/21.29 ! [V_n,V_m,V_k] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insert__mono,axiom,
% 21.40/21.29 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_subset__insertI2,axiom,
% 21.40/21.29 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_subset__insertI,axiom,
% 21.40/21.29 ! [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))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__reduce,axiom,
% 21.40/21.29 ! [V_n_2,V_k_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__diff,axiom,
% 21.40/21.29 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.29 ( class_Rings_Ocomm__ring__1(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__minus__iff,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.29 ( class_Rings_Ocomm__ring__1(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_minus__dvd__iff,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.29 ( class_Rings_Ocomm__ring__1(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_bot__fun__def,axiom,
% 21.40/21.29 ! [V_x_2,T_c,T_b] :
% 21.40/21.29 ( class_Orderings_Obot(T_b)
% 21.40/21.29 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_LoopF,axiom,
% 21.40/21.29 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Diff__insert,axiom,
% 21.40/21.29 ! [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)))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Diff__insert2,axiom,
% 21.40/21.29 ! [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) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insert__Diff__single,axiom,
% 21.40/21.29 ! [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) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_nat__dvd__1__iff__1,axiom,
% 21.40/21.29 ! [V_m_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 21.40/21.29 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_subset__empty,axiom,
% 21.40/21.29 ! [V_A_2,T_b] :
% 21.40/21.29 ( 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))))
% 21.40/21.29 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Diff__cancel,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Diff__empty,axiom,
% 21.40/21.29 ! [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 ).
% 21.40/21.29
% 21.40/21.29 fof(fact_empty__Diff,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_not__psubset__empty,axiom,
% 21.40/21.29 ! [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)))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_weak__Body,axiom,
% 21.40/21.29 ! [V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_b] :
% 21.40/21.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 21.40/21.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_BodyN,axiom,
% 21.40/21.29 ! [V_Ga_2,V_Q_2,V_pn_2,V_P_2,T_b] :
% 21.40/21.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 21.40/21.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_bot__least,axiom,
% 21.40/21.29 ! [V_x,T_a] :
% 21.40/21.29 ( class_Orderings_Obot(T_a)
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__mult__cancel__left,axiom,
% 21.40/21.29 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 21.40/21.29 ( class_Rings_Oidom(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 21.40/21.29 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 21.40/21.29 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__mult__cancel__right,axiom,
% 21.40/21.29 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 21.40/21.29 ( class_Rings_Oidom(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
% 21.40/21.29 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 21.40/21.29 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__imp__mod__0,axiom,
% 21.40/21.29 ! [V_b,V_a,T_a] :
% 21.40/21.29 ( class_Divides_Osemiring__div(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 21.40/21.29 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__eq__mod__eq__0,axiom,
% 21.40/21.29 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.29 ( class_Divides_Osemiring__div(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 21.40/21.29 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_div__add,axiom,
% 21.40/21.29 ! [V_y,V_x,V_z,T_a] :
% 21.40/21.29 ( class_Divides_Osemiring__div(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
% 21.40/21.29 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_z)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_y),V_z)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__mult__div__cancel,axiom,
% 21.40/21.29 ! [V_b,V_a,T_a] :
% 21.40/21.29 ( class_Divides_Osemiring__div(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 21.40/21.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)) = V_b ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_div__mult__swap,axiom,
% 21.40/21.29 ! [V_a,V_b,V_c,T_a] :
% 21.40/21.29 ( class_Divides_Osemiring__div(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 21.40/21.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__div__mult__self,axiom,
% 21.40/21.29 ! [V_b,V_a,T_a] :
% 21.40/21.29 ( class_Divides_Osemiring__div(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 21.40/21.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_a) = V_b ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__div__mult,axiom,
% 21.40/21.29 ! [V_c,V_b,V_a,T_a] :
% 21.40/21.29 ( class_Divides_Osemiring__div(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 21.40/21.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_c) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_a) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_div__mult__div__if__dvd,axiom,
% 21.40/21.29 ! [V_w,V_z,V_x,V_y,T_a] :
% 21.40/21.29 ( class_Divides_Osemiring__div(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
% 21.40/21.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_w),V_z)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__neg__div,axiom,
% 21.40/21.29 ! [V_x,V_y,T_a] :
% 21.40/21.29 ( class_Divides_Oring__div(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 21.40/21.29 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__div__neg,axiom,
% 21.40/21.29 ! [V_x,V_y,T_a] :
% 21.40/21.29 ( class_Divides_Oring__div(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 21.40/21.29 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_le__imp__power__dvd,axiom,
% 21.40/21.29 ! [V_a,V_n,V_m,T_a] :
% 21.40/21.29 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__power__le,axiom,
% 21.40/21.29 ! [V_m,V_n,V_y,V_x,T_a] :
% 21.40/21.29 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_power__le__dvd,axiom,
% 21.40/21.29 ! [V_m,V_b,V_n,V_a,T_a] :
% 21.40/21.29 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_div__power,axiom,
% 21.40/21.29 ! [V_n,V_x,V_y,T_a] :
% 21.40/21.29 ( class_Divides_Osemiring__div(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 21.40/21.29 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_hoare__derivs_OLocal,axiom,
% 21.40/21.29 ! [V_a_2,V_s_H_2,V_X_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_b] :
% 21.40/21.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Q_2)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),hAPP(hAPP(c_Natural_Ogetlocs,V_s_H_2),V_X_2))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 21.40/21.29 => 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_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,V_s_H_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),V_a_2)))),c_Com_Ocom_OLocal(V_X_2,V_a_2,V_c_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__1__iff__1,axiom,
% 21.40/21.29 ! [V_m_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 21.40/21.29 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_nat__dvd__not__less,axiom,
% 21.40/21.29 ! [V_n,V_m] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 21.40/21.29 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 21.40/21.29 ! [V_n_2,V_m_2,V_k_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 21.40/21.29 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.29 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__diffD,axiom,
% 21.40/21.29 ! [V_n,V_m,V_k] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__diffD1,axiom,
% 21.40/21.29 ! [V_n,V_m,V_k] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_subset__Compl__self__eq,axiom,
% 21.40/21.29 ! [V_A_2,T_b] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_unity__coeff__ex,axiom,
% 21.40/21.29 ! [V_l_2,V_P_2,T_b] :
% 21.40/21.29 ( ( class_Rings_Odvd(T_b)
% 21.40/21.29 & class_Rings_Osemiring__0(T_b) )
% 21.40/21.29 => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
% 21.40/21.29 <=> ? [B_x] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b))))
% 21.40/21.29 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__period_I3_J,axiom,
% 21.40/21.29 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 21.40/21.29 ( ( class_Rings_Ocomm__ring(T_b)
% 21.40/21.29 & class_Rings_Odvd(T_b) )
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 21.40/21.29 => ! [B_x,B_k] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__period_I4_J,axiom,
% 21.40/21.29 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 21.40/21.29 ( ( class_Rings_Ocomm__ring(T_b)
% 21.40/21.29 & class_Rings_Odvd(T_b) )
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 21.40/21.29 => ! [B_x,B_k] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.29 ( ( class_Divides_Osemiring__div(T_b)
% 21.40/21.29 & class_Int_Onumber(T_b) )
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 21.40/21.29 <=> c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__div__div__eq__mult,axiom,
% 21.40/21.29 ! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] :
% 21.40/21.29 ( class_Divides_Osemiring__div(T_b)
% 21.40/21.29 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 21.40/21.29 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2))
% 21.40/21.29 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2)
% 21.40/21.29 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__div__eq__mult,axiom,
% 21.40/21.29 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.29 ( class_Divides_Osemiring__div(T_b)
% 21.40/21.29 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 21.40/21.29 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
% 21.40/21.29 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) ) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__imp__le,axiom,
% 21.40/21.29 ! [V_n,V_k] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_nat__mult__dvd__cancel1,axiom,
% 21.40/21.29 ! [V_n_2,V_m_2,V_k_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__mult__cancel,axiom,
% 21.40/21.29 ! [V_n,V_m,V_k] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Powp__mono,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__power,axiom,
% 21.40/21.29 ! [V_x,V_n,T_a] :
% 21.40/21.29 ( class_Rings_Ocomm__semiring__1(T_a)
% 21.40/21.29 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 21.40/21.29 | V_x = c_Groups_Oone__class_Oone(T_a) )
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_the__elem__def,axiom,
% 21.40/21.29 ! [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))))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_the__elem__eq,axiom,
% 21.40/21.29 ! [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 ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 21.40/21.29 ! [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))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd_Ostrict__monoD,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,V_f_2,T_b] :
% 21.40/21.29 ( class_Orderings_Oorder(T_b)
% 21.40/21.29 => ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
% 21.40/21.29 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 21.40/21.29 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd_OmonoD,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,V_f_2,T_b] :
% 21.40/21.29 ( class_Orderings_Oorder(T_b)
% 21.40/21.29 => ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 21.40/21.29 => 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))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__zmod__imp__zdvd,axiom,
% 21.40/21.29 ! [V_n,V_m,V_k] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__zmod,axiom,
% 21.40/21.29 ! [V_n,V_m,V_f] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_uminus__dvd__conv_I2_J,axiom,
% 21.40/21.29 ! [V_t_2,V_d_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_uminus__dvd__conv_I1_J,axiom,
% 21.40/21.29 ! [V_t_2,V_d_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d_2)),V_t_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__zdiffD,axiom,
% 21.40/21.29 ! [V_n,V_m,V_k] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),V_n)))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__antisym__abs,axiom,
% 21.40/21.29 ! [V_b,V_a] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_b),V_a))
% 21.40/21.29 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_a) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_b) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_bot__nat__def,axiom,
% 21.40/21.29 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__antisym__nonneg,axiom,
% 21.40/21.29 ! [V_n,V_m] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 21.40/21.29 => V_m = V_n ) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__not__zless,axiom,
% 21.40/21.29 ! [V_n,V_m] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_m),V_n))
% 21.40/21.29 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__mult__cancel,axiom,
% 21.40/21.29 ! [V_n,V_m,V_k] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n)))
% 21.40/21.29 => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__mono,axiom,
% 21.40/21.29 ! [V_t_2,V_m_2,V_k_2] :
% 21.40/21.29 ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__period,axiom,
% 21.40/21.29 ! [V_c_2,V_t_2,V_x_2,V_d_2,V_a_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2)))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2))),V_t_2))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__reduce,axiom,
% 21.40/21.29 ! [V_m_2,V_n_2,V_k_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__int,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_transfer__int__nat__relations_I4_J,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__mult__div__cancel,axiom,
% 21.40/21.29 ! [V_m,V_n] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 21.40/21.29 => 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)) = V_m ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zmod__eq__dvd__iff,axiom,
% 21.40/21.29 ! [V_y_2,V_n_2,V_x_2] :
% 21.40/21.29 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_n_2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_n_2)
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x_2),V_y_2))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd1__eq,axiom,
% 21.40/21.29 ! [V_x_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 21.40/21.29 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_abs__div,axiom,
% 21.40/21.29 ! [V_x,V_y] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_y),V_x))
% 21.40/21.29 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd_Ostrict__mono__mono,axiom,
% 21.40/21.29 ! [V_f_2,T_b] :
% 21.40/21.29 ( class_Orderings_Oorder(T_b)
% 21.40/21.29 => ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
% 21.40/21.29 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__imp__le,axiom,
% 21.40/21.29 ! [V_n,V_z] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_n)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2)))
% 21.40/21.29 <=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__imp__le__int,axiom,
% 21.40/21.29 ! [V_d,V_i] :
% 21.40/21.29 ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d),V_i))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_d)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_transfer__nat__int__relations_I4_J,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_zdvd__mult__cancel1,axiom,
% 21.40/21.29 ! [V_n_2,V_m_2] :
% 21.40/21.29 ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)),V_m_2))
% 21.40/21.29 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_dvd__int__iff,axiom,
% 21.40/21.29 ! [V_m_2,V_z_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2))),V_m_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_int__dvd__iff,axiom,
% 21.40/21.29 ! [V_z_2,V_m_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_set__empty__eq,axiom,
% 21.40/21.29 ! [V_xo_2,T_b] :
% 21.40/21.29 ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.29 <=> V_xo_2 = c_Option_Ooption_ONone(T_b) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_nat__dvd__iff,axiom,
% 21.40/21.29 ! [V_m_2,V_z_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),V_m_2))
% 21.40/21.29 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) )
% 21.40/21.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 21.40/21.29 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_escape,axiom,
% 21.40/21.29 ! [V_Q_2,V_c_2,V_Ga_2,T_b,V_P_2] :
% 21.40/21.29 ( ! [B_Z,B_s] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 21.40/21.29 => 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_c_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) )
% 21.40/21.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_conseq2,axiom,
% 21.40/21.29 ! [V_Q_2,V_Q_H_2,V_c_2,V_P_2,V_Ga_2,T_b] :
% 21.40/21.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 21.40/21.29 => ( ! [B_Z,B_s] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 21.40/21.29 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) )
% 21.40/21.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_conseq1,axiom,
% 21.40/21.29 ! [V_P_2,V_Q_2,V_c_2,V_P_H_2,V_Ga_2,T_b] :
% 21.40/21.29 ( 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_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 21.40/21.29 => ( ! [B_Z,B_s] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 21.40/21.29 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 21.40/21.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_psubset__insert__iff,axiom,
% 21.40/21.29 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 21.40/21.29 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 21.40/21.29 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => 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)) )
% 21.40/21.29 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_equalityCE,axiom,
% 21.40/21.29 ! [V_c_2,T_b,V_B_2,V_A_2] :
% 21.40/21.29 ( V_A_2 = V_B_2
% 21.40/21.29 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.29 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
% 21.40/21.29 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_emptyE,axiom,
% 21.40/21.29 ! [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)))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insertE,axiom,
% 21.40/21.29 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 21.40/21.29 => ( V_a_2 != V_b_2
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insertCI,axiom,
% 21.40/21.29 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 21.40/21.29 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 21.40/21.29 => V_a_2 = V_b_2 )
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_subsetD,axiom,
% 21.40/21.29 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_DiffE,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 21.40/21.29 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_DiffI,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_ComplI,axiom,
% 21.40/21.29 ! [V_A_2,V_c_2,T_b] :
% 21.40/21.29 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_mem__splitI,axiom,
% 21.40/21.29 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
% 21.40/21.29 => 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_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insertI1,axiom,
% 21.40/21.29 ! [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))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_all__not__in__conv,axiom,
% 21.40/21.29 ! [V_A_2,T_b] :
% 21.40/21.29 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.29 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_ex__in__conv,axiom,
% 21.40/21.29 ! [V_A_2,T_b] :
% 21.40/21.29 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.29 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_empty__iff,axiom,
% 21.40/21.29 ! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insert__iff,axiom,
% 21.40/21.29 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 21.40/21.29 <=> ( V_a_2 = V_b_2
% 21.40/21.29 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insert__ident,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 21.40/21.29 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 21.40/21.29 => ( 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)
% 21.40/21.29 <=> V_A_2 = V_B_2 ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_equals0D,axiom,
% 21.40/21.29 ! [V_a_2,T_b,V_A_2] :
% 21.40/21.29 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.29 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insertI2,axiom,
% 21.40/21.29 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insert__absorb,axiom,
% 21.40/21.29 ! [V_A_2,V_a_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.29 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_in__mono,axiom,
% 21.40/21.29 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_set__rev__mp,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_set__mp,axiom,
% 21.40/21.29 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Compl__iff,axiom,
% 21.40/21.29 ! [V_A_2,V_c_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 21.40/21.29 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_ComplD,axiom,
% 21.40/21.29 ! [V_A_2,V_c_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 21.40/21.29 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_ComplE,axiom,
% 21.40/21.29 ! [V_A_2,V_c_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 21.40/21.29 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_pred__equals__eq,axiom,
% 21.40/21.29 ! [V_S_2,V_R_2,T_b] :
% 21.40/21.29 ( 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)
% 21.40/21.29 <=> V_R_2 = V_S_2 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_eq__mem,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 21.40/21.29 <=> V_x_2 = V_y_2 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Diff__iff,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 21.40/21.29 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.29 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_DiffD1,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_DiffD2,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 21.40/21.29 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_mem__def,axiom,
% 21.40/21.29 ! [V_A_2,V_x_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_eqset__imp__iff,axiom,
% 21.40/21.29 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 21.40/21.29 ( V_A_2 = V_B_2
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_eqelem__imp__iff,axiom,
% 21.40/21.29 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 21.40/21.29 ( V_x_2 = V_y_2
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_eq__mem__trans,axiom,
% 21.40/21.29 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 21.40/21.29 ( V_a_2 = V_b_2
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_psubsetD,axiom,
% 21.40/21.29 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_bot__empty__eq,axiom,
% 21.40/21.29 ! [V_x_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_pred__equals__eq2,axiom,
% 21.40/21.29 ! [V_S_2,V_R_2,T_c,T_b] :
% 21.40/21.29 ( 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)
% 21.40/21.29 <=> V_R_2 = V_S_2 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_bot__empty__eq2,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,T_c,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 <=> 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)))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_pred__subset__eq,axiom,
% 21.40/21.29 ! [V_S_2,V_R_2,T_b] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_singleton__iff,axiom,
% 21.40/21.29 ! [V_a_2,V_b_2,T_b] :
% 21.40/21.29 ( 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)))))
% 21.40/21.29 <=> V_b_2 = V_a_2 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_singletonE,axiom,
% 21.40/21.29 ! [V_a_2,V_b_2,T_b] :
% 21.40/21.29 ( 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)))))
% 21.40/21.29 => V_b_2 = V_a_2 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_subset__insert,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 21.40/21.29 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => ( 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)))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insert__subset,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 21.40/21.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insert__Diff__if,axiom,
% 21.40/21.29 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 21.40/21.29 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 21.40/21.29 => 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) )
% 21.40/21.29 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 21.40/21.29 => 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)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insert__Diff1,axiom,
% 21.40/21.29 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 21.40/21.29 => 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) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_elem__set,axiom,
% 21.40/21.29 ! [V_xo_2,V_x_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2)))
% 21.40/21.29 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_pred__subset__eq2,axiom,
% 21.40/21.29 ! [V_S_2,V_R_2,T_c,T_b] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 <=> 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Diff__insert__absorb,axiom,
% 21.40/21.29 ! [V_A_2,V_x_2,T_b] :
% 21.40/21.29 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => 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 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insert__Diff,axiom,
% 21.40/21.29 ! [V_A_2,V_a_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.29 => 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 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_subset__insert__iff,axiom,
% 21.40/21.29 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => 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)) )
% 21.40/21.29 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_diff__single__insert,axiom,
% 21.40/21.29 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_in__rel__def,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 21.40/21.29 <=> 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 21.40/21.29 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => ( 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)
% 21.40/21.29 => 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)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nitpick_Orefl_H__def,axiom,
% 21.40/21.29 ! [V_r_2,T_b] :
% 21.40/21.29 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 21.40/21.29 <=> ! [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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_flat__lub__def,axiom,
% 21.40/21.29 ! [V_b_2,V_A_2,T_b] :
% 21.40/21.29 ( ( 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)))))
% 21.40/21.29 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 21.40/21.29 & ( ~ 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)))))
% 21.40/21.29 => 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)))))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_bot2E,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_less__by__empty,axiom,
% 21.40/21.29 ! [V_B_2,T_b,V_A_2] :
% 21.40/21.29 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 21.40/21.29 ! [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) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 21.40/21.29 ! [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) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_in__measure,axiom,
% 21.40/21.29 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 <=> 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_mlex__leq,axiom,
% 21.40/21.29 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 => ( 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))
% 21.40/21.29 => 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_mlex__less,axiom,
% 21.40/21.29 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nats__number__of,axiom,
% 21.40/21.29 ! [V_w_2,T_b] :
% 21.40/21.29 ( class_Int_Onumber__ring(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 21.40/21.29 => 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nats__0,axiom,
% 21.40/21.29 ! [T_b] :
% 21.40/21.29 ( class_Rings_Osemiring__1(T_b)
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nats__add,axiom,
% 21.40/21.29 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.29 ( class_Rings_Osemiring__1(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 21.40/21.29 => 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))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nats__mult,axiom,
% 21.40/21.29 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.29 ( class_Rings_Osemiring__1(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 21.40/21.29 => 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))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nats__1,axiom,
% 21.40/21.29 ! [T_b] :
% 21.40/21.29 ( class_Rings_Osemiring__1(T_b)
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_of__nat__in__Nats,axiom,
% 21.40/21.29 ! [V_n_2,T_b] :
% 21.40/21.29 ( class_Rings_Osemiring__1(T_b)
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Ints__odd__less__0,axiom,
% 21.40/21.29 ! [V_a_2,T_b] :
% 21.40/21.29 ( class_Rings_Olinordered__idom(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 21.40/21.29 => ( 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)))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 21.40/21.29 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.29 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 21.40/21.29 | ? [B_x,B_y] :
% 21.40/21.29 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 21.40/21.29 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 21.40/21.29 & 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) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_in__lex__prod,axiom,
% 21.40/21.29 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 <=> ( 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))
% 21.40/21.29 | ( V_a_2 = V_a_H_2
% 21.40/21.29 & 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)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_pair__lessI2,axiom,
% 21.40/21.29 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 21.40/21.29 => 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)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Ints__0,axiom,
% 21.40/21.29 ! [T_b] :
% 21.40/21.29 ( class_Rings_Oring__1(T_b)
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Ints__add,axiom,
% 21.40/21.29 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.29 ( class_Rings_Oring__1(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 21.40/21.29 => 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))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Ints__mult,axiom,
% 21.40/21.29 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.29 ( class_Rings_Oring__1(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 21.40/21.29 => 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))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Ints__diff,axiom,
% 21.40/21.29 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.29 ( class_Rings_Oring__1(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 21.40/21.29 => 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))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Ints__number__of,axiom,
% 21.40/21.29 ! [V_w_2,T_b] :
% 21.40/21.29 ( class_Int_Onumber__ring(T_b)
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Ints__1,axiom,
% 21.40/21.29 ! [T_b] :
% 21.40/21.29 ( class_Rings_Oring__1(T_b)
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Ints__minus,axiom,
% 21.40/21.29 ! [V_a_2,T_b] :
% 21.40/21.29 ( class_Rings_Oring__1(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 21.40/21.29 => 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Ints__of__nat,axiom,
% 21.40/21.29 ! [V_n_2,T_b] :
% 21.40/21.29 ( class_Rings_Oring__1(T_b)
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Ints__power,axiom,
% 21.40/21.29 ! [V_n_2,V_a_2,T_b] :
% 21.40/21.29 ( class_Rings_Oring__1(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 21.40/21.29 => 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Ints__of__int,axiom,
% 21.40/21.29 ! [V_z_2,T_b] :
% 21.40/21.29 ( class_Rings_Oring__1(T_b)
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Ints__double__eq__0__iff,axiom,
% 21.40/21.29 ! [V_a_2,T_b] :
% 21.40/21.29 ( class_Int_Oring__char__0(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 21.40/21.29 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 21.40/21.29 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_pair__lessI1,axiom,
% 21.40/21.29 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Ints__odd__nonzero,axiom,
% 21.40/21.29 ! [V_a_2,T_b] :
% 21.40/21.29 ( class_Int_Oring__char__0(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 21.40/21.29 => 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) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_same__fstI,axiom,
% 21.40/21.29 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
% 21.40/21.29 ( hBOOL(hAPP(V_P_2,V_x_2))
% 21.40/21.29 => ( 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)))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_pair__leqI2,axiom,
% 21.40/21.29 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 21.40/21.29 => 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)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_smax__insertI,axiom,
% 21.40/21.29 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 21.40/21.29 => ( 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))
% 21.40/21.29 => ( 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))
% 21.40/21.29 => 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)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_smin__insertI,axiom,
% 21.40/21.29 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 21.40/21.29 => ( 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))
% 21.40/21.29 => ( 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))
% 21.40/21.29 => 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)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_smin__emptyI,axiom,
% 21.40/21.29 ! [V_X_2] :
% 21.40/21.29 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_pair__leqI1,axiom,
% 21.40/21.29 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_wmin__insertI,axiom,
% 21.40/21.29 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 21.40/21.29 => ( 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))
% 21.40/21.29 => ( 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))
% 21.40/21.29 => 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)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_wmax__insertI,axiom,
% 21.40/21.29 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 21.40/21.29 => ( 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))
% 21.40/21.29 => ( 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))
% 21.40/21.29 => 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)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_wmin__emptyI,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_min__strict__def,axiom,
% 21.40/21.29 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_min__weak__def,axiom,
% 21.40/21.29 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)))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_max__rpair__set,axiom,
% 21.40/21.29 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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_min__rpair__set,axiom,
% 21.40/21.29 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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_less__than__iff,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2] :
% 21.40/21.29 ( 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))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup1E,axiom,
% 21.40/21.29 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 21.40/21.29 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup1CI,axiom,
% 21.40/21.29 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 21.40/21.29 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 21.40/21.29 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_UnE,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 21.40/21.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_UnCI,axiom,
% 21.40/21.29 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 21.40/21.29 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__eq__bot__iff,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.29 ( class_Lattices_Obounded__lattice__bot(T_b)
% 21.40/21.29 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 21.40/21.29 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 21.40/21.29 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__bot__right,axiom,
% 21.40/21.29 ! [V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Obounded__lattice__bot(T_a)
% 21.40/21.29 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__bot__left,axiom,
% 21.40/21.29 ! [V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Obounded__lattice__bot(T_a)
% 21.40/21.29 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__empty,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.29 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__empty__right,axiom,
% 21.40/21.29 ! [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 ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__empty__left,axiom,
% 21.40/21.29 ! [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 ).
% 21.40/21.29
% 21.40/21.29 fof(fact_le__supE,axiom,
% 21.40/21.29 ! [V_x,V_b,V_a,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => ( 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))
% 21.40/21.29 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 21.40/21.29 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__mono,axiom,
% 21.40/21.29 ! [V_d,V_b,V_c,V_a,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 21.40/21.29 => 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))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__least,axiom,
% 21.40/21.29 ! [V_z,V_x,V_y,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 21.40/21.29 => 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)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_le__supI,axiom,
% 21.40/21.29 ! [V_b,V_x,V_a,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 21.40/21.29 => 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)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__absorb1,axiom,
% 21.40/21.29 ! [V_x,V_y,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 21.40/21.29 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__absorb2,axiom,
% 21.40/21.29 ! [V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.40/21.29 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_le__supI2,axiom,
% 21.40/21.29 ! [V_a,V_b,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 21.40/21.29 => 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_le__supI1,axiom,
% 21.40/21.29 ! [V_b,V_a,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 21.40/21.29 => 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_le__sup__iff,axiom,
% 21.40/21.29 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_b)
% 21.40/21.29 => ( 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))
% 21.40/21.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 21.40/21.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_le__iff__sup,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.40/21.29 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__ge2,axiom,
% 21.40/21.29 ! [V_x,V_y,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__sup__ord_I4_J,axiom,
% 21.40/21.29 ! [V_x,V_y,T_a] :
% 21.40/21.29 ( class_Lattices_Olattice(T_a)
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__ge1,axiom,
% 21.40/21.29 ! [V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__sup__ord_I3_J,axiom,
% 21.40/21.29 ! [V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Olattice(T_a)
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__mono,axiom,
% 21.40/21.29 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 21.40/21.29 => 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__least,axiom,
% 21.40/21.29 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 21.40/21.29 => 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)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__absorb2,axiom,
% 21.40/21.29 ! [V_A_2,V_B_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.29 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__absorb1,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_subset__Un__eq,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__upper2,axiom,
% 21.40/21.29 ! [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))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__upper1,axiom,
% 21.40/21.29 ! [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))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup1I1,axiom,
% 21.40/21.29 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 21.40/21.29 ( hBOOL(hAPP(V_A_2,V_x_2))
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup1I2,axiom,
% 21.40/21.29 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 21.40/21.29 ( hBOOL(hAPP(V_B_2,V_x_2))
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__Diff__cancel,axiom,
% 21.40/21.29 ! [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) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__Diff__cancel2,axiom,
% 21.40/21.29 ! [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) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__Diff,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__absorb,axiom,
% 21.40/21.29 ! [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 ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__commute,axiom,
% 21.40/21.29 ! [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) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__left__absorb,axiom,
% 21.40/21.29 ! [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) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__left__commute,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__assoc,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_bex__Un,axiom,
% 21.40/21.29 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( ? [B_x] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 & hBOOL(hAPP(V_P_2,B_x)) )
% 21.40/21.29 <=> ( ? [B_x] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.29 & hBOOL(hAPP(V_P_2,B_x)) )
% 21.40/21.29 | ? [B_x] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 21.40/21.29 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_ball__Un,axiom,
% 21.40/21.29 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( ! [B_x] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 => hBOOL(hAPP(V_P_2,B_x)) )
% 21.40/21.29 <=> ( ! [B_x] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(V_P_2,B_x)) )
% 21.40/21.29 & ! [B_x] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 21.40/21.29 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup_Oidem,axiom,
% 21.40/21.29 ! [V_a,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__idem,axiom,
% 21.40/21.29 ! [V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup_Ocommute,axiom,
% 21.40/21.29 ! [V_b,V_a,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => 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) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__sup__aci_I5_J,axiom,
% 21.40/21.29 ! [V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Olattice(T_a)
% 21.40/21.29 => 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) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__commute,axiom,
% 21.40/21.29 ! [V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => 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) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup_Oleft__idem,axiom,
% 21.40/21.29 ! [V_b,V_a,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => 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) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__sup__aci_I8_J,axiom,
% 21.40/21.29 ! [V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Olattice(T_a)
% 21.40/21.29 => 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) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__left__idem,axiom,
% 21.40/21.29 ! [V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => 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) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup_Oleft__commute,axiom,
% 21.40/21.29 ! [V_c,V_a,V_b,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__sup__aci_I7_J,axiom,
% 21.40/21.29 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Olattice(T_a)
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__left__commute,axiom,
% 21.40/21.29 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup_Oassoc,axiom,
% 21.40/21.29 ! [V_c,V_b,V_a,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__sup__aci_I6_J,axiom,
% 21.40/21.29 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Olattice(T_a)
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__assoc,axiom,
% 21.40/21.29 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__apply,axiom,
% 21.40/21.29 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 21.40/21.29 ( class_Lattices_Olattice(T_b)
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_less__supI1,axiom,
% 21.40/21.29 ! [V_b,V_a,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 21.40/21.29 => 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_less__supI2,axiom,
% 21.40/21.29 ! [V_a,V_b,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__sup(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 21.40/21.29 => 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__fun__def,axiom,
% 21.40/21.29 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 21.40/21.29 ( class_Lattices_Olattice(T_b)
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Sup__fin_Oidem,axiom,
% 21.40/21.29 ! [V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Olattice(T_a)
% 21.40/21.29 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__max,axiom,
% 21.40/21.29 ! [T_b] :
% 21.40/21.29 ( ( class_Lattices_Osemilattice__sup(T_b)
% 21.40/21.29 & class_Orderings_Olinorder(T_b) )
% 21.40/21.29 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__insert__left,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__insert__right,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__iff,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 21.40/21.29 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.29 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_UnI1,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_UnI2,axiom,
% 21.40/21.29 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__Un__eq,axiom,
% 21.40/21.29 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 <=> 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insert__is__Un,axiom,
% 21.40/21.29 ! [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) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Diff__subset__conv,axiom,
% 21.40/21.29 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 <=> 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Diff__partition,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 => 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 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Compl__Diff__eq,axiom,
% 21.40/21.29 ! [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) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_pair__less__def,axiom,
% 21.40/21.29 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_max__weak__def,axiom,
% 21.40/21.29 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)))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_mlex__prod__def,axiom,
% 21.40/21.29 ! [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))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_intrel__iff,axiom,
% 21.40/21.29 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 21.40/21.29 ( 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))
% 21.40/21.29 <=> 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) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_rp__inv__image__rp,axiom,
% 21.40/21.29 ! [V_f_2,T_c,V_P_2,T_b] :
% 21.40/21.29 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 21.40/21.29 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__nat__def,axiom,
% 21.40/21.29 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_rp__inv__image__def,axiom,
% 21.40/21.29 ! [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))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup__Un__eq2,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 <=> 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_max__strict__def,axiom,
% 21.40/21.29 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_max__ext__additive,axiom,
% 21.40/21.29 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 => ( 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)))
% 21.40/21.29 => 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_max__extp__max__ext__eq,axiom,
% 21.40/21.29 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 21.40/21.29 ( 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)
% 21.40/21.29 <=> 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_in__inv__image,axiom,
% 21.40/21.29 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 <=> 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Body1,axiom,
% 21.40/21.29 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
% 21.40/21.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2))
% 21.40/21.29 => 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(V_P_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Q_2,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Body__sound__lemma,axiom,
% 21.40/21.29 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
% 21.40/21.29 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2))
% 21.40/21.29 => c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup2E,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup2CI,axiom,
% 21.40/21.29 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 21.40/21.29 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_image__eqI,axiom,
% 21.40/21.29 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 21.40/21.29 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup2I1,axiom,
% 21.40/21.29 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_sup2I2,axiom,
% 21.40/21.29 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_image__Un,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_image__mono,axiom,
% 21.40/21.29 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_subset__image__iff,axiom,
% 21.40/21.29 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 <=> ? [B_AA] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 21.40/21.29 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_image__image,axiom,
% 21.40/21.29 ! [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) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_image__iff,axiom,
% 21.40/21.29 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 21.40/21.29 <=> ? [B_x] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 21.40/21.29 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_imageI,axiom,
% 21.40/21.29 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_rev__image__eqI,axiom,
% 21.40/21.29 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_image__insert,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_empty__is__image,axiom,
% 21.40/21.29 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.29 ( 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)
% 21.40/21.29 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_image__empty,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_image__is__empty,axiom,
% 21.40/21.29 ! [V_A_2,V_f_2,T_b,T_c] :
% 21.40/21.29 ( 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))
% 21.40/21.29 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_insert__image,axiom,
% 21.40/21.29 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => 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) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_image__diff__subset,axiom,
% 21.40/21.29 ! [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)))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_image__constant__conv,axiom,
% 21.40/21.29 ! [V_c_2,T_c,T_b,V_A_2] :
% 21.40/21.29 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.29 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 21.40/21.29 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.29 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_image__constant,axiom,
% 21.40/21.29 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_measure__def,axiom,
% 21.40/21.29 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_hoare__derivs_OBody,axiom,
% 21.40/21.29 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
% 21.40/21.29 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2))
% 21.40/21.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_irrefl__def,axiom,
% 21.40/21.29 ! [V_r_2,T_b] :
% 21.40/21.29 ( c_Relation_Oirrefl(T_b,V_r_2)
% 21.40/21.29 <=> ! [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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Field__insert,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_equiv__intrel__iff,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2] :
% 21.40/21.29 ( 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))))
% 21.40/21.29 <=> 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_accp__acc__eq,axiom,
% 21.40/21.29 ! [V_x_2,V_r_2,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_pair__imageI,axiom,
% 21.40/21.29 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Image__Un,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 21.40/21.29 ! [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))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 <=> 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 21.40/21.29 ! [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 ).
% 21.40/21.29
% 21.40/21.29 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2] :
% 21.40/21.29 ( V_A_2 = V_B_2
% 21.40/21.29 <=> 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) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 <=> 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 21.40/21.29 ! [V_A_2,V_x_2] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 21.40/21.29 <=> 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Image__empty,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 21.40/21.29 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))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 21.40/21.29 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))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Image__mono,axiom,
% 21.40/21.29 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 21.40/21.29 => 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Un__Image,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_acc__subset,axiom,
% 21.40/21.29 ! [V_R2_2,V_R1_2,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_rev__ImageI,axiom,
% 21.40/21.29 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.29 => ( 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))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Image__iff,axiom,
% 21.40/21.29 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 21.40/21.29 <=> ? [B_x] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 21.40/21.29 & 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)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Field__empty,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_mono__Field,axiom,
% 21.40/21.29 ! [V_s_2,V_r_2,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Field__Un,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_acc__downward,axiom,
% 21.40/21.29 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 21.40/21.29 => ( 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))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_acc_Osimps,axiom,
% 21.40/21.29 ! [V_r_2,V_a_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 21.40/21.29 <=> ! [B_x] :
% 21.40/21.29 ( 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))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Image__singleton__iff,axiom,
% 21.40/21.29 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 21.40/21.29 ( 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))))))
% 21.40/21.29 <=> 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_of__int,axiom,
% 21.40/21.29 ! [V_j_2,V_i_2,T_b] :
% 21.40/21.29 ( class_Rings_Oring__1(T_b)
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_One__int__def,axiom,
% 21.40/21.29 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))))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_mult,axiom,
% 21.40/21.29 ! [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))))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_le,axiom,
% 21.40/21.29 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 21.40/21.29 ( 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)))))))
% 21.40/21.29 <=> 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_minus,axiom,
% 21.40/21.29 ! [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))))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Zero__int__def,axiom,
% 21.40/21.29 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))))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_int__def,axiom,
% 21.40/21.29 ! [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))))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_add,axiom,
% 21.40/21.29 ! [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))))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_nat,axiom,
% 21.40/21.29 ! [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) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_less,axiom,
% 21.40/21.29 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 21.40/21.29 ( 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)))))))
% 21.40/21.29 <=> 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2] :
% 21.40/21.29 ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.29 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 21.40/21.29 => 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_eq__Abs__Integ,axiom,
% 21.40/21.29 ! [V_z_2] :
% 21.40/21.29 ~ ! [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))))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2] :
% 21.40/21.29 ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.29 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 <=> 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))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2] :
% 21.40/21.29 ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.29 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 <=> 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))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 21.40/21.29 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2] :
% 21.40/21.29 ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.29 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 21.40/21.29 => 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)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_nat__set__def,axiom,
% 21.40/21.29 ! [V_S_2] :
% 21.40/21.29 ( c_Nat__Transfer_Onat__set(V_S_2)
% 21.40/21.29 <=> ! [B_x] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2] :
% 21.40/21.29 ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.29 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 21.40/21.29 => ( V_A_2 = V_B_2
% 21.40/21.29 <=> 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) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 21.40/21.29 ! [V_x_2,V_A_2] :
% 21.40/21.29 ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 21.40/21.29 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 21.40/21.29 ! [V_x_2,V_A_2] :
% 21.40/21.29 ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 21.40/21.29 ! [V_A_2] :
% 21.40/21.29 ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.29 => 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 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 21.40/21.29 ! [V_A_2,V_x_2] :
% 21.40/21.29 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 21.40/21.29 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 21.40/21.29 <=> 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))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_ImageE,axiom,
% 21.40/21.29 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 21.40/21.29 => ~ ! [B_x] :
% 21.40/21.29 ( 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))
% 21.40/21.29 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_subset__equiv__class,axiom,
% 21.40/21.29 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 21.40/21.29 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.29 => ( 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))))))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 21.40/21.29 => 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)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_wmax__emptyI,axiom,
% 21.40/21.29 ! [V_X_2] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_smax__emptyI,axiom,
% 21.40/21.29 ! [V_Y_2] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 21.40/21.29 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 21.40/21.29 => 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)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__Field,axiom,
% 21.40/21.29 ! [V_r_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 21.40/21.29 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_equiv__class__self,axiom,
% 21.40/21.29 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 21.40/21.29 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.29 => 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)))))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_equiv__class__eq,axiom,
% 21.40/21.29 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 21.40/21.29 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.29 => ( 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))
% 21.40/21.29 => 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)))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_equiv__class__eq__iff,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 21.40/21.29 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.29 => ( 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))
% 21.40/21.29 <=> ( 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))))
% 21.40/21.29 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_eq__equiv__class,axiom,
% 21.40/21.29 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 21.40/21.29 ( 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))))
% 21.40/21.29 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 21.40/21.29 => 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)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_eq__equiv__class__iff,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 21.40/21.29 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 21.40/21.29 => ( 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))))
% 21.40/21.29 <=> 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)) ) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_equiv__class__subset,axiom,
% 21.40/21.29 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 21.40/21.29 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.29 => ( 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))
% 21.40/21.29 => 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)))))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__Diff,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__imageI,axiom,
% 21.40/21.29 ! [V_h_2,T_c,V_F_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 21.40/21.29 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite_OinsertI,axiom,
% 21.40/21.29 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.29 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite_OemptyI,axiom,
% 21.40/21.29 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 21.40/21.29 ! [V_A_2] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 21.40/21.29 <=> 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 21.40/21.29 ! [V_A_2] :
% 21.40/21.29 ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 21.40/21.29 <=> 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite,axiom,
% 21.40/21.29 ! [V_A_2,T_b] :
% 21.40/21.29 ( class_Finite__Set_Ofinite(T_b)
% 21.40/21.29 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__code,axiom,
% 21.40/21.29 ! [V_A_2,T_b] :
% 21.40/21.29 ( class_Finite__Set_Ofinite(T_b)
% 21.40/21.29 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite_Oequations_I1_J,axiom,
% 21.40/21.29 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__insert,axiom,
% 21.40/21.29 ! [V_A_2,V_a_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 21.40/21.29 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_rev__finite__subset,axiom,
% 21.40/21.29 ! [V_A_2,V_B_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__subset,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.29 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__Un,axiom,
% 21.40/21.29 ! [V_Ga_2,V_F_2,T_b] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 21.40/21.29 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__UnI,axiom,
% 21.40/21.29 ! [V_Ga_2,V_F_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 21.40/21.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
% 21.40/21.29 => 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))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__Diff2,axiom,
% 21.40/21.29 ! [V_A_2,V_B_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.29 => ( 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)))
% 21.40/21.29 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__surj,axiom,
% 21.40/21.29 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.29 => ( 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)))
% 21.40/21.29 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__Diff__insert,axiom,
% 21.40/21.29 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 21.40/21.29 ( 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))))
% 21.40/21.29 <=> 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_in__finite__psubset,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( 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)))
% 21.40/21.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.29 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__pointwise,axiom,
% 21.40/21.29 ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_c,V_U_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_U_2))
% 21.40/21.29 => ( ! [B_p] :
% 21.40/21.29 ( 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))))
% 21.40/21.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_P_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) )
% 21.40/21.29 => ( 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))
% 21.40/21.29 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_P_2)),V_c0_2)),V_Q_2)),V_U_2)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_folding__one_Oremove,axiom,
% 21.40/21.29 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 21.40/21.29 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 21.40/21.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.29 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 21.40/21.29 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.29 => 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)))))) ) ) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_folding__image__simple_Oremove,axiom,
% 21.40/21.29 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.29 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 21.40/21.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 21.40/21.29 => 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)))))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_folding__image__simple_Oempty,axiom,
% 21.40/21.29 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.29 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 21.40/21.29 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_folding__one_Osingleton,axiom,
% 21.40/21.29 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 21.40/21.29 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 21.40/21.29 => 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 ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_folding__image__simple_Oinsert,axiom,
% 21.40/21.29 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.29 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 21.40/21.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 21.40/21.29 => 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)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_folding__one_Oinsert,axiom,
% 21.40/21.29 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 21.40/21.29 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 21.40/21.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.29 => 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)) ) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_folding__one_Oinsert__remove,axiom,
% 21.40/21.29 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 21.40/21.29 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 21.40/21.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.29 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.29 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 21.40/21.29 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.29 => 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)))))) ) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 21.40/21.29 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.29 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 21.40/21.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.29 => 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)))))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 21.40/21.29 ! [V_N_2] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 21.40/21.29 <=> ? [B_m] :
% 21.40/21.29 ! [B_x] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__nat__set__iff__bounded,axiom,
% 21.40/21.29 ! [V_N_2] :
% 21.40/21.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 21.40/21.29 <=> ? [B_m] :
% 21.40/21.29 ! [B_x] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_eq__equiv__class__iff2,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 21.40/21.29 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 21.40/21.29 => ( 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)
% 21.40/21.29 <=> 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)) ) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_equiv__class__nondisjoint,axiom,
% 21.40/21.29 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 21.40/21.29 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.29 => ( 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)))))))
% 21.40/21.29 => 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)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf1E,axiom,
% 21.40/21.29 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 21.40/21.29 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf1I,axiom,
% 21.40/21.29 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 21.40/21.29 ( hBOOL(hAPP(V_A_2,V_x_2))
% 21.40/21.29 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 21.40/21.29 => 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)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_IntI,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 21.40/21.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_IntE,axiom,
% 21.40/21.29 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 21.40/21.29 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.29 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_finite__Int,axiom,
% 21.40/21.29 ! [V_Ga_2,V_F_2,T_b] :
% 21.40/21.29 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 21.40/21.29 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) )
% 21.40/21.29 => 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_quotient__disj,axiom,
% 21.40/21.29 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 21.40/21.29 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.29 => ( 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)))
% 21.40/21.29 => ( 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)))
% 21.40/21.29 => ( V_X_2 = V_Y_2
% 21.40/21.29 | 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)) ) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_quotient__empty,axiom,
% 21.40/21.29 ! [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)) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_quotient__is__empty2,axiom,
% 21.40/21.29 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.29 ( 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)
% 21.40/21.29 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_quotient__is__empty,axiom,
% 21.40/21.29 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__Int__eq,axiom,
% 21.40/21.29 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 21.40/21.29 ( 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))
% 21.40/21.29 <=> 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))) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_le__infE,axiom,
% 21.40/21.29 ! [V_b,V_a,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.29 => ( 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)))
% 21.40/21.29 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 21.40/21.29 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__mono,axiom,
% 21.40/21.29 ! [V_d,V_b,V_c,V_a,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 21.40/21.29 => 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))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__greatest,axiom,
% 21.40/21.29 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 21.40/21.29 => 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))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_le__infI,axiom,
% 21.40/21.29 ! [V_b,V_a,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 21.40/21.29 => 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))) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__absorb2,axiom,
% 21.40/21.29 ! [V_x,V_y,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 21.40/21.29 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__absorb1,axiom,
% 21.40/21.29 ! [V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.40/21.29 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_le__infI2,axiom,
% 21.40/21.29 ! [V_a,V_x,V_b,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 21.40/21.29 => 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)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_le__infI1,axiom,
% 21.40/21.29 ! [V_b,V_x,V_a,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 21.40/21.29 => 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)) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_le__inf__iff,axiom,
% 21.40/21.29 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 21.40/21.29 ( class_Lattices_Osemilattice__inf(T_b)
% 21.40/21.29 => ( 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)))
% 21.40/21.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.40/21.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_le__iff__inf,axiom,
% 21.40/21.29 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.29 ( class_Lattices_Osemilattice__inf(T_b)
% 21.40/21.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.40/21.29 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__le2,axiom,
% 21.40/21.29 ! [V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__sup__ord_I2_J,axiom,
% 21.40/21.29 ! [V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Olattice(T_a)
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__le1,axiom,
% 21.40/21.29 ! [V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_inf__sup__ord_I1_J,axiom,
% 21.40/21.29 ! [V_y,V_x,T_a] :
% 21.40/21.29 ( class_Lattices_Olattice(T_a)
% 21.40/21.29 => 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)) ) ).
% 21.40/21.29
% 21.40/21.29 fof(fact_Int__mono,axiom,
% 21.40/21.29 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 21.40/21.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 21.40/21.30 => 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))) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__greatest,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 21.40/21.30 => 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))) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__absorb1,axiom,
% 21.40/21.30 ! [V_A_2,V_B_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.30 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__absorb2,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.30 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__lower2,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__lower1,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_less__infI1,axiom,
% 21.40/21.30 ! [V_b,V_x,V_a,T_a] :
% 21.40/21.30 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_less__infI2,axiom,
% 21.40/21.30 ! [V_a,V_x,V_b,T_a] :
% 21.40/21.30 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__empty__left,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__empty__right,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_disjoint__iff__not__equal,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( 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))
% 21.40/21.30 <=> ! [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.30 => ! [B_xa] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 21.40/21.30 => B_x != B_xa ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__bot__left,axiom,
% 21.40/21.30 ! [V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Obounded__lattice__bot(T_a)
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__bot__right,axiom,
% 21.40/21.30 ! [V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Obounded__lattice__bot(T_a)
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_IntD2,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_IntD1,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__iff,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 21.40/21.30 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.30 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_sup__inf__distrib2,axiom,
% 21.40/21.30 ! [V_x,V_z,V_y,T_a] :
% 21.40/21.30 ( class_Lattices_Odistrib__lattice(T_a)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__sup__distrib2,axiom,
% 21.40/21.30 ! [V_x,V_z,V_y,T_a] :
% 21.40/21.30 ( class_Lattices_Odistrib__lattice(T_a)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_sup__inf__distrib1,axiom,
% 21.40/21.30 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Odistrib__lattice(T_a)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__sup__distrib1,axiom,
% 21.40/21.30 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Odistrib__lattice(T_a)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_sup__inf__absorb,axiom,
% 21.40/21.30 ! [V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Olattice(T_a)
% 21.40/21.30 => 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 ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__sup__absorb,axiom,
% 21.40/21.30 ! [V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Olattice(T_a)
% 21.40/21.30 => 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 ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Un__Int__crazy,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Un__Int__distrib2,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__Un__distrib2,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Un__Int__distrib,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__Un__distrib,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Inf__fin_Oidem,axiom,
% 21.40/21.30 ! [V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Olattice(T_a)
% 21.40/21.30 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Diff__Int2,axiom,
% 21.40/21.30 ! [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) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Diff__Int__distrib2,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__Diff,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Diff__Int__distrib,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__min,axiom,
% 21.40/21.30 ! [T_b] :
% 21.40/21.30 ( ( class_Lattices_Osemilattice__inf(T_b)
% 21.40/21.30 & class_Orderings_Olinorder(T_b) )
% 21.40/21.30 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__fun__def,axiom,
% 21.40/21.30 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__apply,axiom,
% 21.40/21.30 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__assoc,axiom,
% 21.40/21.30 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__sup__aci_I2_J,axiom,
% 21.40/21.30 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Olattice(T_a)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf_Oassoc,axiom,
% 21.40/21.30 ! [V_c,V_b,V_a,T_a] :
% 21.40/21.30 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__left__commute,axiom,
% 21.40/21.30 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__sup__aci_I3_J,axiom,
% 21.40/21.30 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Olattice(T_a)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf_Oleft__commute,axiom,
% 21.40/21.30 ! [V_c,V_a,V_b,T_a] :
% 21.40/21.30 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__left__idem,axiom,
% 21.40/21.30 ! [V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__sup__aci_I4_J,axiom,
% 21.40/21.30 ! [V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Olattice(T_a)
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf_Oleft__idem,axiom,
% 21.40/21.30 ! [V_b,V_a,T_a] :
% 21.40/21.30 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__commute,axiom,
% 21.40/21.30 ! [V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__sup__aci_I1_J,axiom,
% 21.40/21.30 ! [V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Olattice(T_a)
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf_Ocommute,axiom,
% 21.40/21.30 ! [V_b,V_a,T_a] :
% 21.40/21.30 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__idem,axiom,
% 21.40/21.30 ! [V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.30 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf_Oidem,axiom,
% 21.40/21.30 ! [V_a,T_a] :
% 21.40/21.30 ( class_Lattices_Osemilattice__inf(T_a)
% 21.40/21.30 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__assoc,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__left__commute,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__left__absorb,axiom,
% 21.40/21.30 ! [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) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__commute,axiom,
% 21.40/21.30 ! [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) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__absorb,axiom,
% 21.40/21.30 ! [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 ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf1D2,axiom,
% 21.40/21.30 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( 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))
% 21.40/21.30 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf1D1,axiom,
% 21.40/21.30 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( 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))
% 21.40/21.30 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_insert__inter__insert,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2] :
% 21.40/21.30 ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.30 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_distrib__sup__le,axiom,
% 21.40/21.30 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Olattice(T_a)
% 21.40/21.30 => 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)))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_distrib__inf__le,axiom,
% 21.40/21.30 ! [V_z,V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Olattice(T_a)
% 21.40/21.30 => 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)))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_compl__inf__bot,axiom,
% 21.40/21.30 ! [V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Oboolean__algebra(T_a)
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__compl__bot,axiom,
% 21.40/21.30 ! [V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Oboolean__algebra(T_a)
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_diff__eq,axiom,
% 21.40/21.30 ! [V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Oboolean__algebra(T_a)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_compl__sup,axiom,
% 21.40/21.30 ! [V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Oboolean__algebra(T_a)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_compl__inf,axiom,
% 21.40/21.30 ! [V_y,V_x,T_a] :
% 21.40/21.30 ( class_Lattices_Oboolean__algebra(T_a)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__insert__left__if1,axiom,
% 21.40/21.30 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__insert__right__if1,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__insert__left__if0,axiom,
% 21.40/21.30 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 21.40/21.30 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__insert__right__if0,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 21.40/21.30 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__insert__left,axiom,
% 21.40/21.30 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 21.40/21.30 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 21.40/21.30 => 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)) )
% 21.40/21.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 21.40/21.30 => 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) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__insert__right,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 21.40/21.30 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => 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)) )
% 21.40/21.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => 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) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_image__Int__subset,axiom,
% 21.40/21.30 ! [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)))) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Diff__triv,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( 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))
% 21.40/21.30 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Diff__disjoint,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Un__Int__assoc__eq,axiom,
% 21.40/21.30 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( 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))
% 21.40/21.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Un__Diff__Int,axiom,
% 21.40/21.30 ! [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 ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Diff__Un,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Diff__Int,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 21.40/21.30 ! [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))) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Compl__disjoint2,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Compl__disjoint,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Image__Int__subset,axiom,
% 21.40/21.30 ! [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)))) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Compl__Un,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Compl__Int,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Diff__Compl,axiom,
% 21.40/21.30 ! [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) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Diff__eq,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2] :
% 21.40/21.30 ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.30 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 21.40/21.30 => 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))) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_disjoint__eq__subset__Compl,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( 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))
% 21.40/21.30 <=> 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))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.30 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_singleton__quotient,axiom,
% 21.40/21.30 ! [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))) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_folding__one_Ounion__inter,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 21.40/21.30 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_folding__one_Ounion__disjoint,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 21.40/21.30 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.30 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_quotientI,axiom,
% 21.40/21.30 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_quotient__eq__iff,axiom,
% 21.40/21.30 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 21.40/21.30 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.30 => ( 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)))
% 21.40/21.30 => ( 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)))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 21.40/21.30 => ( V_X_2 = V_Y_2
% 21.40/21.30 <=> 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)) ) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_quotient__eqI,axiom,
% 21.40/21.30 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 21.40/21.30 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.30 => ( 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)))
% 21.40/21.30 => ( 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)))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
% 21.40/21.30 ! [V_k_2,V_l_2] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 21.40/21.30 => c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OlessThan__iff,axiom,
% 21.40/21.30 ! [V_k_2,V_i_2] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
% 21.40/21.30 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
% 21.40/21.30 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OgreaterThan__iff,axiom,
% 21.40/21.30 ! [V_k_2,V_i_2] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
% 21.40/21.30 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
% 21.40/21.30 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OatMost__iff,axiom,
% 21.40/21.30 ! [V_k_2,V_i_2] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
% 21.40/21.30 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__nat__def,axiom,
% 21.40/21.30 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__Int__eq2,axiom,
% 21.40/21.30 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 21.40/21.30 ( 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))
% 21.40/21.30 <=> 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))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 21.40/21.30 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 21.40/21.30 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_ord_OgreaterThan__iff,axiom,
% 21.40/21.30 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 21.40/21.30 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_ord_OlessThan__iff,axiom,
% 21.40/21.30 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 21.40/21.30 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_ord_OatMost__iff,axiom,
% 21.40/21.30 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 21.40/21.30 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OatLeast__iff,axiom,
% 21.40/21.30 ! [V_k_2,V_i_2] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
% 21.40/21.30 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_quotientE,axiom,
% 21.40/21.30 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 => ~ ! [B_x] :
% 21.40/21.30 ( 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))))
% 21.40/21.30 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 21.40/21.30 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 21.40/21.30 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 21.40/21.30 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 21.40/21.30 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf2E,axiom,
% 21.40/21.30 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.30 ( 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))
% 21.40/21.30 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 21.40/21.30 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf2I,axiom,
% 21.40/21.30 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf2D2,axiom,
% 21.40/21.30 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.30 ( 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))
% 21.40/21.30 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf2D1,axiom,
% 21.40/21.30 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.30 ( 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))
% 21.40/21.30 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
% 21.40/21.30 ! [V_k_2,V_l_2] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 21.40/21.30 => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OatLeastLessThan__empty,axiom,
% 21.40/21.30 ! [V_a_2,V_b_2] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 21.40/21.30 => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
% 21.40/21.30 ! [V_l_2,V_k_2] :
% 21.40/21.30 ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 21.40/21.30 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 21.40/21.30 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
% 21.40/21.30 ! [V_b_2,V_a_2] :
% 21.40/21.30 ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 21.40/21.30 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 21.40/21.30 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
% 21.40/21.30 ! [V_l_2,V_k_2] :
% 21.40/21.30 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2)
% 21.40/21.30 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 21.40/21.30 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
% 21.40/21.30 ! [V_b_2,V_a_2] :
% 21.40/21.30 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2)
% 21.40/21.30 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 21.40/21.30 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_ord_OatLeast__iff,axiom,
% 21.40/21.30 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 21.40/21.30 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 21.40/21.30 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 21.40/21.30 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Inf__fin_Oremove,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 21.40/21.30 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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)))))) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Sup__fin_Oremove,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 21.40/21.30 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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)))))) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Max_Oremove,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 21.40/21.30 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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)))))) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Inf__le__Sup,axiom,
% 21.40/21.30 ! [V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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))) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Max_Osingleton,axiom,
% 21.40/21.30 ! [V_x_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => 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 ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Inf__fin_Osingleton,axiom,
% 21.40/21.30 ! [V_x_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => 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 ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Sup__fin_Osingleton,axiom,
% 21.40/21.30 ! [V_x_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => 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 ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Max__ge,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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))) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Max__in,axiom,
% 21.40/21.30 ! [V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_sup__Inf__absorb,axiom,
% 21.40/21.30 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => 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 ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Sup__fin_Oin__idem,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Inf__fin_Oin__idem,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_inf__Sup__absorb,axiom,
% 21.40/21.30 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => 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 ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Max_Oin__idem,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
% 21.40/21.30 ! [V_b_2,V_a_2] :
% 21.40/21.30 ( V_a_2 = V_b_2
% 21.40/21.30 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OatLeastAtMost__singleton,axiom,
% 21.40/21.30 ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
% 21.40/21.30 ! [V_c_2,V_b_2,V_a_2] :
% 21.40/21.30 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
% 21.40/21.30 <=> ( V_a_2 = V_b_2
% 21.40/21.30 & V_b_2 = V_c_2 ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OatLeastatMost__empty,axiom,
% 21.40/21.30 ! [V_a_2,V_b_2] :
% 21.40/21.30 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 21.40/21.30 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) )
% 21.40/21.30 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
% 21.40/21.30 ! [V_b_2,V_a_2] :
% 21.40/21.30 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 21.40/21.30 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
% 21.40/21.30 ! [V_b_2,V_a_2] :
% 21.40/21.30 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)
% 21.40/21.30 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Max__mono,axiom,
% 21.40/21.30 ! [V_N_2,V_M_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 21.40/21.30 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 21.40/21.30 => 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))) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Max__insert,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Sup__fin_Osubset__idem,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Inf__fin_Osubset__idem,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Sup__fin_Ounion__idem,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Max_Osubset__idem,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Inf__fin_Ounion__idem,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Max__Un,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
% 21.40/21.30 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
% 21.40/21.30 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 21.40/21.30 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 21.40/21.30 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd_OatLeastatMost__psubset__iff,axiom,
% 21.40/21.30 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
% 21.40/21.30 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 21.40/21.30 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 21.40/21.30 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 21.40/21.30 & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 21.40/21.30 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2)) )
% 21.40/21.30 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 21.40/21.30 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2)) ) ) ) )
% 21.40/21.30 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_d_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Sup__fin_Oinsert,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Inf__fin_Oinsert,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Max_Oinsert,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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 )
% 21.40/21.30 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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)))))) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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 )
% 21.40/21.30 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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)))))) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Sup__fin_Ounion__inter,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Max_Oinsert__remove,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 21.40/21.30 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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)))))) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Inf__fin_Ounion__inter,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Max_Ounion__inter,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Max_Ounion__disjoint,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Max_Oclosed,axiom,
% 21.40/21.30 ! [V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( ! [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))))))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Inf__fin_Oclosed,axiom,
% 21.40/21.30 ! [V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( ! [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))))))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Sup__fin_Oclosed,axiom,
% 21.40/21.30 ! [V_A_2,T_b] :
% 21.40/21.30 ( class_Lattices_Olattice(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( ! [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))))))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Min_Oremove,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 21.40/21.30 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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)))))) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Min_Osingleton,axiom,
% 21.40/21.30 ! [V_x_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => 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 ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Min__le,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Min__in,axiom,
% 21.40/21.30 ! [V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Min_Oin__idem,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Min__antimono,axiom,
% 21.40/21.30 ! [V_N_2,V_M_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 21.40/21.30 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 21.40/21.30 => 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))) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Min__insert,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Min_Osubset__idem,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Min__Un,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Min_Oinsert,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Min_Oinsert__remove,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 21.40/21.30 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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)))))) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Min_Ounion__inter,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Min_Ounion__disjoint,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_minus__Max__eq__Min,axiom,
% 21.40/21.30 ! [V_S_2,T_b] :
% 21.40/21.30 ( class_Groups_Olinordered__ab__group__add(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.30 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_minus__Min__eq__Max,axiom,
% 21.40/21.30 ! [V_S_2,T_b] :
% 21.40/21.30 ( class_Groups_Olinordered__ab__group__add(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.30 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Min_Oclosed,axiom,
% 21.40/21.30 ! [V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( ! [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))))))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 21.40/21.30 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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)))))) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 21.40/21.30 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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)))))) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OInf__le__Sup,axiom,
% 21.40/21.30 ! [V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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))) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 21.40/21.30 ! [V_x_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => 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 ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 21.40/21.30 ! [V_x_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => 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 ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 21.40/21.30 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => 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 ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 21.40/21.30 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => 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 ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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 )
% 21.40/21.30 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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)))))) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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 )
% 21.40/21.30 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 21.40/21.30 => 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)))))) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 21.40/21.30 ! [V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( ! [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))))))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 21.40/21.30 ! [V_A_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( ! [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))))))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_folding__one_Oclosed,axiom,
% 21.40/21.30 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 21.40/21.30 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => ( ! [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))))))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__Diff__singleton,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__Diff__singleton__if,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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)) )
% 21.40/21.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card_Oremove,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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)))))) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 21.40/21.30 ! [V_A_2] :
% 21.40/21.30 ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card_Oempty,axiom,
% 21.40/21.30 ! [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) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__infinite,axiom,
% 21.40/21.30 ! [V_A_2,T_b] :
% 21.40/21.30 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__eq__0__iff,axiom,
% 21.40/21.30 ! [V_A_2,T_b] :
% 21.40/21.30 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.30 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__ge__0__finite,axiom,
% 21.40/21.30 ! [V_A_2,T_b] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__insert__le,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => 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)))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__seteq,axiom,
% 21.40/21.30 ! [V_A_2,V_B_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.30 => ( 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)))
% 21.40/21.30 => V_A_2 = V_B_2 ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__mono,axiom,
% 21.40/21.30 ! [V_A_2,V_B_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.30 => 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))) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__image__le,axiom,
% 21.40/21.30 ! [V_f_2,T_c,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => 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))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_psubset__card__mono,axiom,
% 21.40/21.30 ! [V_A_2,V_B_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.30 => 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))) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__insert__if,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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) )
% 21.40/21.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__insert__disjoint,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__gt__0__iff,axiom,
% 21.40/21.30 ! [V_A_2,T_b] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__Un__Int,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => 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))) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card_Ounion__inter,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__Diff__subset,axiom,
% 21.40/21.30 ! [V_A_2,V_B_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__Diff__subset__Int,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 => 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))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_diff__card__le__card__Diff,axiom,
% 21.40/21.30 ! [V_A_2,V_B_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => 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)))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__psubset,axiom,
% 21.40/21.30 ! [V_A_2,V_B_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.30 => ( 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)))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__insert,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => 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)))))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__Un__disjoint,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__Diff1__le,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => 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))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card_Oinsert,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__Suc__Diff1,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__Diff2__less,axiom,
% 21.40/21.30 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 21.40/21.30 => 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))) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__Diff1__less,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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))) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__Diff__insert,axiom,
% 21.40/21.30 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card_Oinsert__remove,axiom,
% 21.40/21.30 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => 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)))))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card_Ounion__inter__neutral,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( ( ? [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)))
% 21.40/21.30 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__Suc__eq,axiom,
% 21.40/21.30 ! [V_k_2,V_A_2,T_b] :
% 21.40/21.30 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 21.40/21.30 <=> ? [B_b,B_B] :
% 21.40/21.30 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 21.40/21.30 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 21.40/21.30 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 21.40/21.30 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.30 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_equiv__imp__dvd__card,axiom,
% 21.40/21.30 ! [V_k_2,V_r_2,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.30 => ( ! [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),B_x))) )
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__greaterThanLessThan__int,axiom,
% 21.40/21.30 ! [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)))) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__Plus__conv__if,axiom,
% 21.40/21.30 ! [V_B_2,T_c,V_A_2,T_b] :
% 21.40/21.30 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 21.40/21.30 => 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)) )
% 21.40/21.30 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 21.40/21.30 => 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) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__gen__delta,axiom,
% 21.40/21.30 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.30 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 21.40/21.30 => 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_c_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_c_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)))) )
% 21.40/21.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 21.40/21.30 => 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_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_finite__greaterThanLessThan__int,axiom,
% 21.40/21.30 ! [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))) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_InrI,axiom,
% 21.40/21.30 ! [V_A_2,T_c,V_B_2,V_b_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_member(tc_sum(T_c,T_b)),hAPP(c_Sum__Type_OInr(T_b,T_c),V_b_2)),c_Sum__Type_OPlus(T_c,T_b,V_A_2,V_B_2))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_InlI,axiom,
% 21.40/21.30 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_member(tc_sum(T_b,T_c)),hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_2)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_abs__setprod,axiom,
% 21.40/21.30 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.30 ( class_Fields_Olinordered__field(T_b)
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__timesf,axiom,
% 21.40/21.30 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_b)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__1,axiom,
% 21.40/21.30 ! [V_A_2,T_c,T_b] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_b)
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_int__setprod,axiom,
% 21.40/21.30 ! [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) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_of__nat__setprod,axiom,
% 21.40/21.30 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.30 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 21.40/21.30 & class_Rings_Osemiring__1(T_b) )
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_of__int__setprod,axiom,
% 21.40/21.30 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.30 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 21.40/21.30 & class_Rings_Oring__1(T_b) )
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 21.40/21.30 ! [V_A_2,V_f_2,T_b] :
% 21.40/21.30 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.30 & class_Groups_Ocomm__monoid__mult(T_b) )
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__zero__iff,axiom,
% 21.40/21.30 ! [V_f_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 21.40/21.30 & class_Rings_Ono__zero__divisors(T_c) )
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( 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)
% 21.40/21.30 <=> ? [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.30 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__zero,axiom,
% 21.40/21.30 ! [V_f_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Rings_Ocomm__semiring__1(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ? [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.30 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 21.40/21.30 => 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) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod_Oempty,axiom,
% 21.40/21.30 ! [V_g_2,T_c,T_b] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_b)
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__empty,axiom,
% 21.40/21.30 ! [V_f_2,T_c,T_b] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_b)
% 21.40/21.30 => 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) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod_Oinfinite,axiom,
% 21.40/21.30 ! [V_g_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => 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) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__infinite,axiom,
% 21.40/21.30 ! [V_f_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => 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) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__eq__1__iff,axiom,
% 21.40/21.30 ! [V_f_2,V_F_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 21.40/21.30 => ( 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)
% 21.40/21.30 <=> ! [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 21.40/21.30 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Plus__eq__empty__conv,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.30 ( 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))
% 21.40/21.30 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_finite__Plus__iff,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_finite__Plus,axiom,
% 21.40/21.30 ! [V_B_2,T_c,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 21.40/21.30 => 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))) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_finite__PlusD_I1_J,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_finite__PlusD_I2_J,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 21.40/21.30 ! [V_f_2,V_A_2,T_b] :
% 21.40/21.30 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.30 & class_Groups_Ocomm__monoid__mult(T_b) )
% 21.40/21.30 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod_Odistrib,axiom,
% 21.40/21.30 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__dividef,axiom,
% 21.40/21.30 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Fields_Ofield__inverse__zero(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_dvd__setprod,axiom,
% 21.40/21.30 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Rings_Ocomm__semiring__1(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__pos__nat__iff,axiom,
% 21.40/21.30 ! [V_f_2,V_S_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.30 => ( 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)))
% 21.40/21.30 <=> ! [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 21.40/21.30 => 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))) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__dvd__setprod__subset,axiom,
% 21.40/21.30 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 21.40/21.30 ( ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 & class_Rings_Odvd(T_c) )
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_greaterThanLessThan__empty,axiom,
% 21.40/21.30 ! [V_k_2,V_l_2,T_b] :
% 21.40/21.30 ( class_Orderings_Oorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 21.40/21.30 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.30 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__delta,axiom,
% 21.40/21.30 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.30 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 21.40/21.30 => 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) )
% 21.40/21.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 21.40/21.30 => 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) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__delta_H,axiom,
% 21.40/21.30 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.30 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 21.40/21.30 => 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) )
% 21.40/21.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 21.40/21.30 => 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) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__constant,axiom,
% 21.40/21.30 ! [V_y_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__insert,axiom,
% 21.40/21.30 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod_Oinsert,axiom,
% 21.40/21.30 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__Un__Int,axiom,
% 21.40/21.30 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod_Ounion__inter,axiom,
% 21.40/21.30 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => 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)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Plus__def,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_sum(T_b,T_c),c_Sum__Type_OInl(T_b,T_c)),V_A_2)),hAPP(c_Set_Oimage(T_c,tc_sum(T_b,T_c),c_Sum__Type_OInr(T_c,T_b)),V_B_2)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__greaterThanLessThan,axiom,
% 21.40/21.30 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod_Oinsert__remove,axiom,
% 21.40/21.30 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => 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)))))) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__Un__disjoint,axiom,
% 21.40/21.30 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod_Ounion__disjoint,axiom,
% 21.40/21.30 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( 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))
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__Plus,axiom,
% 21.40/21.30 ! [V_B_2,T_c,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod_Oremove,axiom,
% 21.40/21.30 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.30 => 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)))))) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__diff1,axiom,
% 21.40/21.30 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Fields_Ofield(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 21.40/21.30 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => 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)) )
% 21.40/21.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__Un,axiom,
% 21.40/21.30 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Fields_Ofield(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( ! [B_x] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 21.40/21.30 => 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))) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 21.40/21.30 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.30 => ( ! [B_x] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_setprod__Un__one,axiom,
% 21.40/21.30 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 21.40/21.30 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 21.40/21.30 => ( ! [B_x] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 21.40/21.30 => 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)) ) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_finite__greaterThanLessThan,axiom,
% 21.40/21.30 ! [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))) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__greaterThanLessThan,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 21.40/21.30 ! [V_f_2,V_A_2,T_b] :
% 21.40/21.30 ( ! [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.30 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_ivl__disj__un_I4_J,axiom,
% 21.40/21.30 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 21.40/21.30 => 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) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_quotient__def,axiom,
% 21.40/21.30 ! [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)))) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_finite__greaterThanAtMost,axiom,
% 21.40/21.30 ! [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))) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_finite__greaterThanAtMost__int,axiom,
% 21.40/21.30 ! [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))) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_SUP1__I,axiom,
% 21.40/21.30 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_finite__UN,axiom,
% 21.40/21.30 ! [V_B_2,T_c,V_A_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.30 => ( 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)))
% 21.40/21.30 <=> ! [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_SUP1__iff,axiom,
% 21.40/21.30 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.30 ( 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))
% 21.40/21.30 <=> ? [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.30 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Image__UN,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_greaterThanAtMost__empty,axiom,
% 21.40/21.30 ! [V_k_2,V_l_2,T_b] :
% 21.40/21.30 ( class_Orderings_Oorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 21.40/21.30 ! [V_l_2,V_k_2,T_b] :
% 21.40/21.30 ( class_Orderings_Oorder(T_b)
% 21.40/21.30 => ( 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))
% 21.40/21.30 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 21.40/21.30 ! [V_l_2,V_k_2,T_b] :
% 21.40/21.30 ( class_Orderings_Oorder(T_b)
% 21.40/21.30 => ( 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)
% 21.40/21.30 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_ivl__disj__un_I20_J,axiom,
% 21.40/21.30 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 21.40/21.30 => 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) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_ivl__disj__int_I14_J,axiom,
% 21.40/21.30 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.30 ( class_Orderings_Oorder(T_b)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__greaterThanAtMost,axiom,
% 21.40/21.30 ! [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) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Image__eq__UN,axiom,
% 21.40/21.30 ! [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))))) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__greaterThanAtMost,axiom,
% 21.40/21.30 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_ivl__disj__int_I10_J,axiom,
% 21.40/21.30 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.30 ( class_Orderings_Oorder(T_b)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_card__greaterThanAtMost__int,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_ivl__disj__un_I16_J,axiom,
% 21.40/21.30 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.30 ( class_Orderings_Olinorder(T_b)
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 21.40/21.30 => 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) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__I,axiom,
% 21.40/21.30 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 21.40/21.30 => 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))) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_image__eq__UN,axiom,
% 21.40/21.30 ! [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)))) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__equiv__class,axiom,
% 21.40/21.30 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 21.40/21.30 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.30 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => 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) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_ball__UN,axiom,
% 21.40/21.30 ! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.30 ( ! [B_x] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 => hBOOL(hAPP(V_P_2,B_x)) )
% 21.40/21.30 <=> ! [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 21.40/21.30 => ! [B_xa] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 21.40/21.30 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_congruent__def,axiom,
% 21.40/21.30 ! [V_f_2,V_r_2,T_c,T_b] :
% 21.40/21.30 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 21.40/21.30 <=> ! [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_SUP__commute,axiom,
% 21.40/21.30 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 21.40/21.30 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.30 => 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))) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__extend__simps_I9_J,axiom,
% 21.40/21.30 ! [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) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__simps_I9_J,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__UN__flatten,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_congruentD,axiom,
% 21.40/21.30 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 21.40/21.30 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 21.40/21.30 => ( 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))
% 21.40/21.30 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_SUP__le__iff,axiom,
% 21.40/21.30 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 21.40/21.30 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.30 => ( 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))
% 21.40/21.30 <=> ! [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 21.40/21.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_less__SUP__iff,axiom,
% 21.40/21.30 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 21.40/21.30 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.30 & class_Orderings_Olinorder(T_b) )
% 21.40/21.30 => ( 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)))
% 21.40/21.30 <=> ? [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 21.40/21.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__iff,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 21.40/21.30 ( 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)))
% 21.40/21.30 <=> ? [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 21.40/21.30 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_SUP__const,axiom,
% 21.40/21.30 ! [V_M_2,T_b,V_A_2,T_c] :
% 21.40/21.30 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 21.40/21.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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 ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UNION__empty__conv_I2_J,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( 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))
% 21.40/21.30 <=> ! [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 21.40/21.30 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__constant,axiom,
% 21.40/21.30 ! [V_c_2,T_c,T_b,V_A_2] :
% 21.40/21.30 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 21.40/21.30 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.30 => 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_c_2)) = V_c_2 ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__empty2,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UNION__empty__conv_I1_J,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.30 ( 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)
% 21.40/21.30 <=> ! [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 21.40/21.30 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__subset__iff,axiom,
% 21.40/21.30 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 21.40/21.30 ( 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))
% 21.40/21.30 <=> ! [B_x] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 21.40/21.30 => 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)) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__simps_I10_J,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_image__UN,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__extend__simps_I10_J,axiom,
% 21.40/21.30 ! [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) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__Un,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__Un__distrib,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__UN__distrib2,axiom,
% 21.40/21.30 ! [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))) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__extend__simps_I4_J,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_Int__UN__distrib,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__extend__simps_I5_J,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__simps_I4_J,axiom,
% 21.40/21.30 ! [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) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__simps_I5_J,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_SUPR__apply,axiom,
% 21.40/21.30 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 21.40/21.30 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__extend__simps_I6_J,axiom,
% 21.40/21.30 ! [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)) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__simps_I6_J,axiom,
% 21.40/21.30 ! [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) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_SUP__subset,axiom,
% 21.40/21.30 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.30 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.30 => 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))) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_le__SUPI,axiom,
% 21.40/21.30 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 21.40/21.30 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 21.40/21.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 21.40/21.30 => 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))) ) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__insert__distrib,axiom,
% 21.40/21.30 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 21.40/21.30 => 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)) ) ).
% 21.40/21.30
% 21.40/21.30 fof(fact_UN__upper,axiom,
% 21.40/21.30 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 21.40/21.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.30 => 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))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__absorb,axiom,
% 21.40/21.31 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__extend__simps_I1_J,axiom,
% 21.40/21.31 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 21.40/21.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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))) )
% 21.40/21.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__singleton,axiom,
% 21.40/21.31 ! [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 ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__simps_I1_J,axiom,
% 21.40/21.31 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 21.40/21.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) )
% 21.40/21.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__simps_I3_J,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 21.40/21.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) )
% 21.40/21.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__simps_I2_J,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 21.40/21.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) )
% 21.40/21.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__extend__simps_I3_J,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 21.40/21.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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 )
% 21.40/21.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__extend__simps_I2_J,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 21.40/21.31 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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 )
% 21.40/21.31 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__insert,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_congruent2__implies__congruent__UN,axiom,
% 21.40/21.31 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 21.40/21.31 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 21.40/21.31 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 21.40/21.31 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_minus__int__def,axiom,
% 21.40/21.31 ! [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))))))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__equiv__class2,axiom,
% 21.40/21.31 ! [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] :
% 21.40/21.31 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 21.40/21.31 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 21.40/21.31 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 21.40/21.31 => 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) ) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_SUP2__I,axiom,
% 21.40/21.31 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 21.40/21.31 => 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_c_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Rep__Integ__inject,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2] :
% 21.40/21.31 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 21.40/21.31 <=> V_x_2 = V_y_2 ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Rep__Integ__inverse,axiom,
% 21.40/21.31 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 21.40/21.31
% 21.40/21.31 fof(fact_congruent2D,axiom,
% 21.40/21.31 ! [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] :
% 21.40/21.31 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 21.40/21.31 => ( 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))
% 21.40/21.31 => ( 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))
% 21.40/21.31 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_nat__def,axiom,
% 21.40/21.31 ! [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)))))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_congruent2__implies__congruent,axiom,
% 21.40/21.31 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 21.40/21.31 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 21.40/21.31 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.31 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__equiv__class__inject,axiom,
% 21.40/21.31 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 21.40/21.31 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.31 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 21.40/21.31 => ( 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)
% 21.40/21.31 => ( 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)))
% 21.40/21.31 => ( 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)))
% 21.40/21.31 => ( ! [B_x] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.31 => ! [B_y] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 21.40/21.31 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 21.40/21.31 => 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)) ) ) )
% 21.40/21.31 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__equiv__class__type2,axiom,
% 21.40/21.31 ! [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] :
% 21.40/21.31 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 21.40/21.31 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 21.40/21.31 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 21.40/21.31 => ( 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)))
% 21.40/21.31 => ( 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)))
% 21.40/21.31 => ( ! [B_x1] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 21.40/21.31 => ! [B_x2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 21.40/21.31 => 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)) ) ) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__equiv__class__type,axiom,
% 21.40/21.31 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 21.40/21.31 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.31 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 21.40/21.31 => ( 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)))
% 21.40/21.31 => ( ! [B_x] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_SUP2__iff,axiom,
% 21.40/21.31 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 21.40/21.31 ( 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_c_2))
% 21.40/21.31 <=> ? [B_x] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.31 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Id__on__def,axiom,
% 21.40/21.31 ! [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)))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_refl__on__def_H,axiom,
% 21.40/21.31 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.31 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 21.40/21.31 <=> ( ! [B_x] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 21.40/21.31 => 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)) )
% 21.40/21.31 & ! [B_x] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fold__Un__disjoint,axiom,
% 21.40/21.31 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.31 => ( 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))
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fold__image__empty,axiom,
% 21.40/21.31 ! [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 ).
% 21.40/21.31
% 21.40/21.31 fof(fact_refl__on__Id__on,axiom,
% 21.40/21.31 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Id__on__def_H,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 21.40/21.31 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_refl__on__empty,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_refl__on__Un,axiom,
% 21.40/21.31 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 21.40/21.31 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 21.40/21.31 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_refl__on__Int,axiom,
% 21.40/21.31 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 21.40/21.31 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 21.40/21.31 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Id__on__empty,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Image__Id__on,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fold__image__distrib,axiom,
% 21.40/21.31 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_refl__onD2,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 21.40/21.31 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 21.40/21.31 => ( 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))
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_refl__onD1,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 21.40/21.31 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 21.40/21.31 => ( 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))
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_refl__onD,axiom,
% 21.40/21.31 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 21.40/21.31 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fold__image__insert,axiom,
% 21.40/21.31 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Oab__semigroup__mult(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setprod_OF__eq,axiom,
% 21.40/21.31 ! [V_g_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.31 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setprod_Oeq__fold,axiom,
% 21.40/21.31 ! [V_g_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Id__on__iff,axiom,
% 21.40/21.31 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 <=> ( V_x_2 = V_y_2
% 21.40/21.31 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Id__on__eqI,axiom,
% 21.40/21.31 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 21.40/21.31 ( V_a_2 = V_b_2
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.31 => 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))) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fold__image__Un__Int,axiom,
% 21.40/21.31 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.31 => 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))) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__eq__fold__image,axiom,
% 21.40/21.31 ! [V_f_2,T_c,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card_Oeq__fold__g,axiom,
% 21.40/21.31 ! [V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card__def,axiom,
% 21.40/21.31 ! [V_A_2,T_b] :
% 21.40/21.31 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_comm__monoid__big_OF__eq,axiom,
% 21.40/21.31 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 21.40/21.31 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.31 => 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) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.31 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fold__image__Un__one,axiom,
% 21.40/21.31 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 21.40/21.31 => ( ! [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Id__onE,axiom,
% 21.40/21.31 ! [V_A_2,V_c_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
% 21.40/21.31 => ~ ! [B_x] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.31 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 21.40/21.31 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 21.40/21.31 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.31 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 21.40/21.31 ! [V_N_2,V_h_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( ! [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))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 21.40/21.31 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 21.40/21.31 ! [V_N_2,V_h_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( ! [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))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 21.40/21.31 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Max_Ohom__commute,axiom,
% 21.40/21.31 ! [V_N_2,V_h_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( ! [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))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 21.40/21.31 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Min_Ohom__commute,axiom,
% 21.40/21.31 ! [V_N_2,V_h_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( ! [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))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 21.40/21.31 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Inf__fin_Ohom__commute,axiom,
% 21.40/21.31 ! [V_N_2,V_h_2,T_b] :
% 21.40/21.31 ( class_Lattices_Olattice(T_b)
% 21.40/21.31 => ( ! [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))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 21.40/21.31 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Sup__fin_Ohom__commute,axiom,
% 21.40/21.31 ! [V_N_2,V_h_2,T_b] :
% 21.40/21.31 ( class_Lattices_Olattice(T_b)
% 21.40/21.31 => ( ! [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))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 21.40/21.31 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setprod__mono__one__right,axiom,
% 21.40/21.31 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 21.40/21.31 => ( ! [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 21.40/21.31 => 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) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setprod__mono__one__left,axiom,
% 21.40/21.31 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 21.40/21.31 => ( ! [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 21.40/21.31 => 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) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card__Pow,axiom,
% 21.40/21.31 ! [V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_PowI,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Pow__top,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_finite__Pow__iff,axiom,
% 21.40/21.31 ! [V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 21.40/21.31 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__Pow__surj,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 21.40/21.31 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Pow__insert,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Pow__not__empty,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Pow__Int__eq,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Pow__bottom,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_PowD,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Pow__iff,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 21.40/21.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Pow__mono,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.31 => 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))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Un__Pow__subset,axiom,
% 21.40/21.31 ! [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)))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__Pow__mono,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( 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))
% 21.40/21.31 => 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))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Pow__empty,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Powp__Pow__eq,axiom,
% 21.40/21.31 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.31 ( 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))
% 21.40/21.31 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__Pow__subset,axiom,
% 21.40/21.31 ! [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)))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card__quotient__disjoint,axiom,
% 21.40/21.31 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( 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)
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_finite__empty__induct,axiom,
% 21.40/21.31 ! [V_P_2,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 21.40/21.31 => ( ! [B_a,B_A] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 21.40/21.31 => ( hBOOL(hAPP(V_P_2,B_A))
% 21.40/21.31 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
% 21.40/21.31 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__un_I19_J,axiom,
% 21.40/21.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 21.40/21.31 => 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) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_finite__atLeastAtMost,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_finite__atLeastAtMost__int,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__add__atLeastAtMost,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__Suc__atLeastAtMost,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_finite__imageD,axiom,
% 21.40/21.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 21.40/21.31 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 21.40/21.31 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card__image,axiom,
% 21.40/21.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 21.40/21.31 ! [V_n_2,V_m_2] :
% 21.40/21.31 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 21.40/21.31 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 21.40/21.31 => 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))) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2] :
% 21.40/21.31 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 21.40/21.31 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastatMost__empty__iff,axiom,
% 21.40/21.31 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => ( 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))
% 21.40/21.31 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastatMost__empty__iff2,axiom,
% 21.40/21.31 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => ( 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)
% 21.40/21.31 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastatMost__empty,axiom,
% 21.40/21.31 ! [V_a_2,V_b_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastatMost__subset__iff,axiom,
% 21.40/21.31 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => ( 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_c_2,V_d_2)))
% 21.40/21.31 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 21.40/21.31 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 21.40/21.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastAtMost__singleton_H,axiom,
% 21.40/21.31 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => ( V_a_2 = V_b_2
% 21.40/21.31 => 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))) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 21.40/21.31 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.31 <=> ( V_a_2 = V_b_2
% 21.40/21.31 & V_b_2 = V_c_2 ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastAtMost__singleton,axiom,
% 21.40/21.31 ! [V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => 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))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__uminus__atLeastAtMost,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.31 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_finite__surj__inj,axiom,
% 21.40/21.31 ! [V_f_2,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( 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)))
% 21.40/21.31 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_endo__inj__surj,axiom,
% 21.40/21.31 ! [V_f_2,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( 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))
% 21.40/21.31 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 21.40/21.31 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__iff__eq__card,axiom,
% 21.40/21.31 ! [V_f_2,T_c,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 <=> 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_eq__card__imp__inj__on,axiom,
% 21.40/21.31 ! [V_f_2,T_c,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( 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)
% 21.40/21.31 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_pigeonhole,axiom,
% 21.40/21.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 21.40/21.31 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card__atLeastAtMost,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastAtMostSuc__conv,axiom,
% 21.40/21.31 ! [V_n_2,V_m_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card__bij__eq,axiom,
% 21.40/21.31 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => ( 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))
% 21.40/21.31 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 21.40/21.31 => ( 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))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 21.40/21.31 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Int__atLeastAtMost,axiom,
% 21.40/21.31 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastatMost__psubset__iff,axiom,
% 21.40/21.31 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => ( 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_c_2,V_d_2)))
% 21.40/21.31 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 21.40/21.31 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 21.40/21.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 21.40/21.31 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2))
% 21.40/21.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 21.40/21.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__un_I22_J,axiom,
% 21.40/21.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 21.40/21.31 => 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) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__int_I16_J,axiom,
% 21.40/21.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__int_I12_J,axiom,
% 21.40/21.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__int_I13_J,axiom,
% 21.40/21.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_simp__from__to,axiom,
% 21.40/21.31 ! [V_i_2,V_j_2] :
% 21.40/21.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 21.40/21.31 => 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)) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__iff__card__le,axiom,
% 21.40/21.31 ! [V_B_2,T_c,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 21.40/21.31 => ( ? [B_f] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 21.40/21.31 & 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)) )
% 21.40/21.31 <=> 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))) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card__inj__on__le,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => ( 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))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 21.40/21.31 => 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))) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_quotient__diff1,axiom,
% 21.40/21.31 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 21.40/21.31 ( 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)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card__atLeastAtMost__int,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__un_I5_J,axiom,
% 21.40/21.31 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__Un,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( 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))
% 21.40/21.31 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 21.40/21.31 & 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__insert,axiom,
% 21.40/21.31 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 21.40/21.31 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 & ~ 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))))))) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__uminus,axiom,
% 21.40/21.31 ! [V_A_2,T_b] :
% 21.40/21.31 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.40/21.31 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__empty,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__Inl,axiom,
% 21.40/21.31 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(T_b,tc_sum(T_b,T_c),c_Sum__Type_OInl(T_b,T_c),V_A_2) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__Inr,axiom,
% 21.40/21.31 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(T_b,tc_sum(T_c,T_b),c_Sum__Type_OInr(T_b,T_c),V_A_2) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__Suc,axiom,
% 21.40/21.31 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__Some,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__add__nat,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_swap__inj__on,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__def,axiom,
% 21.40/21.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 <=> ! [B_x] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.31 => ! [B_xa] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 21.40/21.31 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 21.40/21.31 => B_x = B_xa ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__ident,axiom,
% 21.40/21.31 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__id2,axiom,
% 21.40/21.31 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__onD,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 21.40/21.31 => V_x_2 = V_y_2 ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__iff,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 21.40/21.31 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 21.40/21.31 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__contraD,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => ( V_x_2 != V_y_2
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 21.40/21.31 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_subset__inj__on,axiom,
% 21.40/21.31 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.31 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__Int,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__diff,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Cantors__paradox,axiom,
% 21.40/21.31 ! [V_A_2,T_b] :
% 21.40/21.31 ~ ? [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( 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))
% 21.40/21.31 => ( 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)
% 21.40/21.31 <=> V_A_2 = V_B_2 ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__strict__subset,axiom,
% 21.40/21.31 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.31 => 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))) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__image__Int,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__image__set__diff,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__iff__surj,axiom,
% 21.40/21.31 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 21.40/21.31 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => ( ? [B_f] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 21.40/21.31 & 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)) )
% 21.40/21.31 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ex__nat__less,axiom,
% 21.40/21.31 ! [V_P_2,V_n_2] :
% 21.40/21.31 ( ? [B_m] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 21.40/21.31 & hBOOL(hAPP(V_P_2,B_m)) )
% 21.40/21.31 <=> ? [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_all__nat__less,axiom,
% 21.40/21.31 ! [V_P_2,V_n_2] :
% 21.40/21.31 ( ! [B_m] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 21.40/21.31 => hBOOL(hAPP(V_P_2,B_m)) )
% 21.40/21.31 <=> ! [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_bset_I8_J,axiom,
% 21.40/21.31 ! [V_B_2,V_t_2,V_D_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 21.40/21.31 => ( 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))
% 21.40/21.31 => ! [B_x] :
% 21.40/21.31 ( ! [B_xa] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xb] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 21.40/21.31 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 21.40/21.31 => 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))) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_aset_I6_J,axiom,
% 21.40/21.31 ! [V_A_2,V_t_2,V_D_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 21.40/21.31 => ( 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))
% 21.40/21.31 => ! [B_x] :
% 21.40/21.31 ( ! [B_xa] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xb] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 21.40/21.31 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_aset_I4_J,axiom,
% 21.40/21.31 ! [V_A_2,V_t_2,V_D_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 21.40/21.31 => ! [B_x] :
% 21.40/21.31 ( ! [B_xa] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xb] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 21.40/21.31 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 21.40/21.31 => ( B_x != V_t_2
% 21.40/21.31 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_bset_I3_J,axiom,
% 21.40/21.31 ! [V_B_2,V_t_2,V_D_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 21.40/21.31 => ( 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))
% 21.40/21.31 => ( ! [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xa] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 21.40/21.31 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 21.40/21.31 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_aset_I3_J,axiom,
% 21.40/21.31 ! [V_A_2,V_t_2,V_D_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 21.40/21.31 => ( 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))
% 21.40/21.31 => ( ! [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xa] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 21.40/21.31 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 21.40/21.31 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_aset_I5_J,axiom,
% 21.40/21.31 ! [V_A_2,V_t_2,V_D_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 21.40/21.31 => ! [B_x] :
% 21.40/21.31 ( ! [B_xa] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xb] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 21.40/21.31 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_bset_I4_J,axiom,
% 21.40/21.31 ! [V_B_2,V_t_2,V_D_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 21.40/21.31 => ! [B_x] :
% 21.40/21.31 ( ! [B_xa] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xb] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 21.40/21.31 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 21.40/21.31 => ( B_x != V_t_2
% 21.40/21.31 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_bset_I7_J,axiom,
% 21.40/21.31 ! [V_B_2,V_t_2,V_D_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 21.40/21.31 => ! [B_x] :
% 21.40/21.31 ( ! [B_xa] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xb] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 21.40/21.31 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 21.40/21.31 => 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))) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_aset_I8_J,axiom,
% 21.40/21.31 ! [V_t_2,V_A_2,V_D_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 21.40/21.31 => ! [B_x] :
% 21.40/21.31 ( ! [B_xa] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xb] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 21.40/21.31 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 21.40/21.31 => 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))) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_bset_I6_J,axiom,
% 21.40/21.31 ! [V_t_2,V_B_2,V_D_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 21.40/21.31 => ! [B_x] :
% 21.40/21.31 ( ! [B_xa] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xb] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 21.40/21.31 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_periodic__finite__ex,axiom,
% 21.40/21.31 ! [V_P_2,V_d_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 21.40/21.31 => ( ! [B_x,B_k] :
% 21.40/21.31 ( hBOOL(hAPP(V_P_2,B_x))
% 21.40/21.31 <=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
% 21.40/21.31 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 21.40/21.31 <=> ? [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_aset_I7_J,axiom,
% 21.40/21.31 ! [V_t_2,V_A_2,V_D_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 21.40/21.31 => ! [B_x] :
% 21.40/21.31 ( ! [B_xa] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xb] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 21.40/21.31 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 21.40/21.31 => 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))) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_bset_I5_J,axiom,
% 21.40/21.31 ! [V_t_2,V_B_2,V_D_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 21.40/21.31 => ! [B_x] :
% 21.40/21.31 ( ! [B_xa] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xb] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 21.40/21.31 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 21.40/21.31 ! [V_x_2,V_y_2,V_c_2] :
% 21.40/21.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 21.40/21.31 => 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_c_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_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 21.40/21.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 21.40/21.31 => 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_c_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))) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 21.40/21.31 => 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_c_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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_bset_I9_J,axiom,
% 21.40/21.31 ! [V_t_2,V_B_2,V_D_2,V_d_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 21.40/21.31 => ! [B_x] :
% 21.40/21.31 ( ! [B_xa] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xb] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 21.40/21.31 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_finite__atLeastLessThan,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 21.40/21.31 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 21.40/21.31 => V_b_2 = V_d_2 ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 21.40/21.31 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 21.40/21.31 => V_a_2 = V_c_2 ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastLessThan__eq__iff,axiom,
% 21.40/21.31 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 21.40/21.31 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 21.40/21.31 <=> ( V_a_2 = V_c_2
% 21.40/21.31 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_all__nat__less__eq,axiom,
% 21.40/21.31 ! [V_P_2,V_n_2] :
% 21.40/21.31 ( ! [B_m] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 21.40/21.31 => hBOOL(hAPP(V_P_2,B_m)) )
% 21.40/21.31 <=> ! [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ex__nat__less__eq,axiom,
% 21.40/21.31 ! [V_P_2,V_n_2] :
% 21.40/21.31 ( ? [B_m] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 21.40/21.31 & hBOOL(hAPP(V_P_2,B_m)) )
% 21.40/21.31 <=> ? [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastLessThan0,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card__atLeastLessThan,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__Suc__atLeastLessThan,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastLessThan__empty,axiom,
% 21.40/21.31 ! [V_a_2,V_b_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 21.40/21.31 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => ( 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)
% 21.40/21.31 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastLessThan__empty__iff,axiom,
% 21.40/21.31 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => ( 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))
% 21.40/21.31 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastLessThan__subset__iff,axiom,
% 21.40/21.31 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( 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_c_2),V_d_2)))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 21.40/21.31 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 21.40/21.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__un_I17_J,axiom,
% 21.40/21.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 21.40/21.31 => 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) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__diff,axiom,
% 21.40/21.31 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__int_I11_J,axiom,
% 21.40/21.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__add__atLeastLessThan,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastLessThan__singleton,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__un_I21_J,axiom,
% 21.40/21.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 21.40/21.31 => 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) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastLessThan__add__Un,axiom,
% 21.40/21.31 ! [V_k_2,V_j_2,V_i_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 21.40/21.31 => 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))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__int_I15_J,axiom,
% 21.40/21.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Int__atLeastLessThan,axiom,
% 21.40/21.31 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => 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_c_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_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_subset__card__intvl__is__intvl,axiom,
% 21.40/21.31 ! [V_k_2,V_A_2] :
% 21.40/21.31 ( 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)))))
% 21.40/21.31 => 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))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__int_I9_J,axiom,
% 21.40/21.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.31 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__uminus__atLeastLessThan,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.31 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastLessThanSuc,axiom,
% 21.40/21.31 ! [V_n_2,V_m_2] :
% 21.40/21.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.40/21.31 => 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)) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__un_I15_J,axiom,
% 21.40/21.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 21.40/21.31 => 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) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__un_I6_J,axiom,
% 21.40/21.31 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__un_I3_J,axiom,
% 21.40/21.31 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__un_I18_J,axiom,
% 21.40/21.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 21.40/21.31 => 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) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_aset_I10_J,axiom,
% 21.40/21.31 ! [V_t_2,V_A_2,V_D_2,V_d_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 21.40/21.31 => ! [B_x] :
% 21.40/21.31 ( ! [B_xa] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xb] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 21.40/21.31 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 21.40/21.31 => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
% 21.40/21.31 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_bset_I10_J,axiom,
% 21.40/21.31 ! [V_t_2,V_B_2,V_D_2,V_d_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 21.40/21.31 => ! [B_x] :
% 21.40/21.31 ( ! [B_xa] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xb] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 21.40/21.31 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 21.40/21.31 => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
% 21.40/21.31 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_aset_I9_J,axiom,
% 21.40/21.31 ! [V_t_2,V_A_2,V_D_2,V_d_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 21.40/21.31 => ! [B_x] :
% 21.40/21.31 ( ! [B_xa] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => ! [B_xb] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 21.40/21.31 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_finite__atLeastLessThan__int,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__add__int__atLeastLessThan,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card__atLeastLessThan__int,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fun__upd__image,axiom,
% 21.40/21.31 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 21.40/21.31 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => 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)))))) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_the__inv__into__into,axiom,
% 21.40/21.31 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fun__upd__triv,axiom,
% 21.40/21.31 ! [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 ).
% 21.40/21.31
% 21.40/21.31 fof(fact_finite__atMost,axiom,
% 21.40/21.31 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atMost__eq__iff,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 21.40/21.31 <=> V_x_2 = V_y_2 ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fun__upd__def,axiom,
% 21.40/21.31 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 21.40/21.31 ( ( V_x_2 = V_a_2
% 21.40/21.31 => 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 )
% 21.40/21.31 & ( V_x_2 != V_a_2
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fun__upd__idem__iff,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2
% 21.40/21.31 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fun__upd__upd,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fun__upd__same,axiom,
% 21.40/21.31 ! [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 ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fun__upd__apply,axiom,
% 21.40/21.31 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 21.40/21.31 ( ( V_z_2 = V_x_2
% 21.40/21.31 => 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 )
% 21.40/21.31 & ( V_z_2 != V_x_2
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fun__upd__twist,axiom,
% 21.40/21.31 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
% 21.40/21.31 ( V_a_2 != V_c_2
% 21.40/21.31 => 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_c_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_c_2),V_d_2)),V_a_2),V_b_2) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fun__upd__other,axiom,
% 21.40/21.31 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 21.40/21.31 ( V_z_2 != V_x_2
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fun__upd__idem,axiom,
% 21.40/21.31 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 21.40/21.31 ( hAPP(V_f_2,V_x_2) = V_y_2
% 21.40/21.31 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeast0AtMost,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card__atMost,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atMost__Suc,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atMost__iff,axiom,
% 21.40/21.31 ! [V_k_2,V_i_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oord(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 21.40/21.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atMost__subset__iff,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => ( 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)))
% 21.40/21.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__le__add__shift,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_the__inv__into__f__eq,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_the__inv__into__f__f,axiom,
% 21.40/21.31 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => 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 ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__the__inv__into,axiom,
% 21.40/21.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_the__inv__into__onto,axiom,
% 21.40/21.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => 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 ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_inj__on__fun__updI,axiom,
% 21.40/21.31 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_the__inv__into__def,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atMost__0,axiom,
% 21.40/21.31 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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Int__atLeastAtMostR1,axiom,
% 21.40/21.31 ! [V_d_2,V_c_2,V_b_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_Int__atLeastAtMostL1,axiom,
% 21.40/21.31 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__un_I9_J,axiom,
% 21.40/21.31 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__int_I3_J,axiom,
% 21.40/21.31 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__int_I1_J,axiom,
% 21.40/21.31 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_f__the__inv__into__f,axiom,
% 21.40/21.31 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 21.40/21.31 => 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 ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_UN__le__eq__Un0,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_map__upd__nonempty,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 21.40/21.31 ! [V_u_2] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 21.40/21.31 => 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))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_image__map__upd,axiom,
% 21.40/21.31 ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 21.40/21.31 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_finite__lessThan,axiom,
% 21.40/21.31 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card__lessThan,axiom,
% 21.40/21.31 ! [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 ).
% 21.40/21.31
% 21.40/21.31 fof(fact_lessThan__eq__iff,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 21.40/21.31 <=> V_x_2 = V_y_2 ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_atLeast0LessThan,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_lessThan__0,axiom,
% 21.40/21.31 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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_lessThan__Suc,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_lessThan__Suc__atMost,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_lessThan__iff,axiom,
% 21.40/21.31 ! [V_k_2,V_i_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oord(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 21.40/21.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_lessThan__subset__iff,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( 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)))
% 21.40/21.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_lessThan__strict__subset__iff,axiom,
% 21.40/21.31 ! [V_n_2,V_m_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( 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)))
% 21.40/21.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_map__upd__eqD1,axiom,
% 21.40/21.31 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] :
% 21.40/21.31 ( 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))
% 21.40/21.31 => V_x_2 = V_y_2 ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_map__upd__triv,axiom,
% 21.40/21.31 ! [T_c,V_x_2,T_b,V_k_2,V_t_2] :
% 21.40/21.31 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 21.40/21.31 => 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 ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_map__upd__Some__unfold,axiom,
% 21.40/21.31 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_b,T_c] :
% 21.40/21.31 ( 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)
% 21.40/21.31 <=> ( ( V_x_2 = V_a_2
% 21.40/21.31 & V_b_2 = V_y_2 )
% 21.40/21.31 | ( V_x_2 != V_a_2
% 21.40/21.31 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_single__Diff__lessThan,axiom,
% 21.40/21.31 ! [V_k_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => 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))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__un_I8_J,axiom,
% 21.40/21.31 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__int_I4_J,axiom,
% 21.40/21.31 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__int_I2_J,axiom,
% 21.40/21.31 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Oorder(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_empty__upd__none,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 21.40/21.31 ! [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))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__un_I2_J,axiom,
% 21.40/21.31 ! [V_u_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__un_I10_J,axiom,
% 21.40/21.31 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ivl__disj__un_I7_J,axiom,
% 21.40/21.31 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.31 ( class_Orderings_Olinorder(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_arith__series__int,axiom,
% 21.40/21.31 ! [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)))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ran__map__upd,axiom,
% 21.40/21.31 ! [V_b_2,T_c,T_b,V_a_2,V_m_2] :
% 21.40/21.31 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fun__upd__None__restrict,axiom,
% 21.40/21.31 ! [V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 21.40/21.31 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 21.40/21.31 => 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))))) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__abs,axiom,
% 21.40/21.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 21.40/21.31 => 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))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__abs__ge__zero,axiom,
% 21.40/21.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 21.40/21.31 => 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))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_restrict__in,axiom,
% 21.40/21.31 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_restrict__restrict,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_abs__setsum__abs,axiom,
% 21.40/21.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__divide__distrib,axiom,
% 21.40/21.31 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( class_Fields_Ofield(T_b)
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__negf,axiom,
% 21.40/21.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( class_Groups_Oab__group__add(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__0,axiom,
% 21.40/21.31 ! [V_A_2,T_c,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_of__nat__setsum,axiom,
% 21.40/21.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( class_Rings_Osemiring__1(T_b)
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_of__int__setsum,axiom,
% 21.40/21.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( class_Rings_Oring__1(T_b)
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__commute,axiom,
% 21.40/21.31 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__product,axiom,
% 21.40/21.31 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( class_Rings_Osemiring__0(T_b)
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__left__distrib,axiom,
% 21.40/21.31 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( class_Rings_Osemiring__0(T_b)
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__right__distrib,axiom,
% 21.40/21.31 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 21.40/21.31 ( class_Rings_Osemiring__0(T_b)
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__addf,axiom,
% 21.40/21.31 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum_Oinfinite,axiom,
% 21.40/21.31 ! [V_g_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__infinite,axiom,
% 21.40/21.31 ! [V_f_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum_Oempty,axiom,
% 21.40/21.31 ! [V_g_2,T_c,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__empty,axiom,
% 21.40/21.31 ! [V_f_2,T_c,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__subtractf,axiom,
% 21.40/21.31 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 21.40/21.31 ( class_Groups_Oab__group__add(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_restrict__map__empty,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum_Odistrib,axiom,
% 21.40/21.31 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 21.40/21.31 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 21.40/21.31 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 21.40/21.31 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 21.40/21.31 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_restrict__out,axiom,
% 21.40/21.31 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 21.40/21.31 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_restrict__map__insert,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__add__nat__ivl,axiom,
% 21.40/21.31 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__diff__nat__ivl,axiom,
% 21.40/21.31 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 21.40/21.31 ( class_Groups_Oab__group__add(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__delta_H,axiom,
% 21.40/21.31 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.31 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 21.40/21.31 => 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) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 21.40/21.31 => 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) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__delta,axiom,
% 21.40/21.31 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.31 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 21.40/21.31 => 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) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 21.40/21.31 => 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) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_restrict__map__def,axiom,
% 21.40/21.31 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 21.40/21.31 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => 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) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_restrict__map__to__empty,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__constant,axiom,
% 21.40/21.31 ! [V_A_2,V_y_2,T_c,T_b] :
% 21.40/21.31 ( class_Rings_Osemiring__1(T_b)
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__lessThan__Suc,axiom,
% 21.40/21.31 ! [V_n_2,V_f_2,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__atMost__Suc,axiom,
% 21.40/21.31 ! [V_n_2,V_f_2,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => 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))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__insert,axiom,
% 21.40/21.31 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 21.40/21.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum_Oinsert,axiom,
% 21.40/21.31 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__Un__Int,axiom,
% 21.40/21.31 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__diff,axiom,
% 21.40/21.31 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Oab__group__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum_OF__eq,axiom,
% 21.40/21.31 ! [V_g_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum_Oeq__fold,axiom,
% 21.40/21.31 ! [V_g_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 21.40/21.31 ! [V_k_2,V_f_2,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__head__upt__Suc,axiom,
% 21.40/21.31 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 21.40/21.31 => 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))) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__head__Suc,axiom,
% 21.40/21.31 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.40/21.31 => 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))) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__restrict__set,axiom,
% 21.40/21.31 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ranI,axiom,
% 21.40/21.31 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 21.40/21.31 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum_Oinsert__remove,axiom,
% 21.40/21.31 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => 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)))))) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__Un__disjoint,axiom,
% 21.40/21.31 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.31 => ( 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))
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__Un,axiom,
% 21.40/21.31 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Oab__group__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.31 => 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))) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__op__ivl__Suc,axiom,
% 21.40/21.31 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 21.40/21.31 => 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) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__cl__ivl__Suc,axiom,
% 21.40/21.31 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 21.40/21.31 => 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) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 21.40/21.31 => 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))) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__head,axiom,
% 21.40/21.31 ! [V_P_2,V_n_2,V_m_2,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.40/21.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__ub__add__nat,axiom,
% 21.40/21.31 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 => ( 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))))
% 21.40/21.31 => 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)))) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fun__upd__restrict,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_ran__empty,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum_Oremove,axiom,
% 21.40/21.31 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => 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)))))) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__diff1_H,axiom,
% 21.40/21.31 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.31 => 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)))))) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__diff1,axiom,
% 21.40/21.31 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Oab__group__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.31 => 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)) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.31 => 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) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__diff1__ring,axiom,
% 21.40/21.31 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Rings_Oring(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_geometric__sum,axiom,
% 21.40/21.31 ! [V_n_2,V_x_2,T_b] :
% 21.40/21.31 ( class_Fields_Ofield(T_b)
% 21.40/21.31 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 21.40/21.31 => 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))) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_gauss__sum,axiom,
% 21.40/21.31 ! [V_n_2,T_b] :
% 21.40/21.31 ( class_Rings_Ocomm__semiring__1(T_b)
% 21.40/21.31 => 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))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__natinterval__difff,axiom,
% 21.40/21.31 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 21.40/21.31 ( class_Groups_Oab__group__add(T_b)
% 21.40/21.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.40/21.31 => 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)))) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.40/21.31 => 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) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_fun__upd__restrict__conv,axiom,
% 21.40/21.31 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 21.40/21.31 => 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) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_restrict__fun__upd,axiom,
% 21.40/21.31 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 21.40/21.31 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 21.40/21.31 => 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) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_restrict__complement__singleton__eq,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_restrict__upd__same,axiom,
% 21.40/21.31 ! [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))))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_arith__series__general,axiom,
% 21.40/21.31 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 21.40/21.31 ( class_Rings_Ocomm__semiring__1(T_b)
% 21.40/21.31 => 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)))) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__mono2,axiom,
% 21.40/21.31 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.31 => ( ! [B_b] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 21.40/21.31 => 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))) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__bounded,axiom,
% 21.40/21.31 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 21.40/21.31 & class_Rings_Osemiring__1(T_c) )
% 21.40/21.31 => ( ! [B_i] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 21.40/21.31 => 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))) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__Un__zero,axiom,
% 21.40/21.31 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 21.40/21.31 => ( ! [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__eq__0__iff,axiom,
% 21.40/21.31 ! [V_f_2,V_F_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 21.40/21.31 => ( 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)
% 21.40/21.31 <=> ! [B_x] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 21.40/21.31 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_card__eq__setsum,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_int__setsum,axiom,
% 21.40/21.31 ! [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) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__eq__Suc0__iff,axiom,
% 21.40/21.31 ! [V_f_2,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( 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))
% 21.40/21.31 <=> ? [B_x] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.31 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 21.40/21.31 & ! [B_xa] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 21.40/21.31 => ( B_x != B_xa
% 21.40/21.31 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__eq__1__iff,axiom,
% 21.40/21.31 ! [V_f_2,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( 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)
% 21.40/21.31 <=> ? [B_x] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.31 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 21.40/21.31 & ! [B_xa] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 21.40/21.31 => ( B_x != B_xa
% 21.40/21.31 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 21.40/21.31 ! [V_k_2,V_f_2] :
% 21.40/21.31 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 21.40/21.31 ! [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)) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__diff__nat,axiom,
% 21.40/21.31 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 21.40/21.31 ! [V_A_2,V_f_2,T_b] :
% 21.40/21.31 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 & class_Groups_Ocomm__monoid__mult(T_b) )
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__diff1__nat,axiom,
% 21.40/21.31 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 21.40/21.31 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.31 => 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)) )
% 21.40/21.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.31 => 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) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__Un__nat,axiom,
% 21.40/21.31 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.31 => 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))) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 21.40/21.31 ! [V_f_2,V_A_2,T_b] :
% 21.40/21.31 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.31 & class_Groups_Ocomm__monoid__mult(T_b) )
% 21.40/21.31 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 21.40/21.31 => 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)) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_arith__series__nat,axiom,
% 21.40/21.31 ! [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)))) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 21.40/21.31 ! [V_f_2,V_A_2,T_b] :
% 21.40/21.31 ( ! [B_x] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.31 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 21.40/21.31 => 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)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 21.40/21.31 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.31 => ( ! [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 21.40/21.31 => 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)) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__mono3,axiom,
% 21.40/21.31 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 21.40/21.31 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.31 => ( ! [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 21.40/21.31 => 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))) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__nonneg__0,axiom,
% 21.40/21.31 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Oordered__ab__group__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 21.40/21.31 => ( ! [B_i] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 21.40/21.31 => ( 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)
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 21.40/21.31 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__nonneg__leq__bound,axiom,
% 21.40/21.31 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Oordered__ab__group__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 21.40/21.31 => ( ! [B_i] :
% 21.40/21.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 21.40/21.31 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 21.40/21.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_sum__diff__distrib,axiom,
% 21.40/21.31 ! [V_n_2,V_P_2,V_Q_2] :
% 21.40/21.31 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x)))
% 21.40/21.31 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__mono__zero__left,axiom,
% 21.40/21.31 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 21.40/21.31 => ( ! [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 21.40/21.31 => 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) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_setsum__mono__zero__right,axiom,
% 21.40/21.31 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 21.40/21.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 21.40/21.31 => ( ! [B_x] :
% 21.40/21.31 ( 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)))
% 21.40/21.31 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 21.40/21.31 => 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) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 21.40/21.31 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.31 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) ) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_folding__one__idem_Oidem,axiom,
% 21.40/21.31 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 21.40/21.31 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 21.40/21.31 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_folding__one__idem_Oin__idem,axiom,
% 21.40/21.31 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 21.40/21.31 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.31 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 21.40/21.31 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 21.40/21.31 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => 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)) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 21.40/21.31 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 21.40/21.31 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 21.40/21.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.31 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.31 => 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) ) ) ) ) ).
% 21.40/21.31
% 21.40/21.31 fof(fact_finite__subset__induct,axiom,
% 21.40/21.31 ! [V_P_2,V_A_2,V_F_2,T_b] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 21.40/21.31 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 21.40/21.31 => ( ! [B_a,B_F] :
% 21.40/21.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 21.40/21.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 21.40/21.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 21.40/21.32 => ( hBOOL(hAPP(V_P_2,B_F))
% 21.40/21.32 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 21.40/21.32 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum__strict__mono,axiom,
% 21.40/21.32 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 21.40/21.32 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.32 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 21.40/21.32 => 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))) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_atMost__Int__atLeast,axiom,
% 21.40/21.32 ! [V_n_2,T_b] :
% 21.40/21.32 ( class_Orderings_Oorder(T_b)
% 21.40/21.32 => 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_atLeast__eq__iff,axiom,
% 21.40/21.32 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 21.40/21.32 <=> V_x_2 = V_y_2 ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_atLeast__iff,axiom,
% 21.40/21.32 ! [V_k_2,V_i_2,T_b] :
% 21.40/21.32 ( class_Orderings_Oord(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 21.40/21.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_atLeast__subset__iff,axiom,
% 21.40/21.32 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.32 ( class_Orderings_Oorder(T_b)
% 21.40/21.32 => ( 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)))
% 21.40/21.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Compl__lessThan,axiom,
% 21.40/21.32 ! [V_k_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Compl__atLeast,axiom,
% 21.40/21.32 ! [V_k_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_ivl__disj__un_I14_J,axiom,
% 21.40/21.32 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_ivl__disj__int_I8_J,axiom,
% 21.40/21.32 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.32 ( class_Orderings_Oorder(T_b)
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Int__atLeastAtMostL2,axiom,
% 21.40/21.32 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => 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_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Int__atLeastAtMostR2,axiom,
% 21.40/21.32 ! [V_d_2,V_c_2,V_a_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_ivl__disj__int_I6_J,axiom,
% 21.40/21.32 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.32 ( class_Orderings_Oorder(T_b)
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_image__uminus__atLeast,axiom,
% 21.40/21.32 ! [V_x_2,T_b] :
% 21.40/21.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_image__uminus__atMost,axiom,
% 21.40/21.32 ! [V_x_2,T_b] :
% 21.40/21.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_atLeast__Suc,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_ivl__disj__un_I12_J,axiom,
% 21.40/21.32 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_ivl__disj__un_I13_J,axiom,
% 21.40/21.32 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_ivl__disj__un_I1_J,axiom,
% 21.40/21.32 ! [V_l_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_atLeast__Suc__greaterThan,axiom,
% 21.40/21.32 ! [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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_greaterThan__eq__iff,axiom,
% 21.40/21.32 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 21.40/21.32 <=> V_x_2 = V_y_2 ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_greaterThan__iff,axiom,
% 21.40/21.32 ! [V_k_2,V_i_2,T_b] :
% 21.40/21.32 ( class_Orderings_Oord(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 21.40/21.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_greaterThan__subset__iff,axiom,
% 21.40/21.32 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( 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)))
% 21.40/21.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Compl__atMost,axiom,
% 21.40/21.32 ! [V_k_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Compl__greaterThan,axiom,
% 21.40/21.32 ! [V_k_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_ivl__disj__int_I7_J,axiom,
% 21.40/21.32 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.32 ( class_Orderings_Oorder(T_b)
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_ivl__disj__un_I11_J,axiom,
% 21.40/21.32 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_image__uminus__greaterThan,axiom,
% 21.40/21.32 ! [V_x_2,T_b] :
% 21.40/21.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_image__uminus__lessThan,axiom,
% 21.40/21.32 ! [V_x_2,T_b] :
% 21.40/21.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_ivl__disj__int_I5_J,axiom,
% 21.40/21.32 ! [V_u_2,V_l_2,T_b] :
% 21.40/21.32 ( class_Orderings_Oorder(T_b)
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_greaterThan__Suc,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum__Plus,axiom,
% 21.40/21.32 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__add(T_d)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 21.40/21.32 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(T_b,T_c),T_d),V_f_2),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(tc_sum(T_b,T_c),T_d,T_b,V_f_2),c_Sum__Type_OInl(T_b,T_c))),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(c_Fun_Ocomp(tc_sum(T_b,T_c),T_d,T_c,V_f_2),c_Sum__Type_OInr(T_c,T_b))),V_B_2)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 21.40/21.32 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 21.40/21.32 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.32 & class_Groups_Ocomm__monoid__mult(T_b) )
% 21.40/21.32 => ( V_A_2 = V_B_2
% 21.40/21.32 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 21.40/21.32 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 21.40/21.32 => 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) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_dom__eq__singleton__conv,axiom,
% 21.40/21.32 ! [V_x_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( 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)))
% 21.40/21.32 <=> ? [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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__on__imageI,axiom,
% 21.40/21.32 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 21.40/21.32 ( 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)
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_comp__inj__on,axiom,
% 21.40/21.32 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.32 => ( 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))
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_comp__inj__on__iff,axiom,
% 21.40/21.32 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.32 => ( 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))
% 21.40/21.32 <=> 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_o__eq__elim,axiom,
% 21.40/21.32 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 21.40/21.32 ( 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_c_2),V_d_2)
% 21.40/21.32 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_o__eq__dest,axiom,
% 21.40/21.32 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 21.40/21.32 ( 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_c_2),V_d_2)
% 21.40/21.32 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_o__apply,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_o__assoc,axiom,
% 21.40/21.32 ! [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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_o__def,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_comp__cong,axiom,
% 21.40/21.32 ! [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] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_apsnd__compose,axiom,
% 21.40/21.32 ! [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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_apfst__compose,axiom,
% 21.40/21.32 ! [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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__dom__body,axiom,
% 21.40/21.32 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__on__imageI2,axiom,
% 21.40/21.32 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 21.40/21.32 ( 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)
% 21.40/21.32 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fun__upd__comp,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_image__compose,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_domIff,axiom,
% 21.40/21.32 ! [V_m_2,T_c,V_a_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2)))
% 21.40/21.32 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_domI,axiom,
% 21.40/21.32 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 21.40/21.32 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 21.40/21.32 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_insert__dom,axiom,
% 21.40/21.32 ! [T_c,V_y_2,T_b,V_x_2,V_f_2] :
% 21.40/21.32 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_dom__restrict,axiom,
% 21.40/21.32 ! [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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_dom__eq__empty__conv,axiom,
% 21.40/21.32 ! [V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_dom__empty,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum__reindex,axiom,
% 21.40/21.32 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__add(T_d)
% 21.40/21.32 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setprod__reindex__cong,axiom,
% 21.40/21.32 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__mult(T_d)
% 21.40/21.32 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.32 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 21.40/21.32 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 21.40/21.32 => 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) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setprod__reindex,axiom,
% 21.40/21.32 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__mult(T_d)
% 21.40/21.32 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_dom__minus,axiom,
% 21.40/21.32 ! [V_A_2,T_c,T_b,V_x_2,V_f_2] :
% 21.40/21.32 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_b)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum_Oreindex,axiom,
% 21.40/21.32 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 21.40/21.32 => 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) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setprod_Oreindex,axiom,
% 21.40/21.32 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 21.40/21.32 => 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) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_the__inv__into__comp,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 21.40/21.32 => ( 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))))
% 21.40/21.32 => 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) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold__image__reindex,axiom,
% 21.40/21.32 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 21.40/21.32 ( class_Groups_Oab__semigroup__mult(T_d)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 21.40/21.32 => 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) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_dom__fun__upd,axiom,
% 21.40/21.32 ! [V_x_2,V_f_2,T_c,T_b,V_y_2] :
% 21.40/21.32 ( ( V_y_2 = c_Option_Ooption_ONone(T_b)
% 21.40/21.32 => 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)))) )
% 21.40/21.32 & ( V_y_2 != c_Option_Ooption_ONone(T_b)
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding_Oremove,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.32 => 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)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding__image_Oreindex,axiom,
% 21.40/21.32 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.32 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 21.40/21.32 => 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) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding_Ounion,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.32 => ( 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))
% 21.40/21.32 => 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)) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UN__o,axiom,
% 21.40/21.32 ! [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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding_Ocommute__left__comp,axiom,
% 21.40/21.32 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding_Ocommute__comp,axiom,
% 21.40/21.32 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 21.40/21.32 ! [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] :
% 21.40/21.32 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding__image_Odistrib,axiom,
% 21.40/21.32 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_split__comp,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding_Ocommute__comp_H,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 21.40/21.32 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.32 => 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)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 21.40/21.32 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.32 => 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)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_number__of__code__numeral__def,axiom,
% 21.40/21.32 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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_int__of__def,axiom,
% 21.40/21.32 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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding__image_Oeq__fold,axiom,
% 21.40/21.32 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding_Oinsert,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.32 => 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)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding_Ounion__inter,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.32 => 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)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding_Oinsert__remove,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Loop__sound__lemma,axiom,
% 21.40/21.32 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
% 21.40/21.32 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 21.40/21.32 => c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Nitpick_Onum__def,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Nitpick_Odenom__def,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_peek__and__def,axiom,
% 21.40/21.32 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_p_2),V_Z_2),V_s_2))
% 21.40/21.32 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2))
% 21.40/21.32 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Loop,axiom,
% 21.40/21.32 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
% 21.40/21.32 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 21.40/21.32 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_hoare__derivs_OIf,axiom,
% 21.40/21.32 ! [V_d_2,V_Q_2,V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
% 21.40/21.32 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_b_2)),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 21.40/21.32 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 21.40/21.32 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum__reindex__nonzero,axiom,
% 21.40/21.32 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__add(T_d)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 21.40/21.32 => ! [B_y] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 21.40/21.32 => ( B_x != B_y
% 21.40/21.32 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 21.40/21.32 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 21.40/21.32 => 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) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Random__Sequence_Omap__def,axiom,
% 21.40/21.32 ! [V_P_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_P_2) = c_Random__Sequence_Obind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding__idem_Ounion__idem,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.32 => 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)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding__idem_Oidem__comp,axiom,
% 21.40/21.32 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 21.40/21.32 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.32 => 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) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding__idem_Oinsert__idem,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.32 => 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) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_strong__setprod__reindex__cong,axiom,
% 21.40/21.32 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__mult(T_d)
% 21.40/21.32 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.32 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.32 => 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) )
% 21.40/21.32 => 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) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold__graph__permute__diff,axiom,
% 21.40/21.32 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 21.40/21.32 ( class_Groups_Oab__semigroup__mult(T_b)
% 21.40/21.32 => ( 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))
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 21.40/21.32 => 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)) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_ran__restrictD,axiom,
% 21.40/21.32 ! [V_A_2,V_m_2,T_c,V_y_2,T_b] :
% 21.40/21.32 ( 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))))
% 21.40/21.32 => ? [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 21.40/21.32 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold__graph__imp__finite,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold__graph_OemptyI,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_empty__fold__graphE,axiom,
% 21.40/21.32 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => V_x_2 = V_z_2 ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold__graph_OinsertI,axiom,
% 21.40/21.32 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 21.40/21.32 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 21.40/21.32 => 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))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold__graph__insert__swap,axiom,
% 21.40/21.32 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 21.40/21.32 ( class_Groups_Oab__semigroup__mult(T_b)
% 21.40/21.32 => ( 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))
% 21.40/21.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 21.40/21.32 => 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))) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Diff1__fold__graph,axiom,
% 21.40/21.32 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.32 => 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))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1Set_Ointros,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 21.40/21.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_compl__unique,axiom,
% 21.40/21.32 ! [V_y,V_x,T_a] :
% 21.40/21.32 ( class_Lattices_Oboolean__algebra(T_a)
% 21.40/21.32 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 21.40/21.32 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 21.40/21.32 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 21.40/21.32 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 21.40/21.32 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.32 & class_Groups_Ocomm__monoid__mult(T_b) )
% 21.40/21.32 => ( V_A_2 = V_B_2
% 21.40/21.32 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 21.40/21.32 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 21.40/21.32 => 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) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UNIV__I,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UNIV__option__conv,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_range__composition,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UN__atMost__UNIV,axiom,
% 21.40/21.32 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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__int,axiom,
% 21.40/21.32 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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__eq,axiom,
% 21.40/21.32 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 21.40/21.32 <=> V_x_2 = V_y_2 ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_injD,axiom,
% 21.40/21.32 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 21.40/21.32 => V_x_2 = V_y_2 ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Int__UNIV__left,axiom,
% 21.40/21.32 ! [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 ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Int__UNIV__right,axiom,
% 21.40/21.32 ! [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 ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inf__top__left,axiom,
% 21.40/21.32 ! [V_x,T_a] :
% 21.40/21.32 ( class_Lattices_Obounded__lattice__top(T_a)
% 21.40/21.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inf__top__right,axiom,
% 21.40/21.32 ! [V_x,T_a] :
% 21.40/21.32 ( class_Lattices_Obounded__lattice__top(T_a)
% 21.40/21.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inf__eq__top__iff,axiom,
% 21.40/21.32 ! [V_y_2,V_x_2,T_b] :
% 21.40/21.32 ( class_Lattices_Obounded__lattice__top(T_b)
% 21.40/21.32 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 21.40/21.32 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 21.40/21.32 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_sup__top__left,axiom,
% 21.40/21.32 ! [V_x,T_a] :
% 21.40/21.32 ( class_Lattices_Obounded__lattice__top(T_a)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_sup__top__right,axiom,
% 21.40/21.32 ! [V_x,T_a] :
% 21.40/21.32 ( class_Lattices_Obounded__lattice__top(T_a)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Un__UNIV__left,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Un__UNIV__right,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UNIV__not__empty,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_top__apply,axiom,
% 21.40/21.32 ! [V_x_2,T_c,T_b] :
% 21.40/21.32 ( class_Orderings_Otop(T_b)
% 21.40/21.32 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_subset__UNIV,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_equiv__intrel,axiom,
% 21.40/21.32 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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_top__greatest,axiom,
% 21.40/21.32 ! [V_x,T_a] :
% 21.40/21.32 ( class_Orderings_Otop(T_a)
% 21.40/21.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UNIV__Plus__UNIV,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_card__UNIV__unit,axiom,
% 21.40/21.32 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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Pow__UNIV,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UN__lessThan__UNIV,axiom,
% 21.40/21.32 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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__Prod__UNIV,axiom,
% 21.40/21.32 ! [T_c,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 21.40/21.32 => 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)))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__fun__UNIVD2,axiom,
% 21.40/21.32 ! [T_c,T_b] :
% 21.40/21.32 ( 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))))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__Plus__UNIV__iff,axiom,
% 21.40/21.32 ! [T_c,T_b] :
% 21.40/21.32 ( 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))))
% 21.40/21.32 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 21.40/21.32 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__option__UNIV,axiom,
% 21.40/21.32 ! [T_b] :
% 21.40/21.32 ( 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))))
% 21.40/21.32 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_infinite__UNIV__nat,axiom,
% 21.40/21.32 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__UNIV,axiom,
% 21.40/21.32 ! [T_b] :
% 21.40/21.32 ( class_Finite__Set_Ofinite(T_b)
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_infinite__UNIV__int,axiom,
% 21.40/21.32 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_empty__fold1SetE,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1Set__nonempty,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 21.40/21.32 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_rangeI,axiom,
% 21.40/21.32 ! [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))))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_range__eqI,axiom,
% 21.40/21.32 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 21.40/21.32 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 21.40/21.32 => 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))))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UN__atLeast__UNIV,axiom,
% 21.40/21.32 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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Diff__UNIV,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_comp__surj,axiom,
% 21.40/21.32 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => ( 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))
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 21.40/21.32 ! [V_A_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 21.40/21.32 => ( 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)))
% 21.40/21.32 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__image__eq__iff,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => ( 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)
% 21.40/21.32 <=> V_A_2 = V_B_2 ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__comp,axiom,
% 21.40/21.32 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 21.40/21.32 => 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))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Compl__empty__eq,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Compl__UNIV__eq,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__compl,axiom,
% 21.40/21.32 ! [V_A_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 21.40/21.32 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Compl__partition,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Compl__partition2,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 21.40/21.32 ! [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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 21.40/21.32 ! [V_y_2,V_x_2] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 21.40/21.32 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 21.40/21.32 <=> V_x_2 = V_y_2 ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_SUP__UN__eq,axiom,
% 21.40/21.32 ! [V_x_2,V_r_2,T_c,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 <=> 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__range__imageI,axiom,
% 21.40/21.32 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 21.40/21.32 ( 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)))))
% 21.40/21.32 => 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))))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_nat__of,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_the__inv__f__f,axiom,
% 21.40/21.32 ! [V_x_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => 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 ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__fun__UNIVD1,axiom,
% 21.40/21.32 ! [T_c,T_b] :
% 21.40/21.32 ( 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))))
% 21.40/21.32 => ( 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))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__of__nat,axiom,
% 21.40/21.32 ! [T_b] :
% 21.40/21.32 ( class_Nat_Osemiring__char__0(T_b)
% 21.40/21.32 => 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_dom__const,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_atLeast__0,axiom,
% 21.40/21.32 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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__fun,axiom,
% 21.40/21.32 ! [T_d,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_compl__top__eq,axiom,
% 21.40/21.32 ! [T_a] :
% 21.40/21.32 ( class_Lattices_Oboolean__algebra(T_a)
% 21.40/21.32 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_compl__bot__eq,axiom,
% 21.40/21.32 ! [T_a] :
% 21.40/21.32 ( class_Lattices_Oboolean__algebra(T_a)
% 21.40/21.32 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_sup__compl__top,axiom,
% 21.40/21.32 ! [V_x,T_a] :
% 21.40/21.32 ( class_Lattices_Oboolean__algebra(T_a)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_compl__sup__top,axiom,
% 21.40/21.32 ! [V_x,T_a] :
% 21.40/21.32 ( class_Lattices_Oboolean__algebra(T_a)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__image__mem__iff,axiom,
% 21.40/21.32 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => ( 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)))
% 21.40/21.32 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_range__ex1__eq,axiom,
% 21.40/21.32 ! [V_b_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => ( 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)))))
% 21.40/21.32 <=> ? [B_x] :
% 21.40/21.32 ( V_b_2 = hAPP(V_f_2,B_x)
% 21.40/21.32 & ! [B_y] :
% 21.40/21.32 ( V_b_2 = hAPP(V_f_2,B_y)
% 21.40/21.32 => B_y = B_x ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__UNIV__inj__surj,axiom,
% 21.40/21.32 ! [V_f_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 21.40/21.32 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__UNIV__surj__inj,axiom,
% 21.40/21.32 ! [V_f_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 21.40/21.32 => ( 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))
% 21.40/21.32 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__image__subset__iff,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => ( 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)))
% 21.40/21.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_image__Int,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_image__set__diff,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_surj__Compl__image__subset,axiom,
% 21.40/21.32 ! [V_A_2,V_f_2,T_b,T_c] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => 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)))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_of__nat__inverse,axiom,
% 21.40/21.32 ! [V_y_2] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 21.40/21.32 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1Set__sing,axiom,
% 21.40/21.32 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 <=> V_a_2 = V_b_2 ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__range__updI,axiom,
% 21.40/21.32 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( 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)))))
% 21.40/21.32 => 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))))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UN__UN__finite__eq,axiom,
% 21.40/21.32 ! [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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__singleton,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__UNIV__card__ge__0,axiom,
% 21.40/21.32 ! [T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 21.40/21.32 => 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))))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_card__UNIV__bool,axiom,
% 21.40/21.32 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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__image__Compl__subset,axiom,
% 21.40/21.32 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => 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)))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_greaterThan__0,axiom,
% 21.40/21.32 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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_SUP__UN__eq2,axiom,
% 21.40/21.32 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 <=> 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UN__finite2__subset,axiom,
% 21.40/21.32 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 21.40/21.32 ( ! [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)))
% 21.40/21.32 => 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UN__finite2__eq,axiom,
% 21.40/21.32 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 21.40/21.32 ( ! [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)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UN__finite__subset,axiom,
% 21.40/21.32 ! [V_C_2,V_A_2,T_b] :
% 21.40/21.32 ( ! [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))
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_top1I,axiom,
% 21.40/21.32 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Integ__def,axiom,
% 21.40/21.32 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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_iso__tuple__UNIV__I,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_equivp__equiv,axiom,
% 21.40/21.32 ! [V_A_2,T_b] :
% 21.40/21.32 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 21.40/21.32 <=> 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_identity__equivp,axiom,
% 21.40/21.32 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_equivp__def,axiom,
% 21.40/21.32 ! [V_R_2,T_b] :
% 21.40/21.32 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 21.40/21.32 <=> ! [B_x,B_y] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 21.40/21.32 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_equivp__reflp,axiom,
% 21.40/21.32 ! [V_x_2,V_R_2,T_b] :
% 21.40/21.32 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 21.40/21.32 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_equivp__symp,axiom,
% 21.40/21.32 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 21.40/21.32 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 21.40/21.32 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_equivp__transp,axiom,
% 21.40/21.32 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 21.40/21.32 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 21.40/21.32 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Rep__Integ,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_o__eq__dest__lhs,axiom,
% 21.40/21.32 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 21.40/21.32 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
% 21.40/21.32 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_K__record__comp,axiom,
% 21.40/21.32 ! [V_x_2,V_f_2,V_c_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_c_2)),V_f_2),V_x_2) = V_c_2 ).
% 21.40/21.32
% 21.40/21.32 fof(fact_type__definition__Integ,axiom,
% 21.40/21.32 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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__vimage__singleton,axiom,
% 21.40/21.32 ! [V_a_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => 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))))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_type__definition__code__numeral,axiom,
% 21.40/21.32 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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimageI,axiom,
% 21.40/21.32 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 21.40/21.32 ( hAPP(V_f_2,V_a_2) = V_b_2
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 21.40/21.32 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__compose,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__Diff,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__ident,axiom,
% 21.40/21.32 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__mono,axiom,
% 21.40/21.32 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.32 => 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__code,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 21.40/21.32 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__Compl,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__empty,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimageI2,axiom,
% 21.40/21.32 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 21.40/21.32 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimageD,axiom,
% 21.40/21.32 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 21.40/21.32 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__eq,axiom,
% 21.40/21.32 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 21.40/21.32 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__Un,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__Int,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_image__vimage__subset,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__UN,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__UNIV,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_surj__image__vimage__eq,axiom,
% 21.40/21.32 ! [V_A_2,V_f_2,T_b,T_c] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => 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 ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__singleton__eq,axiom,
% 21.40/21.32 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 21.40/21.32 ( 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))))))
% 21.40/21.32 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__insert,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__vimageD,axiom,
% 21.40/21.32 ! [V_F_2,V_h_2,T_c,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 21.40/21.32 => ( 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))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__subsetD,axiom,
% 21.40/21.32 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => ( 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))
% 21.40/21.32 => 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))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_image__vimage__eq,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__vimageI,axiom,
% 21.40/21.32 ! [V_h_2,T_c,V_F_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 21.40/21.32 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__vimage__image__eq,axiom,
% 21.40/21.32 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => 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 ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__const,axiom,
% 21.40/21.32 ! [T_c,V_A_2,V_c_2,T_b] :
% 21.40/21.32 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.32 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 21.40/21.32 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.32 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__eq__UN,axiom,
% 21.40/21.32 ! [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))))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__subsetI,axiom,
% 21.40/21.32 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.32 => ( 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)))
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__if,axiom,
% 21.40/21.32 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
% 21.40/21.32 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.32 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 21.40/21.32 => 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_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 21.40/21.32 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 21.40/21.32 => 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_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) )
% 21.40/21.32 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 21.40/21.32 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 21.40/21.32 => 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_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) )
% 21.40/21.32 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 21.40/21.32 => 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_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_type__definition_ORep__range,axiom,
% 21.40/21.32 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 21.40/21.32 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 21.40/21.32 => 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 ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_type__definition_OAbs__image,axiom,
% 21.40/21.32 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 21.40/21.32 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_type__definition_ORep,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 21.40/21.32 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 21.40/21.32 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_type__definition_ORep__inject,axiom,
% 21.40/21.32 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 21.40/21.32 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 21.40/21.32 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 21.40/21.32 <=> V_x_2 = V_y_2 ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_type__definition_ORep__inverse,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 21.40/21.32 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 21.40/21.32 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_type__definition_OAbs__inject,axiom,
% 21.40/21.32 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 21.40/21.32 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 21.40/21.32 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 21.40/21.32 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_type__definition_OAbs__inverse,axiom,
% 21.40/21.32 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 21.40/21.32 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 21.40/21.32 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_max__extp_Oequations,axiom,
% 21.40/21.32 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 21.40/21.32 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 21.40/21.32 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 21.40/21.32 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 21.40/21.32 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 & ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 21.40/21.32 => ? [B_xa] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 21.40/21.32 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_max__ext_Ointros,axiom,
% 21.40/21.32 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 21.40/21.32 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 21.40/21.32 => ? [B_xa] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 21.40/21.32 & 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)) ) )
% 21.40/21.32 => 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))) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1Set_Oequations,axiom,
% 21.40/21.32 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 <=> ? [B_a,B_A] :
% 21.40/21.32 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 21.40/21.32 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 21.40/21.32 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_insert__fold1SetE,axiom,
% 21.40/21.32 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => ~ ! [B_a,B_A] :
% 21.40/21.32 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 21.40/21.32 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_image__split__eq__Sigma,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1__Un,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Groups_Oab__semigroup__mult(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( 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))
% 21.40/21.32 => 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)) ) ) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_SigmaI,axiom,
% 21.40/21.32 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 21.40/21.32 => 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))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Times__eq__cancel2,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 21.40/21.32 => ( 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))
% 21.40/21.32 <=> V_A_2 = V_B_2 ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Sigma__empty1,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Sigma__Diff__distrib1,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Times__Diff__distrib1,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Sigma__Diff__distrib2,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_card__cartesian__product,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum__cartesian__product,axiom,
% 21.40/21.32 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.32 => 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Sigma__empty2,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Times__empty,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Compl__Times__UNIV1,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Compl__Times__UNIV2,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setprod__cartesian__product,axiom,
% 21.40/21.32 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__mult(T_b)
% 21.40/21.32 => 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Sigma__Un__distrib2,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Times__Un__distrib1,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Sigma__Un__distrib1,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_swap__product,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1__singleton__def,axiom,
% 21.40/21.32 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 21.40/21.32 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 21.40/21.32 => 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 ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1__singleton,axiom,
% 21.40/21.32 ! [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 ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__cartesian__product,axiom,
% 21.40/21.32 ! [V_B_2,T_c,V_A_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 21.40/21.32 => 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)))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_equiv__type,axiom,
% 21.40/21.32 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.32 => 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)))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Sigma__Int__distrib2,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Times__Int__distrib1,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Sigma__Int__distrib1,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Id__on__subset__Times,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UNIV__Times__UNIV,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_SigmaE2,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 21.40/21.32 ( 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)))
% 21.40/21.32 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.32 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_SigmaD2,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 21.40/21.32 ( 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)))
% 21.40/21.32 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_SigmaD1,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 21.40/21.32 ( 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)))
% 21.40/21.32 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_mem__Sigma__iff,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 21.40/21.32 ( 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)))
% 21.40/21.32 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.32 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding__one_Oeq__fold,axiom,
% 21.40/21.32 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_card__cartesian__product__singleton,axiom,
% 21.40/21.32 ! [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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Times__subset__cancel2,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 21.40/21.32 => ( 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))))
% 21.40/21.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Image__subset,axiom,
% 21.40/21.32 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 21.40/21.32 ( 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))))
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__cartesian__productD2,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.32 ( 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))))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__cartesian__productD1,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.32 ( 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))))
% 21.40/21.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fst__image__times,axiom,
% 21.40/21.32 ! [V_A_2,T_c,T_b,V_B_2] :
% 21.40/21.32 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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)) )
% 21.40/21.32 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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 ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_snd__image__times,axiom,
% 21.40/21.32 ! [V_B_2,T_c,T_b,V_A_2] :
% 21.40/21.32 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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)) )
% 21.40/21.32 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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 ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1__def,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Sup__fin_OF__eq,axiom,
% 21.40/21.32 ! [V_A_2,T_b] :
% 21.40/21.32 ( class_Lattices_Olattice(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Inf__fin_OF__eq,axiom,
% 21.40/21.32 ! [V_A_2,T_b] :
% 21.40/21.32 ( class_Lattices_Olattice(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Min_OF__eq,axiom,
% 21.40/21.32 ! [V_A_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Max_OF__eq,axiom,
% 21.40/21.32 ! [V_A_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 21.40/21.32 ! [V_A_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 21.40/21.32 ! [V_A_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_refl__on__def,axiom,
% 21.40/21.32 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.32 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 21.40/21.32 <=> ( 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))))
% 21.40/21.32 & ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.32 => 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)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_insert__times__insert,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__equiv__class,axiom,
% 21.40/21.32 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( 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))))
% 21.40/21.32 => ( 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)))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UN__Times__distrib,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Sigma__def,axiom,
% 21.40/21.32 ! [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))))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1__belowI,axiom,
% 21.40/21.32 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Lattices_Osemilattice__inf(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.32 => 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)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__quotient,axiom,
% 21.40/21.32 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( 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))))
% 21.40/21.32 => 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))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_below__fold1__iff,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Lattices_Osemilattice__inf(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( 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)))
% 21.40/21.32 <=> ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_min__max_Ofold1__belowI,axiom,
% 21.40/21.32 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.32 => 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)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1__insert__idem,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => 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)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1__below__iff,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( 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))
% 21.40/21.32 <=> ? [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( 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)))
% 21.40/21.32 <=> ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1__Un2,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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)) ) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1__strict__below__iff,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( 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))
% 21.40/21.32 <=> ? [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_strict__below__fold1__iff,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( 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)))
% 21.40/21.32 <=> ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__Times,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1__insert,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Groups_Oab__semigroup__mult(T_b)
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.32 => 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)) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1__antimono,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.32 => 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))) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_semilattice__big_OF__eq,axiom,
% 21.40/21.32 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 21.40/21.32 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 21.40/21.32 ! [V_A_2,V_I_2,T_c,T_b] :
% 21.40/21.32 ? [B_f] :
% 21.40/21.32 ( 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))
% 21.40/21.32 & 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_refl__onI,axiom,
% 21.40/21.32 ! [V_A_2,V_r_2,T_b] :
% 21.40/21.32 ( 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))))
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.32 => 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)) )
% 21.40/21.32 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setprod__Sigma,axiom,
% 21.40/21.32 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__mult(T_d)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 21.40/21.32 => 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)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum__Sigma,axiom,
% 21.40/21.32 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__add(T_d)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 21.40/21.32 => 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)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold__image__Sigma,axiom,
% 21.40/21.32 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__mult(T_d)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 21.40/21.32 => 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)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_card__SigmaI,axiom,
% 21.40/21.32 ! [V_B_2,T_c,V_A_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fold1__in,axiom,
% 21.40/21.32 ! [V_A_2,T_b] :
% 21.40/21.32 ( class_Groups_Oab__semigroup__mult(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( ! [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))))))
% 21.40/21.32 => 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)) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__SigmaI,axiom,
% 21.40/21.32 ! [V_B_2,T_c,V_A_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( ! [B_a] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 21.40/21.32 => 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))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_hom__fold1__commute,axiom,
% 21.40/21.32 ! [V_N_2,V_h_2,T_b] :
% 21.40/21.32 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 21.40/21.32 => ( ! [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))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 21.40/21.32 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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)) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_SigmaE,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 21.40/21.32 => ~ ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.32 => ! [B_y] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 21.40/21.32 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_map__pair__surj,axiom,
% 21.40/21.32 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => ( 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))
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_map__pair__inj__on,axiom,
% 21.40/21.32 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.32 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 21.40/21.32 => 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))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_map__pair__imageI,axiom,
% 21.40/21.32 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fst__comp__map__pair,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_snd__comp__map__pair,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_map__pair_Ocompositionality,axiom,
% 21.40/21.32 ! [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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_map__pair__compose,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_map__pair_Ocomp,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_map__pair__ident,axiom,
% 21.40/21.32 ! [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 ).
% 21.40/21.32
% 21.40/21.32 fof(fact_map__pair__simp,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_snd__prod__fun,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fst__map__pair,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_map__pair__def,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_map__pair__surj__on,axiom,
% 21.40/21.32 ! [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] :
% 21.40/21.32 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 21.40/21.32 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_prod__fun__imageE,axiom,
% 21.40/21.32 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_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)))
% 21.40/21.32 => ~ ! [B_x,B_y] :
% 21.40/21.32 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
% 21.40/21.32 => ~ 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setprod__pos__nat,axiom,
% 21.40/21.32 ! [V_f_2,V_S_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 21.40/21.32 => 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))) )
% 21.40/21.32 => 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))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 21.40/21.32 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 21.40/21.32 => ( ! [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))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 21.40/21.32 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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)) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Rep__Integ__induct,axiom,
% 21.40/21.32 ! [V_P_2,V_y_2] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 21.40/21.32 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 21.40/21.32 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Rep__Integ__cases,axiom,
% 21.40/21.32 ! [V_y_2] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 21.40/21.32 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( 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)))
% 21.40/21.32 => hAPP(V_g_2,B_x) = V_z_2 )
% 21.40/21.32 => 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)) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fun__left__comm__idem__remove,axiom,
% 21.40/21.32 ! [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))))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_card__less__Suc2,axiom,
% 21.40/21.32 ! [V_i_2,V_M_2] :
% 21.40/21.32 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 21.40/21.32 => 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))))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_CollectI,axiom,
% 21.40/21.32 ! [T_b,V_a_2,V_P_2] :
% 21.40/21.32 ( hBOOL(hAPP(V_P_2,V_a_2))
% 21.40/21.32 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__Collect__conjI,axiom,
% 21.40/21.32 ! [V_Q_2,V_P_2,T_b] :
% 21.40/21.32 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 21.40/21.32 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) )
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__Collect__less__nat,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__Collect__le__nat,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 21.40/21.32 ! [V_x_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Collect__conv__if,axiom,
% 21.40/21.32 ! [T_b,V_a_2,V_P_2] :
% 21.40/21.32 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 21.40/21.32 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 21.40/21.32 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 21.40/21.32 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Collect__conv__if2,axiom,
% 21.40/21.32 ! [T_b,V_a_2,V_P_2] :
% 21.40/21.32 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 21.40/21.32 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 21.40/21.32 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 21.40/21.32 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_singleton__conv,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_singleton__conv2,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Collect__split,axiom,
% 21.40/21.32 ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_SetCompr__Sigma__eq,axiom,
% 21.40/21.32 ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Collect__neg__eq,axiom,
% 21.40/21.32 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__Collect__eq,axiom,
% 21.40/21.32 ! [V_P_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_P_2),V_f_2)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_insert__compr__raw,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_insert__compr,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Collect__mem__eq,axiom,
% 21.40/21.32 ! [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 ).
% 21.40/21.32
% 21.40/21.32 fof(fact_mem__Collect__eq,axiom,
% 21.40/21.32 ! [V_P_2,V_a_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 21.40/21.32 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_CollectD,axiom,
% 21.40/21.32 ! [V_P_2,V_a_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 21.40/21.32 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_CollectE,axiom,
% 21.40/21.32 ! [V_P_2,V_a_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 21.40/21.32 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_UNIV__def,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__Collect__disjI,axiom,
% 21.40/21.32 ! [V_Q_2,V_P_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2))))
% 21.40/21.32 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 21.40/21.32 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_insert__Collect,axiom,
% 21.40/21.32 ! [V_P_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fun__left__comm__idem__insert,axiom,
% 21.40/21.32 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 21.40/21.32 ! [T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fun__left__comm__idem,axiom,
% 21.40/21.32 ! [T_b] :
% 21.40/21.32 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 21.40/21.32 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Collect__conj__eq,axiom,
% 21.40/21.32 ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Collect__disj__eq,axiom,
% 21.40/21.32 ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_empty__def,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Collect__empty__eq,axiom,
% 21.40/21.32 ! [V_P_2,T_b] :
% 21.40/21.32 ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_empty__Collect__eq,axiom,
% 21.40/21.32 ! [V_P_2,T_b] :
% 21.40/21.32 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
% 21.40/21.32 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 21.40/21.32 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 21.40/21.32 => 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 21.40/21.32 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Collect__def,axiom,
% 21.40/21.32 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2 ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fun__left__comm__idem__inf,axiom,
% 21.40/21.32 ! [T_b] :
% 21.40/21.32 ( class_Lattices_Osemilattice__inf(T_b)
% 21.40/21.32 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_fun__left__comm__idem__sup,axiom,
% 21.40/21.32 ! [T_b] :
% 21.40/21.32 ( class_Lattices_Osemilattice__sup(T_b)
% 21.40/21.32 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 21.40/21.32 ! [T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Int__Collect,axiom,
% 21.40/21.32 ! [V_P_2,V_A_2,V_x_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))
% 21.40/21.32 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.32 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Int__def,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Un__def,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_set__diff__eq,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__Collect__not,axiom,
% 21.40/21.32 ! [V_P_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))
% 21.40/21.32 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_insert__def,axiom,
% 21.40/21.32 ! [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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Compl__eq,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__def,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Collect__imp__eq,axiom,
% 21.40/21.32 ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_dom__def,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__M__bounded__by__nat,axiom,
% 21.40/21.32 ! [V_i_2,V_P_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_P_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum__setsum__restrict,axiom,
% 21.40/21.32 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__add(T_d)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 21.40/21.32 => 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) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_if__image__distrib,axiom,
% 21.40/21.32 ! [V_S_2,V_g_2,V_f_2,V_P_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_P_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_P_2))))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_dom__if,axiom,
% 21.40/21.32 ! [V_g_2,V_f_2,V_P_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),T_b),c_If(tc_Option_Ooption(T_c))),V_P_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_f_2)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_g_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_nat__seg__image__imp__finite,axiom,
% 21.40/21.32 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 21.40/21.32 ( 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)))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum__restrict__set_H,axiom,
% 21.40/21.32 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum__image__gen,axiom,
% 21.40/21.32 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Image__singleton,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum__cases,axiom,
% 21.40/21.32 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_card__less__Suc,axiom,
% 21.40/21.32 ! [V_i_2,V_M_2] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 21.40/21.32 => 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))))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_card__less,axiom,
% 21.40/21.32 ! [V_i_2,V_M_2] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_dom__override__on,axiom,
% 21.40/21.32 ! [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))))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum__multicount,axiom,
% 21.40/21.32 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 21.40/21.32 => 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 )
% 21.40/21.32 => 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)) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__Collect__subsets,axiom,
% 21.40/21.32 ! [V_A_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => 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)))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Pow__def,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_override__on__apply__notin,axiom,
% 21.40/21.32 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 21.40/21.32 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_override__on__apply__in,axiom,
% 21.40/21.32 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.32 => 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) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_override__on__emptyset,axiom,
% 21.40/21.32 ! [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 ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__graph,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 21.40/21.32 ! [V_P_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_override__on__def,axiom,
% 21.40/21.32 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 21.40/21.32 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.32 => 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) )
% 21.40/21.32 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.32 => 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) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__psubset__def,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inv__image__def,axiom,
% 21.40/21.32 ! [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))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 21.40/21.32 ! [V_P_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 21.40/21.32 ! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_P_2),c_Int_Onat)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Nitpick_Oprod__def,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_int__ge__less__than2__def,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_int__ge__less__than__def,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_reflp__def,axiom,
% 21.40/21.32 ! [V_r_2,T_b] :
% 21.40/21.32 ( c_Predicate_Oreflp(T_b,V_r_2)
% 21.40/21.32 <=> 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_reflpE,axiom,
% 21.40/21.32 ! [V_x_2,V_r_2,T_b] :
% 21.40/21.32 ( c_Predicate_Oreflp(T_b,V_r_2)
% 21.40/21.32 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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))))))) ) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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))))))) ) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__image__set,axiom,
% 21.40/21.32 ! [V_f_2,T_c,V_P_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 21.40/21.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_P_2))))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__Collect__bounded__ex,axiom,
% 21.40/21.32 ! [V_Q_2,T_c,V_P_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2)))))
% 21.40/21.32 <=> ! [B_y] :
% 21.40/21.32 ( hBOOL(hAPP(V_P_2,B_y))
% 21.40/21.32 => 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_Q_2),B_y)))) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_ran__def,axiom,
% 21.40/21.32 ! [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)))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_Pow__Compl,axiom,
% 21.40/21.32 ! [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))))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_add__Max__commute,axiom,
% 21.40/21.32 ! [V_k_2,V_N_2,T_b] :
% 21.40/21.32 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 21.40/21.32 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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))))) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_add__Min__commute,axiom,
% 21.40/21.32 ! [V_k_2,V_N_2,T_b] :
% 21.40/21.32 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 21.40/21.32 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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))))) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_sup__Inf2__distrib,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Lattices_Odistrib__lattice(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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))))))) ) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_sup__Inf1__distrib,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Lattices_Odistrib__lattice(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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))))) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inf__Sup1__distrib,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Lattices_Odistrib__lattice(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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))))) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inf__Sup2__distrib,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Lattices_Odistrib__lattice(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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))))))) ) ) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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))))) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 21.40/21.32 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.32 ( class_Orderings_Olinorder(T_b)
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.32 => 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))))) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 21.40/21.32 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 21.40/21.32 ( class_Rings_Osemiring__0(T_d)
% 21.40/21.32 => ( 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)))
% 21.40/21.32 => 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))))))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum__multicount__gen,axiom,
% 21.40/21.32 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 21.40/21.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 21.40/21.32 => ( ! [B_x] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 21.40/21.32 => 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) )
% 21.40/21.32 => 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) ) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_inj__on__id,axiom,
% 21.40/21.32 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_map__pair_Oid,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_map__pair_Oidentity,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_id__apply,axiom,
% 21.40/21.32 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 21.40/21.32
% 21.40/21.32 fof(fact_id__def,axiom,
% 21.40/21.32 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 21.40/21.32
% 21.40/21.32 fof(fact_apsnd__id,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_apfst__id,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_of__int__eq__id,axiom,
% 21.40/21.32 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_vimage__id,axiom,
% 21.40/21.32 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 21.40/21.32
% 21.40/21.32 fof(fact_o__eq__id__dest,axiom,
% 21.40/21.32 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 21.40/21.32 ( 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_c_2)
% 21.40/21.32 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_o__id,axiom,
% 21.40/21.32 ! [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 ).
% 21.40/21.32
% 21.40/21.32 fof(fact_id__o,axiom,
% 21.40/21.32 ! [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 ).
% 21.40/21.32
% 21.40/21.32 fof(fact_image__id,axiom,
% 21.40/21.32 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 21.40/21.32
% 21.40/21.32 fof(fact_surj__id,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_folding_Oempty,axiom,
% 21.40/21.32 ! [V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.32 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.32 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_apsnd__def,axiom,
% 21.40/21.32 ! [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) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_apfst__def,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_split__Pair,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setsum__reindex__id,axiom,
% 21.40/21.32 ! [V_B_2,V_f_2,T_b,T_c] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.32 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_setprod__reindex__id,axiom,
% 21.40/21.32 ! [V_B_2,V_f_2,T_b,T_c] :
% 21.40/21.32 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.32 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_finite__conv__nat__seg__image,axiom,
% 21.40/21.32 ! [V_A_2,T_b] :
% 21.40/21.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.32 <=> ? [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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_rel__comp__def,axiom,
% 21.40/21.32 ! [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))))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_rel__compI,axiom,
% 21.40/21.32 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => ( 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_c_2)),V_s_2))
% 21.40/21.32 => 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_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_rel__comp__UNION__distrib,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_rel__comp__UNION__distrib2,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_rel__comp__distrib2,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_rel__comp__distrib,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_rel__comp__empty2,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_rel__comp__empty1,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_O__assoc,axiom,
% 21.40/21.32 ! [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)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_rel__comp__mono,axiom,
% 21.40/21.32 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => ( 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))
% 21.40/21.32 => 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))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_union__comp__emptyL,axiom,
% 21.40/21.32 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => ( 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))
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_union__comp__emptyR,axiom,
% 21.40/21.32 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => ( 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))
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_rel__comp__subset__Sigma,axiom,
% 21.40/21.32 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 21.40/21.32 ( 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))))
% 21.40/21.32 => ( 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))))
% 21.40/21.32 => 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)))) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_max__ext__compat,axiom,
% 21.40/21.32 ! [V_S_2,V_R_2,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_min__ext__compat,axiom,
% 21.40/21.32 ! [V_S_2,V_R_2,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_pred__comp__rel__comp__eq,axiom,
% 21.40/21.32 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 21.40/21.32 ( 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)
% 21.40/21.32 <=> 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))) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_reduction__pairI,axiom,
% 21.40/21.32 ! [V_S_2,V_R_2,T_b] :
% 21.40/21.32 ( c_Wellfounded_Owf(T_b,V_R_2)
% 21.40/21.32 => ( 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))
% 21.40/21.32 => 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)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_wf__less__than,axiom,
% 21.40/21.32 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_pred__comp_Ointros,axiom,
% 21.40/21.32 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 21.40/21.32 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 21.40/21.32 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
% 21.40/21.32 => c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a_2,V_c_2) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_wf__empty,axiom,
% 21.40/21.32 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_wf__inv__image,axiom,
% 21.40/21.32 ! [V_f_2,T_c,V_r_2,T_b] :
% 21.40/21.32 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.32 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_wf__lex__prod,axiom,
% 21.40/21.32 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 21.40/21.32 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 21.40/21.32 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 21.40/21.32 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_wf__measure,axiom,
% 21.40/21.32 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_wf__union__merge,axiom,
% 21.40/21.32 ! [V_S_2,V_R_2,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 <=> 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)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_wf__no__loop,axiom,
% 21.40/21.32 ! [V_R_2,T_b] :
% 21.40/21.32 ( 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))
% 21.40/21.32 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_wf__comp__self,axiom,
% 21.40/21.32 ! [V_R_2,T_b] :
% 21.40/21.32 ( c_Wellfounded_Owf(T_b,V_R_2)
% 21.40/21.32 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 21.40/21.32
% 21.40/21.32 fof(fact_wf__less,axiom,
% 21.40/21.33 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)))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__int__ge__less__than2,axiom,
% 21.40/21.33 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__pair__less,axiom,
% 21.40/21.33 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__subset,axiom,
% 21.40/21.33 ! [V_p_2,V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => ( 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))
% 21.40/21.33 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_max__ext__wf,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_pred__comp_Oequations,axiom,
% 21.40/21.33 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 21.40/21.33 ( c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a1_2,V_a3_2)
% 21.40/21.33 <=> ? [B_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 21.40/21.33 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_min__ext__wf,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__finite__psubset,axiom,
% 21.40/21.33 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__mlex,axiom,
% 21.40/21.33 ! [V_f_2,V_R_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_R_2)
% 21.40/21.33 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__Int2,axiom,
% 21.40/21.33 ! [V_r_H_2,V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__Int1,axiom,
% 21.40/21.33 ! [V_r_H_2,V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__not__refl,axiom,
% 21.40/21.33 ! [V_a_2,V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => ~ 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__not__sym,axiom,
% 21.40/21.33 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => ( 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))
% 21.40/21.33 => ~ 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__asym,axiom,
% 21.40/21.33 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => ( 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))
% 21.40/21.33 => ~ 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__irrefl,axiom,
% 21.40/21.33 ! [V_a_2,V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => ~ 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_acc__wfD,axiom,
% 21.40/21.33 ! [V_x_2,V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__acc__iff,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__int__ge__less__than,axiom,
% 21.40/21.33 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 <=> ~ ? [B_f] :
% 21.40/21.33 ! [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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wfE__pf,axiom,
% 21.40/21.33 ! [V_A_2,V_R_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_R_2)
% 21.40/21.33 => ( 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)))
% 21.40/21.33 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__union__compatible,axiom,
% 21.40/21.33 ! [V_S_2,V_R_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_R_2)
% 21.40/21.33 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 21.40/21.33 => ( 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))
% 21.40/21.33 => 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)) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf,axiom,
% 21.40/21.33 ! [T_b] :
% 21.40/21.33 ( class_Orderings_Owellorder(T_b)
% 21.40/21.33 => 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)))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_reduction__pair__def,axiom,
% 21.40/21.33 ! [V_P_2,T_b] :
% 21.40/21.33 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 21.40/21.33 <=> ( c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))
% 21.40/21.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_reduction__pair__lemma,axiom,
% 21.40/21.33 ! [V_S_2,V_R_2,V_P_2,T_b] :
% 21.40/21.33 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
% 21.40/21.33 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 21.40/21.33 => 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)) ) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__map__pair__image,axiom,
% 21.40/21.33 ! [V_f_2,T_c,V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__lenlex,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__if__measure,axiom,
% 21.40/21.33 ! [T_b,V_g_2,V_f_2,V_P_2] :
% 21.40/21.33 ( ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(V_P_2,B_x))
% 21.40/21.33 => 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))) )
% 21.40/21.33 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_pred__nat__def,axiom,
% 21.40/21.33 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))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__lex,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__pred__nat,axiom,
% 21.40/21.33 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_lex__def,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__lexn,axiom,
% 21.40/21.33 ! [V_n_2,V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_lexn_Osimps_I1_J,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__same__fst,axiom,
% 21.40/21.33 ! [T_b,V_R_2,T_c,V_P_2] :
% 21.40/21.33 ( ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(V_P_2,B_x))
% 21.40/21.33 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 21.40/21.33 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Range__Collect__split,axiom,
% 21.40/21.33 ! [V_P_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_RangeI,axiom,
% 21.40/21.33 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Range__Id__on,axiom,
% 21.40/21.33 ! [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 ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Range__empty__iff,axiom,
% 21.40/21.33 ! [V_r_2,T_b,T_c] :
% 21.40/21.33 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Range__empty,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Range__Un__eq,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_finite__Range,axiom,
% 21.40/21.33 ! [V_r_2,T_c,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 21.40/21.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_snd__eq__Range,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Range__iff,axiom,
% 21.40/21.33 ! [V_r_2,T_c,V_a_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 21.40/21.33 <=> ? [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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Range__insert,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Range__Int__subset,axiom,
% 21.40/21.33 ! [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)))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Range__Diff__subset,axiom,
% 21.40/21.33 ! [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)))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_RangeP__Range__eq,axiom,
% 21.40/21.33 ! [V_x_2,V_r_2,T_c,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_RangeE,axiom,
% 21.40/21.33 ! [V_r_2,T_c,V_b_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 21.40/21.33 => ~ ! [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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_RangeP_Ointros,axiom,
% 21.40/21.33 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 21.40/21.33 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_RangeP_Oequations,axiom,
% 21.40/21.33 ! [V_a2_2,V_r_2,T_c,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 21.40/21.33 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__Un,axiom,
% 21.40/21.33 ! [V_s_2,V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 21.40/21.33 => ( 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))
% 21.40/21.33 => 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)) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wfP__def,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 21.40/21.33 <=> 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wfP__empty,axiom,
% 21.40/21.33 ! [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))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_DomainI,axiom,
% 21.40/21.33 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Domain__Id__on,axiom,
% 21.40/21.33 ! [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 ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wfP__accp__iff,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 21.40/21.33 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_accp__wfPD,axiom,
% 21.40/21.33 ! [V_x_2,V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 21.40/21.33 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wfP__subset,axiom,
% 21.40/21.33 ! [V_p_2,V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 21.40/21.33 => ( 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))
% 21.40/21.33 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Domain__empty__iff,axiom,
% 21.40/21.33 ! [V_r_2,T_c,T_b] :
% 21.40/21.33 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Domain__empty,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Domain__mono,axiom,
% 21.40/21.33 ! [V_s_2,V_r_2,T_c,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Domain__Un__eq,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_finite__Domain,axiom,
% 21.40/21.33 ! [V_r_2,T_c,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 21.40/21.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fst__eq__Domain,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Domain__iff,axiom,
% 21.40/21.33 ! [V_r_2,T_c,V_a_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 21.40/21.33 <=> ? [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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Domain__insert,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Domain__Int__subset,axiom,
% 21.40/21.33 ! [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)))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Domain__Diff__subset,axiom,
% 21.40/21.33 ! [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)))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Field__def,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__in__rel,axiom,
% 21.40/21.33 ! [V_R_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_R_2)
% 21.40/21.33 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wfP__wf__eq,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Domain__Collect__split,axiom,
% 21.40/21.33 ! [V_P_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_P_2)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_DomainP__Domain__eq,axiom,
% 21.40/21.33 ! [V_x_2,V_r_2,T_c,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_DomainE,axiom,
% 21.40/21.33 ! [V_r_2,T_c,V_a_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 21.40/21.33 => ~ ! [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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_DomainP_Ointros,axiom,
% 21.40/21.33 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 21.40/21.33 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_DomainP_Oequations,axiom,
% 21.40/21.33 ! [V_a1_2,V_r_2,T_c,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 21.40/21.33 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wfP__acyclicP,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_pos__map__def,axiom,
% 21.40/21.33 ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__acyclic,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_acyclic__subset,axiom,
% 21.40/21.33 ! [V_r_2,V_s_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 21.40/21.33 => ( 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))
% 21.40/21.33 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 21.40/21.33 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_finite__acyclic__wf,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 21.40/21.33 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 21.40/21.33 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_pos__single__def,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Nitpick_Owf_H__def,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 21.40/21.33 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 21.40/21.33 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 21.40/21.33 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_New__DSequence_Opos__single__def,axiom,
% 21.40/21.33 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Osingle(T_a,V_x) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_neg__map__def,axiom,
% 21.40/21.33 ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_neg__single__def,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_pigeonhole__infinite,axiom,
% 21.40/21.33 ! [V_f_2,T_c,V_A_2,T_b] :
% 21.40/21.33 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 21.40/21.33 => ? [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.33 & ~ 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)))))) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Abs__Integ__cases,axiom,
% 21.40/21.33 ! [V_x_2] :
% 21.40/21.33 ~ ! [B_y] :
% 21.40/21.33 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 21.40/21.33 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Abs__Integ__induct,axiom,
% 21.40/21.33 ! [V_x_2,V_P_2] :
% 21.40/21.33 ( ! [B_y] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 21.40/21.33 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 21.40/21.33 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_finite__UN__I,axiom,
% 21.40/21.33 ! [V_B_2,T_c,V_A_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ! [B_a] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 21.40/21.33 => 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_inj__on__diff__nat,axiom,
% 21.40/21.33 ! [V_k_2,V_N_2] :
% 21.40/21.33 ( ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 21.40/21.33 => 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) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wfP__SUP,axiom,
% 21.40/21.33 ! [T_b,V_r_2,T_c] :
% 21.40/21.33 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 21.40/21.33 => ( ! [B_i,B_j] :
% 21.40/21.33 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 21.40/21.33 => 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)) )
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_dvd_Ostrict__monoI,axiom,
% 21.40/21.33 ! [V_f_2,T_b] :
% 21.40/21.33 ( class_Orderings_Oorder(T_b)
% 21.40/21.33 => ( ! [B_x,B_y] :
% 21.40/21.33 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y))
% 21.40/21.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x)) )
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
% 21.40/21.33 => c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_finite__map__freshness,axiom,
% 21.40/21.33 ! [V_f_2,T_c,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2)))
% 21.40/21.33 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 21.40/21.33 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_mem__splitE,axiom,
% 21.40/21.33 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
% 21.40/21.33 ( 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_c_2),V_p_2)))
% 21.40/21.33 => ~ ! [B_x,B_y] :
% 21.40/21.33 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 21.40/21.33 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_mem__splitI2,axiom,
% 21.40/21.33 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 21.40/21.33 ( ! [B_a,B_b] :
% 21.40/21.33 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
% 21.40/21.33 => 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_c_2),V_p_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_setsum__SucD,axiom,
% 21.40/21.33 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 21.40/21.33 ( 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)
% 21.40/21.33 => ? [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.33 & 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Eps__split,axiom,
% 21.40/21.33 ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_exE__some,axiom,
% 21.40/21.33 ! [T_b,V_c_2,V_P_2] :
% 21.40/21.33 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 21.40/21.33 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_P_2)
% 21.40/21.33 => hBOOL(hAPP(V_P_2,V_c_2)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_some__sym__eq__trivial,axiom,
% 21.40/21.33 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 21.40/21.33
% 21.40/21.33 fof(fact_some__eq__trivial,axiom,
% 21.40/21.33 ! [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 ).
% 21.40/21.33
% 21.40/21.33 fof(fact_some__eq__ex,axiom,
% 21.40/21.33 ! [T_b,V_P_2] :
% 21.40/21.33 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
% 21.40/21.33 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_someI__ex,axiom,
% 21.40/21.33 ! [T_b,V_P_2] :
% 21.40/21.33 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 21.40/21.33 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_tfl__some,axiom,
% 21.40/21.33 ! [T_b,B_P] :
% 21.40/21.33 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 21.40/21.33 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_someI,axiom,
% 21.40/21.33 ! [T_b,V_x_2,V_P_2] :
% 21.40/21.33 ( hBOOL(hAPP(V_P_2,V_x_2))
% 21.40/21.33 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_split__paired__Eps,axiom,
% 21.40/21.33 ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Eps__split__eq,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wfI__pf,axiom,
% 21.40/21.33 ! [V_R_2,T_b] :
% 21.40/21.33 ( ! [B_A] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 21.40/21.33 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Sigma__mono,axiom,
% 21.40/21.33 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 21.40/21.33 => ( ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.33 => 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))) )
% 21.40/21.33 => 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_acc_OaccI,axiom,
% 21.40/21.33 ! [V_r_2,V_x_2,T_b] :
% 21.40/21.33 ( ! [B_y] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_not__acc__down,axiom,
% 21.40/21.33 ! [V_R_2,V_x_2,T_b] :
% 21.40/21.33 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 21.40/21.33 => ~ ! [B_z] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fold__image__1,axiom,
% 21.40/21.33 ! [V_f_2,V_S_2,T_b,T_c] :
% 21.40/21.33 ( class_Groups_Ocomm__monoid__mult(T_c)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 21.40/21.33 => ( ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 21.40/21.33 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 21.40/21.33 => 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) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_card_Oneutral,axiom,
% 21.40/21.33 ! [V_A_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.33 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 21.40/21.33 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_max__ext_Osimps,axiom,
% 21.40/21.33 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 21.40/21.33 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 21.40/21.33 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 & ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 21.40/21.33 => ? [B_xa] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 21.40/21.33 & 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)) ) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fold__image__cong,axiom,
% 21.40/21.33 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 21.40/21.33 ( class_Groups_Oab__semigroup__mult(T_c)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.33 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 21.40/21.33 => 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) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_setprod__dvd__setprod__subset2,axiom,
% 21.40/21.33 ! [V_g_2,V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 21.40/21.33 ( class_Rings_Ocomm__semiring__1(T_c)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.33 => ( ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_B_2))) ) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Max__eqI,axiom,
% 21.40/21.33 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Orderings_Olinorder(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ! [B_y] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Min__eqI,axiom,
% 21.40/21.33 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Orderings_Olinorder(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ! [B_y] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__no__infinite__down__chainE,axiom,
% 21.40/21.33 ! [V_f_2,V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => ~ ! [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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_setsum__reindex__cong,axiom,
% 21.40/21.33 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 21.40/21.33 ( class_Groups_Ocomm__monoid__add(T_d)
% 21.40/21.33 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 21.40/21.33 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 21.40/21.33 => ( ! [B_a] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 21.40/21.33 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 21.40/21.33 => 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) ) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_setsum__ivl__cong,axiom,
% 21.40/21.33 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
% 21.40/21.33 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.33 & class_Orderings_Oord(T_b) )
% 21.40/21.33 => ( V_a_2 = V_c_2
% 21.40/21.33 => ( V_b_2 = V_d_2
% 21.40/21.33 => ( ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 21.40/21.33 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 21.40/21.33 => 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_c_2),V_d_2)) ) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_less__eq,axiom,
% 21.40/21.33 ! [V_n_2,V_m_2] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 21.40/21.33 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Orderings_Olinorder(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => 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) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fold__empty,axiom,
% 21.40/21.33 ! [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 ).
% 21.40/21.33
% 21.40/21.33 fof(fact_folding_Oeq__fold,axiom,
% 21.40/21.33 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fold__image__def,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__trancl,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fold__def,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_union__fold__insert,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fold__sup__insert,axiom,
% 21.40/21.33 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Lattices_Osemilattice__sup(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fold__inf__insert,axiom,
% 21.40/21.33 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Lattices_Osemilattice__inf(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_less__than__def,axiom,
% 21.40/21.33 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_min__max_Ofold__inf__insert,axiom,
% 21.40/21.33 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Orderings_Olinorder(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_min__max_Ofold__sup__insert,axiom,
% 21.40/21.33 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Orderings_Olinorder(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_acyclic__def,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 21.40/21.33 <=> ! [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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 21.40/21.33 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 21.40/21.33 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_sup__SUPR__fold__sup,axiom,
% 21.40/21.33 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 21.40/21.33 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_sup__le__fold__sup,axiom,
% 21.40/21.33 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Lattices_Osemilattice__sup(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.33 => 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))) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fold__inf__le__inf,axiom,
% 21.40/21.33 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Lattices_Osemilattice__inf(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.33 => 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))) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 21.40/21.33 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Orderings_Olinorder(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.33 => 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))) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 21.40/21.33 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Orderings_Olinorder(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.33 => 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))) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fold1__eq__fold__idem,axiom,
% 21.40/21.33 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 21.40/21.33 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Lattices_Olattice(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 21.40/21.33 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Lattices_Olattice(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 21.40/21.33 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Orderings_Olinorder(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 21.40/21.33 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Orderings_Olinorder(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 21.40/21.33 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Orderings_Olinorder(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 21.40/21.33 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Orderings_Olinorder(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_minus__fold__remove,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_folding__one_Oeq__fold_H,axiom,
% 21.40/21.33 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => 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) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_SUPR__fold__sup,axiom,
% 21.40/21.33 ! [V_f_2,V_A_2,T_b,T_c] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fold1__eq__fold,axiom,
% 21.40/21.33 ! [V_a_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Groups_Oab__semigroup__mult(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.33 => 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) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 21.40/21.33 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Lattices_Olattice(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => 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) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 21.40/21.33 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Lattices_Olattice(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => 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) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Min_Oeq__fold_H,axiom,
% 21.40/21.33 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Orderings_Olinorder(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => 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) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Max_Oeq__fold_H,axiom,
% 21.40/21.33 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Orderings_Olinorder(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => 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) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 21.40/21.33 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Orderings_Olinorder(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => 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) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl_Or__into__trancl,axiom,
% 21.40/21.33 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__subset__Field2,axiom,
% 21.40/21.33 ! [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))))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_r__into__trancl_H,axiom,
% 21.40/21.33 ! [V_r_2,V_p_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__empty,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__domain,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__range,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_finite__trancl,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 21.40/21.33 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__trans,axiom,
% 21.40/21.33 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 21.40/21.33 => 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 21.40/21.33 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( 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_c_2)),V_r_2))
% 21.40/21.33 => 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__into__trancl2,axiom,
% 21.40/21.33 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => ( 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 21.40/21.33 => 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_r__r__into__trancl,axiom,
% 21.40/21.33 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => ( 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_c_2)),V_R_2))
% 21.40/21.33 => 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__mono,axiom,
% 21.40/21.33 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 21.40/21.33 => ( 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))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__unfold,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__subset__Sigma,axiom,
% 21.40/21.33 ! [V_A_2,V_r_2,T_b] :
% 21.40/21.33 ( 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))))
% 21.40/21.33 => 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)))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__Int__subset,axiom,
% 21.40/21.33 ! [V_s_2,V_r_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => ( 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))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 21.40/21.33 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => 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)))))) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 21.40/21.33 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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)))))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 21.40/21.33 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 21.40/21.33 => 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 21.40/21.33 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 21.40/21.33 => V_y_2 = V_x_2 ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 21.40/21.33 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 21.40/21.33 => 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 21.40/21.33 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 21.40/21.33 => 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm,axiom,
% 21.40/21.33 ! [T_b] :
% 21.40/21.33 ( class_Groups_Oab__semigroup__mult(T_b)
% 21.40/21.33 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 21.40/21.33 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 21.40/21.33 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 21.40/21.33 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 21.40/21.33 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 21.40/21.33 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => 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) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 21.40/21.33 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => 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)) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 21.40/21.33 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.33 => ? [B_y_H] :
% 21.40/21.33 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 21.40/21.33 & 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)) ) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__insert,axiom,
% 21.40/21.33 ! [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)))))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_r__into__rtrancl,axiom,
% 21.40/21.33 ! [V_r_2,V_p_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 21.40/21.33 ! [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))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__into__rtrancl,axiom,
% 21.40/21.33 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Domain__rtrancl,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Range__rtrancl,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__idemp__self__comp,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_r__comp__rtrancl__eq,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Image__closed__trancl,axiom,
% 21.40/21.33 ! [V_X_2,V_r_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__mono,axiom,
% 21.40/21.33 ! [V_s_2,V_r_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__subset,axiom,
% 21.40/21.33 ! [V_S_2,V_R_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => ( 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)))
% 21.40/21.33 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__subset__rtrancl,axiom,
% 21.40/21.33 ! [V_s_2,V_r_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__Un__subset,axiom,
% 21.40/21.33 ! [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)))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__Un__rtrancl,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_in__rtrancl__UnI,axiom,
% 21.40/21.33 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 21.40/21.33 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 21.40/21.33 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 21.40/21.33 => 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)))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 21.40/21.33 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 21.40/21.33 => 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 21.40/21.33 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( 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_c_2)),V_r_2))
% 21.40/21.33 => 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__trans,axiom,
% 21.40/21.33 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 21.40/21.33 => 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_refl__rtrancl,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__idemp,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__trancl__absorb,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__rtrancl__absorb,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__unfold__left,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__unfold__right,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__eq__or__trancl,axiom,
% 21.40/21.33 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 <=> ( V_x_2 = V_y_2
% 21.40/21.33 | ( V_x_2 != V_y_2
% 21.40/21.33 & 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))) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__into__trancl2,axiom,
% 21.40/21.33 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 21.40/21.33 => 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtranclD,axiom,
% 21.40/21.33 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( V_a_2 = V_b_2
% 21.40/21.33 | ( V_a_2 != V_b_2
% 21.40/21.33 & 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))) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__into__trancl1,axiom,
% 21.40/21.33 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( 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_c_2)),V_r_2))
% 21.40/21.33 => 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__rtrancl__trancl,axiom,
% 21.40/21.33 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 21.40/21.33 => 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__trancl__trancl,axiom,
% 21.40/21.33 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( 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)))
% 21.40/21.33 => 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Not__Domain__rtrancl,axiom,
% 21.40/21.33 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 21.40/21.33 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 21.40/21.33 => ( 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)))
% 21.40/21.33 <=> V_x_2 = V_y_2 ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_acc__downwards,axiom,
% 21.40/21.33 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 21.40/21.33 => ( 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)))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_acc__downwards__aux,axiom,
% 21.40/21.33 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__insert,axiom,
% 21.40/21.33 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.33 & ~ 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_acyclic__insert,axiom,
% 21.40/21.33 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 21.40/21.33 & ~ 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_pred__nat__trancl__eq__le,axiom,
% 21.40/21.33 ! [V_n_2,V_m_2] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__subset__Sigma__aux,axiom,
% 21.40/21.33 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( 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))))
% 21.40/21.33 => ( V_a_2 = V_b_2
% 21.40/21.33 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_irrefl__tranclI,axiom,
% 21.40/21.33 ! [V_x_2,V_r_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => ~ 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INFI__fold__inf,axiom,
% 21.40/21.33 ! [V_f_2,V_A_2,T_b,T_c] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INF1__E,axiom,
% 21.40/21.33 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 21.40/21.33 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INF1__D,axiom,
% 21.40/21.33 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__E,axiom,
% 21.40/21.33 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 21.40/21.33 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__D,axiom,
% 21.40/21.33 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INF2__E,axiom,
% 21.40/21.33 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 21.40/21.33 ( 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_c_2))
% 21.40/21.33 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 21.40/21.33 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INF2__D,axiom,
% 21.40/21.33 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 21.40/21.33 ( 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_c_2))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_finite__INT,axiom,
% 21.40/21.33 ! [V_A_2,T_c,V_I_2,T_b] :
% 21.40/21.33 ( ? [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 21.40/21.33 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__converse,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__converse,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__converse__trancl,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 21.40/21.33 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_acyclic__converse,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 21.40/21.33 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__extend__simps_I1_J,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 21.40/21.33 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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 )
% 21.40/21.33 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__extend__simps_I2_J,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 21.40/21.33 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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 )
% 21.40/21.33 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INF__const,axiom,
% 21.40/21.33 ! [V_M_2,T_b,V_A_2,T_c] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 21.40/21.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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 ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__constant,axiom,
% 21.40/21.33 ! [V_c_2,T_c,T_b,V_A_2] :
% 21.40/21.33 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 21.40/21.33 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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_c_2)) = V_c_2 ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__empty,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_converse__rel__comp,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__insert,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__Un,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__subset__iff,axiom,
% 21.40/21.33 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 <=> ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 21.40/21.33 => 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Un__INT__distrib2,axiom,
% 21.40/21.33 ! [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))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__extend__simps_I6_J,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Un__INT__distrib,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__extend__simps_I7_J,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__simps_I6_J,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__simps_I7_J,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_converse__Un,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_le__INF__iff,axiom,
% 21.40/21.33 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => ( 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)))
% 21.40/21.33 <=> ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__simps_I5_J,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__extend__simps_I5_J,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__insert__distrib,axiom,
% 21.40/21.33 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 21.40/21.33 => 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__lower,axiom,
% 21.40/21.33 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Image__INT__subset,axiom,
% 21.40/21.33 ! [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)))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__simps_I10_J,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__extend__simps_I10_J,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_vimage__INT,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__iff,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 <=> ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__absorb,axiom,
% 21.40/21.33 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 21.40/21.33 => 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) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_converseD,axiom,
% 21.40/21.33 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_converseI,axiom,
% 21.40/21.33 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_converse__iff,axiom,
% 21.40/21.33 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 <=> 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INF__INT__eq,axiom,
% 21.40/21.33 ! [V_x_2,V_r_2,T_c,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 <=> 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INF__INT__eq2,axiom,
% 21.40/21.33 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 <=> 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.33 ( 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)
% 21.40/21.33 <=> ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 21.40/21.33 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.33 ( 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))
% 21.40/21.33 <=> ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 21.40/21.33 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_finite__converse,axiom,
% 21.40/21.33 ! [V_r_2,T_c,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 21.40/21.33 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INF__less__iff,axiom,
% 21.40/21.33 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 21.40/21.33 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 & class_Orderings_Olinorder(T_b) )
% 21.40/21.33 => ( 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))
% 21.40/21.33 <=> ? [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 21.40/21.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_converse__Int,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__Int__distrib,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INF__commute,axiom,
% 21.40/21.33 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INFI__apply,axiom,
% 21.40/21.33 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_converse__inv__image,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Field__converse,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_converse__INTER,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_converse__converse,axiom,
% 21.40/21.33 ! [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 ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INFI__bool__eq,axiom,
% 21.40/21.33 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_refl__on__converse,axiom,
% 21.40/21.33 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.33 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 21.40/21.33 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_converse__Id__on,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Pow__INT__eq,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Collect__ball__eq,axiom,
% 21.40/21.33 ! [V_P_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_P_2))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_UN__extend__simps_I7_J,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_UN__simps_I7_J,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_converse__UNION,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__extend__simps_I9_J,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__simps_I9_J,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Compl__UN,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Compl__INT,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_equiv__comp__eq,axiom,
% 21.40/21.33 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.33 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.33 => 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 ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Range__converse,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Domain__converse,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Range__def,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INF__subset,axiom,
% 21.40/21.33 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.33 => 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INTER__def,axiom,
% 21.40/21.33 ! [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)))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__simps_I2_J,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 21.40/21.33 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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)) )
% 21.40/21.33 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__simps_I1_J,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 21.40/21.33 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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)) )
% 21.40/21.33 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__simps_I3_J,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 21.40/21.33 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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)) )
% 21.40/21.33 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__extend__simps_I3_J,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 21.40/21.33 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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) )
% 21.40/21.33 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__extend__simps_I4_J,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 21.40/21.33 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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 )
% 21.40/21.33 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__converseD,axiom,
% 21.40/21.33 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 21.40/21.33 ( 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))))
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__converseI,axiom,
% 21.40/21.33 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => 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)))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__converseD,axiom,
% 21.40/21.33 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 21.40/21.33 ( 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))))
% 21.40/21.33 => 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)))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__converseI,axiom,
% 21.40/21.33 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 21.40/21.33 ( 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))))
% 21.40/21.33 => 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)))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Image__subset__eq,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 <=> 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))))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INF__leI,axiom,
% 21.40/21.33 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 21.40/21.33 => 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_refl__on__comp__subset,axiom,
% 21.40/21.33 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.33 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_comp__equivI,axiom,
% 21.40/21.33 ! [V_A_2,V_r_2,T_b] :
% 21.40/21.33 ( 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
% 21.40/21.33 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 21.40/21.33 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_finite__acyclic__wf__converse,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 21.40/21.33 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 21.40/21.33 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__greaterThan__UNIV,axiom,
% 21.40/21.33 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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__simps_I4_J,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 21.40/21.33 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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)) )
% 21.40/21.33 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_converse__def,axiom,
% 21.40/21.33 ! [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))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_inf__INFI__fold__inf,axiom,
% 21.40/21.33 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_sequence__trans,axiom,
% 21.40/21.33 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 21.40/21.33 ( ! [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)))
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_reflcl__set__eq,axiom,
% 21.40/21.33 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 <=> 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)))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_IdI,axiom,
% 21.40/21.33 ! [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))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INF1__iff,axiom,
% 21.40/21.33 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 <=> ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INF2__iff,axiom,
% 21.40/21.33 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 21.40/21.33 ( 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_c_2))
% 21.40/21.33 <=> ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_converse__Id,axiom,
% 21.40/21.33 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Image__Id,axiom,
% 21.40/21.33 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 21.40/21.33
% 21.40/21.33 fof(fact_R__O__Id,axiom,
% 21.40/21.33 ! [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 ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Id__O__R,axiom,
% 21.40/21.33 ! [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 ).
% 21.40/21.33
% 21.40/21.33 fof(fact_pair__in__Id__conv,axiom,
% 21.40/21.33 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 <=> V_a_2 = V_b_2 ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Domain__Id,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__empty,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Range__Id,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__reflcl,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__reflcl__absorb,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_refl__Id,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__r__diff__Id,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_pair__leq__def,axiom,
% 21.40/21.33 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))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_reflcl__trancl,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__reflcl,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__unfold,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_refl__reflcl,axiom,
% 21.40/21.33 ! [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))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Id__def,axiom,
% 21.40/21.33 ! [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))))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_irrefl__diff__Id,axiom,
% 21.40/21.33 ! [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))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__Int__subset,axiom,
% 21.40/21.33 ! [V_r_2,V_s_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => ( 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))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Image__INT__eq,axiom,
% 21.40/21.33 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 21.40/21.33 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 21.40/21.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_image__INT,axiom,
% 21.40/21.33 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 21.40/21.33 => ( ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 21.40/21.33 => 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)) )
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 21.40/21.33 => 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)) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_single__valued__Id,axiom,
% 21.40/21.33 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_single__valued__rel__comp,axiom,
% 21.40/21.33 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 21.40/21.33 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 21.40/21.33 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_single__valued__subset,axiom,
% 21.40/21.33 ! [V_s_2,V_r_2,T_c,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 21.40/21.33 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_single__valued__Id__on,axiom,
% 21.40/21.33 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_single__valued__def,axiom,
% 21.40/21.33 ! [V_r_2,T_c,T_b] :
% 21.40/21.33 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 21.40/21.33 <=> ! [B_x,B_y] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => ! [B_z] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => B_y = B_z ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_single__valuedD,axiom,
% 21.40/21.33 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 21.40/21.33 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 21.40/21.33 => ( 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))
% 21.40/21.33 => ( 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))
% 21.40/21.33 => V_y_2 = V_z_2 ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_single__valued__confluent,axiom,
% 21.40/21.33 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 21.40/21.33 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 21.40/21.33 => ( 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)))
% 21.40/21.33 => ( 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)))
% 21.40/21.33 => ( 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)))
% 21.40/21.33 | 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))) ) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Image__Int__eq,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 21.40/21.33 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 21.40/21.33 => 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_total__on__diff__Id,axiom,
% 21.40/21.33 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 21.40/21.33 ! [V_R_2,V_p_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 21.40/21.33 => 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)))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_relpow_Osimps_I1_J,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_single__valued__rel__pow,axiom,
% 21.40/21.33 ! [V_n_2,V_R_2,T_b] :
% 21.40/21.33 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 21.40/21.33 => 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__power,axiom,
% 21.40/21.33 ! [V_R_2,V_p_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 21.40/21.33 <=> ? [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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rel__pow__imp__rtrancl,axiom,
% 21.40/21.33 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_wf__exp,axiom,
% 21.40/21.33 ! [V_R_2,V_n_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_funpow__mult,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_funpow__swap1,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_comp__funpow,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rel__pow__add,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_relpow_Osimps_I2_J,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rel__pow__commute,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rel__pow__1,axiom,
% 21.40/21.33 ! [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 ).
% 21.40/21.33
% 21.40/21.33 fof(fact_total__on__empty,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_total__on__converse,axiom,
% 21.40/21.33 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.33 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 21.40/21.33 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rel__pow__0__E,axiom,
% 21.40/21.33 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => V_x_2 = V_y_2 ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rel__pow__0__I,axiom,
% 21.40/21.33 ! [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))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rel__pow__Suc__I2,axiom,
% 21.40/21.33 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => ( 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)))
% 21.40/21.33 => 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rel__pow__Suc__I,axiom,
% 21.40/21.33 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( 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))
% 21.40/21.33 => 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_funpow_Osimps_I2_J,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_funpow__add,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_funpow_Osimps_I1_J,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_trancl__power,axiom,
% 21.40/21.33 ! [V_R_2,V_p_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 21.40/21.33 <=> ? [B_n] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 21.40/21.33 & 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_total__on__def,axiom,
% 21.40/21.33 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.33 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 21.40/21.33 <=> ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.33 => ! [B_xa] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 21.40/21.33 => ( B_x != B_xa
% 21.40/21.33 => ( 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))
% 21.40/21.33 | 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)) ) ) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_funpow__code__def,axiom,
% 21.40/21.33 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rel__pow__E,axiom,
% 21.40/21.33 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.33 => V_x_2 != V_z_2 )
% 21.40/21.33 => ~ ! [B_y,B_m] :
% 21.40/21.33 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 21.40/21.33 => ( 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)))
% 21.40/21.33 => ~ 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)) ) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rel__pow__E2,axiom,
% 21.40/21.33 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.33 => V_x_2 != V_z_2 )
% 21.40/21.33 => ~ ! [B_y,B_m] :
% 21.40/21.33 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 21.40/21.33 => ( 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))
% 21.40/21.33 => ~ 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))) ) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inf__fold__inf,axiom,
% 21.40/21.33 ! [V_A_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_finite__Inter,axiom,
% 21.40/21.33 ! [V_M_2,T_b] :
% 21.40/21.33 ( ? [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 21.40/21.33 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 21.40/21.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_InterD,axiom,
% 21.40/21.33 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_InterE,axiom,
% 21.40/21.33 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Un__Inter,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inf__less__iff,axiom,
% 21.40/21.33 ! [V_a_2,V_S_2,T_b] :
% 21.40/21.33 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 & class_Orderings_Olinorder(T_b) )
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 21.40/21.33 <=> ? [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 21.40/21.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inter__lower,axiom,
% 21.40/21.33 ! [V_A_2,V_B_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.33 => 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_le__Inf__iff,axiom,
% 21.40/21.33 ! [V_A_2,V_b_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => ( 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)))
% 21.40/21.33 <=> ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inter__insert,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inter__eq,axiom,
% 21.40/21.33 ! [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)))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inter__empty,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inter__anti__mono,axiom,
% 21.40/21.33 ! [V_A_2,V_B_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inter__UNIV,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inf__lower,axiom,
% 21.40/21.33 ! [V_A_2,V_x_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inter__Un__distrib,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inf__singleton,axiom,
% 21.40/21.33 ! [V_a_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => 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 ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inf__empty,axiom,
% 21.40/21.33 ! [T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => 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) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inf__UNIV,axiom,
% 21.40/21.33 ! [T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => 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) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inf__insert,axiom,
% 21.40/21.33 ! [V_A_2,V_a_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INTER__eq__Inter__image,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inter__image__eq,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Int__eq__Inter,axiom,
% 21.40/21.33 ! [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))))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Int__Inter__image,axiom,
% 21.40/21.33 ! [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))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inter__Un__subset,axiom,
% 21.40/21.33 ! [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)))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inf__binary,axiom,
% 21.40/21.33 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => 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) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_inf__Inf__fold__inf,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inf__fin__Inf,axiom,
% 21.40/21.33 ! [V_A_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inf__Sup,axiom,
% 21.40/21.33 ! [V_A_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => 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))))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Sup__Inf,axiom,
% 21.40/21.33 ! [V_A_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => 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)))))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_UnionI,axiom,
% 21.40/21.33 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 21.40/21.33 => 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inter__def,axiom,
% 21.40/21.33 ! [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))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_image__Union,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Sigma__Union,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_UN__simps_I8_J,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_UN__extend__simps_I8_J,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Int__Union2,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Int__Union,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_vimage__Union,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Range__Union,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Domain__Union,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__extend__simps_I8_J,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_INT__simps_I8_J,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Union__UNIV,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_subset__Pow__Union,axiom,
% 21.40/21.33 ! [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)))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_finite__UnionD,axiom,
% 21.40/21.33 ! [V_A_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 21.40/21.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Union__disjoint,axiom,
% 21.40/21.33 ! [V_A_2,V_C_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 <=> ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Union__empty,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Union__mono,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.33 ( 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))
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Sup__le__iff,axiom,
% 21.40/21.33 ! [V_b_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => ( 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))
% 21.40/21.33 <=> ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Union__upper,axiom,
% 21.40/21.33 ! [V_A_2,V_B_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.33 => 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))) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Field__Union,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_less__Sup__iff,axiom,
% 21.40/21.33 ! [V_S_2,V_a_2,T_b] :
% 21.40/21.33 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 & class_Orderings_Olinorder(T_b) )
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 21.40/21.33 <=> ? [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 21.40/21.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Union__Pow__eq,axiom,
% 21.40/21.33 ! [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 ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Union__quotient,axiom,
% 21.40/21.33 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.33 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.33 => 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 ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Union__insert,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Union__Un__distrib,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Union__image__eq,axiom,
% 21.40/21.33 ! [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) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_UNION__eq__Union__image,axiom,
% 21.40/21.33 ! [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)) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Sup__upper,axiom,
% 21.40/21.33 ! [V_A_2,V_x_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => 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))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Sup__empty,axiom,
% 21.40/21.33 ! [T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => 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) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Sup__singleton,axiom,
% 21.40/21.33 ! [V_a_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => 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 ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Sup__insert,axiom,
% 21.40/21.33 ! [V_A_2,V_a_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => 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)) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Sup__UNIV,axiom,
% 21.40/21.33 ! [T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => 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) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Un__eq__Union,axiom,
% 21.40/21.33 ! [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))))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Un__Union__image,axiom,
% 21.40/21.33 ! [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))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Union__Int__subset,axiom,
% 21.40/21.33 ! [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)))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Sup__binary,axiom,
% 21.40/21.33 ! [V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => 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) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_sup__Sup__fold__sup,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Sup__fin__Sup,axiom,
% 21.40/21.33 ! [V_A_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Sup__fold__sup,axiom,
% 21.40/21.33 ! [V_A_2,T_b] :
% 21.40/21.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.33 => 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) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_inj__on__Inter,axiom,
% 21.40/21.33 ! [V_f_2,T_c,T_b,V_S_2] :
% 21.40/21.33 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 21.40/21.33 => ( ! [B_A] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 21.40/21.33 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Inter__subset,axiom,
% 21.40/21.33 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.33 ( ! [B_X] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 21.40/21.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_Union__def,axiom,
% 21.40/21.33 ! [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))) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_finite__Union,axiom,
% 21.40/21.33 ! [V_A_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 21.40/21.33 => ( ! [B_M] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 21.40/21.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 21.40/21.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_insert__partition,axiom,
% 21.40/21.33 ! [V_F_2,V_x_2,T_b] :
% 21.40/21.33 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 21.40/21.33 => ( ! [B_x] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ! [B_xa] :
% 21.40/21.33 ( 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)))
% 21.40/21.33 => ( B_x != B_xa
% 21.40/21.33 => 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)) ) ) )
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_card__partition,axiom,
% 21.40/21.33 ! [V_k_2,V_C_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 21.40/21.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 21.40/21.33 => ( ! [B_c] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 21.40/21.33 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 21.40/21.33 => ( ! [B_c1] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 21.40/21.33 => ! [B_c2] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 21.40/21.33 => ( B_c1 != B_c2
% 21.40/21.33 => 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)) ) ) )
% 21.40/21.33 => 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)) ) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_inj__on__INTER,axiom,
% 21.40/21.33 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 21.40/21.33 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.33 => ( ! [B_i] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 21.40/21.33 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 21.40/21.33 => 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)) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 21.40/21.33 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 21.40/21.33 => ( 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))
% 21.40/21.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.33 => ~ ! [B_y] :
% 21.40/21.33 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 21.40/21.33 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_acyclicI,axiom,
% 21.40/21.33 ! [V_r_2,T_b] :
% 21.40/21.33 ( ! [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)))
% 21.40/21.33 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 21.40/21.33 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
% 21.40/21.33 => ( ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
% 21.40/21.33 => ! [B_y] :
% 21.40/21.33 ( 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_Q_2))
% 21.40/21.33 => B_y = B_x ) )
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rtrancl__Un__separatorE,axiom,
% 21.40/21.33 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
% 21.40/21.33 => ( ! [B_x] :
% 21.40/21.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
% 21.40/21.33 => ! [B_y] :
% 21.40/21.33 ( 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_Q_2))
% 21.40/21.33 => B_x = B_y ) )
% 21.40/21.33 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ) ).
% 21.40/21.33
% 21.40/21.33 fof(fact_rel__pow__Suc__E,axiom,
% 21.40/21.34 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ~ ! [B_y] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ~ 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rel__pow__Suc__E2,axiom,
% 21.40/21.34 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ~ ! [B_y] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => ~ 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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rel__pow__Suc__D2,axiom,
% 21.40/21.34 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ? [B_y] :
% 21.40/21.34 ( 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))
% 21.40/21.34 & 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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_tranclD,axiom,
% 21.40/21.34 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ? [B_z] :
% 21.40/21.34 ( 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))
% 21.40/21.34 & 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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_tranclD2,axiom,
% 21.40/21.34 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ? [B_z] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 & 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 21.40/21.34 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.34 => ( ! [B_x] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 21.40/21.34 => 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_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2))) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 21.40/21.34 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.34 => ( ! [B_x] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2))) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_InterI,axiom,
% 21.40/21.34 ! [V_A_2,V_C_2,T_b] :
% 21.40/21.34 ( ! [B_X] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_inf__le__fold__inf,axiom,
% 21.40/21.34 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 21.40/21.34 ( class_Lattices_Osemilattice__inf(T_b)
% 21.40/21.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.34 => ( ! [B_x] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 21.40/21.34 => 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_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2))) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_fold__sup__le__sup,axiom,
% 21.40/21.34 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 21.40/21.34 ( class_Lattices_Osemilattice__sup(T_b)
% 21.40/21.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.34 => ( ! [B_x] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 21.40/21.34 => 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_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2))) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_IdE,axiom,
% 21.40/21.34 ! [V_p_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 21.40/21.34 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_wf__eq__minimal,axiom,
% 21.40/21.34 ! [V_r_2,T_b] :
% 21.40/21.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 21.40/21.34 <=> ! [B_Q] :
% 21.40/21.34 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 21.40/21.34 => ? [B_x] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 21.40/21.34 & ! [B_y] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 21.40/21.34 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 21.40/21.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 21.40/21.34 => 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)) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_transfer__nat__int__set__cong,axiom,
% 21.40/21.34 ! [V_P_H_2,V_P_2] :
% 21.40/21.34 ( ! [B_x] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 21.40/21.34 => ( hBOOL(hAPP(V_P_2,B_x))
% 21.40/21.34 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 21.40/21.34 => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 21.40/21.34 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 21.40/21.34 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 21.40/21.34 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 21.40/21.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.34 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 21.40/21.34 => 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) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 21.40/21.34 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 21.40/21.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 21.40/21.34 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 21.40/21.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 21.40/21.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 21.40/21.34 => 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) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Int__Collect__mono,axiom,
% 21.40/21.34 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.34 => ( ! [B_x] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 21.40/21.34 => ( hBOOL(hAPP(V_P_2,B_x))
% 21.40/21.34 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2)))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_UnionE,axiom,
% 21.40/21.34 ! [V_C_2,V_A_2,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ~ ! [B_X] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 21.40/21.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__upd__left,axiom,
% 21.40/21.34 ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] :
% 21.40/21.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2)))
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rel__compE,axiom,
% 21.40/21.34 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ~ ! [B_x,B_y,B_z] :
% 21.40/21.34 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 21.40/21.34 => ( 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))
% 21.40/21.34 => ~ 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)) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__upd,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__SomeD,axiom,
% 21.40/21.34 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 21.40/21.34 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 21.40/21.34 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__Some__iff,axiom,
% 21.40/21.34 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 21.40/21.34 ( 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)
% 21.40/21.34 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 21.40/21.34 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 21.40/21.34 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__def,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__empty,axiom,
% 21.40/21.34 ! [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 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_empty__map__add,axiom,
% 21.40/21.34 ! [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 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__None,axiom,
% 21.40/21.34 ! [V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 21.40/21.34 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b)
% 21.40/21.34 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 21.40/21.34 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__find__right,axiom,
% 21.40/21.34 ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] :
% 21.40/21.34 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__assoc,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 21.40/21.34 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 21.40/21.34 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 21.40/21.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 21.40/21.34 ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] :
% 21.40/21.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2)))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_dom__map__add,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_inj__on__map__add__dom,axiom,
% 21.40/21.34 ! [V_m_H_2,V_m_2,T_c,T_b] :
% 21.40/21.34 ( 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))
% 21.40/21.34 <=> 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__comm,axiom,
% 21.40/21.34 ! [V_m2_2,V_m1_2,T_c,T_b] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_finite__range__map__of__map__add,axiom,
% 21.40/21.34 ! [V_l_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( 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)))))
% 21.40/21.34 => 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,c_Map_Omap__of(T_c,T_b,V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_converseE,axiom,
% 21.40/21.34 ! [V_r_2,V_yx_2,T_c,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ~ ! [B_x,B_y] :
% 21.40/21.34 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 21.40/21.34 => ~ 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_finite__dom__map__of,axiom,
% 21.40/21.34 ! [V_l_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_l_2)))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_finite__range__map__of,axiom,
% 21.40/21.34 ! [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),c_Map_Omap__of(T_c,T_b,V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__map__of__foldr,axiom,
% 21.40/21.34 ! [V_ps_2,V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_full__small__int__def,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_small_H_Osimps,axiom,
% 21.40/21.34 ! [V_f_2,V_i_2,V_d_2] :
% 21.40/21.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 21.40/21.34 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 21.40/21.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_small_H_Opsimps,axiom,
% 21.40/21.34 ! [V_i_2,V_d_2,V_f_2] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 21.40/21.34 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 21.40/21.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 21.40/21.34 => 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)) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_small__int__def,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_small__prod__def,axiom,
% 21.40/21.34 ! [V_d_2,V_f_2,T_b,T_c] :
% 21.40/21.34 ( ( class_Smallcheck_Osmall(T_c)
% 21.40/21.34 & class_Smallcheck_Osmall(T_b) )
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_small_H_Opinduct,axiom,
% 21.40/21.34 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => ( ! [B_f,B_d,B_i] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 21.40/21.34 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 21.40/21.34 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) )
% 21.40/21.34 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) )
% 21.40/21.34 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_body__def,axiom,
% 21.40/21.34 c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__mapk__SomeI,axiom,
% 21.40/21.34 ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] :
% 21.40/21.34 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.34 => ( 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)
% 21.40/21.34 => 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__comp__def,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_inj__mapI,axiom,
% 21.40/21.34 ! [V_f_2,T_c,T_b] :
% 21.40/21.34 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__comp__Some__iff,axiom,
% 21.40/21.34 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 21.40/21.34 ( 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)
% 21.40/21.34 <=> ? [B_k_H] :
% 21.40/21.34 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 21.40/21.34 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__comp__simps_I2_J,axiom,
% 21.40/21.34 ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] :
% 21.40/21.34 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__comp__simps_I1_J,axiom,
% 21.40/21.34 ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] :
% 21.40/21.34 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__map,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_List_Omap_Ocompositionality,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__comp__map,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_List_Omap_Ocomp,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__injective,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 21.40/21.34 => V_xs_2 = V_ys_2 ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_inj__mapD,axiom,
% 21.40/21.34 ! [V_f_2,T_c,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_inj__map__eq__map,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 21.40/21.34 => ( 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)
% 21.40/21.34 <=> V_xs_2 = V_ys_2 ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_inj__map,axiom,
% 21.40/21.34 ! [V_f_2,T_c,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__ident,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_List_Omap_Oidentity,axiom,
% 21.40/21.34 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_List_Omap_Oid,axiom,
% 21.40/21.34 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_foldr__map,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__comp__empty_I1_J,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__comp__empty_I2_J,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__comp__None__iff,axiom,
% 21.40/21.34 ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 21.40/21.34 ( 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)
% 21.40/21.34 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c)
% 21.40/21.34 | ? [B_k_H] :
% 21.40/21.34 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 21.40/21.34 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__map,axiom,
% 21.40/21.34 ! [V_xs_2,V_f_2,T_d,T_c,T_b] : 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)),c_Map_Omap__of(T_b,T_d,V_xs_2)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__map__keys,axiom,
% 21.40/21.34 ! [V_m_2,T_c,V_xs_2,T_b] :
% 21.40/21.34 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Map_Odom(T_b,T_c,V_m_2)
% 21.40/21.34 => 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 ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_finite__set,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__map,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__eq__conv,axiom,
% 21.40/21.34 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 21.40/21.34 ( 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)
% 21.40/21.34 <=> ! [B_x] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 21.40/21.34 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Option_Omap_Oidentity,axiom,
% 21.40/21.34 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Option_Omap_Oid,axiom,
% 21.40/21.34 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_dom__option__map,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_infinite__UNIV__listI,axiom,
% 21.40/21.34 ! [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)))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Option_Omap_Ocomp,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Option_Omap_Ocompositionality,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_option__map__comp,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_option__map__o__sum__case,axiom,
% 21.40/21.34 ! [V_h_2,V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),tc_sum(T_b,T_c),hAPP(c_Option_Omap(T_e,T_d),V_f_2)),c_Sum__Type_Osum_Osum__case(T_b,tc_Option_Ooption(T_e),T_c,V_g_2,V_h_2)) = c_Sum__Type_Osum_Osum__case(T_b,tc_Option_Ooption(T_d),T_c,hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),T_b,hAPP(c_Option_Omap(T_e,T_d),V_f_2)),V_g_2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),T_c,hAPP(c_Option_Omap(T_e,T_d),V_f_2)),V_h_2)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_option__map__o__empty,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_option__map__Some,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_option__map__eq__Some,axiom,
% 21.40/21.34 ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] :
% 21.40/21.34 ( 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)
% 21.40/21.34 <=> ? [B_z] :
% 21.40/21.34 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z)
% 21.40/21.34 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_option__map__None,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_option__map__is__None,axiom,
% 21.40/21.34 ! [V_opt_2,V_f_2,T_b,T_c] :
% 21.40/21.34 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b)
% 21.40/21.34 <=> V_opt_2 = c_Option_Ooption_ONone(T_c) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_option__map__o__map__upd,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_inj__on__map__eq__map,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ( 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)
% 21.40/21.34 <=> V_xs_2 = V_ys_2 ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__inj__on,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => ( 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)))
% 21.40/21.34 => V_xs_2 = V_ys_2 ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__fun__upd,axiom,
% 21.40/21.34 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 21.40/21.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_inj__on__mapI,axiom,
% 21.40/21.34 ! [V_A_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__eq__dom,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 21.40/21.34 ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__SomeD,axiom,
% 21.40/21.34 ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__is__SomeD,axiom,
% 21.40/21.34 ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_dom__map__of__conv__image__fst,axiom,
% 21.40/21.34 ! [V_xys_2,T_c,T_b] : c_Map_Odom(T_b,T_c,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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__eq__None__iff,axiom,
% 21.40/21.34 ! [V_x_2,V_xys_2,T_b,T_c] :
% 21.40/21.34 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b)
% 21.40/21.34 <=> ~ 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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Option_Omap__def,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_WT__bodies__def,axiom,
% 21.40/21.34 ( c_Com_OWT__bodies
% 21.40/21.34 <=> ! [B_x] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__map__restrict,axiom,
% 21.40/21.34 ! [V_ks_2,V_f_2,T_c,T_b] : 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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_ran__distinct,axiom,
% 21.40/21.34 ! [V_al_2,T_c,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => c_Map_Oran(T_b,T_c,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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__map__of__compr,axiom,
% 21.40/21.34 ! [V_xs_2,T_c,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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),c_Map_Omap__of(T_b,T_c,V_xs_2)))),c_Option_Ooption_OSome(T_c)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__map,axiom,
% 21.40/21.34 ! [V_xs_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 21.40/21.34 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 21.40/21.34 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__inject__set,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ( 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)))
% 21.40/21.34 => ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
% 21.40/21.34 <=> 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) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__is__SomeI,axiom,
% 21.40/21.34 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ( 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)))
% 21.40/21.34 => 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__eq__Some__iff,axiom,
% 21.40/21.34 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ( 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)
% 21.40/21.34 <=> 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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Some__eq__map__of__iff,axiom,
% 21.40/21.34 ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ( hAPP(c_Option_Ooption_OSome(T_c),V_y_2) = hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2)
% 21.40/21.34 <=> 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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_greaterThanLessThan__upto,axiom,
% 21.40/21.34 ! [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)))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_weak__map__of__SomeI,axiom,
% 21.40/21.34 ! [V_l_2,V_x_2,V_k_2,T_c,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ? [B_x] : hAPP(c_Map_Omap__of(T_b,T_c,V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_x) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_atLeastAtMost__upto,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__upto,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__upto,axiom,
% 21.40/21.34 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_atLeastLessThan__upto,axiom,
% 21.40/21.34 ! [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)))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_greaterThanAtMost__upto,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nat__list__def,axiom,
% 21.40/21.34 ! [V_l_2] :
% 21.40/21.34 ( c_List_Onat__list(V_l_2)
% 21.40/21.34 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__remove1__eq,axiom,
% 21.40/21.34 ! [V_x_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 21.40/21.34 => 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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_in__set__remove1,axiom,
% 21.40/21.34 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 21.40/21.34 ( V_a_2 != V_b_2
% 21.40/21.34 => ( 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))))
% 21.40/21.34 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_notin__set__remove1,axiom,
% 21.40/21.34 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => ~ 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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_remove1__idem,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__remove1__subset,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_remove1__commute,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__remove1,axiom,
% 21.40/21.34 ! [V_x,V_xs,T_a] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 21.40/21.34 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_sorted__list__of__set__remove,axiom,
% 21.40/21.34 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__zip__map,axiom,
% 21.40/21.34 ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => 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)) )
% 21.40/21.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__zipI2,axiom,
% 21.40/21.34 ! [V_xs,T_b,V_ys,T_a] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 21.40/21.34 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__zipI1,axiom,
% 21.40/21.34 ! [V_ys,T_b,V_xs,T_a] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 21.40/21.34 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__same__conv__map,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__map__fst__snd,axiom,
% 21.40/21.34 ! [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 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__zip__map2,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__zip__map,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_in__set__zipE,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__zip__rightD,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__zip__leftD,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__same,axiom,
% 21.40/21.34 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 & V_a_2 = V_b_2 ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__map2,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__map1,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__map__map,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_sorted__list__of__set__insert,axiom,
% 21.40/21.34 ! [V_x_2,V_A_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.34 => 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)))))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__zip__upd,axiom,
% 21.40/21.34 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => ( 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)
% 21.40/21.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
% 21.40/21.34 => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),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)),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))
% 21.40/21.34 => c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2)) ) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__zip,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__insort,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_c)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_insort__left__comm,axiom,
% 21.40/21.34 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_insort__key__left__comm,axiom,
% 21.40/21.34 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_neq__if__length__neq,axiom,
% 21.40/21.34 ! [V_ys,V_xs,T_a] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => V_xs != V_ys ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__insort,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_c)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_fun__left__comm__insort,axiom,
% 21.40/21.34 ! [T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lexn__length,axiom,
% 21.40/21.34 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 21.40/21.34 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__eq__imp__length__eq,axiom,
% 21.40/21.34 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__map,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_remove1__insort,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => 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 ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_card__length,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_card__distinct,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__card,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__zip__inject,axiom,
% 21.40/21.34 ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => ( 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)
% 21.40/21.34 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 21.40/21.34 => ( c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))
% 21.40/21.34 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__fst__zip,axiom,
% 21.40/21.34 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => 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 ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__snd__zip,axiom,
% 21.40/21.34 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => 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 ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__insort,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_c)
% 21.40/21.34 => ( 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)))
% 21.40/21.34 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__pos__if__in__set,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__eq__conv,axiom,
% 21.40/21.34 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 21.40/21.34 <=> ( 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
% 21.40/21.34 & 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 ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lenlex__conv,axiom,
% 21.40/21.34 ! [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)))))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lenlex__def,axiom,
% 21.40/21.34 ! [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)))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_finite__lists__length__eq,axiom,
% 21.40/21.34 ! [V_n_2,V_A_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.34 => 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))))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__eq__iff__zip__eq,axiom,
% 21.40/21.34 ! [T_b,V_ys_2,V_xs_2] :
% 21.40/21.34 ( V_xs_2 = V_ys_2
% 21.40/21.34 <=> ( 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)
% 21.40/21.34 & ! [B_x] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__zip__is__None,axiom,
% 21.40/21.34 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => ( 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)
% 21.40/21.34 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__zip__is__Some,axiom,
% 21.40/21.34 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 <=> ? [B_y] : 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__remove1,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => 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)) )
% 21.40/21.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_dom__map__of__zip,axiom,
% 21.40/21.34 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 21.40/21.34 => c_Map_Odom(T_b,T_c,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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_finite__lists__length__le,axiom,
% 21.40/21.34 ! [V_n_2,V_A_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.34 => 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))))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Nitpick_Ocard_H__def,axiom,
% 21.40/21.34 ! [V_A_2,T_b] :
% 21.40/21.34 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.34 => 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)))) )
% 21.40/21.34 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.34 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__iff__zip,axiom,
% 21.40/21.34 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 <=> ( 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)
% 21.40/21.34 & ! [B_x] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => 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)) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__rtrancl__refl,axiom,
% 21.40/21.34 ! [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)))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__eq__len,axiom,
% 21.40/21.34 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__rtrancl__trans,axiom,
% 21.40/21.34 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 21.40/21.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__mono,axiom,
% 21.40/21.34 ! [V_s_2,V_r_2,T_b] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrelp__listrel__eq,axiom,
% 21.40/21.34 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lexn_Osimps_I2_J,axiom,
% 21.40/21.34 ! [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)))))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_impossible__Cons,axiom,
% 21.40/21.34 ! [V_x,V_ys,V_xs,T_a] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__ConsD,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => ( V_y_2 = V_x_2
% 21.40/21.34 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__Cons__Cons,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__subset__Cons,axiom,
% 21.40/21.34 ! [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)))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_foldr_Osimps_I2_J,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_not__Cons__self,axiom,
% 21.40/21.34 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_not__Cons__self2,axiom,
% 21.40/21.34 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list_Oinject,axiom,
% 21.40/21.34 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 <=> ( V_a_2 = V_a_H_2
% 21.40/21.34 & V_list_2 = V_list_H_2 ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrelp_Oequations_I2_J,axiom,
% 21.40/21.34 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 21.40/21.34 ( 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))
% 21.40/21.34 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 21.40/21.34 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrelp_OCons,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 21.40/21.34 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map_Osimps_I2_J,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_remove1_Osimps_I2_J,axiom,
% 21.40/21.34 ! [V_xs,T_a,V_y,V_x] :
% 21.40/21.34 ( ( V_x = V_y
% 21.40/21.34 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 21.40/21.34 & ( V_x != V_y
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_insort__key_Osimps_I2_J,axiom,
% 21.40/21.34 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => ( ( 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)))
% 21.40/21.34 => 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)) )
% 21.40/21.34 & ( ~ 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)))
% 21.40/21.34 => 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)) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct_Osimps_I2_J,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 21.40/21.34 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__Cons__code_I2_J,axiom,
% 21.40/21.34 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 21.40/21.34 ( ( V_l = V_k
% 21.40/21.34 => 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) )
% 21.40/21.34 & ( V_l != V_k
% 21.40/21.34 => 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_Map_Omap__of(T_b,T_c,V_ps),V_k) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list_Osize_I4_J,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel_OCons,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of_Osimps_I2_J,axiom,
% 21.40/21.34 ! [V_ps_2,V_p_2,T_c,T_b] : 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)),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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Cons__in__lex,axiom,
% 21.40/21.34 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 <=> ( ( 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))
% 21.40/21.34 & 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) )
% 21.40/21.34 | ( V_x_2 = V_y_2
% 21.40/21.34 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__Cons,axiom,
% 21.40/21.34 ! [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))))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__Cons__def,axiom,
% 21.40/21.34 ! [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)))))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__Cons1,axiom,
% 21.40/21.34 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 => ~ ! [B_y,B_ys] :
% 21.40/21.34 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 21.40/21.34 => ( 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))
% 21.40/21.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__Cons2,axiom,
% 21.40/21.34 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 => ~ ! [B_x,B_xs] :
% 21.40/21.34 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 21.40/21.34 => ( 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))
% 21.40/21.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__sublist,axiom,
% 21.40/21.34 ! [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)))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_pick_Osimps,axiom,
% 21.40/21.34 ! [V_xs,V_x,T_a,V_i] :
% 21.40/21.34 ( ( 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)))
% 21.40/21.34 => 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) )
% 21.40/21.34 & ( ~ 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)))
% 21.40/21.34 => 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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__sublistI,axiom,
% 21.40/21.34 ! [V_I_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 21.40/21.34 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_notin__set__sublistI,axiom,
% 21.40/21.34 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => ~ 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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_in__set__sublistD,axiom,
% 21.40/21.34 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__sublist__subset,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_select__weight__cons__zero,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_pick__member,axiom,
% 21.40/21.34 ! [V_xs_2,T_b,V_i_2] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => 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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__simps_I2_J,axiom,
% 21.40/21.34 ! [V_xs,V_x,T_a] :
% 21.40/21.34 ( class_Groups_Omonoid__add(T_a)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__subtractf,axiom,
% 21.40/21.34 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( class_Groups_Oab__group__add(T_b)
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__mult__const,axiom,
% 21.40/21.34 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( class_Rings_Osemiring__0(T_b)
% 21.40/21.34 => 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_c_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_c_2) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__const__mult,axiom,
% 21.40/21.34 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
% 21.40/21.34 ( class_Rings_Osemiring__0(T_b)
% 21.40/21.34 => 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_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__addf,axiom,
% 21.40/21.34 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__0,axiom,
% 21.40/21.34 ! [V_xs_2,T_c,T_b] :
% 21.40/21.34 ( class_Groups_Omonoid__add(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__abs,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 21.40/21.34 => 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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_uminus__listsum__map,axiom,
% 21.40/21.34 ! [V_xs_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( class_Groups_Oab__group__add(T_b)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.34 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_select__weight__def,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 21.40/21.34 ! [V_f_2,V_xs_2,T_b,T_c] :
% 21.40/21.34 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.34 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 21.40/21.34 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 21.40/21.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 21.40/21.34 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 21.40/21.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__triv,axiom,
% 21.40/21.34 ! [V_xs_2,V_r_2,T_c,T_b] :
% 21.40/21.34 ( class_Rings_Osemiring__1(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__map__remove1,axiom,
% 21.40/21.34 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 21.40/21.34 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => 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)))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_select__weight__member,axiom,
% 21.40/21.34 ! [V_s_2,V_xs_2,T_b] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => 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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 21.40/21.34 ! [V_f_2,V_A_2,T_b,T_c] :
% 21.40/21.34 ( class_Groups_Ocomm__monoid__add(T_c)
% 21.40/21.34 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.34 => 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))))) )
% 21.40/21.34 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.34 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_insort__insert__insort__key,axiom,
% 21.40/21.34 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => ( ~ 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))))
% 21.40/21.34 => 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 21.40/21.34 ! [V_ns_2] :
% 21.40/21.34 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 <=> ! [B_x] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 21.40/21.34 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__insort__insert,axiom,
% 21.40/21.34 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_c)
% 21.40/21.34 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 21.40/21.34 => 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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_insort__insert__triv,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__insort__insert,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_insort__insert__key__triv,axiom,
% 21.40/21.34 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => ( 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))))
% 21.40/21.34 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_insort__insert__insort,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lexord__cons__cons,axiom,
% 21.40/21.34 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 <=> ( 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))
% 21.40/21.34 | ( V_a_2 = V_b_2
% 21.40/21.34 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__zip,axiom,
% 21.40/21.34 ! [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)))))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__zip,axiom,
% 21.40/21.34 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ( 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)))
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__map,axiom,
% 21.40/21.34 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_elem__le__listsum__nat,axiom,
% 21.40/21.34 ! [V_ns,V_k] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__Cons__Suc,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__Cons__0,axiom,
% 21.40/21.34 ! [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 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth_Osimps,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_all__set__conv__all__nth,axiom,
% 21.40/21.34 ! [V_P_2,V_xs_2,T_b] :
% 21.40/21.34 ( ! [B_x] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => hBOOL(hAPP(V_P_2,B_x)) )
% 21.40/21.34 <=> ! [B_i] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__eq__iff__nth__eq,axiom,
% 21.40/21.34 ! [T_b,V_ys_2,V_xs_2] :
% 21.40/21.34 ( V_xs_2 = V_ys_2
% 21.40/21.34 <=> ( 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)
% 21.40/21.34 & ! [B_i] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__conv__nth,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 21.40/21.34 <=> ! [B_i] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ! [B_j] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ( B_i != B_j
% 21.40/21.34 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__eq__iff__index__eq,axiom,
% 21.40/21.34 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 21.40/21.34 => ( 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)))
% 21.40/21.34 => ( 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)))
% 21.40/21.34 => ( 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)
% 21.40/21.34 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__mem,axiom,
% 21.40/21.34 ! [V_xs_2,T_b,V_n_2] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_in__set__conv__nth,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 <=> ? [B_i] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__Cons_H,axiom,
% 21.40/21.34 ! [V_xs,V_x,T_a,V_n] :
% 21.40/21.34 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 21.40/21.34 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 => 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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__conv__nth,axiom,
% 21.40/21.34 ! [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))))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__Cons__number__of,axiom,
% 21.40/21.34 ! [V_xs,V_x,T_a,V_v] :
% 21.40/21.34 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 => 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 )
% 21.40/21.34 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 => 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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__setsum__nth,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__sublist,axiom,
% 21.40/21.34 ! [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))))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lexord__lex,axiom,
% 21.40/21.34 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 & 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__iff__nth,axiom,
% 21.40/21.34 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 <=> ( 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)
% 21.40/21.34 & ! [B_n] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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)) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_pick__same,axiom,
% 21.40/21.34 ! [V_xs_2,T_b,V_l_2] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_select__def,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lexord__take__index__conv,axiom,
% 21.40/21.34 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 <=> ( ( 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)))
% 21.40/21.34 & 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 )
% 21.40/21.34 | ? [B_i] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 21.40/21.34 & 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)) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_in__set__takeD,axiom,
% 21.40/21.34 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__take,axiom,
% 21.40/21.34 ! [V_xs,T_a,V_n,V_i] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__take__subset,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__take__subset__set__take,axiom,
% 21.40/21.34 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.40/21.34 => 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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__all,axiom,
% 21.40/21.34 ! [V_n,V_xs,T_a] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__take,axiom,
% 21.40/21.34 ! [V_i,V_xs,T_a] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 21.40/21.34 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__take,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__zip,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__take,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__Suc__Cons,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_sublist__upt__eq__take,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__map,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__update__nat,axiom,
% 21.40/21.34 ! [V_n,V_ns,V_k] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_select__weigth__select,axiom,
% 21.40/21.34 ! [T_b,V_xs_2] :
% 21.40/21.34 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__Nil1,axiom,
% 21.40/21.34 ! [V_r_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__Nil2,axiom,
% 21.40/21.34 ! [V_r_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__update__id,axiom,
% 21.40/21.34 ! [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 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__list__update__neq,axiom,
% 21.40/21.34 ! [V_x,V_xs,T_a,V_j,V_i] :
% 21.40/21.34 ( V_i != V_j
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__update__beyond,axiom,
% 21.40/21.34 ! [V_x,V_i,V_xs,T_a] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__Nil,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__eq__Nil,axiom,
% 21.40/21.34 ! [V_xs_2,V_n_2,T_b] :
% 21.40/21.34 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 21.40/21.34 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__0,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list_Osize_I3_J,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__0__conv,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__list__update,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__Cons,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Nil__is__map__conv,axiom,
% 21.40/21.34 ! [V_xs_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 21.40/21.34 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map_Osimps_I1_J,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__update,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__is__Nil__conv,axiom,
% 21.40/21.34 ! [V_xs_2,V_f_2,T_b,T_c] :
% 21.40/21.34 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 21.40/21.34 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__update,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_update__zip,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_sublist__nil,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_sublist__empty,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_insort__key_Osimps_I1_J,axiom,
% 21.40/21.34 ! [V_x_2,V_f_2,T_b,T_c] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_c)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__update__code_I3_J,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list_Osimps_I3_J,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list_Osimps_I2_J,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__update__code_I2_J,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__update_Osimps_I2_J,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_sorted__list__of__set__empty,axiom,
% 21.40/21.34 ! [T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip_Osimps_I1_J,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__Nil,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_upto__empty,axiom,
% 21.40/21.34 ! [V_i,V_j] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 21.40/21.34 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_foldr_Osimps_I1_J,axiom,
% 21.40/21.34 ! [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 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__Cons__code_I1_J,axiom,
% 21.40/21.34 ! [V_k,T_a,T_b] : 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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of_Osimps_I1_J,axiom,
% 21.40/21.34 ! [V_x_1,T_b,T_a] : 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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__update__nonempty,axiom,
% 21.40/21.34 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 21.40/21.34 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 21.40/21.34 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__update_Osimps_I1_J,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__update__code_I1_J,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__update__overwrite,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__update__swap,axiom,
% 21.40/21.34 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 21.40/21.34 ( V_i != V_i_H
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_remove1_Osimps_I1_J,axiom,
% 21.40/21.34 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct_Osimps_I1_J,axiom,
% 21.40/21.34 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_insort__not__Nil,axiom,
% 21.40/21.34 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_c)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrelp_ONil,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrelp_Oequations_I1_J,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__empty2,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 21.40/21.34 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__empty,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 21.40/21.34 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__simps_I1_J,axiom,
% 21.40/21.34 ! [T_a] :
% 21.40/21.34 ( class_Groups_Omonoid__add(T_a)
% 21.40/21.34 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__greater__0__conv,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__update__subsetI,axiom,
% 21.40/21.34 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__1__Cons,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__update__subset__insert,axiom,
% 21.40/21.34 ! [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)))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__list__update__eq,axiom,
% 21.40/21.34 ! [V_x,V_xs,T_a,V_i] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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 ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__update__same__conv,axiom,
% 21.40/21.34 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 21.40/21.34 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__list__update,axiom,
% 21.40/21.34 ! [V_x,V_j,V_xs,T_a,V_i] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ( ( V_i = V_j
% 21.40/21.34 => 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 )
% 21.40/21.34 & ( V_i != V_j
% 21.40/21.34 => 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) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel_ONil,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lexord__Nil__right,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Nil2__notin__lex,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Nil__notin__lex,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__update__memI,axiom,
% 21.40/21.34 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_upto_Osimps,axiom,
% 21.40/21.34 ! [V_j,V_i] :
% 21.40/21.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 21.40/21.34 => 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)) )
% 21.40/21.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 21.40/21.34 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_sublist__singleton,axiom,
% 21.40/21.34 ! [V_x_2,T_b,V_A_2] :
% 21.40/21.34 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 21.40/21.34 => 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)) )
% 21.40/21.34 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 21.40/21.34 => 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__Cons_H,axiom,
% 21.40/21.34 ! [V_xs,V_x,T_a,V_n] :
% 21.40/21.34 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 => 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) )
% 21.40/21.34 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_upto__rec__number__of,axiom,
% 21.40/21.34 ! [V_n,V_m] :
% 21.40/21.34 ( ( 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)))
% 21.40/21.34 => 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))) )
% 21.40/21.34 & ( ~ 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)))
% 21.40/21.34 => 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_select,axiom,
% 21.40/21.34 ! [V_s_2,T_b,V_xs_2] :
% 21.40/21.34 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__Nil,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__Cons__sing__Nil,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__Cons__number__of,axiom,
% 21.40/21.34 ! [V_xs,V_x,T_a,V_v] :
% 21.40/21.34 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 => 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) )
% 21.40/21.34 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__list__update,axiom,
% 21.40/21.34 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 21.40/21.34 => ( ~ 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))))))
% 21.40/21.34 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_upto_Opsimps,axiom,
% 21.40/21.34 ! [V_j_2,V_i_2] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 21.40/21.34 => 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)) )
% 21.40/21.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 21.40/21.34 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_anamorph_Osimps,axiom,
% 21.40/21.34 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 21.40/21.34 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 21.40/21.34 => 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) )
% 21.40/21.34 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 21.40/21.34 => 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))))),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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listset_Osimps_I1_J,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__Cons1,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list_Osimps_I5_J,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list_Osimps_I4_J,axiom,
% 21.40/21.34 ! [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 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listset_Osimps_I2_J,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__Cons,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_upto_Opinduct,axiom,
% 21.40/21.34 ! [V_P_2,V_a1_2,V_a0_2] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ( ! [B_i,B_j] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 21.40/21.34 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
% 21.40/21.34 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 21.40/21.34 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__upd__upds__conv__if,axiom,
% 21.40/21.34 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] :
% 21.40/21.34 ( ( 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))))
% 21.40/21.34 => 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) )
% 21.40/21.34 & ( ~ 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))))
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__upds__Nil1,axiom,
% 21.40/21.34 ! [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 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__upds__Nil2,axiom,
% 21.40/21.34 ! [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 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__upds__apply__nontin,axiom,
% 21.40/21.34 ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__add__upds,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__upds__Cons,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__upds__list__update2__drop,axiom,
% 21.40/21.34 ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => ( 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)))
% 21.40/21.34 => 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__upds__twist,axiom,
% 21.40/21.34 ! [V_bs_2,V_b_2,V_m_2,T_c,V_as_2,V_a_2,T_b] :
% 21.40/21.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2)))
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_restrict__map__upds,axiom,
% 21.40/21.34 ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => ( 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))
% 21.40/21.34 => 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_dom__map__upds,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__upds__append1,axiom,
% 21.40/21.34 ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_sublist__Cons,axiom,
% 21.40/21.34 ! [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)))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append1__eq__conv,axiom,
% 21.40/21.34 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 <=> ( V_xs_2 = V_ys_2
% 21.40/21.34 & V_x_2 = V_y_2 ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Cons__eq__append__conv,axiom,
% 21.40/21.34 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 21.40/21.34 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 21.40/21.34 | ? [B_ys_H] :
% 21.40/21.34 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 21.40/21.34 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__eq__Cons__conv,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 21.40/21.34 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 21.40/21.34 | ? [B_ys_H] :
% 21.40/21.34 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 21.40/21.34 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_fun__upds__append2__drop,axiom,
% 21.40/21.34 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_fun__upds__append__drop,axiom,
% 21.40/21.34 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__append__length,axiom,
% 21.40/21.34 ! [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 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Cons__eq__appendI,axiom,
% 21.40/21.34 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 21.40/21.34 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 21.40/21.34 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 21.40/21.34 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__Cons,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__update__length,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__update__append1,axiom,
% 21.40/21.34 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__append__length__plus,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__append,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__append,axiom,
% 21.40/21.34 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => ( 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)
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__append,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_remove1__append,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => 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) )
% 21.40/21.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_foldr__append,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__of__append,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,T_c,T_b] : 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,c_Map_Omap__of(T_b,T_c,V_ys_2),c_Map_Omap__of(T_b,T_c,V_xs_2)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__assoc,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__eq__append__conv2,axiom,
% 21.40/21.34 ! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_tsa_2)
% 21.40/21.34 <=> ? [B_us] :
% 21.40/21.34 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 21.40/21.34 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2 )
% 21.40/21.34 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 21.40/21.34 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_same__append__eq,axiom,
% 21.40/21.34 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 <=> V_ys_2 = V_zs_2 ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__same__eq,axiom,
% 21.40/21.34 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 21.40/21.34 ( 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)
% 21.40/21.34 <=> V_ys_2 = V_zs_2 ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__eq__appendI,axiom,
% 21.40/21.34 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 21.40/21.34 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 21.40/21.34 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 21.40/21.34 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__append,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__append,axiom,
% 21.40/21.34 ! [V_ys,V_xs,T_a] :
% 21.40/21.34 ( class_Groups_Omonoid__add(T_a)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__append,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_eq__Nil__appendI,axiom,
% 21.40/21.34 ! [T_a,V_ys,V_xs] :
% 21.40/21.34 ( V_xs = V_ys
% 21.40/21.34 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__self__conv2,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 21.40/21.34 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__self__conv,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 21.40/21.34 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__is__Nil__conv,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 21.40/21.34 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 21.40/21.34 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_self__append__conv2,axiom,
% 21.40/21.34 ! [V_xs_2,T_b,V_ys_2] :
% 21.40/21.34 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 21.40/21.34 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_self__append__conv,axiom,
% 21.40/21.34 ! [V_ys_2,T_b,V_xs_2] :
% 21.40/21.34 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 21.40/21.34 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__Nil2,axiom,
% 21.40/21.34 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Nil__is__append__conv,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 21.40/21.34 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 21.40/21.34 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__Nil,axiom,
% 21.40/21.34 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lexord__append__leftI,axiom,
% 21.40/21.34 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__append,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 21.40/21.34 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 21.40/21.34 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 21.40/21.34 & 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__append,axiom,
% 21.40/21.34 ! [V_ys,V_xs,T_a,V_n] :
% 21.40/21.34 ( ( 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)))
% 21.40/21.34 => 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) )
% 21.40/21.34 & ( ~ 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)))
% 21.40/21.34 => 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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__update__append,axiom,
% 21.40/21.34 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 21.40/21.34 ( ( 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)))
% 21.40/21.34 => 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) )
% 21.40/21.34 & ( ~ 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)))
% 21.40/21.34 => 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)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_sublist__append,axiom,
% 21.40/21.34 ! [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)))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lexord__append__left__rightI,axiom,
% 21.40/21.34 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__Suc__conv__app__nth,axiom,
% 21.40/21.34 ! [V_xs,T_a,V_i] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 21.40/21.34 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 & V_x_2 = V_y_2 )
% 21.40/21.34 | ( V_xs_2 = V_ys_2
% 21.40/21.34 & 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)) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lexord__append__leftD,axiom,
% 21.40/21.34 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 => ( ! [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))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Cons__acc__listrel1I,axiom,
% 21.40/21.34 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 21.40/21.34 => ( 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))))
% 21.40/21.34 => 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)))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel1__mono,axiom,
% 21.40/21.34 ! [V_s_2,V_r_2,T_b] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel1__converse,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 21.40/21.34 ! [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)))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 21.40/21.34 ! [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)))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 21.40/21.34 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel1I2,axiom,
% 21.40/21.34 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 21.40/21.34 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel1__eq__len,axiom,
% 21.40/21.34 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_not__listrel1__Nil,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_not__Nil__listrel1,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__listrel1I,axiom,
% 21.40/21.34 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 & V_us_2 = V_vs_2 )
% 21.40/21.34 | ( V_xs_2 = V_ys_2
% 21.40/21.34 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) )
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_in__listrel1__converse,axiom,
% 21.40/21.34 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 21.40/21.34 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 21.40/21.34 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 21.40/21.34 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Cons__listrel1__Cons,axiom,
% 21.40/21.34 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 <=> ( ( 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))
% 21.40/21.34 & V_xs_2 = V_ys_2 )
% 21.40/21.34 | ( V_x_2 = V_y_2
% 21.40/21.34 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel1I1,axiom,
% 21.40/21.34 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel1__subset__listrel,axiom,
% 21.40/21.34 ! [V_r_H_2,V_r_2,T_b] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 21.40/21.34 => 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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel1I,axiom,
% 21.40/21.34 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => ( 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))
% 21.40/21.34 => ( 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))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel1__iff__update,axiom,
% 21.40/21.34 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 <=> ? [B_y,B_n] :
% 21.40/21.34 ( 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))
% 21.40/21.34 & 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)))
% 21.40/21.34 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel1E,axiom,
% 21.40/21.34 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.34 => ~ ! [B_x,B_y] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => ! [B_us,B_vs] :
% 21.40/21.34 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 21.40/21.34 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate1__def,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_upd__conv__take__nth__drop,axiom,
% 21.40/21.34 ! [V_a,V_xs,T_a,V_i] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__Nil,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate1__is__Nil__conv,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 21.40/21.34 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__all,axiom,
% 21.40/21.34 ! [V_n,V_xs,T_a] :
% 21.40/21.34 ( 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))
% 21.40/21.34 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__eq__Nil,axiom,
% 21.40/21.34 ! [V_xs_2,V_n_2,T_b] :
% 21.40/21.34 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 21.40/21.34 <=> 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__drop,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__take,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_in__set__dropD,axiom,
% 21.40/21.34 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__rotate1,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__drop__subset,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct1__rotate,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 21.40/21.34 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__drop,axiom,
% 21.40/21.34 ! [V_i,V_xs,T_a] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 21.40/21.34 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__drop,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__0,axiom,
% 21.40/21.34 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__zip,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__map,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__drop,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__rotate1,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__drop__subset__set__drop,axiom,
% 21.40/21.34 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 21.40/21.34 => 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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__1__Cons,axiom,
% 21.40/21.34 ! [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 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__Suc__Cons,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__via__drop,axiom,
% 21.40/21.34 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 21.40/21.34 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 21.40/21.34 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__eq__conv__conj,axiom,
% 21.40/21.34 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 21.40/21.34 <=> ( 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)
% 21.40/21.34 & 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__take__drop__id,axiom,
% 21.40/21.34 ! [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 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__append,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__Cons,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__Cons_H,axiom,
% 21.40/21.34 ! [V_xs,V_x,T_a,V_n] :
% 21.40/21.34 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 => 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) )
% 21.40/21.34 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 => 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__drop,axiom,
% 21.40/21.34 ! [V_xs,T_a,V_i,V_n] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__eq__append__conv__if,axiom,
% 21.40/21.34 ! [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] :
% 21.40/21.34 ( 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)
% 21.40/21.34 <=> ( ( 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)))
% 21.40/21.34 => ( 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)
% 21.40/21.34 & 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) ) )
% 21.40/21.34 & ( ~ 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)))
% 21.40/21.34 => ( 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
% 21.40/21.34 & 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 ) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_nth__drop_H,axiom,
% 21.40/21.34 ! [V_xs,T_a,V_i] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate__simps,axiom,
% 21.40/21.34 ! [V_xs,V_x,T_b,T_a] :
% 21.40/21.34 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 21.40/21.34 & 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__Cons__number__of,axiom,
% 21.40/21.34 ! [V_xs,V_x,T_a,V_v] :
% 21.40/21.34 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 => 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) )
% 21.40/21.34 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 => 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__add,axiom,
% 21.40/21.34 ! [V_xs,T_a,V_j,V_i] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate1__length01,axiom,
% 21.40/21.34 ! [V_xs,T_a] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__append2,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_zip__append1,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_id__take__nth__drop,axiom,
% 21.40/21.34 ! [V_xs,T_a,V_i] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__hd__drop,axiom,
% 21.40/21.34 ! [V_xs,T_a,V_n] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_hd__drop__conv__nth,axiom,
% 21.40/21.34 ! [V_n,T_a,V_xs] :
% 21.40/21.34 ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.34 => ( 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)))
% 21.40/21.34 => 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_hd__append2,axiom,
% 21.40/21.34 ! [V_ys,T_a,V_xs] :
% 21.40/21.34 ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_hd__append,axiom,
% 21.40/21.34 ! [V_ys,T_a,V_xs] :
% 21.40/21.34 ( ( V_xs = c_List_Olist_ONil(T_a)
% 21.40/21.34 => 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) )
% 21.40/21.34 & ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.34 => 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) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_hd_Osimps,axiom,
% 21.40/21.34 ! [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 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_hd__map,axiom,
% 21.40/21.34 ! [V_f_2,T_c,T_b,V_xs_2] :
% 21.40/21.34 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_hd__in__set,axiom,
% 21.40/21.34 ! [T_b,V_xs_2] :
% 21.40/21.34 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_hd__conv__nth,axiom,
% 21.40/21.34 ! [T_a,V_xs] :
% 21.40/21.34 ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate1__hd__tl,axiom,
% 21.40/21.34 ! [T_a,V_xs] :
% 21.40/21.34 ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.34 => hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_hd__rotate__conv__nth,axiom,
% 21.40/21.34 ! [V_n,T_a,V_xs] :
% 21.40/21.34 ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__Suc,axiom,
% 21.40/21.34 ! [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),c_List_Otl(T_a,V_xs)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_drop__tl,axiom,
% 21.40/21.34 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Otl(T_a,V_xs)) = c_List_Otl(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_tl__drop,axiom,
% 21.40/21.34 ! [V_xs,V_n,T_a] : 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),c_List_Otl(T_a,V_xs)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_tl_Osimps_I1_J,axiom,
% 21.40/21.34 ! [T_a] : c_List_Otl(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate__is__Nil__conv,axiom,
% 21.40/21.34 ! [V_xs_2,V_n_2,T_b] :
% 21.40/21.34 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 21.40/21.34 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__tl,axiom,
% 21.40/21.34 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Otl(T_a,V_xs)) = c_List_Otl(T_a,hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_set__rotate,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__rotate,axiom,
% 21.40/21.34 ! [V_xs_2,V_n_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 21.40/21.34 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_distinct__tl,axiom,
% 21.40/21.34 ! [V_xs,T_a] :
% 21.40/21.34 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 21.40/21.34 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Otl(T_a,V_xs))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate__rotate,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate__map,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__tl,axiom,
% 21.40/21.34 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Otl(T_c,V_xs_2)) = c_List_Otl(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__rotate,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate__conv__mod,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_tl_Osimps_I2_J,axiom,
% 21.40/21.34 ! [V_xs,V_x,T_a] : c_List_Otl(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs ).
% 21.40/21.34
% 21.40/21.34 fof(fact_tl__append2,axiom,
% 21.40/21.34 ! [V_ys,T_a,V_xs] :
% 21.40/21.34 ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.34 => c_List_Otl(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Otl(T_a,V_xs)),V_ys) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate1__rotate__swap,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate__Suc,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate__def,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_tl__append,axiom,
% 21.40/21.34 ! [V_ys_2,V_xs_2,T_b] : 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,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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate0,axiom,
% 21.40/21.34 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate__add,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate__id,axiom,
% 21.40/21.34 ! [V_xs,T_a,V_n] :
% 21.40/21.34 ( 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)
% 21.40/21.34 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate__length01,axiom,
% 21.40/21.34 ! [V_n,V_xs,T_a] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_length__tl,axiom,
% 21.40/21.34 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_tl__take,axiom,
% 21.40/21.34 ! [V_xs,V_n,T_a] : 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))),c_List_Otl(T_a,V_xs)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_take__Suc,axiom,
% 21.40/21.34 ! [V_n,T_a,V_xs] :
% 21.40/21.34 ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.34 => 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),c_List_Otl(T_a,V_xs))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_rotate__drop__take,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_fold1__set,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 21.40/21.34 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 21.40/21.34 => 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)),c_List_Otl(T_b,V_xs_2)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list_Osize_I2_J,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_foldl__append,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_foldl__Cons,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__size__map,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_foldl__map,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_foldr__conv__foldl,axiom,
% 21.40/21.34 ! [V_a_2,V_xs_2,T_b] :
% 21.40/21.34 ( class_Groups_Oab__semigroup__add(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_foldl__absorb0,axiom,
% 21.40/21.34 ! [V_zs_2,V_x_2,T_b] :
% 21.40/21.34 ( class_Groups_Omonoid__add(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_foldl__assoc,axiom,
% 21.40/21.34 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 21.40/21.34 ( class_Groups_Osemigroup__add(T_b)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_start__le__sum,axiom,
% 21.40/21.34 ! [V_ns_2,V_n_2,V_m_2] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_foldl__Nil,axiom,
% 21.40/21.34 ! [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 ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listsum__foldl,axiom,
% 21.40/21.34 ! [T_b] :
% 21.40/21.34 ( class_Groups_Omonoid__add(T_b)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_foldl__foldr1,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( class_Groups_Omonoid__add(T_b)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_foldl__foldr1__lemma,axiom,
% 21.40/21.34 ! [V_xs_2,V_a_2,T_b] :
% 21.40/21.34 ( class_Groups_Omonoid__add(T_b)
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_sum__eq__0__conv,axiom,
% 21.40/21.34 ! [V_ns_2,V_m_2] :
% 21.40/21.34 ( 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)
% 21.40/21.34 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.34 & ! [B_x] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 21.40/21.34 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list_Osize_I1_J,axiom,
% 21.40/21.34 ! [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) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 21.40/21.34 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 21.40/21.34 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Sup__set__fold,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Inf__set__fold,axiom,
% 21.40/21.34 ! [V_xs_2,T_b] :
% 21.40/21.34 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Sup__fin__set__fold,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( class_Lattices_Olattice(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Inf__fin__set__fold,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( class_Lattices_Olattice(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Min__fin__set__fold,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Max__fin__set__fold,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 21.40/21.34 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( class_Orderings_Olinorder(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_SUPR__set__fold,axiom,
% 21.40/21.34 ! [V_f_2,V_xs_2,T_c,T_b] :
% 21.40/21.34 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_INFI__set__fold,axiom,
% 21.40/21.34 ! [V_f_2,V_xs_2,T_c,T_b] :
% 21.40/21.34 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 21.40/21.34 => 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) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__size__estimation,axiom,
% 21.40/21.34 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 21.40/21.34 => 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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__size__estimation_H,axiom,
% 21.40/21.34 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 21.40/21.34 => 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))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_map__upds__fold__map__upd,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_elem__le__sum,axiom,
% 21.40/21.34 ! [V_ns_2,V_n_2] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_list__size__conv__listsum,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__subset,axiom,
% 21.40/21.34 ! [V_A_2,V_r_2,T_b] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => 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))))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lists__accD,axiom,
% 21.40/21.34 ! [V_r_2,V_xs_2,T_b] :
% 21.40/21.34 ( 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))))
% 21.40/21.34 => 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)))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lists_ONil,axiom,
% 21.40/21.34 ! [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))) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_listrel__refl__on,axiom,
% 21.40/21.34 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.34 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_equiv__listrel,axiom,
% 21.40/21.34 ! [V_r_2,V_A_2,T_b] :
% 21.40/21.34 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 21.40/21.34 => 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)) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lists__mono,axiom,
% 21.40/21.34 ! [V_B_2,V_A_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 21.40/21.34 => 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))) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lists__UNIV,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_append__in__lists__conv,axiom,
% 21.40/21.34 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 21.40/21.34 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_Cons__in__lists__iff,axiom,
% 21.40/21.34 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 21.40/21.34 ( 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)))
% 21.40/21.34 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 21.40/21.34 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_in__lists__conv__set,axiom,
% 21.40/21.34 ! [V_A_2,V_xs_2,T_b] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 21.40/21.34 <=> ! [B_x] :
% 21.40/21.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.34 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 21.40/21.34
% 21.40/21.34 fof(fact_lists__eq__set,axiom,
% 21.40/21.34 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_lists__empty,axiom,
% 21.40/21.35 ! [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))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_lists__accI,axiom,
% 21.40/21.35 ! [V_r_2,V_xs_2,T_b] :
% 21.40/21.35 ( 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))))
% 21.40/21.35 => 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)))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_lexord__append__rightI,axiom,
% 21.40/21.35 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 21.40/21.35 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 21.40/21.35 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_lexord__Nil__left,axiom,
% 21.40/21.35 ! [V_r_2,V_y_2,T_b] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.35 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_last__list__update,axiom,
% 21.40/21.35 ! [V_x,V_k,T_a,V_xs] :
% 21.40/21.35 ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.35 => ( ( 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))
% 21.40/21.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 21.40/21.35 & ( 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))
% 21.40/21.35 => 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) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_listsum__mono,axiom,
% 21.40/21.35 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 21.40/21.35 ( ( class_Groups_Omonoid__add(T_c)
% 21.40/21.35 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 21.40/21.35 => ( ! [B_x] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 21.40/21.35 => 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)))) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_last_Osimps,axiom,
% 21.40/21.35 ! [V_x,T_a,V_xs] :
% 21.40/21.35 ( ( V_xs = c_List_Olist_ONil(T_a)
% 21.40/21.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 21.40/21.35 & ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_last__ConsR,axiom,
% 21.40/21.35 ! [V_x,T_a,V_xs] :
% 21.40/21.35 ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_last__ConsL,axiom,
% 21.40/21.35 ! [V_x,T_a,V_xs] :
% 21.40/21.35 ( V_xs = c_List_Olist_ONil(T_a)
% 21.40/21.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_last__append,axiom,
% 21.40/21.35 ! [V_xs,T_a,V_ys] :
% 21.40/21.35 ( ( V_ys = c_List_Olist_ONil(T_a)
% 21.40/21.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 21.40/21.35 & ( V_ys != c_List_Olist_ONil(T_a)
% 21.40/21.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_last__appendR,axiom,
% 21.40/21.35 ! [V_xs,T_a,V_ys] :
% 21.40/21.35 ( V_ys != c_List_Olist_ONil(T_a)
% 21.40/21.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_last__appendL,axiom,
% 21.40/21.35 ! [V_xs,T_a,V_ys] :
% 21.40/21.35 ( V_ys = c_List_Olist_ONil(T_a)
% 21.40/21.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_last__map,axiom,
% 21.40/21.35 ! [V_f_2,T_c,T_b,V_xs_2] :
% 21.40/21.35 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 21.40/21.35 => 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)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_last__in__set,axiom,
% 21.40/21.35 ! [T_b,V_as_2] :
% 21.40/21.35 ( V_as_2 != c_List_Olist_ONil(T_b)
% 21.40/21.35 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_last__snoc,axiom,
% 21.40/21.35 ! [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 ).
% 21.40/21.35
% 21.40/21.35 fof(fact_last__drop,axiom,
% 21.40/21.35 ! [V_xs,T_a,V_n] :
% 21.40/21.35 ( 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)))
% 21.40/21.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_last__conv__nth,axiom,
% 21.40/21.35 ! [T_a,V_xs] :
% 21.40/21.35 ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.35 => 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))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_lexord__irreflexive,axiom,
% 21.40/21.35 ! [V_y_2,V_r_2,T_b] :
% 21.40/21.35 ( ! [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))
% 21.40/21.35 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_lexord__linear,axiom,
% 21.40/21.35 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 21.40/21.35 ( ! [B_a,B_b] :
% 21.40/21.35 ( 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))
% 21.40/21.35 | B_a = B_b
% 21.40/21.35 | 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)) )
% 21.40/21.35 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 21.40/21.35 | V_x_2 = V_y_2
% 21.40/21.35 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_lists_Osimps,axiom,
% 21.40/21.35 ! [V_A_2,V_a_2,T_b] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 21.40/21.35 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 21.40/21.35 | ? [B_a,B_l] :
% 21.40/21.35 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 21.40/21.35 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 21.40/21.35 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_list__size__pointwise,axiom,
% 21.40/21.35 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 21.40/21.35 ( ! [B_x] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 21.40/21.35 => 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))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_butlast__take,axiom,
% 21.40/21.35 ! [V_xs,T_a,V_n] :
% 21.40/21.35 ( 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)))
% 21.40/21.35 => 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) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_nth__take__lemma,axiom,
% 21.40/21.35 ! [V_ys,V_xs,T_a,V_k] :
% 21.40/21.35 ( 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)))
% 21.40/21.35 => ( 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)))
% 21.40/21.35 => ( ! [B_i] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 21.40/21.35 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 21.40/21.35 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_map__butlast,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_butlast__append,axiom,
% 21.40/21.35 ! [V_xs,T_a,V_ys] :
% 21.40/21.35 ( ( V_ys = c_List_Olist_ONil(T_a)
% 21.40/21.35 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 21.40/21.35 & ( V_ys != c_List_Olist_ONil(T_a)
% 21.40/21.35 => 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)) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_butlast_Osimps_I2_J,axiom,
% 21.40/21.35 ! [V_x,T_a,V_xs] :
% 21.40/21.35 ( ( V_xs = c_List_Olist_ONil(T_a)
% 21.40/21.35 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 21.40/21.35 & ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.35 => 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)) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_in__set__butlastD,axiom,
% 21.40/21.35 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 21.40/21.35 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_distinct__butlast,axiom,
% 21.40/21.35 ! [T_a,V_xs] :
% 21.40/21.35 ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.35 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 21.40/21.35 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_butlast_Osimps_I1_J,axiom,
% 21.40/21.35 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_butlast__drop,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_drop__butlast,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_in__set__butlast__appendI,axiom,
% 21.40/21.35 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 21.40/21.35 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 21.40/21.35 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 21.40/21.35 => 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))))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_butlast__snoc,axiom,
% 21.40/21.35 ! [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 ).
% 21.40/21.35
% 21.40/21.35 fof(fact_take__butlast,axiom,
% 21.40/21.35 ! [V_xs,T_a,V_n] :
% 21.40/21.35 ( 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)))
% 21.40/21.35 => 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) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_length__butlast,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_butlast__conv__take,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_butlast__list__update,axiom,
% 21.40/21.35 ! [V_x,V_xs,T_a,V_k] :
% 21.40/21.35 ( ( 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))
% 21.40/21.35 => 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) )
% 21.40/21.35 & ( 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))
% 21.40/21.35 => 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) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_append__butlast__last__id,axiom,
% 21.40/21.35 ! [T_a,V_xs] :
% 21.40/21.35 ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.35 => 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 ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_snoc__eq__iff__butlast,axiom,
% 21.40/21.35 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 21.40/21.35 ( 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
% 21.40/21.35 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 21.40/21.35 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 21.40/21.35 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_transpose__aux__max,axiom,
% 21.40/21.35 ! [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)))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_partition__set,axiom,
% 21.40/21.35 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 21.40/21.35 ( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 21.40/21.35 => 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) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_length__filter__le,axiom,
% 21.40/21.35 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_filter__is__subset,axiom,
% 21.40/21.35 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_filter_Osimps_I1_J,axiom,
% 21.40/21.35 ! [V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_filter__empty__conv,axiom,
% 21.40/21.35 ! [V_xs_2,V_P_2,T_b] :
% 21.40/21.35 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 21.40/21.35 <=> ! [B_x] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.35 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_filter__id__conv,axiom,
% 21.40/21.35 ! [V_xs_2,V_P_2,T_b] :
% 21.40/21.35 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
% 21.40/21.35 <=> ! [B_x] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.35 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_filter__insort__triv,axiom,
% 21.40/21.35 ! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_c)
% 21.40/21.35 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 21.40/21.35 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_distinct__filter,axiom,
% 21.40/21.35 ! [V_P_2,V_xs_2,T_b] :
% 21.40/21.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 21.40/21.35 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_filter__remove1,axiom,
% 21.40/21.35 ! [V_xs_2,V_x_2,V_Q_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Q_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_Q_2),V_xs_2)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_remove1__filter__not,axiom,
% 21.40/21.35 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 21.40/21.35 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 21.40/21.35 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_filter__filter,axiom,
% 21.40/21.35 ! [V_xs_2,V_Q_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Ofilter(T_b,V_Q_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_Q_2)),V_P_2)),V_xs_2) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_partition__filter1,axiom,
% 21.40/21.35 ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sum__length__filter__compl,axiom,
% 21.40/21.35 ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_filter_Osimps_I2_J,axiom,
% 21.40/21.35 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 21.40/21.35 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 21.40/21.35 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) )
% 21.40/21.35 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 21.40/21.35 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_filter__append,axiom,
% 21.40/21.35 ! [V_ys_2,V_xs_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_length__filter__map,axiom,
% 21.40/21.35 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_set__filter,axiom,
% 21.40/21.35 ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_P_2)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_partition__filter__conv,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_filter__map,axiom,
% 21.40/21.35 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_partition__filter2,axiom,
% 21.40/21.35 ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_P_2)),V_xs_2) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_length__filter__less,axiom,
% 21.40/21.35 ! [V_P_2,V_xs_2,V_x_2,T_b] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.35 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 21.40/21.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_set__minus__filter__out,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_partition__P,axiom,
% 21.40/21.35 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 21.40/21.35 ( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 21.40/21.35 => ( ! [B_x] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 21.40/21.35 => hBOOL(hAPP(V_P_2,B_x)) )
% 21.40/21.35 & ! [B_x] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 21.40/21.35 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_partition_Osimps_I1_J,axiom,
% 21.40/21.35 ! [V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_filter__in__sublist,axiom,
% 21.40/21.35 ! [V_s_2,V_xs_2,T_b] :
% 21.40/21.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 21.40/21.35 => 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) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_partition_Osimps_I2_J,axiom,
% 21.40/21.35 ! [V_xs_2,V_x_2,V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_P_2,V_xs_2)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_length__filter__conv__card,axiom,
% 21.40/21.35 ! [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))))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_map__filter__def,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_transpose__max__length,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_map__of__filter__in,axiom,
% 21.40/21.35 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] :
% 21.40/21.35 ( 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)
% 21.40/21.35 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
% 21.40/21.35 => hAPP(c_Map_Omap__of(T_c,T_b,hAPP(c_List_Ofilter(tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_transpose__map__map,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_transpose_Osimps_I2_J,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_transpose__empty,axiom,
% 21.40/21.35 ! [V_xs_2,T_b] :
% 21.40/21.35 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 21.40/21.35 <=> ! [B_x] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 21.40/21.35 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_map__filter__simps_I2_J,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_transpose_Osimps_I1_J,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_map__filter__simps_I1_J,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sublist__shift__lemma__Suc,axiom,
% 21.40/21.35 ! [V_is_2,V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_select__weigth__drop__zero,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_pick__drop__zero,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_nth__transpose,axiom,
% 21.40/21.35 ! [V_xs_2,T_b,V_i_2] :
% 21.40/21.35 ( 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))))
% 21.40/21.35 => 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)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_length__transpose,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_map__filter__map__filter,axiom,
% 21.40/21.35 ! [V_xs_2,V_P_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)) = c_List_Omap__filter(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_c,tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),T_c),c_If(tc_Option_Ooption(T_b))),V_P_2)),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_c),c_Option_Ooption_OSome(T_b)),V_f_2))),c_Option_Ooption_ONone(T_b)),V_xs_2) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_insort__key__remove1,axiom,
% 21.40/21.35 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_c)
% 21.40/21.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 21.40/21.35 => ( 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
% 21.40/21.35 => 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 ) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sublist__def,axiom,
% 21.40/21.35 ! [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))))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted_ONil,axiom,
% 21.40/21.35 ! [T_a] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_a)
% 21.40/21.35 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__single,axiom,
% 21.40/21.35 ! [V_x,T_a] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_a)
% 21.40/21.35 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__same,axiom,
% 21.40/21.35 ! [V_xs_2,V_g_2,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => 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)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__map__same,axiom,
% 21.40/21.35 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => 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))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__filter,axiom,
% 21.40/21.35 ! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 21.40/21.35 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2))) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_length__upt,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__butlast,axiom,
% 21.40/21.35 ! [V_xs,T_a] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_a)
% 21.40/21.35 => ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 21.40/21.35 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_upt__Suc__append,axiom,
% 21.40/21.35 ! [V_j,V_i] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.40/21.35 => 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))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_upt__Suc,axiom,
% 21.40/21.35 ! [V_j,V_i] :
% 21.40/21.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.40/21.35 => 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))) )
% 21.40/21.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.40/21.35 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_upt__add__eq__append,axiom,
% 21.40/21.35 ! [V_k,V_j,V_i] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.40/21.35 => 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))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__many__eq,axiom,
% 21.40/21.35 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( 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)))
% 21.40/21.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 21.40/21.35 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__many,axiom,
% 21.40/21.35 ! [V_zs,V_y,V_x,T_a] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_a)
% 21.40/21.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 21.40/21.35 => 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))) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_take__upt,axiom,
% 21.40/21.35 ! [V_n,V_m,V_i] :
% 21.40/21.35 ( 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))
% 21.40/21.35 => 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)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_upt__eq__Nil__conv,axiom,
% 21.40/21.35 ! [V_j_2,V_i_2] :
% 21.40/21.35 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 21.40/21.35 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 21.40/21.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_upt__conv__Nil,axiom,
% 21.40/21.35 ! [V_i,V_j] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 21.40/21.35 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__Cons,axiom,
% 21.40/21.35 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 21.40/21.35 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 21.40/21.35 & ! [B_x] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__append,axiom,
% 21.40/21.35 ! [V_ys_2,V_xs_2,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 21.40/21.35 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 21.40/21.35 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 21.40/21.35 & ! [B_x] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.35 => ! [B_xa] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 21.40/21.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_upt__eq__Cons__conv,axiom,
% 21.40/21.35 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 21.40/21.35 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 21.40/21.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 21.40/21.35 & V_i_2 = V_x_2
% 21.40/21.35 & 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 ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_upt__rec__number__of,axiom,
% 21.40/21.35 ! [V_n,V_m] :
% 21.40/21.35 ( ( 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)))
% 21.40/21.35 => 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))) )
% 21.40/21.35 & ( ~ 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)))
% 21.40/21.35 => 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) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_drop__upt,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__drop,axiom,
% 21.40/21.35 ! [V_n,V_xs,T_a] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_a)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 21.40/21.35 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_hd__upt,axiom,
% 21.40/21.35 ! [V_j,V_i] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 21.40/21.35 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_upt__0,axiom,
% 21.40/21.35 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted_Oequations_I1_J,axiom,
% 21.40/21.35 ! [T_a] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_a)
% 21.40/21.35 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__take,axiom,
% 21.40/21.35 ! [V_n,V_xs,T_a] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_a)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 21.40/21.35 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_set__upt,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_atLeastLessThan__upt,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__distinct__set__unique,axiom,
% 21.40/21.35 ! [V_ys_2,V_xs_2,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 21.40/21.35 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 21.40/21.35 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 21.40/21.35 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 21.40/21.35 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__insort,axiom,
% 21.40/21.35 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( 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))
% 21.40/21.35 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_distinct__upt,axiom,
% 21.40/21.35 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__remove1,axiom,
% 21.40/21.35 ! [V_a,V_xs,T_a] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_a)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 21.40/21.35 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__upt,axiom,
% 21.40/21.35 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__upto,axiom,
% 21.40/21.35 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__list__of__set__range,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__insort__insert,axiom,
% 21.40/21.35 ! [V_x_2,V_xs_2,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 21.40/21.35 => 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)) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_upt__conv__Cons,axiom,
% 21.40/21.35 ! [V_j,V_i] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 21.40/21.35 => 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)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_upt__rec,axiom,
% 21.40/21.35 ! [V_j,V_i] :
% 21.40/21.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 21.40/21.35 => 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)) )
% 21.40/21.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 21.40/21.35 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__tl,axiom,
% 21.40/21.35 ! [V_xs,T_a] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_a)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 21.40/21.35 => c_List_Olinorder__class_Osorted(T_a,c_List_Otl(T_a,V_xs)) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__insort__key,axiom,
% 21.40/21.35 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( 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)))
% 21.40/21.35 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__map__remove1,axiom,
% 21.40/21.35 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 21.40/21.35 => 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))) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__insort__insert__key,axiom,
% 21.40/21.35 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 21.40/21.35 => 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))) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_map__Suc__upt,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_last__upt,axiom,
% 21.40/21.35 ! [V_j,V_i] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 21.40/21.35 => 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)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_filter__insort,axiom,
% 21.40/21.35 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 21.40/21.35 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 21.40/21.35 => hAPP(c_List_Ofilter(T_c,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_map__nth,axiom,
% 21.40/21.35 ! [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 ).
% 21.40/21.35
% 21.40/21.35 fof(fact_atLeastAtMost__upt,axiom,
% 21.40/21.35 ! [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))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_atLeast__upt,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 21.40/21.35 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 21.40/21.35 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.35 => 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))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 21.40/21.35 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 21.40/21.35 ( class_Groups_Ocomm__monoid__add(T_b)
% 21.40/21.35 => 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))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_nth__upt,axiom,
% 21.40/21.35 ! [V_j,V_k,V_i] :
% 21.40/21.35 ( 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))
% 21.40/21.35 => 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) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_greaterThanAtMost__upt,axiom,
% 21.40/21.35 ! [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))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted_Oequations_I2_J,axiom,
% 21.40/21.35 ! [V_a1_2,V_a2_2,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 21.40/21.35 <=> ( ! [B_x] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 21.40/21.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 21.40/21.35 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_greaterThanLessThan__upt,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_nth__map__upt,axiom,
% 21.40/21.35 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 21.40/21.35 ( 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)))
% 21.40/21.35 => 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)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__list__of__set,axiom,
% 21.40/21.35 ! [V_A_2,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 21.40/21.35 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 21.40/21.35 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 21.40/21.35 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_atMost__upto,axiom,
% 21.40/21.35 ! [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))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_insort__remove1,axiom,
% 21.40/21.35 ! [V_xs_2,V_a_2,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 21.40/21.35 => 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 ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__nth__mono,axiom,
% 21.40/21.35 ! [V_j,V_i,V_xs,T_a] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_a)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 21.40/21.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.40/21.35 => ( 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)))
% 21.40/21.35 => 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))) ) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__equals__nth__mono,axiom,
% 21.40/21.35 ! [V_xs_2,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 21.40/21.35 <=> ! [B_j] :
% 21.40/21.35 ( 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)))
% 21.40/21.35 => ! [B_i] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 21.40/21.35 => 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))) ) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_map__sorted__distinct__set__unique,axiom,
% 21.40/21.35 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_c)
% 21.40/21.35 => ( 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)))
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 21.40/21.35 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 21.40/21.35 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 21.40/21.35 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 21.40/21.35 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sublist__shift__lemma,axiom,
% 21.40/21.35 ! [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))))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_transpose__rectangle,axiom,
% 21.40/21.35 ! [V_n_2,T_b,V_xs_2] :
% 21.40/21.35 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 21.40/21.35 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 21.40/21.35 => ( ! [B_i] :
% 21.40/21.35 ( 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)))
% 21.40/21.35 => 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 )
% 21.40/21.35 => 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)) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_transpose_Opsimps_I2_J,axiom,
% 21.40/21.35 ! [V_xss_2,T_b] :
% 21.40/21.35 ( 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)))
% 21.40/21.35 => 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) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_transpose_Opsimps_I1_J,axiom,
% 21.40/21.35 ! [T_b] :
% 21.40/21.35 ( 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))))
% 21.40/21.35 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_transpose__column,axiom,
% 21.40/21.35 ! [V_i_2,V_xs_2,T_b] :
% 21.40/21.35 ( 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)))
% 21.40/21.35 => ( 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)))
% 21.40/21.35 => 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) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_transpose__aux__filter__head,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_inj__on__rev,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_filter__concat,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_length__concat,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__eq__Cons__iff,axiom,
% 21.40/21.35 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 21.40/21.35 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 21.40/21.35 <=> 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))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev_Osimps_I2_J,axiom,
% 21.40/21.35 ! [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))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev_Osimps_I1_J,axiom,
% 21.40/21.35 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_concat_Osimps_I1_J,axiom,
% 21.40/21.35 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_Nil__is__rev__conv,axiom,
% 21.40/21.35 ! [V_xs_2,T_b] :
% 21.40/21.35 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 21.40/21.35 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__is__Nil__conv,axiom,
% 21.40/21.35 ! [V_xs_2,T_b] :
% 21.40/21.35 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 21.40/21.35 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_Nil__eq__concat__conv,axiom,
% 21.40/21.35 ! [V_xss_2,T_b] :
% 21.40/21.35 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 21.40/21.35 <=> ! [B_x] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 21.40/21.35 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_concat__eq__Nil__conv,axiom,
% 21.40/21.35 ! [V_xss_2,T_b] :
% 21.40/21.35 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 21.40/21.35 <=> ! [B_x] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 21.40/21.35 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__singleton__conv,axiom,
% 21.40/21.35 ! [V_x_2,V_xs_2,T_b] :
% 21.40/21.35 ( 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))
% 21.40/21.35 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_singleton__rev__conv,axiom,
% 21.40/21.35 ! [V_xs_2,V_x_2,T_b] :
% 21.40/21.35 ( 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)
% 21.40/21.35 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_concat_Osimps_I2_J,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__concat,axiom,
% 21.40/21.35 ! [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))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__map,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_map__concat,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__foldl__cons,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_concat__conv__foldl,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_foldl__conv__concat,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__append,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_concat__append,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_distinct__rev,axiom,
% 21.40/21.35 ! [V_xs_2,T_b] :
% 21.40/21.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 21.40/21.35 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_length__rev,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_listsum__rev,axiom,
% 21.40/21.35 ! [V_xs,T_a] :
% 21.40/21.35 ( class_Groups_Ocomm__monoid__add(T_a)
% 21.40/21.35 => 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) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__is__rev__conv,axiom,
% 21.40/21.35 ! [V_ys_2,V_xs_2,T_b] :
% 21.40/21.35 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 21.40/21.35 <=> V_xs_2 = V_ys_2 ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__swap,axiom,
% 21.40/21.35 ! [V_ys_2,V_xs_2,T_b] :
% 21.40/21.35 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 21.40/21.35 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__rev__ident,axiom,
% 21.40/21.35 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 21.40/21.35
% 21.40/21.35 fof(fact_foldr__foldl,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_foldl__foldr,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_set__concat,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_set__rev,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_zip__rev,axiom,
% 21.40/21.35 ! [V_ys,T_b,V_xs,T_a] :
% 21.40/21.35 ( 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)
% 21.40/21.35 => 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)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__filter,axiom,
% 21.40/21.35 ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_last__rev,axiom,
% 21.40/21.35 ! [T_a,V_xs] :
% 21.40/21.35 ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.35 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_hd__rev,axiom,
% 21.40/21.35 ! [T_a,V_xs] :
% 21.40/21.35 ( V_xs != c_List_Olist_ONil(T_a)
% 21.40/21.35 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__transpose,axiom,
% 21.40/21.35 ! [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)))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__take,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__drop,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rotate__rev,axiom,
% 21.40/21.35 ! [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)) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_transpose_Osimps_I3_J,axiom,
% 21.40/21.35 ! [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))))) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__nth,axiom,
% 21.40/21.35 ! [V_xs,T_a,V_n] :
% 21.40/21.35 ( 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)))
% 21.40/21.35 => 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))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_concat__injective,axiom,
% 21.40/21.35 ! [V_ys_2,V_xs_2,T_b] :
% 21.40/21.35 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 21.40/21.35 => ( 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)
% 21.40/21.35 => ( ! [B_x] :
% 21.40/21.35 ( 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))))
% 21.40/21.35 => 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)) )
% 21.40/21.35 => V_xs_2 = V_ys_2 ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_concat__eq__concat__iff,axiom,
% 21.40/21.35 ! [V_ys_2,V_xs_2,T_b] :
% 21.40/21.35 ( ! [B_x] :
% 21.40/21.35 ( 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))))
% 21.40/21.35 => 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)) )
% 21.40/21.35 => ( 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)
% 21.40/21.35 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 21.40/21.35 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_rev__update,axiom,
% 21.40/21.35 ! [V_y,V_xs,T_a,V_k] :
% 21.40/21.35 ( 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)))
% 21.40/21.35 => 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) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_concat__map__singleton,axiom,
% 21.40/21.35 ! [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) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_sorted__rev__nth__mono,axiom,
% 21.40/21.35 ! [V_j,V_i,V_xs,T_a] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_a)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 21.40/21.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 21.40/21.35 => ( 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)))
% 21.40/21.35 => 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))) ) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_foldr__max__sorted,axiom,
% 21.40/21.35 ! [V_y_2,V_xs_2,T_b] :
% 21.40/21.35 ( class_Orderings_Olinorder(T_b)
% 21.40/21.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 21.40/21.35 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 21.40/21.35 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 21.40/21.35 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 21.40/21.35 => 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) ) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_transpose_Opsimps_I3_J,axiom,
% 21.40/21.35 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 21.40/21.35 ( 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)))
% 21.40/21.35 => 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))))) ) ).
% 21.40/21.35
% 21.40/21.35 fof(fact_length__transpose__sorted,axiom,
% 21.40/21.35 ! [V_xs_2,T_b] :
% 21.40/21.35 ( 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)))
% 21.40/21.35 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 21.40/21.35 => 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) )
% 21.40/21.35 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 21.40/21.35 => 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))) ) ) ) ).
% 21.40/21.35
% 21.40/21.35 %----Arity declarations (201)
% 21.40/21.35 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 21.40/21.35 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Lattices_Obounded__lattice(T_1)
% 21.40/21.35 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 21.40/21.35 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Lattices_Obounded__lattice(T_1)
% 21.40/21.35 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Lattices_Obounded__lattice(T_1)
% 21.40/21.35 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Lattices_Olattice(T_1)
% 21.40/21.35 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Lattices_Olattice(T_1)
% 21.40/21.35 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Lattices_Odistrib__lattice(T_1)
% 21.40/21.35 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Lattices_Oboolean__algebra(T_1)
% 21.40/21.35 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Orderings_Opreorder,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Orderings_Opreorder(T_1)
% 21.40/21.35 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 21.40/21.35 ! [T_1,T_2] :
% 21.40/21.35 ( ( class_Finite__Set_Ofinite(T_2)
% 21.40/21.35 & class_Finite__Set_Ofinite(T_1) )
% 21.40/21.35 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Lattices_Olattice,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Lattices_Olattice(T_1)
% 21.40/21.35 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Orderings_Oorder,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Orderings_Oorder(T_1)
% 21.40/21.35 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Orderings_Otop,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Orderings_Otop(T_1)
% 21.40/21.35 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Orderings_Oord,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Orderings_Oord(T_1)
% 21.40/21.35 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Orderings_Obot,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Orderings_Obot(T_1)
% 21.40/21.35 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Groups_Ouminus,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Groups_Ouminus(T_1)
% 21.40/21.35 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_fun__Groups_Ominus,axiom,
% 21.40/21.35 ! [T_2,T_1] :
% 21.40/21.35 ( class_Groups_Ominus(T_1)
% 21.40/21.35 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 21.40/21.35 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 21.40/21.35 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 21.40/21.35 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 21.40/21.35 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 21.40/21.35 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 21.40/21.35 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 21.40/21.35 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 21.40/21.35 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 21.40/21.35 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 21.40/21.35 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 21.40/21.35 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 21.40/21.35 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 21.40/21.35 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 21.40/21.35 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 21.40/21.35 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 21.40/21.35 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 21.40/21.35 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 21.40/21.35 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 21.40/21.35 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 21.40/21.35 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 21.40/21.35 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 21.40/21.35 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 21.40/21.35 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 21.40/21.35 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 21.40/21.35 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 21.40/21.35 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 21.40/21.35 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 21.40/21.35 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 21.40/21.35 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 21.40/21.35 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 21.40/21.35 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 21.40/21.35 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 21.40/21.35 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 21.40/21.35 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 21.40/21.35 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 21.40/21.35 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 21.40/21.35 class_Orderings_Opreorder(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 21.40/21.35 class_Orderings_Olinorder(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 21.40/21.35 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 21.40/21.35 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 21.40/21.35 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 21.40/21.35 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 21.40/21.35 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 21.40/21.35 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 21.40/21.35 class_Lattices_Olattice(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 21.40/21.35 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 21.40/21.35 class_Divides_Oring__div(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 21.40/21.35 class_Rings_Omult__zero(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 21.40/21.35 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 21.40/21.35 class_Orderings_Oorder(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 21.40/21.35 class_Int_Oring__char__0(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 21.40/21.35 class_Int_Onumber__ring(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 21.40/21.35 class_Rings_Osemiring(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 21.40/21.35 class_Orderings_Oord(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 21.40/21.35 class_Groups_Ouminus(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 21.40/21.35 class_Groups_Osgn__if(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 21.40/21.35 class_Groups_Oabs__if(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 21.40/21.35 class_Rings_Oring__1(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 21.40/21.35 class_Groups_Ominus(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Power_Opower,axiom,
% 21.40/21.35 class_Power_Opower(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 21.40/21.35 class_Groups_Ozero(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Oring,axiom,
% 21.40/21.35 class_Rings_Oring(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 21.40/21.35 class_Rings_Oidom(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Int_Onumber,axiom,
% 21.40/21.35 class_Int_Onumber(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Groups_Oone,axiom,
% 21.40/21.35 class_Groups_Oone(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 21.40/21.35 class_Rings_Odvd(tc_Int_Oint) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 21.40/21.35 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 21.40/21.35 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 21.40/21.35 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 21.40/21.35 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 21.40/21.35 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 21.40/21.35 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 21.40/21.35 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 21.40/21.35 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 21.40/21.35 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 21.40/21.35 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 21.40/21.35 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 21.40/21.35 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 21.40/21.35 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 21.40/21.35 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 21.40/21.35 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 21.40/21.35 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 21.40/21.35 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 21.40/21.35 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 21.40/21.35 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 21.40/21.35 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 21.40/21.35 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 21.40/21.35 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 21.40/21.35 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 21.40/21.35 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 21.40/21.35 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 21.40/21.35 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 21.40/21.35 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 21.40/21.35 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 21.40/21.35 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 21.40/21.35 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 21.40/21.35 class_Lattices_Olattice(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 21.40/21.35 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 21.40/21.35 class_Orderings_Oorder(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 21.40/21.35 class_Rings_Osemiring(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 21.40/21.35 class_Orderings_Oord(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 21.40/21.35 class_Orderings_Obot(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 21.40/21.35 class_Groups_Ominus(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Power_Opower,axiom,
% 21.40/21.35 class_Power_Opower(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 21.40/21.35 class_Groups_Ozero(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 21.40/21.35 class_Int_Onumber(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 21.40/21.35 class_Groups_Oone(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 21.40/21.35 class_Rings_Odvd(tc_Nat_Onat) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 21.40/21.35 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 21.40/21.35 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 21.40/21.35 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 21.40/21.35 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 21.40/21.35 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 21.40/21.35 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 21.40/21.35 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 21.40/21.35 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 21.40/21.35 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 21.40/21.35 class_Lattices_Olattice(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 21.40/21.35 class_Orderings_Oorder(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 21.40/21.35 class_Orderings_Otop(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 21.40/21.35 class_Orderings_Oord(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 21.40/21.35 class_Orderings_Obot(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 21.40/21.35 class_Groups_Ouminus(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 21.40/21.35 class_Groups_Ominus(tc_HOL_Obool) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 21.40/21.35 ! [T_1,T_2] :
% 21.40/21.35 ( ( class_Finite__Set_Ofinite(T_2)
% 21.40/21.35 & class_Finite__Set_Ofinite(T_1) )
% 21.40/21.35 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 21.40/21.35 ! [T_1] :
% 21.40/21.35 ( class_Finite__Set_Ofinite(T_1)
% 21.40/21.35 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 21.40/21.35 ! [T_1,T_2] :
% 21.40/21.35 ( ( class_Finite__Set_Ofinite(T_2)
% 21.40/21.35 & class_Finite__Set_Ofinite(T_1) )
% 21.40/21.35 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_prod__Smallcheck_Osmall,axiom,
% 21.40/21.35 ! [T_1,T_2] :
% 21.40/21.35 ( ( class_Smallcheck_Osmall(T_2)
% 21.40/21.35 & class_Smallcheck_Osmall(T_1) )
% 21.40/21.35 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 21.40/21.35 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 21.40/21.35 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 21.40/21.35 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 21.40/21.35 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 21.40/21.35 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 21.40/21.35 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 21.40/21.35 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 21.40/21.35 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 21.40/21.35 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 21.40/21.35 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 21.40/21.35 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 21.40/21.35 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 21.40/21.35 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 21.40/21.35 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 21.40/21.35 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 21.40/21.35 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 21.40/21.35 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 21.40/21.35 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 21.40/21.35 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 21.40/21.35 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 21.40/21.35 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 21.40/21.35 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 21.40/21.35 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 21.40/21.35 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 21.40/21.35 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 21.40/21.35 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 21.40/21.35 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 21.40/21.35 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 21.40/21.35 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 21.40/21.35 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 21.40/21.35 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 21.40/21.35 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 21.40/21.35 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 21.40/21.35 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 21.40/21.35 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 21.40/21.35 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 21.40/21.35 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
% 21.40/21.35 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ).
% 21.40/21.35
% 21.40/21.35 %----Helper facts (20)
% 21.40/21.35 fof(help_c__COMBI__1,axiom,
% 21.40/21.35 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__COMBK__1,axiom,
% 21.40/21.35 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__COMBB__1,axiom,
% 21.40/21.35 ! [V_R_2,V_Q_2,V_P_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__COMBC__1,axiom,
% 21.40/21.35 ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__COMBS__1,axiom,
% 21.40/21.35 ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fequal__1,axiom,
% 21.40/21.35 ! [V_y_2,V_x_2] :
% 21.40/21.35 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 21.40/21.35 | V_x_2 = V_y_2 ) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fequal__2,axiom,
% 21.40/21.35 ! [V_y_2,V_x_2] :
% 21.40/21.35 ( V_x_2 != V_y_2
% 21.40/21.35 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fFalse__1,axiom,
% 21.40/21.35 ~ hBOOL(c_fFalse) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fTrue__1,axiom,
% 21.40/21.35 hBOOL(c_fTrue) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fNot__1,axiom,
% 21.40/21.35 ! [V_P_2] :
% 21.40/21.35 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 21.40/21.35 | ~ hBOOL(V_P_2) ) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fNot__2,axiom,
% 21.40/21.35 ! [V_P_2] :
% 21.40/21.35 ( ~ ~ hBOOL(V_P_2)
% 21.40/21.35 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fconj__1,axiom,
% 21.40/21.35 ! [V_Q_2,V_P_2] :
% 21.40/21.35 ( ~ hBOOL(V_P_2)
% 21.40/21.35 | ~ hBOOL(V_Q_2)
% 21.40/21.35 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fconj__2,axiom,
% 21.40/21.35 ! [V_Q_2,V_P_2] :
% 21.40/21.35 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 21.40/21.35 | hBOOL(V_P_2) ) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fconj__3,axiom,
% 21.40/21.35 ! [V_Q_2,V_P_2] :
% 21.40/21.35 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 21.40/21.35 | hBOOL(V_Q_2) ) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fdisj__1,axiom,
% 21.40/21.35 ! [V_Q_2,V_P_2] :
% 21.40/21.35 ( ~ hBOOL(V_P_2)
% 21.40/21.35 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fdisj__2,axiom,
% 21.40/21.35 ! [V_P_2,V_Q_2] :
% 21.40/21.35 ( ~ hBOOL(V_Q_2)
% 21.40/21.35 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fdisj__3,axiom,
% 21.40/21.35 ! [V_Q_2,V_P_2] :
% 21.40/21.35 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 21.40/21.35 | hBOOL(V_P_2)
% 21.40/21.35 | hBOOL(V_Q_2) ) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fimplies__1,axiom,
% 21.40/21.35 ! [V_Q_2,V_P_2] :
% 21.40/21.35 ( hBOOL(V_P_2)
% 21.40/21.35 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fimplies__2,axiom,
% 21.40/21.35 ! [V_P_2,V_Q_2] :
% 21.40/21.35 ( ~ hBOOL(V_Q_2)
% 21.40/21.35 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 21.40/21.35
% 21.40/21.35 fof(help_c__fimplies__3,axiom,
% 21.40/21.35 ! [V_Q_2,V_P_2] :
% 21.40/21.35 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 21.40/21.35 | ~ hBOOL(V_P_2)
% 21.40/21.35 | hBOOL(V_Q_2) ) ).
% 21.40/21.35
% 21.40/21.35 %----Conjectures (2)
% 21.40/21.35 fof(conj_0,hypothesis,
% 21.40/21.35 ! [B_x] :
% 21.40/21.35 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
% 21.40/21.35 => c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x) ) ).
% 21.40/21.35
% 21.40/21.35 fof(conj_1,conjecture,
% 21.40/21.35 ! [B_Z,B_s] :
% 21.40/21.35 ( v_P(B_Z,B_s)
% 21.40/21.35 => ! [B_s_H] :
% 21.40/21.35 ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,B_s,v_n,B_s_H)
% 21.40/21.35 => v_P(B_Z,B_s_H) ) ) ).
% 21.40/21.35
% 21.40/21.35 %------------------------------------------------------------------------------
% 21.40/21.35 %-------------------------------------------
% 21.40/21.35 % Proof found
% 21.40/21.35 % SZS status Theorem for theBenchmark
% 21.40/21.35 % SZS output start Proof
% 21.40/21.35 %ClaNum:10090(EqnAxiom:2850)
% 21.40/21.35 %VarNum:77848(SingletonVarNum:23584)
% 21.40/21.35 %MaxLitNum:8
% 21.40/21.35 %MaxfuncDepth:13
% 21.40/21.35 %SharedTerms:1073
% 21.40/21.35 %goalClause: 3048 3439 4406
% 21.40/21.35 %singleGoalClaCount:3
% 21.40/21.35 [2854]P1(a182)
% 21.40/21.35 [2855]P2(a863)
% 21.40/21.35 [2856]P2(a1)
% 21.40/21.35 [2857]P2(a108)
% 21.40/21.35 [2858]P3(a1)
% 21.40/21.35 [2859]P137(a863)
% 21.40/21.35 [2860]P137(a1)
% 21.40/21.35 [2861]P4(a863)
% 21.40/21.35 [2862]P4(a1)
% 21.40/21.35 [2863]P4(a108)
% 21.40/21.35 [2864]P70(a863)
% 21.40/21.35 [2865]P70(a1)
% 21.40/21.35 [2866]P70(a108)
% 21.40/21.35 [2867]P71(a863)
% 21.40/21.35 [2868]P71(a1)
% 21.40/21.35 [2869]P71(a108)
% 21.40/21.35 [2870]P74(a863)
% 21.40/21.35 [2871]P74(a1)
% 21.40/21.35 [2872]P74(a108)
% 21.40/21.35 [2873]P5(a863)
% 21.40/21.35 [2874]P5(a1)
% 21.40/21.35 [2875]P5(a108)
% 21.40/21.35 [2876]P64(a863)
% 21.40/21.35 [2877]P64(a1)
% 21.40/21.35 [2878]P64(a108)
% 21.40/21.35 [2879]P65(a863)
% 21.40/21.35 [2880]P65(a1)
% 21.40/21.35 [2881]P65(a108)
% 21.40/21.35 [2882]P75(a863)
% 21.40/21.35 [2883]P75(a1)
% 21.40/21.35 [2884]P75(a108)
% 21.40/21.35 [2885]P81(a863)
% 21.40/21.35 [2886]P81(a1)
% 21.40/21.35 [2887]P81(a108)
% 21.40/21.35 [2888]P82(a863)
% 21.40/21.35 [2889]P82(a1)
% 21.40/21.35 [2890]P82(a108)
% 21.40/21.35 [2891]P110(a1)
% 21.40/21.35 [2892]P117(a863)
% 21.40/21.35 [2893]P117(a1)
% 21.40/21.35 [2894]P117(a108)
% 21.40/21.35 [2895]P86(a863)
% 21.40/21.35 [2896]P86(a1)
% 21.40/21.35 [2897]P86(a108)
% 21.40/21.35 [2898]P99(a863)
% 21.40/21.35 [2899]P99(a856)
% 21.40/21.35 [2900]P99(a1)
% 21.40/21.35 [2901]P99(a108)
% 21.40/21.35 [2902]P68(a1)
% 21.40/21.35 [2903]P120(a1)
% 21.40/21.35 [2904]P87(a1)
% 21.40/21.35 [2905]P66(a863)
% 21.40/21.35 [2906]P66(a1)
% 21.40/21.35 [2907]P66(a108)
% 21.40/21.35 [2908]P121(a1)
% 21.40/21.35 [2909]P111(a1)
% 21.40/21.35 [2910]P76(a1)
% 21.40/21.35 [2911]P6(a1)
% 21.40/21.35 [2912]P122(a863)
% 21.40/21.35 [2913]P122(a1)
% 21.40/21.35 [2914]P122(a108)
% 21.40/21.35 [2915]P133(a1)
% 21.40/21.35 [2916]P123(a863)
% 21.40/21.35 [2917]P123(a1)
% 21.40/21.35 [2918]P123(a108)
% 21.40/21.35 [2919]P135(a863)
% 21.40/21.35 [2920]P135(a1)
% 21.40/21.35 [2921]P135(a108)
% 21.40/21.35 [2922]P103(a863)
% 21.40/21.35 [2923]P103(a1)
% 21.40/21.35 [2924]P103(a108)
% 21.40/21.35 [2925]P118(a1)
% 21.40/21.35 [2926]P115(a863)
% 21.40/21.35 [2927]P115(a1)
% 21.40/21.35 [2928]P115(a108)
% 21.40/21.35 [2929]P124(a863)
% 21.40/21.35 [2930]P124(a1)
% 21.40/21.35 [2931]P124(a108)
% 21.40/21.35 [2932]P119(a1)
% 21.40/21.35 [2933]P77(a863)
% 21.40/21.35 [2934]P77(a1)
% 21.40/21.35 [2935]P77(a108)
% 21.40/21.35 [2936]P138(a863)
% 21.40/21.35 [2937]P138(a1)
% 21.40/21.35 [2938]P138(a108)
% 21.40/21.35 [2939]P69(a863)
% 21.40/21.35 [2940]P69(a1)
% 21.40/21.35 [2941]P69(a108)
% 21.40/21.35 [2942]P78(a863)
% 21.40/21.35 [2943]P78(a1)
% 21.40/21.35 [2944]P78(a108)
% 21.40/21.35 [2945]P79(a863)
% 21.40/21.35 [2946]P79(a1)
% 21.40/21.35 [2947]P79(a108)
% 21.40/21.35 [2948]P125(a1)
% 21.40/21.35 [2949]P127(a1)
% 21.40/21.35 [2950]P128(a863)
% 21.40/21.35 [2951]P128(a1)
% 21.40/21.35 [2952]P128(a108)
% 21.40/21.35 [2953]P129(a1)
% 21.40/21.35 [2954]P131(a863)
% 21.40/21.35 [2955]P131(a1)
% 21.40/21.35 [2956]P131(a108)
% 21.40/21.35 [2957]P130(a863)
% 21.40/21.35 [2958]P130(a1)
% 21.40/21.35 [2959]P130(a108)
% 21.40/21.35 [2960]P134(a1)
% 21.40/21.35 [2961]P104(a1)
% 21.40/21.35 [2962]P126(a863)
% 21.40/21.35 [2963]P126(a1)
% 21.40/21.35 [2964]P126(a108)
% 21.40/21.35 [2965]P105(a863)
% 21.40/21.35 [2966]P105(a856)
% 21.40/21.35 [2967]P105(a1)
% 21.40/21.35 [2968]P105(a108)
% 21.40/21.35 [2969]P90(a856)
% 21.40/21.35 [2970]P100(a863)
% 21.40/21.35 [2971]P100(a856)
% 21.40/21.35 [2972]P100(a1)
% 21.40/21.35 [2973]P100(a108)
% 21.40/21.35 [2974]P101(a863)
% 21.40/21.35 [2975]P101(a1)
% 21.40/21.35 [2976]P101(a108)
% 21.40/21.35 [2977]P83(a856)
% 21.40/21.35 [2978]P83(a1)
% 21.40/21.35 [2979]P84(a1)
% 21.40/21.35 [2980]P7(a863)
% 21.40/21.35 [2981]P7(a1)
% 21.40/21.35 [2982]P7(a108)
% 21.40/21.35 [2983]P8(a1)
% 21.40/21.35 [2984]P72(a863)
% 21.40/21.35 [2985]P72(a856)
% 21.40/21.35 [2986]P72(a1)
% 21.40/21.35 [2987]P72(a108)
% 21.40/21.35 [2988]P88(a1)
% 21.40/21.35 [2989]P89(a863)
% 21.40/21.35 [2990]P89(a1)
% 21.40/21.35 [2991]P89(a108)
% 21.40/21.35 [2992]P80(a1)
% 21.40/21.35 [2993]P132(a1)
% 21.40/21.35 [2994]P67(a1)
% 21.40/21.35 [2995]P106(a863)
% 21.40/21.35 [2996]P106(a1)
% 21.40/21.35 [2997]P106(a108)
% 21.40/21.35 [2998]P136(a863)
% 21.40/21.35 [2999]P136(a1)
% 21.40/21.35 [3000]P136(a108)
% 21.40/21.35 [3001]P102(a863)
% 21.40/21.35 [3002]P102(a856)
% 21.40/21.35 [3003]P112(a863)
% 21.40/21.35 [3004]P112(a1)
% 21.40/21.35 [3005]P112(a108)
% 21.40/21.35 [3006]P109(a1)
% 21.40/21.35 [3007]P92(a856)
% 21.40/21.35 [3008]P94(a863)
% 21.40/21.35 [3009]P94(a856)
% 21.40/21.35 [3010]P94(a1)
% 21.40/21.35 [3011]P95(a863)
% 21.40/21.35 [3012]P95(a856)
% 21.40/21.35 [3013]P95(a1)
% 21.40/21.35 [3014]P59(a856)
% 21.40/21.35 [3015]P59(a866)
% 21.40/21.35 [3016]P98(a863)
% 21.40/21.35 [3017]P98(a856)
% 21.40/21.35 [3018]P98(a1)
% 21.40/21.35 [3019]P96(a863)
% 21.40/21.35 [3020]P96(a856)
% 21.40/21.35 [3021]P96(a1)
% 21.40/21.35 [3022]P9(a856)
% 21.40/21.35 [3023]P97(a856)
% 21.40/21.35 [3024]P107(a856)
% 21.40/21.35 [3025]P73(a863)
% 21.40/21.35 [3026]P73(a1)
% 21.40/21.35 [3027]P73(a108)
% 21.40/21.35 [3028]P108(a863)
% 21.40/21.35 [3029]P139(a1)
% 21.40/21.35 [3030]P139(a866)
% 21.40/21.35 [3031]P85(a863)
% 21.40/21.35 [3032]P85(a1)
% 21.40/21.35 [3033]P85(a108)
% 21.40/21.35 [3034]P93(a856)
% 21.40/21.35 [3046]P36(a863,a245)
% 21.40/21.35 [3047]P36(a863,a331)
% 21.40/21.35 [3048]P142(a337,a788)
% 21.40/21.35 [3439]P39(a25,a788,a872,a790)
% 21.40/21.35 [4400]~E(a106,a92)
% 21.40/21.35 [4401]~E(a106,a92)
% 21.40/21.35 [4402]~P1(a183)
% 21.40/21.35 [4406]~P142(a337,a790)
% 21.40/21.35 [2851]E(f2(a1),a92)
% 21.40/21.35 [2852]E(f3(a108),a4)
% 21.40/21.35 [2853]E(f109(a108),a5)
% 21.40/21.35 [3035]E(f36(a25),f2(a863))
% 21.40/21.35 [3036]E(f93(a182),f2(a863))
% 21.40/21.35 [3037]E(f93(a183),f2(a863))
% 21.40/21.35 [3038]E(f184(a863),f2(a863))
% 21.40/21.35 [3039]E(f239(a863),f110(a863))
% 21.40/21.35 [3040]E(f244(a863),f111(a863))
% 21.40/21.35 [3041]E(f112(a1),f41(a1))
% 21.40/21.35 [3042]P10(f2(a1))
% 21.40/21.35 [3043]P10(f87(a1))
% 21.40/21.35 [3088]P1(f789(a26,a25))
% 21.40/21.35 [3089]P1(f789(a26,a25))
% 21.40/21.35 [3099]P36(f869(a863,a863),a47)
% 21.40/21.35 [3128]E(f170(a859,a857,a31),a32)
% 21.40/21.35 [3438]E(f333(a863,a863,a245,a245),a47)
% 21.40/21.35 [4403]~E(f87(a1),f2(a1))
% 21.40/21.35 [3044]E(f120(f2(a863)),f2(a863))
% 21.40/21.35 [3045]E(f6(f2(a108)),f2(a863))
% 21.40/21.35 [3052]E(f789(f88(a1),a92),a92)
% 21.40/21.35 [3055]E(f789(a114,f2(a1)),f2(a863))
% 21.40/21.35 [3056]E(f789(a5,f2(a863)),f2(a108))
% 21.40/21.35 [3057]E(f789(a121,f2(a863)),f87(a863))
% 21.40/21.35 [3058]E(f789(a114,f87(a1)),f87(a863))
% 21.40/21.35 [3059]E(f789(a5,f87(a863)),f87(a108))
% 21.40/21.35 [3060]E(f789(f113(a863),a92),f2(a863))
% 21.40/21.35 [3061]E(f789(f113(a1),a92),f2(a1))
% 21.40/21.35 [3062]E(f789(f113(a108),a92),f2(a108))
% 21.40/21.35 [3063]E(f789(a114,f2(a1)),f2(a863))
% 21.40/21.35 [3064]E(f789(f185(a857),a25),f2(a863))
% 21.40/21.35 [3065]E(f789(f185(a856),a182),f2(a863))
% 21.40/21.35 [3066]E(f789(f185(a856),a183),f2(a863))
% 21.40/21.35 [3067]E(f789(f113(a863),a92),f2(a863))
% 21.40/21.35 [3073]E(f789(f88(a1),f87(a1)),a106)
% 21.40/21.35 [3078]E(f789(f109(a1),f2(a863)),f2(a1))
% 21.40/21.35 [3079]E(f789(f109(a1),f87(a863)),f87(a1))
% 21.40/21.35 [3080]E(f789(f185(a863),f2(a863)),f2(a863))
% 21.40/21.35 [3081]E(f789(f185(a108),f2(a108)),f2(a863))
% 21.40/21.35 [3082]E(f789(f109(a1),f2(a863)),f2(a1))
% 21.40/21.35 [3083]E(f789(f109(a1),f87(a863)),f87(a1))
% 21.40/21.35 [3084]E(f789(f88(a1),f2(a1)),f2(a1))
% 21.40/21.35 [3095]E(f789(a114,f87(a1)),f789(a121,f2(a863)))
% 21.40/21.35 [3097]E(f332(f869(a863,a863),a47),a48)
% 21.40/21.35 [3098]E(f334(f869(a863,a863),a47),a77)
% 21.40/21.35 [3119]E(f789(f265(a863),f2(a863)),f184(f870(a863,a856)))
% 21.40/21.35 [3120]E(f789(f266(a863),f2(a863)),f247(f870(a863,a856)))
% 21.40/21.35 [3130]P38(f184(f870(a1,a856)))
% 21.40/21.35 [3165]E(f789(f789(f3(a108),f2(a108)),f87(a108)),f2(a108))
% 21.40/21.35 [3234]P1(f789(f789(f241(a1),a106),f2(a1)))
% 21.40/21.35 [3259]P1(f789(f789(f241(a1),f2(a1)),f87(a1)))
% 21.40/21.35 [3260]P1(f789(f789(f240(a1),f2(a1)),f2(a1)))
% 21.40/21.35 [3261]P1(f789(f789(f240(a1),f2(a1)),f87(a1)))
% 21.40/21.35 [3428]P1(f789(f70(a859),f173(a859,a857,a32)))
% 21.40/21.35 [3471]E(f789(f789(f289(a863,a863,a863),a331),f308(a863,a331)),a245)
% 21.40/21.35 [3512]P40(a1,a863,a114,f789(f240(a1),f2(a1)))
% 21.40/21.35 [3515]E(f789(f789(f53(a863,f870(a863,a856)),f247(f870(a863,a856))),f301(a863)),f247(f870(a863,a856)))
% 21.40/21.35 [3516]E(f789(f789(f53(a863,f870(a863,a856)),f247(f870(a863,a856))),f265(a863)),f247(f870(a863,a856)))
% 21.40/21.35 [3517]E(f789(f789(f53(a863,f870(a863,a856)),f247(f870(a863,a856))),f266(a863)),f247(f870(a863,a856)))
% 21.40/21.35 [3518]E(f789(f789(f54(a863,f870(a863,a856)),f247(f870(a863,a856))),f304(a863)),f184(f870(a863,a856)))
% 21.40/21.35 [3535]P29(a863,a1,f109(a1),f247(f870(a863,a856)))
% 21.40/21.35 [3547]P40(a863,a1,f109(a1),f789(f18(a856,a863),a182))
% 21.40/21.35 [3678]E(f789(f82(a863,a108,a1,a5),a114),f113(a108))
% 21.40/21.35 [3896]P55(a108,a863,a22,a5,f247(f870(a863,a856)))
% 21.40/21.35 [3904]P55(a1,f870(f869(a863,a863),a856),a117,a98,a107)
% 21.40/21.35 [4166]E(f260(a1,a1,a1,a1,f41(a1),f88(a1)),a65)
% 21.40/21.35 [4437]~E(f789(f113(a1),a106),f789(f113(a1),a92))
% 21.40/21.35 [4438]~P1(f789(a190,f2(a1)))
% 21.40/21.35 [4439]~P1(f789(a190,f87(a1)))
% 21.40/21.35 [4495]~P1(f789(f789(f241(a1),a92),f2(a1)))
% 21.40/21.35 [3111]E(f789(f789(f89(a1),a92),a106),a106)
% 21.40/21.35 [3112]E(f789(f789(f89(a1),a92),a92),a92)
% 21.40/21.35 [3113]E(f789(f789(f3(a1),a106),a106),a92)
% 21.40/21.35 [3127]E(f789(f109(a1),f789(a121,f2(a863))),f87(a1))
% 21.40/21.35 [3188]E(f789(f49(a866),f247(f870(a866,a856))),f87(a863))
% 21.40/21.35 [3209]P1(f789(a190,f789(f113(a1),a106)))
% 21.40/21.35 [3210]P1(f789(f789(f241(a1),a106),a92))
% 21.40/21.35 [3211]P1(f789(f789(f240(a1),a106),a106))
% 21.40/21.35 [3212]P1(f789(f789(f240(a1),a106),a92))
% 21.40/21.35 [3213]P1(f789(f789(f240(a1),a92),a92))
% 21.40/21.35 [3271]E(f789(f789(f310(a863),f2(a863)),f184(f870(a863,a856))),f789(f301(a863),f2(a863)))
% 21.40/21.35 [3326]P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),a92)))
% 21.40/21.35 [3338]E(f789(f311(a863,a863,a121),f247(f870(a863,a856))),f789(f304(a863),f2(a863)))
% 21.40/21.35 [3343]E(f789(f311(a1,a863,a114),f184(f870(a1,a856))),f184(f870(a863,a856)))
% 21.40/21.35 [3351]E(f789(f311(a863,a1,f109(a1)),f184(f870(a863,a856))),f184(f870(a1,a856)))
% 21.40/21.35 [3377]P12(f869(a863,a863),f247(f870(f869(a863,a863),a856)),a118)
% 21.40/21.35 [3685]E(f789(f82(a863,a1,a108,f109(a1)),a22),a23)
% 21.40/21.35 [3745]P36(a863,f789(f264(f869(a863,a863)),f789(f259(a863,a863,a856),f241(a863))))
% 21.40/21.35 [4486]~P1(f789(a190,f789(f113(a1),a92)))
% 21.40/21.35 [4487]~P1(f789(f789(f241(a1),a106),a106))
% 21.40/21.35 [4488]~P1(f789(f789(f241(a1),a92),a106))
% 21.40/21.35 [4489]~P1(f789(f789(f241(a1),a92),a92))
% 21.40/21.35 [4490]~P1(f789(f789(f240(a1),a92),a106))
% 21.40/21.35 [4505]~P1(f789(f70(a863),f247(f870(a863,a856))))
% 21.40/21.35 [4506]~P1(f789(f70(a1),f247(f870(a1,a856))))
% 21.40/21.35 [4330]E(f789(f259(a1,a1,a856),f789(f789(f10(f870(a1,a856),f870(a1,a856),a1),f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f241(a1),f2(a1))))),f789(f789(f9(a1,a1,f870(a1,a856)),f789(f789(f10(f870(a1,f870(a1,a856)),f870(a1,f870(a1,a856)),a1),f9(a1,a1,a856)),f789(f789(f10(f870(a1,a1),f870(a1,f870(a1,a856)),a1),f789(f10(a1,f870(a1,a856),a1),a338)),a219))),f87(a1)))),a215)
% 21.40/21.35 [3380]E(f789(f789(f3(a1),f789(f789(f89(a1),a106),a106)),a106),a106)
% 21.40/21.35 [3410]E(f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106),f789(f88(a1),a106))
% 21.40/21.35 [3453]E(f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106),f789(f789(f3(a1),a92),a106))
% 21.40/21.35 [3611]E(f789(f789(f68(f869(a863,a863)),f247(f870(f869(a863,a863),a856))),a118),a107)
% 21.40/21.35 [3639]E(f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f87(a863))
% 21.40/21.35 [3640]E(f789(f113(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f87(a1))
% 21.40/21.35 [3641]E(f789(f113(a108),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f87(a108))
% 21.40/21.35 [3642]E(f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f87(a863))
% 21.40/21.35 [3645]E(f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(a121,f2(a863)))
% 21.40/21.35 [4029]E(f789(f789(f110(f870(f869(f869(a863,a863),f869(a863,a863)),a856)),a47),f308(f869(a863,a863),f184(f870(f869(f869(a863,a863),f869(a863,a863)),a856)))),a79)
% 21.40/21.35 [4099]E(f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),f2(a863)),f2(a863))),f184(f870(f869(a863,a863),a856))))),f2(a1))
% 21.40/21.35 [4100]E(f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),f87(a863)),f2(a863))),f184(f870(f869(a863,a863),a856))))),f87(a1))
% 21.40/21.35 [4114]E(f789(f264(f869(a863,a863)),f789(f259(a863,a863,a856),f789(f789(f10(a863,f870(a863,a856),a863),f789(f9(a863,a863,a856),a338)),a121))),a331)
% 21.40/21.35 [4082]E(f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),f789(a121,f789(a121,f2(a863))))
% 21.40/21.35 [4083]E(f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),f789(a121,f789(a121,f2(a863))))
% 21.40/21.35 [4086]E(f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),f789(f789(f89(a863),f87(a863)),f87(a863)))
% 21.40/21.35 [4087]E(f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),f789(f49(a856),f247(f870(a856,a856))))
% 21.40/21.35 [4152]P10(f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))
% 21.40/21.35 [4225]P30(f870(f869(a863,a863),a856),f789(f789(f249(f870(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),a856),f870(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),a856)),a48),a78))
% 21.40/21.35 [4226]P30(f870(f869(a863,a863),a856),f789(f789(f249(f870(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),a856),f870(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),a856)),a77),a80))
% 21.40/21.35 [4263]E(f789(f789(f110(f870(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),a856)),f334(f869(a863,a863),a79)),f789(f789(f310(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f249(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),f184(f870(f869(a863,a863),a856))),f184(f870(f869(a863,a863),a856)))),f184(f870(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),a856)))),a80)
% 21.40/21.35 [4264]E(f789(f789(f110(f870(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),a856)),f332(f869(a863,a863),a79)),f789(f789(f310(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f249(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),f184(f870(f869(a863,a863),a856))),f184(f870(f869(a863,a863),a856)))),f184(f870(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),a856)))),a78)
% 21.40/21.35 [4154]E(f789(a114,f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(a121,f789(a121,f2(a863))))
% 21.40/21.35 [4201]E(f789(a114,f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))
% 21.40/21.35 [4202]E(f789(f109(a1),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))
% 21.40/21.35 [4235]P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))
% 21.40/21.35 [4236]E(f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106)),f789(a121,f789(a121,f789(a121,f2(a863)))))
% 21.40/21.35 [4276]P10(f789(f113(a1),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106)))
% 21.40/21.35 [4301]E(f789(a114,f789(f113(a1),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106))),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106)))
% 21.40/21.35 [4302]E(f789(f109(a1),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106))),f789(f113(a1),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106)))
% 21.40/21.35 [4316]P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106))))
% 21.40/21.35 [3049]P11(x30491,a338)
% 21.40/21.35 [3440]P29(a863,a863,a121,x34401)
% 21.40/21.35 [3068]P36(a1,f115(x30681))
% 21.40/21.35 [3069]P36(a1,f116(x30691))
% 21.40/21.35 [3072]P37(x30721,f187(x30721))
% 21.40/21.35 [3116]P36(f870(x31161,a856),f307(x31161))
% 21.40/21.35 [3156]E(f59(a1,x31561,x31561),f2(a1))
% 21.40/21.35 [3206]P19(x32061,f870(x32061,a856),f310(x32061))
% 21.40/21.35 [4407]~E(f789(a29,x44071),a25)
% 21.40/21.35 [4408]~E(f789(a29,x44081),a25)
% 21.40/21.35 [4409]~E(f789(a121,x44091),x44091)
% 21.40/21.35 [4410]~E(f789(a121,x44101),x44101)
% 21.40/21.35 [4417]~E(f789(a121,x44171),f2(a863))
% 21.40/21.35 [4418]~E(f789(a121,x44181),f2(a863))
% 21.40/21.35 [4419]~E(f789(a121,x44191),f2(a863))
% 21.40/21.35 [4420]~E(f789(a121,x44201),f2(a863))
% 21.40/21.35 [4421]~E(f789(a121,x44211),f2(a863))
% 21.40/21.35 [4422]~E(f789(a121,x44221),f2(a863))
% 21.40/21.35 [3050]E(f44(f42(x30501)),f2(a863))
% 21.40/21.35 [3051]E(f44(f43(x30511)),f2(a863))
% 21.40/21.35 [3053]E(f789(f185(a863),x30531),x30531)
% 21.40/21.35 [3054]E(f789(f113(a1),x30541),x30541)
% 21.40/21.35 [3070]E(f789(a98,f341(x30701)),x30701)
% 21.40/21.35 [3071]E(f246(x30711,f2(a108)),f2(a108))
% 21.40/21.35 [3085]E(f147(x30851,f122(x30851)),f122(x30851))
% 21.40/21.35 [3086]E(f123(x30861,f122(x30861)),f122(x30861))
% 21.40/21.35 [3090]E(f789(f185(a858),f42(x30901)),f2(a863))
% 21.40/21.35 [3091]E(f789(f185(a858),f43(x30911)),f2(a863))
% 21.40/21.35 [3092]E(f36(f789(a29,x30921)),f2(a863))
% 21.40/21.35 [3093]E(f789(f148(x30931),f122(x30931)),f122(x30931))
% 21.40/21.35 [3094]E(f789(f149(x30941),f122(x30941)),f122(x30941))
% 21.40/21.35 [3100]E(f789(f113(a1),x31001),f789(f112(a1),x31001))
% 21.40/21.35 [3101]E(f789(a5,f789(a22,x31011)),x31011)
% 21.40/21.35 [3102]E(f789(a5,f789(a22,x31021)),x31021)
% 21.40/21.35 [3103]E(f789(a22,f789(a5,x31031)),x31031)
% 21.40/21.35 [3104]E(f789(a98,f789(a117,x31041)),x31041)
% 21.40/21.35 [3105]P10(f789(f109(a1),x31051))
% 21.40/21.35 [3109]E(f789(f185(f867(x31091)),f187(x31091)),f2(a863))
% 21.40/21.35 [3110]E(f789(f185(f864(x31101)),f122(x31101)),f2(a863))
% 21.40/21.35 [3115]E(f789(f185(a857),f789(a29,x31151)),f2(a863))
% 21.40/21.35 [3125]E(f233(x31251,f187(x31251)),f184(f870(x31251,a856)))
% 21.40/21.35 [3133]E(f789(f789(f89(a863),x31331),f2(a863)),x31331)
% 21.40/21.35 [3134]E(f789(f789(f89(a1),x31341),f2(a1)),x31341)
% 21.40/21.35 [3135]E(f789(f789(f90(a863),x31351),f87(a863)),x31351)
% 21.40/21.35 [3136]E(f789(f789(f90(a1),x31361),f87(a1)),x31361)
% 21.40/21.35 [3137]E(f789(f789(f3(a863),x31371),f2(a863)),x31371)
% 21.40/21.35 [3138]E(f789(f789(f239(a863),x31381),f2(a863)),x31381)
% 21.40/21.35 [3139]E(f789(f789(f90(a863),x31391),f2(a863)),f2(a863))
% 21.40/21.35 [3140]E(f789(f789(f50(a1),x31401),f2(a1)),f2(a1))
% 21.40/21.35 [3141]E(f789(f789(f244(a863),x31411),f2(a863)),f2(a863))
% 21.40/21.35 [3147]E(f789(f163(x31471),f122(x31471)),f184(f870(x31471,a856)))
% 21.40/21.35 [3151]P1(f789(f134(x31511),f122(x31511)))
% 21.40/21.35 [3157]E(f789(f150(x31571,x31571),f7(x31571)),f41(f864(x31571)))
% 21.40/21.35 [3158]E(f789(f150(x31581,x31581),f41(x31581)),f41(f864(x31581)))
% 21.40/21.35 [3159]E(f789(f203(x31591,x31591),f7(x31591)),f41(f867(x31591)))
% 21.40/21.35 [3160]E(f789(f203(x31601,x31601),f41(x31601)),f41(f867(x31601)))
% 21.40/21.35 [3161]E(f59(a1,x31611,f2(a1)),x31611)
% 21.40/21.35 [3162]E(f789(f240(a863),f789(a121,x31621)),f789(f241(a863),x31621))
% 21.40/21.35 [3163]E(f789(f265(a863),f789(a121,x31631)),f789(f301(a863),x31631))
% 21.40/21.35 [3164]E(f789(f266(a863),f789(a121,x31641)),f789(f304(a863),x31641))
% 21.40/21.35 [3166]E(f59(a1,f2(a1),x31661),f2(a1))
% 21.40/21.35 [3173]E(f789(f789(f89(a863),x31731),f87(a863)),f789(a121,x31731))
% 21.40/21.35 [3183]E(f789(f302(a863,x31831),f2(a863)),f184(f870(a863,a856)))
% 21.40/21.35 [3193]E(f303(a863,f2(a863),x31931),f789(f301(a863),x31931))
% 21.40/21.35 [3237]E(f789(f789(f3(a863),f789(a121,x32371)),f87(a863)),x32371)
% 21.40/21.35 [3250]E(f61(f2(a1),x32501),f789(f789(f249(a1,a1),f2(a1)),f2(a1)))
% 21.40/21.35 [3254]E(f789(f789(f89(a863),f789(a22,x32541)),f2(a863)),f789(a22,x32541))
% 21.40/21.35 [3300]P1(f789(f789(f241(a863),x33001),f789(a121,x33001)))
% 21.40/21.35 [3314]P1(f789(f789(f241(a863),f2(a863)),f789(a121,x33141)))
% 21.40/21.35 [3324]E(f789(f789(f178(f864(x33241),f864(x33241)),f2(a863)),f148(x33241)),f41(f864(x33241)))
% 21.40/21.35 [3597]E(f789(f789(f3(a108),f789(a5,f789(a121,f789(a22,x35971)))),f87(a108)),x35971)
% 21.40/21.35 [3667]P1(f789(f789(f240(a1),f789(f88(a1),f789(f109(a1),x36671))),f2(a1)))
% 21.40/21.35 [3818]P1(f789(f789(f241(a1),f789(f88(a1),f789(f109(a1),f789(a121,x38181)))),f2(a1)))
% 21.40/21.35 [4445]~E(f247(f870(x44451,a856)),f184(f870(x44451,a856)))
% 21.40/21.35 [4496]~P1(f789(f789(f241(a863),x44961),f2(a863)))
% 21.40/21.35 [4497]~P1(f789(f789(f241(a863),x44971),f2(a863)))
% 21.40/21.35 [4498]~P1(f789(f789(f241(a863),x44981),f2(a863)))
% 21.40/21.35 [4514]~P1(f789(f789(f241(a1),f789(f109(a1),x45141)),f2(a1)))
% 21.40/21.35 [3114]E(f168(x31141,f122(f864(x31141))),f122(f864(x31141)))
% 21.40/21.35 [3117]E(f789(f789(f90(a1),a92),x31171),a92)
% 21.40/21.35 [3118]E(f789(f789(f89(a1),a92),x31181),x31181)
% 21.40/21.35 [3121]E(f789(a114,f789(f109(a1),x31211)),x31211)
% 21.40/21.35 [3122]E(f789(f789(f89(a1),x31221),a92),x31221)
% 21.40/21.35 [3123]E(f789(f789(f3(a1),x31231),a92),x31231)
% 21.40/21.35 [3126]E(f789(f789(f3(a863),x31261),x31261),f2(a863))
% 21.40/21.35 [3131]E(f789(f88(a1),f789(f88(a1),x31311)),x31311)
% 21.40/21.35 [3132]E(f789(f49(a863),f789(f265(a863),x31321)),x31321)
% 21.40/21.35 [3142]E(f789(f789(f89(a863),f2(a863)),x31421),x31421)
% 21.40/21.35 [3143]E(f789(f789(f89(a1),f2(a1)),x31431),x31431)
% 21.40/21.35 [3144]E(f789(f789(f90(a863),f87(a863)),x31441),x31441)
% 21.40/21.35 [3145]E(f789(f789(f90(a1),f87(a1)),x31451),x31451)
% 21.40/21.35 [3146]E(f789(f789(f239(a863),f2(a863)),x31461),x31461)
% 21.40/21.35 [3152]E(f789(f789(f90(a863),f2(a863)),x31521),f2(a863))
% 21.40/21.35 [3153]E(f789(f789(f50(a1),f2(a1)),x31531),f2(a1))
% 21.40/21.35 [3154]E(f789(f789(f3(a863),f2(a863)),x31541),f2(a863))
% 21.40/21.35 [3155]E(f789(f789(f244(a863),f2(a863)),x31551),f2(a863))
% 21.40/21.35 [3171]E(f789(f302(a863,f2(a863)),x31711),f789(f265(a863),x31711))
% 21.40/21.35 [3172]E(f789(f789(f90(a1),a106),x31721),f789(f88(a1),x31721))
% 21.40/21.35 [3174]E(f789(a114,f789(f113(a1),x31741)),f789(f113(a863),x31741))
% 21.40/21.35 [3175]E(f789(a114,f789(f113(a1),x31751)),f789(f113(a863),x31751))
% 21.40/21.35 [3176]E(f789(a22,f789(f113(a108),x31761)),f789(f113(a863),x31761))
% 21.40/21.35 [3177]E(f789(f49(a863),f789(f301(a863),x31771)),f789(a121,x31771))
% 21.40/21.35 [3186]E(f789(f789(f89(a863),f87(a863)),x31861),f789(a121,x31861))
% 21.40/21.35 [3189]E(f789(f112(a1),f789(f109(a1),x31891)),f789(f109(a1),x31891))
% 21.40/21.35 [3190]E(f789(f84(a1),f789(f109(a1),x31901)),f789(f109(a1),x31901))
% 21.40/21.35 [3195]E(f789(f49(x31951),f184(f870(x31951,a856))),f2(a863))
% 21.40/21.35 [3197]E(f789(f789(f50(a863),x31971),f789(a121,f2(a863))),x31971)
% 21.40/21.35 [3207]E(f59(a863,x32071,f789(a121,f2(a863))),f2(a863))
% 21.40/21.35 [3208]E(f59(a1,x32081,f789(f113(a1),a106)),f2(a1))
% 21.40/21.35 [3215]E(f789(f789(f89(a1),a106),x32151),f789(f789(f89(a1),x32151),a106))
% 21.40/21.35 [3222]E(f789(f789(f50(a1),x32221),f789(f113(a1),a106)),f789(f88(a1),x32221))
% 21.40/21.35 [3226]E(f136(a863,f789(f302(a863,x32261),f2(a863))),f122(a863))
% 21.40/21.35 [3227]E(f789(f789(f3(a1),x32271),f87(a1)),f789(f789(f89(a1),x32271),a106))
% 21.40/21.35 [3228]E(f789(f789(f89(a1),x32281),f87(a1)),f789(f789(f3(a1),x32281),a106))
% 21.40/21.35 [3229]P1(f789(f789(f191(a25),x32291),x32291))
% 21.40/21.35 [3230]P1(f789(f789(f191(a25),x32301),x32301))
% 21.40/21.35 [3231]P1(f789(f789(f240(a863),x32311),x32311))
% 21.40/21.35 [3232]P1(f789(f789(f240(a1),x32321),x32321))
% 21.40/21.35 [3233]P1(f789(f789(f287(a863),x32331),x32331))
% 21.40/21.35 [3238]E(f789(f88(a1),f789(f113(a1),x32381)),f789(f113(a1),f789(f88(a1),x32381)))
% 21.40/21.35 [3239]P1(f789(f70(a863),f789(f301(a863),x32391)))
% 21.40/21.35 [3240]P1(f789(f70(a863),f789(f265(a863),x32401)))
% 21.40/21.35 [3248]E(f156(x32481,f247(f870(x32481,a856))),f247(f870(f864(x32481),a856)))
% 21.40/21.35 [3252]P1(f789(f789(f240(a863),f2(a863)),x32521))
% 21.40/21.35 [3253]P1(f789(f789(f240(a863),f2(a863)),x32531))
% 21.40/21.35 [3264]E(f789(f789(f89(a863),f120(x32641)),f789(a121,f2(a863))),f120(f789(a121,x32641)))
% 21.40/21.35 [3265]E(f789(f264(x32651),f789(f18(a856,x32651),a183)),f184(f870(x32651,a856)))
% 21.40/21.35 [3266]E(f789(f264(x32661),f789(f18(a856,x32661),a182)),f247(f870(x32661,a856)))
% 21.40/21.35 [3270]E(f789(f789(f310(a863),x32701),f789(f265(a863),x32701)),f789(f265(a863),f789(a121,x32701)))
% 21.40/21.35 [3280]E(f789(f789(f89(a1),f87(a1)),f789(f109(a1),x32801)),f789(f109(a1),f789(a121,x32801)))
% 21.40/21.35 [3303]E(f184(f870(f869(x33031,x33031),a856)),f268(x33031,f184(f870(x33031,a856))))
% 21.40/21.35 [3304]E(f789(f309(x33041),f247(f870(x33041,a856))),f247(f870(f870(x33041,a856),a856)))
% 21.40/21.35 [3305]E(f789(f88(f870(x33051,a856)),f184(f870(x33051,a856))),f247(f870(x33051,a856)))
% 21.40/21.35 [3306]E(f789(f88(f870(x33061,a856)),f247(f870(x33061,a856))),f184(f870(x33061,a856)))
% 21.40/21.35 [3307]P1(f789(f70(x33071),f184(f870(x33071,a856))))
% 21.40/21.35 [3308]P1(f789(f70(x33081),f184(f870(x33081,a856))))
% 21.40/21.35 [3310]E(f789(f302(a863,x33101),f789(a121,x33101)),f789(f789(f310(a863),x33101),f184(f870(a863,a856))))
% 21.40/21.35 [3311]E(f94(f869(a863,a863),f62(x33111,f2(a863))),f789(f789(f249(a863,a863),f2(a863)),x33111))
% 21.40/21.35 [3325]E(f789(f789(f310(a863),f789(a121,x33251)),f789(f301(a863),x33251)),f789(f301(a863),f789(a121,x33251)))
% 21.40/21.35 [3328]P36(x33281,f184(f870(f869(x33281,x33281),a856)))
% 21.40/21.35 [3330]P1(f789(f789(f240(a1),f2(a1)),f789(f109(a1),x33301)))
% 21.40/21.35 [3331]P1(f789(f789(f240(a1),f2(a1)),f789(f109(a1),x33311)))
% 21.40/21.35 [3340]E(f789(f789(f89(a863),f789(f185(a863),x33401)),f789(a121,f2(a863))),f789(f185(a863),f789(a121,x33401)))
% 21.40/21.35 [3392]E(f789(f311(x33921,x33921,f41(x33921)),f247(f870(x33921,a856))),f247(f870(x33921,a856)))
% 21.40/21.35 [3447]P38(f789(f311(a863,a1,f109(a1)),x34471))
% 21.40/21.35 [3486]P47(x34861,f184(f870(x34861,a856)),f184(f870(f869(x34861,x34861),a856)))
% 21.40/21.35 [3509]E(f789(f789(f249(a1,a1),f789(f113(a1),a106)),f789(f789(f3(a1),x35091),f87(a1))),f64(f789(f113(a1),a106),x35091))
% 21.40/21.35 [3510]P1(f789(f789(f342(a863),f789(a22,x35101)),f247(f870(a863,a856))))
% 21.40/21.35 [3560]P58(x35601,f789(f18(f870(x35601,a856),x35601),f789(f18(a856,x35601),a183)))
% 21.40/21.35 [3568]E(f290(a863,f287(a863),x35681,x35681),f789(f789(f310(a863),x35681),f184(f870(a863,a856))))
% 21.40/21.35 [3739]E(f789(f138(f864(x37391),f864(x37391),f132(x37391),f122(x37391)),f122(f864(x37391))),f122(x37391))
% 21.40/21.35 [3759]P1(f789(f789(f342(f870(f869(a863,a863),a856)),f341(x37591)),a107))
% 21.40/21.35 [3782]P1(f789(f789(f342(f870(f869(a863,a863),a856)),f789(a117,x37821)),a107))
% 21.40/21.35 [3914]P29(x39141,f870(x39141,a856),f789(f789(f9(x39141,f870(x39141,a856),f870(x39141,a856)),f310(x39141)),f184(f870(x39141,a856))),f247(f870(x39141,a856)))
% 21.40/21.35 [4440]~E(f789(f789(f89(a1),x44401),x44401),a106)
% 21.40/21.35 [4441]~E(f789(f789(f89(a1),x44411),x44411),a106)
% 21.40/21.35 [4484]~E(f789(a5,f789(a121,f789(a22,x44841))),f2(a108))
% 21.40/21.35 [4485]~E(f789(a5,f789(a121,f789(a22,x44851))),f2(a108))
% 21.40/21.35 [4491]~P1(f789(a190,f789(f109(a1),x44911)))
% 21.40/21.35 [4493]~P1(f789(f789(f241(a863),x44931),x44931))
% 21.40/21.35 [4494]~P1(f789(f789(f241(a863),x44941),x44941))
% 21.40/21.35 [4507]~P1(f789(f789(f240(a863),f789(a121,x45071)),x45071))
% 21.40/21.35 [3255]E(f789(a114,f789(f88(a1),f789(f109(a1),x32551))),f2(a863))
% 21.40/21.35 [3258]E(f789(f789(f89(a1),f789(f88(a1),x32581)),x32581),f2(a1))
% 21.40/21.35 [3263]E(f789(f49(a1),f789(f302(a1,f2(a1)),x32631)),f789(a114,x32631))
% 21.40/21.35 [3274]E(f789(f789(f250(a863),f789(a121,f2(a863))),x32741),f789(a121,f2(a863)))
% 21.40/21.35 [3374]E(f789(f284(x33741),f184(f870(f869(x33741,x33741),a856))),f184(f870(x33741,a856)))
% 21.40/21.35 [3376]P1(f789(f70(a1),f789(f302(a1,f2(a1)),x33761)))
% 21.40/21.35 [3382]E(f52(f870(x33821,a856),f184(f870(f870(x33821,a856),a856))),f247(f870(x33821,a856)))
% 21.40/21.35 [3383]E(f52(f870(x33831,a856),f247(f870(f870(x33831,a856),a856))),f184(f870(x33831,a856)))
% 21.40/21.35 [3384]E(f51(f870(x33841,a856),f184(f870(f870(x33841,a856),a856))),f184(f870(x33841,a856)))
% 21.40/21.35 [3385]E(f51(f870(x33851,a856),f247(f870(f870(x33851,a856),a856))),f247(f870(x33851,a856)))
% 21.40/21.35 [3390]P1(f789(f789(f287(a863),f789(a121,f2(a863))),x33901))
% 21.40/21.35 [3426]E(f789(f789(f310(f864(x34261)),f122(x34261)),f184(f870(f864(x34261),a856))),f157(x34261,f122(f870(x34261,a856))))
% 21.40/21.35 [3427]E(f789(f789(f310(f864(x34271)),f122(x34271)),f184(f870(f864(x34271),a856))),f156(x34271,f184(f870(x34271,a856))))
% 21.40/21.35 [3459]E(f789(f789(f89(a1),f789(f88(a1),x34591)),f789(f88(a1),x34591)),f789(f88(a1),f789(f789(f89(a1),x34591),x34591)))
% 21.40/21.35 [3470]E(f789(f789(f89(a863),f6(x34701)),f789(a121,f2(a863))),f6(f789(a5,f789(a121,f789(a22,x34701)))))
% 21.40/21.35 [3501]E(f789(f49(a1),f789(f311(a863,a1,f109(a1)),x35011)),f789(f49(a863),x35011))
% 21.40/21.35 [3504]P1(f789(f789(f240(a863),x35041),f789(f789(f90(a863),x35041),x35041)))
% 21.40/21.35 [3541]E(f789(f311(a1,a863,a114),f303(a1,f2(a1),f789(f109(a1),x35411))),f789(f301(a863),x35411))
% 21.40/21.35 [3555]E(f789(f789(f50(a863),f789(a121,f2(a863))),f789(f113(a863),x35551)),f789(a114,f789(f789(f50(a1),f87(a1)),f789(f113(a1),x35551))))
% 21.40/21.35 [3557]E(f789(f163(a863),f136(a863,f789(f302(a863,f2(a863)),f789(a121,x35571)))),f789(f301(a863),x35571))
% 21.40/21.35 [3558]E(f789(f789(f89(a863),f789(f185(a108),x35581)),f789(a121,f2(a863))),f789(f185(a108),f789(a5,f789(a121,f789(a22,x35581)))))
% 21.40/21.35 [3573]E(f789(f311(a1,a863,a114),f789(f311(a863,a1,f109(a1)),x35731)),x35731)
% 21.40/21.35 [3602]E(f789(f789(f310(a863),f2(a863)),f789(f311(a863,a863,a121),f789(f265(a863),x36021))),f789(f265(a863),f789(a121,x36021)))
% 21.40/21.35 [3610]P53(x36101,x36101,f308(x36101,f184(f870(f869(x36101,x36101),a856))))
% 21.40/21.35 [3616]P1(f789(a190,f789(f88(a1),f789(f109(a1),f789(a121,x36161)))))
% 21.40/21.35 [3626]E(f789(f789(f3(f870(a863,a856)),f789(f266(a863),x36261)),f789(f789(f310(a863),x36261),f184(f870(a863,a856)))),f789(f266(a863),f789(a121,x36261)))
% 21.40/21.35 [3643]E(f789(f789(f89(a1),f789(f789(f3(a1),a92),x36431)),f789(f789(f3(a1),a92),x36431)),f789(f789(f3(a1),a92),f789(f789(f89(a1),x36431),x36431)))
% 21.40/21.35 [3646]P47(x36461,f247(f870(x36461,a856)),f308(x36461,f184(f870(f869(x36461,x36461),a856))))
% 21.40/21.35 [3657]E(f789(f789(f310(f870(x36571,a856)),f184(f870(x36571,a856))),f184(f870(f870(x36571,a856),a856))),f789(f309(x36571),f184(f870(x36571,a856))))
% 21.40/21.35 [3686]E(f789(f789(f3(f870(a863,a856)),f789(f304(a863),x36861)),f789(f789(f310(a863),f789(a121,x36861)),f184(f870(a863,a856)))),f789(f304(a863),f789(a121,x36861)))
% 21.40/21.35 [3695]E(f789(f789(f310(f867(x36951)),f187(x36951)),f789(f311(x36951,f867(x36951),f234(x36951)),f247(f870(x36951,a856)))),f247(f870(f867(x36951),a856)))
% 21.40/21.35 [3794]E(f789(f113(a863),f789(f789(f89(a1),x37941),x37941)),f789(f789(f95(a863,a863),f789(f113(a863),x37941)),f789(f789(f20(a863,a863,a863),f89(a863)),f7(a863))))
% 21.40/21.35 [4177]P19(x41771,f870(x41771,a856),f789(f789(f10(f870(x41771,a856),f870(f870(x41771,a856),f870(x41771,a856)),x41771),f789(f9(f870(x41771,a856),f870(x41771,a856),f870(x41771,a856)),f3(f870(x41771,a856)))),f789(f789(f9(x41771,f870(x41771,a856),f870(x41771,a856)),f310(x41771)),f184(f870(x41771,a856)))))
% 21.40/21.35 [4262]E(f789(f264(f869(a1,a1)),f789(f259(a1,a1,a856),f789(f789(f10(f870(a1,a856),f870(a1,a856),a1),f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f240(a1),x42621)))),f241(a1)))),f115(x42621))
% 21.40/21.35 [4294]E(f789(f264(f869(a1,a1)),f789(f259(a1,a1,a856),f789(f789(f20(a1,f870(a1,a856),f870(a1,a856)),f789(f789(f10(f870(a856,a856),f870(f870(a1,a856),f870(a1,a856)),a1),f10(a856,a856,a1)),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f240(a1),x42941)))),f241(a1)))),f116(x42941))
% 21.40/21.35 [4345]E(f789(f264(f869(f870(x43451,a856),f870(x43451,a856))),f789(f259(f870(x43451,a856),f870(x43451,a856),a856),f789(f789(f9(f870(x43451,a856),f870(f870(x43451,a856),a856),f870(f870(x43451,a856),a856)),f789(f789(f10(f870(f870(x43451,a856),f870(a856,a856)),f870(f870(f870(x43451,a856),a856),f870(f870(x43451,a856),a856)),f870(x43451,a856)),f20(f870(x43451,a856),a856,a856)),f789(f789(f10(f870(f870(x43451,a856),a856),f870(f870(x43451,a856),f870(a856,a856)),f870(x43451,a856)),f789(f10(a856,f870(a856,a856),f870(x43451,a856)),a339)),f241(f870(x43451,a856))))),f70(x43451)))),f307(x43451))
% 21.40/21.35 [4511]~P1(f789(f70(f864(x45111)),f247(f870(f864(x45111),a856))))
% 21.40/21.35 [4524]~P1(f789(f789(f240(a1),f2(a1)),f789(f88(a1),f789(f109(a1),f789(a121,x45241)))))
% 21.40/21.35 [3404]E(f789(f789(f3(a1),f789(f789(f89(a1),x34041),a106)),a106),x34041)
% 21.40/21.35 [3420]E(f789(f163(a863),f136(a863,f789(f302(a863,f2(a863)),x34201))),f789(f265(a863),x34201))
% 21.40/21.35 [3618]E(f789(f267(x36181,x36181),f308(x36181,f184(f870(f869(x36181,x36181),a856)))),f247(f870(x36181,a856)))
% 21.40/21.35 [3619]E(f789(f269(x36191,x36191),f308(x36191,f184(f870(f869(x36191,x36191),a856)))),f247(f870(x36191,a856)))
% 21.40/21.35 [3663]E(f789(f789(f89(a1),f789(f789(f89(a1),f87(a1)),x36631)),x36631),f789(f789(f3(a1),f789(f789(f89(a1),x36631),x36631)),a106))
% 21.40/21.35 [3713]E(f789(f286(x37131,x37131),f308(x37131,f184(f870(f869(x37131,x37131),a856)))),f308(x37131,f184(f870(f869(x37131,x37131),a856))))
% 21.40/21.35 [3762]P1(f789(f789(f240(a863),x37621),f789(f789(f90(a863),x37621),f789(f789(f90(a863),x37621),x37621))))
% 21.40/21.35 [3848]E(f789(f789(f289(x38481,x38481,x38481),f184(f870(f869(x38481,x38481),a856))),f308(x38481,f184(f870(f869(x38481,x38481),a856)))),f184(f870(f869(x38481,x38481),a856)))
% 21.40/21.35 [4033]P1(f789(f70(a863),f789(f264(a863),f789(f789(f9(a863,a863,a856),f241(a863)),x40331))))
% 21.40/21.35 [4034]P1(f789(f70(a863),f789(f264(a863),f789(f789(f9(a863,a863,a856),f240(a863)),x40341))))
% 21.40/21.35 [4312]E(f789(f264(f869(x43121,x43121)),f789(f789(f10(f870(x43121,a856),a856,f869(x43121,x43121)),f96(x43121)),f789(f789(f9(f869(x43121,x43121),f870(x43121,f869(x43121,x43121)),f870(x43121,a856)),f789(f789(f10(f870(f869(x43121,x43121),a856),f870(f870(x43121,f869(x43121,x43121)),f870(x43121,a856)),f869(x43121,x43121)),f10(f869(x43121,x43121),a856,x43121)),a338)),f789(f789(f20(x43121,x43121,f869(x43121,x43121)),f249(x43121,x43121)),f7(x43121))))),f308(x43121,f184(f870(f869(x43121,x43121),a856))))
% 21.40/21.35 [4512]~E(f789(f789(f3(a1),f789(f789(f89(a1),x45121),x45121)),a106),a92)
% 21.40/21.35 [4513]~E(f789(f789(f3(a1),f789(f789(f89(a1),x45131),x45131)),a106),a92)
% 21.40/21.35 [4515]~E(f789(f789(f89(a1),f789(f789(f89(a1),f87(a1)),x45151)),x45151),f2(a1))
% 21.40/21.35 [3806]E(f789(f789(f89(a1),f789(f789(f3(a1),a106),x38061)),f789(f789(f3(a1),a106),x38061)),f789(f789(f3(a1),a106),f789(f789(f3(a1),f789(f789(f89(a1),x38061),x38061)),a106)))
% 21.40/21.35 [3921]E(f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),a106),x39211)),f789(f789(f3(a1),a106),x39211))),a106),f789(f789(f3(a1),a106),f789(f789(f89(a1),x39211),x39211)))
% 21.40/21.35 [3955]E(f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f89(a1),x39551),a106)),f789(f789(f89(a1),x39551),a106))),a106),f789(f789(f89(a1),f789(f789(f89(a1),x39551),x39551)),a106))
% 21.40/21.35 [3993]E(f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),a106),x39931)),f789(f789(f3(a1),a106),x39931))),a106),f789(f789(f3(a1),a92),f789(f789(f3(a1),f789(f789(f89(a1),x39931),x39931)),a106)))
% 21.40/21.35 [4095]E(f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x40951),f2(a863))),f184(f870(f869(a863,a863),a856))))),f789(f109(a1),x40951))
% 21.40/21.35 [4104]E(f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),f345(x41041)),f376(x41041))),f184(f870(f869(a863,a863),a856))))),x41041)
% 21.40/21.35 [4137]E(f789(f264(a1),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f240(a1),f2(a1)))),x41371)),f789(f311(a863,a1,f109(a1)),f789(f264(a863),f789(f789(f10(a1,a856,a863),x41371),f109(a1)))))
% 21.40/21.35 [4185]P38(f789(f264(a1),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f240(a1),f2(a1)))),x41851)))
% 21.40/21.35 [4205]P1(f789(f789(f342(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f249(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),x42051),f184(f870(f869(a863,a863),a856)))),a80))
% 21.40/21.35 [4211]E(f789(f311(a1,a863,a114),f789(f264(a1),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f240(a1),f2(a1)))),f789(f789(f10(a863,a856,a1),x42111),a114)))),f789(f264(a863),x42111))
% 21.40/21.35 [4359]E(f314(a863,f789(f789(f53(f869(a863,a863),f870(a863,a856)),f789(a117,x43591)),f789(f259(a863,a863,f870(a863,a856)),f789(f789(f9(a863,f870(a863,a856),f870(a863,f870(a863,a856))),f789(f789(f10(f870(a863,f870(f870(a863,a856),f870(a863,a856))),f870(f870(a863,a856),f870(a863,f870(a863,a856))),a863),f9(a863,f870(a863,a856),f870(a863,a856))),f789(f789(f10(f870(a863,a863),f870(a863,f870(f870(a863,a856),f870(a863,a856))),a863),f789(f10(a863,f870(f870(a863,a856),f870(a863,a856)),a863),f310(a863))),f3(a863)))),f184(f870(a863,a856)))))),f789(a114,x43591))
% 21.40/21.35 [3849]E(f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),x38491),x38491)),a106)),a106),f789(f789(f89(a1),x38491),x38491))
% 21.40/21.35 [3897]E(f789(f789(f3(a1),f789(f789(f3(a1),f789(f789(f89(a1),x38971),x38971)),a106)),a106),f789(f789(f89(a1),f789(f789(f3(a1),x38971),a106)),f789(f789(f3(a1),x38971),a106)))
% 21.40/21.35 [4112]E(f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f89(a1),f789(f88(a1),x41121)),a106)),f789(f789(f89(a1),f789(f88(a1),x41121)),a106))),a106),f789(f88(a1),f789(f789(f3(a1),f789(f789(f89(a1),x41121),x41121)),a106)))
% 21.40/21.35 [4155]E(f789(f789(f89(a863),x41551),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(a121,f789(a121,x41551)))
% 21.40/21.35 [4156]E(f789(f789(f90(a863),x41561),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f789(f89(a863),x41561),x41561))
% 21.40/21.35 [4157]E(f789(f789(f50(a863),f789(f789(f89(a863),x41571),x41571)),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x41571)
% 21.40/21.35 [4238]E(f59(a863,f789(a121,f789(a121,x42381)),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f59(a863,x42381,f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))
% 21.40/21.35 [4376]E(f789(a98,f789(f789(f53(f869(a863,a863),f870(f869(a863,a863),a856)),f789(a117,x43761)),f789(f259(a863,a863,f870(f869(a863,a863),a856)),f789(f789(f10(f870(a863,f870(f869(a863,a863),a856)),f870(a863,f870(f869(a863,a863),a856)),a863),f789(f10(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856),a863),f285(f869(a863,a863),f869(a863,a863),a118))),f789(f789(f9(a863,f870(f869(a863,a863),a856),f870(a863,f870(f869(a863,a863),a856))),f789(f789(f10(f870(a863,f870(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f870(f870(f869(a863,a863),a856),f870(a863,f870(f869(a863,a863),a856))),a863),f9(a863,f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f10(f870(a863,f869(a863,a863)),f870(a863,f870(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),a863),f789(f10(f869(a863,a863),f870(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),a863),f310(f869(a863,a863)))),f789(f9(a863,a863,f869(a863,a863)),f249(a863,a863))))),f184(f870(f869(a863,a863),a856))))))),f789(f88(a1),x43761))
% 21.40/21.35 [4233]E(f789(f789(f89(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x42331),f789(a121,f789(a121,x42331)))
% 21.40/21.35 [4234]E(f789(f789(f90(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x42341),f789(f789(f89(a863),x42341),x42341))
% 21.40/21.35 [4267]E(f789(f789(f50(a863),f789(a121,f789(a121,x42671))),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(a121,f789(f789(f50(a863),x42671),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))
% 21.40/21.35 [4317]E(f789(f789(f89(a863),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106))),x43171),f789(a121,f789(a121,f789(a121,x43171))))
% 21.40/21.35 [4397]E(f789(f259(a1,a1,f869(a1,a1)),f789(f789(f20(a1,f870(a1,f869(a1,a1)),f870(a1,f869(a1,a1))),f789(f789(f10(f870(a1,f870(f869(a1,a1),f869(a1,a1))),f870(f870(a1,f869(a1,a1)),f870(a1,f869(a1,a1))),a1),f20(a1,f869(a1,a1),f869(a1,a1))),f789(f789(f10(f870(a1,f869(a1,a1)),f870(a1,f870(f869(a1,a1),f869(a1,a1))),a1),f789(f20(a1,f869(a1,a1),f870(f869(a1,a1),f869(a1,a1))),f789(f789(f10(a856,f870(f869(a1,a1),f870(f869(a1,a1),f869(a1,a1))),a1),f105(f869(a1,a1))),f789(f789(f10(a1,a856,a1),f789(f240(a1),f2(a1))),f789(f789(f9(a1,a1,a1),f3(a1)),x43971))))),f789(f789(f9(a1,f870(a1,a1),f870(a1,f869(a1,a1))),f789(f789(f10(f870(a1,f869(a1,a1)),f870(f870(a1,a1),f870(a1,f869(a1,a1))),a1),f10(a1,f869(a1,a1),a1)),f789(f789(f10(a1,f870(a1,f869(a1,a1)),a1),f249(a1,a1)),f789(f789(f9(a1,a1,a1),f789(f789(f10(a1,f870(a1,a1),a1),f89(a1)),f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))),f87(a1))))),f789(f789(f9(a1,a1,a1),f3(a1)),x43971))))),f789(f789(f10(a1,f870(a1,f869(a1,a1)),a1),f249(a1,a1)),f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))),f57(x43971))
% 21.40/21.35 [3448]P39(a25,x34481,x34482,x34481)
% 21.40/21.35 [3449]P39(a25,x34491,x34492,x34491)
% 21.40/21.35 [3108]P18(a1,f167(x31081,x31082))
% 21.40/21.35 [3203]P47(x32031,x32032,f268(x32031,x32032))
% 21.40/21.35 [3204]P53(x32041,x32041,f268(x32041,x32042))
% 21.40/21.35 [3473]P29(x34731,x34731,f7(x34731),x34732)
% 21.40/21.35 [3474]P29(x34741,x34741,f41(x34741),x34742)
% 21.40/21.35 [3480]P34(x34801,x34802,f122(x34801),f122(x34801))
% 21.40/21.35 [3481]P34(x34811,x34812,f122(x34811),f122(x34811))
% 21.40/21.35 [3482]P29(x34821,f867(x34821),f234(x34821),x34822)
% 21.40/21.35 [3491]P29(f864(x34911),f864(x34911),f149(x34911),x34912)
% 21.40/21.35 [4404]~E(f43(x44041),f42(x44042))
% 21.40/21.35 [4405]~E(f43(x44051),f42(x44052))
% 21.40/21.35 [4411]~E(f38(x44111,x44112),a25)
% 21.40/21.35 [4412]~E(f30(x44121,x44122),a25)
% 21.40/21.35 [4413]~E(f37(x44131,x44132),a25)
% 21.40/21.35 [4414]~E(f38(x44141,x44142),a25)
% 21.40/21.35 [4415]~E(f30(x44151,x44152),a25)
% 21.40/21.35 [4416]~E(f37(x44161,x44162),a25)
% 21.40/21.35 [3074]E(f789(f7(x30741),x30742),x30742)
% 21.40/21.35 [3075]E(f789(f264(x30751),x30752),x30752)
% 21.40/21.35 [3076]E(f789(f41(x30761),x30762),x30762)
% 21.40/21.35 [3077]E(f789(f41(x30771),x30772),x30772)
% 21.40/21.35 [3087]E(f789(f188(x30871),x30872),f124(x30871))
% 21.40/21.35 [3096]E(f36(f30(x30961,x30962)),f2(a863))
% 21.40/21.35 [3106]E(f94(x31061,f789(a338,x31062)),x31062)
% 21.40/21.35 [3107]E(f99(x31071,f789(a338,x31072)),x31072)
% 21.40/21.35 [3124]E(f789(f185(a857),f30(x31241,x31242)),f2(a863))
% 21.40/21.36 [3129]E(f789(f133(x31291,x31292),f122(x31291)),f122(x31291))
% 21.40/21.36 [3148]E(f308(x31481,f308(x31481,x31482)),f308(x31481,x31482))
% 21.40/21.36 [3169]E(f789(f789(f132(x31691),x31692),f122(x31691)),x31692)
% 21.40/21.36 [3178]E(f789(f789(f164(x31781),x31782),f122(x31781)),f122(x31781))
% 21.40/21.36 [3179]E(f789(f789(f135(x31791),x31792),f122(x31791)),f122(x31791))
% 21.40/21.36 [3181]E(f235(x31811,x31812,f187(x31811)),f2(a863))
% 21.40/21.36 [3182]E(f151(x31821,x31822,f122(x31821)),f2(a863))
% 21.40/21.36 [3184]E(f158(x31841,x31842,f122(x31841)),f122(x31841))
% 21.40/21.36 [3185]E(f165(x31851,f122(x31851),x31852),f122(x31851))
% 21.40/21.36 [3191]E(f789(f267(x31911,x31911),f268(x31911,x31912)),x31912)
% 21.40/21.36 [3192]E(f789(f269(x31921,x31921),f268(x31921,x31922)),x31922)
% 21.40/21.36 [3200]P1(f789(a26,f30(x32001,x32002)))
% 21.40/21.36 [3201]P1(f789(a26,f30(x32011,x32012)))
% 21.40/21.36 [3202]E(f789(f286(x32021,x32021),f268(x32021,x32022)),f268(x32021,x32022))
% 21.40/21.36 [3214]E(f308(f864(x32141),f153(x32141,x32142)),f154(x32141,f308(x32141,x32142)))
% 21.40/21.36 [3216]P1(f789(f134(a1),f167(x32161,x32162)))
% 21.40/21.36 [3224]E(f789(f267(x32241,x32241),f308(x32241,x32242)),f247(f870(x32241,a856)))
% 21.40/21.36 [3225]E(f789(f269(x32251,x32251),f308(x32251,x32252)),f247(f870(x32251,a856)))
% 21.40/21.36 [3235]E(f789(f163(a1),f167(x32351,x32352)),f303(a1,x32351,x32352))
% 21.40/21.36 [3236]E(f789(f163(a1),f167(x32361,x32362)),f303(a1,x32361,x32362))
% 21.40/21.36 [3251]P54(x32511,f184(f870(x32511,a856)),x32512)
% 21.40/21.36 [3256]E(f789(f258(a1,a1),f60(x32561,x32562)),f59(a1,x32561,x32562))
% 21.40/21.36 [3257]E(f789(f302(a863,x32571),f789(a121,x32572)),f303(a863,x32571,x32572))
% 21.40/21.36 [3284]E(f303(a863,f789(a121,x32841),x32842),f305(a863,x32841,x32842))
% 21.40/21.36 [3287]P47(x32871,f247(f870(x32871,a856)),f308(x32871,x32872))
% 21.40/21.36 [3350]E(f789(f789(f3(a863),x33501),f789(a121,x33502)),f789(f49(a863),f306(a863,x33502,x33501)))
% 21.40/21.36 [3405]E(f162(x34051,x34052,f122(x34051)),f789(f789(f249(f864(x34051),f864(x34051)),f122(x34051)),f122(x34051)))
% 21.40/21.36 [3424]E(f789(f259(x34241,x34242,f869(x34241,x34242)),f249(x34241,x34242)),f41(f869(x34241,x34242)))
% 21.40/21.36 [3429]P1(f789(f789(f342(f864(x34291)),f122(x34291)),f156(x34291,x34292)))
% 21.40/21.36 [3430]E(f789(f185(f864(x34301)),f147(x34301,x34302)),f789(f789(f3(a863),f789(f185(f864(x34301)),x34302)),f87(a863)))
% 21.40/21.36 [3431]E(f789(f185(f864(x34311)),f123(x34311,x34312)),f789(f789(f3(a863),f789(f185(f864(x34311)),x34312)),f87(a863)))
% 21.40/21.36 [3441]P1(f789(f70(a863),f306(a863,x34411,x34412)))
% 21.40/21.36 [3442]P1(f789(f70(a863),f305(a863,x34421,x34422)))
% 21.40/21.36 [3443]P1(f789(f70(a863),f303(a863,x34431,x34432)))
% 21.40/21.36 [3444]P1(f789(f70(a1),f306(a1,x34441,x34442)))
% 21.40/21.36 [3445]P1(f789(f70(a1),f305(a1,x34451,x34452)))
% 21.40/21.36 [3446]P1(f789(f70(a1),f303(a1,x34461,x34462)))
% 21.40/21.36 [3554]E(f789(f311(a863,a863,a121),f303(a863,x35541,x35542)),f303(a863,f789(a121,x35541),f789(a121,x35542)))
% 21.40/21.36 [3570]E(f789(f789(f289(x35701,x35701,x35701),f308(x35701,x35702)),f308(x35701,x35702)),f308(x35701,x35702))
% 21.40/21.36 [3600]E(f789(f789(f249(a1,a1),f789(f789(f50(a1),x36001),x36002)),f59(a1,x36001,x36002)),f60(x36001,x36002))
% 21.40/21.36 [3601]E(f789(f789(f249(a108,a108),f789(f789(f50(a108),x36011),x36012)),f59(a108,x36011,x36012)),f24(x36011,x36012))
% 21.40/21.36 [3630]E(f789(f789(f249(a863,a863),f789(f789(f50(a863),x36301),x36302)),f59(a863,x36301,x36302)),f94(f869(a863,a863),f62(x36301,x36302)))
% 21.40/21.36 [3682]P1(f789(f789(f241(a863),f789(f789(f3(a863),x36821),x36822)),f789(a121,x36821)))
% 21.40/21.36 [3781]E(f789(f789(f89(a1),f789(f789(f90(a1),x37811),f789(f789(f50(a1),x37812),x37811))),f59(a1,x37812,x37811)),x37812)
% 21.40/21.36 [3785]E(f789(f789(f53(a863,f870(f869(f864(x37851),f864(x37851)),a856)),f247(f870(a863,a856))),f139(x37851,x37852)),f141(x37851,x37852))
% 21.40/21.36 [4007]P1(f789(f789(f342(f869(f864(x40071),f864(x40071))),f789(f789(f249(f864(x40071),f864(x40071)),f122(x40071)),f122(x40071))),f154(x40071,x40072)))
% 21.40/21.36 [4167]E(f260(x41671,x41671,x41672,x41672,f41(x41671),f41(x41672)),f41(f869(x41671,x41672)))
% 21.40/21.36 [4168]E(f260(x41681,x41681,x41682,x41682,f7(x41681),f7(x41682)),f41(f869(x41681,x41682)))
% 21.40/21.36 [4169]E(f260(x41691,x41691,x41692,x41692,f41(x41691),f41(x41692)),f41(f869(x41691,x41692)))
% 21.40/21.36 [4170]E(f260(x41701,x41701,x41702,x41702,f41(x41701),f41(x41702)),f41(f869(x41701,x41702)))
% 21.40/21.36 [4423]~E(f789(f234(x44231),x44232),f187(x44231))
% 21.40/21.36 [4424]~E(f789(f234(x44241),x44242),f187(x44241))
% 21.40/21.36 [4442]~P37(x44421,f789(f234(x44421),x44422))
% 21.40/21.36 [3167]E(f789(f238(x31671),f789(f234(x31671),x31672)),x31672)
% 21.40/21.36 [3168]E(f789(f149(x31681),f789(f149(x31681),x31682)),x31682)
% 21.40/21.36 [3170]E(f789(f789(f135(x31701),f2(a863)),x31702),x31702)
% 21.40/21.36 [3180]E(f789(f789(f164(x31801),f2(a863)),x31802),f122(x31801))
% 21.40/21.36 [3187]E(f789(f789(f132(x31871),f122(x31871)),x31872),x31872)
% 21.40/21.36 [3194]E(f789(f185(f867(x31941)),f789(f234(x31941),x31942)),f2(a863))
% 21.40/21.36 [3196]E(f51(f870(x31961,a856),f789(f309(x31961),x31962)),x31962)
% 21.40/21.36 [3198]E(f789(f163(x31981),f789(f148(x31981),x31982)),f789(f163(x31981),x31982))
% 21.40/21.36 [3199]E(f789(f163(x31991),f789(f149(x31991),x31992)),f789(f163(x31991),x31992))
% 21.40/21.36 [3205]E(f789(f789(f3(a108),x32051),x32052),f789(f789(a4,x32051),x32052))
% 21.40/21.36 [3218]E(f789(f789(f89(a863),x32181),x32182),f789(f789(f89(a863),x32182),x32181))
% 21.40/21.36 [3219]E(f789(f789(f89(a1),x32191),x32192),f789(f789(f89(a1),x32192),x32191))
% 21.40/21.36 [3220]E(f789(f789(f90(a863),x32201),x32202),f789(f789(f90(a863),x32202),x32201))
% 21.40/21.36 [3221]E(f789(f789(f90(a1),x32211),x32212),f789(f789(f90(a1),x32212),x32211))
% 21.40/21.36 [3243]E(f789(f789(f178(x32431,x32431),f2(a863)),x32432),f41(x32431))
% 21.40/21.36 [3244]E(f789(f185(f864(x32441)),f789(f148(x32441),x32442)),f789(f185(f864(x32441)),x32442))
% 21.40/21.36 [3245]E(f789(f185(f864(x32451)),f789(f149(x32451),x32452)),f789(f185(f864(x32451)),x32452))
% 21.40/21.36 [3246]E(f165(x32461,x32462,f184(f870(a863,a856))),f122(x32461))
% 21.40/21.36 [3247]E(f789(f789(f150(x32471,x32471),f7(x32471)),x32472),x32472)
% 21.40/21.36 [3249]E(f789(f248(a1,a1),f60(x32491,x32492)),f789(f789(f50(a1),x32491),x32492))
% 21.40/21.36 [3268]E(f36(f37(x32681,x32682)),f789(f789(f89(a863),f36(x32682)),f789(a121,f2(a863))))
% 21.40/21.36 [3269]E(f789(f284(x32691),f789(f286(x32691,x32691),x32692)),f789(f284(x32691),x32692))
% 21.40/21.36 [3273]P1(f789(f70(x32731),f789(f163(x32731),x32732)))
% 21.40/21.36 [3278]E(f789(f789(f89(a1),x32781),f789(f88(a1),x32782)),f789(f789(f3(a1),x32781),x32782))
% 21.40/21.36 [3279]E(f789(f789(f89(a1),x32791),f789(f88(a1),x32792)),f789(f789(f3(a1),x32791),x32792))
% 21.40/21.36 [3285]P28(x32851,x32852,f184(f870(f862(x32851),a856)))
% 21.40/21.36 [3286]P28(x32861,x32862,f184(f870(f862(x32861),a856)))
% 21.40/21.36 [3290]E(f789(f311(x32901,x32901,f7(x32901)),x32902),x32902)
% 21.40/21.36 [3291]E(f789(f311(x32911,x32911,f41(x32911)),x32912),x32912)
% 21.40/21.36 [3292]E(f789(f313(x32921,x32921,f7(x32921)),x32922),x32922)
% 21.40/21.36 [3293]E(f789(f313(x32931,x32931,f41(x32931)),x32932),x32932)
% 21.40/21.36 [3294]P1(f789(f247(f870(x32941,a856)),x32942))
% 21.40/21.36 [3296]E(f789(f49(a863),f789(f302(a863,x32961),x32962)),f789(f789(f3(a863),x32962),x32961))
% 21.40/21.36 [3297]E(f789(f302(a863,f789(a121,x32971)),x32972),f306(a863,x32971,x32972))
% 21.40/21.36 [3309]E(f789(f789(f310(x33091),x33092),f184(f870(x33091,a856))),f789(f264(x33091),f789(a338,x33092)))
% 21.40/21.36 [3315]E(f789(f789(f310(x33151),x33152),f184(f870(x33151,a856))),f233(x33151,f789(f234(x33151),x33152)))
% 21.40/21.36 [3317]E(f308(x33171,f789(f286(x33171,x33171),x33172)),f789(f286(x33171,x33171),f308(x33171,x33172)))
% 21.40/21.36 [3321]E(f789(f789(f89(a863),f789(a121,x33211)),x33212),f789(f789(f89(a863),x33211),f789(a121,x33212)))
% 21.40/21.36 [3322]E(f789(f789(f3(a863),f789(a121,x33221)),f789(a121,x33222)),f789(f789(f3(a863),x33221),x33222))
% 21.40/21.36 [3327]E(f789(f49(a863),f305(a863,x33271,x33272)),f789(f789(f3(a863),x33272),x33271))
% 21.40/21.36 [3337]P36(x33371,f789(f789(f288(a863,x33371),a245),x33372))
% 21.40/21.36 [3339]P18(a863,f136(a863,f789(f302(a863,x33391),x33392)))
% 21.40/21.36 [3341]P1(f789(f70(a863),f789(f302(a863,x33411),x33412)))
% 21.40/21.36 [3342]P1(f789(f70(a1),f789(f302(a1,x33421),x33422)))
% 21.40/21.36 [3344]E(f789(f286(f864(x33441),f864(x33441)),f153(x33441,x33442)),f153(x33441,f789(f286(x33441,x33441),x33442)))
% 21.40/21.36 [3345]E(f789(f185(a857),f37(x33451,x33452)),f789(f789(f89(a863),f789(f185(a857),x33452)),f789(a121,f2(a863))))
% 21.40/21.36 [3347]E(f789(f302(a1,x33471),f789(f789(f89(a1),x33472),f87(a1))),f303(a1,x33471,x33472))
% 21.40/21.36 [3349]E(f789(f789(f50(a1),f789(f88(a1),x33491)),f789(f88(a1),x33492)),f789(f789(f50(a1),x33491),x33492))
% 21.40/21.36 [3359]E(f175(x33591,x33592,f789(f18(f867(x33592),x33591),f187(x33592))),f184(f870(x33592,a856)))
% 21.40/21.36 [3360]E(f173(x33601,x33602,f789(f18(f867(x33602),x33601),f187(x33602))),f184(f870(x33601,a856)))
% 21.40/21.36 [3361]E(f789(f789(f178(f869(x33611,x33611),a856),f87(a863)),x33612),x33612)
% 21.40/21.36 [3363]E(f789(f789(f3(f870(x33631,a856)),x33632),f184(f870(x33631,a856))),x33632)
% 21.40/21.36 [3364]E(f789(f789(f110(f870(x33641,a856)),x33642),f184(f870(x33641,a856))),x33642)
% 21.40/21.36 [3365]E(f789(f789(f111(f870(x33651,a856)),x33652),f247(f870(x33651,a856))),x33652)
% 21.40/21.36 [3366]E(f789(f248(a863,a863),f94(f869(a863,a863),f62(x33661,x33662))),f789(f789(f50(a863),x33661),x33662))
% 21.40/21.36 [3372]E(f315(x33721,f789(a23,x33722),f789(f88(a1),f789(a23,x33722))),f789(f789(f318(a1),x33721),x33722))
% 21.40/21.36 [3373]E(f303(a1,f789(f789(f89(a1),x33731),f87(a1)),x33732),f305(a1,x33731,x33732))
% 21.40/21.36 [3378]E(f789(f258(a863,a863),f94(f869(a863,a863),f62(x33781,x33782))),f59(a863,x33781,x33782))
% 21.40/21.36 [3386]E(f316(x33861,f789(a23,x33862),f789(f88(a1),f789(a23,x33862))),f317(a1,x33861,x33862))
% 21.40/21.36 [3388]P1(f789(f789(f342(x33881),x33882),f247(f870(x33881,a856))))
% 21.40/21.36 [3389]P1(f789(f789(f342(x33891),x33892),f247(f870(x33891,a856))))
% 21.40/21.36 [3393]E(f789(f789(f3(a863),f789(a121,x33931)),x33932),f789(f49(a863),f303(a863,x33932,x33931)))
% 21.40/21.36 [3416]E(f789(f789(f3(f870(x34161,a856)),x34162),f247(f870(x34161,a856))),f184(f870(x34161,a856)))
% 21.40/21.36 [3417]E(f789(f789(f110(f870(x34171,a856)),x34172),f247(f870(x34171,a856))),f247(f870(x34171,a856)))
% 21.40/21.36 [3418]E(f789(f789(f111(f870(x34181,a856)),x34182),f184(f870(x34181,a856))),f184(f870(x34181,a856)))
% 21.40/21.36 [3432]E(f59(a1,f789(f109(a1),x34321),f789(f109(a1),x34322)),f789(f109(a1),f59(a863,x34321,x34322)))
% 21.40/21.36 [3433]E(f59(a1,f789(f109(a1),x34331),f789(f109(a1),x34332)),f789(f109(a1),f59(a863,x34331,x34332)))
% 21.40/21.36 [3434]E(f59(a1,f789(f88(a1),x34341),f789(f88(a1),x34342)),f789(f88(a1),f59(a1,x34341,x34342)))
% 21.40/21.36 [3475]E(f789(f789(f50(a1),f59(a1,x34751,x34752)),x34752),f2(a1))
% 21.40/21.36 [3484]E(f789(a5,f59(a863,f789(a22,x34841),f789(a22,x34842))),f59(a108,x34841,x34842))
% 21.40/21.36 [3521]E(f789(a5,f789(f789(f89(a863),f789(a22,x35211)),f789(a22,x35212))),f789(f789(f89(a108),x35211),x35212))
% 21.40/21.36 [3522]E(f789(a5,f789(f789(f90(a863),f789(a22,x35221)),f789(a22,x35222))),f789(f789(f90(a108),x35221),x35222))
% 21.40/21.36 [3523]E(f789(a5,f789(f789(f50(a863),f789(a22,x35231)),f789(a22,x35232))),f789(f789(f50(a108),x35231),x35232))
% 21.40/21.36 [3524]E(f789(a5,f789(f789(f3(a863),f789(a22,x35241)),f789(a22,x35242))),f789(f789(f3(a108),x35241),x35242))
% 21.40/21.36 [3533]E(f789(f311(a863,a863,a121),f789(f302(a863,x35331),x35332)),f789(f302(a863,f789(a121,x35331)),f789(a121,x35332)))
% 21.40/21.36 [3559]P1(f789(f62(x35591,x35592),f94(f869(a863,a863),f62(x35591,x35592))))
% 21.40/21.36 [3575]E(f789(f789(f89(a863),f789(f789(f89(a863),f36(x35751)),f36(x35752))),f789(a121,f2(a863))),f36(f38(x35751,x35752)))
% 21.40/21.36 [3576]E(f59(a863,f789(a121,f59(a863,x35761,x35762)),x35762),f59(a863,f789(a121,x35761),x35762))
% 21.40/21.36 [3590]E(f789(f789(f54(f870(x35901,a856),f870(x35901,a856)),x35902),f7(f870(x35901,a856))),f52(f870(x35901,a856),x35902))
% 21.40/21.36 [3591]E(f789(f789(f53(f870(x35911,a856),f870(x35911,a856)),x35912),f7(f870(x35911,a856))),f51(f870(x35911,a856),x35912))
% 21.40/21.36 [3594]P1(f789(f789(f342(f870(x35941,a856)),x35942),f789(f309(x35941),x35942)))
% 21.40/21.36 [3599]E(f59(a1,f789(f88(a1),f59(a1,x35991,x35992)),x35992),f59(a1,f789(f88(a1),x35991),x35992))
% 21.40/21.36 [3612]P1(f789(f789(f240(f870(x36121,a856)),x36122),f247(f870(x36121,a856))))
% 21.40/21.36 [3614]E(f789(f789(f289(x36141,x36141,x36141),f308(x36141,x36142)),f308(x36141,f308(x36141,x36142))),f308(x36141,x36142))
% 21.40/21.36 [3615]E(f789(f789(f110(f870(x36151,a856)),f789(f269(x36151,x36151),x36152)),f789(f267(x36151,x36151),x36152)),f789(f284(x36151),x36152))
% 21.40/21.36 [3636]E(f322(x36361,x36362,f247(f870(x36361,a856)),f247(f870(x36362,a856))),f247(f870(f871(x36361,x36362),a856)))
% 21.40/21.36 [3687]P1(f789(f789(f240(a863),f59(a863,x36871,x36872)),x36871))
% 21.40/21.36 [3711]P1(f789(f789(f240(a1),f789(f88(a1),f789(f109(a1),x37111))),f789(f109(a1),x37112)))
% 21.40/21.36 [3736]P1(f789(f789(f342(f870(x37361,a856)),f184(f870(x37361,a856))),f789(f309(x37361),x37362)))
% 21.40/21.36 [3741]E(f308(x37411,f789(f789(f289(x37411,x37411,x37411),x37412),f308(x37411,x37412))),f308(x37411,x37412))
% 21.40/21.36 [3743]E(f789(f789(f289(x37431,x37431,x37431),f308(x37431,x37432)),x37432),f789(f789(f289(x37431,x37431,x37431),x37432),f308(x37431,x37432)))
% 21.40/21.36 [3744]E(f789(f789(f289(x37441,x37441,x37441),f308(x37441,x37442)),x37442),f789(f789(f289(x37441,x37441,x37441),x37442),f308(x37441,x37442)))
% 21.40/21.36 [3746]E(f789(a114,f789(f789(f89(a1),f789(f789(f3(a1),x37461),x37462)),f87(a1))),f789(f49(a1),f303(a1,x37462,x37461)))
% 21.40/21.36 [3763]E(f789(f267(x37631,x37631),f789(f789(f289(x37631,x37631,x37631),x37632),f308(x37631,x37632))),f789(f267(x37631,x37631),x37632))
% 21.40/21.36 [3764]E(f789(f269(x37641,x37641),f789(f789(f289(x37641,x37641,x37641),x37642),f308(x37641,x37642))),f789(f269(x37641,x37641),x37642))
% 21.40/21.36 [3777]E(f789(f789(f89(a863),f789(f789(f89(a863),f789(f185(a857),x37771)),f789(f185(a857),x37772))),f789(a121,f2(a863))),f789(f185(a857),f38(x37771,x37772)))
% 21.40/21.36 [3789]P29(a863,a863,f789(f789(f9(a863,a863,a863),f89(a863)),x37891),x37892)
% 21.40/21.36 [3791]P18(a863,f789(f149(a863),f789(f789(f150(f864(x37911),a863),f185(f864(x37911))),f168(x37911,x37912))))
% 21.40/21.36 [3838]P1(f789(f789(f241(a1),f789(f88(a1),f789(f109(a1),f789(a121,x38381)))),f789(f109(a1),x38382)))
% 21.40/21.36 [3878]E(f789(f138(f864(x38781),x38781,f789(f9(x38781,f864(x38781),f864(x38781)),f146(x38781)),f122(x38781)),x38782),f789(f149(x38781),x38782))
% 21.40/21.36 [3928]P1(f789(f789(f240(f870(f869(f864(x39281),f864(x39281)),a856)),f154(x39281,x39282)),f308(f864(x39281),f153(x39281,x39282))))
% 21.40/21.36 [3959]P1(f789(f62(x39591,x39592),f789(f789(f249(a863,a863),f789(f789(f50(a863),x39591),x39592)),f59(a863,x39591,x39592))))
% 21.40/21.36 [3970]P1(f789(f789(f240(f870(f869(f864(x39701),f864(x39701)),a856)),f153(x39701,f308(x39701,x39702))),f308(f864(x39701),f153(x39701,x39702))))
% 21.40/21.36 [4197]E(f789(f789(f261(f869(a108,a108),a108,f869(a108,a108),f869(x41971,f869(a108,a108))),f272(f789(f161(a108),f789(f789(f150(f869(a108,x41971),a108),f248(a108,x41971)),x41972)))),f789(f789(f10(x41971,f870(f869(a108,a108),f869(x41971,f869(a108,a108))),a108),f249(x41971,f869(a108,a108))),f273(x41971,x41972))),f271(x41971,x41972))
% 21.40/21.36 [4341]E(f59(a863,f789(f789(f89(a863),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106))),x43411),f789(f113(a863),x43412)),f59(a863,f789(a121,f789(a121,f789(a121,x43411))),f789(f113(a863),x43412)))
% 21.40/21.36 [4355]E(f789(f789(f50(a863),f789(f789(f89(a863),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106))),x43551)),f789(f113(a863),x43552)),f789(f789(f50(a863),f789(a121,f789(a121,f789(a121,x43551)))),f789(f113(a863),x43552)))
% 21.40/21.36 [4375]E(f789(f259(f870(f869(x43751,x43751),a856),f870(f869(x43751,x43751),a856),f870(f870(x43752,x43751),f869(f870(f869(x43752,x43752),a856),f870(f869(x43752,x43752),a856)))),f789(f789(f9(f870(f869(x43751,x43751),a856),f870(f870(f869(x43751,x43751),a856),f870(f870(x43752,x43751),f870(f869(x43752,x43752),a856))),f870(f870(f869(x43751,x43751),a856),f870(f870(x43752,x43751),f869(f870(f869(x43752,x43752),a856),f870(f869(x43752,x43752),a856))))),f789(f789(f10(f870(f870(f870(x43752,x43751),f870(f869(x43752,x43752),a856)),f870(f870(x43752,x43751),f869(f870(f869(x43752,x43752),a856),f870(f869(x43752,x43752),a856)))),f870(f870(f870(f869(x43751,x43751),a856),f870(f870(x43752,x43751),f870(f869(x43752,x43752),a856))),f870(f870(f869(x43751,x43751),a856),f870(f870(x43752,x43751),f869(f870(f869(x43752,x43752),a856),f870(f869(x43752,x43752),a856))))),f870(f869(x43751,x43751),a856)),f10(f870(f870(x43752,x43751),f870(f869(x43752,x43752),a856)),f870(f870(x43752,x43751),f869(f870(f869(x43752,x43752),a856),f870(f869(x43752,x43752),a856))),f870(f869(x43751,x43751),a856))),f789(f789(f10(f870(f870(x43752,x43751),f870(f870(f869(x43752,x43752),a856),f869(f870(f869(x43752,x43752),a856),f870(f869(x43752,x43752),a856)))),f870(f870(f870(x43752,x43751),f870(f869(x43752,x43752),a856)),f870(f870(x43752,x43751),f869(f870(f869(x43752,x43752),a856),f870(f869(x43752,x43752),a856)))),f870(f869(x43751,x43751),a856)),f20(f870(x43752,x43751),f870(f869(x43752,x43752),a856),f869(f870(f869(x43752,x43752),a856),f870(f869(x43752,x43752),a856)))),f789(f789(f10(f870(f870(x43752,x43751),f870(f869(x43752,x43752),a856)),f870(f870(x43752,x43751),f870(f870(f869(x43752,x43752),a856),f869(f870(f869(x43752,x43752),a856),f870(f869(x43752,x43752),a856)))),f870(f869(x43751,x43751),a856)),f789(f10(f870(f869(x43752,x43752),a856),f870(f870(f869(x43752,x43752),a856),f869(f870(f869(x43752,x43752),a856),f870(f869(x43752,x43752),a856))),f870(x43752,x43751)),f249(f870(f869(x43752,x43752),a856),f870(f869(x43752,x43752),a856)))),f288(x43751,x43752))))),f288(x43751,x43752))),f83(x43751,x43752))
% 21.40/21.36 [4492]~E(f789(f309(x44921),x44922),f184(f870(f870(x44921,a856),a856)))
% 21.40/21.36 [4509]~P1(f789(f789(f342(x45091),x45092),f184(f870(x45091,a856))))
% 21.40/21.36 [4510]~P1(f789(f789(f342(x45101),x45102),f184(f870(x45101,a856))))
% 21.40/21.36 [4519]~P1(f789(f789(f241(f870(x45191,a856)),x45192),f184(f870(x45191,a856))))
% 21.40/21.36 [3299]E(f789(f789(f3(a863),x32991),f789(f789(f89(a863),x32991),x32992)),f2(a863))
% 21.40/21.36 [3301]E(f789(f789(f110(f870(x33011,a856)),x33012),x33012),x33012)
% 21.40/21.36 [3302]E(f789(f789(f111(f870(x33021,a856)),x33022),x33022),x33022)
% 21.40/21.36 [3329]E(f789(f789(f3(f870(x33291,a856)),x33292),x33292),f184(f870(x33291,a856)))
% 21.40/21.36 [3332]E(f789(f139(x33321,x33322),f2(a863)),f184(f870(f869(f864(x33321),f864(x33321)),a856)))
% 21.40/21.36 [3333]E(f789(f789(f89(a863),x33331),f789(a121,x33332)),f789(a121,f789(f789(f89(a863),x33331),x33332)))
% 21.40/21.36 [3346]E(f192(f789(f109(a1),x33461),f789(f109(a1),x33462)),f789(f109(a1),f789(f789(f3(a863),x33461),x33462)))
% 21.40/21.36 [3348]E(f789(f789(f50(a1),f789(f88(a1),x33481)),x33482),f789(f789(f50(a1),x33481),f789(f88(a1),x33482)))
% 21.40/21.36 [3352]E(f789(f49(a1),f789(f302(a1,x33521),x33522)),f789(a114,f789(f789(f3(a1),x33522),x33521)))
% 21.40/21.36 [3357]E(f789(f789(f89(a863),f789(a121,x33571)),x33572),f789(a121,f789(f789(f89(a863),x33571),x33572)))
% 21.40/21.36 [3362]E(f789(f88(f870(x33621,a856)),f789(f88(f870(x33621,a856)),x33622)),x33622)
% 21.40/21.36 [3375]E(f168(x33751,f789(f789(f146(f864(x33751)),f122(x33751)),x33752)),f168(x33751,x33752))
% 21.40/21.36 [3379]E(f789(f789(f89(a863),x33791),f789(f789(f90(a863),x33791),x33792)),f789(f789(f90(a863),x33791),f789(a121,x33792)))
% 21.40/21.36 [3387]E(f789(f789(a4,f789(a5,x33871)),f789(a5,x33872)),f789(a5,f789(f789(f3(a863),x33871),x33872)))
% 21.40/21.36 [3395]E(f789(f789(f250(a1),f789(f109(a1),x33951)),x33952),f789(f109(a1),f789(f789(f250(a863),x33951),x33952)))
% 21.40/21.36 [3396]E(f789(f789(f90(a1),f789(f88(a1),x33961)),x33962),f789(f88(a1),f789(f789(f90(a1),x33961),x33962)))
% 21.40/21.36 [3397]E(f789(f789(f250(a1),f789(f109(a1),x33971)),x33972),f789(f109(a1),f789(f789(f250(a863),x33971),x33972)))
% 21.40/21.36 [3398]E(f789(f789(f250(a1),f789(f109(a1),x33981)),x33982),f789(f109(a1),f789(f789(f250(a863),x33981),x33982)))
% 21.40/21.36 [3399]E(f789(f789(f89(a108),f789(a5,x33991)),f789(a5,x33992)),f789(a5,f789(f789(f89(a863),x33991),x33992)))
% 21.40/21.36 [3400]E(f789(f789(f90(a108),f789(a5,x34001)),f789(a5,x34002)),f789(a5,f789(f789(f90(a863),x34001),x34002)))
% 21.40/21.36 [3401]E(f789(f789(f244(a863),f789(a121,x34011)),f789(a121,x34012)),f789(a121,f789(f789(f244(a863),x34011),x34012)))
% 21.40/21.36 [3402]E(f789(f789(f239(a863),f789(a121,x34021)),f789(a121,x34022)),f789(a121,f789(f789(f239(a863),x34021),x34022)))
% 21.40/21.36 [3407]E(f789(f163(a863),f136(a863,f789(f302(a863,x34071),x34072))),f789(f302(a863,x34071),x34072))
% 21.40/21.36 [3408]E(f789(f163(a863),f136(a863,f789(f302(a863,x34081),x34082))),f789(f302(a863,x34081),x34082))
% 21.40/21.36 [3409]E(f314(x34091,f789(f789(f310(x34091),x34092),f184(f870(x34091,a856)))),x34092)
% 21.40/21.36 [3414]E(f789(f267(x34141,x34142),f184(f870(f869(x34141,x34142),a856))),f184(f870(x34142,a856)))
% 21.40/21.36 [3415]E(f789(f269(x34151,x34152),f184(f870(f869(x34151,x34152),a856))),f184(f870(x34151,a856)))
% 21.40/21.36 [3419]E(f789(a114,f789(f789(f3(a1),x34191),x34192)),f789(f49(a1),f305(a1,x34192,x34191)))
% 21.40/21.36 [3423]E(f789(f789(f89(a863),x34231),f789(f789(f90(a863),x34232),x34231)),f789(f789(f90(a863),f789(a121,x34232)),x34231))
% 21.40/21.36 [3425]E(f789(f789(f68(x34251),f184(f870(x34251,a856))),x34252),f184(f870(f870(x34251,a856),a856)))
% 21.40/21.36 [3435]E(f789(f185(f864(a863)),f136(a863,f789(f302(a863,x34351),x34352))),f789(f789(f3(a863),x34352),x34351))
% 21.40/21.36 [3454]E(f789(f789(f110(f870(x34541,a856)),f184(f870(x34541,a856))),x34542),x34542)
% 21.40/21.36 [3455]E(f789(f789(f111(f870(x34551,a856)),f247(f870(x34551,a856))),x34552),x34552)
% 21.40/21.36 [3456]E(f789(f789(f90(a1),f789(f109(a1),x34561)),f789(f109(a1),x34562)),f789(f109(a1),f789(f789(f90(a863),x34561),x34562)))
% 21.40/21.36 [3457]E(f789(f789(f50(a1),f789(f109(a1),x34571)),f789(f109(a1),x34572)),f789(f109(a1),f789(f789(f50(a863),x34571),x34572)))
% 21.40/21.36 [3458]E(f789(f789(f89(a1),f789(f88(a1),x34581)),f789(f88(a1),x34582)),f789(f88(a1),f789(f789(f89(a1),x34581),x34582)))
% 21.40/21.36 [3460]E(f789(f789(f89(a1),f789(f109(a1),x34601)),f789(f109(a1),x34602)),f789(f109(a1),f789(f789(f89(a863),x34601),x34602)))
% 21.40/21.36 [3461]E(f789(f789(f89(a1),f789(f109(a1),x34611)),f789(f109(a1),x34612)),f789(f109(a1),f789(f789(f89(a863),x34611),x34612)))
% 21.40/21.36 [3462]E(f789(f789(f89(a1),f789(f113(a1),x34621)),f789(f113(a1),x34622)),f789(f113(a1),f789(f789(f89(a1),x34621),x34622)))
% 21.40/21.36 [3463]E(f789(f789(f90(a1),f789(f109(a1),x34631)),f789(f109(a1),x34632)),f789(f109(a1),f789(f789(f90(a863),x34631),x34632)))
% 21.40/21.36 [3464]E(f789(f789(f90(a1),f789(f109(a1),x34641)),f789(f109(a1),x34642)),f789(f109(a1),f789(f789(f90(a863),x34641),x34642)))
% 21.40/21.36 [3465]E(f789(f789(f90(a1),f789(f113(a1),x34651)),f789(f113(a1),x34652)),f789(f113(a1),f789(f789(f90(a1),x34651),x34652)))
% 21.40/21.36 [3466]E(f789(f789(f50(a1),f789(f109(a1),x34661)),f789(f109(a1),x34662)),f789(f109(a1),f789(f789(f50(a863),x34661),x34662)))
% 21.40/21.36 [3485]E(f789(f789(f8(x34851,a863),f789(f18(a863,x34851),f87(a863))),x34852),f789(f49(x34851),x34852))
% 21.40/21.36 [3496]E(f789(f88(a1),f59(a1,f789(f88(a1),x34961),x34962)),f59(a1,x34961,f789(f88(a1),x34962)))
% 21.40/21.36 [3498]E(f789(f163(a1),f167(x34981,f789(f789(f3(a1),x34982),f87(a1)))),f789(f302(a1,x34981),x34982))
% 21.40/21.36 [3502]P1(f789(f789(f240(a863),x35021),f789(f789(f89(a863),x35022),x35021)))
% 21.40/21.36 [3503]P1(f789(f789(f240(a863),x35031),f789(f789(f89(a863),x35031),x35032)))
% 21.40/21.36 [3506]E(f789(f789(f3(f870(x35061,a856)),f184(f870(x35061,a856))),x35062),f184(f870(x35061,a856)))
% 21.40/21.36 [3507]E(f789(f789(f110(f870(x35071,a856)),f247(f870(x35071,a856))),x35072),f247(f870(x35071,a856)))
% 21.40/21.36 [3508]E(f789(f789(f111(f870(x35081,a856)),f184(f870(x35081,a856))),x35082),f184(f870(x35081,a856)))
% 21.40/21.36 [3513]E(f789(f789(f249(a1,a1),x35131),f789(f88(a1),x35132)),f789(a65,f789(f789(f249(a1,a1),x35131),x35132)))
% 21.40/21.36 [3514]E(f789(f302(a1,f789(f789(f89(a1),x35141),f87(a1))),x35142),f306(a1,x35141,x35142))
% 21.40/21.36 [3525]E(f789(f789(f90(a863),x35251),f789(f789(f50(a863),x35252),x35251)),f789(f789(f3(a863),x35252),f59(a863,x35252,x35251)))
% 21.40/21.36 [3526]E(f789(f789(f90(a1),x35261),f789(f789(f50(a1),x35262),x35261)),f789(f789(f3(a1),x35262),f59(a1,x35262,x35261)))
% 21.40/21.36 [3530]E(f789(f163(a1),f167(f789(f789(f89(a1),x35301),f87(a1)),x35302)),f305(a1,x35301,x35302))
% 21.40/21.36 [3534]P1(f789(f789(f240(f870(x35341,a856)),x35342),x35342))
% 21.40/21.36 [3539]E(f789(f789(f110(f870(x35391,a856)),x35392),f789(f88(f870(x35391,a856)),x35392)),f247(f870(x35391,a856)))
% 21.40/21.36 [3540]E(f789(f789(f111(f870(x35401,a856)),x35402),f789(f88(f870(x35401,a856)),x35402)),f184(f870(x35401,a856)))
% 21.40/21.36 [3545]E(f789(f789(f3(a863),f789(f789(f3(a863),x35451),f87(a863))),x35452),f789(f789(f3(a863),x35451),f789(a121,x35452)))
% 21.40/21.36 [3551]E(f789(f789(f3(f870(x35511,a856)),f247(f870(x35511,a856))),x35512),f789(f88(f870(x35511,a856)),x35512))
% 21.40/21.36 [3552]E(f789(f789(f3(a1),f789(f113(a1),x35521)),f789(f113(a1),x35522)),f789(f113(a1),f789(f789(f89(a1),x35521),f789(f88(a1),x35522))))
% 21.40/21.36 [3564]E(f789(f163(a863),f136(a863,f789(f302(a863,x35641),f789(a121,x35642)))),f303(a863,x35641,x35642))
% 21.40/21.36 [3592]E(f789(f789(f178(f869(x35921,x35921),a856),f2(a863)),x35922),f308(x35921,f184(f870(f869(x35921,x35921),a856))))
% 21.40/21.36 [3596]P1(f789(f134(a863),f136(a863,f789(f302(a863,x35961),x35962))))
% 21.40/21.36 [3613]E(f789(f311(a1,a863,a114),f303(a1,f789(f109(a1),x36131),f789(f109(a1),x36132))),f303(a863,x36131,x36132))
% 21.40/21.36 [3622]E(f180(a863,f2(a863),f7(a863),f789(f789(f3(a863),x36221),x36222)),f789(f789(f3(a863),x36221),f789(a121,x36222)))
% 21.40/21.36 [3623]E(f789(a114,f789(f789(f3(a1),x36231),f789(f789(f89(a1),x36232),f87(a1)))),f789(f49(a1),f306(a1,x36232,x36231)))
% 21.40/21.36 [3658]E(f789(f789(f150(a863,a863),a121),f136(a863,f789(f302(a863,x36581),x36582))),f136(a863,f789(f302(a863,f789(a121,x36581)),f789(a121,x36582))))
% 21.40/21.36 [3665]E(f789(f163(a1),f167(f789(f789(f89(a1),x36651),f87(a1)),f789(f789(f3(a1),x36652),f87(a1)))),f306(a1,x36651,x36652))
% 21.40/21.36 [3679]P1(f789(f789(f240(f870(x36791,a856)),f184(f870(x36791,a856))),x36792))
% 21.40/21.36 [3683]E(f94(x36831,f789(f789(f9(x36831,x36831,a856),a338),x36832)),x36832)
% 21.40/21.36 [3684]E(f99(x36841,f789(f789(f9(x36841,x36841,a856),a338),x36842)),x36842)
% 21.40/21.36 [3688]E(f789(f163(a863),f136(a863,f789(f302(a863,f789(a121,x36881)),f789(a121,x36882)))),f305(a863,x36881,x36882))
% 21.40/21.36 [3714]E(f789(f789(f256(x37141,x37142),f247(f870(x37141,a856))),f789(f18(f870(x37142,a856),x37141),f247(f870(x37142,a856)))),f247(f870(f869(x37141,x37142),a856)))
% 21.40/21.36 [3750]E(f789(f264(x37501),f789(f789(f10(a856,a856,x37501),a336),x37502)),f789(f88(f870(x37501,a856)),f789(f264(x37501),x37502)))
% 21.40/21.36 [3753]E(f789(f264(x37531),f789(f789(f9(x37531,x37531,a856),a338),x37532)),f789(f789(f310(x37531),x37532),f184(f870(x37531,a856))))
% 21.40/21.36 [3760]E(f789(f789(f89(a1),f789(f789(f89(a1),x37601),x37601)),f789(f789(f89(a1),x37602),x37602)),f789(f789(f89(a1),f789(f789(f89(a1),x37601),x37602)),f789(f789(f89(a1),x37601),x37602)))
% 21.40/21.36 [3761]E(f789(f789(f3(a1),f789(f789(f89(a1),x37611),x37611)),f789(f789(f89(a1),x37612),x37612)),f789(f789(f89(a1),f789(f789(f3(a1),x37611),x37612)),f789(f789(f3(a1),x37611),x37612)))
% 21.40/21.36 [3775]P1(f789(f789(f240(a863),f789(f49(x37751),f789(f163(x37751),x37752))),f789(f185(f864(x37751)),x37752)))
% 21.40/21.36 [3786]E(f789(f264(x37861),f789(f789(f9(x37861,f870(x37861,a856),a856),f342(x37861)),x37862)),x37862)
% 21.40/21.36 [3802]E(f789(f789(f164(x38021),f789(f789(f3(a863),f789(f185(f864(x38021)),x38022)),f87(a863))),x38022),f123(x38021,x38022))
% 21.40/21.36 [3825]E(f180(a863,f2(a863),f789(f789(f10(a863,a863,a863),a121),f789(f244(a863),x38251)),x38252),f789(f789(f244(a863),f789(a121,x38251)),x38252))
% 21.40/21.36 [3829]E(f51(f870(x38291,a856),f789(f311(f870(f869(x38291,x38291),a856),f870(x38291,a856),f284(x38291)),x38292)),f789(f284(x38291),f51(f870(f869(x38291,x38291),a856),x38292)))
% 21.40/21.36 [3830]E(f180(a863,f789(a121,x38301),f789(f789(f10(a863,a863,a863),a121),f789(f239(a863),x38301)),x38302),f789(f789(f239(a863),f789(a121,x38301)),x38302))
% 21.40/21.36 [3832]E(f789(f789(f249(a1,a1),f789(f789(f50(a1),f789(f84(a1),x38321)),f789(f84(a1),x38322))),f59(a1,f789(f84(a1),x38321),f789(f84(a1),x38322))),f67(x38321,x38322))
% 21.40/21.36 [3852]P1(f789(f789(f240(f870(f870(x38521,a856),a856)),x38522),f789(f309(x38521),f51(f870(x38521,a856),x38522))))
% 21.40/21.36 [3883]E(f789(f789(f53(x38831,f870(x38831,a856)),x38832),f789(f789(f9(x38831,f870(x38831,a856),f870(x38831,a856)),f310(x38831)),f184(f870(x38831,a856)))),x38832)
% 21.40/21.36 [3884]E(f789(f789(f289(x38841,x38841,x38841),f789(f286(x38841,x38841),x38842)),f308(x38841,f789(f286(x38841,x38841),x38842))),f789(f286(x38841,x38841),f789(f789(f289(x38841,x38841,x38841),x38842),f308(x38841,x38842))))
% 21.40/21.36 [3951]E(f789(f163(x39511),f789(f138(f864(x39511),f864(x39511),f132(x39511),f122(x39511)),x39512)),f789(f789(f53(f864(x39511),f870(x39511,a856)),f789(f163(f864(x39511)),x39512)),f163(x39511)))
% 21.40/21.36 [3981]E(f789(f789(f110(f870(f869(x39811,x39811),a856)),f308(x39811,f184(f870(f869(x39811,x39811),a856)))),f789(f789(f289(x39811,x39811,x39811),f308(x39811,x39812)),x39812)),f308(x39811,x39812))
% 21.40/21.36 [4018]E(f789(f789(f171(x40181,x40181),x40182),x40182),f789(f789(f150(x40181,f869(x40181,x40181)),f789(f789(f20(x40181,x40181,f869(x40181,x40181)),f249(x40181,x40181)),f7(x40181))),x40182))
% 21.40/21.36 [4131]E(f789(f138(a863,f864(x41311),f789(f9(f864(x41311),a863,a863),f789(f789(f10(a863,f870(a863,a863),f864(x41311)),f239(a863)),f185(f864(x41311)))),f2(a863)),f789(f149(f864(x41311)),x41312)),f789(f185(f864(f864(x41311))),f168(x41311,x41312)))
% 21.40/21.36 [4210]E(f789(f789(f288(f869(a863,f864(x42101)),f864(x42101)),f333(a863,f864(x42101),a245,f141(x42101,x42102))),f789(f789(f20(f864(x42101),f864(x42101),f869(a863,f864(x42101))),f789(f789(f10(a863,f870(f864(x42101),f869(a863,f864(x42101))),f864(x42101)),f249(a863,f864(x42101))),f185(f864(x42101)))),f7(f864(x42101)))),f142(x42101,x42102))
% 21.40/21.36 [4332]E(f789(f264(x43321),f789(f789(f10(f870(f870(x43321,a856),a856),a856,x43321),f97(f870(x43321,a856))),f789(f789(f10(f870(f870(x43321,a856),a856),f870(f870(x43321,a856),a856),x43321),f789(f20(f870(x43321,a856),a856,a856),f789(f789(f10(a856,f870(a856,a856),f870(x43321,a856)),a343),f789(f789(f9(f870(x43321,a856),f870(f870(x43321,a856),a856),a856),f342(f870(x43321,a856))),x43322)))),f342(x43321)))),f52(f870(x43321,a856),x43322))
% 21.40/21.36 [4520]~P1(f789(f789(f241(a1),f789(f109(a1),x45201)),f789(f88(a1),f789(f109(a1),x45202))))
% 21.40/21.36 [3421]E(f789(f789(f3(a863),f789(f789(f89(a863),x34211),x34212)),x34212),x34211)
% 21.40/21.36 [3422]E(f789(f789(f3(a863),f789(f789(f89(a863),x34221),x34222)),x34221),x34222)
% 21.40/21.36 [3497]E(f789(f789(f89(a863),f789(f789(f3(a863),x34971),x34972)),x34972),f789(f789(f239(a863),x34971),x34972))
% 21.40/21.36 [3598]E(f789(f789(f90(a863),f789(f789(f50(a863),x35981),x35982)),x35982),f789(f789(f3(a863),x35981),f59(a863,x35981,x35982)))
% 21.40/21.36 [3627]E(f789(f163(a863),f136(a863,f789(f302(a863,f789(a121,x36271)),x36272))),f306(a863,x36271,x36272))
% 21.40/21.36 [3635]E(f789(f109(a1),f218(f789(a114,f789(f84(a1),x36351)),f789(a114,f789(f84(a1),x36352)))),f789(f789(a219,x36351),x36352))
% 21.40/21.36 [3637]E(f789(f789(f110(f870(x36371,a856)),f789(f88(f870(x36371,a856)),x36372)),x36372),f247(f870(x36371,a856)))
% 21.40/21.36 [3638]E(f789(f789(f111(f870(x36381,a856)),f789(f88(f870(x36381,a856)),x36382)),x36382),f184(f870(x36381,a856)))
% 21.40/21.36 [3654]P1(f789(f789(f240(a863),f789(f789(f50(a863),x36541),x36542)),x36541))
% 21.40/21.36 [3655]P1(f789(f789(f240(a863),f789(f789(f3(a863),x36551),x36552)),x36551))
% 21.40/21.36 [3680]P1(f789(f789(f241(a863),x36801),f789(a121,f789(f789(f89(a863),x36802),x36801))))
% 21.40/21.36 [3681]P1(f789(f789(f241(a863),x36811),f789(a121,f789(f789(f89(a863),x36811),x36812))))
% 21.40/21.36 [3700]E(f789(f789(f90(a863),f789(a114,f789(f84(a1),x37001))),f789(a114,f789(f84(a1),x37002))),f789(a114,f789(f84(a1),f789(f789(f90(a1),x37001),x37002))))
% 21.40/21.36 [3707]E(f789(f789(f89(a1),f789(f789(f90(a1),x37071),x37072)),f789(f789(f90(a1),x37071),x37072)),f789(f789(f90(a1),f789(f789(f89(a1),x37071),x37071)),x37072))
% 21.40/21.36 [3710]P1(f789(f789(f240(a1),f2(a1)),f789(f789(f250(a1),f789(f84(a1),x37101)),x37102)))
% 21.40/21.36 [3780]E(f789(f285(f864(x37801),f864(x37801),f154(x37801,x37802)),f789(f789(f310(f864(x37801)),f122(x37801)),f184(f870(f864(x37801),a856)))),f789(f789(f310(f864(x37801)),f122(x37801)),f184(f870(f864(x37801),a856))))
% 21.40/21.36 [3798]E(f789(f789(f110(f870(f869(x37981,x37981),a856)),f308(x37981,x37982)),f308(x37981,f184(f870(f869(x37981,x37981),a856)))),f308(x37981,x37982))
% 21.40/21.36 [3814]E(f789(f789(f50(a1),f789(f113(a1),f789(f789(f89(a1),x38141),x38141))),f789(f113(a1),f789(f789(f89(a1),x38142),x38142))),f789(f789(f50(a1),f789(f113(a1),x38141)),f789(f113(a1),x38142)))
% 21.40/21.36 [3873]E(f789(f789(f250(a1),x38731),f789(f113(a863),f789(f789(f89(a1),x38732),x38732))),f789(f789(f95(a1,a1),f789(f789(f250(a1),x38731),f789(f113(a863),x38732))),f789(f789(f20(a1,a1,a1),f90(a1)),f7(a1))))
% 21.40/21.36 [3879]E(f789(f264(f870(x38791,a856)),f789(f789(f9(f870(x38791,a856),f870(x38791,a856),a856),f240(f870(x38791,a856))),x38792)),f789(f309(x38791),x38792))
% 21.40/21.36 [3927]E(f789(f311(a1,a1,f789(f789(f9(a1,a1,a1),f89(a1)),x39271)),f789(f302(a1,f2(a1)),f789(f789(f3(a1),x39272),x39271))),f789(f302(a1,x39271),x39272))
% 21.40/21.36 [3930]P48(x39301,f789(f789(f3(f870(f869(x39301,x39301),a856)),x39302),f308(x39301,f184(f870(f869(x39301,x39301),a856)))))
% 21.40/21.36 [3949]E(f789(f185(f864(x39491)),f789(f138(f864(x39491),f864(x39491),f132(x39491),f122(x39491)),x39492)),f789(f161(a863),f789(f789(f150(f864(x39491),a863),f185(f864(x39491))),x39492)))
% 21.40/21.36 [3953]P47(x39531,f247(f870(x39531,a856)),f789(f789(f110(f870(f869(x39531,x39531),a856)),x39532),f308(x39531,f184(f870(f869(x39531,x39531),a856)))))
% 21.40/21.36 [3992]P1(f789(f789(f342(f869(x39921,x39921)),f789(f789(f249(x39921,x39921),x39922),x39922)),f308(x39921,f184(f870(f869(x39921,x39921),a856)))))
% 21.40/21.36 [3997]E(f180(a863,f2(a863),f789(f789(f10(a863,a863,a863),a121),f789(f789(f9(a863,a863,a863),f244(a863)),x39971)),x39972),f789(f789(f244(a863),x39972),f789(a121,x39971)))
% 21.40/21.36 [4000]E(f180(a863,f789(a121,x40001),f789(f789(f10(a863,a863,a863),a121),f789(f789(f9(a863,a863,a863),f239(a863)),x40001)),x40002),f789(f789(f239(a863),x40002),f789(a121,x40001)))
% 21.40/21.36 [4003]E(f789(f311(x40031,f864(x40031),f789(f789(f9(x40031,f864(x40031),f864(x40031)),f146(x40031)),f122(x40031))),x40032),f166(x40031,x40032,f789(f789(f310(f864(x40031)),f122(x40031)),f184(f870(f864(x40031),a856)))))
% 21.40/21.36 [4004]E(f789(f789(f110(f870(f869(x40041,x40041),a856)),f789(f789(f289(x40041,x40041,x40041),x40042),f308(x40041,x40042))),f308(x40041,f184(f870(f869(x40041,x40041),a856)))),f308(x40041,x40042))
% 21.40/21.36 [4012]P1(f789(f789(f240(f870(f869(x40121,x40121),a856)),f268(x40121,x40122)),f789(f789(f256(x40121,x40121),x40122),f789(f18(f870(x40121,a856),x40121),x40122))))
% 21.40/21.36 [4016]E(f789(f311(a1,a863,a114),f789(f789(f110(f870(a1,a856)),f789(f311(a863,a1,f109(a1)),x40161)),f789(f311(a863,a1,f109(a1)),x40162))),f789(f789(f110(f870(a863,a856)),x40161),x40162))
% 21.40/21.36 [4017]E(f789(f311(a1,a863,a114),f789(f789(f111(f870(a1,a856)),f789(f311(a863,a1,f109(a1)),x40171)),f789(f311(a863,a1,f109(a1)),x40172))),f789(f789(f111(f870(a863,a856)),x40171),x40172))
% 21.40/21.36 [4021]E(f789(f264(x40211),f789(f789(f10(a856,a856,x40211),a336),f789(f789(f9(x40211,f870(x40211,a856),a856),f342(x40211)),x40212))),f789(f88(f870(x40211,a856)),x40212))
% 21.40/21.36 [4048]E(f789(f138(f864(x40481),f864(x40481),f132(x40481),f122(x40481)),f789(f789(f150(f864(x40481),f864(x40481)),f149(x40481)),f789(f149(f864(x40481)),x40482))),f789(f149(x40481),f789(f138(f864(x40481),f864(x40481),f132(x40481),f122(x40481)),x40482)))
% 21.40/21.36 [4074]E(f789(f789(f53(a863,f870(f869(x40741,x40741),a856)),f247(f870(a863,a856))),f789(f789(f9(a863,f870(f869(x40741,x40741),a856),f870(f869(x40741,x40741),a856)),f178(f869(x40741,x40741),a856)),x40742)),f308(x40741,x40742))
% 21.40/21.36 [4096]E(f94(x40961,f789(f789(f10(f870(x40961,a856),a856,x40961),f789(a338,x40962)),f789(f789(f9(x40961,f870(x40961,a856),f870(x40961,a856)),f310(x40961)),f184(f870(x40961,a856))))),f314(x40961,x40962))
% 21.40/21.36 [4119]E(f789(f789(f110(f870(f869(x41191,x41191),a856)),x41192),f789(f789(f289(x41191,x41191,x41191),f789(f789(f289(x41191,x41191,x41191),x41192),f308(x41191,x41192))),x41192)),f789(f789(f289(x41191,x41191,x41191),x41192),f308(x41191,x41192)))
% 21.40/21.36 [4141]P1(f789(f789(f240(f870(f869(x41411,x41411),a856)),f789(f789(f289(x41411,x41411,x41411),x41412),f308(x41411,x41412))),f789(f789(f256(x41411,x41411),f789(f284(x41411),x41412)),f789(f18(f870(x41411,a856),x41411),f789(f284(x41411),x41412)))))
% 21.40/21.36 [4186]E(f789(f264(f864(x41861)),f789(f789(f9(f864(x41861),f870(x41861,a856),a856),f789(f789(f10(f870(x41861,a856),f870(f870(x41861,a856),a856),f864(x41861)),f240(f870(x41861,a856))),f163(x41861))),x41862)),f156(x41861,x41862))
% 21.40/21.36 [4198]E(f789(f152(f864(x41981),x41981,f122(x41981),f789(f789(f10(f864(x41981),f870(f864(x41981),f864(x41981)),x41981),f789(f9(f864(x41981),f864(x41981),f864(x41981)),f132(x41981))),f789(f789(f9(x41981,f864(x41981),f864(x41981)),f146(x41981)),f122(x41981)))),x41982),f789(f148(x41981),x41982))
% 21.40/21.36 [4237]P29(f870(x42371,x42372),f870(f869(x42371,x42372),a856),f789(f789(f10(f870(f869(x42371,x42372),a856),f870(f869(x42371,x42372),a856),f870(x42371,x42372)),f264(f869(x42371,x42372))),f789(f789(f10(f870(x42371,f870(x42372,a856)),f870(f869(x42371,x42372),a856),f870(x42371,x42372)),f259(x42371,x42372,a856)),f789(f10(x42372,f870(x42372,a856),x42371),f789(f9(x42372,x42372,a856),a338)))),f247(f870(f870(x42371,x42372),a856)))
% 21.40/21.36 [4242]E(f59(a1,f789(f113(a1),f789(f789(f89(a1),x42421),x42421)),f789(f113(a1),f789(f789(f89(a1),x42422),x42422))),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f59(a1,f789(f113(a1),x42421),f789(f113(a1),x42422))))
% 21.40/21.36 [4283]E(f789(f789(f53(x42831,f870(f869(x42831,x42831),a856)),x42832),f789(f789(f9(x42831,f870(f869(x42831,x42831),a856),f870(f869(x42831,x42831),a856)),f789(f789(f10(f869(x42831,x42831),f870(f870(f869(x42831,x42831),a856),f870(f869(x42831,x42831),a856)),x42831),f310(f869(x42831,x42831))),f789(f789(f20(x42831,x42831,f869(x42831,x42831)),f249(x42831,x42831)),f7(x42831)))),f184(f870(f869(x42831,x42831),a856)))),f268(x42831,x42832))
% 21.40/21.36 [4291]E(f205(x42911,f789(f789(f249(a1,a1),f789(f88(a1),f789(f789(f82(f869(a1,a1),a1,x42911,f248(a1,a1)),f214(x42911)),x42912))),f789(f789(f82(f869(a1,a1),a1,x42911,f258(a1,a1)),f214(x42911)),x42912))),f228(x42911,x42912))
% 21.40/21.36 [4370]E(f789(f264(f870(x43701,a856)),f789(f789(f10(f870(f870(x43701,a856),a856),a856,f870(x43701,a856)),f96(f870(x43701,a856))),f789(f789(f9(f870(x43701,a856),f870(f870(x43701,a856),a856),f870(f870(x43701,a856),a856)),f789(f789(f10(f870(f870(x43701,a856),f870(a856,a856)),f870(f870(f870(x43701,a856),a856),f870(f870(x43701,a856),a856)),f870(x43701,a856)),f20(f870(x43701,a856),a856,a856)),f789(f789(f10(f870(f870(x43701,a856),a856),f870(f870(x43701,a856),f870(a856,a856)),f870(x43701,a856)),f789(f10(a856,f870(a856,a856),f870(x43701,a856)),a339)),f789(f789(f9(f870(x43701,a856),f870(f870(x43701,a856),f870(x43701,a856)),f870(f870(x43701,a856),a856)),f789(f789(f10(f870(f870(x43701,a856),a856),f870(f870(f870(x43701,a856),f870(x43701,a856)),f870(f870(x43701,a856),a856)),f870(x43701,a856)),f10(f870(x43701,a856),a856,f870(x43701,a856))),a338)),f88(f870(x43701,a856)))))),f789(f789(f10(f870(f870(x43701,a856),a856),a856,f870(x43701,a856)),f789(f342(f870(x43701,a856)),x43702)),f309(x43701))))),f789(f309(x43701),f789(f88(f870(x43701,a856)),x43702)))
% 21.40/21.36 [4516]~E(f789(f789(f89(a1),x45161),x45161),f789(f789(f3(a1),f789(f789(f89(a1),x45162),x45162)),a106))
% 21.40/21.36 [4517]~E(f789(f789(f89(a1),x45171),x45171),f789(f789(f3(a1),f789(f789(f89(a1),x45172),x45172)),a106))
% 21.40/21.36 [4522]~P1(f789(f789(f241(a863),f789(f789(f89(a863),x45221),x45222)),x45222))
% 21.40/21.36 [4523]~P1(f789(f789(f241(a863),f789(f789(f89(a863),x45231),x45232)),x45231))
% 21.40/21.36 [3715]E(f789(f789(f3(a863),x37151),f789(f789(f90(a863),f789(f789(f50(a863),x37151),x37152)),x37152)),f59(a863,x37151,x37152))
% 21.40/21.36 [3716]E(f789(f789(f3(a1),x37161),f789(f789(f90(a1),f789(f789(f50(a1),x37161),x37162)),x37162)),f59(a1,x37161,x37162))
% 21.40/21.36 [3751]E(f789(f789(f150(a863,x37511),f789(f159(x37511),x37512)),f136(a863,f789(f302(a863,f2(a863)),f789(f185(f864(x37511)),x37512)))),x37512)
% 21.40/21.36 [3810]E(f789(f285(x38101,x38101,f308(x38101,f184(f870(f869(x38101,x38101),a856)))),x38102),x38102)
% 21.40/21.36 [3931]E(f308(x39311,f789(f789(f3(f870(f869(x39311,x39311),a856)),x39312),f308(x39311,f184(f870(f869(x39311,x39311),a856))))),f308(x39311,x39312))
% 21.40/21.36 [3932]E(f308(x39321,f789(f789(f110(f870(f869(x39321,x39321),a856)),x39322),f308(x39321,f184(f870(f869(x39321,x39321),a856))))),f308(x39321,x39322))
% 21.40/21.36 [3985]E(f789(f789(f3(a1),f789(f789(f3(a1),f789(f789(f89(a1),x39851),x39851)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),x39852),x39852)),a106)),f789(f789(f89(a1),f789(f789(f3(a1),x39851),x39852)),f789(f789(f3(a1),x39851),x39852)))
% 21.40/21.36 [4026]E(f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f89(a1),x40261),x40262)),f789(f789(f89(a1),x40261),x40262))),a106),f789(f789(f89(a1),f789(f789(f89(a1),x40261),x40261)),f789(f789(f3(a1),f789(f789(f89(a1),x40262),x40262)),a106)))
% 21.40/21.36 [4052]E(f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),x40521),x40521)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),x40522),x40522)),a106)),f789(f789(f89(a1),f789(f789(f89(a1),x40521),f789(f789(f3(a1),x40522),a106))),f789(f789(f89(a1),x40521),f789(f789(f3(a1),x40522),a106))))
% 21.40/21.36 [4063]E(f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f89(a1),x40631),x40632)),f789(f789(f89(a1),x40631),x40632))),a106),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),x40631),x40631)),a106)),f789(f789(f89(a1),x40632),x40632)))
% 21.40/21.36 [4064]E(f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),x40641),x40642)),f789(f789(f3(a1),x40641),x40642))),a106),f789(f789(f3(a1),f789(f789(f3(a1),f789(f789(f89(a1),x40641),x40641)),a106)),f789(f789(f89(a1),x40642),x40642)))
% 21.40/21.36 [4116]E(f789(f109(a1),f789(f789(f50(a863),f789(f789(f90(a863),f789(a114,f789(f84(a1),x41161))),f789(a114,f789(f84(a1),x41162)))),f218(f789(a114,f789(f84(a1),x41161)),f789(a114,f789(f84(a1),x41162))))),f220(x41161,x41162))
% 21.40/21.36 [4161]E(f789(f789(f261(f869(a108,a108),a108,f869(a108,a108),f869(x41611,f869(a108,a108))),f272(f789(a5,f789(f185(f864(x41611)),x41612)))),f789(f789(f10(x41611,f870(f869(a108,a108),f869(x41611,f869(a108,a108))),a108),f249(x41611,f869(a108,a108))),f789(f789(f10(a863,x41611,a108),f789(f159(x41611),x41612)),a22))),f278(x41611,x41612))
% 21.40/21.36 [4243]E(f789(f138(a863,f864(x42431),f789(f9(f864(x42431),a863,a863),f789(f789(f10(a863,f870(a863,a863),f864(x42431)),f239(a863)),f185(f864(x42431)))),f2(a863)),f789(f149(f864(x42431)),f168(x42431,x42432))),f789(f185(f864(f864(x42431))),f789(f133(f864(x42431),f789(f789(f10(a856,a856,f864(x42431)),a336),f789(f789(f9(f864(x42431),f864(x42431),a856),a338),f122(x42431)))),x42432)))
% 21.40/21.36 [4249]E(f789(f789(f53(a863,f870(x42491,a856)),f247(f870(a863,a856))),f789(f789(f9(a863,f870(a863,f870(x42491,a856)),f870(x42491,a856)),f789(f789(f10(f870(a863,a856),f870(f870(a863,f870(x42491,a856)),f870(x42491,a856)),a863),f53(a863,f870(x42491,a856))),f302(a863,f2(a863)))),x42492)),f789(f789(f53(a863,f870(x42491,a856)),f247(f870(a863,a856))),x42492))
% 21.40/21.36 [4268]P1(f789(f70(a863),f789(f264(a863),f789(f789(f20(a863,a856,a856),f789(f789(f10(a856,f870(a856,a856),a863),a339),x42681)),f789(f789(f9(a863,a863,a856),f241(a863)),x42682)))))
% 21.40/21.36 [4380]E(f789(f264(f869(f864(x43801),f864(x43801))),f789(f259(f864(x43801),f864(x43801),a856),f789(f789(f20(f864(x43801),f870(f864(x43801),a856),f870(f864(x43801),a856)),f789(f789(f10(f870(f864(x43801),f870(a856,a856)),f870(f870(f864(x43801),a856),f870(f864(x43801),a856)),f864(x43801)),f20(f864(x43801),a856,a856)),f789(f789(f10(f870(f864(x43801),a856),f870(f864(x43801),f870(a856,a856)),f864(x43801)),f789(f10(a856,f870(a856,a856),f864(x43801)),a340)),f789(f789(f9(f864(x43801),f870(f864(x43801),a863),f870(f864(x43801),a856)),f789(f789(f10(f870(a863,a856),f870(f870(f864(x43801),a863),f870(f864(x43801),a856)),f864(x43801)),f10(a863,a856,f864(x43801))),f789(f789(f10(a863,f870(a863,a856),f864(x43801)),f241(a863)),f185(f864(x43801))))),f185(f864(x43801)))))),f789(f789(f20(f864(x43801),f870(f864(x43801),a856),f870(f864(x43801),a856)),f789(f789(f10(f870(f864(x43801),f870(a856,a856)),f870(f870(f864(x43801),a856),f870(f864(x43801),a856)),f864(x43801)),f20(f864(x43801),a856,a856)),f789(f789(f10(f870(f864(x43801),a856),f870(f864(x43801),f870(a856,a856)),f864(x43801)),f789(f10(a856,f870(a856,a856),f864(x43801)),a339)),f789(f789(f9(f864(x43801),f870(f864(x43801),a863),f870(f864(x43801),a856)),f789(f789(f10(f870(a863,a856),f870(f870(f864(x43801),a863),f870(f864(x43801),a856)),f864(x43801)),f10(a863,a856,f864(x43801))),f789(f789(f10(a863,f870(a863,a856),f864(x43801)),a338),f185(f864(x43801))))),f185(f864(x43801)))))),f789(f789(f9(f864(x43801),f870(f869(f864(x43801),f864(x43801)),a856),f870(f864(x43801),a856)),f789(f789(f10(f870(f864(x43801),f870(f870(f869(f864(x43801),f864(x43801)),a856),a856)),f870(f870(f869(f864(x43801),f864(x43801)),a856),f870(f864(x43801),a856)),f864(x43801)),f9(f864(x43801),f870(f869(f864(x43801),f864(x43801)),a856),a856)),f789(f789(f10(f870(f864(x43801),f869(f864(x43801),f864(x43801))),f870(f864(x43801),f870(f870(f869(f864(x43801),f864(x43801)),a856),a856)),f864(x43801)),f789(f10(f869(f864(x43801),f864(x43801)),f870(f870(f869(f864(x43801),f864(x43801)),a856),a856),f864(x43801)),f342(f869(f864(x43801),f864(x43801))))),f249(f864(x43801),f864(x43801))))),f141(x43801,x43802)))))),f142(x43801,x43802))
% 21.40/21.36 [4055]E(f789(f789(f89(a1),f789(f789(f89(a1),f789(f789(f90(a1),x40551),x40552)),f789(f789(f90(a1),x40551),x40552))),x40552),f789(f789(f90(a1),f789(f789(f3(a1),f789(f789(f89(a1),x40551),x40551)),a106)),x40552))
% 21.40/21.36 [4159]E(f789(a114,f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x41591),x41592)),f184(f870(f869(a863,a863),a856)))))),f789(f789(f3(a863),x41591),x41592))
% 21.40/21.36 [4164]E(f789(f789(f289(x41641,x41641,x41641),f789(f789(f110(f870(f869(x41641,x41641),a856)),x41642),f308(x41641,f184(f870(f869(x41641,x41641),a856))))),f308(x41641,f789(f789(f110(f870(f869(x41641,x41641),a856)),x41642),f308(x41641,f184(f870(f869(x41641,x41641),a856)))))),f308(x41641,x41642))
% 21.40/21.36 [4203]E(f273(x42031,f789(f133(f869(a108,x42031),f789(f259(a108,x42031,a856),f789(f789(f10(a856,f870(x42031,a856),a108),f18(a856,x42031)),f789(f241(a108),f2(a108))))),x42032)),f273(x42031,x42032))
% 21.40/21.36 [4204]E(f271(x42041,f789(f133(f869(a108,x42041),f789(f259(a108,x42041,a856),f789(f789(f10(a856,f870(x42041,a856),a108),f18(a856,x42041)),f789(f241(a108),f2(a108))))),x42042)),f271(x42041,x42042))
% 21.40/21.36 [4206]E(f789(f88(a1),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x42061),x42062)),f184(f870(f869(a863,a863),a856)))))),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x42062),x42061)),f184(f870(f869(a863,a863),a856))))))
% 21.40/21.36 [4280]E(f789(f789(f95(a1,a863),f789(f113(a1),f789(f789(f89(a1),x42801),a106))),f789(f789(f20(a1,a863,a863),f789(f789(f9(a1,a863,f870(a863,a863)),f789(f789(f10(a856,f870(a863,f870(a863,a863)),a1),f105(a863)),a190)),f2(a863))),f789(f789(f10(a863,a863,a1),a121),f789(f789(f10(a863,a863,a1),f789(f244(a863),x42802)),a114)))),f789(f789(f244(a863),f789(a121,x42802)),f789(f113(a863),x42801)))
% 21.40/21.36 [4281]E(f789(f789(f95(a1,a863),f789(f113(a1),f789(f789(f89(a1),x42811),a106))),f789(f789(f20(a1,a863,a863),f789(f789(f9(a1,a863,f870(a863,a863)),f789(f789(f10(a856,f870(a863,f870(a863,a863)),a1),f105(a863)),a190)),f789(a121,x42812))),f789(f789(f10(a863,a863,a1),a121),f789(f789(f10(a863,a863,a1),f789(f239(a863),x42812)),a114)))),f789(f789(f239(a863),f789(a121,x42812)),f789(f113(a863),x42811)))
% 21.40/21.36 [4300]E(f789(f138(f864(x43001),f864(x43001),f132(x43001),f122(x43001)),f789(f789(f150(f864(x43001),f864(x43001)),f152(f864(x43001),x43001,f122(x43001),f789(f789(f10(f864(x43001),f870(f864(x43001),f864(x43001)),x43001),f18(f864(x43001),f864(x43001))),f789(f789(f9(x43001,f864(x43001),f864(x43001)),f146(x43001)),f122(x43001))))),x43002)),f789(f789(f150(f864(x43001),x43001),f137(x43001)),f789(f133(f864(x43001),f789(f789(f10(a856,a856,f864(x43001)),a336),f789(f789(f9(f864(x43001),f864(x43001),a856),a338),f122(x43001)))),x43002)))
% 21.40/21.36 [4360]E(f789(f259(a1,a1,a856),f789(f789(f9(a1,f870(a1,a856),f870(a1,a856)),f789(f789(f10(f870(a1,f870(a856,a856)),f870(f870(a1,a856),f870(a1,a856)),a1),f20(a1,a856,a856)),f789(f789(f10(f870(a1,a856),f870(a1,f870(a856,a856)),a1),f789(f10(a856,f870(a856,a856),a1),a339)),f789(f789(f10(f870(a1,a1),f870(a1,a856),a1),f789(f10(a1,a856,a1),f789(a338,x43601))),f789(f789(f10(a1,f870(a1,a1),a1),f89(a1)),f789(f90(a1),x43602)))))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f789(f10(a856,a856,a1),f789(a343,f789(f789(f241(a1),f2(a1)),x43602))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f240(a1),f2(a1)))),f789(f789(f9(a1,a1,a856),f241(a1)),x43602))))),f789(f789(f10(a856,a856,a1),f789(a343,f789(a336,f789(f789(f241(a1),f2(a1)),x43602)))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f241(a1),x43602))),f789(f789(f9(a1,a1,a856),f240(a1)),f2(a1))))))),f63(x43601,x43602))
% 21.40/21.36 [4362]E(f789(f264(x43621),f789(f789(f10(f870(a863,a856),a856,x43621),f96(a863)),f789(f789(f9(x43621,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),x43621),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),x43621),f789(f10(a856,f870(a856,a856),a863),a339)),f789(f789(f9(x43621,f870(a863,x43621),f870(a863,a856)),f789(f789(f10(f870(x43621,a856),f870(f870(a863,x43621),f870(a863,a856)),x43621),f10(x43621,a856,a863)),a338)),f789(f159(x43621),x43622))))),f789(f789(f9(a863,a863,a856),f241(a863)),f789(f185(f864(x43621)),x43622))))),f789(f163(x43621),x43622))
% 21.40/21.36 [4176]E(f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),x41761),a106)),x41762)),f789(f789(f3(a1),f789(f789(f89(a1),x41761),a106)),x41762))),a106),f789(f789(f3(a1),f789(f789(f89(a1),x41761),x41761)),f789(f789(f3(a1),f789(f789(f89(a1),x41762),x41762)),a106)))
% 21.40/21.36 [4305]E(f789(f789(f95(a1,a863),f789(f113(a1),f789(f789(f89(a1),x43051),a106))),f789(f789(f20(a1,a863,a863),f789(f789(f9(a1,a863,f870(a863,a863)),f789(f789(f10(a856,f870(a863,f870(a863,a863)),a1),f105(a863)),a190)),f2(a863))),f789(f789(f10(a863,a863,a1),a121),f789(f789(f9(a1,a863,a863),f789(f789(f10(a863,f870(a863,a863),a1),f244(a863)),a114)),x43052)))),f789(f789(f244(a863),f789(f113(a863),x43051)),f789(a121,x43052)))
% 21.40/21.36 [4306]E(f789(f789(f95(a1,a863),f789(f113(a1),f789(f789(f89(a1),x43061),a106))),f789(f789(f20(a1,a863,a863),f789(f789(f9(a1,a863,f870(a863,a863)),f789(f789(f10(a856,f870(a863,f870(a863,a863)),a1),f105(a863)),a190)),f789(a121,x43062))),f789(f789(f10(a863,a863,a1),a121),f789(f789(f9(a1,a863,a863),f789(f789(f10(a863,f870(a863,a863),a1),f239(a863)),a114)),x43062)))),f789(f789(f239(a863),f789(f113(a863),x43061)),f789(a121,x43062)))
% 21.40/21.36 [4295]E(f789(f259(x42951,x42951,a856),f789(f789(f20(x42951,a856,f870(x42951,a856)),f789(f789(f10(f870(x42951,f870(a856,a856)),f870(a856,f870(x42951,a856)),x42951),f9(x42951,a856,a856)),f789(f789(f10(f870(x42951,a856),f870(x42951,f870(a856,a856)),x42951),f789(f10(a856,f870(a856,a856),x42951),a339)),a338))),x42952)),f268(x42951,x42952))
% 21.40/21.36 [4338]E(f789(f789(f50(a863),x43381),f789(f789(f89(a863),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106))),x43382)),f789(f789(f50(a863),x43381),f789(a121,f789(a121,f789(a121,x43382)))))
% 21.40/21.36 [4339]E(f59(a863,x43391,f789(f789(f89(a863),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106))),x43392)),f59(a863,x43391,f789(a121,f789(a121,f789(a121,x43392)))))
% 21.40/21.36 [4340]E(f59(a863,f789(f789(f89(a863),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106))),x43401),x43402),f59(a863,f789(a121,f789(a121,f789(a121,x43401))),x43402))
% 21.40/21.36 [4353]E(f130(f789(x43531,f789(f789(f90(a108),f789(f113(a108),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106))),x43532))),f789(f202(x43531),x43532))
% 21.40/21.36 [4354]E(f789(f789(f50(a863),f789(f789(f89(a863),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106))),x43541)),x43542),f789(f789(f50(a863),f789(a121,f789(a121,f789(a121,x43541)))),x43542))
% 21.40/21.36 [3537]P29(x35371,f871(x35372,x35371),f321(x35371,x35372),x35373)
% 21.40/21.36 [3538]P29(x35381,f871(x35381,x35382),f312(x35381,x35382),x35383)
% 21.40/21.36 [4425]~E(f38(x44251,x44252),f789(a29,x44253))
% 21.40/21.36 [4426]~E(f30(x44261,x44262),f789(a29,x44263))
% 21.40/21.36 [4427]~E(f37(x44271,x44272),f789(a29,x44273))
% 21.40/21.36 [4428]~E(f789(a29,x44281),f38(x44282,x44283))
% 21.40/21.36 [4429]~E(f789(a29,x44291),f30(x44292,x44293))
% 21.40/21.36 [4430]~E(f789(a29,x44301),f37(x44302,x44303))
% 21.40/21.36 [4446]~E(f35(x44461,x44462,x44463),a25)
% 21.40/21.36 [4447]~E(f34(x44471,x44472,x44473),a25)
% 21.40/21.36 [4448]~E(f33(x44481,x44482,x44483),a25)
% 21.40/21.36 [4449]~E(f35(x44491,x44492,x44493),a25)
% 21.40/21.36 [4450]~E(f34(x44501,x44502,x44503),a25)
% 21.40/21.36 [4451]~E(f33(x44511,x44512,x44513),a25)
% 21.40/21.36 [3149]E(f789(f201(x31491,x31492),x31493),f127(x31491,x31492))
% 21.40/21.36 [3150]E(f789(f189(x31501,x31502),x31503),f128(x31501,x31502))
% 21.40/21.36 [3241]E(f789(f789(f150(x32411,x32412),x32413),f122(x32411)),f122(x32412))
% 21.40/21.36 [3242]E(f789(f789(f203(x32421,x32422),x32423),f187(x32421)),f187(x32422))
% 21.40/21.36 [3262]E(f36(f33(x32621,x32622,x32623)),f2(a863))
% 21.40/21.36 [3281]E(f789(f179(x32811,x32812,x32813),f2(a863)),x32812)
% 21.40/21.36 [3282]E(f789(f185(a857),f33(x32821,x32822,x32823)),f2(a863))
% 21.40/21.36 [3283]E(f789(f789(f171(x32831,x32832),x32833),f122(x32832)),f122(f869(x32831,x32832)))
% 21.40/21.36 [3320]E(f94(x33201,f71(x33201,x33202,x33203)),f789(f72(x33201,x33202),x33203))
% 21.40/21.36 [3391]E(f789(f248(f864(x33911),f864(x33911)),f162(x33911,x33912,x33913)),f789(f133(x33911,x33912),x33913))
% 21.40/21.36 [3467]E(f180(x34671,x34672,x34673,f2(a863)),x34672)
% 21.40/21.36 [3468]E(f19(x34681,x34682,x34683,f2(a108)),x34682)
% 21.40/21.36 [3469]E(f21(x34691,x34692,x34693,f2(a108)),x34692)
% 21.40/21.36 [3476]E(f160(x34761,x34762,x34763,f122(x34761)),f122(x34762))
% 21.40/21.36 [3483]E(f789(f789(f159(x34831),f789(f789(f146(x34831),x34832),x34833)),f2(a863)),x34832)
% 21.40/21.36 [3536]P29(x35361,x35362,x35363,f184(f870(x35361,a856)))
% 21.40/21.36 [3631]E(f270(x36311,x36312,x36313),f789(f249(f870(a108,f870(a856,f867(f865(x36311)))),f869(a108,a108)),f55(x36311)))
% 21.40/21.36 [3690]E(f789(f82(x36901,x36902,x36901,x36903),f41(x36901)),x36903)
% 21.40/21.36 [3864]P1(f789(f789(f342(f869(x38641,x38641)),f789(f789(f249(x38641,x38641),x38642),x38642)),f308(x38641,x38643)))
% 21.40/21.36 [4526]~P1(f789(f789(f342(f869(f864(x45261),f864(x45261))),f789(f789(f249(f864(x45261),f864(x45261)),x45262),f122(x45261))),f141(x45261,x45263)))
% 21.40/21.36 [4527]~P1(f789(f789(f342(f869(f864(x45271),f864(x45271))),f789(f789(f249(f864(x45271),f864(x45271)),x45272),f122(x45271))),f143(x45271,x45273)))
% 21.40/21.36 [4528]~P1(f789(f789(f342(f869(f864(x45281),f864(x45281))),f789(f789(f249(f864(x45281),f864(x45281)),x45282),f122(x45281))),f153(x45281,x45283)))
% 21.40/21.36 [4529]~P1(f789(f789(f342(f869(f864(x45291),f864(x45291))),f789(f789(f249(f864(x45291),f864(x45291)),f122(x45291)),x45292)),f141(x45291,x45293)))
% 21.40/21.36 [4530]~P1(f789(f789(f342(f869(f864(x45301),f864(x45301))),f789(f789(f249(f864(x45301),f864(x45301)),f122(x45301)),x45302)),f153(x45301,x45303)))
% 21.40/21.36 [3217]E(f789(f789(f204(x32171),x32172),x32173),f205(x32171,f217(x32172,x32173)))
% 21.40/21.36 [3272]E(f789(f286(x32721,x32722),f789(f286(x32722,x32721),x32723)),x32723)
% 21.40/21.36 [3288]E(f320(x32881,x32882,f789(f312(x32881,x32882),x32883)),x32883)
% 21.40/21.36 [3289]E(f323(x32891,x32892,f789(f321(x32892,x32891),x32893)),x32893)
% 21.40/21.36 [3295]E(f789(f789(f171(x32951,x32952),f122(x32951)),x32953),f122(f869(x32951,x32952)))
% 21.40/21.36 [3298]E(f165(x32981,x32982,f789(f265(a863),x32983)),f789(f789(f164(x32981),x32983),x32982))
% 21.40/21.36 [3312]E(f789(f185(f871(x33121,x33122)),f789(f312(x33121,x33122),x33123)),f2(a863))
% 21.40/21.36 [3313]E(f789(f185(f871(x33131,x33132)),f789(f321(x33132,x33131),x33133)),f2(a863))
% 21.40/21.36 [3316]E(f789(f269(x33161,x33162),f789(f286(x33162,x33161),x33163)),f789(f267(x33162,x33161),x33163))
% 21.40/21.36 [3318]E(f789(f267(x33181,x33182),f789(f286(x33182,x33181),x33183)),f789(f269(x33182,x33181),x33183))
% 21.40/21.36 [3319]E(f789(f269(x33191,x33192),f789(f286(x33192,x33191),x33193)),f789(f267(x33192,x33191),x33193))
% 21.40/21.36 [3334]E(f789(f133(x33341,x33342),f789(f149(x33341),x33343)),f789(f149(x33341),f789(f133(x33341,x33342),x33343)))
% 21.40/21.36 [3336]E(f789(f789(f135(x33361),f789(a121,x33362)),x33363),f789(f789(f135(x33361),x33362),f147(x33361,x33363)))
% 21.40/21.36 [3367]E(f36(f34(x33671,x33672,x33673)),f789(f789(f89(a863),f36(x33673)),f789(a121,f2(a863))))
% 21.40/21.36 [3368]E(f789(f311(x33681,x33682,x33683),f184(f870(x33681,a856))),f184(f870(x33682,a856)))
% 21.40/21.36 [3369]E(f789(f285(x33691,x33692,x33693),f184(f870(x33691,a856))),f184(f870(x33692,a856)))
% 21.40/21.36 [3370]E(f789(f313(x33701,x33702,x33703),f184(f870(x33702,a856))),f184(f870(x33701,a856)))
% 21.40/21.36 [3371]E(f789(f313(x33711,x33712,x33713),f247(f870(x33712,a856))),f247(f870(x33711,a856)))
% 21.40/21.36 [3406]E(f235(x34061,x34062,f789(f234(x34061),x34063)),f789(f789(f89(a863),f789(x34062,x34063)),f789(a121,f2(a863))))
% 21.40/21.36 [3487]E(f789(f185(a857),f34(x34871,x34872,x34873)),f789(f789(f89(a863),f789(f185(a857),x34873)),f789(a121,f2(a863))))
% 21.40/21.36 [3488]E(f789(f311(f869(x34881,x34882),x34882,f258(x34881,x34882)),x34883),f789(f267(x34881,x34882),x34883))
% 21.40/21.36 [3489]E(f789(f311(f869(x34891,x34892),x34891,f248(x34891,x34892)),x34893),f789(f269(x34891,x34892),x34893))
% 21.40/21.36 [3562]E(f789(f789(f249(x35621,x35622),f789(f248(x35621,x35622),x35623)),f789(f258(x35621,x35622),x35623)),x35623)
% 21.40/21.36 [3563]E(f789(f789(f249(x35631,x35632),f789(f248(x35631,x35632),x35633)),f789(f258(x35631,x35632),x35633)),x35633)
% 21.40/21.36 [3569]E(f789(f789(f259(x35691,x35692,x35691),f18(x35691,x35692)),x35693),f789(f248(x35691,x35692),x35693))
% 21.40/21.36 [3588]E(f174(x35881,x35882,x35883,f789(f18(f867(x35882),x35881),f187(x35882))),x35883)
% 21.40/21.36 [3589]E(f174(x35891,x35892,f789(f18(f867(x35892),x35891),f187(x35892)),x35893),x35893)
% 21.40/21.36 [3644]E(f36(f35(x36441,x36442,x36443)),f789(f789(f89(a863),f789(f789(f89(a863),f36(x36442)),f36(x36443))),f789(a121,f2(a863))))
% 21.40/21.36 [3694]E(f789(f82(x36941,x36941,x36942,f41(x36941)),x36943),x36943)
% 21.40/21.36 [3778]P1(f789(f70(x37781),f173(x37781,x37782,f170(x37781,x37782,x37783))))
% 21.40/21.36 [3800]P1(f789(f789(f191(f30(x38001,x38002)),x38003),f789(f789(f789(a193,x38003),x38001),f789(x38002,x38003))))
% 21.40/21.36 [3801]P1(f789(f789(f191(f30(x38011,x38012)),x38013),f789(f789(f789(a193,x38013),x38011),f789(x38012,x38013))))
% 21.40/21.36 [3803]E(f789(f185(a857),f35(x38031,x38032,x38033)),f789(f789(f89(a863),f789(f789(f89(a863),f789(f185(a857),x38032)),f789(f185(a857),x38033))),f789(a121,f2(a863))))
% 21.40/21.36 [3874]P1(f789(f789(f240(f870(x38741,a856)),f789(f163(x38741),f789(f133(x38741,x38742),x38743))),f789(f163(x38741),x38743)))
% 21.40/21.36 [3918]P1(f789(f789(f240(f870(x39181,a856)),f789(f163(x39181),f789(f789(f164(x39181),x39182),x39183))),f789(f163(x39181),x39183)))
% 21.40/21.36 [3919]P1(f789(f789(f240(f870(x39191,a856)),f789(f163(x39191),f789(f789(f135(x39191),x39192),x39193))),f789(f163(x39191),x39193)))
% 21.40/21.36 [3923]P1(f789(f789(f240(f870(x39231,a856)),f789(f163(x39231),f158(x39231,x39232,x39233))),f789(f163(x39231),x39233)))
% 21.40/21.36 [3924]P1(f789(f789(f240(f870(x39241,a856)),f789(f163(x39241),f165(x39241,x39242,x39243))),f789(f163(x39241),x39242)))
% 21.40/21.36 [3947]P29(f869(x39471,x39472),f869(x39472,x39471),f789(f259(x39471,x39472,f869(x39472,x39471)),f789(f9(x39472,x39471,f869(x39472,x39471)),f249(x39472,x39471))),x39473)
% 21.40/21.36 [3958]E(f789(f789(f789(f178(f864(x39581),f864(x39581)),f59(a863,x39582,f789(f185(f864(x39581)),x39583))),f148(x39581)),x39583),f789(f789(f789(f178(f864(x39581),f864(x39581)),x39582),f148(x39581)),x39583))
% 21.40/21.36 [3998]E(f789(f82(f864(x39981),f864(x39981),f864(x39981),f789(f789(f178(f864(x39981),f864(x39981)),x39982),f148(x39981))),f789(f789(f178(f864(x39981),f864(x39981)),x39983),f148(x39981))),f789(f789(f178(f864(x39981),f864(x39981)),f789(f789(f89(a863),x39982),x39983)),f148(x39981)))
% 21.40/21.36 [4001]P1(f789(f789(f342(f869(f864(x40011),f864(x40011))),f789(f789(f249(f864(x40011),f864(x40011)),x40012),x40012)),f154(x40011,f308(x40011,x40013))))
% 21.40/21.36 [4144]E(f94(f869(x41441,x41442),f789(f789(f20(f869(x41441,x41442),x41442,a856),f789(f789(f10(x41441,f870(x41442,a856),f869(x41441,x41442)),x41443),f248(x41441,x41442))),f258(x41441,x41442))),f94(f869(x41441,x41442),f789(f259(x41441,x41442,a856),x41443)))
% 21.40/21.36 [4145]E(f99(f869(x41451,x41452),f789(f789(f20(f869(x41451,x41452),x41452,a856),f789(f789(f10(x41451,f870(x41452,a856),f869(x41451,x41452)),x41453),f248(x41451,x41452))),f258(x41451,x41452))),f99(f869(x41451,x41452),f789(f259(x41451,x41452,a856),x41453)))
% 21.40/21.36 [4183]E(f789(f789(f288(f869(a863,x41831),x41831),f333(a863,x41831,a245,x41832)),f789(f789(f20(x41831,x41831,f869(a863,x41831)),f789(f789(f10(a863,f870(x41831,f869(a863,x41831)),x41831),f249(a863,x41831)),x41833)),f7(x41831))),f335(x41831,x41833,x41832))
% 21.40/21.36 [4245]E(f789(f260(x42451,x42451,x42452,x42452,f7(x42451),f7(x42452)),x42453),x42453)
% 21.40/21.36 [4379]E(f789(f789(f95(a1,x43791),f220(f789(f789(f82(f869(a1,a1),a1,x43791,f258(a1,a1)),f214(x43791)),x43792),f789(f789(f82(f869(a1,a1),a1,x43791,f258(a1,a1)),f214(x43791)),x43793))),f789(f789(f20(a1,a1,x43791),f789(f789(f10(a1,f870(a1,x43791),a1),f204(x43791)),f789(f789(f20(a1,a1,a1),f789(f789(f10(a1,f870(a1,a1),a1),f89(a1)),f789(f789(f10(a1,a1,a1),f789(f90(a1),f789(f789(f82(f869(a1,a1),a1,x43791,f248(a1,a1)),f214(x43791)),x43792))),f789(f789(f9(a1,a1,a1),f50(a1)),f789(f789(f82(f869(a1,a1),a1,x43791,f258(a1,a1)),f214(x43791)),x43792))))),f789(f789(f10(a1,a1,a1),f789(f90(a1),f789(f789(f82(f869(a1,a1),a1,x43791,f248(a1,a1)),f214(x43791)),x43793))),f789(f789(f9(a1,a1,a1),f50(a1)),f789(f789(f82(f869(a1,a1),a1,x43791,f258(a1,a1)),f214(x43791)),x43793)))))),f7(a1))),f231(x43791,x43792,x43793))
% 21.40/21.36 [4443]~E(f789(f789(f146(x44431),x44432),x44433),x44433)
% 21.40/21.36 [4444]~E(f789(f789(f146(x44441),x44442),x44443),x44443)
% 21.40/21.36 [4452]~E(f789(f789(f146(x44521),x44522),x44523),f122(x44521))
% 21.40/21.36 [4453]~E(f789(f789(f146(x44531),x44532),x44533),f122(x44531))
% 21.40/21.36 [4478]~E(f789(f789(f310(x44781),x44782),x44783),f184(f870(x44781,a856)))
% 21.40/21.36 [4479]~E(f789(f789(f310(x44791),x44792),x44793),f184(f870(x44791,a856)))
% 21.40/21.36 [4508]~E(f789(f311(x45081,f870(x45081,a856),x45082),x45083),f789(f309(x45081),x45083))
% 21.40/21.36 [3267]E(f147(x32671,f789(f789(f146(x32671),x32672),x32673)),x32673)
% 21.40/21.36 [3275]E(f789(f789(f155(x32751,f122(x32751)),x32752),x32753),f122(x32751))
% 21.40/21.36 [3276]E(f789(f789(f155(x32761,f122(x32761)),x32762),x32763),f122(x32761))
% 21.40/21.36 [3277]E(f789(f137(x32771),f789(f789(f146(x32771),x32772),x32773)),x32772)
% 21.40/21.36 [3323]E(f789(f789(f135(x33231),f87(a863)),f789(f789(f146(x33231),x33232),x33233)),x33233)
% 21.40/21.36 [3353]E(f147(x33531,f789(f789(f135(x33531),x33532),x33533)),f789(f789(f135(x33531),x33532),f147(x33531,x33533)))
% 21.40/21.36 [3354]E(f123(x33541,f789(f789(f135(x33541),x33542),x33543)),f789(f789(f135(x33541),x33542),f123(x33541,x33543)))
% 21.40/21.36 [3355]E(f147(x33551,f789(f789(f135(x33551),x33552),x33553)),f789(f789(f135(x33551),x33552),f147(x33551,x33553)))
% 21.40/21.36 [3356]E(f123(x33561,f789(f789(f135(x33561),x33562),x33563)),f789(f789(f135(x33561),x33562),f123(x33561,x33563)))
% 21.40/21.36 [3358]E(f789(f789(f155(x33581,x33582),x33583),f789(f789(f159(x33581),x33582),x33583)),x33582)
% 21.40/21.36 [3381]E(f789(f789(f310(x33811),x33812),f789(f789(f310(x33811),x33812),x33813)),f789(f789(f310(x33811),x33812),x33813))
% 21.40/21.36 [3394]E(f789(f789(f310(x33941),x33942),f789(f163(x33941),x33943)),f789(f163(x33941),f789(f789(f146(x33941),x33942),x33943)))
% 21.40/21.36 [3403]E(f789(f789(f164(x34031),f87(a863)),f789(f789(f146(x34031),x34032),x34033)),f789(f789(f146(x34031),x34032),f122(x34031)))
% 21.40/21.36 [3436]E(f789(f170(x34361,x34362,f122(f869(x34361,x34362))),x34363),f187(x34362))
% 21.40/21.36 [3437]E(f789(f170(x34371,x34372,f122(f869(x34371,x34372))),x34373),f187(x34372))
% 21.40/21.36 [3452]E(f789(f72(x34521,x34522),f789(f789(f310(x34521),x34523),f184(f870(x34521,a856)))),x34523)
% 21.40/21.36 [3499]E(f789(f789(f89(a863),x34991),f789(f789(f89(a863),x34992),x34993)),f789(f789(f89(a863),x34992),f789(f789(f89(a863),x34991),x34993)))
% 21.40/21.36 [3500]E(f789(f789(f89(a1),x35001),f789(f789(f89(a1),x35002),x35003)),f789(f789(f89(a1),x35002),f789(f789(f89(a1),x35001),x35003)))
% 21.40/21.36 [3505]E(f789(f789(f256(x35051,x35052),f184(f870(x35051,a856))),x35053),f184(f870(f869(x35051,x35052),a856)))
% 21.40/21.36 [3520]E(f147(x35201,f789(f789(f164(x35201),f789(a121,x35202)),x35203)),f789(f789(f164(x35201),x35202),f147(x35201,x35203)))
% 21.40/21.36 [3528]E(f789(f789(f110(f870(x35281,a856)),x35282),x35283),f789(f789(f110(f870(x35281,a856)),x35283),x35282))
% 21.40/21.36 [3529]E(f789(f789(f111(f870(x35291,a856)),x35292),x35293),f789(f789(f111(f870(x35291,a856)),x35293),x35292))
% 21.40/21.36 [3531]E(f789(f789(f132(x35311),x35312),f789(f789(f146(x35311),x35313),f122(x35311))),f789(f148(x35311),f789(f789(f146(x35311),x35313),x35312)))
% 21.40/21.36 [3532]E(f789(f789(f132(x35321),f789(f149(x35321),x35322)),f789(f149(x35321),x35323)),f789(f149(x35321),f789(f789(f132(x35321),x35323),x35322)))
% 21.40/21.36 [3548]P1(f789(f789(f342(x35481),x35482),f789(f789(f310(x35481),x35482),x35483)))
% 21.40/21.36 [3553]E(f789(f789(f54(x35531,f870(x35532,a856)),f184(f870(x35531,a856))),x35533),f247(f870(x35532,a856)))
% 21.40/21.36 [3556]E(f789(f285(x35561,x35561,f268(x35561,x35562)),x35563),f789(f789(f111(f870(x35561,a856)),x35562),x35563))
% 21.40/21.36 [3567]E(f789(f185(f864(x35671)),f789(f789(f146(x35671),x35672),x35673)),f789(f789(f89(a863),f789(f185(f864(x35671)),x35673)),f789(a121,f2(a863))))
% 21.40/21.36 [3571]E(f140(x35711,f789(f789(f132(x35711),x35712),f789(f789(f146(x35711),x35713),f122(x35711)))),x35713)
% 21.40/21.36 [3572]E(f123(x35721,f789(f789(f132(x35721),x35722),f789(f789(f146(x35721),x35723),f122(x35721)))),x35722)
% 21.40/21.36 [3577]E(f789(f789(f132(x35771),f789(f789(f164(x35771),x35772),x35773)),f789(f789(f135(x35771),x35772),x35773)),x35773)
% 21.40/21.36 [3586]E(f789(f789(f3(a863),f789(f789(f89(a863),x35861),x35862)),f789(f789(f89(a863),x35863),x35862)),f789(f789(f3(a863),x35861),x35863))
% 21.40/21.36 [3587]E(f789(f789(f3(a863),f789(f789(f89(a863),x35871),x35872)),f789(f789(f89(a863),x35871),x35873)),f789(f789(f3(a863),x35872),x35873))
% 21.40/21.36 [3593]E(f789(f789(f132(x35931),f789(f149(x35931),x35932)),f789(f789(f146(x35931),x35933),f122(x35931))),f789(f149(x35931),f789(f789(f146(x35931),x35933),x35932)))
% 21.40/21.36 [3595]E(f789(f789(f89(a863),f789(f185(f864(x35951)),x35952)),f789(f185(f864(x35951)),x35953)),f789(f185(f864(x35951)),f789(f789(f132(x35951),x35952),x35953)))
% 21.40/21.36 [3605]E(f789(f789(f110(f870(x36051,a856)),f789(f163(x36051),x36052)),f789(f163(x36051),x36053)),f789(f163(x36051),f789(f789(f132(x36051),x36052),x36053)))
% 21.40/21.36 [3606]E(f59(a863,f789(f789(f90(a863),x36061),x36062),f789(f789(f90(a863),x36061),x36063)),f789(f789(f90(a863),x36061),f59(a863,x36062,x36063)))
% 21.40/21.36 [3609]E(f789(f789(f164(x36091),f789(f789(f3(a863),x36092),f87(a863))),f147(x36091,x36093)),f147(x36091,f789(f789(f164(x36091),x36092),x36093)))
% 21.40/21.36 [3624]E(f789(f789(f111(f870(x36241,a856)),x36242),f789(f88(f870(x36241,a856)),x36243)),f789(f789(f3(f870(x36241,a856)),x36242),x36243))
% 21.40/21.36 [3625]E(f789(f789(f3(f870(x36251,a856)),x36252),f789(f88(f870(x36251,a856)),x36253)),f789(f789(f111(f870(x36251,a856)),x36252),x36253))
% 21.40/21.36 [3647]E(f789(f789(f256(x36471,x36472),x36473),f789(f18(f870(x36472,a856),x36471),f184(f870(x36472,a856)))),f184(f870(f869(x36471,x36472),a856)))
% 21.40/21.36 [3649]E(f789(f789(f89(a863),f789(f789(f90(a863),x36491),x36492)),f789(f789(f90(a863),x36491),x36493)),f789(f789(f90(a863),x36491),f789(f789(f89(a863),x36492),x36493)))
% 21.40/21.36 [3650]E(f789(f789(f3(a863),f789(f789(f90(a863),x36501),x36502)),f789(f789(f90(a863),x36501),x36503)),f789(f789(f90(a863),x36501),f789(f789(f3(a863),x36502),x36503)))
% 21.40/21.36 [3651]E(f789(f789(f89(a1),f789(f789(f90(a1),x36511),x36512)),f789(f789(f90(a1),x36511),x36513)),f789(f789(f90(a1),x36511),f789(f789(f89(a1),x36512),x36513)))
% 21.40/21.36 [3652]E(f789(f789(f3(a1),f789(f789(f90(a1),x36521),x36522)),f789(f789(f90(a1),x36521),x36523)),f789(f789(f90(a1),x36521),f789(f789(f3(a1),x36522),x36523)))
% 21.40/21.36 [3653]E(f789(f789(f90(a1),f789(f789(f250(a1),x36531),x36532)),f789(f789(f250(a1),x36531),x36533)),f789(f789(f250(a1),x36531),f789(f789(f89(a863),x36532),x36533)))
% 21.40/21.36 [3666]E(f789(f789(f53(x36661,f870(x36662,a856)),x36663),f789(f18(f870(x36662,a856),x36661),f184(f870(x36662,a856)))),f184(f870(x36662,a856)))
% 21.40/21.36 [3668]E(f59(a863,f789(f789(f90(a863),x36681),x36682),f789(f789(f90(a863),x36683),x36682)),f789(f789(f90(a863),f59(a863,x36681,x36683)),x36682))
% 21.40/21.36 [3672]E(f59(a1,f789(f789(f90(a1),x36721),f59(a1,x36722,x36723)),x36723),f59(a1,f789(f789(f90(a1),x36721),x36722),x36723))
% 21.40/21.36 [3673]E(f59(a1,f789(f789(f90(a1),x36731),f59(a1,x36732,x36733)),x36733),f59(a1,f789(f789(f90(a1),x36731),x36732),x36733))
% 21.40/21.36 [3674]E(f59(a1,f789(f789(f3(a1),x36741),f59(a1,x36742,x36743)),x36743),f59(a1,f789(f789(f3(a1),x36741),x36742),x36743))
% 21.40/21.36 [3675]P1(f789(f789(f240(f870(x36751,a856)),x36752),f789(f789(f310(x36751),x36753),x36752)))
% 21.40/21.36 [3699]E(f789(f311(f869(x36991,x36992),x36991,f248(x36991,x36992)),f789(f163(f869(x36991,x36992)),x36993)),f173(x36991,x36992,f170(x36991,x36992,x36993)))
% 21.40/21.36 [3756]E(f789(f789(f54(f870(x37561,a856),f870(x37561,a856)),x37562),f789(f110(f870(x37561,a856)),x37563)),f789(f789(f110(f870(x37561,a856)),x37563),f52(f870(x37561,a856),x37562)))
% 21.40/21.36 [3757]E(f789(f789(f53(f870(x37571,a856),f870(x37571,a856)),x37572),f789(f111(f870(x37571,a856)),x37573)),f789(f789(f111(f870(x37571,a856)),x37573),f51(f870(x37571,a856),x37572)))
% 21.40/21.36 [3767]E(f789(f163(x37671),f789(f789(f789(f178(f864(x37671),f864(x37671)),x37672),f148(x37671)),x37673)),f789(f163(x37671),x37673))
% 21.40/21.36 [3771]E(f173(x37711,x37712,f789(f789(f10(x37712,f867(x37712),x37711),f234(x37712)),x37713)),f247(f870(x37711,a856)))
% 21.40/21.36 [3774]E(f789(f185(f864(x37741)),f789(f789(f789(f178(f864(x37741),f864(x37741)),x37742),f148(x37741)),x37743)),f789(f185(f864(x37741)),x37743))
% 21.40/21.36 [3776]E(f789(f789(f259(x37761,x37762,x37762),f789(f18(f870(x37762,x37762),x37761),f7(x37762))),x37763),f789(f258(x37761,x37762),x37763))
% 21.40/21.36 [3783]E(f59(a1,f789(f789(f3(a1),f59(a1,x37831,x37832)),x37833),x37832),f59(a1,f789(f789(f3(a1),x37831),x37833),x37832))
% 21.40/21.36 [3784]E(f59(a1,f789(f789(f250(a1),f59(a1,x37841,x37842)),x37843),x37842),f59(a1,f789(f789(f250(a1),x37841),x37843),x37842))
% 21.40/21.36 [3787]E(f789(f789(f53(f870(f869(x37871,x37872),a856),f870(x37872,a856)),x37873),f267(x37871,x37872)),f789(f267(x37871,x37872),f51(f870(f869(x37871,x37872),a856),x37873)))
% 21.40/21.36 [3788]E(f789(f789(f53(f870(f869(x37881,x37882),a856),f870(x37881,a856)),x37883),f269(x37881,x37882)),f789(f269(x37881,x37882),f51(f870(f869(x37881,x37882),a856),x37883)))
% 21.40/21.36 [3816]E(f789(f82(x38161,x38161,x38161,x38162),f789(f789(f178(x38161,x38161),x38163),x38162)),f789(f789(f178(x38161,x38161),f789(a121,x38163)),x38162))
% 21.40/21.36 [3826]E(f236(f867(x38261),x38262,f187(x38261),f789(f789(f10(x38261,f867(x38261),x38262),f234(x38261)),x38263)),f789(f203(x38262,x38261),x38263))
% 21.40/21.36 [3833]E(f789(f789(f135(x38331),f789(f789(f3(a863),f789(f185(f864(x38331)),x38332)),x38333)),f789(f149(x38331),x38332)),f789(f149(x38331),f789(f789(f164(x38331),x38333),x38332)))
% 21.40/21.36 [3834]E(f789(f789(f164(x38341),f789(f789(f3(a863),f789(f185(f864(x38341)),x38342)),x38343)),f789(f149(x38341),x38342)),f789(f149(x38341),f789(f789(f135(x38341),x38343),x38342)))
% 21.40/21.36 [3837]E(f789(f789(f89(a863),f789(f161(a863),f789(f789(f150(x38371,a863),x38372),x38373))),f789(f185(f864(x38371)),x38373)),f151(x38371,x38372,x38373))
% 21.40/21.36 [3846]E(f789(f789(f789(f178(f864(x38461),f864(x38461)),x38462),f148(x38461)),f789(f148(x38461),x38463)),f789(f148(x38461),f789(f789(f789(f178(f864(x38461),f864(x38461)),x38462),f148(x38461)),x38463)))
% 21.40/21.36 [3853]E(f789(f148(x38531),f789(f789(f789(f178(f864(x38531),f864(x38531)),x38532),f148(x38531)),x38533)),f789(f789(f789(f178(f864(x38531),f864(x38531)),f789(a121,x38532)),f148(x38531)),x38533))
% 21.40/21.36 [3865]P1(f789(f789(f240(a863),f789(f185(f864(x38651)),f789(f133(x38651,x38652),x38653))),f789(f185(f864(x38651)),x38653)))
% 21.40/21.36 [3882]E(f789(f789(f110(f870(f870(x38821,a856),a856)),f789(f309(x38821),x38822)),f789(f311(f870(x38821,a856),f870(x38821,a856),f789(f310(x38821),x38823)),f789(f309(x38821),x38822))),f789(f309(x38821),f789(f789(f310(x38821),x38823),x38822)))
% 21.40/21.36 [3899]P28(x38991,x38992,f789(f789(f310(f862(x38991)),f789(f789(f789(f100(x38991),x38993),a25),x38993)),f184(f870(f862(x38991),a856))))
% 21.40/21.36 [3900]P28(x39001,x39002,f789(f789(f310(f862(x39001)),f789(f789(f789(f100(x39001),x39003),a25),x39003)),f184(f870(f862(x39001),a856))))
% 21.40/21.36 [3922]E(f789(f269(x39221,x39222),f789(f264(f869(x39221,x39222)),f789(f259(x39221,x39222,a856),x39223))),f789(f264(x39221),f789(f789(f10(f870(x39222,a856),a856,x39221),f96(x39222)),x39223)))
% 21.40/21.36 [3935]E(f789(f311(a863,a863,f789(f789(f9(a863,a863,a863),f89(a863)),x39351)),f303(a863,x39352,x39353)),f303(a863,f789(f789(f89(a863),x39352),x39351),f789(f789(f89(a863),x39353),x39351)))
% 21.40/21.36 [3950]E(f789(f311(a863,a863,f789(f789(f9(a863,a863,a863),f89(a863)),x39501)),f789(f302(a863,x39502),x39503)),f789(f302(a863,f789(f789(f89(a863),x39502),x39501)),f789(f789(f89(a863),x39503),x39501)))
% 21.40/21.36 [3967]E(f789(f789(f171(x39671,x39672),f789(f789(f150(f869(x39671,x39672),x39671),f248(x39671,x39672)),x39673)),f789(f789(f150(f869(x39671,x39672),x39672),f258(x39671,x39672)),x39673)),x39673)
% 21.40/21.36 [3972]E(f789(f789(f89(a863),f789(f789(f90(a863),x39721),f59(a863,f789(f789(f50(a863),x39722),x39721),x39723))),f59(a863,x39722,x39721)),f59(a863,x39722,f789(f789(f90(a863),x39721),x39723)))
% 21.40/21.36 [3982]P1(f789(f70(f867(x39821)),f789(f311(x39822,f867(x39821),f170(x39822,x39821,x39823)),f247(f870(x39822,a856)))))
% 21.40/21.36 [3986]E(f789(f789(f132(x39861),x39862),f789(f138(f864(x39861),f864(x39861),f132(x39861),f122(x39861)),x39863)),f789(f138(f864(x39861),f864(x39861),f132(x39861),x39862),x39863))
% 21.40/21.36 [4005]P1(f789(f789(f342(f869(x40051,x40051)),f789(f789(f249(x40051,x40051),x40052),x40052)),f789(f789(f178(f869(x40051,x40051),a856),f2(a863)),x40053)))
% 21.40/21.36 [4011]E(f789(f264(x40111),f789(f789(f10(f870(x40112,a856),a856,x40111),f96(x40112)),f789(f9(x40112,x40111,a856),x40113))),f789(f267(x40112,x40111),f789(f264(f869(x40112,x40111)),f789(f259(x40112,x40111,a856),x40113))))
% 21.40/21.36 [4030]E(f789(f789(f110(f870(x40301,a856)),f789(f789(f53(a863,f870(x40301,a856)),f303(a863,f87(a863),x40302)),x40303)),f789(x40303,f2(a863))),f789(f789(f53(a863,f870(x40301,a856)),f789(f301(a863),x40302)),x40303))
% 21.40/21.36 [4045]E(f789(f138(f864(x40451),f864(x40451),f132(x40451),f122(x40451)),f789(f789(f150(f864(x40451),f864(x40451)),f133(x40451,x40452)),x40453)),f789(f133(x40451,x40452),f789(f138(f864(x40451),f864(x40451),f132(x40451),f122(x40451)),x40453)))
% 21.40/21.36 [4050]E(f789(f258(f864(x40501),f864(x40501)),f162(x40501,x40502,x40503)),f789(f133(x40501,f789(f82(a856,a856,x40501,a336),x40502)),x40503))
% 21.40/21.36 [4098]E(f789(f789(f89(a1),f789(f789(f89(a1),f789(f789(f90(a1),x40981),f789(f789(f50(a1),x40982),x40981))),f59(a1,x40982,x40981))),x40983),f789(f789(f89(a1),x40982),x40983))
% 21.40/21.36 [4133]E(f789(f789(f89(a1),f789(f789(f89(a1),f789(f789(f90(a1),f789(f789(f50(a1),x41331),x41332)),x41332)),f59(a1,x41331,x41332))),x41333),f789(f789(f89(a1),x41331),x41333))
% 21.40/21.36 [4162]E(f94(f869(x41621,x41622),f789(f259(x41621,x41622,a856),f789(f789(f10(f870(x41622,f869(x41621,x41622)),f870(x41622,a856),x41621),f789(f10(f869(x41621,x41622),a856,x41622),x41623)),f249(x41621,x41622)))),f94(f869(x41621,x41622),x41623))
% 21.40/21.36 [4163]E(f99(f869(x41631,x41632),f789(f259(x41631,x41632,a856),f789(f789(f10(f870(x41632,f869(x41631,x41632)),f870(x41632,a856),x41631),f789(f10(f869(x41631,x41632),a856,x41632),x41633)),f249(x41631,x41632)))),f99(f869(x41631,x41632),x41633))
% 21.40/21.36 [4194]P1(f789(f789(f240(f870(x41941,a856)),f51(f870(x41941,a856),f789(f789(f111(f870(f870(x41941,a856),a856)),x41942),x41943))),f789(f789(f111(f870(x41941,a856)),f51(f870(x41941,a856),x41942)),f51(f870(x41941,a856),x41943))))
% 21.40/21.36 [4195]E(f789(f149(x41951),f789(f789(f789(f178(f864(x41951),f864(x41951)),f789(f789(f3(a863),f789(f185(f864(x41951)),x41952)),f59(a863,x41953,f789(f185(f864(x41951)),x41952)))),f148(x41951)),x41952)),f789(f789(f789(f178(f864(x41951),f864(x41951)),x41953),f148(x41951)),f789(f149(x41951),x41952)))
% 21.40/21.36 [4207]E(f789(f264(x42071),f789(f789(f10(a856,a856,x42071),a336),f789(f789(f9(x42071,f867(x42072),a856),f789(f789(f10(f867(x42072),f870(f867(x42072),a856),x42071),a338),x42073)),f187(x42072)))),f173(x42071,x42072,x42073))
% 21.40/21.36 [4270]E(f789(f264(x42701),f789(f789(f10(f870(x42702,a856),a856,x42701),f96(x42702)),f789(f789(f10(f867(x42701),f870(x42702,a856),x42701),f789(f9(x42702,f867(x42701),a856),f789(f789(f10(f867(x42701),f870(f867(x42701),a856),x42702),a338),x42703))),f234(x42701)))),f175(x42702,x42701,x42703))
% 21.40/21.36 [4521]~P1(f789(f71(x45211,x45212,f184(f870(x45211,a856))),x45213))
% 21.40/21.36 [3542]E(f789(f185(f864(x35421)),f789(f789(f164(x35421),x35422),x35423)),f789(f789(f244(a863),f789(f185(f864(x35421)),x35423)),x35422))
% 21.40/21.36 [3543]E(f789(f185(f864(x35431)),f789(f789(f135(x35431),x35432),x35433)),f789(f789(f3(a863),f789(f185(f864(x35431)),x35433)),x35432))
% 21.40/21.36 [3579]E(f789(f789(f50(a863),f789(f789(f50(a863),x35791),x35792)),x35793),f789(f789(f50(a863),x35791),f789(f789(f90(a863),x35792),x35793)))
% 21.40/21.36 [3580]E(f789(f789(f89(a863),f789(f789(f89(a863),x35801),x35802)),x35803),f789(f789(f89(a863),x35801),f789(f789(f89(a863),x35802),x35803)))
% 21.40/21.36 [3581]E(f789(f789(f89(a1),f789(f789(f89(a1),x35811),x35812)),x35813),f789(f789(f89(a1),x35811),f789(f789(f89(a1),x35812),x35813)))
% 21.40/21.36 [3582]E(f789(f789(f90(a863),f789(f789(f90(a863),x35821),x35822)),x35823),f789(f789(f90(a863),x35821),f789(f789(f90(a863),x35822),x35823)))
% 21.40/21.36 [3583]E(f789(f789(f90(a1),f789(f789(f90(a1),x35831),x35832)),x35833),f789(f789(f90(a1),x35831),f789(f789(f90(a1),x35832),x35833)))
% 21.40/21.36 [3584]E(f789(f789(f3(a863),f789(f789(f3(a863),x35841),x35842)),x35843),f789(f789(f3(a863),x35841),f789(f789(f89(a863),x35842),x35843)))
% 21.40/21.36 [3585]E(f789(f789(f250(a1),f789(f789(f250(a1),x35851),x35852)),x35853),f789(f789(f250(a1),x35851),f789(f789(f90(a863),x35852),x35853)))
% 21.40/21.36 [3603]E(f157(x36031,f789(f789(f146(f870(x36031,a856)),x36032),x36033)),f166(x36031,x36032,f157(x36031,x36033)))
% 21.40/21.36 [3648]E(f789(f789(f3(a863),f789(f789(f3(a863),x36481),x36482)),x36483),f789(f789(f3(a863),f789(f789(f3(a863),x36481),x36483)),x36482))
% 21.40/21.36 [3656]E(f789(f789(f111(f870(x36561,a856)),x36562),f789(f789(f3(f870(x36561,a856)),x36563),x36562)),f184(f870(x36561,a856)))
% 21.40/21.36 [3701]E(f52(f870(x37011,a856),f789(f789(f310(f870(x37011,a856)),x37012),x37013)),f789(f789(f111(f870(x37011,a856)),x37012),f52(f870(x37011,a856),x37013)))
% 21.40/21.36 [3702]E(f51(f870(x37021,a856),f789(f789(f310(f870(x37021,a856)),x37022),x37023)),f789(f789(f110(f870(x37021,a856)),x37022),f51(f870(x37021,a856),x37023)))
% 21.40/21.36 [3704]E(f789(f789(f89(a863),f789(f789(f90(a863),x37041),x37042)),f789(f789(f90(a863),x37043),x37042)),f789(f789(f90(a863),f789(f789(f89(a863),x37041),x37043)),x37042))
% 21.40/21.36 [3705]E(f789(f789(f3(a863),f789(f789(f90(a863),x37051),x37052)),f789(f789(f90(a863),x37053),x37052)),f789(f789(f90(a863),f789(f789(f3(a863),x37051),x37053)),x37052))
% 21.40/21.36 [3706]E(f789(f789(f89(a1),f789(f789(f90(a1),x37061),x37062)),f789(f789(f90(a1),x37063),x37062)),f789(f789(f90(a1),f789(f789(f89(a1),x37061),x37063)),x37062))
% 21.40/21.36 [3708]E(f789(f789(f3(a1),f789(f789(f90(a1),x37081),x37082)),f789(f789(f90(a1),x37083),x37082)),f789(f789(f90(a1),f789(f789(f3(a1),x37081),x37083)),x37082))
% 21.40/21.36 [3709]E(f789(f789(f244(a863),f789(f789(f3(a863),x37091),x37092)),f789(f789(f3(a863),x37093),x37092)),f789(f789(f3(a863),f789(f789(f244(a863),x37091),x37093)),x37092))
% 21.40/21.36 [3733]E(f789(f789(f110(f870(x37331,a856)),x37332),f789(f789(f3(f870(x37331,a856)),x37333),x37332)),f789(f789(f110(f870(x37331,a856)),x37332),x37333))
% 21.40/21.36 [3734]E(f789(f789(f110(f870(x37341,a856)),x37342),f789(f789(f110(f870(x37341,a856)),x37342),x37343)),f789(f789(f110(f870(x37341,a856)),x37342),x37343))
% 21.40/21.36 [3735]E(f789(f789(f111(f870(x37351,a856)),x37352),f789(f789(f111(f870(x37351,a856)),x37352),x37353)),f789(f789(f111(f870(x37351,a856)),x37352),x37353))
% 21.40/21.36 [3747]E(f789(f789(f289(x37471,x37472,x37472),x37473),f308(x37472,f184(f870(f869(x37472,x37472),a856)))),x37473)
% 21.40/21.36 [3752]E(f789(f789(f110(f870(x37521,a856)),f789(f789(f310(x37521),x37522),f184(f870(x37521,a856)))),x37523),f789(f789(f310(x37521),x37522),x37523))
% 21.40/21.36 [3770]E(f789(f789(f3(a863),f789(f789(f3(a863),f789(a121,x37701)),x37702)),f789(a121,x37703)),f789(f789(f3(a863),f789(f789(f3(a863),x37701),x37702)),x37703))
% 21.40/21.36 [3796]E(f789(f789(f111(f870(f870(x37961,a856),a856)),f789(f309(x37961),x37962)),f789(f309(x37961),x37963)),f789(f309(x37961),f789(f789(f111(f870(x37961,a856)),x37962),x37963)))
% 21.40/21.36 [3799]E(f789(f789(f110(f870(x37991,a856)),f789(f88(f870(x37991,a856)),x37992)),x37993),f789(f88(f870(x37991,a856)),f789(f789(f3(f870(x37991,a856)),x37992),x37993)))
% 21.40/21.36 [3812]E(f789(f789(f310(x38121),x38122),f789(f789(f3(f870(x38121,a856)),x38123),f789(f789(f310(x38121),x38122),f184(f870(x38121,a856))))),f789(f789(f310(x38121),x38122),x38123))
% 21.40/21.36 [3823]P1(f789(f789(f240(f870(x38231,a856)),x38232),f789(f789(f110(f870(x38231,a856)),x38233),x38232)))
% 21.40/21.36 [3824]P1(f789(f789(f240(f870(x38241,a856)),x38242),f789(f789(f110(f870(x38241,a856)),x38242),x38243)))
% 21.40/21.36 [3827]E(f789(f789(f111(f870(x38271,a856)),f789(f88(f870(x38271,a856)),x38272)),f789(f88(f870(x38271,a856)),x38273)),f789(f88(f870(x38271,a856)),f789(f789(f110(f870(x38271,a856)),x38272),x38273)))
% 21.40/21.36 [3828]E(f789(f789(f110(f870(x38281,a856)),f789(f88(f870(x38281,a856)),x38282)),f789(f88(f870(x38281,a856)),x38283)),f789(f88(f870(x38281,a856)),f789(f789(f111(f870(x38281,a856)),x38282),x38283)))
% 21.40/21.36 [3841]P1(f789(f789(f240(f870(x38411,a856)),f789(f163(x38411),x38412)),f789(f163(x38411),f789(f789(f146(x38411),x38413),x38412))))
% 21.40/21.36 [3850]E(f789(f789(f110(f870(x38501,a856)),f789(f789(f3(f870(x38501,a856)),x38502),x38503)),f789(f789(f111(f870(x38501,a856)),x38502),x38503)),x38502)
% 21.40/21.36 [3902]E(f789(f789(f11(x39021,a1),f789(f789(f10(a863,a1,x39021),f109(a1)),x39022)),x39023),f789(f109(a1),f789(f789(f11(x39021,a863),x39022),x39023)))
% 21.40/21.36 [3903]E(f789(f789(f8(x39031,a1),f789(f789(f10(a863,a1,x39031),f109(a1)),x39032)),x39033),f789(f109(a1),f789(f789(f8(x39031,a863),x39032),x39033)))
% 21.40/21.36 [3956]E(f789(f88(f870(f869(x39561,x39562),a856)),f789(f789(f256(x39561,x39562),x39563),f789(f18(f870(x39562,a856),x39561),f247(f870(x39562,a856))))),f789(f789(f256(x39561,x39562),f789(f88(f870(x39561,a856)),x39563)),f789(f18(f870(x39562,a856),x39561),f247(f870(x39562,a856)))))
% 21.40/21.36 [3957]E(f789(f88(f870(f869(x39571,x39572),a856)),f789(f789(f256(x39571,x39572),f247(f870(x39571,a856))),f789(f18(f870(x39572,a856),x39571),x39573))),f789(f789(f256(x39571,x39572),f247(f870(x39571,a856))),f789(f18(f870(x39572,a856),x39571),f789(f88(f870(x39572,a856)),x39573))))
% 21.40/21.36 [4006]E(f789(f789(f53(f870(x40061,a856),f870(x40061,a856)),x40062),f789(f789(f9(f870(x40061,a856),f870(x40061,a856),f870(x40061,a856)),f111(f870(x40061,a856))),x40063)),f789(f789(f111(f870(x40061,a856)),f51(f870(x40061,a856),x40062)),x40063))
% 21.40/21.36 [4013]E(f789(f138(f864(x40131),f864(x40131),f132(x40131),f122(x40131)),f789(f789(f146(f864(x40131)),x40132),x40133)),f789(f789(f132(x40131),x40132),f789(f138(f864(x40131),f864(x40131),f132(x40131),f122(x40131)),x40133)))
% 21.40/21.36 [4036]E(f789(f789(f310(f870(x40361,a856)),f789(f285(x40361,x40361,x40362),f789(f789(f310(x40361),x40363),f184(f870(x40361,a856))))),f184(f870(f870(x40361,a856),a856))),f789(f789(f68(x40361),f789(f789(f310(x40361),x40363),f184(f870(x40361,a856)))),x40362))
% 21.40/21.36 [4046]E(f789(f789(f89(a863),f789(f789(f90(a863),x40461),f789(f789(f50(a863),x40462),x40463))),f789(f789(f50(a863),f789(f789(f90(a863),x40461),f59(a863,x40462,x40463))),x40463)),f789(f789(f50(a863),f789(f789(f90(a863),x40461),x40462)),x40463))
% 21.40/21.36 [4047]E(f789(f789(f89(a1),f789(f789(f90(a1),x40471),f789(f789(f50(a1),x40472),x40473))),f789(f789(f50(a1),f789(f789(f90(a1),x40471),f59(a1,x40472,x40473))),x40473)),f789(f789(f50(a1),f789(f789(f90(a1),x40471),x40472)),x40473))
% 21.40/21.36 [4130]E(f789(f789(f132(x41301),f789(f138(f864(x41301),f864(x41301),f132(x41301),f122(x41301)),x41302)),f789(f138(f864(x41301),f864(x41301),f132(x41301),f122(x41301)),x41303)),f789(f138(f864(x41301),f864(x41301),f132(x41301),f122(x41301)),f789(f789(f132(f864(x41301)),x41302),x41303)))
% 21.40/21.36 [4135]E(f789(f789(f249(f864(x41351),f864(x41351)),f789(f133(x41351,x41352),x41353)),f789(f133(x41351,f789(f82(a856,a856,x41351,a336),x41352)),x41353)),f162(x41351,x41352,x41353))
% 21.40/21.36 [4138]E(f789(f789(f89(a863),f789(f789(f89(a863),f789(f789(f50(a863),x41381),x41382)),f789(f789(f50(a863),x41383),x41382))),f789(f789(f50(a863),f789(f789(f89(a863),f59(a863,x41381,x41382)),f59(a863,x41383,x41382))),x41382)),f789(f789(f50(a863),f789(f789(f89(a863),x41381),x41383)),x41382))
% 21.40/21.36 [4139]E(f789(f789(f89(a1),f789(f789(f89(a1),f789(f789(f50(a1),x41391),x41392)),f789(f789(f50(a1),x41393),x41392))),f789(f789(f50(a1),f789(f789(f89(a1),f59(a1,x41391,x41392)),f59(a1,x41393,x41392))),x41392)),f789(f789(f50(a1),f789(f789(f89(a1),x41391),x41393)),x41392))
% 21.40/21.36 [4208]E(f789(f264(x42081),f789(f789(f20(x42081,a856,a856),f789(f789(f10(a856,f870(a856,a856),x42081),a340),f789(f789(f9(x42081,x42081,a856),a338),x42082))),f789(f789(f9(x42081,f870(x42081,a856),a856),f342(x42081)),x42083))),f789(f789(f310(x42081),x42082),x42083))
% 21.40/21.36 [4209]E(f789(f264(x42091),f789(f789(f20(x42091,a856,a856),f789(f789(f10(a856,f870(a856,a856),x42091),a340),f789(f789(f9(x42091,x42091,a856),a338),x42092))),f789(f789(f9(x42091,f870(x42091,a856),a856),f342(x42091)),x42093))),f789(f789(f310(x42091),x42092),x42093))
% 21.40/21.36 [4231]E(f789(f264(x42311),f789(f789(f20(x42311,a856,a856),f789(f789(f10(a856,f870(a856,a856),x42311),a340),f789(f789(f9(x42311,f870(x42311,a856),a856),f342(x42311)),x42312))),f789(f789(f9(x42311,f870(x42311,a856),a856),f342(x42311)),x42313))),f789(f789(f110(f870(x42311,a856)),x42312),x42313))
% 21.40/21.36 [4232]E(f789(f264(x42321),f789(f789(f20(x42321,a856,a856),f789(f789(f10(a856,f870(a856,a856),x42321),a339),f789(f789(f9(x42321,f870(x42321,a856),a856),f342(x42321)),x42322))),f789(f789(f9(x42321,f870(x42321,a856),a856),f342(x42321)),x42323))),f789(f789(f111(f870(x42321,a856)),x42322),x42323))
% 21.40/21.36 [4318]E(f789(f789(f53(x43181,f870(f870(x43181,a856),a856)),x43182),f789(f789(f9(x43181,f870(f870(x43181,a856),a856),f870(f870(x43181,a856),a856)),f789(f789(f10(f870(x43181,a856),f870(f870(f870(x43181,a856),a856),f870(f870(x43181,a856),a856)),x43181),f310(f870(x43181,a856))),f789(f789(f10(f870(x43181,a856),f870(x43181,a856),x43181),f285(x43181,x43181,x43183)),f789(f789(f9(x43181,f870(x43181,a856),f870(x43181,a856)),f310(x43181)),f184(f870(x43181,a856)))))),f184(f870(f870(x43181,a856),a856)))),f789(f789(f68(x43181),x43182),x43183))
% 21.40/21.36 [4320]E(f789(f789(f204(x43201),f789(f789(f90(a1),f789(f789(f82(f869(a1,a1),a1,x43201,f248(a1,a1)),f214(x43201)),x43202)),f789(f789(f82(f869(a1,a1),a1,x43201,f248(a1,a1)),f214(x43201)),x43203))),f789(f789(f90(a1),f789(f789(f82(f869(a1,a1),a1,x43201,f258(a1,a1)),f214(x43201)),x43202)),f789(f789(f82(f869(a1,a1),a1,x43201,f258(a1,a1)),f214(x43201)),x43203))),f229(x43201,x43202,x43203))
% 21.40/21.36 [3722]E(f59(a863,f789(f789(f89(a863),f789(f789(f90(a863),x37221),x37222)),x37223),x37222),f59(a863,x37223,x37222))
% 21.40/21.36 [3769]E(f136(a863,f789(f302(a863,f789(f789(f89(a863),x37691),x37692)),x37693)),f789(f789(f135(a863),x37692),f136(a863,f789(f302(a863,x37691),x37693))))
% 21.40/21.36 [3811]E(f789(f789(f89(a1),f789(f109(a1),x38111)),f789(f789(f89(a1),f789(f109(a1),x38112)),x38113)),f789(f789(f89(a1),f789(f109(a1),f789(f789(f89(a863),x38111),x38112))),x38113))
% 21.40/21.36 [3819]E(f789(f789(f3(f870(x38191,a856)),f789(f789(f3(f870(x38191,a856)),x38192),x38193)),x38193),f789(f789(f3(f870(x38191,a856)),x38192),x38193))
% 21.40/21.36 [3820]E(f789(f789(f110(f870(x38201,a856)),f789(f789(f3(f870(x38201,a856)),x38202),x38203)),x38203),f789(f789(f110(f870(x38201,a856)),x38202),x38203))
% 21.40/21.36 [3842]E(f789(f789(f289(x38421,x38421,x38422),f308(x38421,f184(f870(f869(x38421,x38421),a856)))),x38423),x38423)
% 21.40/21.36 [3847]E(f789(f789(f110(f870(x38471,a856)),f789(f284(x38471),x38472)),f789(f284(x38471),x38473)),f789(f284(x38471),f789(f789(f110(f870(f869(x38471,x38471),a856)),x38472),x38473)))
% 21.40/21.36 [3856]E(f271(x38561,f789(f789(f146(f869(a108,x38561)),f789(f789(f249(a108,x38561),f2(a108)),x38562)),x38563)),f271(x38561,x38563))
% 21.40/21.36 [3859]E(f789(f789(f111(f870(x38591,a856)),f52(f870(x38591,a856),x38592)),f52(f870(x38591,a856),x38593)),f52(f870(x38591,a856),f789(f789(f110(f870(f870(x38591,a856),a856)),x38592),x38593)))
% 21.40/21.36 [3860]E(f789(f789(f110(f870(x38601,a856)),f51(f870(x38601,a856),x38602)),f51(f870(x38601,a856),x38603)),f51(f870(x38601,a856),f789(f789(f110(f870(f870(x38601,a856),a856)),x38602),x38603)))
% 21.40/21.36 [3895]E(f789(f789(f289(x38951,x38951,x38951),f789(f789(f178(f869(x38951,x38951),a856),x38952),x38953)),x38953),f789(f789(f178(f869(x38951,x38951),a856),f789(a121,x38952)),x38953))
% 21.40/21.36 [3943]P1(f789(f789(f240(f870(x39431,a856)),f789(f789(f3(f870(x39431,a856)),x39432),x39433)),x39432))
% 21.40/21.36 [3944]P1(f789(f789(f240(f870(x39441,a856)),f789(f789(f111(f870(x39441,a856)),x39442),x39443)),x39443))
% 21.40/21.36 [3945]P1(f789(f789(f240(f870(x39451,a856)),f789(f789(f111(f870(x39451,a856)),x39452),x39453)),x39452))
% 21.40/21.36 [3969]E(f308(x39691,f789(f789(f110(f870(f869(x39691,x39691),a856)),f308(x39691,x39692)),f308(x39691,x39693))),f308(x39691,f789(f789(f110(f870(f869(x39691,x39691),a856)),x39692),x39693)))
% 21.40/21.36 [3973]E(f51(f870(x39731,a856),f789(f789(f310(f870(x39731,a856)),x39732),f789(f789(f310(f870(x39731,a856)),x39733),f184(f870(f870(x39731,a856),a856))))),f789(f789(f110(f870(x39731,a856)),x39732),x39733))
% 21.40/21.36 [3974]E(f52(f870(x39741,a856),f789(f789(f310(f870(x39741,a856)),x39742),f789(f789(f310(f870(x39741,a856)),x39743),f184(f870(f870(x39741,a856),a856))))),f789(f789(f111(f870(x39741,a856)),x39742),x39743))
% 21.40/21.36 [3979]E(f789(f789(f289(x39791,x39791,x39791),f789(f789(f178(f869(x39791,x39791),a856),x39792),x39793)),x39793),f789(f789(f289(x39791,x39791,x39791),x39793),f789(f789(f178(f869(x39791,x39791),a856),x39792),x39793)))
% 21.40/21.36 [4051]E(f789(f789(f110(f870(x40511,a856)),f789(f264(x40511),f789(f789(f9(x40511,x40511,a856),a338),x40512))),x40513),f789(f789(f310(x40511),x40512),x40513))
% 21.40/21.36 [4053]E(f789(a114,f789(f789(f11(x40531,a1),f789(f789(f10(a863,a1,x40531),f109(a1)),x40532)),x40533)),f789(f789(f11(x40531,a863),x40532),x40533))
% 21.40/21.36 [4054]E(f789(a114,f789(f789(f8(x40541,a1),f789(f789(f10(a863,a1,x40541),f109(a1)),x40542)),x40543)),f789(f789(f8(x40541,a863),x40542),x40543))
% 21.40/21.36 [4126]E(f789(f152(f864(x41261),x41261,f147(x41261,x41262),f789(f18(f870(f864(x41261),f864(x41261)),x41261),f789(f789(f9(f864(x41261),f864(x41261),f864(x41261)),f132(x41261)),x41262))),x41263),f147(x41261,f789(f789(f132(x41261),x41263),x41262)))
% 21.40/21.36 [4158]P1(f789(f789(f240(f870(f870(x41581,a856),a856)),f789(f789(f110(f870(f870(x41581,a856),a856)),f789(f309(x41581),x41582)),f789(f309(x41581),x41583))),f789(f309(x41581),f789(f789(f110(f870(x41581,a856)),x41582),x41583))))
% 21.40/21.36 [4250]E(f789(f264(x42501),f789(f789(f20(x42501,a856,a856),f789(f789(f10(a856,f870(a856,a856),x42501),a339),f789(f789(f9(x42501,f870(x42501,a856),a856),f342(x42501)),x42502))),f789(f789(f10(a856,a856,x42501),a336),f789(f789(f9(x42501,f870(x42501,a856),a856),f342(x42501)),x42503)))),f789(f789(f3(f870(x42501,a856)),x42502),x42503))
% 21.40/21.36 [4271]E(f789(f49(a863),f789(f264(a863),f789(f789(f20(a863,a856,a856),f789(f789(f10(a856,f870(a856,a856),a863),a339),f789(f789(f9(a863,a863,a856),f241(a863)),f789(f185(f864(x42711)),x42712)))),f789(f789(f10(x42711,a856,a863),x42713),f789(f159(x42711),x42712))))),f789(f185(f864(x42711)),f789(f133(x42711,x42713),x42712)))
% 21.40/21.36 [4273]E(f789(f185(f864(x42731)),f165(x42731,x42732,x42733)),f789(f49(a863),f789(f264(a863),f789(f789(f20(a863,a856,a856),f789(f789(f10(a856,f870(a856,a856),a863),a339),f789(f789(f9(a863,a863,a856),f241(a863)),f789(f185(f864(x42731)),x42732)))),f789(f789(f9(a863,f870(a863,a856),a856),f342(a863)),x42733)))))
% 21.40/21.36 [4365]E(f789(f789(f111(f870(f869(f864(x43651),f864(x43651)),a856)),f789(f311(f869(f869(x43651,f864(x43651)),f869(x43651,f864(x43651))),f869(f864(x43651),f864(x43651)),f260(f869(x43651,f864(x43651)),f864(x43651),f869(x43651,f864(x43651)),f864(x43651),f789(f259(x43651,f864(x43651),f864(x43651)),f146(x43651)),f789(f259(x43651,f864(x43651),f864(x43651)),f146(x43651)))),f333(x43651,f864(x43651),x43652,f789(f139(x43651,x43652),x43653)))),f789(f264(f869(f864(x43651),f864(x43651))),f789(f259(f864(x43651),f864(x43651),a856),f789(f789(f9(f864(x43651),f870(f864(x43651),a856),f870(f864(x43651),a856)),f789(f789(f10(f870(a856,a856),f870(f870(f864(x43651),a856),f870(f864(x43651),a856)),f864(x43651)),f10(a856,a856,f864(x43651))),f789(f789(f10(a856,f870(a856,a856),f864(x43651)),a339),f789(f789(f9(f864(x43651),a863,a856),f789(f789(f10(a863,f870(a863,a856),f864(x43651)),a338),f185(f864(x43651)))),f789(a121,x43653))))),f789(f789(f9(f864(x43651),a863,a856),f789(f789(f10(a863,f870(a863,a856),f864(x43651)),a338),f185(f864(x43651)))),f789(a121,x43653)))))),f789(f139(x43651,x43652),f789(a121,x43653)))
% 21.40/21.36 [3861]E(f59(a863,f789(a121,f789(f789(f89(a863),f789(f789(f90(a863),x38611),x38612)),x38613)),x38612),f59(a863,f789(a121,x38613),x38612))
% 21.40/21.36 [4117]E(f789(f264(x41171),f789(f789(f20(x41171,a856,a856),f789(f789(f10(a856,f870(a856,a856),x41171),a339),x41172)),x41173)),f789(f789(f111(f870(x41171,a856)),f789(f264(x41171),x41172)),f789(f264(x41171),x41173)))
% 21.40/21.36 [4118]E(f789(f264(x41181),f789(f789(f20(x41181,a856,a856),f789(f789(f10(a856,f870(a856,a856),x41181),a340),x41182)),x41183)),f789(f789(f110(f870(x41181,a856)),f789(f264(x41181),x41182)),f789(f264(x41181),x41183)))
% 21.40/21.36 [4120]E(f789(f789(f132(x41201),f789(f789(f135(x41201),f59(a863,x41202,f789(f185(f864(x41201)),x41203))),x41203)),f789(f789(f164(x41201),f59(a863,x41202,f789(f185(f864(x41201)),x41203))),x41203)),f789(f789(f789(f178(f864(x41201),f864(x41201)),x41202),f148(x41201)),x41203))
% 21.40/21.36 [4125]E(f789(f264(x41251),f789(f789(f20(x41251,a856,a856),f789(f789(f10(a856,f870(a856,a856),x41251),a343),x41252)),x41253)),f789(f789(f110(f870(x41251,a856)),f789(f88(f870(x41251,a856)),f789(f264(x41251),x41252))),f789(f264(x41251),x41253)))
% 21.40/21.36 [4140]E(f789(f789(f89(a863),f789(f185(f864(x41401)),f789(f133(x41401,x41402),x41403))),f789(f185(f864(x41401)),f789(f133(x41401,f789(f789(f10(a856,a856,x41401),a336),x41402)),x41403))),f789(f185(f864(x41401)),x41403))
% 21.40/21.36 [4165]P1(f789(f789(f240(f870(x41651,a856)),f789(f789(f110(f870(x41651,a856)),f52(f870(x41651,a856),x41652)),f52(f870(x41651,a856),x41653))),f52(f870(x41651,a856),f789(f789(f111(f870(f870(x41651,a856),a856)),x41652),x41653))))
% 21.40/21.36 [4181]E(f789(f163(x41811),f789(f133(x41811,f789(f789(f10(a856,a856,x41811),a336),f789(f789(f9(x41811,x41811,a856),a338),x41812))),x41813)),f789(f789(f3(f870(x41811,a856)),f789(f163(x41811),x41813)),f789(f789(f310(x41811),x41812),f184(f870(x41811,a856)))))
% 21.40/21.36 [4190]P1(f789(f789(f240(f870(f869(x41901,x41901),a856)),f789(f789(f110(f870(f869(x41901,x41901),a856)),f308(x41901,x41902)),f308(x41901,x41903))),f308(x41901,f789(f789(f110(f870(f869(x41901,x41901),a856)),x41902),x41903))))
% 21.40/21.36 [4214]E(f789(f789(f90(a863),f789(a121,f789(a121,f2(a863)))),f789(f789(f8(a863,a863),f789(f789(f10(a863,a863,a863),f789(f89(a863),x42141)),f789(f789(f9(a863,a863,a863),f90(a863)),x42142))),f789(f265(a863),x42143))),f789(f789(f90(a863),x42143),f789(f789(f89(a863),x42141),f789(f789(f89(a863),x42141),f789(f789(f90(a863),f789(f789(f3(a863),x42143),f87(a863))),x42142)))))
% 21.40/21.36 [4224]E(f789(f264(x42241),f789(f789(f20(x42241,a856,a856),f789(f789(f10(a856,f870(a856,a856),x42241),a339),f789(f789(f9(x42241,f870(x42241,a856),a856),f342(x42241)),f789(f163(x42241),x42242)))),x42243)),f789(f163(x42241),f789(f133(x42241,x42243),x42242)))
% 21.40/21.36 [4364]E(f789(f264(x43641),f789(f789(f10(f870(a863,a856),a856,x43641),f96(a863)),f789(f789(f9(x43641,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),x43641),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),x43641),f789(f10(a856,f870(a856,a856),a863),a339)),f789(f789(f9(x43641,f870(a863,x43641),f870(a863,a856)),f789(f789(f10(f870(x43641,a856),f870(f870(a863,x43641),f870(a863,a856)),x43641),f10(x43641,a856,a863)),a338)),f789(f159(x43641),x43642))))),f789(f789(f20(a863,a856,a856),f789(f789(f10(a856,f870(a856,a856),a863),a339),f789(f789(f9(a863,a863,a856),f241(a863)),f789(f185(f864(x43641)),x43642)))),f789(f789(f9(a863,f870(a863,a856),a856),f342(a863)),x43643))))),f789(f163(x43641),f165(x43641,x43642,x43643)))
% 21.40/21.36 [4261]E(f789(f264(x42611),f789(f789(f20(x42611,a856,a856),f789(f789(f10(a856,f870(a856,a856),x42611),a343),f789(f789(f10(a856,a856,x42611),a336),f789(f789(f9(x42611,x42611,a856),a338),x42612)))),x42613)),f789(f789(f310(x42611),x42612),f789(f264(x42611),x42613)))
% 21.40/21.36 [4292]E(f789(f789(f150(f869(x42921,a863),x42921),f248(x42921,a863)),f789(f133(f869(x42921,a863),f789(f789(f9(f869(x42921,a863),f870(a863,a856),a856),f789(f789(f10(a863,f870(f870(a863,a856),a856),f869(x42921,a863)),f342(a863)),f258(x42921,a863))),x42922)),f789(f789(f171(x42921,a863),x42923),f136(a863,f789(f302(a863,f2(a863)),f789(f185(f864(x42921)),x42923)))))),f165(x42921,x42923,x42922))
% 21.40/21.36 [4319]E(f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f789(f8(a863,a1),f789(f789(f10(a1,a1,a863),f789(f89(a1),x43191)),f789(f789(f9(a863,a1,a1),f789(f789(f10(a1,f870(a1,a1),a863),f90(a1)),f109(a1))),x43192))),f789(f265(a863),x43193))),f789(f789(f90(a1),f789(f109(a1),x43193)),f789(f789(f89(a1),x43191),f789(f789(f89(a1),x43191),f789(f789(f90(a1),f789(f109(a1),f789(f789(f3(a863),x43193),f87(a863)))),x43192)))))
% 21.40/21.36 [4358]E(f789(f264(f869(x43581,x43582)),f789(f259(x43581,x43582,a856),f789(f789(f9(x43581,f870(f869(x43582,x43581),a856),f870(x43582,a856)),f789(f789(f10(f870(x43582,f870(f870(f869(x43582,x43581),a856),a856)),f870(f870(f869(x43582,x43581),a856),f870(x43582,a856)),x43581),f9(x43582,f870(f869(x43582,x43581),a856),a856)),f789(f789(f10(f870(x43582,f869(x43582,x43581)),f870(x43582,f870(f870(f869(x43582,x43581),a856),a856)),x43581),f789(f10(f869(x43582,x43581),f870(f870(f869(x43582,x43581),a856),a856),x43582),f342(f869(x43582,x43581)))),f789(f9(x43582,x43581,f869(x43582,x43581)),f249(x43582,x43581))))),x43583))),f789(f286(x43582,x43581),x43583))
% 21.40/21.36 [4393]E(f789(f264(f864(x43931)),f789(f789(f10(f870(x43931,a856),a856,f864(x43931)),f96(x43931)),f789(f789(f10(f870(x43931,f870(f864(x43931),a856)),f870(x43931,a856),f864(x43931)),f789(f10(f870(f864(x43931),a856),a856,x43931),f96(f864(x43931)))),f789(f789(f9(f864(x43931),f870(x43931,f870(f864(x43931),a856)),f870(x43931,f870(f864(x43931),a856))),f789(f789(f10(f870(x43931,f870(f870(f864(x43931),a856),f870(f864(x43931),a856))),f870(f870(x43931,f870(f864(x43931),a856)),f870(x43931,f870(f864(x43931),a856))),f864(x43931)),f20(x43931,f870(f864(x43931),a856),f870(f864(x43931),a856))),f789(f789(f10(f870(x43931,f870(f864(x43931),f870(a856,a856))),f870(x43931,f870(f870(f864(x43931),a856),f870(f864(x43931),a856))),f864(x43931)),f789(f10(f870(f864(x43931),f870(a856,a856)),f870(f870(f864(x43931),a856),f870(f864(x43931),a856)),x43931),f20(f864(x43931),a856,a856))),f789(f789(f10(f870(x43931,f870(f864(x43931),a856)),f870(x43931,f870(f864(x43931),f870(a856,a856))),f864(x43931)),f789(f10(f870(f864(x43931),a856),f870(f864(x43931),f870(a856,a856)),x43931),f789(f10(a856,f870(a856,a856),f864(x43931)),a339))),f789(f789(f9(f864(x43931),f870(x43931,f870(f864(x43931),f864(x43931))),f870(x43931,f870(f864(x43931),a856))),f789(f789(f10(f870(f870(f864(x43931),f864(x43931)),f870(f864(x43931),a856)),f870(f870(x43931,f870(f864(x43931),f864(x43931))),f870(x43931,f870(f864(x43931),a856))),f864(x43931)),f10(f870(f864(x43931),f864(x43931)),f870(f864(x43931),a856),x43931)),f789(f789(f10(f870(f864(x43931),a856),f870(f870(f864(x43931),f864(x43931)),f870(f864(x43931),a856)),f864(x43931)),f10(f864(x43931),a856,f864(x43931))),a338))),f146(x43931)))))),f789(f789(f9(x43931,f870(f864(x43931),a856),f870(f864(x43931),a856)),f789(f789(f10(f870(a856,a856),f870(f870(f864(x43931),a856),f870(f864(x43931),a856)),x43931),f10(a856,a856,f864(x43931))),f789(f789(f10(a856,f870(a856,a856),x43931),a339),f789(f789(f9(x43931,f870(x43931,a856),a856),f342(x43931)),x43932)))),f789(f789(f9(f864(x43931),f870(f864(x43931),a856),a856),f342(f864(x43931))),x43933)))))),f166(x43931,x43932,x43933))
% 21.40/21.36 [4378]E(f789(f789(f95(a1,f869(a1,a1)),f789(f789(f3(a1),x43781),x43782)),f789(f789(f9(a1,f869(a1,a1),f869(a1,a1)),f789(f789(f20(a1,f869(a1,a1),f870(f869(a1,a1),f869(a1,a1))),f789(f789(f10(a856,f870(f869(a1,a1),f870(f869(a1,a1),f869(a1,a1))),a1),f105(f869(a1,a1))),f789(f240(a1),f2(a1)))),f789(f249(a1,a1),f789(f789(f89(a1),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x43783)),f87(a1))))),f789(f789(f249(a1,a1),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x43783)),x43781))),f789(f57(x43782),f789(f789(f249(a1,a1),x43783),x43781)))
% 21.40/21.36 [4431]~E(f30(x44311,x44312),f38(x44313,x44314))
% 21.40/21.36 [4432]~E(f30(x44321,x44322),f38(x44323,x44324))
% 21.40/21.36 [4433]~E(f37(x44331,x44332),f38(x44333,x44334))
% 21.40/21.36 [4434]~E(f37(x44341,x44342),f30(x44343,x44344))
% 21.40/21.36 [4435]~E(f37(x44351,x44352),f38(x44353,x44354))
% 21.40/21.36 [4436]~E(f37(x44361,x44362),f30(x44363,x44364))
% 21.40/21.36 [4454]~E(f789(a29,x44541),f35(x44542,x44543,x44544))
% 21.40/21.36 [4455]~E(f789(a29,x44551),f34(x44552,x44553,x44554))
% 21.40/21.36 [4456]~E(f789(a29,x44561),f33(x44562,x44563,x44564))
% 21.40/21.36 [4457]~E(f35(x44571,x44572,x44573),f789(a29,x44574))
% 21.40/21.36 [4458]~E(f34(x44581,x44582,x44583),f789(a29,x44584))
% 21.40/21.36 [4459]~E(f33(x44591,x44592,x44593),f789(a29,x44594))
% 21.40/21.36 [3413]E(f789(f789(f789(f81(x34131,x34132),x34133),x34134),f789(x34133,x34134)),x34133)
% 21.40/21.36 [3477]E(f789(f789(f251(x34771,x34772,x34773),x34774),f2(a863)),x34772)
% 21.40/21.36 [3492]E(f45(x34921,x34922,x34923,f42(x34924)),f789(x34923,x34924))
% 21.40/21.36 [3493]E(f45(x34931,x34932,x34933,f43(x34934)),f789(x34932,x34934))
% 21.40/21.36 [3494]E(f46(x34941,x34942,x34943,f42(x34944)),f789(x34943,x34944))
% 21.40/21.36 [3495]E(f46(x34951,x34952,x34953,f43(x34954)),f789(x34952,x34954))
% 21.40/21.36 [3519]E(f180(x35191,x35192,x35193,f789(a121,x35194)),f789(x35193,x35194))
% 21.40/21.36 [3561]E(f158(x35611,x35612,f158(x35611,x35613,x35614)),f158(x35611,x35613,f158(x35611,x35612,x35614)))
% 21.40/21.36 [3676]P39(f30(x36761,x36762),x36763,x36764,f789(f789(f789(a193,x36763),x36761),f789(x36762,x36763)))
% 21.40/21.36 [3677]P39(f30(x36771,x36772),x36773,x36774,f789(f789(f789(a193,x36773),x36771),f789(x36772,x36773)))
% 21.40/21.36 [3689]E(f789(f236(x36891,x36892,x36893,x36894),f187(x36892)),x36893)
% 21.40/21.36 [3691]E(f789(f152(x36911,x36912,x36913,x36914),f122(x36912)),x36913)
% 21.40/21.36 [3692]E(f789(f138(x36921,x36922,x36923,x36924),f122(x36922)),x36924)
% 21.40/21.36 [3729]E(f789(f185(f868(x37291,x37292)),f222(x37291,x37292,x37293,x37294)),f2(a863))
% 21.40/21.36 [3754]E(f789(f259(x37541,x37542,x37543),f257(x37541,x37542,x37543,x37544)),x37544)
% 21.40/21.36 [3808]E(f789(f236(f867(x38081),x38082,f187(x38081),f789(f18(f867(x38081),x38082),f187(x38081))),f789(x38083,x38084)),f187(x38081))
% 21.40/21.36 [3851]E(f789(f789(f110(f870(x38511,a856)),f173(x38511,x38512,x38513)),f173(x38511,x38512,x38514)),f173(x38511,x38512,f174(x38511,x38512,x38514,x38513)))
% 21.40/21.36 [3880]E(f789(f789(f261(x38801,x38802,x38803,f869(x38802,x38803)),x38804),f249(x38802,x38803)),x38804)
% 21.40/21.36 [3889]E(f237(x38891,x38892,x38893,x38894,f187(x38892)),x38893)
% 21.40/21.36 [3890]E(f176(x38901,x38902,x38903,x38904,f122(x38902)),x38903)
% 21.40/21.36 [3891]E(f176(x38911,x38912,x38913,f122(x38911),x38914),x38913)
% 21.40/21.36 [4171]P41(x41711,x41712,x41713,x41714,f184(f870(x41711,a856)),x41714)
% 21.40/21.36 [4172]P41(x41721,x41722,x41723,x41724,f184(f870(x41721,a856)),x41724)
% 21.40/21.36 [4480]~E(f789(f321(x44801,x44802),x44803),f789(f312(x44802,x44801),x44804))
% 21.40/21.36 [4481]~E(f789(f321(x44811,x44812),x44813),f789(f312(x44812,x44811),x44814))
% 21.40/21.36 [4482]~E(f789(f321(x44821,x44822),x44823),f789(f312(x44822,x44821),x44824))
% 21.40/21.36 [4483]~E(f789(f321(x44831,x44832),x44833),f789(f312(x44832,x44831),x44834))
% 21.40/21.36 [3223]E(f789(f789(f18(x32231,x32232),x32233),x32234),x32233)
% 21.40/21.36 [3335]E(f789(f789(f203(x33351,x33352),x33353),f789(f234(x33351),x33354)),f789(f234(x33352),f789(x33353,x33354)))
% 21.40/21.36 [3511]E(f158(x35111,x35112,f789(f133(x35111,x35113),x35114)),f789(f133(x35111,x35113),f158(x35111,x35112,x35114)))
% 21.40/21.36 [3544]E(f789(f789(f73(x35441,x35442,x35443),x35444),f184(f870(x35441,a856))),x35444)
% 21.40/21.36 [3566]E(f789(f789(f159(x35661),f789(f789(f146(x35661),x35662),x35663)),f789(a121,x35664)),f789(f789(f159(x35661),x35663),x35664))
% 21.40/21.36 [3604]P31(x36041,f2(a863),f789(f789(f789(f100(x36041),x36042),f789(a29,x36043)),x36044))
% 21.40/21.36 [3629]E(f789(f789(x36291,x36292),f789(f179(x36293,x36294,x36291),x36292)),f789(f179(x36293,x36294,x36291),f789(a121,x36292)))
% 21.40/21.36 [3669]E(f257(x36691,x36692,x36693,f789(f259(x36691,x36692,x36693),x36694)),x36694)
% 21.40/21.36 [3727]E(f789(f789(f155(x37271,f789(f789(f146(x37271),x37272),x37273)),f2(a863)),x37274),f789(f789(f146(x37271),x37274),x37273))
% 21.40/21.36 [3737]E(f789(f789(f53(f870(x37371,a856),f870(x37372,a856)),x37373),f311(x37371,x37372,x37374)),f789(f311(x37371,x37372,x37374),f51(f870(x37371,a856),x37373)))
% 21.40/21.36 [3738]E(f789(f789(f53(f870(x37381,a856),f870(x37382,a856)),x37383),f313(x37382,x37381,x37384)),f789(f313(x37382,x37381,x37384),f51(f870(x37381,a856),x37383)))
% 21.40/21.36 [3836]E(f173(x38361,x38362,f177(x38361,x38362,x38363,x38364)),f789(f789(f111(f870(x38361,a856)),f173(x38361,x38362,x38363)),x38364))
% 21.40/21.36 [3855]E(f789(f138(x38551,x38552,f789(f9(x38552,x38551,x38551),x38553),x38554),f789(f149(x38552),f122(x38552))),x38554)
% 21.40/21.36 [3901]E(f85(x39011,x39012,x39013,x39014,f184(f870(x39011,a856))),x39013)
% 21.40/21.36 [3946]E(f789(f789(f789(f789(f81(x39461,f867(x39462)),f789(f18(f867(x39462),x39461),f187(x39462))),x39463),f187(x39462)),x39464),f187(x39462))
% 21.40/21.36 [4091]E(f327(x40911,x40912,x40913,f789(f789(f10(f871(x40911,x40913),x40912,x40911),x40914),f312(x40911,x40913)),f789(f789(f10(f871(x40911,x40913),x40912,x40913),x40914),f321(x40913,x40911))),x40914)
% 21.40/21.36 [4101]E(f789(f259(x41011,x41012,x41013),f789(f789(f10(f870(x41012,f869(x41011,x41012)),f870(x41012,x41013),x41011),f789(f10(f869(x41011,x41012),x41013,x41012),x41014)),f249(x41011,x41012))),x41014)
% 21.40/21.36 [3411]E(f789(f258(x34111,x34112),f789(f789(f249(x34111,x34112),x34113),x34114)),x34114)
% 21.40/21.36 [3412]E(f789(f248(x34121,x34122),f789(f789(f249(x34121,x34122),x34123),x34124)),x34123)
% 21.40/21.36 [3450]E(f789(f185(f864(x34501)),f789(f789(f150(x34502,x34501),x34503),x34504)),f789(f185(f864(x34502)),x34504))
% 21.40/21.36 [3451]E(f789(f185(f864(x34511)),f789(f789(f155(x34511,x34512),x34513),x34514)),f789(f185(f864(x34511)),x34512))
% 21.40/21.36 [3472]E(f789(f789(f135(x34721),f789(a121,x34722)),f789(f789(f146(x34721),x34723),x34724)),f789(f789(f135(x34721),x34722),x34724))
% 21.40/21.36 [3546]E(f789(f789(f310(x35461),x35462),f789(f789(f310(x35461),x35463),x35464)),f789(f789(f310(x35461),x35463),f789(f789(f310(x35461),x35462),x35464)))
% 21.40/21.36 [3549]E(f789(f789(f150(x35491,x35492),x35493),f147(x35491,x35494)),f147(x35492,f789(f789(f150(x35491,x35492),x35493),x35494)))
% 21.40/21.36 [3550]E(f789(f789(f150(x35501,x35502),x35503),f123(x35501,x35504)),f123(x35502,f789(f789(f150(x35501,x35502),x35503),x35504)))
% 21.40/21.36 [3565]E(f789(f149(x35651),f789(f789(f150(x35652,x35651),x35653),x35654)),f789(f789(f150(x35652,x35651),x35653),f789(f149(x35652),x35654)))
% 21.40/21.36 [3574]E(f789(f789(f164(x35741),f789(a121,x35742)),f789(f789(f146(x35741),x35743),x35744)),f789(f789(f146(x35741),x35743),f789(f789(f164(x35741),x35742),x35744)))
% 21.40/21.36 [3578]E(f789(f163(x35781),f789(f789(f150(x35782,x35781),x35783),x35784)),f789(f311(x35782,x35781,x35783),f789(f163(x35782),x35784)))
% 21.40/21.36 [3628]E(f19(x36281,x36282,x36283,f789(a5,f789(a121,f789(a22,x36284)))),f789(x36283,x36284))
% 21.40/21.36 [3632]E(f789(f789(f132(x36321),f789(f133(x36321,x36322),x36323)),f789(f133(x36321,x36322),x36324)),f789(f133(x36321,x36322),f789(f789(f132(x36321),x36323),x36324)))
% 21.40/21.36 [3659]E(f789(f286(x36591,x36591),f789(f789(f288(x36592,x36591),x36593),x36594)),f789(f789(f288(x36592,x36591),f789(f286(x36592,x36592),x36593)),x36594))
% 21.40/21.36 [3670]E(f789(f789(f289(x36701,x36702,x36703),x36704),f184(f870(f869(x36702,x36703),a856))),f184(f870(f869(x36701,x36703),a856)))
% 21.40/21.36 [3671]E(f789(f789(f164(x36711),f789(f789(f3(a863),x36712),x36713)),f789(f789(f135(x36711),x36713),x36714)),f789(f789(f135(x36711),x36713),f789(f789(f164(x36711),x36712),x36714)))
% 21.40/21.36 [3693]E(f789(f789(f789(f281(x36931),x36932),x36933),x36934),f789(f249(f870(a108,f870(a856,f867(f865(x36931)))),f869(a108,a108)),f789(f56(x36931),x36932)))
% 21.40/21.36 [3717]E(f51(f870(x37171,a856),f789(f311(x37172,f870(x37171,a856),x37173),x37174)),f789(f789(f53(x37172,f870(x37171,a856)),x37174),x37173))
% 21.40/21.36 [3718]E(f52(f870(x37181,a856),f789(f311(x37182,f870(x37181,a856),x37183),x37184)),f789(f789(f54(x37182,f870(x37181,a856)),x37184),x37183))
% 21.40/21.36 [3719]E(f52(f870(x37191,a856),f789(f311(x37192,f870(x37191,a856),x37193),x37194)),f789(f789(f54(x37192,f870(x37191,a856)),x37194),x37193))
% 21.40/21.36 [3720]E(f51(f870(x37201,a856),f789(f311(x37202,f870(x37201,a856),x37203),x37204)),f789(f789(f53(x37202,f870(x37201,a856)),x37204),x37203))
% 21.40/21.36 [3721]E(f789(f185(f864(f869(x37211,x37212))),f789(f789(f171(x37211,x37212),x37213),x37214)),f789(f789(f244(a863),f789(f185(f864(x37211)),x37213)),f789(f185(f864(x37212)),x37214)))
% 21.40/21.36 [3723]E(f789(f313(x37231,x37232,x37233),f789(f88(f870(x37232,a856)),x37234)),f789(f88(f870(x37231,a856)),f789(f313(x37231,x37232,x37233),x37234)))
% 21.40/21.36 [3755]E(f789(f177(x37551,x37552,x37553,f184(f870(x37551,a856))),x37554),f187(x37552))
% 21.40/21.36 [3773]E(f789(f313(x37731,x37732,x37733),f789(f264(x37732),x37734)),f789(f264(x37731),f789(f789(f10(x37732,a856,x37731),x37734),x37733)))
% 21.40/21.36 [3790]E(f789(f789(f159(x37901),f789(f789(f132(x37901),x37902),f789(f789(f146(x37901),x37903),x37904))),f789(f185(f864(x37901)),x37902)),x37903)
% 21.40/21.36 [3795]E(f789(f177(x37951,x37952,f789(f18(f867(x37952),x37951),f187(x37952)),x37953),x37954),f187(x37952))
% 21.40/21.36 [3817]E(f789(f311(x38171,x38172,x38173),f789(f313(x38171,x38172,x38173),x38174)),f789(f789(f111(f870(x38172,a856)),x38174),f789(f311(x38171,x38172,x38173),f247(f870(x38171,a856)))))
% 21.40/21.36 [3835]P1(f789(f789(f342(x38351),f789(x38352,x38353)),f789(f311(x38354,x38351,x38352),f247(f870(x38354,a856)))))
% 21.40/21.36 [3843]E(f21(x38431,x38432,x38433,f789(a5,f789(a121,f789(a22,x38434)))),f789(f789(x38433,x38434),f21(x38431,x38432,x38433,x38434)))
% 21.40/21.36 [3858]E(f151(x38581,x38582,f789(f789(f146(x38581),x38583),x38584)),f789(f789(f89(a863),f789(f789(f89(a863),f789(x38582,x38583)),f151(x38581,x38582,x38584))),f789(a121,f2(a863))))
% 21.40/21.36 [3871]E(f180(f864(x38711),f789(f789(f146(x38711),x38712),x38713),f789(f789(f9(a863,f864(x38711),f864(x38711)),f135(x38711)),x38713),x38714),f789(f789(f135(x38711),x38714),f789(f789(f146(x38711),x38712),x38713)))
% 21.40/21.36 [3872]P29(x38721,f869(x38722,x38721),f344(x38723,x38724,x38722,x38721),f789(f789(f53(x38722,f870(x38721,a856)),x38724),x38723))
% 21.40/21.36 [3881]E(f789(f789(f3(f870(x38811,a856)),f789(f789(f3(f870(x38811,a856)),x38812),x38813)),f789(f789(f310(x38811),x38814),f184(f870(x38811,a856)))),f789(f789(f3(f870(x38811,a856)),x38812),f789(f789(f310(x38811),x38814),x38813)))
% 21.40/21.36 [3894]E(f789(f789(f178(f870(x38941,x38942),f870(x38941,x38942)),x38943),f82(x38942,x38942,x38941,x38944)),f82(x38942,x38942,x38941,f789(f789(f178(x38942,x38942),x38943),x38944)))
% 21.40/21.36 [3968]E(f789(f789(f789(f178(f864(x39681),f864(x39681)),x39682),f148(x39681)),f789(f789(f789(f178(f864(x39681),f864(x39681)),x39683),f148(x39681)),x39684)),f789(f789(f789(f178(f864(x39681),f864(x39681)),f789(f789(f89(a863),x39682),x39683)),f148(x39681)),x39684))
% 21.40/21.36 [4015]E(f789(f789(f110(f870(f871(x40151,x40152),a856)),f789(f311(x40151,f871(x40151,x40152),f312(x40151,x40152)),x40153)),f789(f311(x40152,f871(x40151,x40152),f321(x40152,x40151)),x40154)),f322(x40151,x40152,x40153,x40154))
% 21.40/21.36 [4056]P1(f789(f789(f240(f870(x40561,a856)),f789(f163(x40561),f789(f789(f155(x40561,x40562),x40563),x40564))),f789(f789(f310(x40561),x40564),f789(f163(x40561),x40562))))
% 21.40/21.36 [4089]E(f789(f789(f53(f870(x40891,a856),f870(f869(x40891,x40892),a856)),x40893),f789(f789(f9(f870(x40891,a856),f870(x40891,f870(x40892,a856)),f870(f869(x40891,x40892),a856)),f256(x40891,x40892)),x40894)),f789(f789(f256(x40891,x40892),f51(f870(x40891,a856),x40893)),x40894))
% 21.40/21.36 [4127]E(f211(x41271,x41272,x41273,f789(f82(x41272,f870(a108,f870(a108,f870(f869(a108,a108),f870(a108,f865(x41272))))),x41271,f206(x41272)),x41274)),f212(x41271,x41272,x41274,x41273))
% 21.40/21.36 [4143]E(f208(x41431,x41432,x41433,f789(f82(x41432,f870(a108,f870(a108,f870(f869(a108,a108),f870(a108,f865(f867(x41432)))))),x41431,f207(x41432)),x41434)),f209(x41431,x41432,x41434,x41433))
% 21.40/21.36 [4146]P1(f789(f75(x41461,x41462,x41463,x41464,f184(f870(x41461,a856))),x41464))
% 21.40/21.36 [4147]P1(f789(f75(x41471,x41472,x41473,x41474,f184(f870(x41471,a856))),x41474))
% 21.40/21.36 [4193]E(f789(f789(f53(x41931,f870(x41932,a856)),x41933),f789(f789(f9(x41931,f870(x41932,a856),f870(x41932,a856)),f789(f789(f10(x41932,f870(f870(x41932,a856),f870(x41932,a856)),x41931),f310(x41932)),x41934)),f184(f870(x41932,a856)))),f789(f311(x41931,x41932,x41934),x41933))
% 21.40/21.36 [4199]P1(f789(f789(f240(f870(x41991,a856)),f789(f267(x41992,x41991),f789(f789(f111(f870(f869(x41992,x41991),a856)),x41993),x41994))),f789(f789(f111(f870(x41991,a856)),f789(f267(x41992,x41991),x41993)),f789(f267(x41992,x41991),x41994))))
% 21.40/21.36 [4200]P1(f789(f789(f240(f870(x42001,a856)),f789(f269(x42001,x42002),f789(f789(f111(f870(f869(x42001,x42002),a856)),x42003),x42004))),f789(f789(f111(f870(x42001,a856)),f789(f269(x42001,x42002),x42003)),f789(f269(x42001,x42002),x42004))))
% 21.40/21.36 [4259]P1(f789(f789(f240(f870(f869(x42591,x42592),a856)),f789(f311(x42592,f869(x42591,x42592),f344(x42593,x42594,x42591,x42592)),f789(f789(f53(x42591,f870(x42592,a856)),x42594),x42593))),f789(f789(f256(x42591,x42592),x42594),x42593)))
% 21.40/21.36 [4260]E(f279(x42601,x42602,x42603,f789(f82(x42602,f870(a108,f870(a108,f870(f869(a108,a108),f869(f870(a108,f870(a856,f867(f865(x42602)))),f869(a108,a108))))),x42601,f281(x42602)),x42604)),f282(x42601,x42602,x42604,x42603))
% 21.40/21.36 [4297]E(f94(f869(x42971,x42972),f789(f259(x42971,x42972,a856),f789(f789(f9(x42971,f870(x42972,a856),f870(x42972,a856)),f789(f789(f10(f870(a856,a856),f870(f870(x42972,a856),f870(x42972,a856)),x42971),f10(a856,a856,x42972)),f789(f789(f10(a856,f870(a856,a856),x42971),a339),f789(a338,x42973)))),f789(a338,x42974)))),f789(f789(f249(x42971,x42972),x42973),x42974))
% 21.40/21.36 [4298]E(f99(f869(x42981,x42982),f789(f259(x42981,x42982,a856),f789(f789(f9(x42981,f870(x42982,a856),f870(x42982,a856)),f789(f789(f10(f870(a856,a856),f870(f870(x42982,a856),f870(x42982,a856)),x42981),f10(a856,a856,x42982)),f789(f789(f10(a856,f870(a856,a856),x42981),a339),f789(a338,x42983)))),f789(a338,x42984)))),f789(f789(f249(x42981,x42982),x42983),x42984))
% 21.40/21.36 [4368]E(f789(f789(f259(f864(x43681),f864(x43681),f869(f864(x43681),f864(x43681))),f789(f789(f20(f864(x43681),f870(f864(x43681),f869(f864(x43681),f864(x43681))),f870(f864(x43681),f869(f864(x43681),f864(x43681)))),f789(f789(f10(f870(f864(x43681),f870(f869(f864(x43681),f864(x43681)),f869(f864(x43681),f864(x43681)))),f870(f870(f864(x43681),f869(f864(x43681),f864(x43681))),f870(f864(x43681),f869(f864(x43681),f864(x43681)))),f864(x43681)),f20(f864(x43681),f869(f864(x43681),f864(x43681)),f869(f864(x43681),f864(x43681)))),f789(f789(f10(f870(f864(x43681),f869(f864(x43681),f864(x43681))),f870(f864(x43681),f870(f869(f864(x43681),f864(x43681)),f869(f864(x43681),f864(x43681)))),f864(x43681)),f789(f10(f869(f864(x43681),f864(x43681)),f870(f869(f864(x43681),f864(x43681)),f869(f864(x43681),f864(x43681))),f864(x43681)),f789(f105(f869(f864(x43681),f864(x43681))),f789(x43682,x43683)))),f789(f789(f10(f864(x43681),f870(f864(x43681),f869(f864(x43681),f864(x43681))),f864(x43681)),f249(f864(x43681),f864(x43681))),f789(f146(x43681),x43683))))),f789(f789(f9(f864(x43681),f870(f864(x43681),f864(x43681)),f870(f864(x43681),f869(f864(x43681),f864(x43681)))),f789(f789(f10(f870(f864(x43681),f869(f864(x43681),f864(x43681))),f870(f870(f864(x43681),f864(x43681)),f870(f864(x43681),f869(f864(x43681),f864(x43681)))),f864(x43681)),f10(f864(x43681),f869(f864(x43681),f864(x43681)),f864(x43681))),f249(f864(x43681),f864(x43681)))),f789(f146(x43681),x43683)))),f162(x43681,x43682,x43684)),f162(x43681,x43682,f789(f789(f146(x43681),x43683),x43684)))
% 21.40/21.36 [4374]E(f789(f138(f870(x43741,f867(x43742)),f869(x43741,x43742),f789(f9(f869(x43741,x43742),f870(x43741,f867(x43742)),f870(x43741,f867(x43742))),f789(f259(x43741,x43742,f870(f870(x43741,f867(x43742)),f870(x43741,f867(x43742)))),f789(f789(f9(x43741,f870(x43742,f867(x43742)),f870(x43742,f870(f870(x43741,f867(x43742)),f870(x43741,f867(x43742))))),f789(f789(f10(f870(f867(x43742),f870(f870(x43741,f867(x43742)),f870(x43741,f867(x43742)))),f870(f870(x43742,f867(x43742)),f870(x43742,f870(f870(x43741,f867(x43742)),f870(x43741,f867(x43742))))),x43741),f10(f867(x43742),f870(f870(x43741,f867(x43742)),f870(x43741,f867(x43742))),x43742)),f789(f789(f10(f870(f870(x43741,f867(x43742)),f870(f867(x43742),f870(x43741,f867(x43742)))),f870(f867(x43742),f870(f870(x43741,f867(x43742)),f870(x43741,f867(x43742)))),x43741),f9(f870(x43741,f867(x43742)),f867(x43742),f870(x43741,f867(x43742)))),f789(f9(f870(x43741,f867(x43742)),x43741,f870(f867(x43742),f870(x43741,f867(x43742)))),f81(x43741,f867(x43742)))))),f234(x43742)))),x43743),f789(f149(f869(x43741,x43742)),x43744)),f174(x43741,x43742,x43743,f170(x43741,x43742,x43744)))
% 21.40/21.36 [3490]E(f789(f185(f862(x34901)),f789(f789(f789(f100(x34901),x34902),x34903),x34904)),f2(a863))
% 21.40/21.36 [3607]E(f789(f789(f164(x36071),x36072),f789(f789(f164(x36071),x36073),x36074)),f789(f789(f164(x36071),f789(f789(f244(a863),x36072),x36073)),x36074))
% 21.40/21.36 [3608]E(f789(f789(f135(x36081),x36082),f789(f789(f135(x36081),x36083),x36084)),f789(f789(f135(x36081),f789(f789(f89(a863),x36082),x36083)),x36084))
% 21.40/21.36 [3620]E(f789(f789(f132(x36201),f789(f789(f146(x36201),x36202),x36203)),x36204),f789(f789(f146(x36201),x36202),f789(f789(f132(x36201),x36203),x36204)))
% 21.40/21.36 [3621]E(f789(f789(f132(x36211),f789(f789(f132(x36211),x36212),x36213)),x36214),f789(f789(f132(x36211),x36212),f789(f789(f132(x36211),x36213),x36214)))
% 21.40/21.36 [3703]E(f789(f789(f159(x37031),f789(f789(f146(x37031),x37032),x37033)),x37034),f180(x37031,x37032,f789(f159(x37031),x37033),x37034))
% 21.40/21.36 [3712]E(f789(f789(f178(x37121,x37121),x37122),f789(f789(f178(x37121,x37121),x37123),x37124)),f789(f789(f178(x37121,x37121),f789(f789(f90(a863),x37123),x37122)),x37124))
% 21.40/21.36 [3740]E(f789(f789(f110(f870(x37401,a856)),x37402),f789(f789(f310(x37401),x37403),x37404)),f789(f789(f310(x37401),x37403),f789(f789(f110(f870(x37401,a856)),x37402),x37404)))
% 21.40/21.36 [3758]E(f789(f789(f789(f178(x37581,x37581),x37582),x37583),f789(x37583,x37584)),f789(x37583,f789(f789(f789(f178(x37581,x37581),x37582),x37583),x37584)))
% 21.40/21.36 [3765]E(f789(f789(f289(x37651,x37652,x37653),f184(f870(f869(x37651,x37652),a856))),x37654),f184(f870(f869(x37651,x37653),a856)))
% 21.40/21.36 [3779]E(f789(f789(f110(f870(x37791,a856)),f789(f789(f310(x37791),x37792),x37793)),x37794),f789(f789(f310(x37791),x37792),f789(f789(f110(f870(x37791,a856)),x37793),x37794)))
% 21.40/21.36 [3797]E(f789(f49(f869(x37971,x37972)),f789(f789(f256(x37971,x37972),x37973),f789(f18(f870(x37972,a856),x37971),x37974))),f789(f789(f90(a863),f789(f49(x37971),x37973)),f789(f49(x37972),x37974)))
% 21.40/21.36 [3805]E(f789(f789(f111(f870(x38051,a856)),f789(f789(f310(x38051),x38052),x38053)),f789(f789(f310(x38051),x38052),x38054)),f789(f789(f310(x38051),x38052),f789(f789(f111(f870(x38051,a856)),x38053),x38054)))
% 21.40/21.36 [3815]E(f174(x38151,x38152,f170(x38151,x38152,x38153),f170(x38151,x38152,x38154)),f170(x38151,x38152,f789(f789(f132(f869(x38151,x38152)),x38154),x38153)))
% 21.40/21.36 [3821]E(f789(f789(f110(f870(x38211,a856)),x38212),f789(f789(f110(f870(x38211,a856)),x38213),x38214)),f789(f789(f110(f870(x38211,a856)),x38213),f789(f789(f110(f870(x38211,a856)),x38212),x38214)))
% 21.40/21.36 [3822]E(f789(f789(f111(f870(x38221,a856)),x38222),f789(f789(f111(f870(x38221,a856)),x38223),x38224)),f789(f789(f111(f870(x38221,a856)),x38223),f789(f789(f111(f870(x38221,a856)),x38222),x38224)))
% 21.40/21.36 [3831]E(f73(x38311,x38312,f789(f789(f10(x38312,f870(x38312,x38312),x38311),x38313),x38314)),f789(f74(x38312,x38311,x38313),x38314))
% 21.40/21.36 [3840]E(f168(x38401,f789(f789(f150(f864(x38402),f864(x38401)),f789(f150(x38402,x38401),x38403)),x38404)),f789(f789(f150(f864(x38402),f864(x38401)),f789(f150(x38402,x38401),x38403)),f168(x38402,x38404)))
% 21.40/21.36 [3857]E(f177(x38571,x38572,x38573,f789(f88(f870(x38571,a856)),f789(f789(f310(x38571),x38574),f184(f870(x38571,a856))))),f789(f789(f789(f81(x38571,f867(x38572)),x38573),x38574),f187(x38572)))
% 21.40/21.36 [3915]E(f789(f82(x39151,x39151,x39151,f789(f789(f178(x39151,x39151),x39152),x39153)),f789(f789(f178(x39151,x39151),x39154),x39153)),f789(f789(f178(x39151,x39151),f789(f789(f89(a863),x39152),x39154)),x39153))
% 21.40/21.36 [3929]E(f789(f789(f789(f81(x39291,f867(x39292)),f170(x39291,x39292,x39293)),f789(f248(x39291,x39292),x39294)),f789(f234(x39292),f789(f258(x39291,x39292),x39294))),f170(x39291,x39292,f789(f789(f146(f869(x39291,x39292)),x39294),x39293)))
% 21.40/21.36 [3938]E(f789(f789(f111(f870(x39381,a856)),f789(f789(f3(f870(x39381,a856)),x39382),x39383)),f789(f789(f3(f870(x39381,a856)),x39382),x39384)),f789(f789(f3(f870(x39381,a856)),x39382),f789(f789(f110(f870(x39381,a856)),x39383),x39384)))
% 21.40/21.36 [3939]E(f789(f789(f110(f870(x39391,a856)),f789(f789(f3(f870(x39391,a856)),x39392),x39393)),f789(f789(f3(f870(x39391,a856)),x39392),x39394)),f789(f789(f3(f870(x39391,a856)),x39392),f789(f789(f111(f870(x39391,a856)),x39393),x39394)))
% 21.40/21.36 [3940]E(f789(f789(f111(f870(x39401,a856)),f789(f789(f110(f870(x39401,a856)),x39402),x39403)),f789(f789(f110(f870(x39401,a856)),x39402),x39404)),f789(f789(f110(f870(x39401,a856)),x39402),f789(f789(f111(f870(x39401,a856)),x39403),x39404)))
% 21.40/21.36 [3941]E(f789(f789(f3(f870(x39411,a856)),f789(f789(f111(f870(x39411,a856)),x39412),x39413)),f789(f789(f111(f870(x39411,a856)),x39412),x39414)),f789(f789(f111(f870(x39411,a856)),x39412),f789(f789(f3(f870(x39411,a856)),x39413),x39414)))
% 21.40/21.36 [3942]E(f789(f789(f110(f870(x39421,a856)),f789(f789(f111(f870(x39421,a856)),x39422),x39423)),f789(f789(f111(f870(x39421,a856)),x39422),x39424)),f789(f789(f111(f870(x39421,a856)),x39422),f789(f789(f110(f870(x39421,a856)),x39423),x39424)))
% 21.40/21.36 [3948]E(f789(f49(f869(x39481,x39482)),f789(f789(f256(x39481,x39482),f789(f789(f310(x39481),x39483),f184(f870(x39481,a856)))),f789(f18(f870(x39482,a856),x39481),x39484))),f789(f49(x39482),x39484))
% 21.40/21.36 [3983]E(f789(f789(f54(x39831,f870(x39832,a856)),x39833),f789(f789(f10(f870(x39832,a856),f870(x39832,a856),x39831),f88(f870(x39832,a856))),x39834)),f789(f88(f870(x39832,a856)),f789(f789(f53(x39831,f870(x39832,a856)),x39833),x39834)))
% 21.40/21.36 [3984]E(f789(f789(f53(x39841,f870(x39842,a856)),x39843),f789(f789(f10(f870(x39842,a856),f870(x39842,a856),x39841),f88(f870(x39842,a856))),x39844)),f789(f88(f870(x39842,a856)),f789(f789(f54(x39841,f870(x39842,a856)),x39843),x39844)))
% 21.40/21.36 [3999]E(f789(f789(f289(x39991,x39991,x39991),f789(f789(f178(f869(x39991,x39991),a856),x39992),x39993)),f789(f789(f178(f869(x39991,x39991),a856),x39994),x39993)),f789(f789(f178(f869(x39991,x39991),a856),f789(f789(f89(a863),x39992),x39994)),x39993))
% 21.40/21.36 [4031]E(f789(f789(f54(x40311,f870(f870(x40312,a856),a856)),x40313),f789(f789(f10(f870(x40312,a856),f870(f870(x40312,a856),a856),x40311),f309(x40312)),x40314)),f789(f309(x40312),f789(f789(f54(x40311,f870(x40312,a856)),x40313),x40314)))
% 21.40/21.36 [4059]E(f789(f789(f53(f870(x40591,a856),f870(x40592,a856)),x40593),f789(f789(f9(f870(x40591,a856),f870(x40591,f870(x40592,a856)),f870(x40592,a856)),f53(x40591,f870(x40592,a856))),x40594)),f789(f789(f53(x40591,f870(x40592,a856)),f51(f870(x40591,a856),x40593)),x40594))
% 21.40/21.36 [4060]E(f789(f789(f54(f870(x40601,a856),f870(x40602,a856)),x40603),f789(f789(f9(f870(x40601,a856),f870(x40601,f870(x40602,a856)),f870(x40602,a856)),f54(x40601,f870(x40602,a856))),x40604)),f789(f789(f54(x40601,f870(x40602,a856)),f51(f870(x40601,a856),x40603)),x40604))
% 21.40/21.36 [4061]E(f789(f789(f53(f870(x40611,a856),f870(x40612,a856)),x40613),f789(f789(f9(f870(x40611,a856),f870(x40611,f870(x40612,a856)),f870(x40612,a856)),f53(x40611,f870(x40612,a856))),x40614)),f789(f789(f53(x40611,f870(x40612,a856)),f51(f870(x40611,a856),x40613)),x40614))
% 21.40/21.36 [4062]E(f789(f789(f54(f870(x40621,a856),f870(x40622,a856)),x40623),f789(f789(f9(f870(x40621,a856),f870(x40621,f870(x40622,a856)),f870(x40622,a856)),f54(x40621,f870(x40622,a856))),x40624)),f789(f789(f54(x40621,f870(x40622,a856)),f51(f870(x40621,a856),x40623)),x40624))
% 21.40/21.36 [4067]E(f789(f789(f150(x40671,x40672),x40673),f789(f138(f864(x40671),f864(x40671),f132(x40671),f122(x40671)),x40674)),f789(f138(f864(x40672),f864(x40672),f132(x40672),f122(x40672)),f789(f789(f150(f864(x40671),f864(x40672)),f789(f150(x40671,x40672),x40673)),x40674)))
% 21.40/21.36 [4069]E(f180(f864(x40691),f122(x40691),f789(f789(f10(f864(x40691),f864(x40691),a863),f789(f146(x40691),x40692)),f789(f789(f9(a863,f864(x40691),f864(x40691)),f164(x40691)),x40693)),x40694),f789(f789(f164(x40691),x40694),f789(f789(f146(x40691),x40692),x40693)))
% 21.40/21.36 [4110]P1(f789(f789(f240(f870(x41101,a856)),f789(f311(x41102,x41101,x41103),f789(f313(x41102,x41101,x41103),x41104))),x41104))
% 21.40/21.36 [4113]E(f789(f311(f869(x41131,x41132),f869(x41132,x41131),f789(f259(x41131,x41132,f869(x41132,x41131)),f789(f9(x41132,x41131,f869(x41132,x41131)),f249(x41132,x41131)))),f789(f789(f256(x41131,x41132),x41133),f789(f18(f870(x41132,a856),x41131),x41134))),f789(f789(f256(x41132,x41131),x41134),f789(f18(f870(x41131,a856),x41132),x41133)))
% 21.40/21.36 [4122]E(f789(f789(f53(x41221,f870(x41222,a856)),x41223),f789(f789(f10(f870(x41221,a856),f870(x41222,a856),x41221),f285(x41221,x41222,x41224)),f789(f789(f9(x41221,f870(x41221,a856),f870(x41221,a856)),f310(x41221)),f184(f870(x41221,a856))))),f789(f285(x41221,x41222,x41224),x41223))
% 21.40/21.36 [4123]E(f789(f789(f53(x41231,f870(x41232,a856)),x41233),f789(f789(f10(f870(x41231,a856),f870(x41232,a856),x41231),f313(x41232,x41231,x41234)),f789(f789(f9(x41231,f870(x41231,a856),f870(x41231,a856)),f310(x41231)),f184(f870(x41231,a856))))),f789(f313(x41232,x41231,x41234),x41233))
% 21.40/21.36 [4213]E(f789(f789(f111(f870(x42131,a856)),f789(f789(f111(f870(x42131,a856)),f789(f789(f110(f870(x42131,a856)),x42132),x42133)),f789(f789(f110(f870(x42131,a856)),x42133),x42134))),f789(f789(f110(f870(x42131,a856)),x42134),x42132)),f789(f789(f110(f870(x42131,a856)),f789(f789(f110(f870(x42131,a856)),f789(f789(f111(f870(x42131,a856)),x42132),x42133)),f789(f789(f111(f870(x42131,a856)),x42133),x42134))),f789(f789(f111(f870(x42131,a856)),x42134),x42132)))
% 21.40/21.36 [4272]E(f789(f138(f864(x42721),f864(x42721),f132(x42721),f122(x42721)),f789(f789(f150(x42722,f864(x42721)),f789(f789(f9(x42722,f864(x42721),f864(x42721)),f789(f789(f10(x42721,f870(f864(x42721),f864(x42721)),x42722),f146(x42721)),x42723)),f122(x42721))),x42724)),f789(f789(f150(x42722,x42721),x42723),x42724))
% 21.40/21.36 [4282]E(f789(f789(f95(a1,x42821),f789(f113(a1),f789(f789(f89(a1),x42822),a106))),f789(f789(f20(a1,x42821,x42821),f789(f789(f9(a1,x42821,f870(x42821,x42821)),f789(f789(f10(a856,f870(x42821,f870(x42821,x42821)),a1),f105(x42821)),a190)),x42823)),f789(f789(f10(a863,x42821,a1),x42824),a114))),f180(x42821,x42823,x42824,f789(f113(a863),x42822)))
% 21.40/21.36 [4525]~P1(f789(f789(f184(f870(x45251,f870(x45252,a856))),x45253),x45254))
% 21.40/21.36 [3768]E(f789(f789(f159(x37681),f789(f789(f132(x37681),x37682),x37683)),f789(f789(f89(a863),f789(f185(f864(x37681)),x37682)),x37684)),f789(f789(f159(x37681),x37683),x37684))
% 21.40/21.36 [3772]E(f789(f789(f135(x37721),x37722),f789(f789(f164(x37721),f789(f789(f89(a863),x37723),x37722)),x37724)),f789(f789(f164(x37721),x37723),f789(f789(f135(x37721),x37722),x37724)))
% 21.40/21.36 [3869]E(f789(f789(f110(f870(x38691,a856)),f789(f267(x38692,x38691),x38693)),f789(f267(x38692,x38691),x38694)),f789(f267(x38692,x38691),f789(f789(f110(f870(f869(x38692,x38691),a856)),x38693),x38694)))
% 21.40/21.36 [3870]E(f789(f789(f110(f870(x38701,a856)),f789(f269(x38701,x38702),x38703)),f789(f269(x38701,x38702),x38704)),f789(f269(x38701,x38702),f789(f789(f110(f870(f869(x38701,x38702),a856)),x38703),x38704)))
% 21.40/21.36 [3875]E(f789(f789(f3(f870(x38751,a856)),f789(f789(f111(f870(x38751,a856)),x38752),x38753)),x38754),f789(f789(f111(f870(x38751,a856)),x38752),f789(f789(f3(f870(x38751,a856)),x38753),x38754)))
% 21.40/21.36 [3876]E(f789(f789(f110(f870(x38761,a856)),f789(f789(f110(f870(x38761,a856)),x38762),x38763)),x38764),f789(f789(f110(f870(x38761,a856)),x38762),f789(f789(f110(f870(x38761,a856)),x38763),x38764)))
% 21.40/21.36 [3877]E(f789(f789(f111(f870(x38771,a856)),f789(f789(f111(f870(x38771,a856)),x38772),x38773)),x38774),f789(f789(f111(f870(x38771,a856)),x38772),f789(f789(f111(f870(x38771,a856)),x38773),x38774)))
% 21.40/21.36 [3916]E(f789(f789(f110(f870(f869(x39161,x39162),a856)),f789(f286(x39162,x39161),x39163)),f789(f286(x39162,x39161),x39164)),f789(f286(x39162,x39161),f789(f789(f110(f870(f869(x39162,x39161),a856)),x39163),x39164)))
% 21.40/21.36 [3917]E(f789(f789(f111(f870(f869(x39171,x39172),a856)),f789(f286(x39172,x39171),x39173)),f789(f286(x39172,x39171),x39174)),f789(f286(x39172,x39171),f789(f789(f111(f870(f869(x39172,x39171),a856)),x39173),x39174)))
% 21.40/21.36 [3987]E(f789(f789(f110(f870(x39871,a856)),f789(f789(f3(f870(x39871,a856)),x39872),x39873)),f789(f789(f3(f870(x39871,a856)),x39874),x39873)),f789(f789(f3(f870(x39871,a856)),f789(f789(f110(f870(x39871,a856)),x39872),x39874)),x39873))
% 21.40/21.36 [3988]E(f789(f789(f111(f870(x39881,a856)),f789(f789(f110(f870(x39881,a856)),x39882),x39883)),f789(f789(f110(f870(x39881,a856)),x39884),x39883)),f789(f789(f110(f870(x39881,a856)),f789(f789(f111(f870(x39881,a856)),x39882),x39884)),x39883))
% 21.40/21.36 [3989]E(f789(f789(f3(f870(x39891,a856)),f789(f789(f111(f870(x39891,a856)),x39892),x39893)),f789(f789(f111(f870(x39891,a856)),x39894),x39893)),f789(f789(f111(f870(x39891,a856)),f789(f789(f3(f870(x39891,a856)),x39892),x39894)),x39893))
% 21.40/21.36 [3990]E(f789(f789(f110(f870(x39901,a856)),f789(f789(f111(f870(x39901,a856)),x39902),x39903)),f789(f789(f111(f870(x39901,a856)),x39904),x39903)),f789(f789(f111(f870(x39901,a856)),f789(f789(f110(f870(x39901,a856)),x39902),x39904)),x39903))
% 21.40/21.36 [3991]E(f789(f789(f3(f870(x39911,a856)),f789(f789(f111(f870(x39911,a856)),x39912),x39913)),f789(f789(f111(f870(x39911,a856)),x39914),x39913)),f789(f789(f3(f870(x39911,a856)),f789(f789(f111(f870(x39911,a856)),x39912),x39913)),x39914))
% 21.40/21.36 [4002]E(f789(f789(f3(f870(x40021,a856)),f789(f789(f3(f870(x40021,a856)),x40022),f789(f789(f310(x40021),x40023),f184(f870(x40021,a856))))),x40024),f789(f789(f3(f870(x40021,a856)),x40022),f789(f789(f310(x40021),x40023),x40024)))
% 21.40/21.36 [4058]E(f789(f789(f110(f870(x40581,a856)),f789(f789(f310(x40581),x40582),f789(f789(f310(x40581),x40583),f184(f870(x40581,a856))))),f789(f284(x40581),x40584)),f789(f284(x40581),f789(f789(f310(f869(x40581,x40581)),f789(f789(f249(x40581,x40581),x40582),x40583)),x40584)))
% 21.40/21.36 [4084]E(f789(f789(f53(a863,f870(x40841,a856)),f789(f301(a863),x40842)),f789(f789(f10(a863,f870(x40841,a856),a863),x40843),f789(f789(f9(a863,a863,a863),f89(a863)),x40844))),f789(f789(f53(a863,f870(x40841,a856)),f303(a863,x40844,f789(f789(f89(a863),x40842),x40844))),x40843))
% 21.40/21.36 [4085]E(f166(x40851,f789(f285(x40851,x40851,x40852),f789(f789(f310(x40851),x40853),f184(f870(x40851,a856)))),f789(f285(f864(x40851),f864(x40851),f154(x40851,x40852)),f789(f789(f310(f864(x40851)),x40854),f184(f870(f864(x40851),a856))))),f789(f285(f864(x40851),f864(x40851),f154(x40851,x40852)),f789(f789(f310(f864(x40851)),f789(f789(f146(x40851),x40853),x40854)),f184(f870(f864(x40851),a856)))))
% 21.40/21.36 [4148]E(f170(x41481,x41482,f789(f789(f150(x41481,f869(x41481,x41482)),f789(f789(f20(x41481,x41482,f869(x41481,x41482)),f249(x41481,x41482)),x41483)),x41484)),f177(x41481,x41482,f789(f82(x41482,f867(x41482),x41481,f234(x41482)),x41483),f789(f163(x41481),x41484)))
% 21.40/21.36 [4151]E(f789(f264(x41511),f789(f789(f9(x41511,f870(x41512,a856),a856),f789(f789(f10(x41512,f870(f870(x41512,a856),a856),x41511),f342(x41512)),x41513)),x41514)),f789(f313(x41511,x41512,x41513),x41514))
% 21.40/21.36 [4244]E(f789(f264(x42441),f789(f789(f9(x42441,f870(f869(x42442,x42441),a856),a856),f789(f789(f10(f869(x42442,x42441),f870(f870(f869(x42442,x42441),a856),a856),x42441),f342(f869(x42442,x42441))),f789(f249(x42442,x42441),x42443))),x42444)),f789(f285(x42442,x42441,x42444),f789(f789(f310(x42442),x42443),f184(f870(x42442,a856)))))
% 21.40/21.36 [4258]E(f789(f789(f150(f869(x42581,a863),x42581),f248(x42581,a863)),f789(f133(f869(x42581,a863),f789(f789(f10(a863,a856,f869(x42581,a863)),x42582),f789(f789(f10(a863,a863,f869(x42581,a863)),a121),f258(x42581,a863)))),f789(f789(f171(x42581,a863),x42583),x42584))),f789(f789(f150(f869(x42581,a863),x42581),f248(x42581,a863)),f789(f133(f869(x42581,a863),f789(f789(f10(a863,a856,f869(x42581,a863)),x42582),f258(x42581,a863))),f789(f789(f171(x42581,a863),x42583),f789(f789(f150(a863,a863),a121),x42584)))))
% 21.40/21.36 [4265]P1(f789(f789(f240(f870(f870(x42651,a856),a856)),f789(f789(f53(x42652,f870(f870(x42651,a856),a856)),x42653),f789(f789(f10(f870(x42651,a856),f870(f870(x42651,a856),a856),x42652),f309(x42651)),x42654))),f789(f309(x42651),f789(f789(f53(x42652,f870(x42651,a856)),x42653),x42654))))
% 21.40/21.36 [4304]E(f789(f789(f95(a1,x43041),f789(f113(a1),f789(f789(f89(a1),x43042),a106))),f789(f789(f20(a1,x43041,x43041),f789(f789(f9(a1,x43041,f870(x43041,x43041)),f789(f789(f10(a856,f870(x43041,f870(x43041,x43041)),a1),f105(x43041)),a190)),x43043)),f789(f789(f20(a1,x43041,x43041),f789(f789(f10(a863,f870(x43041,x43041),a1),x43044),a114)),f789(f789(f10(a863,x43041,a1),f179(x43041,x43043,x43044)),a114)))),f789(f179(x43041,x43043,x43044),f789(f113(a863),x43042)))
% 21.40/21.36 [4307]E(f789(f789(f150(x43071,x43072),f789(f82(f867(x43072),x43072,x43071,f238(x43072)),x43073)),f789(f133(x43071,f789(f789(f10(a856,a856,x43071),a336),f789(f789(f9(x43071,f867(x43072),a856),f789(f789(f10(f867(x43072),f870(f867(x43072),a856),x43071),a338),x43073)),f187(x43072)))),x43074)),f160(x43071,x43072,x43073,x43074))
% 21.40/21.36 [4328]E(f789(f264(f869(x43281,x43282)),f789(f259(x43281,x43282,a856),f789(f789(f9(x43281,f870(x43282,a856),f870(x43282,a856)),f789(f789(f10(f870(a856,a856),f870(f870(x43282,a856),f870(x43282,a856)),x43281),f10(a856,a856,x43282)),f789(f789(f10(a856,f870(a856,a856),x43281),a339),f789(f789(f9(x43281,f870(x43281,a856),a856),f342(x43281)),x43283)))),f789(f789(f9(x43282,f870(x43282,a856),a856),f342(x43282)),x43284)))),f230(x43281,x43282,x43283,x43284))
% 21.40/21.36 [4361]E(f789(f789(f53(x43611,f870(f869(x43611,x43612),a856)),x43613),f789(f789(f20(x43611,f870(x43612,f870(f869(x43611,x43612),a856)),f870(f869(x43611,x43612),a856)),f789(f789(f10(f870(x43612,a856),f870(f870(x43612,f870(f869(x43611,x43612),a856)),f870(f869(x43611,x43612),a856)),x43611),f53(x43612,f870(f869(x43611,x43612),a856))),x43614)),f789(f789(f9(x43611,f870(f869(x43611,x43612),a856),f870(x43612,f870(f869(x43611,x43612),a856))),f789(f789(f10(f870(x43612,f870(f870(f869(x43611,x43612),a856),f870(f869(x43611,x43612),a856))),f870(f870(f869(x43611,x43612),a856),f870(x43612,f870(f869(x43611,x43612),a856))),x43611),f9(x43612,f870(f869(x43611,x43612),a856),f870(f869(x43611,x43612),a856))),f789(f789(f10(f870(x43612,f869(x43611,x43612)),f870(x43612,f870(f870(f869(x43611,x43612),a856),f870(f869(x43611,x43612),a856))),x43611),f789(f10(f869(x43611,x43612),f870(f870(f869(x43611,x43612),a856),f870(f869(x43611,x43612),a856)),x43612),f310(f869(x43611,x43612)))),f249(x43611,x43612)))),f184(f870(f869(x43611,x43612),a856))))),f789(f789(f256(x43611,x43612),x43613),x43614))
% 21.40/21.36 [3925]E(f789(f789(f132(x39251),f789(f789(f164(x39251),x39252),x39253)),f789(f789(f164(x39251),f789(f789(f3(a863),x39252),f789(f185(f864(x39251)),x39253))),x39254)),f789(f789(f164(x39251),x39252),f789(f789(f132(x39251),x39253),x39254)))
% 21.40/21.36 [3926]E(f789(f789(f132(x39261),f789(f789(f135(x39261),x39262),x39263)),f789(f789(f135(x39261),f789(f789(f3(a863),x39262),f789(f185(f864(x39261)),x39263))),x39264)),f789(f789(f135(x39261),x39262),f789(f789(f132(x39261),x39263),x39264)))
% 21.40/21.36 [3976]E(f789(f789(f89(a863),f789(f789(f90(a863),x39761),x39762)),f789(f789(f89(a863),f789(f789(f90(a863),x39763),x39762)),x39764)),f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f89(a863),x39761),x39763)),x39762)),x39764))
% 21.40/21.36 [4178]P1(f789(f789(f240(f870(x41781,a856)),f789(f789(f3(f870(x41781,a856)),f789(f267(x41782,x41781),x41783)),f789(f267(x41782,x41781),x41784))),f789(f267(x41782,x41781),f789(f789(f3(f870(f869(x41782,x41781),a856)),x41783),x41784))))
% 21.40/21.36 [4179]P1(f789(f789(f240(f870(x41791,a856)),f789(f789(f3(f870(x41791,a856)),f789(f269(x41791,x41792),x41793)),f789(f269(x41791,x41792),x41794))),f789(f269(x41791,x41792),f789(f789(f3(f870(f869(x41791,x41792),a856)),x41793),x41794))))
% 21.40/21.36 [4284]E(f789(f789(f89(a1),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x42841),x42842)),f184(f870(f869(a863,a863),a856)))))),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x42843),x42844)),f184(f870(f869(a863,a863),a856)))))),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),f789(f789(f89(a863),x42841),x42843)),f789(f789(f89(a863),x42842),x42844))),f184(f870(f869(a863,a863),a856))))))
% 21.40/21.36 [4323]E(f789(f789(f90(a1),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x43231),x43232)),f184(f870(f869(a863,a863),a856)))))),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x43233),x43234)),f184(f870(f869(a863,a863),a856)))))),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),f789(f789(f89(a863),f789(f789(f90(a863),x43231),x43233)),f789(f789(f90(a863),x43232),x43234))),f789(f789(f89(a863),f789(f789(f90(a863),x43231),x43234)),f789(f789(f90(a863),x43232),x43233)))),f184(f870(f869(a863,a863),a856))))))
% 21.40/21.36 [4343]E(f789(f264(x43431),f789(f789(f10(f870(x43432,a856),a856,x43431),f97(x43432)),f789(f789(f10(f870(x43432,a856),f870(x43432,a856),x43431),f789(f20(x43432,a856,a856),f789(f789(f10(a856,f870(a856,a856),x43432),a343),f789(f789(f9(x43432,f870(x43432,a856),a856),f342(x43432)),x43433)))),f789(f789(f9(x43431,f870(x43432,f870(x43431,a856)),f870(x43432,a856)),f789(f789(f10(f870(f870(x43431,a856),a856),f870(f870(x43432,f870(x43431,a856)),f870(x43432,a856)),x43431),f10(f870(x43431,a856),a856,x43432)),f342(x43431))),x43434)))),f789(f789(f54(x43432,f870(x43431,a856)),x43433),x43434))
% 21.40/21.36 [4377]E(f789(f789(f289(x43771,x43771,x43771),f789(f789(f310(f869(x43771,x43771)),f789(f789(f249(x43771,x43771),x43772),x43773)),x43774)),f308(x43771,f789(f789(f310(f869(x43771,x43771)),f789(f789(f249(x43771,x43771),x43772),x43773)),x43774))),f789(f789(f110(f870(f869(x43771,x43771),a856)),f789(f789(f289(x43771,x43771,x43771),x43774),f308(x43771,x43774))),f789(f264(f869(x43771,x43771)),f789(f259(x43771,x43771,a856),f789(f789(f9(x43771,f870(x43771,a856),f870(x43771,a856)),f789(f789(f10(f870(a856,a856),f870(f870(x43771,a856),f870(x43771,a856)),x43771),f10(a856,a856,x43771)),f789(f789(f10(a856,f870(a856,a856),x43771),a339),f789(f789(f9(x43771,f870(f869(x43771,x43771),a856),a856),f789(f789(f10(f869(x43771,x43771),f870(f870(f869(x43771,x43771),a856),a856),x43771),f342(f869(x43771,x43771))),f789(f789(f9(x43771,x43771,f869(x43771,x43771)),f249(x43771,x43771)),x43772))),f308(x43771,x43774))))),f789(f789(f9(x43771,f870(f869(x43771,x43771),a856),a856),f789(f789(f10(f869(x43771,x43771),f870(f870(f869(x43771,x43771),a856),a856),x43771),f342(f869(x43771,x43771))),f789(f249(x43771,x43771),x43773))),f308(x43771,x43774)))))))
% 21.40/21.36 [4180]E(f789(f133(x41801,f789(f789(f20(x41801,a856,a856),f789(f789(f10(a856,f870(a856,a856),x41801),a339),x41802)),x41803)),x41804),f789(f133(x41801,x41803),f789(f133(x41801,x41802),x41804)))
% 21.40/21.36 [4278]E(f789(f789(f132(x42781),f789(f789(f789(f105(f864(x42781)),f789(f789(f342(a863),f2(a863)),x42782)),f789(f789(f146(x42781),x42783),f122(x42781))),f122(x42781))),f165(x42781,x42784,f789(f264(a863),f789(f789(f9(a863,f870(a863,a856),a856),f789(f789(f10(a863,f870(f870(a863,a856),a856),a863),f342(a863)),a121)),x42782)))),f165(x42781,f789(f789(f146(x42781),x42783),x42784),x42782))
% 21.40/21.36 [4372]E(f789(f264(f869(x43721,x43722)),f789(f789(f10(f870(a863,a856),a856,f869(x43721,x43722)),f96(a863)),f789(f789(f9(f869(x43721,x43722),f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),f869(x43721,x43722)),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),f869(x43721,x43722)),f789(f10(a856,f870(a856,a856),a863),a339)),f789(f789(f9(f869(x43721,x43722),f870(a863,f869(x43721,x43722)),f870(a863,a856)),f789(f789(f10(f870(f869(x43721,x43722),a856),f870(f870(a863,f869(x43721,x43722)),f870(a863,a856)),f869(x43721,x43722)),f10(f869(x43721,x43722),a856,a863)),a338)),f789(f789(f20(a863,x43722,f869(x43721,x43722)),f789(f789(f10(x43721,f870(x43722,f869(x43721,x43722)),a863),f249(x43721,x43722)),f789(f159(x43721),x43723))),f789(f159(x43722),x43724)))))),f789(f789(f9(a863,a863,a856),f241(a863)),f789(f789(f244(a863),f789(f185(f864(x43721)),x43723)),f789(f185(f864(x43722)),x43724)))))),f789(f163(f869(x43721,x43722)),f789(f789(f171(x43721,x43722),x43723),x43724)))
% 21.40/21.36 [4296]E(f789(f264(f869(x42961,x42962)),f789(f259(x42961,x42962,a856),f789(f789(f9(x42961,f870(x42962,a856),f870(x42962,a856)),f789(f789(f10(f870(a856,a856),f870(f870(x42962,a856),f870(x42962,a856)),x42961),f10(a856,a856,x42962)),f789(f789(f10(a856,f870(a856,a856),x42961),a339),x42963))),x42964))),f789(f789(f256(x42961,x42962),f789(f264(x42961),x42963)),f789(f18(f870(x42962,a856),x42961),f789(f264(x42962),x42964))))
% 21.40/21.36 [4299]E(f789(f264(f869(x42991,x42992)),f789(f259(x42991,x42992,a856),f789(f789(f20(x42991,f870(x42992,a856),f870(x42992,a856)),f789(f789(f10(f870(a856,a856),f870(f870(x42992,a856),f870(x42992,a856)),x42991),f10(a856,a856,x42992)),f789(f789(f10(a856,f870(a856,a856),x42991),a339),x42993))),x42994))),f789(f789(f256(x42991,x42992),f789(f264(x42991),x42993)),f789(f789(f10(f870(x42992,a856),f870(x42992,a856),x42991),f264(x42992)),x42994)))
% 21.40/21.36 [4314]E(f789(f264(x43141),f789(f789(f10(f870(x43142,a856),a856,x43141),f97(x43142)),f789(f789(f10(f870(x43142,a856),f870(x43142,a856),x43141),f789(f20(x43142,a856,a856),f789(f789(f10(a856,f870(a856,a856),x43142),a343),f789(f789(f9(x43142,f870(x43142,a856),a856),f342(x43142)),x43143)))),x43144))),f789(f789(f54(x43142,f870(x43141,a856)),x43143),f789(f789(f10(f870(x43141,a856),f870(x43141,a856),x43142),f264(x43141)),f789(f9(x43141,x43142,a856),x43144))))
% 21.40/21.36 [4356]E(f789(f789(f150(f869(x43561,a863),x43561),f248(x43561,a863)),f789(f133(f869(x43561,a863),f789(f789(f9(f869(x43561,a863),f870(a863,a856),a856),f789(f789(f10(a863,f870(f870(a863,a856),a856),f869(x43561,a863)),f342(a863)),f258(x43561,a863))),x43562)),f789(f789(f171(x43561,a863),x43563),f136(a863,f789(f302(a863,x43564),f789(f789(f89(a863),x43564),f789(f185(f864(x43561)),x43563))))))),f789(f789(f150(f869(x43561,a863),x43561),f248(x43561,a863)),f789(f133(f869(x43561,a863),f789(f789(f9(f869(x43561,a863),f870(a863,a856),a856),f789(f789(f10(a863,f870(f870(a863,a856),a856),f869(x43561,a863)),f342(a863)),f789(f789(f9(f869(x43561,a863),a863,a863),f789(f789(f10(a863,f870(a863,a863),f869(x43561,a863)),f89(a863)),f258(x43561,a863))),x43564))),x43562)),f789(f789(f171(x43561,a863),x43563),f136(a863,f789(f302(a863,f2(a863)),f789(f185(f864(x43561)),x43563)))))))
% 21.40/21.36 [4357]E(f789(a121,f789(f789(f239(a863),f789(f185(f864(x43571)),x43572)),f789(f138(a863,f864(x43573),f789(f9(f864(x43573),a863,a863),f789(f789(f10(a863,f870(a863,a863),f864(x43573)),f239(a863)),f789(f789(f9(f864(x43573),a863,a863),f789(f789(f10(a863,f870(a863,a863),f864(x43573)),f3(a863)),f185(f864(x43573)))),f789(a121,f2(a863))))),f2(a863)),f789(f149(f864(x43573)),f789(f133(f864(x43573),f789(f789(f10(a856,a856,f864(x43573)),a336),f789(f789(f9(f864(x43573),f864(x43573),a856),a338),f122(x43573)))),x43574))))),f789(f789(f239(a863),f789(a121,f789(f185(f864(x43571)),x43572))),f789(f138(a863,f864(x43573),f789(f9(f864(x43573),a863,a863),f789(f789(f10(a863,f870(a863,a863),f864(x43573)),f239(a863)),f185(f864(x43573)))),f2(a863)),f789(f149(f864(x43573)),x43574))))
% 21.40/21.36 [4313]E(f789(f789(f132(x43131),f165(x43131,x43132,x43133)),f165(x43131,x43134,f789(f264(a863),f789(f789(f9(a863,f870(a863,a856),a856),f789(f789(f10(a863,f870(f870(a863,a856),a856),a863),f342(a863)),f789(f789(f9(a863,a863,a863),f89(a863)),f789(f185(f864(x43131)),x43132)))),x43133)))),f165(x43131,f789(f789(f132(x43131),x43132),x43134),x43133))
% 21.40/21.36 [4363]E(f789(f789(f146(f864(x43631)),f789(f789(f146(x43631),x43632),f789(f138(f864(x43631),f864(x43631),f132(x43631),f122(x43631)),f789(f789(f150(f864(x43631),f864(x43631)),f152(f864(x43631),x43631,f122(x43631),f789(f789(f10(f864(x43631),f870(f864(x43631),f864(x43631)),x43631),f18(f864(x43631),f864(x43631))),f789(f789(f9(x43631,f864(x43631),f864(x43631)),f146(x43631)),f122(x43631))))),x43633)))),f168(x43631,f789(f789(f146(f864(x43631)),x43634),f789(f138(f864(f864(x43631)),f864(f864(x43631)),f132(f864(x43631)),f122(f864(x43631))),f789(f789(f150(f864(x43631),f864(f864(x43631))),f152(f864(f864(x43631)),x43631,f122(f864(x43631)),f789(f18(f870(f864(x43631),f864(f864(x43631))),x43631),f789(f789(f9(f864(x43631),f864(f864(x43631)),f864(f864(x43631))),f146(f864(x43631))),f122(f864(x43631)))))),x43633))))),f168(x43631,f789(f789(f146(f864(x43631)),f789(f789(f146(x43631),x43632),x43634)),x43633)))
% 21.40/21.36 [4373]E(f789(f264(f869(x43731,x43731)),f789(f259(x43731,x43731,a856),f789(f789(f9(x43731,f870(f869(x43732,x43732),a856),f870(x43731,a856)),f789(f789(f10(f870(x43731,f870(f870(f869(x43732,x43732),a856),a856)),f870(f870(f869(x43732,x43732),a856),f870(x43731,a856)),x43731),f9(x43731,f870(f869(x43732,x43732),a856),a856)),f789(f789(f10(f870(x43731,f869(x43732,x43732)),f870(x43731,f870(f870(f869(x43732,x43732),a856),a856)),x43731),f789(f10(f869(x43732,x43732),f870(f870(f869(x43732,x43732),a856),a856),x43731),f342(f869(x43732,x43732)))),f789(f789(f9(x43731,f870(x43731,x43732),f870(x43731,f869(x43732,x43732))),f789(f789(f10(f870(x43732,f869(x43732,x43732)),f870(f870(x43731,x43732),f870(x43731,f869(x43732,x43732))),x43731),f10(x43732,f869(x43732,x43732),x43731)),f789(f789(f10(x43732,f870(x43732,f869(x43732,x43732)),x43731),f249(x43732,x43732)),x43733))),x43733)))),x43734))),f789(f789(f288(x43732,x43731),x43734),x43733))
% 21.40/21.36 [4460]~E(f38(x44601,x44602),f35(x44603,x44604,x44605))
% 21.40/21.36 [4461]~E(f38(x44611,x44612),f34(x44613,x44614,x44615))
% 21.40/21.36 [4462]~E(f38(x44621,x44622),f33(x44623,x44624,x44625))
% 21.40/21.36 [4463]~E(f30(x44631,x44632),f35(x44633,x44634,x44635))
% 21.40/21.36 [4464]~E(f30(x44641,x44642),f34(x44643,x44644,x44645))
% 21.40/21.36 [4465]~E(f30(x44651,x44652),f33(x44653,x44654,x44655))
% 21.40/21.36 [4466]~E(f37(x44661,x44662),f35(x44663,x44664,x44665))
% 21.40/21.36 [4467]~E(f37(x44671,x44672),f34(x44673,x44674,x44675))
% 21.40/21.36 [4468]~E(f37(x44681,x44682),f33(x44683,x44684,x44685))
% 21.40/21.36 [4469]~E(f35(x44691,x44692,x44693),f38(x44694,x44695))
% 21.40/21.36 [4470]~E(f35(x44701,x44702,x44703),f30(x44704,x44705))
% 21.40/21.36 [4471]~E(f35(x44711,x44712,x44713),f37(x44714,x44715))
% 21.40/21.36 [4472]~E(f34(x44721,x44722,x44723),f38(x44724,x44725))
% 21.40/21.36 [4473]~E(f34(x44731,x44732,x44733),f30(x44734,x44735))
% 21.40/21.36 [4474]~E(f34(x44741,x44742,x44743),f37(x44744,x44745))
% 21.40/21.36 [4475]~E(f33(x44751,x44752,x44753),f38(x44754,x44755))
% 21.40/21.36 [4476]~E(f33(x44761,x44762,x44763),f30(x44764,x44765))
% 21.40/21.36 [4477]~E(f33(x44771,x44772,x44773),f37(x44774,x44775))
% 21.40/21.36 [3867]E(f789(f174(x38671,x38672,x38673,x38674),x38675),f789(f236(f867(x38672),x38672,f789(x38673,x38675),f234(x38672)),f789(x38674,x38675)))
% 21.40/21.36 [3952]E(f174(x39521,x39522,f174(x39521,x39522,x39523,x39524),x39525),f174(x39521,x39522,x39523,f174(x39521,x39522,x39524,x39525)))
% 21.40/21.36 [4132]E(f789(f789(f110(f870(x41321,a856)),f789(f163(x41321),f789(f789(f164(x41321),f789(f185(f864(x41322)),x41323)),x41324))),f173(x41321,x41322,x41325)),f173(x41321,x41322,f176(x41321,x41322,x41325,x41324,x41323)))
% 21.40/21.36 [3696]E(f789(f789(f259(x36961,x36962,x36963),x36964),x36965),f789(f789(x36964,f789(f248(x36961,x36962),x36965)),f789(f258(x36961,x36962),x36965)))
% 21.40/21.36 [3697]E(f789(f789(f259(x36971,x36972,x36973),x36974),x36975),f789(f789(x36974,f789(f248(x36971,x36972),x36975)),f789(f258(x36971,x36972),x36975)))
% 21.40/21.36 [3698]E(f789(f789(f259(x36981,x36982,x36983),x36984),x36985),f789(f789(x36984,f789(f248(x36981,x36982),x36985)),f789(f258(x36981,x36982),x36985)))
% 21.40/21.36 [3724]E(f789(f236(x37241,x37242,x37243,x37244),f789(f234(x37242),x37245)),f789(x37244,x37245))
% 21.40/21.36 [3732]E(f789(f789(f789(f74(x37321,x37322,x37323),x37324),x37325),f184(f870(x37322,a856))),x37325)
% 21.40/21.36 [3748]E(f789(f324(x37481,x37482,x37483,x37484),f789(f312(x37481,x37483),x37485)),f789(x37484,x37485))
% 21.40/21.36 [3749]E(f789(f325(x37491,x37492,x37493,x37494),f789(f321(x37491,x37493),x37495)),f789(x37494,x37495))
% 21.40/21.36 [3898]E(f237(x38981,x38982,x38983,x38984,f789(f234(x38982),x38985)),f789(x38984,x38985))
% 21.40/21.36 [3933]E(f326(x39331,x39332,x39333,x39334,f789(f312(x39331,x39332),x39335)),f789(f789(f89(a863),f789(x39333,x39335)),f789(a121,f2(a863))))
% 21.40/21.36 [3934]E(f326(x39341,x39342,x39343,x39344,f789(f321(x39342,x39341),x39345)),f789(f789(f89(a863),f789(x39344,x39345)),f789(a121,f2(a863))))
% 21.40/21.36 [4008]E(f789(f82(f867(x40081),f867(x40082),f867(x40083),f789(f203(x40081,x40082),x40084)),f789(f203(x40083,x40081),x40085)),f789(f203(x40083,x40082),f789(f82(x40081,x40082,x40083,x40084),x40085)))
% 21.40/21.36 [4009]E(f789(f82(f864(x40091),f864(x40092),f864(x40093),f789(f150(x40091,x40092),x40094)),f789(f150(x40093,x40091),x40095)),f789(f150(x40093,x40092),f789(f82(x40091,x40092,x40093,x40094),x40095)))
% 21.40/21.36 [4010]E(f789(f82(f864(x40101),f864(x40102),f864(x40103),f789(f150(x40101,x40102),x40104)),f789(f150(x40103,x40101),x40105)),f789(f150(x40103,x40102),f789(f82(x40101,x40102,x40103,x40104),x40105)))
% 21.40/21.36 [4088]E(f94(x40881,f75(x40882,x40881,x40883,x40884,x40885)),f789(f789(f73(x40882,x40881,x40883),x40884),x40885))
% 21.40/21.36 [4124]E(f789(f789(f89(a863),f789(f789(f89(a863),f789(x41241,f789(f248(x41242,x41243),x41244))),f789(x41245,f789(f258(x41242,x41243),x41244)))),f789(a121,f2(a863))),f263(x41242,x41243,x41241,x41245,x41244))
% 21.40/21.36 [4309]E(f160(x43091,x43092,f789(f789(f9(x43091,f867(x43092),f867(x43092)),f789(f789(f20(x43091,f867(x43092),f870(f867(x43092),f867(x43092))),f789(f789(f10(a856,f870(f867(x43092),f870(f867(x43092),f867(x43092))),x43091),f105(f867(x43092))),x43093)),f789(f789(f10(x43092,f867(x43092),x43091),f234(x43092)),x43094))),f187(x43092)),x43095),f789(f789(f150(x43091,x43092),x43094),f789(f133(x43091,x43093),x43095)))
% 21.40/21.36 [4518]~E(f789(f789(f789(f81(x45181,f867(x45182)),x45183),x45184),f789(f234(x45182),x45185)),f789(f18(f867(x45182),x45181),f187(x45182)))
% 21.40/21.36 [3633]E(f789(f789(f164(x36331),x36332),f789(f789(f150(x36333,x36331),x36334),x36335)),f789(f789(f150(x36333,x36331),x36334),f789(f789(f164(x36333),x36332),x36335)))
% 21.40/21.36 [3634]E(f789(f789(f135(x36341),x36342),f789(f789(f150(x36343,x36341),x36344),x36345)),f789(f789(f150(x36343,x36341),x36344),f789(f789(f135(x36343),x36342),x36345)))
% 21.40/21.36 [3664]E(f789(f789(f150(x36641,x36642),x36643),f789(f789(f146(x36641),x36644),x36645)),f789(f789(f146(x36642),f789(x36643,x36644)),f789(f789(f150(x36641,x36642),x36643),x36645)))
% 21.40/21.36 [3728]E(f789(f311(x37281,x37282,x37283),f789(f789(f310(x37281),x37284),x37285)),f789(f789(f310(x37282),f789(x37283,x37284)),f789(f311(x37281,x37282,x37283),x37285)))
% 21.40/21.36 [3792]E(f789(f789(f171(x37921,x37922),f789(f789(f164(x37921),x37923),x37924)),f789(f789(f164(x37922),x37923),x37925)),f789(f789(f164(f869(x37921,x37922)),x37923),f789(f789(f171(x37921,x37922),x37924),x37925)))
% 21.40/21.36 [3793]E(f789(f789(f171(x37931,x37932),f789(f789(f135(x37931),x37933),x37934)),f789(f789(f135(x37932),x37933),x37935)),f789(f789(f135(f869(x37931,x37932)),x37933),f789(f789(f171(x37931,x37932),x37934),x37935)))
% 21.40/21.36 [3804]E(f789(f789(f155(x38041,f789(f789(f146(x38041),x38042),x38043)),f789(a121,x38044)),x38045),f789(f789(f146(x38041),x38042),f789(f789(f155(x38041,x38043),x38044),x38045)))
% 21.40/21.36 [3807]E(f789(f236(f867(x38071),x38072,f187(x38071),x38073),f789(f789(f18(f867(x38072),x38074),f187(x38072)),x38075)),f187(x38071))
% 21.40/21.36 [3809]E(f789(f789(f132(x38091),f789(f789(f150(x38092,x38091),x38093),x38094)),f789(f789(f150(x38092,x38091),x38093),x38095)),f789(f789(f150(x38092,x38091),x38093),f789(f789(f132(x38092),x38094),x38095)))
% 21.40/21.36 [3813]E(f789(f789(x38131,x38132),f789(f789(f251(x38133,x38134,x38131),x38132),x38135)),f789(f789(f251(x38133,x38134,x38131),x38132),f789(a121,x38135)))
% 21.40/21.36 [3854]E(f789(f789(f289(x38541,x38542,x38543),f789(f286(x38542,x38541),x38544)),f789(f286(x38543,x38542),x38545)),f789(f286(x38543,x38541),f789(f789(f289(x38543,x38542,x38541),x38545),x38544)))
% 21.40/21.36 [3885]E(f789(f789(f789(f178(f864(x38851),f864(x38851)),x38852),f148(x38851)),f789(f789(f150(x38853,x38851),x38854),x38855)),f789(f789(f150(x38853,x38851),x38854),f789(f789(f789(f178(f864(x38853),f864(x38853)),x38852),f148(x38853)),x38855)))
% 21.40/21.36 [3886]E(f789(f789(f261(x38861,x38862,x38861,x38863),f789(f249(x38862,x38861),x38864)),x38865),f789(x38865,x38864))
% 21.40/21.36 [3912]E(f151(x39121,x39122,f789(f789(f150(x39123,x39121),x39124),x39125)),f151(x39123,f789(f82(x39121,a863,x39123,x39122),x39124),x39125))
% 21.40/21.36 [3975]E(f789(f789(f82(f867(x39751),f867(x39752),x39753,f789(f203(x39751,x39752),x39754)),f789(f18(f867(x39751),x39753),f187(x39751))),x39755),f187(x39752))
% 21.40/21.36 [3980]E(f789(f311(x39801,x39802,f789(f789(f10(x39803,x39802,x39801),x39804),x39805)),f247(f870(x39801,a856))),f789(f311(x39803,x39802,x39804),f789(f311(x39801,x39803,x39805),f247(f870(x39801,a856)))))
% 21.40/21.36 [4014]E(f789(f789(f110(f870(x40141,a856)),f789(f313(x40141,x40142,x40143),f789(f789(f310(x40142),x40144),f184(f870(x40142,a856))))),f789(f313(x40141,x40142,x40143),x40145)),f789(f313(x40141,x40142,x40143),f789(f789(f310(x40142),x40144),x40145)))
% 21.40/21.36 [4080]E(f789(f138(x40801,x40802,f789(f9(x40802,x40801,x40801),f789(f9(x40801,x40802,x40801),x40803)),x40804),f789(f149(x40802),f789(f149(x40802),x40805))),f789(f138(x40801,x40802,x40803,x40804),x40805))
% 21.40/21.36 [4081]E(f789(f789(f789(f81(x40811,f867(x40812)),f177(x40811,x40812,x40813,x40814)),x40815),f789(x40813,x40815)),f177(x40811,x40812,x40813,f789(f789(f310(x40811),x40815),x40814)))
% 21.40/21.36 [4090]E(f789(f327(x40901,x40902,x40903,f789(f18(x40902,x40901),x40904),f789(f18(x40902,x40903),x40904)),x40905),x40904)
% 21.40/21.36 [4149]E(f789(f236(f864(x41491),x41491,f160(x41492,x41491,x41493,x41494),f789(f789(f9(x41491,f864(x41491),f864(x41491)),f146(x41491)),f160(x41492,x41491,x41493,x41494))),f789(x41493,x41495)),f160(x41492,x41491,x41493,f789(f789(f146(x41492),x41495),x41494)))
% 21.40/21.36 [4188]P1(f789(f789(f240(f870(x41881,a856)),f789(f311(x41882,x41881,x41883),f789(f789(f111(f870(x41882,a856)),x41884),x41885))),f789(f789(f111(f870(x41881,a856)),f789(f311(x41882,x41881,x41883),x41884)),f789(f311(x41882,x41881,x41883),x41885))))
% 21.40/21.36 [4189]P1(f789(f789(f240(f870(x41891,a856)),f789(f285(x41892,x41891,x41893),f789(f789(f111(f870(x41892,a856)),x41894),x41895))),f789(f789(f111(f870(x41891,a856)),f789(f285(x41892,x41891,x41893),x41894)),f789(f285(x41892,x41891,x41893),x41895))))
% 21.40/21.36 [4285]E(f789(f258(x42851,x42852),f789(f260(x42853,x42851,x42852,x42852,x42854,f41(x42852)),x42855)),f789(f258(x42853,x42852),x42855))
% 21.40/21.36 [4286]E(f789(f248(x42861,x42862),f789(f260(x42861,x42861,x42863,x42862,f41(x42861),x42864),x42865)),f789(f248(x42861,x42863),x42865))
% 21.40/21.36 [4289]E(f789(f248(x42891,x42892),f789(f260(x42893,x42891,x42892,x42892,x42894,f41(x42892)),x42895)),f789(x42894,f789(f248(x42893,x42892),x42895)))
% 21.40/21.36 [4290]E(f789(f258(x42901,x42902),f789(f260(x42901,x42901,x42903,x42902,f41(x42901),x42904),x42905)),f789(x42904,f789(f258(x42901,x42903),x42905)))
% 21.40/21.36 [4366]P28(x43661,x43662,f789(f789(f310(f862(x43661)),f789(f789(f789(f100(x43661),f789(f789(f9(x43661,f870(a861,a861),f870(a861,a856)),f789(f789(f10(f870(a861,a856),f870(f870(a861,a861),f870(a861,a856)),x43661),f10(a861,a856,a861)),x43663)),f789(f789(f20(a861,a863,a861),f789(f789(f9(a861,a858,f870(a863,a861)),a193),x43664)),x43665))),f30(x43664,x43665)),x43663)),f184(f870(f862(x43661),a856))))
% 21.40/21.36 [4367]P28(x43671,x43672,f789(f789(f310(f862(x43671)),f789(f789(f789(f100(x43671),f789(f789(f9(x43671,f870(a861,a861),f870(a861,a856)),f789(f789(f10(f870(a861,a856),f870(f870(a861,a861),f870(a861,a856)),x43671),f10(a861,a856,a861)),x43673)),f789(f789(f20(a861,a863,a861),f789(f789(f9(a861,a858,f870(a863,a861)),a193),x43674)),x43675))),f30(x43674,x43675)),x43673)),f184(f870(f862(x43671),a856))))
% 21.40/21.36 [4369]E(f789(f138(f870(x43691,f867(x43692)),f869(x43691,x43692),f789(f789(f10(f870(x43691,f870(x43692,f870(x43691,f867(x43692)))),f870(f869(x43691,x43692),f870(x43691,f867(x43692))),f870(x43691,f867(x43692))),f259(x43691,x43692,f870(x43691,f867(x43692)))),f789(f789(f9(f870(x43691,f867(x43692)),f870(x43692,f867(x43692)),f870(x43691,f870(x43692,f870(x43691,f867(x43692))))),f789(f789(f10(f870(x43691,f870(f870(x43692,f867(x43692)),f870(x43692,f870(x43691,f867(x43692))))),f870(f870(x43692,f867(x43692)),f870(x43691,f870(x43692,f870(x43691,f867(x43692))))),f870(x43691,f867(x43692))),f9(x43691,f870(x43692,f867(x43692)),f870(x43692,f870(x43691,f867(x43692))))),f789(f789(f10(f870(x43691,f870(f867(x43692),f870(x43691,f867(x43692)))),f870(x43691,f870(f870(x43692,f867(x43692)),f870(x43692,f870(x43691,f867(x43692))))),f870(x43691,f867(x43692))),f789(f10(f870(f867(x43692),f870(x43691,f867(x43692))),f870(f870(x43692,f867(x43692)),f870(x43692,f870(x43691,f867(x43692)))),x43691),f10(f867(x43692),f870(x43691,f867(x43692)),x43692))),f81(x43691,f867(x43692))))),f234(x43692))),x43693),f789(f789(f171(x43691,x43692),x43694),x43695)),f176(x43691,x43692,x43693,x43694,x43695))
% 21.40/21.36 [4371]P28(x43711,x43712,f789(f789(f310(f862(x43711)),f789(f789(f789(f100(x43711),f789(f789(f9(x43711,f870(a861,a856),f870(a861,a856)),f789(f789(f10(f870(a861,f870(a856,a856)),f870(f870(a861,a856),f870(a861,a856)),x43711),f20(a861,a856,a856)),f789(f789(f10(f870(a861,a856),f870(a861,f870(a856,a856)),x43711),f789(f10(a856,f870(a856,a856),a861),a339)),x43713))),f789(f789(f10(a856,a856,a861),a336),x43714))),f37(x43714,x43715)),x43713)),f184(f870(f862(x43711),a856))))
% 21.40/21.36 [3478]E(f789(f789(f789(f789(f206(x34781),x34782),x34783),x34784),x34785),f201(x34781,x34782))
% 21.40/21.36 [3479]E(f789(f789(f789(f789(f207(x34791),x34792),x34793),x34794),x34795),f189(x34791,x34792))
% 21.40/21.36 [3527]E(f102(x35271,x35272,f789(f789(f789(f100(x35271),x35273),x35274),x35275)),f2(a863))
% 21.40/21.36 [3617]E(f789(f789(f789(f789(f81(x36171,x36172),x36173),x36174),x36175),x36174),x36175)
% 21.40/21.36 [3844]E(f789(f789(f53(x38441,f870(x38442,a856)),f789(f789(f310(x38441),x38443),x38444)),x38445),f789(f789(f110(f870(x38442,a856)),f789(x38445,x38443)),f789(f789(f53(x38441,f870(x38442,a856)),x38444),x38445)))
% 21.40/21.36 [3845]E(f789(f789(f54(x38451,f870(x38452,a856)),f789(f789(f310(x38451),x38453),x38454)),x38455),f789(f789(f111(f870(x38452,a856)),f789(x38455,x38453)),f789(f789(f54(x38451,f870(x38452,a856)),x38454),x38455)))
% 21.40/21.36 [3905]E(f789(f789(f110(f870(x39051,a856)),f789(f311(x39052,x39051,x39053),x39054)),f789(f311(x39052,x39051,x39053),x39055)),f789(f311(x39052,x39051,x39053),f789(f789(f110(f870(x39052,a856)),x39054),x39055)))
% 21.40/21.36 [3906]E(f789(f789(f110(f870(x39061,a856)),f789(f285(x39062,x39061,x39063),x39064)),f789(f285(x39062,x39061,x39063),x39065)),f789(f285(x39062,x39061,x39063),f789(f789(f110(f870(x39062,a856)),x39064),x39065)))
% 21.40/21.36 [3907]E(f789(f789(f3(f870(x39071,a856)),f789(f313(x39071,x39072,x39073),x39074)),f789(f313(x39071,x39072,x39073),x39075)),f789(f313(x39071,x39072,x39073),f789(f789(f3(f870(x39072,a856)),x39074),x39075)))
% 21.40/21.36 [3908]E(f789(f789(f110(f870(x39081,a856)),f789(f313(x39081,x39082,x39083),x39084)),f789(f313(x39081,x39082,x39083),x39085)),f789(f313(x39081,x39082,x39083),f789(f789(f110(f870(x39082,a856)),x39084),x39085)))
% 21.40/21.36 [3909]E(f789(f789(f111(f870(x39091,a856)),f789(f313(x39091,x39092,x39093),x39094)),f789(f313(x39091,x39092,x39093),x39095)),f789(f313(x39091,x39092,x39093),f789(f789(f111(f870(x39092,a856)),x39094),x39095)))
% 21.40/21.36 [3911]E(f177(x39111,x39112,f177(x39111,x39112,x39113,x39114),x39115),f177(x39111,x39112,x39113,f789(f789(f111(f870(x39111,a856)),x39114),x39115)))
% 21.40/21.36 [3913]E(f125(x39131,x39132,f789(x39133,x39134),f789(f789(f9(x39131,a108,f865(x39132)),x39135),x39134)),f789(f199(x39131,x39132,x39133,x39135),x39134))
% 21.40/21.36 [3971]E(f789(f789(f155(x39711,f789(f789(f132(x39711),x39712),f789(f789(f146(x39711),x39713),x39714))),f789(f185(f864(x39711)),x39712)),x39715),f789(f789(f132(x39711),x39712),f789(f789(f146(x39711),x39715),x39714)))
% 21.40/21.36 [3977]E(f789(f789(f54(x39771,f870(x39772,a856)),x39773),f789(f789(f10(f870(x39772,a856),f870(x39772,a856),x39771),f789(f310(x39772),x39774)),x39775)),f789(f789(f310(x39772),x39774),f789(f789(f54(x39771,f870(x39772,a856)),x39773),x39775)))
% 21.40/21.36 [3978]E(f789(f789(f54(x39781,f870(x39782,a856)),x39783),f789(f789(f10(f870(x39782,a856),f870(x39782,a856),x39781),f789(f310(x39782),x39784)),x39785)),f789(f789(f310(x39782),x39784),f789(f789(f54(x39781,f870(x39782,a856)),x39783),x39785)))
% 21.40/21.36 [4049]E(f177(x40491,x40492,f789(f789(f789(f81(x40491,f867(x40492)),x40493),x40494),f789(f234(x40492),x40495)),f789(f88(f870(x40491,a856)),f789(f789(f310(x40491),x40494),f184(f870(x40491,a856))))),f177(x40491,x40492,x40493,f789(f88(f870(x40491,a856)),f789(f789(f310(x40491),x40494),f184(f870(x40491,a856))))))
% 21.40/21.36 [4092]E(f789(f789(f3(f870(f869(x40921,x40922),a856)),f789(f789(f256(x40921,x40922),x40923),f789(f18(f870(x40922,a856),x40921),x40924))),f789(f789(f256(x40921,x40922),x40925),f789(f18(f870(x40922,a856),x40921),x40924))),f789(f789(f256(x40921,x40922),f789(f789(f3(f870(x40921,a856)),x40923),x40925)),f789(f18(f870(x40922,a856),x40921),x40924)))
% 21.40/21.36 [4093]E(f789(f789(f110(f870(f869(x40931,x40932),a856)),f789(f789(f256(x40931,x40932),x40933),f789(f18(f870(x40932,a856),x40931),x40934))),f789(f789(f256(x40931,x40932),x40935),f789(f18(f870(x40932,a856),x40931),x40934))),f789(f789(f256(x40931,x40932),f789(f789(f110(f870(x40931,a856)),x40933),x40935)),f789(f18(f870(x40932,a856),x40931),x40934)))
% 21.40/21.36 [4094]E(f789(f789(f111(f870(f869(x40941,x40942),a856)),f789(f789(f256(x40941,x40942),x40943),f789(f18(f870(x40942,a856),x40941),x40944))),f789(f789(f256(x40941,x40942),x40945),f789(f18(f870(x40942,a856),x40941),x40944))),f789(f789(f256(x40941,x40942),f789(f789(f111(f870(x40941,a856)),x40943),x40945)),f789(f18(f870(x40942,a856),x40941),x40944)))
% 21.40/21.36 [4136]E(f789(f789(f150(x41361,x41362),x41363),f789(f133(x41361,f789(f82(x41362,a856,x41361,x41364),x41363)),x41365)),f789(f133(x41362,x41364),f789(f789(f150(x41361,x41362),x41363),x41365)))
% 21.40/21.36 [4142]E(f789(f185(f864(x41421)),f789(f133(x41421,x41422),f789(f789(f150(x41423,x41421),x41424),x41425))),f789(f185(f864(x41423)),f789(f133(x41423,f789(f82(x41421,a856,x41423,x41422),x41424)),x41425)))
% 21.40/21.36 [4277]E(f789(f789(f110(f870(x42771,a856)),f789(f789(f3(f870(x42771,a856)),f173(x42771,x42772,x42773)),f789(f264(x42771),f789(f789(f9(x42771,f870(x42771,a856),a856),f342(x42771)),f789(f789(f3(f870(x42771,a856)),x42774),f173(x42771,x42772,x42775)))))),f789(f264(x42771),f789(f789(f9(x42771,f870(x42771,a856),a856),f342(x42771)),f789(f789(f111(f870(x42771,a856)),x42774),f173(x42771,x42772,x42775))))),f173(x42771,x42772,f85(x42771,f867(x42772),x42773,x42775,x42774)))
% 21.40/21.36 [4348]E(f789(f152(f864(f869(x43481,x43482)),x43482,f122(f869(x43481,x43482)),f789(f789(f9(x43482,f870(f864(x43482),f864(f869(x43481,x43482))),f870(f864(x43482),f864(f869(x43481,x43482)))),f789(f789(f10(f870(f864(f869(x43481,x43482)),f864(f869(x43481,x43482))),f870(f870(f864(x43482),f864(f869(x43481,x43482))),f870(f864(x43482),f864(f869(x43481,x43482)))),x43482),f10(f864(f869(x43481,x43482)),f864(f869(x43481,x43482)),f864(x43482))),f789(f789(f10(f869(x43481,x43482),f870(f864(f869(x43481,x43482)),f864(f869(x43481,x43482))),x43482),f146(f869(x43481,x43482))),f789(f249(x43481,x43482),x43483)))),f789(f171(x43481,x43482),x43484))),x43485),f789(f789(f171(x43481,x43482),f789(f789(f146(x43481),x43483),x43484)),x43485))
% 21.40/21.36 [3839]E(f789(f789(f155(x38391,f789(f789(f155(x38391,x38392),x38393),x38394)),x38393),x38395),f789(f789(f155(x38391,x38392),x38393),x38395))
% 21.40/21.36 [3887]E(f789(f267(x38871,x38872),f789(f789(f310(f869(x38871,x38872)),f789(f789(f249(x38871,x38872),x38873),x38874)),x38875)),f789(f789(f310(x38872),x38874),f789(f267(x38871,x38872),x38875)))
% 21.40/21.36 [3888]E(f789(f269(x38881,x38882),f789(f789(f310(f869(x38881,x38882)),f789(f789(f249(x38881,x38882),x38883),x38884)),x38885)),f789(f789(f310(x38881),x38883),f789(f269(x38881,x38882),x38885)))
% 21.40/21.36 [3936]E(f129(x39361,x39362,f789(x39363,x39364),f789(f789(f9(x39361,a108,f865(f867(x39362))),x39365),x39364)),f789(f197(x39361,x39362,x39363,x39365),x39364))
% 21.40/21.36 [3964]E(f789(f789(f3(f870(f869(x39641,x39642),a856)),f789(f789(f256(x39641,x39642),x39643),x39644)),f789(f789(f256(x39641,x39642),x39645),x39644)),f789(f789(f256(x39641,x39642),f789(f789(f3(f870(x39641,a856)),x39643),x39645)),x39644))
% 21.40/21.36 [3965]E(f789(f789(f110(f870(f869(x39651,x39652),a856)),f789(f789(f256(x39651,x39652),x39653),x39654)),f789(f789(f256(x39651,x39652),x39655),x39654)),f789(f789(f256(x39651,x39652),f789(f789(f110(f870(x39651,a856)),x39653),x39655)),x39654))
% 21.40/21.36 [3966]E(f789(f789(f111(f870(f869(x39661,x39662),a856)),f789(f789(f256(x39661,x39662),x39663),x39664)),f789(f789(f256(x39661,x39662),x39665),x39664)),f789(f789(f256(x39661,x39662),f789(f789(f111(f870(x39661,a856)),x39663),x39665)),x39664))
% 21.40/21.36 [4027]E(f789(f789(f110(f870(x40271,a856)),f789(f789(f53(x40272,f870(x40271,a856)),x40273),x40274)),f789(f789(f53(x40272,f870(x40271,a856)),x40275),x40274)),f789(f789(f53(x40272,f870(x40271,a856)),f789(f789(f110(f870(x40272,a856)),x40273),x40275)),x40274))
% 21.40/21.36 [4028]E(f789(f789(f111(f870(x40281,a856)),f789(f789(f54(x40282,f870(x40281,a856)),x40283),x40284)),f789(f789(f54(x40282,f870(x40281,a856)),x40285),x40284)),f789(f789(f54(x40282,f870(x40281,a856)),f789(f789(f110(f870(x40282,a856)),x40283),x40285)),x40284))
% 21.40/21.36 [4037]E(f789(f789(f53(x40371,f870(x40372,a856)),x40373),f789(f789(f10(f870(x40372,a856),f870(x40372,a856),x40371),f789(f3(f870(x40372,a856)),x40374)),x40375)),f789(f789(f3(f870(x40372,a856)),x40374),f789(f789(f54(x40371,f870(x40372,a856)),x40373),x40375)))
% 21.40/21.36 [4038]E(f789(f789(f54(x40381,f870(x40382,a856)),x40383),f789(f789(f10(f870(x40382,a856),f870(x40382,a856),x40381),f789(f110(f870(x40382,a856)),x40384)),x40385)),f789(f789(f110(f870(x40382,a856)),x40384),f789(f789(f54(x40381,f870(x40382,a856)),x40383),x40385)))
% 21.40/21.36 [4039]E(f789(f789(f54(x40391,f870(x40392,a856)),x40393),f789(f789(f10(f870(x40392,a856),f870(x40392,a856),x40391),f789(f110(f870(x40392,a856)),x40394)),x40395)),f789(f789(f110(f870(x40392,a856)),x40394),f789(f789(f54(x40391,f870(x40392,a856)),x40393),x40395)))
% 21.40/21.36 [4040]E(f789(f789(f53(x40401,f870(x40402,a856)),x40403),f789(f789(f10(f870(x40402,a856),f870(x40402,a856),x40401),f789(f111(f870(x40402,a856)),x40404)),x40405)),f789(f789(f111(f870(x40402,a856)),x40404),f789(f789(f53(x40401,f870(x40402,a856)),x40403),x40405)))
% 21.40/21.36 [4041]E(f789(f789(f53(x40411,f870(x40412,a856)),x40413),f789(f789(f10(f870(x40412,a856),f870(x40412,a856),x40411),f789(f111(f870(x40412,a856)),x40414)),x40415)),f789(f789(f111(f870(x40412,a856)),x40414),f789(f789(f53(x40411,f870(x40412,a856)),x40413),x40415)))
% 21.40/21.36 [4042]E(f789(f789(f53(x40421,f870(x40422,a856)),x40423),f789(f789(f10(f870(x40422,a856),f870(x40422,a856),x40421),f789(f3(f870(x40422,a856)),x40424)),x40425)),f789(f789(f3(f870(x40422,a856)),x40424),f789(f789(f54(x40421,f870(x40422,a856)),x40423),x40425)))
% 21.40/21.36 [4043]E(f789(f789(f53(x40431,f870(x40432,a856)),x40433),f789(f789(f10(f870(x40432,a856),f870(x40432,a856),x40431),f789(f111(f870(x40432,a856)),x40434)),x40435)),f789(f789(f111(f870(x40432,a856)),x40434),f789(f789(f53(x40431,f870(x40432,a856)),x40433),x40435)))
% 21.40/21.36 [4044]E(f789(f789(f54(x40441,f870(x40442,a856)),x40443),f789(f789(f10(f870(x40442,a856),f870(x40442,a856),x40441),f789(f110(f870(x40442,a856)),x40444)),x40445)),f789(f789(f110(f870(x40442,a856)),x40444),f789(f789(f54(x40441,f870(x40442,a856)),x40443),x40445)))
% 21.40/21.36 [4102]E(f180(f864(x41021),f789(f789(f146(x41021),x41022),x41023),f789(f789(f10(f864(x41021),f864(x41021),a863),f789(f146(x41021),x41024)),f789(f789(f9(a863,x41021,f864(x41021)),f155(x41021,x41023)),x41022)),x41025),f789(f789(f155(x41021,f789(f789(f146(x41021),x41024),x41023)),x41025),x41022))
% 21.40/21.36 [4105]E(f789(f789(f53(x41051,f870(f869(x41052,x41053),a856)),x41054),f789(f789(f10(f870(f869(x41053,x41052),a856),f870(f869(x41052,x41053),a856),x41051),f286(x41053,x41052)),x41055)),f789(f286(x41053,x41052),f789(f789(f53(x41051,f870(f869(x41053,x41052),a856)),x41054),x41055)))
% 21.40/21.36 [4106]E(f789(f789(f54(x41061,f870(f869(x41062,x41063),a856)),x41064),f789(f789(f10(f870(f869(x41063,x41062),a856),f870(f869(x41062,x41063),a856),x41061),f286(x41063,x41062)),x41065)),f789(f286(x41063,x41062),f789(f789(f54(x41061,f870(f869(x41063,x41062),a856)),x41064),x41065)))
% 21.40/21.36 [4160]E(f173(x41601,x41602,f789(f789(f20(x41601,f867(x41603),f867(x41602)),f789(f789(f10(f870(x41603,x41602),f870(f867(x41603),f867(x41602)),x41601),f203(x41603,x41602)),x41604)),x41605)),f173(x41601,x41603,x41605))
% 21.40/21.36 [4212]P1(f789(f789(f240(f870(x42121,a856)),f789(f789(f3(f870(x42121,a856)),f789(f311(x42122,x42121,x42123),x42124)),f789(f311(x42122,x42121,x42123),x42125))),f789(f311(x42122,x42121,x42123),f789(f789(f3(f870(x42122,a856)),x42124),x42125))))
% 21.40/21.36 [4352]E(f789(f152(f864(f869(x43521,x43522)),x43521,f122(f869(x43521,x43522)),f789(f789(f9(x43521,f870(f864(x43521),f864(f869(x43521,x43522))),f870(f864(x43521),f864(f869(x43521,x43522)))),f789(f789(f10(f870(f864(f869(x43521,x43522)),f864(f869(x43521,x43522))),f870(f870(f864(x43521),f864(f869(x43521,x43522))),f870(f864(x43521),f864(f869(x43521,x43522)))),x43521),f10(f864(f869(x43521,x43522)),f864(f869(x43521,x43522)),f864(x43521))),f789(f789(f10(f869(x43521,x43522),f870(f864(f869(x43521,x43522)),f864(f869(x43521,x43522))),x43521),f146(f869(x43521,x43522))),f789(f789(f9(x43521,x43522,f869(x43521,x43522)),f249(x43521,x43522)),x43523)))),f789(f789(f9(f864(x43521),f864(x43522),f864(f869(x43521,x43522))),f171(x43521,x43522)),x43524))),x43525),f789(f789(f171(x43521,x43522),x43525),f789(f789(f146(x43522),x43523),x43524)))
% 21.40/21.36 [4068]E(f789(f789(f110(f870(x40681,a856)),f789(f285(x40682,x40681,x40683),x40684)),f789(f285(x40682,x40681,x40685),x40684)),f789(f285(x40682,x40681,f789(f789(f110(f870(f869(x40682,x40681),a856)),x40683),x40685)),x40684))
% 21.40/21.36 [4108]E(f789(f789(f132(f869(x41081,x41082)),f789(f789(f171(x41081,x41082),x41083),f789(f789(f164(x41082),f789(f185(f864(x41081)),x41083)),x41084))),f789(f789(f171(x41081,x41082),x41085),f789(f789(f135(x41082),f789(f185(f864(x41081)),x41083)),x41084))),f789(f789(f171(x41081,x41082),f789(f789(f132(x41081),x41083),x41085)),x41084))
% 21.40/21.36 [4215]E(f789(f789(f256(x42151,x42152),x42153),f789(f789(f20(x42151,f870(x42152,a856),f870(x42152,a856)),f789(f789(f10(f870(x42152,a856),f870(f870(x42152,a856),f870(x42152,a856)),x42151),f3(f870(x42152,a856))),x42154)),x42155)),f789(f789(f3(f870(f869(x42151,x42152),a856)),f789(f789(f256(x42151,x42152),x42153),x42154)),f789(f789(f256(x42151,x42152),x42153),x42155)))
% 21.40/21.36 [4216]E(f789(f789(f256(x42161,x42162),x42163),f789(f789(f20(x42161,f870(x42162,a856),f870(x42162,a856)),f789(f789(f10(f870(x42162,a856),f870(f870(x42162,a856),f870(x42162,a856)),x42161),f110(f870(x42162,a856))),x42164)),x42165)),f789(f789(f110(f870(f869(x42161,x42162),a856)),f789(f789(f256(x42161,x42162),x42163),x42164)),f789(f789(f256(x42161,x42162),x42163),x42165)))
% 21.40/21.36 [4217]E(f789(f789(f256(x42171,x42172),x42173),f789(f789(f20(x42171,f870(x42172,a856),f870(x42172,a856)),f789(f789(f10(f870(x42172,a856),f870(f870(x42172,a856),f870(x42172,a856)),x42171),f111(f870(x42172,a856))),x42174)),x42175)),f789(f789(f111(f870(f869(x42171,x42172),a856)),f789(f789(f256(x42171,x42172),x42173),x42174)),f789(f789(f256(x42171,x42172),x42173),x42175)))
% 21.40/21.36 [4218]E(f789(f789(f53(x42181,f870(x42182,a856)),x42183),f789(f789(f9(x42181,f870(x42182,a856),f870(x42182,a856)),f789(f789(f10(f870(x42182,a856),f870(f870(x42182,a856),f870(x42182,a856)),x42181),f3(f870(x42182,a856))),x42184)),x42185)),f789(f789(f3(f870(x42182,a856)),f789(f789(f53(x42181,f870(x42182,a856)),x42183),x42184)),x42185))
% 21.40/21.36 [4219]E(f789(f789(f54(x42191,f870(x42192,a856)),x42193),f789(f789(f9(x42191,f870(x42192,a856),f870(x42192,a856)),f789(f789(f10(f870(x42192,a856),f870(f870(x42192,a856),f870(x42192,a856)),x42191),f110(f870(x42192,a856))),x42194)),x42195)),f789(f789(f110(f870(x42192,a856)),f789(f789(f54(x42191,f870(x42192,a856)),x42193),x42194)),x42195))
% 21.40/21.36 [4220]E(f789(f789(f53(x42201,f870(x42202,a856)),x42203),f789(f789(f9(x42201,f870(x42202,a856),f870(x42202,a856)),f789(f789(f10(f870(x42202,a856),f870(f870(x42202,a856),f870(x42202,a856)),x42201),f111(f870(x42202,a856))),x42204)),x42205)),f789(f789(f111(f870(x42202,a856)),f789(f789(f53(x42201,f870(x42202,a856)),x42203),x42204)),x42205))
% 21.40/21.36 [4221]E(f789(f789(f53(x42211,f870(x42212,a856)),x42213),f789(f789(f9(x42211,f870(x42212,a856),f870(x42212,a856)),f789(f789(f10(f870(x42212,a856),f870(f870(x42212,a856),f870(x42212,a856)),x42211),f3(f870(x42212,a856))),x42214)),x42215)),f789(f789(f3(f870(x42212,a856)),f789(f789(f53(x42211,f870(x42212,a856)),x42213),x42214)),x42215))
% 21.40/21.36 [4222]E(f789(f789(f53(x42221,f870(x42222,a856)),x42223),f789(f789(f9(x42221,f870(x42222,a856),f870(x42222,a856)),f789(f789(f10(f870(x42222,a856),f870(f870(x42222,a856),f870(x42222,a856)),x42221),f111(f870(x42222,a856))),x42224)),x42225)),f789(f789(f111(f870(x42222,a856)),f789(f789(f53(x42221,f870(x42222,a856)),x42223),x42224)),x42225))
% 21.40/21.36 [4223]E(f789(f789(f54(x42231,f870(x42232,a856)),x42233),f789(f789(f9(x42231,f870(x42232,a856),f870(x42232,a856)),f789(f789(f10(f870(x42232,a856),f870(f870(x42232,a856),f870(x42232,a856)),x42231),f110(f870(x42232,a856))),x42234)),x42235)),f789(f789(f110(f870(x42232,a856)),f789(f789(f54(x42231,f870(x42232,a856)),x42233),x42234)),x42235))
% 21.40/21.36 [4227]E(f789(f789(f53(x42271,f870(x42272,a856)),x42273),f789(f789(f20(x42271,f870(x42272,a856),f870(x42272,a856)),f789(f789(f10(f870(x42272,a856),f870(f870(x42272,a856),f870(x42272,a856)),x42271),f110(f870(x42272,a856))),x42274)),x42275)),f789(f789(f110(f870(x42272,a856)),f789(f789(f53(x42271,f870(x42272,a856)),x42273),x42274)),f789(f789(f53(x42271,f870(x42272,a856)),x42273),x42275)))
% 21.40/21.36 [4228]E(f789(f789(f54(x42281,f870(x42282,a856)),x42283),f789(f789(f20(x42281,f870(x42282,a856),f870(x42282,a856)),f789(f789(f10(f870(x42282,a856),f870(f870(x42282,a856),f870(x42282,a856)),x42281),f111(f870(x42282,a856))),x42284)),x42285)),f789(f789(f111(f870(x42282,a856)),f789(f789(f54(x42281,f870(x42282,a856)),x42283),x42284)),f789(f789(f54(x42281,f870(x42282,a856)),x42283),x42285)))
% 21.40/21.36 [4240]E(f789(f789(f53(x42401,f870(x42402,a856)),x42403),f789(f789(f20(x42401,f870(x42402,a856),f870(x42402,a856)),f789(f789(f10(f870(x42402,a856),f870(f870(x42402,a856),f870(x42402,a856)),x42401),f110(f870(x42402,a856))),x42404)),x42405)),f789(f789(f110(f870(x42402,a856)),f51(f870(x42402,a856),f789(f311(x42401,f870(x42402,a856),x42404),x42403))),f51(f870(x42402,a856),f789(f311(x42401,f870(x42402,a856),x42405),x42403))))
% 21.40/21.36 [4241]E(f789(f789(f54(x42411,f870(x42412,a856)),x42413),f789(f789(f20(x42411,f870(x42412,a856),f870(x42412,a856)),f789(f789(f10(f870(x42412,a856),f870(f870(x42412,a856),f870(x42412,a856)),x42411),f111(f870(x42412,a856))),x42414)),x42415)),f789(f789(f111(f870(x42412,a856)),f52(f870(x42412,a856),f789(f311(x42411,f870(x42412,a856),x42414),x42413))),f52(f870(x42412,a856),f789(f311(x42411,f870(x42412,a856),x42415),x42413))))
% 21.40/21.36 [4150]E(f789(f789(f132(f869(x41501,x41502)),f789(f789(f171(x41501,x41502),f789(f789(f164(x41501),f789(f185(f864(x41502)),x41503)),x41504)),x41503)),f789(f789(f171(x41501,x41502),f789(f789(f135(x41501),f789(f185(f864(x41502)),x41503)),x41504)),x41505)),f789(f789(f171(x41501,x41502),x41504),f789(f789(f132(x41502),x41503),x41505)))
% 21.40/21.36 [4266]E(f94(x42661,f789(f789(f20(x42661,a856,a856),f789(f789(f10(a856,f870(a856,a856),x42661),a339),f789(f789(f9(x42661,f870(x42661,a856),a856),f342(x42661)),x42662))),f789(f789(f9(x42661,x42663,a856),f789(f789(f10(x42663,f870(x42663,a856),x42661),a338),x42664)),x42665))),f789(f86(x42661,x42663,x42662,x42664),x42665))
% 21.40/21.36 [4315]E(f789(f789(f95(a1,x43151),f789(f113(a1),f789(f789(f89(a1),x43152),a106))),f789(f789(f20(a1,x43151,x43151),f789(f789(f9(a1,x43151,f870(x43151,x43151)),f789(f789(f10(a856,f870(x43151,f870(x43151,x43151)),a1),f105(x43151)),a190)),f180(x43151,x43153,x43154,x43155))),f789(f789(f10(a863,x43151,a1),x43154),f789(f789(f9(a1,a863,a863),f789(f789(f10(a863,f870(a863,a863),a1),f89(a863)),a114)),x43155)))),f180(x43151,x43153,x43154,f789(f789(f89(a863),f789(f113(a863),x43152)),x43155)))
% 21.40/21.36 [4349]E(f170(x43491,x43492,f789(f789(f150(f869(x43491,x43493),f869(x43491,x43492)),f789(f259(x43491,x43493,f869(x43491,x43492)),f789(f789(f9(x43491,f870(x43493,x43492),f870(x43493,f869(x43491,x43492))),f789(f789(f10(f870(x43492,f869(x43491,x43492)),f870(f870(x43493,x43492),f870(x43493,f869(x43491,x43492))),x43491),f10(x43492,f869(x43491,x43492),x43493)),f249(x43491,x43492))),x43494))),x43495)),f789(f82(f867(x43493),f867(x43492),x43491,f789(f203(x43493,x43492),x43494)),f170(x43491,x43493,x43495)))
% 21.40/21.36 [4308]E(f173(x43081,x43082,f789(f789(f20(x43081,f867(x43082),f867(x43082)),f789(f789(f20(x43081,f867(x43082),f870(f867(x43082),f867(x43082))),f789(f789(f10(a856,f870(f867(x43082),f870(f867(x43082),f867(x43082))),x43081),f105(f867(x43082))),x43083)),x43084)),x43085)),f789(f789(f110(f870(x43081,a856)),f789(f789(f111(f870(x43081,a856)),f173(x43081,x43082,x43084)),f789(f264(x43081),x43083))),f789(f789(f111(f870(x43081,a856)),f173(x43081,x43082,x43085)),f789(f264(x43081),f789(f789(f10(a856,a856,x43081),a336),x43083)))))
% 21.40/21.36 [4347]E(f789(f789(f95(a1,x43471),f789(f113(a1),f789(f789(f89(a1),x43472),a106))),f789(f789(f20(a1,x43471,x43471),f789(f789(f9(a1,x43471,f870(x43471,x43471)),f789(f789(f10(a856,f870(x43471,f870(x43471,x43471)),a1),f105(x43471)),a190)),f789(f179(x43471,x43473,x43474),x43475))),f789(f789(f20(a1,x43471,x43471),f789(f789(f10(a863,f870(x43471,x43471),a1),x43474),f789(f789(f9(a1,a863,a863),f789(f789(f10(a863,f870(a863,a863),a1),f89(a863)),a114)),x43475))),f789(f789(f10(a863,x43471,a1),f179(x43471,x43473,x43474)),f789(f789(f9(a1,a863,a863),f789(f789(f10(a863,f870(a863,a863),a1),f89(a863)),a114)),x43475))))),f789(f179(x43471,x43473,x43474),f789(f789(f89(a863),f789(f113(a863),x43472)),x43475)))
% 21.40/21.36 [4396]E(f789(f264(f869(x43961,x43962)),f789(f259(x43961,x43962,a856),f789(f789(f10(f870(x43962,f870(x43963,a856)),f870(x43962,a856),x43961),f789(f10(f870(x43963,a856),a856,x43962),f96(x43963))),f789(f789(f9(x43961,f870(x43962,f870(x43963,a856)),f870(x43962,f870(x43963,a856))),f789(f789(f10(f870(f870(x43963,a856),f870(x43963,a856)),f870(f870(x43962,f870(x43963,a856)),f870(x43962,f870(x43963,a856))),x43961),f10(f870(x43963,a856),f870(x43963,a856),x43962)),f789(f789(f10(f870(x43963,f870(a856,a856)),f870(f870(x43963,a856),f870(x43963,a856)),x43961),f20(x43963,a856,a856)),f789(f789(f10(f870(x43963,a856),f870(x43963,f870(a856,a856)),x43961),f789(f10(a856,f870(a856,a856),x43963),a339)),f789(f789(f9(x43961,f870(f869(x43961,x43963),a856),f870(x43963,a856)),f789(f789(f10(f870(x43963,f870(f870(f869(x43961,x43963),a856),a856)),f870(f870(f869(x43961,x43963),a856),f870(x43963,a856)),x43961),f9(x43963,f870(f869(x43961,x43963),a856),a856)),f789(f789(f10(f870(x43963,f869(x43961,x43963)),f870(x43963,f870(f870(f869(x43961,x43963),a856),a856)),x43961),f789(f10(f869(x43961,x43963),f870(f870(f869(x43961,x43963),a856),a856),x43963),f342(f869(x43961,x43963)))),f249(x43961,x43963)))),x43964))))),f789(f789(f9(x43962,f870(f869(x43963,x43962),a856),f870(x43963,a856)),f789(f789(f10(f870(x43963,f870(f870(f869(x43963,x43962),a856),a856)),f870(f870(f869(x43963,x43962),a856),f870(x43963,a856)),x43962),f9(x43963,f870(f869(x43963,x43962),a856),a856)),f789(f789(f10(f870(x43963,f869(x43963,x43962)),f870(x43963,f870(f870(f869(x43963,x43962),a856),a856)),x43962),f789(f10(f869(x43963,x43962),f870(f870(f869(x43963,x43962),a856),a856),x43963),f342(f869(x43963,x43962)))),f789(f9(x43963,x43962,f869(x43963,x43962)),f249(x43963,x43962))))),x43965))))),f789(f789(f289(x43961,x43963,x43962),x43964),x43965))
% 21.40/21.36 [4499]~E(f34(x44991,x44992,x44993),f35(x44994,x44995,x44996))
% 21.40/21.36 [4500]~E(f34(x45001,x45002,x45003),f35(x45004,x45005,x45006))
% 21.40/21.36 [4501]~E(f33(x45011,x45012,x45013),f35(x45014,x45015,x45016))
% 21.40/21.36 [4502]~E(f33(x45021,x45022,x45023),f34(x45024,x45025,x45026))
% 21.40/21.36 [4503]~E(f33(x45031,x45032,x45033),f35(x45034,x45035,x45036))
% 21.40/21.36 [4504]~E(f33(x45041,x45042,x45043),f34(x45044,x45045,x45046))
% 21.40/21.36 [3994]E(f225(x39941,x39942,x39943,x39944,f222(x39941,x39942,x39945,x39946)),f789(f789(x39944,x39945),x39946))
% 21.40/21.36 [3995]E(f226(x39951,x39952,x39953,x39954,f222(x39951,x39952,x39955,x39956)),f789(f789(x39954,x39955),x39956))
% 21.40/21.36 [4134]E(f176(x41341,x41342,f174(x41341,x41342,x41343,x41344),x41345,x41346),f174(x41341,x41342,x41343,f176(x41341,x41342,x41344,x41345,x41346)))
% 21.40/21.36 [4256]E(f789(f82(f869(x42561,x42562),x42562,f869(x42563,x42564),f258(x42561,x42562)),f260(x42563,x42561,x42564,x42562,x42565,x42566)),f789(f82(x42564,x42562,f869(x42563,x42564),x42566),f258(x42563,x42564)))
% 21.40/21.36 [4257]E(f789(f82(f869(x42571,x42572),x42571,f869(x42573,x42574),f248(x42571,x42572)),f260(x42573,x42571,x42574,x42572,x42575,x42576)),f789(f82(x42573,x42571,f869(x42573,x42574),x42575),f248(x42573,x42574)))
% 21.40/21.36 [3862]E(f789(f789(f82(x38621,x38622,x38623,x38624),x38625),x38626),f789(x38624,f789(x38625,x38626)))
% 21.40/21.36 [3863]E(f789(f789(f82(x38631,x38632,x38633,x38634),x38635),x38636),f789(x38634,f789(x38635,x38636)))
% 21.40/21.36 [4057]E(f227(x40571,x40572,x40573,x40574,f222(x40571,x40572,x40575,x40576)),f789(f789(f89(a863),f789(f789(f89(a863),f789(x40573,x40575)),f789(x40574,x40576))),f789(a121,f2(a863))))
% 21.40/21.36 [4078]E(f789(f327(x40781,x40782,x40783,x40784,x40785),f789(f312(x40781,x40783),x40786)),f789(x40784,x40786))
% 21.40/21.36 [4079]E(f789(f327(x40791,x40792,x40793,x40794,x40795),f789(f321(x40793,x40791),x40796)),f789(x40795,x40796))
% 21.40/21.36 [4173]E(f328(x41731,x41732,x41733,x41734,x41735,f789(f312(x41731,x41733),x41736)),f789(x41734,x41736))
% 21.40/21.36 [4174]E(f328(x41741,x41742,x41743,x41744,x41745,f789(f321(x41743,x41741),x41746)),f789(x41745,x41746))
% 21.40/21.36 [3660]E(f789(f789(f259(x36601,x36602,x36603),x36604),f789(f789(f249(x36601,x36602),x36605),x36606)),f789(f789(x36604,x36605),x36606))
% 21.40/21.36 [3661]E(f789(f789(f259(x36611,x36612,x36613),x36614),f789(f789(f249(x36611,x36612),x36615),x36616)),f789(f789(x36614,x36615),x36616))
% 21.40/21.36 [3662]E(f789(f789(f259(x36621,x36622,x36623),x36624),f789(f789(f249(x36621,x36622),x36625),x36626)),f789(f789(x36624,x36625),x36626))
% 21.40/21.36 [3725]E(f789(f789(f789(f10(x37251,x37252,x37253),x37254),x37255),x37256),f789(x37254,f789(x37255,x37256)))
% 21.40/21.36 [3726]E(f789(f789(f789(f9(x37261,x37262,x37263),x37264),x37265),x37266),f789(f789(x37264,x37266),x37265))
% 21.40/21.36 [3742]E(f789(f789(f789(f20(x37421,x37422,x37423),x37424),x37425),x37426),f789(f789(x37424,x37426),f789(x37425,x37426)))
% 21.40/21.36 [3766]E(f789(f152(x37661,x37662,x37663,x37664),f789(f789(f146(x37662),x37665),x37666)),f789(f789(x37664,x37665),x37666))
% 21.40/21.36 [3866]E(f789(f789(f146(f869(x38661,x38662)),f789(f789(f249(x38661,x38662),x38663),x38664)),f789(f789(f171(x38661,x38662),x38665),x38666)),f789(f789(f171(x38661,x38662),f789(f789(f146(x38661),x38663),x38665)),f789(f789(f146(x38662),x38664),x38666)))
% 21.40/21.36 [3868]E(f789(f789(f150(x38681,x38682),x38683),f789(f789(f155(x38681,x38684),x38685),x38686)),f789(f789(f155(x38682,f789(f789(f150(x38681,x38682),x38683),x38684)),x38685),f789(x38683,x38686)))
% 21.40/21.36 [3892]E(f789(f789(f257(x38921,x38922,x38923,x38924),x38925),x38926),f789(x38924,f789(f789(f249(x38921,x38922),x38925),x38926)))
% 21.40/21.36 [3893]E(f789(f789(f257(x38931,x38932,x38933,x38934),x38935),x38936),f789(x38934,f789(f789(f249(x38931,x38932),x38935),x38936)))
% 21.40/21.36 [3910]E(f789(f138(x39101,x39102,x39103,x39104),f789(f789(f146(x39102),x39105),x39106)),f789(f138(x39101,x39102,x39103,f789(f789(x39103,x39104),x39105)),x39106))
% 21.40/21.36 [3937]E(f262(x39371,x39372,x39373,x39374,f789(f789(f249(x39371,x39372),x39375),x39376)),f789(f789(x39374,x39375),x39376))
% 21.40/21.36 [4020]E(f789(f789(f53(x40201,f870(x40202,a856)),x40203),f789(f82(x40204,f870(x40202,a856),x40201,x40205),x40206)),f789(f789(f53(x40204,f870(x40202,a856)),f789(f311(x40201,x40204,x40206),x40203)),x40205))
% 21.40/21.36 [4070]E(f789(f789(f150(x40701,x40702),x40703),f789(f789(f150(x40704,x40701),x40705),x40706)),f789(f789(f150(x40704,x40702),f789(f82(x40701,x40702,x40704,x40703),x40705)),x40706))
% 21.40/21.36 [4071]E(f789(f789(f150(x40711,x40712),x40713),f789(f789(f150(x40714,x40711),x40715),x40716)),f789(f789(f150(x40714,x40712),f789(f82(x40711,x40712,x40714,x40713),x40715)),x40716))
% 21.40/21.36 [4072]E(f789(f789(f203(x40721,x40722),x40723),f789(f789(f203(x40724,x40721),x40725),x40726)),f789(f789(f203(x40724,x40722),f789(f82(x40721,x40722,x40724,x40723),x40725)),x40726))
% 21.40/21.36 [4073]E(f789(f789(f203(x40731,x40732),x40733),f789(f789(f203(x40734,x40731),x40735),x40736)),f789(f789(f203(x40734,x40732),f789(f82(x40731,x40732,x40734,x40733),x40735)),x40736))
% 21.40/21.36 [4076]E(f789(f311(x40761,x40762,f789(f82(x40763,x40762,x40761,x40764),x40765)),x40766),f789(f311(x40763,x40762,x40764),f789(f311(x40761,x40763,x40765),x40766)))
% 21.40/21.36 [4077]E(f789(f313(x40771,x40772,f789(f82(x40773,x40772,x40771,x40774),x40775)),x40776),f789(f313(x40771,x40773,x40775),f789(f313(x40773,x40772,x40774),x40776)))
% 21.40/21.36 [4107]E(f174(x41071,x41072,x41073,f789(f789(f789(f81(x41071,f867(x41072)),x41074),x41075),f789(f234(x41072),x41076))),f789(f789(f789(f81(x41071,f867(x41072)),f174(x41071,x41072,x41073,x41074)),x41075),f789(f234(x41072),x41076)))
% 21.40/21.36 [4109]E(f789(f138(x41091,x41092,x41093,f789(f138(x41091,x41092,x41093,x41094),x41095)),x41096),f789(f138(x41091,x41092,x41093,x41094),f789(f789(f132(x41092),x41095),x41096)))
% 21.40/21.36 [4246]E(f789(f260(x42461,x42461,x42462,x42463,f41(x42461),x42464),f789(f789(f249(x42461,x42462),x42465),x42466)),f789(f789(f249(x42461,x42463),x42465),f789(x42464,x42466)))
% 21.40/21.36 [4247]E(f789(f260(x42471,x42472,x42473,x42473,x42474,f41(x42473)),f789(f789(f249(x42471,x42473),x42475),x42476)),f789(f789(f249(x42472,x42473),f789(x42474,x42475)),x42476))
% 21.40/21.36 [4331]E(f789(f789(f150(f869(x43311,x43312),f869(x43311,x43313)),f789(f259(x43311,x43312,f869(x43311,x43313)),f789(f789(f9(x43311,f870(x43312,x43313),f870(x43312,f869(x43311,x43313))),f789(f789(f10(f870(x43313,f869(x43311,x43313)),f870(f870(x43312,x43313),f870(x43312,f869(x43311,x43313))),x43311),f10(x43313,f869(x43311,x43313),x43312)),f249(x43311,x43313))),x43314))),f789(f789(f171(x43311,x43312),x43315),x43316)),f789(f789(f171(x43311,x43313),x43315),f789(f789(f150(x43312,x43313),x43314),x43316)))
% 21.40/21.36 [3730]E(f103(x37301,x37302,x37303,f789(f789(f789(f100(x37301),x37304),x37305),x37306)),f789(f789(f789(x37303,x37304),x37305),x37306))
% 21.40/21.36 [3731]E(f104(x37311,x37312,x37313,f789(f789(f789(f100(x37311),x37314),x37315),x37316)),f789(f789(f789(x37313,x37314),x37315),x37316))
% 21.40/21.36 [3920]E(f789(f789(f82(x39201,x39202,x39203,f789(f18(x39202,x39201),x39204)),x39205),x39206),x39204)
% 21.40/21.36 [3954]E(f789(f311(x39541,x39542,x39543),f789(f311(x39544,x39541,x39545),x39546)),f789(f311(x39544,x39542,f789(f789(f10(x39541,x39542,x39544),x39543),x39545)),x39546))
% 21.40/21.36 [3960]E(f789(f789(f53(x39601,f870(x39602,a856)),f789(f311(x39603,x39601,x39604),x39605)),x39606),f789(f789(f53(x39603,f870(x39602,a856)),x39605),f789(f789(f10(x39601,f870(x39602,a856),x39603),x39606),x39604)))
% 21.40/21.36 [3961]E(f789(f789(f54(x39611,f870(x39612,a856)),f789(f311(x39613,x39611,x39614),x39615)),x39616),f789(f789(f54(x39613,f870(x39612,a856)),x39615),f789(f789(f10(x39611,f870(x39612,a856),x39613),x39616),x39614)))
% 21.40/21.36 [3962]E(f789(f789(f53(x39621,f870(x39622,a856)),x39623),f789(f789(f10(x39624,f870(x39622,a856),x39621),x39625),x39626)),f789(f789(f53(x39624,f870(x39622,a856)),f789(f311(x39621,x39624,x39626),x39623)),x39625))
% 21.40/21.36 [3963]E(f789(f789(f54(x39631,f870(x39632,a856)),x39633),f789(f789(f10(x39634,f870(x39632,a856),x39631),x39635),x39636)),f789(f789(f54(x39634,f870(x39632,a856)),f789(f311(x39631,x39634,x39636),x39633)),x39635))
% 21.40/21.36 [4022]E(f789(f789(f53(x40221,f870(x40222,a856)),x40223),f789(f789(f10(f870(x40224,a856),f870(x40222,a856),x40221),f311(x40224,x40222,x40225)),x40226)),f789(f311(x40224,x40222,x40225),f789(f789(f53(x40221,f870(x40224,a856)),x40223),x40226)))
% 21.40/21.36 [4023]E(f789(f789(f53(x40231,f870(x40232,a856)),x40233),f789(f789(f10(f870(x40234,a856),f870(x40232,a856),x40231),f285(x40234,x40232,x40235)),x40236)),f789(f285(x40234,x40232,x40235),f789(f789(f53(x40231,f870(x40234,a856)),x40233),x40236)))
% 21.40/21.36 [4024]E(f789(f789(f53(x40241,f870(x40242,a856)),x40243),f789(f789(f10(f870(x40244,a856),f870(x40242,a856),x40241),f313(x40242,x40244,x40245)),x40246)),f789(f313(x40242,x40244,x40245),f789(f789(f53(x40241,f870(x40244,a856)),x40243),x40246)))
% 21.40/21.36 [4025]E(f789(f789(f54(x40251,f870(x40252,a856)),x40253),f789(f789(f10(f870(x40254,a856),f870(x40252,a856),x40251),f313(x40252,x40254,x40255)),x40256)),f789(f313(x40252,x40254,x40255),f789(f789(f54(x40251,f870(x40254,a856)),x40253),x40256)))
% 21.40/21.36 [4115]E(f789(f138(x41151,x41152,f789(f9(x41152,x41151,x41151),x41153),x41154),f789(f149(x41152),f789(f789(f146(x41152),x41155),x41156))),f789(f789(x41153,x41155),f789(f138(x41151,x41152,f789(f9(x41152,x41151,x41151),x41153),x41154),f789(f149(x41152),x41156))))
% 21.40/21.36 [4175]E(f789(f789(f20(f869(x41751,x41752),x41752,x41753),f789(f789(f10(x41754,f870(x41752,x41753),f869(x41751,x41752)),x41755),f789(f789(f10(x41751,x41754,f869(x41751,x41752)),x41756),f248(x41751,x41752)))),f258(x41751,x41752)),f789(f259(x41751,x41752,x41753),f789(f789(f10(x41754,f870(x41752,x41753),x41751),x41755),x41756)))
% 21.40/21.36 [4182]E(f789(f138(x41821,x41822,f789(f9(x41822,x41821,x41821),x41823),f789(f138(x41821,x41822,f789(f9(x41822,x41821,x41821),x41823),x41824),f789(f149(x41822),x41825))),f789(f149(x41822),x41826)),f789(f138(x41821,x41822,f789(f9(x41822,x41821,x41821),x41823),x41824),f789(f149(x41822),f789(f789(f132(x41822),x41826),x41825))))
% 21.40/21.36 [4184]E(f789(f789(f150(f869(x41841,x41842),f869(x41843,x41842)),f789(f259(x41841,x41842,f869(x41843,x41842)),f789(f789(f10(x41843,f870(x41842,f869(x41843,x41842)),x41841),f249(x41843,x41842)),x41844))),f789(f789(f171(x41841,x41842),x41845),x41846)),f789(f789(f171(x41843,x41842),f789(f789(f150(x41841,x41843),x41844),x41845)),x41846))
% 21.40/21.36 [4230]P1(f789(f789(f240(f870(x42301,a856)),f789(f285(x42302,x42301,x42303),f789(f789(f54(x42304,f870(x42302,a856)),x42305),x42306))),f789(f789(f54(x42304,f870(x42301,a856)),x42305),f789(f789(f10(f870(x42302,a856),f870(x42301,a856),x42304),f285(x42302,x42301,x42303)),x42306))))
% 21.40/21.36 [4035]E(f789(f789(f171(x40351,x40352),f789(f789(f155(x40351,x40353),x40354),f789(f248(x40351,x40352),x40355))),f789(f789(f155(x40352,x40356),x40354),f789(f258(x40351,x40352),x40355))),f789(f789(f155(f869(x40351,x40352),f789(f789(f171(x40351,x40352),x40353),x40356)),x40354),x40355))
% 21.40/21.36 [4097]E(f789(f789(f110(f870(f869(x40971,x40972),a856)),f789(f789(f289(x40971,x40973,x40972),x40974),x40975)),f789(f789(f289(x40971,x40973,x40972),x40974),x40976)),f789(f789(f289(x40971,x40973,x40972),x40974),f789(f789(f110(f870(f869(x40973,x40972),a856)),x40975),x40976)))
% 21.40/21.36 [4196]E(f789(f789(f310(f869(x41961,x41962)),f789(f789(f249(x41961,x41962),x41963),x41964)),f789(f789(f110(f870(f869(x41961,x41962),a856)),f789(f789(f256(x41961,x41962),x41965),f789(f18(f870(x41962,a856),x41961),f789(f789(f310(x41962),x41964),x41966)))),f789(f789(f256(x41961,x41962),f789(f789(f310(x41961),x41963),x41965)),f789(f18(f870(x41962,a856),x41961),x41966)))),f789(f789(f256(x41961,x41962),f789(f789(f310(x41961),x41963),x41965)),f789(f18(f870(x41962,a856),x41961),f789(f789(f310(x41962),x41964),x41966))))
% 21.40/21.36 [4269]E(f789(f789(f111(f870(x42691,a856)),f789(f313(x42691,x42692,f789(f82(f869(x42692,x42693),x42692,x42691,f248(x42692,x42693)),x42694)),x42695)),f789(f313(x42691,x42693,f789(f82(f869(x42692,x42693),x42693,x42691,f258(x42692,x42693)),x42694)),x42696)),f789(f313(x42691,f869(x42692,x42693),x42694),f789(f789(f256(x42692,x42693),x42695),f789(f18(f870(x42693,a856),x42692),x42696))))
% 21.40/21.36 [4019]E(f789(f789(f789(f81(x40191,x40192),f789(f789(f789(f81(x40191,x40192),x40193),x40194),x40195)),x40194),x40196),f789(f789(f789(f81(x40191,x40192),x40193),x40194),x40196))
% 21.40/21.36 [4121]E(f789(f789(f110(f870(f869(x41211,x41212),a856)),f789(f789(f289(x41211,x41213,x41212),x41214),x41215)),f789(f789(f289(x41211,x41213,x41212),x41216),x41215)),f789(f789(f289(x41211,x41213,x41212),f789(f789(f110(f870(f869(x41211,x41213),a856)),x41214),x41216)),x41215))
% 21.40/21.36 [4251]E(f789(f789(f53(x42511,f870(x42512,a856)),x42513),f789(f789(f9(x42511,f870(x42514,f870(x42512,a856)),f870(x42512,a856)),f789(f789(f10(f870(x42514,a856),f870(f870(x42514,f870(x42512,a856)),f870(x42512,a856)),x42511),f53(x42514,f870(x42512,a856))),x42515)),x42516)),f789(f789(f53(x42514,f870(x42512,a856)),f789(f789(f53(x42511,f870(x42514,a856)),x42513),x42515)),x42516))
% 21.40/21.36 [4252]E(f789(f789(f53(x42521,f870(x42522,a856)),x42523),f789(f789(f9(x42521,f870(x42524,f870(x42522,a856)),f870(x42522,a856)),f789(f789(f10(f870(x42524,a856),f870(f870(x42524,f870(x42522,a856)),f870(x42522,a856)),x42521),f53(x42524,f870(x42522,a856))),x42525)),x42526)),f789(f789(f53(x42524,f870(x42522,a856)),f789(f789(f53(x42521,f870(x42524,a856)),x42523),x42525)),x42526))
% 21.40/21.36 [4253]E(f789(f789(f54(x42531,f870(x42532,a856)),x42533),f789(f789(f9(x42531,f870(x42534,f870(x42532,a856)),f870(x42532,a856)),f789(f789(f10(f870(x42534,a856),f870(f870(x42534,f870(x42532,a856)),f870(x42532,a856)),x42531),f54(x42534,f870(x42532,a856))),x42535)),x42536)),f789(f789(f54(x42534,f870(x42532,a856)),f789(f789(f53(x42531,f870(x42534,a856)),x42533),x42535)),x42536))
% 21.40/21.36 [4254]E(f789(f789(f53(x42541,f870(x42542,a856)),x42543),f789(f789(f9(x42541,f870(x42544,f870(x42542,a856)),f870(x42542,a856)),f789(f789(f10(f870(x42544,a856),f870(f870(x42544,f870(x42542,a856)),f870(x42542,a856)),x42541),f53(x42544,f870(x42542,a856))),x42545)),x42546)),f789(f789(f53(x42544,f870(x42542,a856)),f789(f789(f53(x42541,f870(x42544,a856)),x42543),x42545)),x42546))
% 21.40/21.36 [4255]E(f789(f789(f54(x42551,f870(x42552,a856)),x42553),f789(f789(f9(x42551,f870(x42554,f870(x42552,a856)),f870(x42552,a856)),f789(f789(f10(f870(x42554,a856),f870(f870(x42554,f870(x42552,a856)),f870(x42552,a856)),x42551),f54(x42554,f870(x42552,a856))),x42555)),x42556)),f789(f789(f54(x42554,f870(x42552,a856)),f789(f789(f53(x42551,f870(x42554,a856)),x42553),x42555)),x42556))
% 21.40/21.36 [4303]E(f789(f259(x43031,x43032,f869(x43033,x43034)),f789(f789(f9(x43031,f870(x43032,x43034),f870(x43032,f869(x43033,x43034))),f789(f789(f10(f870(x43034,f869(x43033,x43034)),f870(f870(x43032,x43034),f870(x43032,f869(x43033,x43034))),x43031),f10(x43034,f869(x43033,x43034),x43032)),f789(f789(f10(x43033,f870(x43034,f869(x43033,x43034)),x43031),f249(x43033,x43034)),x43035))),x43036)),f260(x43031,x43033,x43032,x43034,x43035,x43036))
% 21.40/21.36 [4229]E(f789(f789(f789(f81(x42291,f867(x42292)),f177(x42291,x42292,x42293,f789(f789(f3(f870(x42291,a856)),x42294),f789(f789(f310(x42291),x42295),f184(f870(x42291,a856)))))),x42295),x42296),f789(f789(f789(f81(x42291,f867(x42292)),f177(x42291,x42292,x42293,x42294)),x42295),x42296))
% 21.40/21.36 [4326]E(f789(f311(x43261,x43262,f789(f789(f20(x43261,x43262,x43262),f789(f789(f20(x43261,x43262,f870(x43262,x43262)),f789(f789(f10(a856,f870(x43262,f870(x43262,x43262)),x43261),f105(x43262)),x43263)),x43264)),x43265)),x43266),f789(f789(f110(f870(x43262,a856)),f789(f311(x43261,x43262,x43264),f789(f789(f111(f870(x43261,a856)),x43266),f789(f264(x43261),x43263)))),f789(f311(x43261,x43262,x43265),f789(f789(f111(f870(x43261,a856)),x43266),f789(f264(x43261),f789(f789(f10(a856,a856,x43261),a336),x43263))))))
% 21.40/21.36 [4337]E(f789(f311(x43371,f869(x43372,x43373),f789(f789(f20(x43371,x43373,f869(x43372,x43373)),f789(f789(f10(x43372,f870(x43373,f869(x43372,x43373)),x43371),f249(x43372,x43373)),x43374)),x43375)),x43376),f789(f789(f256(x43372,x43373),f789(f311(x43371,x43372,x43374),x43376)),f789(f789(f10(f870(x43371,a856),f870(x43373,a856),x43372),f311(x43371,x43373,x43375)),f789(f789(f9(x43372,f870(x43371,a856),f870(x43371,a856)),f789(f789(f10(f870(x43371,a856),f870(f870(x43371,a856),f870(x43371,a856)),x43372),f111(f870(x43371,a856))),f789(f789(f10(f870(x43372,a856),f870(x43371,a856),x43372),f313(x43371,x43372,x43374)),f789(f789(f9(x43372,f870(x43372,a856),f870(x43372,a856)),f310(x43372)),f184(f870(x43372,a856)))))),x43376))))
% 21.40/21.36 [4287]E(f789(f258(x42871,x42872),f789(f260(x42873,x42871,x42874,x42872,x42875,x42876),x42877)),f789(x42876,f789(f258(x42873,x42874),x42877)))
% 21.40/21.36 [4288]E(f789(f248(x42881,x42882),f789(f260(x42883,x42881,x42884,x42882,x42885,x42886),x42887)),f789(x42885,f789(f248(x42883,x42884),x42887)))
% 21.40/21.36 [3996]E(f789(f789(f171(x39961,x39962),f789(f789(f155(x39961,x39963),x39964),x39965)),f789(f789(f155(x39962,x39966),x39964),x39967)),f789(f789(f155(f869(x39961,x39962),f789(f789(f171(x39961,x39962),x39963),x39966)),x39964),f789(f789(f249(x39961,x39962),x39965),x39967)))
% 21.40/21.36 [4065]E(f789(f789(f789(f261(x40651,x40652,x40653,x40654),x40655),x40656),x40657),f789(f789(f259(x40652,x40653,x40654),x40656),f789(x40655,x40657)))
% 21.40/21.36 [4066]E(f789(f789(f789(f261(x40661,x40662,x40663,x40664),x40665),x40666),x40667),f789(f789(f259(x40662,x40663,x40664),x40666),f789(x40665,x40667)))
% 21.40/21.36 [4075]E(f789(f789(f789(f261(x40751,x40752,x40753,x40754),x40755),x40756),x40757),f789(f789(x40756,f789(f248(x40752,x40753),f789(x40755,x40757))),f789(f258(x40752,x40753),f789(x40755,x40757))))
% 21.40/21.36 [4111]E(f176(x41111,x41112,f789(f789(f789(f81(x41111,f867(x41112)),x41113),x41114),f789(f234(x41112),x41115)),x41116,x41117),f176(x41111,x41112,x41113,f789(f789(f146(x41111),x41114),x41116),f789(f789(f146(x41112),x41115),x41117)))
% 21.40/21.36 [4128]E(f789(f82(x41281,x41282,x41283,x41284),f789(f82(x41285,x41281,x41283,x41286),x41287)),f789(f82(x41285,x41282,x41283,f789(f82(x41281,x41282,x41285,x41284),x41286)),x41287))
% 21.40/21.36 [4191]E(f789(f82(f867(x41911),f867(x41912),x41913,f789(f203(x41911,x41912),x41914)),f789(f789(f789(f81(x41913,f867(x41911)),x41915),x41916),f789(f234(x41911),x41917))),f789(f789(f789(f81(x41913,f867(x41912)),f789(f82(f867(x41911),f867(x41912),x41913,f789(f203(x41911,x41912),x41914)),x41915)),x41916),f789(f234(x41912),f789(x41914,x41917))))
% 21.40/21.36 [4310]E(f789(f260(x43101,x43102,x43103,x43103,x43104,f41(x43103)),f789(f260(x43101,x43101,x43105,x43103,f41(x43101),x43106),x43107)),f789(f789(f249(x43102,x43103),f789(x43104,f789(f248(x43101,x43105),x43107))),f789(x43106,f789(f258(x43101,x43105),x43107))))
% 21.40/21.36 [4311]E(f789(f260(x43111,x43111,x43112,x43113,f41(x43111),x43114),f789(f260(x43115,x43111,x43112,x43112,x43116,f41(x43112)),x43117)),f789(f789(f249(x43111,x43113),f789(x43116,f789(f248(x43115,x43112),x43117))),f789(x43114,f789(f258(x43115,x43112),x43117))))
% 21.40/21.36 [4324]E(f789(f260(x43241,x43242,x43243,x43243,x43244,f41(x43243)),f789(f260(x43245,x43241,x43243,x43243,x43246,f41(x43243)),x43247)),f789(f260(x43245,x43242,x43243,x43243,f789(f82(x43241,x43242,x43245,x43244),x43246),f41(x43243)),x43247))
% 21.40/21.36 [4325]E(f789(f260(x43251,x43251,x43252,x43253,f41(x43251),x43254),f789(f260(x43251,x43251,x43255,x43252,f41(x43251),x43256),x43257)),f789(f260(x43251,x43251,x43255,x43253,f41(x43251),f789(f82(x43252,x43253,x43255,x43254),x43256)),x43257))
% 21.40/21.36 [4334]E(f789(f260(x43341,x43342,x43343,x43343,x43344,f41(x43343)),f789(f260(x43341,x43341,x43345,x43343,f41(x43341),x43346),x43347)),f789(f260(x43342,x43342,x43345,x43343,f41(x43342),x43346),f789(f260(x43341,x43342,x43345,x43345,x43344,f41(x43345)),x43347)))
% 21.40/21.36 [4032]E(f789(f789(f289(x40321,x40322,x40323),f789(f789(f289(x40321,x40324,x40322),x40325),x40326)),x40327),f789(f789(f289(x40321,x40324,x40323),x40325),f789(f789(f289(x40324,x40322,x40323),x40326),x40327)))
% 21.40/21.36 [4103]E(f789(f789(f259(x41031,x41032,x41033),f789(f82(x41034,f870(x41032,x41033),x41031,x41035),x41036)),x41037),f789(f789(x41035,f789(x41036,f789(f248(x41031,x41032),x41037))),f789(f258(x41031,x41032),x41037)))
% 21.40/21.36 [4153]E(f789(f82(x41531,x41532,x41533,x41534),f789(f789(f789(f81(x41533,x41531),x41535),x41536),x41537)),f789(f789(f789(f81(x41533,x41532),f789(f82(x41531,x41532,x41533,x41534),x41535)),x41536),f789(x41534,x41537)))
% 21.40/21.36 [4187]E(f789(f138(x41871,x41872,f789(f9(x41872,x41871,x41871),x41873),x41874),f789(f149(x41872),f789(f789(f150(x41875,x41872),x41876),x41877))),f789(f138(x41871,x41875,f789(f9(x41875,x41871,x41871),f789(f82(x41872,f870(x41871,x41871),x41875,x41873),x41876)),x41874),f789(f149(x41875),x41877)))
% 21.40/21.36 [4192]E(f327(x41921,f867(x41922),x41923,f789(f82(f867(x41924),f867(x41922),x41921,f789(f203(x41924,x41922),x41925)),x41926),f789(f82(f867(x41924),f867(x41922),x41923,f789(f203(x41924,x41922),x41925)),x41927)),f789(f82(f867(x41924),f867(x41922),f871(x41921,x41923),f789(f203(x41924,x41922),x41925)),f327(x41921,f867(x41924),x41923,x41926,x41927)))
% 21.40/21.36 [4129]E(f789(f789(f53(x41291,f870(f869(x41292,x41293),a856)),x41294),f789(f789(f10(f870(f869(x41295,x41293),a856),f870(f869(x41292,x41293),a856),x41291),f789(f289(x41292,x41295,x41293),x41296)),x41297)),f789(f789(f289(x41292,x41295,x41293),x41296),f789(f789(f53(x41291,f870(f869(x41295,x41293),a856)),x41294),x41297)))
% 21.40/21.36 [4274]E(f789(f789(f53(x42741,f870(f869(x42742,x42743),a856)),x42744),f789(f789(f9(x42741,f870(f869(x42745,x42743),a856),f870(f869(x42742,x42743),a856)),f789(f789(f10(f870(f869(x42742,x42745),a856),f870(f870(f869(x42745,x42743),a856),f870(f869(x42742,x42743),a856)),x42741),f289(x42742,x42745,x42743)),x42746)),x42747)),f789(f789(f289(x42742,x42745,x42743),f789(f789(f53(x42741,f870(f869(x42742,x42745),a856)),x42744),x42746)),x42747))
% 21.40/21.36 [4275]E(f789(f138(x42751,x42752,f789(f789(f9(x42751,f870(x42752,x42753),f870(x42752,x42751)),f789(f789(f10(f870(x42753,x42751),f870(f870(x42752,x42753),f870(x42752,x42751)),x42751),f10(x42753,x42751,x42752)),x42754)),x42755),x42756),x42757),f789(f138(x42751,x42753,x42754,x42756),f789(f789(f150(x42752,x42753),x42755),x42757)))
% 21.40/21.36 [4335]E(f789(f789(f54(x43351,f870(x43352,a856)),x43353),f789(f789(f10(f870(x43354,f870(x43352,a856)),f870(x43352,a856),x43351),f789(f54(x43354,f870(x43352,a856)),x43355)),f789(f789(f9(x43351,f870(x43354,f870(x43352,a856)),f870(x43354,f870(x43352,a856))),f789(f789(f10(f870(f870(x43352,a856),f870(x43352,a856)),f870(f870(x43354,f870(x43352,a856)),f870(x43354,f870(x43352,a856))),x43351),f10(f870(x43352,a856),f870(x43352,a856),x43354)),f789(f789(f10(f870(x43352,a856),f870(f870(x43352,a856),f870(x43352,a856)),x43351),f110(f870(x43352,a856))),x43356))),x43357))),f789(f789(f110(f870(x43352,a856)),f789(f789(f54(x43351,f870(x43352,a856)),x43353),x43356)),f789(f789(f54(x43354,f870(x43352,a856)),x43355),x43357)))
% 21.40/21.36 [4336]E(f789(f789(f53(x43361,f870(x43362,a856)),x43363),f789(f789(f10(f870(x43364,f870(x43362,a856)),f870(x43362,a856),x43361),f789(f53(x43364,f870(x43362,a856)),x43365)),f789(f789(f9(x43361,f870(x43364,f870(x43362,a856)),f870(x43364,f870(x43362,a856))),f789(f789(f10(f870(f870(x43362,a856),f870(x43362,a856)),f870(f870(x43364,f870(x43362,a856)),f870(x43364,f870(x43362,a856))),x43361),f10(f870(x43362,a856),f870(x43362,a856),x43364)),f789(f789(f10(f870(x43362,a856),f870(f870(x43362,a856),f870(x43362,a856)),x43361),f111(f870(x43362,a856))),x43366))),x43367))),f789(f789(f111(f870(x43362,a856)),f789(f789(f53(x43361,f870(x43362,a856)),x43363),x43366)),f789(f789(f53(x43364,f870(x43362,a856)),x43365),x43367)))
% 21.40/21.36 [4329]E(f199(x43291,x43292,f789(f789(f789(x43293,x43294),x43295),x43296),f789(f789(f9(x43291,f869(a108,a108),f870(a108,f865(x43292))),f789(f789(f9(x43291,a108,f870(f869(a108,a108),f870(a108,f865(x43292)))),f789(f789(f9(x43291,a108,f870(a108,f870(f869(a108,a108),f870(a108,f865(x43292))))),x43297),x43294)),x43295)),x43296)),f789(f789(f789(f211(x43291,x43292,x43293,x43297),x43294),x43295),x43296))
% 21.40/21.36 [4342]E(f200(x43421,x43422,f789(f789(f789(x43423,x43424),x43425),x43426),f789(f789(f9(x43421,f869(a108,a108),f870(a108,f865(x43422))),f789(f789(f9(x43421,a108,f870(f869(a108,a108),f870(a108,f865(x43422)))),f789(f789(f9(x43421,a108,f870(a108,f870(f869(a108,a108),f870(a108,f865(x43422))))),x43427),x43424)),x43425)),x43426)),f213(x43421,x43422,x43423,x43427,x43424,x43425,x43426))
% 21.40/21.36 [4333]E(f197(x43331,x43332,f789(f789(f789(x43333,x43334),x43335),x43336),f789(f789(f9(x43331,f869(a108,a108),f870(a108,f865(f867(x43332)))),f789(f789(f9(x43331,a108,f870(f869(a108,a108),f870(a108,f865(f867(x43332))))),f789(f789(f9(x43331,a108,f870(a108,f870(f869(a108,a108),f870(a108,f865(f867(x43332)))))),x43337),x43334)),x43335)),x43336)),f789(f789(f789(f208(x43331,x43332,x43333,x43337),x43334),x43335),x43336))
% 21.40/21.36 [4344]E(f198(x43441,x43442,f789(f789(f789(x43443,x43444),x43445),x43446),f789(f789(f9(x43441,f869(a108,a108),f870(a108,f865(f867(x43442)))),f789(f789(f9(x43441,a108,f870(f869(a108,a108),f870(a108,f865(f867(x43442))))),f789(f789(f9(x43441,a108,f870(a108,f870(f869(a108,a108),f870(a108,f865(f867(x43442)))))),x43447),x43444)),x43445)),x43446)),f210(x43441,x43442,x43443,x43447,x43444,x43445,x43446))
% 21.40/21.36 [4248]E(f789(f260(x42481,x42482,x42483,x42484,x42485,x42486),f789(f789(f249(x42481,x42483),x42487),x42488)),f789(f789(f249(x42482,x42484),f789(x42485,x42487)),f789(x42486,x42488)))
% 21.40/21.36 [4346]E(f789(f789(f150(f869(x43461,x43462),f869(x43463,x43464)),f789(f259(x43461,x43462,f869(x43463,x43464)),f789(f789(f9(x43461,f870(x43462,x43464),f870(x43462,f869(x43463,x43464))),f789(f789(f10(f870(x43464,f869(x43463,x43464)),f870(f870(x43462,x43464),f870(x43462,f869(x43463,x43464))),x43461),f10(x43464,f869(x43463,x43464),x43462)),f789(f789(f10(x43463,f870(x43464,f869(x43463,x43464)),x43461),f249(x43463,x43464)),x43465))),x43466))),f789(f789(f171(x43461,x43462),x43467),x43468)),f789(f789(f171(x43463,x43464),f789(f789(f150(x43461,x43463),x43465),x43467)),f789(f789(f150(x43462,x43464),x43466),x43468)))
% 21.40/21.36 [4350]E(f789(f789(f150(f869(x43501,x43502),x43503),f789(f259(x43501,x43502,x43503),f789(f789(f10(f870(x43502,f869(x43501,x43504)),f870(x43502,x43503),x43501),f789(f10(f869(x43501,x43504),x43503,x43502),x43505)),f789(f789(f9(x43501,f870(x43502,x43504),f870(x43502,f869(x43501,x43504))),f789(f789(f10(f870(x43504,f869(x43501,x43504)),f870(f870(x43502,x43504),f870(x43502,f869(x43501,x43504))),x43501),f10(x43504,f869(x43501,x43504),x43502)),f249(x43501,x43504))),x43506)))),f789(f789(f171(x43501,x43502),x43507),x43508)),f789(f789(f150(f869(x43501,x43504),x43503),x43505),f789(f789(f171(x43501,x43504),x43507),f789(f789(f150(x43502,x43504),x43506),x43508))))
% 21.40/21.36 [4279]E(f789(f789(f150(f869(x42791,x42792),x42793),f789(f259(x42791,x42792,x42793),f789(f789(f10(f870(x42792,f869(x42794,x42792)),f870(x42792,x42793),x42791),f789(f10(f869(x42794,x42792),x42793,x42792),x42795)),f789(f789(f10(x42794,f870(x42792,f869(x42794,x42792)),x42791),f249(x42794,x42792)),x42796)))),f789(f789(f171(x42791,x42792),x42797),x42798)),f789(f789(f150(f869(x42794,x42792),x42793),x42795),f789(f789(f171(x42794,x42792),f789(f789(f150(x42791,x42794),x42796),x42797)),x42798)))
% 21.40/21.36 [4239]E(f789(f789(f259(x42391,x42392,x42393),f789(f789(f10(f870(x42392,f869(x42394,x42395)),f870(x42392,x42393),x42391),f789(f10(f869(x42394,x42395),x42393,x42392),f789(f259(x42394,x42395,x42393),x42396))),x42397)),x42398),f789(f789(f259(x42394,x42395,x42393),x42396),f789(f789(f259(x42391,x42392,f869(x42394,x42395)),x42397),x42398)))
% 21.40/21.36 [4351]E(f789(f789(f53(f869(x43511,x43512),f870(f869(x43513,x43514),a856)),f789(f789(f256(x43511,x43512),x43515),f789(f18(f870(x43512,a856),x43511),x43516))),f789(f259(x43511,x43512,f870(f869(x43513,x43514),a856)),f789(f789(f9(x43511,f870(x43512,f870(x43513,f870(x43514,a856))),f870(x43512,f870(f869(x43513,x43514),a856))),f789(f789(f10(f870(f870(x43513,f870(x43514,a856)),f870(f869(x43513,x43514),a856)),f870(f870(x43512,f870(x43513,f870(x43514,a856))),f870(x43512,f870(f869(x43513,x43514),a856))),x43511),f10(f870(x43513,f870(x43514,a856)),f870(f869(x43513,x43514),a856),x43512)),f789(f789(f10(f870(x43513,a856),f870(f870(x43513,f870(x43514,a856)),f870(f869(x43513,x43514),a856)),x43511),f256(x43513,x43514)),x43517))),f789(f789(f10(f870(x43514,a856),f870(x43513,f870(x43514,a856)),x43512),f18(f870(x43514,a856),x43513)),x43518)))),f789(f789(f256(x43513,x43514),f789(f789(f53(x43511,f870(x43513,a856)),x43515),x43517)),f789(f18(f870(x43514,a856),x43513),f789(f789(f53(x43512,f870(x43514,a856)),x43516),x43518))))
% 21.40/21.36 [4381]E(f39(x43811,x43812,x43813,x43814,x43815,x43816,x43817,x43818,x43819,a25),x43812)
% 21.40/21.36 [4382]E(f40(x43821,x43822,x43823,x43824,x43825,x43826,x43827,x43828,x43829,a25),x43822)
% 21.40/21.36 [4293]E(f789(f789(f261(x42931,x42932,x42933,x42934),f789(f789(f261(x42931,x42935,x42936,f869(x42932,x42933)),x42937),x42938)),x42939),f789(f789(f261(x42931,x42935,x42936,x42934),x42937),f789(f789(f9(x42935,f870(x42932,f870(x42933,x42934)),f870(x42936,x42934)),f789(f789(f10(f870(x42936,f869(x42932,x42933)),f870(f870(x42932,f870(x42933,x42934)),f870(x42936,x42934)),x42935),f261(x42936,x42932,x42933,x42934)),x42938)),x42939)))
% 21.40/21.36 [4383]E(f39(x43831,x43832,x43833,x43834,x43835,x43836,x43837,x43838,x43839,f789(a29,x438310)),f789(x43838,x438310))
% 21.40/21.36 [4384]E(f40(x43841,x43842,x43843,x43844,x43845,x43846,x43847,x43848,x43849,f789(a29,x438410)),f789(x43848,x438410))
% 21.40/21.36 [4321]E(f789(f82(f869(x43211,x43212),f869(x43213,x43214),f869(x43215,x43216),f260(x43211,x43213,x43212,x43214,x43217,x43218)),f260(x43215,x43211,x43216,x43212,x43219,x432110)),f260(x43215,x43213,x43216,x43214,f789(f82(x43211,x43213,x43215,x43217),x43219),f789(f82(x43212,x43214,x43216,x43218),x432110)))
% 21.40/21.36 [4322]E(f789(f82(f869(x43221,x43222),f869(x43223,x43224),f869(x43225,x43226),f260(x43221,x43223,x43222,x43224,x43227,x43228)),f260(x43225,x43221,x43226,x43222,x43229,x432210)),f260(x43225,x43223,x43226,x43224,f789(f82(x43221,x43223,x43225,x43227),x43229),f789(f82(x43222,x43224,x43226,x43228),x432210)))
% 21.40/21.36 [4385]E(f39(x43851,x43852,x43853,x43854,x43855,x43856,x43857,x43858,x43859,f38(x438510,x438511)),f789(f789(x43855,x438510),x438511))
% 21.40/21.36 [4386]E(f39(x43861,x43862,x43863,x43864,x43865,x43866,x43867,x43868,x43869,f30(x438610,x438611)),f789(f789(x43863,x438610),x438611))
% 21.40/21.36 [4387]E(f39(x43871,x43872,x43873,x43874,x43875,x43876,x43877,x43878,x43879,f37(x438710,x438711)),f789(f789(x43877,x438710),x438711))
% 21.40/21.36 [4388]E(f40(x43881,x43882,x43883,x43884,x43885,x43886,x43887,x43888,x43889,f30(x438810,x438811)),f789(f789(x43883,x438810),x438811))
% 21.40/21.36 [4394]E(f789(f789(f789(x43941,x43942),x43943),f40(x43944,x43945,x43946,x43947,x43948,x43949,x43941,x439410,x439411,x43943)),f40(x43944,x43945,x43946,x43947,x43948,x43949,x43941,x439410,x439411,f37(x43942,x43943)))
% 21.40/21.36 [4398]E(f789(f789(f789(f789(x43981,x43982),x43983),f40(x43984,x43985,x43986,x43987,x43981,x43988,x43989,x439810,x439811,x43982)),f40(x43984,x43985,x43986,x43987,x43981,x43988,x43989,x439810,x439811,x43983)),f40(x43984,x43985,x43986,x43987,x43981,x43988,x43989,x439810,x439811,f38(x43982,x43983)))
% 21.40/21.36 [4327]E(f789(f260(x43271,x43272,x43273,x43274,x43275,x43276),f789(f260(x43277,x43271,x43278,x43273,x43279,x432710),x432711)),f789(f260(x43277,x43272,x43278,x43274,f789(f82(x43271,x43272,x43277,x43275),x43279),f789(f82(x43273,x43274,x43278,x43276),x432710)),x432711))
% 21.40/21.36 [4395]E(f789(f789(f789(f789(x43951,x43952),x43953),x43954),f40(x43955,x43956,x43957,x43951,x43958,x43959,x439510,x439511,x439512,x43954)),f40(x43955,x43956,x43957,x43951,x43958,x43959,x439510,x439511,x439512,f34(x43952,x43953,x43954)))
% 21.40/21.36 [4399]E(f789(f789(f789(f789(f789(x43991,x43992),x43993),x43994),f40(x43995,x43996,x43997,x43998,x43999,x43991,x439910,x439911,x439912,x43993)),f40(x43995,x43996,x43997,x43998,x43999,x43991,x439910,x439911,x439912,x43994)),f40(x43995,x43996,x43997,x43998,x43999,x43991,x439910,x439911,x439912,f35(x43992,x43993,x43994)))
% 21.40/21.36 [4389]E(f39(x43891,x43892,x43893,x43894,x43895,x43896,x43897,x43898,x43899,f35(x438910,x438911,x438912)),f789(f789(f789(x43896,x438910),x438911),x438912))
% 21.40/21.36 [4390]E(f39(x43901,x43902,x43903,x43904,x43905,x43906,x43907,x43908,x43909,f34(x439010,x439011,x439012)),f789(f789(f789(x43904,x439010),x439011),x439012))
% 21.40/21.36 [4391]E(f39(x43911,x43912,x43913,x43914,x43915,x43916,x43917,x43918,x43919,f33(x439110,x439111,x439112)),f789(f789(f789(x43919,x439110),x439111),x439112))
% 21.40/21.36 [4392]E(f40(x43921,x43922,x43923,x43924,x43925,x43926,x43927,x43928,x43929,f33(x439210,x439211,x439212)),f789(f789(f789(x43929,x439210),x439211),x439212))
% 21.40/21.36 [6400]P13(a500)+P1(f789(f789(f342(f869(a859,a857)),a722),f789(f163(f869(a859,a857)),a31)))
% 21.40/21.36 [8435]P13(a500)+~P1(f789(f789(f259(a859,a857,a856),f789(f18(f870(a857,a856),a859),a26)),a722))
% 21.40/21.36 [4533]~P59(x45331)+P59(f867(x45331))
% 21.40/21.36 [4535]~P138(x45351)+~E(f87(x45351),f2(x45351))
% 21.40/21.36 [4536]~P138(x45361)+~E(f87(x45361),f2(x45361))
% 21.40/21.36 [4538]~E(x45381,f2(a108))+E(f789(a23,x45381),f2(a1))
% 21.40/21.36 [4539]~E(x45391,f2(a1))+E(f91(a1,x45391),f2(a1))
% 21.40/21.36 [4545]~P2(x45451)+P33(x45451,f2(x45451))
% 21.40/21.36 [4546]~P101(x45461)+P18(x45461,f122(x45461))
% 21.40/21.36 [4547]~P101(x45471)+P18(x45471,f122(x45471))
% 21.40/21.36 [4556]P1(x45561)+P1(f789(a336,x45561))
% 21.40/21.36 [4597]~P2(x45971)+~P33(x45971,f87(x45971))
% 21.40/21.36 [4641]~P1(x46411)+~P1(f789(a336,x46411))
% 21.40/21.36 [4665]E(f789(a114,x46651),f2(a863))+~P1(f789(a190,x46651))
% 21.40/21.36 [4725]~P91(x47251)+P19(x47251,x47251,f90(x47251))
% 21.40/21.36 [4726]~P101(x47261)+P19(x47261,x47261,f244(x47261))
% 21.40/21.36 [4727]~P101(x47271)+P19(x47271,x47271,f239(x47271))
% 21.40/21.36 [4728]~P94(x47281)+P19(x47281,x47281,f110(x47281))
% 21.40/21.36 [4729]~P98(x47291)+P19(x47291,x47291,f111(x47291))
% 21.40/21.36 [4730]~P66(x47301)+P20(x47301,x47301,f90(x47301))
% 21.40/21.36 [4543]E(x45431,f2(a863))+E(f789(a121,f610(x45431)),x45431)
% 21.40/21.36 [4544]~E(x45441,f2(a863))+E(f789(f109(a1),x45441),f2(a1))
% 21.40/21.36 [4549]~P88(x45491)+E(f789(f113(x45491),a92),f2(x45491))
% 21.40/21.36 [4550]~P88(x45501)+E(f789(f113(x45501),a92),f2(x45501))
% 21.40/21.36 [4552]~E(f653(x45521),f2(a863))+E(f789(f161(a863),x45521),f2(a863))
% 21.40/21.36 [4553]~P100(x45531)+E(f242(x45531,f240(x45531)),f244(x45531))
% 21.40/21.36 [4554]~P100(x45541)+E(f243(x45541,f240(x45541)),f239(x45541))
% 21.40/21.36 [4555]~P84(x45551)+E(f91(x45551,f2(x45551)),f2(x45551))
% 21.40/21.36 [4562]~P2(x45621)+E(f789(f109(x45621),f2(a863)),f2(x45621))
% 21.40/21.36 [4563]~P2(x45631)+E(f789(f109(x45631),f87(a863)),f87(x45631))
% 21.40/21.36 [4564]~P120(x45641)+E(f789(f112(x45641),f2(a1)),f2(x45641))
% 21.40/21.36 [4565]~P120(x45651)+E(f789(f112(x45651),f87(a1)),f87(x45651))
% 21.40/21.36 [4566]E(x45661,f2(a863))+~E(f789(f109(a1),x45661),f2(a1))
% 21.40/21.36 [4591]~P68(x45911)+E(f789(f88(x45911),f2(x45911)),f2(x45911))
% 21.40/21.36 [4592]~P90(x45921)+E(f789(f88(x45921),f184(x45921)),f247(x45921))
% 21.40/21.36 [4593]~P90(x45931)+E(f789(f88(x45931),f247(x45931)),f184(x45931))
% 21.40/21.36 [4594]~P80(x45941)+E(f789(f84(x45941),f2(x45941)),f2(x45941))
% 21.40/21.36 [4595]~P110(x45951)+E(f789(f84(x45951),f87(x45951)),f87(x45951))
% 21.40/21.36 [4596]~P71(x45961)+E(f789(f161(x45961),f122(x45961)),f2(x45961))
% 21.40/21.36 [4617]~P35(x46171)+P38(f789(f163(a1),x46171))
% 21.40/21.36 [4645]~P88(x46451)+E(f789(f88(x46451),f87(x46451)),f789(f113(x46451),a106))
% 21.40/21.36 [4646]~P88(x46461)+E(f789(f88(x46461),f87(x46461)),f789(f113(x46461),a106))
% 21.40/21.36 [4664]~P88(x46641)+P33(x46641,f789(f113(x46641),a92))
% 21.40/21.36 [4689]P35(x46891)+~P38(f789(f163(a1),x46891))
% 21.40/21.36 [4731]E(f789(f109(a1),f789(a114,x47311)),x47311)+P1(f789(a190,x47311))
% 21.40/21.36 [4798]~P106(x47981)+E(f251(x47981,f87(x47981),f90(x47981)),f250(x47981))
% 21.40/21.36 [4825]~P88(x48251)+~P33(x48251,f789(f113(x48251),a106))
% 21.40/21.36 [4835]E(f789(a32,x48351),f187(a857))+P1(f789(a26,f789(a29,x48351)))
% 21.40/21.36 [4912]~E(x49121,f2(a863))+P1(f789(f789(f240(a863),x49121),f2(a863)))
% 21.40/21.36 [4913]~E(x49131,f87(a863))+P1(f789(f789(f287(a863),x49131),f87(a863)))
% 21.40/21.36 [4965]E(f789(f84(a1),x49651),x49651)+P1(f789(f789(f241(a1),x49651),f2(a1)))
% 21.40/21.36 [4985]~E(f789(a114,x49851),f2(a863))+P1(f789(f789(f240(a1),x49851),f2(a1)))
% 21.40/21.36 [5020]~E(f789(f84(a1),x50201),f87(a1))+P1(f789(f789(f287(a1),x50201),f87(a1)))
% 21.40/21.36 [5050]~P1(f789(a190,x50501))+P1(f789(f789(f241(a1),x50501),f2(a1)))
% 21.40/21.36 [5090]~P2(x50901)+P1(f789(f789(f342(x50901),f2(x50901)),f181(x50901)))
% 21.40/21.36 [5091]~P120(x50911)+P1(f789(f789(f342(x50911),f2(x50911)),f119(x50911)))
% 21.40/21.36 [5092]~P2(x50921)+P1(f789(f789(f342(x50921),f87(x50921)),f181(x50921)))
% 21.40/21.36 [5093]~P120(x50931)+P1(f789(f789(f342(x50931),f87(x50931)),f119(x50931)))
% 21.40/21.36 [5094]~P117(x50941)+P1(f789(f789(f241(x50941),f2(x50941)),f87(x50941)))
% 21.40/21.36 [5095]~P117(x50951)+P1(f789(f789(f240(x50951),f2(x50951)),f87(x50951)))
% 21.40/21.36 [5098]E(f789(f234(a857),f456(x50981)),f789(a32,x50981))+~P1(f789(a26,f789(a29,x50981)))
% 21.40/21.36 [5099]E(f789(f234(a857),f589(x50991)),f789(a32,x50991))+~P1(f789(a26,f789(a29,x50991)))
% 21.40/21.36 [5149]E(x51491,f2(a863))+~P1(f789(f789(f240(a863),x51491),f2(a863)))
% 21.40/21.36 [5150]E(x51501,f87(a863))+~P1(f789(f789(f287(a863),x51501),f87(a863)))
% 21.40/21.36 [5191]E(f789(a114,x51911),f2(a863))+~P1(f789(f789(f240(a1),x51911),f2(a1)))
% 21.40/21.36 [5192]E(f789(a114,x51921),f2(a863))+~P1(f789(f789(f240(a1),x51921),f2(a1)))
% 21.40/21.36 [5220]E(f789(f84(a1),x52201),f87(a1))+~P1(f789(f789(f287(a1),x52201),f87(a1)))
% 21.40/21.36 [5247]P1(f789(a190,x52471))+~P1(f789(f789(f241(a1),x52471),f2(a1)))
% 21.40/21.36 [5251]~P101(x52511)+P20(x52511,f864(x52511),f144(x52511,x52511,f7(x52511)))
% 21.40/21.36 [5268]P38(x52681)+~P1(f789(f789(f240(a1),f2(a1)),f377(x52681)))
% 21.40/21.36 [5274]E(f789(f84(a1),x52741),f789(f88(a1),x52741))+~P1(f789(f789(f241(a1),x52741),f2(a1)))
% 21.40/21.36 [5445]~P117(x54451)+~P1(f789(f789(f241(x54451),f87(x54451)),f2(x54451)))
% 21.40/21.36 [5446]~P117(x54461)+~P1(f789(f789(f240(x54461),f87(x54461)),f2(x54461)))
% 21.40/21.36 [5458]~E(x54581,f2(a1))+P1(f789(f789(f241(a1),f789(f84(a1),x54581)),f87(a1)))
% 21.40/21.36 [5459]~E(x54591,f2(a863))+P1(f789(f789(f240(a1),f789(f109(a1),x54591)),f2(a1)))
% 21.40/21.36 [5573]~P71(x55731)+E(f138(x55731,x55731,f89(x55731),f2(x55731)),f161(x55731))
% 21.40/21.36 [5748]~P86(x57481)+P29(a863,x57481,f109(x57481),f247(f870(a863,a856)))
% 21.40/21.36 [5944]E(x59441,f2(a863))+~P1(f789(f789(f240(a1),f789(f109(a1),x59441)),f2(a1)))
% 21.40/21.36 [5945]E(x59451,f2(a1))+~P1(f789(f789(f241(a1),f789(f84(a1),x59451)),f87(a1)))
% 21.40/21.36 [6770]~P1(f789(f789(f241(a1),x67701),f2(a1)))+P1(f789(f789(f241(a1),f789(f789(f89(a1),x67701),x67701)),f2(a1)))
% 21.40/21.36 [7343]P1(f789(f789(f241(a1),x73431),f2(a1)))+~P1(f789(f789(f241(a1),f789(f789(f89(a1),x73431),x73431)),f2(a1)))
% 21.40/21.36 [7907]E(x79071,f789(a5,f2(a863)))+P1(f789(f789(f241(a863),f789(f789(f3(a863),f789(a22,x79071)),f789(a121,f2(a863)))),f789(a22,x79071)))
% 21.40/21.36 [8647]~P1(f789(f789(f241(a1),x86471),f2(a1)))+P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),x86471),x86471)),a106)),f2(a1)))
% 21.40/21.36 [8731]~P1(f789(f789(f241(a1),x87311),f2(a1)))+P1(f789(f789(f241(a1),f789(f789(f89(a1),f789(f789(f89(a1),f87(a1)),x87311)),x87311)),f2(a1)))
% 21.40/21.36 [9015]P1(f789(f789(f241(a1),x90151),f2(a1)))+~P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),x90151),x90151)),a106)),f2(a1)))
% 21.40/21.36 [9081]P1(f789(f789(f241(a1),x90811),f2(a1)))+~P1(f789(f789(f241(a1),f789(f789(f89(a1),f789(f789(f89(a1),f87(a1)),x90811)),x90811)),f2(a1)))
% 21.40/21.36 [4634]~E(a92,x46341)+E(f789(f789(f89(a1),x46341),x46341),a92)
% 21.40/21.36 [4635]~E(x46351,a92)+E(f789(f789(f89(a1),x46351),x46351),a92)
% 21.40/21.36 [4650]E(x46501,f2(a1))+E(f789(f789(f50(a1),x46501),x46501),f87(a1))
% 21.40/21.36 [4776]E(x47761,a92)+~E(f789(f789(f89(a1),x47761),x47761),a92)
% 21.40/21.36 [4777]E(a92,x47771)+~E(f789(f789(f89(a1),x47771),x47771),a92)
% 21.40/21.36 [4778]~P88(x47781)+E(f789(f112(x47781),f789(f113(a1),a106)),f789(f113(x47781),a106))
% 21.40/21.36 [4788]~P9(x47881)+E(f52(x47881,f184(f870(x47881,a856))),f247(x47881))
% 21.40/21.36 [4789]~P9(x47891)+E(f52(x47891,f247(f870(x47891,a856))),f184(x47891))
% 21.40/21.36 [4790]~P9(x47901)+E(f51(x47901,f184(f870(x47901,a856))),f184(x47901))
% 21.40/21.36 [4791]~P9(x47911)+E(f51(x47911,f247(f870(x47911,a856))),f247(x47911))
% 21.40/21.36 [4792]~P101(x47921)+E(f136(x47921,f184(f870(x47921,a856))),f122(x47921))
% 21.40/21.36 [4924]E(x49241,f2(a863))+P1(f789(f789(f241(a863),f2(a863)),x49241))
% 21.40/21.36 [4925]E(x49251,f2(a863))+P1(f789(f789(f241(a863),f2(a863)),x49251))
% 21.40/21.36 [4945]~P10(x49451)+P1(f789(f789(f240(a1),f2(a1)),x49451))
% 21.40/21.36 [4975]~E(f789(f113(a863),x49751),f2(a863))+P1(f789(f789(f240(a1),x49751),a92))
% 21.40/21.36 [4976]~E(f789(f113(a863),x49761),f2(a863))+P1(f789(f789(f240(a1),x49761),a92))
% 21.40/21.36 [4981]P38(x49811)+P1(f789(f789(f342(a1),f377(x49811)),x49811))
% 21.40/21.36 [4982]E(x49821,f789(a5,f2(a863)))+P1(f789(f789(f240(a108),f87(a108)),x49821))
% 21.40/21.36 [5025]P1(f789(a190,x50251))+P1(f789(f789(f240(a1),f2(a1)),x50251))
% 21.40/21.36 [5072]E(f789(f109(a1),f789(a114,x50721)),f2(a1))+P1(f789(f789(f240(a1),f2(a1)),x50721))
% 21.40/21.36 [5123]~P59(x51231)+P1(f789(f70(x51231),f247(f870(x51231,a856))))
% 21.40/21.36 [5136]E(f789(f109(a1),f789(f113(a863),x51361)),f789(f113(a1),x51361))+P1(f789(a190,f789(f113(a1),x51361)))
% 21.40/21.36 [5138]~E(x51381,f2(a863))+P1(f789(f789(f241(a863),x51381),f789(a121,f2(a863))))
% 21.40/21.36 [5155]E(f789(f113(a863),x51551),f2(a863))+~P1(f789(f789(f240(a1),x51551),a92))
% 21.40/21.36 [5156]E(f789(f113(a863),x51561),f2(a863))+~P1(f789(a190,f789(f113(a1),x51561)))
% 21.40/21.36 [5157]E(f789(f113(a863),x51571),f2(a863))+~P1(f789(f789(f240(a1),x51571),a92))
% 21.40/21.36 [5189]P10(x51891)+~P1(f789(f789(f240(a1),f2(a1)),x51891))
% 21.40/21.36 [5207]~E(x52071,f2(a863))+~P1(f789(f789(f241(a863),f2(a863)),x52071))
% 21.40/21.36 [5230]~E(x52301,f789(a121,f2(a863)))+P1(f789(f789(f287(a863),x52301),f789(a121,f2(a863))))
% 21.40/21.36 [5254]E(f789(a121,f665(x52541)),x52541)+~P1(f789(f789(f241(a863),f2(a863)),x52541))
% 21.40/21.36 [5255]E(f789(a121,f741(x52551)),x52551)+~P1(f789(f789(f241(a863),f2(a863)),x52551))
% 21.40/21.36 [5263]E(f789(a121,f789(f113(a863),x52631)),f87(a863))+~P1(f789(a190,f789(f113(a1),x52631)))
% 21.40/21.36 [5270]E(f789(f109(a1),f775(x52701)),x52701)+~P1(f789(f789(f241(a1),f2(a1)),x52701))
% 21.40/21.36 [5277]~E(x52771,f789(a5,f2(a863)))+~P1(f789(f789(f240(a108),f87(a108)),x52771))
% 21.40/21.36 [5284]E(f789(f109(a1),f789(f113(a863),x52841)),f2(a1))+~P1(f789(a190,f789(f113(a1),x52841)))
% 21.40/21.36 [5308]E(f789(f161(a863),x53081),f2(a863))+P1(f789(f789(f342(a863),f653(x53081)),f789(f163(a863),x53081)))
% 21.40/21.36 [5327]E(f789(f109(a1),f789(a114,x53271)),x53271)+~P1(f789(f789(f240(a1),f2(a1)),x53271))
% 21.40/21.36 [5328]E(f789(f109(a1),f789(a114,x53281)),x53281)+~P1(f789(f789(f240(a1),f2(a1)),x53281))
% 21.40/21.36 [5337]~P1(f789(a190,x53371))+~P1(f789(f789(f240(a1),f2(a1)),x53371))
% 21.40/21.36 [5438]E(f789(f789(f89(a863),f87(a863)),f789(f113(a863),x54381)),f87(a863))+~P1(f789(f789(f241(a1),x54381),a92))
% 21.40/21.36 [5495]E(x54951,f2(a863))+~P1(f789(f789(f241(a863),x54951),f789(a121,f2(a863))))
% 21.40/21.36 [5515]E(x55151,f789(a121,f2(a863)))+~P1(f789(f789(f287(a863),x55151),f789(a121,f2(a863))))
% 21.40/21.36 [5533]E(f789(f789(f89(a863),f789(f113(a863),x55331)),f87(a863)),f87(a863))+~P1(f789(f789(f241(a1),x55331),a92))
% 21.40/21.36 [5534]E(f789(f789(f3(a863),f789(f113(a863),x55341)),f87(a863)),f2(a863))+~P1(f789(f789(f240(a1),x55341),a92))
% 21.40/21.36 [5544]~P38(x55441)+E(f789(f49(a863),f789(f311(a1,a863,a114),x55441)),f789(f49(a1),x55441))
% 21.40/21.36 [5574]~P101(x55741)+E(f242(x55741,f789(f9(x55741,x55741,a856),f240(x55741))),f239(x55741))
% 21.40/21.36 [5575]~P101(x55751)+E(f243(x55751,f789(f9(x55751,x55751,a856),f240(x55751))),f244(x55751))
% 21.40/21.36 [5584]E(f59(a863,f789(a121,f2(a863)),f789(f113(a863),x55841)),f789(a121,f2(a863)))+~P1(f789(a190,f789(f113(a1),x55841)))
% 21.40/21.36 [5592]P1(f789(f789(f241(a1),f2(a1)),x55921))+~P1(f789(f789(f240(a1),f87(a1)),x55921))
% 21.40/21.36 [5593]~P1(f789(f789(f241(a1),f2(a1)),x55931))+P1(f789(f789(f240(a1),f87(a1)),x55931))
% 21.40/21.36 [5602]E(f789(a121,f789(f789(f3(a863),x56021),f87(a863))),x56021)+~P1(f789(f789(f241(a863),f2(a863)),x56021))
% 21.40/21.36 [5603]E(f789(a121,f789(f789(f3(a863),x56031),f87(a863))),x56031)+~P1(f789(f789(f241(a863),f2(a863)),x56031))
% 21.40/21.36 [5661]P1(f789(f789(f241(a863),f2(a863)),f775(x56611)))+~P1(f789(f789(f241(a1),f2(a1)),x56611))
% 21.40/21.36 [5718]E(f59(a1,f789(f113(a1),a106),x57181),f789(f789(f3(a1),x57181),f87(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x57181))
% 21.40/21.36 [5763]~P1(f789(f789(f241(a1),a92),x57631))+P1(f789(f789(f241(a863),f2(a863)),f789(f113(a863),x57631)))
% 21.40/21.36 [5817]P1(f789(f789(f241(a863),f2(a863)),f789(a114,x58171)))+~P1(f789(f789(f241(a1),f2(a1)),x58171))
% 21.40/21.36 [5838]E(f789(a22,f789(a5,x58381)),x58381)+~P1(f789(f789(f342(a863),x58381),f247(f870(a863,a856))))
% 21.40/21.36 [5863]~P1(f789(f789(f241(a863),f2(a863)),x58631))+P1(f789(f789(f241(a1),f2(a1)),f789(f109(a1),x58631)))
% 21.40/21.36 [5898]~P1(f789(f789(f241(a863),f2(a863)),f789(a114,x58981)))+P1(f789(f789(f241(a1),f2(a1)),x58981))
% 21.40/21.36 [5913]~P38(x59131)+E(f789(f311(a863,a1,f109(a1)),f789(f311(a1,a863,a114),x59131)),x59131)
% 21.40/21.36 [5924]P1(f789(f789(f241(a1),a92),x59241))+~P1(f789(f789(f241(a863),f2(a863)),f789(f113(a863),x59241)))
% 21.40/21.36 [5986]P1(f789(f789(f241(a863),f2(a863)),x59861))+~P1(f789(f789(f241(a1),f2(a1)),f789(f109(a1),x59861)))
% 21.40/21.36 [6018]E(f168(x60181,f122(f864(x60181))),f122(f864(x60181)))+~P1(f789(f329(f864(f864(x60181)),f169(x60181)),f122(f864(x60181))))
% 21.40/21.36 [6103]E(f789(f311(a863,a1,f109(a1)),f789(f265(a863),f789(a114,x61031))),f789(f302(a1,f2(a1)),x61031))+~P1(f789(f789(f240(a1),f2(a1)),x61031))
% 21.40/21.36 [6118]~P117(x61181)+P1(f789(f789(f241(x61181),f2(x61181)),f789(f789(f89(x61181),f87(x61181)),f87(x61181))))
% 21.40/21.36 [6168]P1(f789(f789(f241(a863),f789(a121,f2(a863))),f789(a114,x61681)))+~P1(f789(f789(f241(a1),f87(a1)),x61681))
% 21.40/21.36 [6263]E(x62631,f2(a1))+P1(f789(f63(f2(a1),x62631),f789(f789(f249(a1,a1),f2(a1)),f2(a1))))
% 21.40/21.36 [6442]~P1(f789(f789(f241(a863),f789(a121,f2(a863))),f789(a114,x64421)))+P1(f789(f789(f241(a1),f87(a1)),x64421))
% 21.40/21.36 [6493]E(f789(a121,f789(f789(f3(a863),f789(f113(a863),x64931)),f87(a863))),f789(f113(a863),x64931))+~P1(f789(f789(f241(a863),f2(a863)),f789(f113(a863),x64931)))
% 21.40/21.36 [6891]~P108(x68911)+P36(x68911,f789(f264(f869(x68911,x68911)),f789(f259(x68911,x68911,a856),f241(x68911))))
% 21.40/21.36 [5485]E(f789(f113(a863),f789(f789(f3(a1),x54851),a106)),f789(a121,f789(f113(a863),x54851)))+P1(f789(a190,f789(f113(a1),x54851)))
% 21.40/21.36 [5510]P31(a855,a872,x55101)+~P1(f789(f789(f342(f862(a855)),x55101),a873))
% 21.40/21.36 [5609]E(f789(f88(a1),f789(f109(a1),f789(a121,f794(x56091)))),x56091)+~P1(f789(f789(f241(a1),x56091),f2(a1)))
% 21.40/21.36 [5619]E(f789(f789(f89(a863),f87(a863)),f789(f113(a863),x56191)),f789(f113(a863),f789(f789(f3(a1),x56191),a106)))+P1(f789(f789(f241(a1),x56191),a92))
% 21.40/21.36 [5663]E(f789(f789(f50(a1),f789(f113(a1),a106)),x56631),f789(f113(a1),a106))+~P1(f789(f789(f241(a1),f2(a1)),x56631))
% 21.40/21.36 [5759]E(f789(f789(f89(a863),f789(f113(a863),x57591)),f87(a863)),f789(f113(a863),f789(f789(f3(a1),x57591),a106)))+P1(f789(f789(f241(a1),x57591),a92))
% 21.40/21.36 [5760]E(f789(f789(f3(a863),f789(f113(a863),x57601)),f87(a863)),f789(f113(a863),f789(f789(f89(a1),x57601),a106)))+P1(f789(f789(f240(a1),x57601),a92))
% 21.40/21.36 [5803]E(f789(a114,f789(f789(f89(a1),f87(a1)),x58031)),f789(a121,f789(a114,x58031)))+~P1(f789(f789(f240(a1),f2(a1)),x58031))
% 21.40/21.36 [5840]E(f789(a121,f789(f789(f3(a863),x58401),f789(a121,f2(a863)))),x58401)+~P1(f789(f789(f241(a863),f2(a863)),x58401))
% 21.40/21.36 [6048]E(f59(a863,f789(a121,f2(a863)),f789(f113(a863),x60481)),f789(a114,f59(a1,f87(a1),f789(f113(a1),x60481))))+P1(f789(a190,f789(f113(a1),x60481)))
% 21.40/21.36 [6094]~P1(f789(f789(f241(a1),a106),x60941))+P1(f789(f789(f241(a1),a106),f789(f789(f89(a1),x60941),x60941)))
% 21.40/21.36 [6095]~P1(f789(f789(f241(a1),a92),x60951))+P1(f789(f789(f241(a1),a92),f789(f789(f89(a1),x60951),x60951)))
% 21.40/21.36 [6096]~P1(f789(f789(f241(a1),a106),x60961))+P1(f789(f789(f240(a1),a106),f789(f789(f89(a1),x60961),x60961)))
% 21.40/21.36 [6097]~P1(f789(f789(f240(a1),a92),x60971))+P1(f789(f789(f240(a1),a92),f789(f789(f89(a1),x60971),x60971)))
% 21.40/21.36 [6277]~P1(f789(f70(x62771),f247(f870(x62771,a856))))+P1(f789(f70(f867(x62771)),f247(f870(f867(x62771),a856))))
% 21.40/21.36 [6368]~P1(f789(f789(f240(a1),f2(a1)),x63681))+P1(f789(f789(f241(a1),f2(a1)),f789(f789(f89(a1),f87(a1)),x63681)))
% 21.40/21.36 [6374]E(f789(f248(a1,a1),f61(f87(a1),f789(f113(a1),x63741))),f789(f789(f50(a1),f87(a1)),f789(f113(a1),x63741)))+~P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x63741)))
% 21.40/21.36 [6399]E(f789(f258(a1,a1),f61(f87(a1),f789(f113(a1),x63991))),f59(a1,f87(a1),f789(f113(a1),x63991)))+~P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x63991)))
% 21.40/21.36 [6412]P1(f789(f70(x64121),f247(f870(x64121,a856))))+~P1(f789(f70(f867(x64121)),f247(f870(f867(x64121),a856))))
% 21.40/21.36 [6443]P1(f789(f789(f241(a1),a106),x64431))+~P1(f789(f789(f241(a1),a106),f789(f789(f89(a1),x64431),x64431)))
% 21.40/21.36 [6444]P1(f789(f789(f241(a1),a106),x64441))+~P1(f789(f789(f240(a1),a106),f789(f789(f89(a1),x64441),x64441)))
% 21.40/21.36 [6445]P1(f789(f789(f241(a1),a92),x64451))+~P1(f789(f789(f241(a1),a92),f789(f789(f89(a1),x64451),x64451)))
% 21.40/21.36 [6446]P1(f789(f789(f240(a1),a92),x64461))+~P1(f789(f789(f240(a1),a92),f789(f789(f89(a1),x64461),x64461)))
% 21.40/21.36 [6640]~P1(f789(f70(a863),x66401))+P1(f789(f70(a1),f789(f311(a863,a1,f109(a1)),x66401)))
% 21.40/21.36 [6775]~P1(f789(f70(x67751),f247(f870(x67751,a856))))+P1(f789(f789(f241(a863),f2(a863)),f789(f49(x67751),f247(f870(x67751,a856)))))
% 21.40/21.36 [7388]P1(f789(f70(a863),x73881))+~P1(f789(f70(a1),f789(f311(a863,a1,f109(a1)),x73881)))
% 21.40/21.36 [5413]~E(a106,x54131)+E(f789(f789(f3(a1),f789(f789(f89(a1),x54131),x54131)),a106),a106)
% 21.40/21.36 [5414]~E(x54141,a106)+E(f789(f789(f3(a1),f789(f789(f89(a1),x54141),x54141)),a106),a106)
% 21.40/21.36 [5918]E(x59181,a106)+~E(f789(f789(f3(a1),f789(f789(f89(a1),x59181),x59181)),a106),a106)
% 21.40/21.36 [5919]E(a106,x59191)+~E(f789(f789(f3(a1),f789(f789(f89(a1),x59191),x59191)),a106),a106)
% 21.40/21.36 [6337]~E(f789(f113(a863),x63371),f2(a863))+P1(f789(a190,f789(f113(a1),f789(f789(f89(a1),x63371),a106))))
% 21.40/21.36 [6700]~P1(f789(a190,f789(f113(a1),x67001)))+P1(f789(a190,f789(f113(a1),f789(f789(f89(a1),x67001),x67001))))
% 21.40/21.36 [6701]~P1(f789(f789(f240(a1),x67011),a106))+P1(f789(f789(f241(a1),f789(f789(f89(a1),x67011),x67011)),a106))
% 21.40/21.36 [6702]~P1(f789(f789(f241(a1),x67021),a92))+P1(f789(f789(f241(a1),f789(f789(f89(a1),x67021),x67021)),a92))
% 21.40/21.36 [6703]~P1(f789(f789(f240(a1),x67031),a106))+P1(f789(f789(f240(a1),f789(f789(f89(a1),x67031),x67031)),a106))
% 21.40/21.36 [6704]~P1(f789(f789(f240(a1),x67041),a92))+P1(f789(f789(f240(a1),f789(f789(f89(a1),x67041),x67041)),a92))
% 21.40/21.36 [7032]E(f789(f113(a863),x70321),f2(a863))+~P1(f789(a190,f789(f113(a1),f789(f789(f89(a1),x70321),a106))))
% 21.40/21.36 [7291]~P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x72911)))+P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),f789(f789(f89(a1),x72911),x72911))))
% 21.40/21.36 [7292]P1(f789(a190,f789(f113(a1),x72921)))+~P1(f789(a190,f789(f113(a1),f789(f789(f89(a1),x72921),x72921))))
% 21.40/21.36 [7293]P1(f789(f789(f241(a1),x72931),a92))+~P1(f789(f789(f241(a1),f789(f789(f89(a1),x72931),x72931)),a92))
% 21.40/21.36 [7294]P1(f789(f789(f240(a1),x72941),a106))+~P1(f789(f789(f241(a1),f789(f789(f89(a1),x72941),x72941)),a106))
% 21.40/21.36 [7295]P1(f789(f789(f240(a1),x72951),a106))+~P1(f789(f789(f240(a1),f789(f789(f89(a1),x72951),x72951)),a106))
% 21.40/21.36 [7296]P1(f789(f789(f240(a1),x72961),a92))+~P1(f789(f789(f240(a1),f789(f789(f89(a1),x72961),x72961)),a92))
% 21.40/21.36 [7675]E(f789(a117,f565(x76751)),x76751)+~P1(f789(f789(f342(f870(f869(a863,a863),a856)),x76751),a107))
% 21.40/21.36 [6250]~P88(x62501)+E(f789(f113(x62501),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f87(x62501))
% 21.40/21.36 [6251]~P88(x62511)+E(f789(f113(x62511),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f87(x62511))
% 21.40/21.36 [6754]~P1(f789(a190,f789(f113(a1),x67541)))+E(f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),x67541),x67541)),a106)),f2(a863))
% 21.40/21.36 [7853]~P1(f789(f789(f241(a1),f789(f113(a1),x78531)),f2(a1)))+E(f789(f248(a1,a1),f789(a65,f64(f789(f88(a1),f87(a1)),f789(f88(a1),f789(f113(a1),x78531))))),f789(f789(f50(a1),f87(a1)),f789(f113(a1),x78531)))
% 21.40/21.36 [7866]~P1(f789(f789(f241(a1),f789(f113(a1),x78661)),f2(a1)))+E(f789(f258(a1,a1),f789(a65,f64(f789(f88(a1),f87(a1)),f789(f88(a1),f789(f113(a1),x78661))))),f59(a1,f87(a1),f789(f113(a1),x78661)))
% 21.40/21.36 [7913]~P1(f789(f789(f241(a1),a106),x79131))+P1(f789(f789(f241(a1),a106),f789(f789(f3(a1),f789(f789(f89(a1),x79131),x79131)),a106)))
% 21.40/21.36 [7914]~P1(f789(f789(f240(a1),a92),x79141))+P1(f789(f789(f241(a1),a92),f789(f789(f3(a1),f789(f789(f89(a1),x79141),x79141)),a106)))
% 21.40/21.36 [7915]~P1(f789(f789(f240(a1),a106),x79151))+P1(f789(f789(f240(a1),a106),f789(f789(f3(a1),f789(f789(f89(a1),x79151),x79151)),a106)))
% 21.40/21.36 [7916]~P1(f789(f789(f240(a1),a92),x79161))+P1(f789(f789(f240(a1),a92),f789(f789(f3(a1),f789(f789(f89(a1),x79161),x79161)),a106)))
% 21.40/21.36 [8210]~P88(x82101)+~P33(x82101,f789(f113(x82101),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))
% 21.40/21.36 [8391]P1(f789(f789(f241(a1),a106),x83911))+~P1(f789(f789(f241(a1),a106),f789(f789(f3(a1),f789(f789(f89(a1),x83911),x83911)),a106)))
% 21.40/21.36 [8392]P1(f789(f789(f240(a1),a106),x83921))+~P1(f789(f789(f240(a1),a106),f789(f789(f3(a1),f789(f789(f89(a1),x83921),x83921)),a106)))
% 21.40/21.36 [8393]P1(f789(f789(f240(a1),a92),x83931))+~P1(f789(f789(f241(a1),a92),f789(f789(f3(a1),f789(f789(f89(a1),x83931),x83931)),a106)))
% 21.40/21.36 [8394]P1(f789(f789(f240(a1),a92),x83941))+~P1(f789(f789(f240(a1),a92),f789(f789(f3(a1),f789(f789(f89(a1),x83941),x83941)),a106)))
% 21.40/21.36 [8690]E(f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),x86901),x86901)),a106)),f789(f789(f95(a863,a863),f789(f113(a863),x86901)),f789(f789(f10(a863,a863,a863),a121),f789(f789(f20(a863,a863,a863),f89(a863)),f7(a863)))))+P1(f789(a190,f789(f113(a1),x86901)))
% 21.40/21.36 [9464]E(x94641,f184(f870(f869(a863,a863),a856)))+P1(f789(f789(f342(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f249(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),x94641),f184(f870(f869(a863,a863),a856)))),a77))
% 21.40/21.36 [8624]~P1(f789(a190,f789(f113(a1),x86241)))+P1(f789(a190,f789(f113(a1),f789(f789(f3(a1),f789(f789(f89(a1),x86241),x86241)),a106))))
% 21.40/21.36 [8625]~P1(f789(f789(f241(a1),x86251),a106))+P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),x86251),x86251)),a106)),a106))
% 21.40/21.36 [8626]~P1(f789(f789(f241(a1),x86261),a92))+P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),x86261),x86261)),a106)),a92))
% 21.40/21.36 [8627]~P1(f789(f789(f240(a1),x86271),a106))+P1(f789(f789(f240(a1),f789(f789(f3(a1),f789(f789(f89(a1),x86271),x86271)),a106)),a106))
% 21.40/21.36 [8628]~P1(f789(f789(f241(a1),x86281),a92))+P1(f789(f789(f240(a1),f789(f789(f3(a1),f789(f789(f89(a1),x86281),x86281)),a106)),a92))
% 21.40/21.36 [8724]~P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x87241)))+P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),f789(f789(f3(a1),f789(f789(f89(a1),x87241),x87241)),a106))))
% 21.40/21.36 [8857]~P88(x88571)+E(f789(f789(f89(x88571),f87(x88571)),f87(x88571)),f789(f113(x88571),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))
% 21.40/21.36 [9001]P1(f789(a190,f789(f113(a1),x90011)))+~P1(f789(a190,f789(f113(a1),f789(f789(f3(a1),f789(f789(f89(a1),x90011),x90011)),a106))))
% 21.40/21.36 [9002]P1(f789(f789(f241(a1),x90021),a106))+~P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),x90021),x90021)),a106)),a106))
% 21.40/21.36 [9003]P1(f789(f789(f241(a1),x90031),a92))+~P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),x90031),x90031)),a106)),a92))
% 21.40/21.36 [9004]P1(f789(f789(f241(a1),x90041),a92))+~P1(f789(f789(f240(a1),f789(f789(f3(a1),f789(f789(f89(a1),x90041),x90041)),a106)),a92))
% 21.40/21.36 [9005]P1(f789(f789(f240(a1),x90051),a106))+~P1(f789(f789(f240(a1),f789(f789(f3(a1),f789(f789(f89(a1),x90051),x90051)),a106)),a106))
% 21.40/21.36 [9514]~P1(f789(f70(f869(a863,a863)),x95141))+P1(f789(f789(f342(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f249(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),f184(f870(f869(a863,a863),a856))),x95141)),a78))
% 21.40/21.36 [9296]~P2(x92961)+E(f789(f789(f250(x92961),f2(x92961)),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f2(x92961))
% 21.40/21.36 [9297]~P2(x92971)+E(f789(f789(f250(x92971),f87(x92971)),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f87(x92971))
% 21.40/21.36 [9718]~P1(f789(f789(f241(a863),f87(a863)),x97181))+P1(f789(f789(f241(a863),f2(a863)),f789(f789(f50(a863),x97181),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))
% 21.40/21.36 [9723]~P1(f789(f789(f241(a863),f2(a863)),x97231))+P1(f789(f789(f241(a863),f2(a863)),f789(f789(f50(a863),f789(f789(f89(a863),x97231),f87(a863))),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))
% 21.40/21.36 [9763]~E(f59(a863,x97631,f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f87(a863))+P1(f789(f789(f241(a863),f2(a863)),f59(a863,x97631,f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))
% 21.40/21.36 [9798]E(f59(a863,x97981,f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f87(a863))+~P1(f789(f789(f241(a863),f2(a863)),f59(a863,x97981,f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))
% 21.40/21.36 [4570]~P36(x45701,x45702)+P56(x45701,x45702)
% 21.40/21.36 [4571]~P42(x45711,x45712)+P56(x45711,x45712)
% 21.40/21.36 [4531]E(x45311,x45312)+~E(f42(x45311),f42(x45312))
% 21.40/21.36 [4532]E(x45321,x45322)+~E(f43(x45321),f43(x45322))
% 21.40/21.36 [4534]~E(x45341,x45342)+E(f274(x45341,x45342),f87(a108))
% 21.40/21.36 [4537]E(f218(x45371,x45372),x45371)+~E(x45372,f2(a863))
% 21.40/21.36 [4542]P37(x45421,x45422)+~E(x45422,f187(x45421))
% 21.40/21.36 [4548]~P37(x45482,x45481)+E(x45481,f187(x45482))
% 21.40/21.36 [4575]~P99(x45752)+P99(f870(x45751,x45752))
% 21.40/21.36 [4576]~P105(x45762)+P105(f870(x45761,x45762))
% 21.40/21.36 [4577]~P90(x45772)+P90(f870(x45771,x45772))
% 21.40/21.36 [4578]~P100(x45782)+P100(f870(x45781,x45782))
% 21.40/21.36 [4579]~P83(x45792)+P83(f870(x45791,x45792))
% 21.40/21.36 [4580]~P72(x45802)+P72(f870(x45801,x45802))
% 21.40/21.36 [4581]~P102(x45812)+P102(f870(x45811,x45812))
% 21.40/21.36 [4582]~P93(x45822)+P92(f870(x45821,x45822))
% 21.40/21.36 [4583]~P95(x45832)+P94(f870(x45831,x45832))
% 21.40/21.36 [4584]~P95(x45842)+P95(f870(x45841,x45842))
% 21.40/21.36 [4585]~P95(x45852)+P98(f870(x45851,x45852))
% 21.40/21.36 [4586]~P96(x45862)+P96(f870(x45861,x45862))
% 21.40/21.36 [4587]~P9(x45872)+P9(f870(x45871,x45872))
% 21.40/21.36 [4588]~P93(x45882)+P97(f870(x45881,x45882))
% 21.40/21.36 [4589]~P107(x45892)+P107(f870(x45891,x45892))
% 21.40/21.36 [4590]~P93(x45902)+P93(f870(x45901,x45902))
% 21.40/21.36 [4602]E(x46021,x46022)+~E(f789(a121,x46021),f789(a121,x46022))
% 21.40/21.36 [4603]E(x46031,x46032)+~E(f789(a121,x46031),f789(a121,x46032))
% 21.40/21.36 [4604]E(x46041,x46042)+~E(f789(a29,x46041),f789(a29,x46042))
% 21.40/21.36 [4605]E(x46051,x46052)+~E(f789(a5,x46051),f789(a5,x46052))
% 21.40/21.36 [4606]E(x46061,x46062)+~E(f789(a22,x46061),f789(a22,x46062))
% 21.40/21.36 [4607]E(x46071,x46072)+~E(f789(a22,x46071),f789(a22,x46072))
% 21.40/21.36 [4608]E(x46081,x46082)+~E(f789(a117,x46081),f789(a117,x46082))
% 21.40/21.36 [4705]~P7(x47051)+E(f59(x47051,x47052,x47052),f2(x47051))
% 21.40/21.36 [4738]~P36(x47381,x47382)+P36(f864(x47381),f142(x47381,x47382))
% 21.40/21.36 [4739]~P36(x47391,x47392)+P36(f864(x47391),f141(x47391,x47392))
% 21.40/21.36 [4830]~P36(x48301,x48302)+P36(f870(x48301,a856),f334(x48301,x48302))
% 21.40/21.36 [4831]~P36(x48311,x48312)+P36(f870(x48311,a856),f332(x48311,x48312))
% 21.40/21.36 [4950]~P10(x49501)+P38(f303(a1,x49501,x49502))
% 21.40/21.36 [5053]~P36(x50531,x50532)+P58(x50531,f76(x50531,x50531,x50532))
% 21.40/21.36 [5538]~P76(x55381)+P29(x55381,x55381,f88(x55381),x55382)
% 21.40/21.36 [4557]~E(x45572,f122(x45571))+E(f789(f149(x45571),x45572),f122(x45571))
% 21.40/21.36 [4558]~E(x45582,f122(x45581))+E(f789(f148(x45581),x45582),f122(x45581))
% 21.40/21.36 [4559]~E(x45592,f122(x45591))+E(f789(f149(x45591),x45592),f122(x45591))
% 21.40/21.36 [4612]E(x46121,f789(a114,x46122))+~E(f789(f109(a1),x46121),x46122)
% 21.40/21.36 [4614]E(x46141,f122(x46142))+~E(f789(f149(x46142),x46141),f122(x46142))
% 21.40/21.36 [4615]E(x46151,f122(x46152))+~E(f789(f148(x46152),x46151),f122(x46152))
% 21.40/21.36 [4616]E(x46161,f122(x46162))+~E(f789(f149(x46162),x46161),f122(x46162))
% 21.40/21.36 [4631]~P88(x46311)+E(f789(f113(x46311),x46312),f789(f112(x46311),x46312))
% 21.40/21.36 [4638]~E(x46382,f187(x46381))+E(f233(x46381,x46382),f184(f870(x46381,a856)))
% 21.40/21.36 [4639]~P59(x46391)+P1(f789(f70(x46391),x46392))
% 21.40/21.36 [4640]~P59(x46401)+P1(f789(f70(x46401),x46402))
% 21.40/21.36 [4647]E(x46471,f187(x46472))+E(f789(f234(x46472),f563(x46472,x46471)),x46471)
% 21.40/21.36 [4648]E(x46481,f187(x46482))+E(f789(f234(x46482),f599(x46482,x46481)),x46481)
% 21.40/21.36 [4649]E(x46491,f187(x46492))+E(f789(f234(x46492),f611(x46492,x46491)),x46491)
% 21.40/21.36 [4651]~E(f735(x46512,x46511),f122(x46511))+E(f168(x46511,x46512),f122(f864(x46511)))
% 21.40/21.36 [4660]~E(x46602,f122(x46601))+E(f789(f163(x46601),x46602),f184(f870(x46601,a856)))
% 21.40/21.36 [4661]~E(x46612,f122(x46611))+E(f184(f870(x46611,a856)),f789(f163(x46611),x46612))
% 21.40/21.36 [4662]E(x46621,x46622)+~E(f789(f109(a1),x46621),f789(f109(a1),x46622))
% 21.40/21.36 [4663]E(x46631,x46632)+~E(f789(f109(a1),x46631),f789(f109(a1),x46632))
% 21.40/21.36 [4666]E(f216(x46661,x46662),f2(a863))+P1(f789(f70(x46661),x46662))
% 21.40/21.36 [4684]~P110(x46841)+E(f91(x46841,f91(x46841,x46842)),f91(x46841,x46842))
% 21.40/21.36 [4696]~P70(x46961)+E(f789(f789(f250(x46961),x46962),f87(a863)),x46962)
% 21.40/21.36 [4697]~P78(x46971)+E(f789(f789(f250(x46971),x46972),f87(a863)),x46972)
% 21.40/21.36 [4699]E(x46991,x46992)+E(f274(x46991,x46992),f789(f789(f89(a108),x46992),f87(a108)))
% 21.40/21.36 [4700]E(f789(f49(x47001),x47002),f2(a863))+P1(f789(f70(x47001),x47002))
% 21.40/21.36 [4701]E(f789(f49(x47011),x47012),f2(a863))+P1(f789(f70(x47011),x47012))
% 21.40/21.36 [4702]E(f789(f49(x47021),x47022),f2(a863))+P1(f789(f70(x47021),x47022))
% 21.40/21.36 [4708]~P4(x47081)+E(f789(f789(f89(x47081),x47082),f2(x47081)),x47082)
% 21.40/21.36 [4709]~P70(x47091)+E(f789(f789(f89(x47091),x47092),f2(x47091)),x47092)
% 21.40/21.36 [4710]~P71(x47101)+E(f789(f789(f89(x47101),x47102),f2(x47101)),x47102)
% 21.40/21.36 [4711]~P70(x47111)+E(f789(f789(f90(x47111),x47112),f87(x47111)),x47112)
% 21.40/21.36 [4712]~P69(x47121)+E(f789(f789(f90(x47121),x47122),f87(x47121)),x47122)
% 21.40/21.36 [4713]~P78(x47131)+E(f789(f789(f90(x47131),x47132),f87(x47131)),x47132)
% 21.40/21.36 [4714]~P7(x47141)+E(f789(f789(f50(x47141),x47142),f87(x47141)),x47142)
% 21.40/21.36 [4715]~P68(x47151)+E(f789(f789(f3(x47151),x47152),f2(x47151)),x47152)
% 21.40/21.36 [4716]~P113(x47161)+E(f789(f789(f291(x47161),x47162),f87(x47161)),x47162)
% 21.40/21.36 [4717]~P92(x47171)+E(f789(f789(f110(x47171),x47172),f184(x47171)),x47172)
% 21.40/21.36 [4718]~P97(x47181)+E(f789(f789(f111(x47181),x47182),f247(x47181)),x47182)
% 21.40/21.36 [4719]~P70(x47191)+E(f789(f789(f250(x47191),x47192),f2(a863)),f87(x47191))
% 21.40/21.36 [4720]~P106(x47201)+E(f789(f789(f250(x47201),x47202),f2(a863)),f87(x47201))
% 21.40/21.36 [4721]~E(x47212,f184(f870(x47211,a856)))+E(f789(f49(x47211),x47212),f2(a863))
% 21.40/21.36 [4732]~P7(x47321)+E(f59(x47321,x47322,f2(x47321)),x47322)
% 21.40/21.36 [4740]~P70(x47401)+E(f789(f789(f90(x47401),x47402),f2(x47401)),f2(x47401))
% 21.40/21.36 [4741]~P123(x47411)+E(f789(f789(f90(x47411),x47412),f2(x47411)),f2(x47411))
% 21.40/21.36 [4742]~P7(x47421)+E(f789(f789(f50(x47421),x47422),f2(x47421)),f2(x47421))
% 21.40/21.36 [4743]~P114(x47431)+E(f789(f789(f291(x47431),x47432),f2(x47431)),f2(x47431))
% 21.40/21.36 [4744]~P97(x47441)+E(f789(f789(f110(x47441),x47442),f247(x47441)),f247(x47441))
% 21.40/21.36 [4745]~P92(x47451)+E(f789(f789(f111(x47451),x47452),f184(x47451)),f184(x47451))
% 21.40/21.36 [4746]E(x47461,f187(x47462))+~E(f233(x47462,x47461),f184(f870(x47462,a856)))
% 21.40/21.36 [4748]~P7(x47481)+E(f59(x47481,x47482,f87(x47481)),f2(x47481))
% 21.40/21.36 [4749]~P7(x47491)+E(f59(x47491,f2(x47491),x47492),f2(x47491))
% 21.40/21.36 [4800]P36(x48001,x48002)+~E(f612(x48002,x48001),f184(f870(x48001,a856)))
% 21.40/21.36 [4801]E(x48011,f122(x48012))+~E(f789(f163(x48012),x48011),f184(f870(x48012,a856)))
% 21.40/21.36 [4802]E(x48021,f122(x48022))+~E(f184(f870(x48022,a856)),f789(f163(x48022),x48021))
% 21.40/21.36 [4805]~E(x48051,x48052)+P1(f789(f789(a338,x48051),x48052))
% 21.40/21.36 [4815]P1(x48151)+P1(f789(f789(a343,x48151),x48152))
% 21.40/21.36 [4816]E(x48161,f122(x48162))+E(f789(f789(f159(x48162),x48161),f2(a863)),f789(f137(x48162),x48161))
% 21.40/21.36 [4821]~P1(x48212)+P1(f789(f789(a343,x48211),x48212))
% 21.40/21.36 [4822]~P1(x48222)+P1(f789(f789(a340,x48221),x48222))
% 21.40/21.36 [4823]~P1(x48231)+P1(f789(f789(a340,x48231),x48232))
% 21.40/21.36 [4833]~E(f736(x48332,x48331),f740(x48332,x48331))+P1(f789(f134(x48331),x48332))
% 21.40/21.36 [4841]E(f789(f264(x48411),x48412),f184(f870(x48411,a856)))+P1(f789(x48412,f564(x48412)))
% 21.40/21.36 [4842]E(f184(f870(x48421,a856)),f789(f264(x48421),x48422))+P1(f789(x48422,f588(x48422)))
% 21.40/21.36 [4906]~P110(x49061)+E(f789(f789(f90(x49061),x49062),f91(x49061,x49062)),f789(f84(x49061),x49062))
% 21.40/21.36 [4917]~E(x49171,f2(a1))+E(f60(x49171,x49172),f789(f789(f249(a1,a1),f2(a1)),f2(a1)))
% 21.40/21.36 [4918]~E(x49181,f2(a1))+E(f60(x49181,x49182),f789(f789(f249(a1,a1),f2(a1)),f2(a1)))
% 21.40/21.36 [4949]~P56(x49491,x49492)+P56(x49491,f789(f286(x49491,x49491),x49492))
% 21.40/21.36 [4966]~E(f789(a32,x49661),f789(f234(a857),x49662))+P1(f789(a26,f789(a29,x49661)))
% 21.40/21.36 [4970]E(x49701,x49702)+~P1(f789(f789(a338,x49701),x49702))
% 21.40/21.36 [4973]~P1(f789(a26,x49732))+P1(f789(a26,f37(x49731,x49732)))
% 21.40/21.36 [4974]~P1(f789(a26,x49742))+P1(f789(a26,f37(x49741,x49742)))
% 21.40/21.36 [4983]P1(x49831)+~P1(f789(f789(a339,x49832),x49831))
% 21.40/21.36 [4984]P1(x49841)+~P1(f789(f789(a339,x49841),x49842))
% 21.40/21.36 [4988]~P107(x49881)+P1(f789(f789(f240(x49881),x49882),f247(x49881)))
% 21.40/21.36 [4989]~P70(x49891)+P1(f789(f789(f287(x49891),x49892),f2(x49891)))
% 21.40/21.36 [4993]E(x49931,x49932)+~E(f789(x49931,f379(x49932,x49931)),f789(x49932,f379(x49932,x49931)))
% 21.40/21.36 [5027]E(x50271,f2(a863))+E(f218(x50271,f59(a863,x50272,x50271)),f218(x50272,x50271))
% 21.40/21.36 [5032]~P101(x50321)+P18(x50321,f789(f789(f146(x50321),x50322),f122(x50321)))
% 21.40/21.36 [5034]E(x50341,f2(a1))+P1(f789(f63(x50342,x50341),f60(x50342,x50341)))
% 21.40/21.36 [5051]~E(x50511,x50512)+P1(f789(f789(f241(a863),x50511),f789(a121,x50512)))
% 21.40/21.36 [5061]~E(x50611,f2(a863))+P1(f789(f789(f241(a863),x50611),f789(a121,x50612)))
% 21.40/21.36 [5071]P1(f789(x50711,x50712))+P1(f789(f789(f240(a1),f2(a1)),f792(x50711)))
% 21.40/21.36 [5106]P1(f789(a26,x51061))+~P1(f789(a26,f37(x51062,x51061)))
% 21.40/21.36 [5107]P1(f789(a26,x51071))+~P1(f789(a26,f37(x51072,x51071)))
% 21.40/21.36 [5108]P1(f789(a26,x51081))+~P1(f789(a26,f38(x51082,x51081)))
% 21.40/21.36 [5109]P1(f789(a26,x51091))+~P1(f789(a26,f38(x51092,x51091)))
% 21.40/21.36 [5110]P1(f789(a26,x51101))+~P1(f789(a26,f38(x51101,x51102)))
% 21.40/21.36 [5111]P1(f789(a26,x51111))+~P1(f789(a26,f38(x51111,x51112)))
% 21.40/21.36 [5139]P56(x51391,x51392)+~P56(x51391,f789(f286(x51391,x51391),x51392))
% 21.40/21.36 [5141]~E(f59(a863,x51412,x51411),f2(a863))+E(f789(f789(f90(a863),x51411),f807(x51411,x51412)),x51412)
% 21.40/21.36 [5142]~E(f59(a1,x51422,x51421),f2(a1))+E(f789(f789(f90(a1),x51421),f808(x51421,x51422)),x51422)
% 21.40/21.36 [5146]~P1(f789(f134(x51461),x51462))+P1(f789(f134(x51461),f147(x51461,x51462)))
% 21.40/21.36 [5148]~E(x51481,f789(a121,x51482))+P1(f789(f789(f240(a863),x51481),f789(a121,x51482)))
% 21.40/21.36 [5169]~P1(f789(x51691,x51692))+P1(f789(f789(f240(a1),f2(a1)),f791(x51691)))
% 21.40/21.36 [5181]E(f789(f789(f3(a863),f789(a114,x51811)),f789(a114,x51812)),f789(a114,x51811))+~P1(f789(a190,x51812))
% 21.40/21.36 [5209]E(f275(x52091,x52092),f87(a108))+~P1(f789(f789(f240(a108),x52091),f87(a108)))
% 21.40/21.36 [5296]E(f789(f789(f159(x52961),x52962),f736(x52962,x52961)),f789(f789(f159(x52961),x52962),f740(x52962,x52961)))+P1(f789(f134(x52961),x52962))
% 21.40/21.36 [5338]~P1(f789(x53381,f99(x53382,x53381)))+P1(f789(x53381,f613(x53382,x53381)))
% 21.40/21.36 [5402]P58(x54021,x54022)+~P1(f789(f329(x54021,x54022),f600(x54022,x54021)))
% 21.40/21.36 [5545]~E(f789(a121,f59(a863,x55451,x55452)),x55452)+E(f59(a863,f789(a121,x55451),x55452),f2(a863))
% 21.40/21.36 [5599]P36(x55991,x55992)+P1(f789(f789(f342(x55991),f699(x55992,x55991)),f700(x55992,x55991)))
% 21.40/21.36 [5605]~P2(x56051)+P1(f789(f789(f342(x56051),f789(f109(x56051),x56052)),f181(x56051)))
% 21.40/21.36 [5606]~P120(x56061)+P1(f789(f789(f342(x56061),f789(f109(x56061),x56062)),f119(x56061)))
% 21.40/21.36 [5607]~P120(x56071)+P1(f789(f789(f342(x56071),f789(f112(x56071),x56072)),f119(x56071)))
% 21.40/21.36 [5608]~P88(x56081)+P1(f789(f789(f342(x56081),f789(f113(x56081),x56082)),f119(x56081)))
% 21.40/21.36 [5762]E(f789(a121,f59(a863,x57621,x57622)),x57622)+E(f59(a863,f789(a121,x57621),x57622),f789(a121,f59(a863,x57621,x57622)))
% 21.40/21.36 [6181]P36(x61811,x61812)+~P1(f789(f789(f342(x61811),f590(x61812,x61811)),f330(x61811,x61812)))
% 21.40/21.36 [6215]~P117(x62151)+~P1(f789(f789(f241(x62151),f789(f109(x62151),x62152)),f2(x62151)))
% 21.40/21.36 [6216]~P80(x62161)+~P1(f789(f789(f241(x62161),f789(f84(x62161),x62162)),f2(x62161)))
% 21.40/21.36 [6305]P1(f789(f789(f241(a1),x63051),f59(a1,x63052,x63051)))+~P1(f789(f789(f241(a1),x63051),f2(a1)))
% 21.40/21.36 [6306]P1(f789(f789(f241(a1),x63061),f59(a1,x63062,x63061)))+~P1(f789(f789(f241(a1),x63061),f2(a1)))
% 21.40/21.36 [6414]E(f789(f789(f310(a863),f789(a121,x64141)),f303(a863,x64142,x64141)),f303(a863,x64142,f789(a121,x64141)))+~P1(f789(f789(f240(a863),x64142),f789(a121,x64141)))
% 21.40/21.36 [6638]E(f789(f148(x66381),x66382),x66382)+~P1(f789(f789(f240(a863),f789(f185(f864(x66381)),x66382)),f87(a863)))
% 21.40/21.36 [6661]~P80(x66611)+P1(f789(f789(f240(x66611),f789(f88(x66611),f789(f84(x66611),x66612))),f2(x66611)))
% 21.40/21.36 [6697]~P36(x66971,x66972)+P36(x66971,f789(f789(f289(x66971,x66971,x66971),x66972),f308(x66971,x66972)))
% 21.40/21.36 [6926]~P1(f789(f789(f241(a1),x69262),f2(a1)))+P1(f789(f789(f240(a1),f59(a1,x69261,x69262)),f2(a1)))
% 21.40/21.36 [6927]~P1(f789(f789(f241(a1),x69272),f2(a1)))+P1(f789(f789(f240(a1),f59(a1,x69271,x69272)),f2(a1)))
% 21.40/21.36 [7338]~P2(x73381)+E(f186(x73381,f789(f789(f9(x73381,x73381,x73381),f89(x73381)),f87(x73381)),x73382,f2(x73381)),f789(f109(x73381),x73382))
% 21.40/21.36 [7371]~P119(x73711)+~P1(f789(f789(f241(x73711),f789(f789(f90(x73711),x73712),x73712)),f2(x73711)))
% 21.40/21.36 [9897]~P110(x98971)+~P1(f789(f789(f241(x98971),f789(f789(f250(x98971),x98972),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f2(x98971)))
% 21.40/21.36 [4613]~E(x46132,f122(x46131))+E(f789(f185(f864(x46131)),x46132),f2(a863))
% 21.40/21.36 [4652]~E(x46521,f2(a863))+E(f789(f789(f89(a863),x46521),x46522),x46522)
% 21.40/21.36 [4653]~E(x46532,f2(a863))+E(f789(f789(f90(a863),x46531),x46532),f2(a863))
% 21.40/21.36 [4654]~E(x46541,f2(a863))+E(f789(f789(f90(a863),x46541),x46542),f2(a863))
% 21.40/21.36 [4655]~E(x46551,f2(a863))+E(f789(f789(f90(a863),x46551),x46552),f2(a863))
% 21.40/21.36 [4656]~E(x46562,f2(a1))+E(f789(f789(f50(a1),x46561),x46562),f2(a1))
% 21.40/21.36 [4657]~E(x46572,f2(a863))+E(f789(f789(f250(a863),x46571),x46572),f87(a863))
% 21.40/21.36 [4667]E(x46671,f122(x46672))+~E(f789(f185(f864(x46672)),x46671),f2(a863))
% 21.40/21.36 [4668]~P91(x46681)+E(f789(f789(f90(x46681),x46682),x46682),x46682)
% 21.40/21.36 [4669]~P91(x46691)+E(f789(f789(f90(x46691),x46692),x46692),x46692)
% 21.40/21.36 [4670]~P101(x46701)+E(f789(f789(f244(x46701),x46702),x46702),x46702)
% 21.40/21.36 [4671]~P101(x46711)+E(f789(f789(f244(x46711),x46712),x46712),x46712)
% 21.40/21.36 [4672]~P101(x46721)+E(f789(f789(f239(x46721),x46722),x46722),x46722)
% 21.40/21.36 [4673]~P101(x46731)+E(f789(f789(f239(x46731),x46732),x46732),x46732)
% 21.40/21.36 [4674]~P94(x46741)+E(f789(f789(f110(x46741),x46742),x46742),x46742)
% 21.40/21.36 [4675]~P94(x46751)+E(f789(f789(f110(x46751),x46752),x46752),x46752)
% 21.40/21.36 [4676]~P95(x46761)+E(f789(f789(f110(x46761),x46762),x46762),x46762)
% 21.40/21.36 [4677]~P95(x46771)+E(f789(f789(f111(x46771),x46772),x46772),x46772)
% 21.40/21.36 [4678]~P98(x46781)+E(f789(f789(f111(x46781),x46782),x46782),x46782)
% 21.40/21.36 [4679]~P98(x46791)+E(f789(f789(f111(x46791),x46792),x46792),x46792)
% 21.40/21.36 [4695]~P68(x46951)+E(f789(f789(f3(x46951),x46952),x46952),f2(x46951))
% 21.40/21.36 [4706]~P68(x47061)+E(f789(f88(x47061),f789(f88(x47061),x47062)),x47062)
% 21.40/21.36 [4707]~P90(x47071)+E(f789(f88(x47071),f789(f88(x47071),x47072)),x47072)
% 21.40/21.36 [4724]~E(x47242,f2(a863))+E(f789(f789(f250(a863),x47241),x47242),f789(a121,f2(a863)))
% 21.40/21.36 [4757]~P4(x47571)+E(f789(f789(f89(x47571),f2(x47571)),x47572),x47572)
% 21.40/21.36 [4758]~P70(x47581)+E(f789(f789(f89(x47581),f2(x47581)),x47582),x47582)
% 21.40/21.36 [4759]~P71(x47591)+E(f789(f789(f89(x47591),f2(x47591)),x47592),x47592)
% 21.40/21.36 [4760]~P70(x47601)+E(f789(f789(f90(x47601),f87(x47601)),x47602),x47602)
% 21.40/21.36 [4761]~P69(x47611)+E(f789(f789(f90(x47611),f87(x47611)),x47612),x47612)
% 21.40/21.36 [4762]~P78(x47621)+E(f789(f789(f90(x47621),f87(x47621)),x47622),x47622)
% 21.40/21.36 [4763]~P92(x47631)+E(f789(f789(f110(x47631),f184(x47631)),x47632),x47632)
% 21.40/21.36 [4764]~P97(x47641)+E(f789(f789(f111(x47641),f247(x47641)),x47642),x47642)
% 21.40/21.36 [4781]~P70(x47811)+E(f789(f789(f90(x47811),f2(x47811)),x47812),f2(x47811))
% 21.40/21.36 [4782]~P123(x47821)+E(f789(f789(f90(x47821),f2(x47821)),x47822),f2(x47821))
% 21.40/21.36 [4783]~P7(x47831)+E(f789(f789(f50(x47831),f2(x47831)),x47832),f2(x47831))
% 21.40/21.36 [4784]~P78(x47841)+E(f789(f789(f250(x47841),f87(x47841)),x47842),f87(x47841))
% 21.40/21.36 [4785]~P113(x47851)+E(f789(f789(f291(x47851),f2(x47851)),x47852),f2(x47851))
% 21.40/21.36 [4786]~P97(x47861)+E(f789(f789(f110(x47861),f247(x47861)),x47862),f247(x47861))
% 21.40/21.36 [4787]~P92(x47871)+E(f789(f789(f111(x47871),f184(x47871)),x47872),f184(x47871))
% 21.40/21.36 [4795]E(x47951,f122(x47952))+E(f140(x47952,f789(f149(x47952),x47951)),f789(f137(x47952),x47951))
% 21.40/21.36 [4796]E(x47961,f122(x47962))+E(f789(f137(x47962),f789(f149(x47962),x47961)),f140(x47962,x47961))
% 21.40/21.36 [4797]E(x47971,f2(a863))+~E(f789(f789(f89(a863),x47972),x47971),x47972)
% 21.40/21.36 [4803]~P120(x48031)+E(f789(f112(x48031),f789(f109(a1),x48032)),f789(f109(x48031),x48032))
% 21.40/21.36 [4804]~P88(x48041)+E(f789(f112(x48041),f789(f113(a1),x48042)),f789(f113(x48041),x48042))
% 21.40/21.36 [4809]E(x48091,f87(a863))+~E(f789(f789(f90(a863),x48092),x48091),f87(a863))
% 21.40/21.36 [4810]E(x48101,f87(a863))+~E(f789(f789(f90(a863),x48101),x48102),f87(a863))
% 21.40/21.36 [4811]E(x48111,f2(a863))+~E(f789(f789(f89(a863),x48112),x48111),f2(a863))
% 21.40/21.36 [4812]E(x48121,f2(a863))+~E(f789(f789(f89(a863),x48121),x48122),f2(a863))
% 21.40/21.36 [4813]E(x48131,f87(a863))+~E(f789(f789(f90(a863),x48132),x48131),f87(a863))
% 21.40/21.36 [4814]E(x48141,f87(a863))+~E(f789(f789(f90(a863),x48141),x48142),f87(a863))
% 21.40/21.36 [4826]~P110(x48261)+E(f789(f84(x48261),f789(f109(x48261),x48262)),f789(f109(x48261),x48262))
% 21.40/21.36 [4827]~P80(x48271)+E(f789(f84(x48271),f789(f88(x48271),x48272)),f789(f84(x48271),x48272))
% 21.40/21.36 [4828]~P80(x48281)+E(f789(f84(x48281),f789(f84(x48281),x48282)),f789(f84(x48281),x48282))
% 21.40/21.36 [4829]~P4(x48291)+E(f789(f161(x48291),f789(f149(x48291),x48292)),f789(f161(x48291),x48292))
% 21.40/21.36 [4834]~E(x48341,f789(a121,f2(a863)))+E(f789(f789(f250(a863),x48341),x48342),f789(a121,f2(a863)))
% 21.40/21.36 [4844]~P68(x48441)+E(f789(f789(f3(x48441),f2(x48441)),x48442),f789(f88(x48441),x48442))
% 21.40/21.36 [4845]~E(x48452,f2(a863))+E(f136(a863,f789(f302(a863,x48451),x48452)),f122(a863))
% 21.40/21.36 [4854]~P88(x48541)+E(f789(f789(f89(x48541),x48542),f789(f113(x48541),a92)),x48542)
% 21.40/21.36 [4855]E(x48551,f2(a1))+E(f61(f789(f84(a1),x48552),f789(f84(a1),x48551)),f67(x48552,x48551))
% 21.40/21.36 [4865]~E(x48651,x48652)+P1(f789(f789(f240(a863),x48651),x48652))
% 21.40/21.36 [4866]~E(x48661,x48662)+P1(f789(f789(f240(a863),x48661),x48662))
% 21.40/21.36 [4867]~E(x48671,x48672)+P1(f789(f789(f240(a863),x48671),x48672))
% 21.40/21.36 [4868]~E(x48681,x48682)+P1(f789(f789(f287(a863),x48681),x48682))
% 21.40/21.36 [4869]~E(x48691,x48692)+P1(f789(f789(f287(a863),x48691),x48692))
% 21.40/21.36 [4870]~E(x48701,x48702)+P1(f789(f789(f287(a863),x48701),x48702))
% 21.40/21.36 [4871]~E(x48711,x48712)+P1(f789(f789(f287(a863),x48711),x48712))
% 21.40/21.36 [4878]~E(x48781,f2(a108))+E(f789(f789(f89(a863),f789(a22,x48781)),x48782),x48782)
% 21.40/21.36 [4879]~E(f789(f113(a1),x48792),f789(f109(a1),x48791))+E(x48791,f789(a114,f789(f113(a1),x48792)))
% 21.40/21.36 [4888]~P10(x48881)+P10(f789(f789(f250(a1),x48881),x48882))
% 21.40/21.36 [4889]~P68(x48891)+E(f789(f789(f89(x48891),x48892),f789(f88(x48891),x48892)),f2(x48891))
% 21.40/21.36 [4890]~P90(x48901)+E(f789(f789(f110(x48901),x48902),f789(f88(x48901),x48902)),f247(x48901))
% 21.40/21.36 [4891]~P90(x48911)+E(f789(f789(f111(x48911),x48912),f789(f88(x48911),x48912)),f184(x48911))
% 21.40/21.36 [4915]E(x49151,f2(a863))+~E(f789(f88(a1),f789(f109(a1),x49152)),f789(f109(a1),x49151))
% 21.40/21.36 [4916]E(x49161,f2(a863))+~E(f789(f88(a1),f789(f109(a1),x49161)),f789(f109(a1),x49162))
% 21.40/21.36 [4926]E(f192(x49261,x49262),f2(a1))+P1(f789(f789(f240(a1),x49262),x49261))
% 21.40/21.36 [4927]E(f246(x49271,x49272),f2(a108))+P1(f789(f789(f241(a108),x49271),x49272))
% 21.40/21.36 [4928]E(f167(x49281,x49282),f122(a1))+P1(f789(f789(f240(a1),x49281),x49282))
% 21.40/21.36 [4941]E(x49411,f789(a121,f2(a863)))+~E(f789(f789(f90(a863),x49412),x49411),f789(a121,f2(a863)))
% 21.40/21.36 [4942]E(x49421,f789(a121,f2(a863)))+~E(f789(f789(f90(a863),x49421),x49422),f789(a121,f2(a863)))
% 21.40/21.36 [4943]~P105(x49431)+P1(f789(f789(f240(x49431),x49432),x49432))
% 21.40/21.36 [4944]~P70(x49441)+P1(f789(f789(f287(x49441),x49442),x49442))
% 21.40/21.36 [4947]~P88(x49471)+E(f789(f789(f90(x49471),x49472),f789(f113(x49471),a106)),f789(f88(x49471),x49472))
% 21.40/21.36 [4962]~P88(x49621)+E(f789(f88(x49621),f789(f113(x49621),x49622)),f789(f113(x49621),f789(f88(a1),x49622)))
% 21.40/21.36 [4963]~P120(x49631)+E(f789(f88(x49631),f789(f112(x49631),x49632)),f789(f112(x49631),f789(f88(a1),x49632)))
% 21.40/21.36 [4964]~P88(x49641)+E(f789(f88(x49641),f789(f113(x49641),x49642)),f789(f113(x49641),f789(f88(a1),x49642)))
% 21.40/21.36 [4998]~E(x49981,f789(a121,x49982))+P1(f789(f789(f241(a863),f2(a863)),x49981))
% 21.40/21.36 [5015]~P101(x50151)+E(f789(f88(f870(x50151,a856)),f789(f301(x50151),x50152)),f789(f304(x50151),x50152))
% 21.40/21.36 [5016]~P101(x50161)+E(f789(f88(f870(x50161,a856)),f789(f265(x50161),x50162)),f789(f266(x50161),x50162))
% 21.40/21.36 [5017]~P101(x50171)+E(f789(f88(f870(x50171,a856)),f789(f266(x50171),x50172)),f789(f265(x50171),x50172))
% 21.40/21.36 [5018]~P101(x50181)+E(f789(f88(f870(x50181,a856)),f789(f304(x50181),x50182)),f789(f301(x50181),x50182))
% 21.40/21.36 [5026]~E(f789(f109(a1),x50262),x50261)+P1(f789(f789(f240(a1),f2(a1)),x50261))
% 21.40/21.36 [5033]~E(x50332,f2(a1))+E(f67(x50331,x50332),f789(f789(f249(a1,a1),f2(a1)),f789(f84(a1),x50331)))
% 21.40/21.36 [5035]~P102(x50351)+P1(f789(f789(f240(x50351),f184(x50351)),x50352))
% 21.40/21.36 [5036]~P70(x50361)+P1(f789(f789(f287(x50361),f87(x50361)),x50362))
% 21.40/21.36 [5066]E(x50661,x50662)+~E(f789(f789(f89(a1),x50661),x50661),f789(f789(f89(a1),x50662),x50662))
% 21.40/21.36 [5070]~P1(f789(x50701,x50702))+P1(f789(x50701,f789(a114,f791(x50701))))
% 21.40/21.36 [5096]~P110(x50961)+E(f789(f789(f90(x50961),f91(x50961,x50962)),f789(f84(x50961),x50962)),x50962)
% 21.40/21.36 [5097]E(x50971,x50972)+~P1(f789(f789(f191(a25),x50971),x50972))
% 21.40/21.36 [5105]~E(x51052,f2(a863))+E(f94(f869(a863,a863),f62(x51051,x51052)),f789(f789(f249(a863,a863),f2(a863)),x51051))
% 21.40/21.36 [5112]~E(x51121,x51122)+~P1(f789(f789(f241(a863),x51121),x51122))
% 21.40/21.36 [5113]~E(x51131,x51132)+~P1(f789(f789(f241(a863),x51131),x51132))
% 21.40/21.36 [5114]~E(x51141,x51142)+~P1(f789(f789(f241(a863),x51141),x51142))
% 21.40/21.36 [5115]~E(x51151,x51152)+~P1(f789(f789(f241(a863),x51151),x51152))
% 21.40/21.36 [5116]~E(x51161,x51162)+~P1(f789(f789(f241(a863),x51161),x51162))
% 21.40/21.36 [5117]~E(x51171,x51172)+~P1(f789(f789(f241(a1),x51171),x51172))
% 21.40/21.36 [5120]~P2(x51201)+E(f789(f789(f89(x51201),f87(x51201)),f789(f109(x51201),x51202)),f789(f109(x51201),f789(a121,x51202)))
% 21.40/21.36 [5124]~E(x51241,f2(a863))+~P1(f789(f789(f241(a863),x51242),x51241))
% 21.40/21.36 [5137]E(f789(f49(x51371),f789(f163(x51371),x51372)),f789(f185(f864(x51371)),x51372))+~P1(f789(f134(x51371),x51372))
% 21.40/21.36 [5147]~P1(f789(x51471,f793(x51471)))+P1(f789(x51471,f789(f109(a1),x51472)))
% 21.40/21.36 [5158]E(f246(x51581,x51582),x51582)+~P1(f789(f789(f241(a108),x51581),x51582))
% 21.40/21.36 [5160]E(f275(x51601,x51602),f87(a108))+~P1(f789(f789(f241(a108),x51602),x51601))
% 21.40/21.36 [5161]E(f167(x51611,x51612),f122(a1))+~P1(f789(f789(f241(a1),x51612),x51611))
% 21.40/21.36 [5164]~P99(x51641)+E(f303(x51641,x51642,x51642),f789(f789(f310(x51641),x51642),f184(f870(x51641,a856))))
% 21.40/21.36 [5184]~E(f789(f789(f3(a863),x51841),x51842),f2(a863))+P1(f789(f789(f240(a863),x51841),x51842))
% 21.40/21.36 [5210]~P105(x52101)+~P1(f789(f789(f241(x52101),x52102),x52102))
% 21.40/21.36 [5212]~E(f59(a1,x52121,x52122),f2(a1))+E(f59(a1,x52121,f789(f88(a1),x52122)),f2(a1))
% 21.40/21.36 [5213]~E(f59(a1,x52131,x52132),f2(a1))+E(f59(a1,x52131,f789(f88(a1),x52132)),f2(a1))
% 21.40/21.36 [5214]~E(f59(a1,x52141,x52142),f2(a1))+E(f59(a1,f789(f88(a1),x52141),x52142),f2(a1))
% 21.40/21.36 [5215]~E(f59(a1,x52151,x52152),f2(a1))+E(f59(a1,f789(f88(a1),x52151),x52152),f2(a1))
% 21.40/21.36 [5222]E(f789(f302(a863,x52221),f789(a121,x52222)),f184(f870(a863,a856)))+P1(f789(f789(f240(a863),x52221),x52222))
% 21.40/21.36 [5239]E(f136(a863,f789(f302(a863,x52391),x52392)),f122(a863))+P1(f789(f789(f241(a863),x52391),x52392))
% 21.40/21.36 [5244]~E(f789(f49(x52441),f789(f163(x52441),x52442)),f789(f185(f864(x52441)),x52442))+P1(f789(f134(x52441),x52442))
% 21.40/21.36 [5248]~P1(f789(f134(x52481),x52482))+P1(f789(f134(x52481),f789(f148(x52481),x52482)))
% 21.40/21.36 [5249]~P1(f789(f134(x52491),x52492))+P1(f789(f134(x52491),f789(f149(x52491),x52492)))
% 21.40/21.36 [5257]P1(f789(x52571,x52572))+~P1(f789(x52571,f789(a114,f792(x52571))))
% 21.40/21.36 [5258]P1(f789(f789(f240(a863),x52582),x52581))+P1(f789(f789(f240(a863),x52581),x52582))
% 21.40/21.36 [5259]P1(f789(f789(f240(a1),x52592),x52591))+P1(f789(f789(f240(a1),x52591),x52592))
% 21.40/21.36 [5261]~P80(x52611)+P1(f789(f789(f240(x52611),x52612),f789(f84(x52611),x52612)))
% 21.40/21.36 [5264]P1(f789(x52641,f803(x52641)))+~P1(f789(x52641,f789(f109(a1),x52642)))
% 21.40/21.36 [5287]E(f789(f789(f50(a863),x52871),x52872),f2(a863))+~P1(f789(f789(f241(a863),x52871),x52872))
% 21.40/21.36 [5288]E(f789(f789(f3(a863),x52881),x52882),f2(a863))+~P1(f789(f789(f240(a863),x52881),x52882))
% 21.40/21.36 [5289]E(f789(f789(f3(a863),x52891),x52892),f2(a863))+~P1(f789(f789(f240(a863),x52891),x52892))
% 21.40/21.36 [5305]E(f59(a863,x53051,x53052),x53051)+~P1(f789(f789(f241(a863),x53051),x53052))
% 21.40/21.36 [5306]E(f59(a863,x53061,x53062),x53061)+~P1(f789(f789(f241(a863),x53061),x53062))
% 21.40/21.36 [5313]E(f59(a1,x53131,f789(f88(a1),x53132)),f292(x53131,x53132))+P1(f789(f789(f240(a1),f2(a1)),x53132))
% 21.40/21.36 [5325]E(f789(f789(f3(a1),x53251),x53252),f192(x53251,x53252))+~P1(f789(f789(f240(a1),x53252),x53251))
% 21.40/21.36 [5326]E(f789(f789(f3(a1),x53261),x53262),f192(x53261,x53262))+~P1(f789(f789(f240(a1),x53262),x53261))
% 21.40/21.36 [5344]P1(f789(f789(f240(a1),f2(a1)),f793(x53441)))+P1(f789(x53441,f789(f109(a1),x53442)))
% 21.40/21.36 [5357]~P117(x53571)+P1(f789(f789(f240(x53571),f2(x53571)),f789(f109(x53571),x53572)))
% 21.40/21.36 [5358]~P117(x53581)+P1(f789(f789(f240(x53581),f2(x53581)),f789(f109(x53581),x53582)))
% 21.40/21.36 [5359]~P80(x53591)+P1(f789(f789(f240(x53591),f2(x53591)),f789(f84(x53591),x53592)))
% 21.40/21.36 [5387]E(f789(f789(f89(a863),x53871),f809(x53872,x53871)),x53872)+~P1(f789(f789(f240(a863),x53871),x53872))
% 21.40/21.36 [5388]E(f789(f789(f89(a863),x53881),f742(x53882,x53881)),x53882)+~P1(f789(f789(f241(a863),x53881),x53882))
% 21.40/21.36 [5400]~E(f789(f113(a1),x54001),f789(f109(a1),x54002))+P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x54001)))
% 21.40/21.36 [5403]E(f303(a1,x54031,x54032),f184(f870(a1,a856)))+~P1(f789(f789(f241(a1),x54032),x54031))
% 21.40/21.36 [5407]~P110(x54071)+E(f789(f789(f90(x54071),f789(f84(x54071),x54072)),f789(f84(x54071),x54072)),f789(f789(f90(x54071),x54072),x54072))
% 21.40/21.36 [5412]E(f136(a863,f789(f302(a863,x54121),f789(a121,x54122))),f122(a863))+P1(f789(f789(f240(a863),x54121),x54122))
% 21.40/21.36 [5416]E(f789(f789(f50(a1),x54161),x54162),f293(x54161,x54162))+~P1(f789(f789(f240(a1),f2(a1)),x54162))
% 21.40/21.36 [5436]P1(f789(f134(x54361),x54362))+~P1(f789(f134(x54361),f789(f148(x54361),x54362)))
% 21.40/21.36 [5437]P1(f789(f134(x54371),x54372))+~P1(f789(f134(x54371),f789(f149(x54371),x54372)))
% 21.40/21.36 [5460]P1(f789(f70(a863),x54601))+P1(f789(f789(f342(a863),f381(x54601,x54602)),x54601))
% 21.40/21.36 [5461]P1(f789(f70(a863),x54611))+P1(f789(f789(f342(a863),f385(x54611,x54612)),x54611))
% 21.40/21.36 [5462]P1(f789(f789(f241(a863),x54622),f789(a121,x54621)))+P1(f789(f789(f241(a863),x54621),x54622))
% 21.40/21.36 [5463]E(f59(a1,x54631,x54632),f292(x54631,x54632))+~P1(f789(f789(f240(a1),f2(a1)),x54632))
% 21.40/21.36 [5465]E(f136(a863,f789(f302(a863,x54651),x54652)),f122(a863))+~P1(f789(f789(f240(a863),x54652),x54651))
% 21.40/21.36 [5466]E(f136(a863,f789(f302(a863,x54661),x54662)),f122(a863))+~P1(f789(f789(f240(a863),x54662),x54661))
% 21.40/21.36 [5467]~P76(x54671)+E(f789(f311(x54671,x54671,f88(x54671)),f789(f301(x54671),x54672)),f789(f266(x54671),f789(f88(x54671),x54672)))
% 21.40/21.36 [5468]~P76(x54681)+E(f789(f311(x54681,x54681,f88(x54681)),f789(f265(x54681),x54682)),f789(f304(x54681),f789(f88(x54681),x54682)))
% 21.40/21.36 [5469]~P76(x54691)+E(f789(f311(x54691,x54691,f88(x54691)),f789(f266(x54691),x54692)),f789(f301(x54691),f789(f88(x54691),x54692)))
% 21.40/21.36 [5470]~P76(x54701)+E(f789(f311(x54701,x54701,f88(x54701)),f789(f304(x54701),x54702)),f789(f265(x54701),f789(f88(x54701),x54702)))
% 21.40/21.36 [5481]E(x54811,f184(f870(x54812,a856)))+P1(f789(f789(f342(x54812),f346(x54811,x54812)),x54811))
% 21.40/21.36 [5482]E(x54821,f184(f870(x54822,a856)))+P1(f789(f789(f342(x54822),f360(x54821,x54822)),x54821))
% 21.40/21.36 [5489]~P1(f789(f789(f241(a863),x54891),x54892))+P1(f789(f789(f240(a863),x54891),x54892))
% 21.40/21.36 [5490]~P1(f789(f789(f241(a863),x54901),x54902))+P1(f789(f789(f240(a863),x54901),x54902))
% 21.40/21.36 [5491]~P1(f789(f789(f241(a863),x54911),x54912))+P1(f789(f789(f240(a863),x54911),x54912))
% 21.40/21.36 [5492]~P1(f789(f789(f241(a863),x54921),x54922))+P1(f789(f789(f240(a863),x54921),x54922))
% 21.40/21.36 [5493]~P1(f789(f789(f241(a863),x54931),x54932))+P1(f789(f789(f240(a863),x54931),x54932))
% 21.40/21.36 [5494]~P1(f789(f789(f241(a1),x54941),x54942))+P1(f789(f789(f240(a1),x54941),x54942))
% 21.40/21.36 [5506]E(f61(x55061,x55062),f789(f789(f249(a1,a1),f2(a1)),x55061))+~P1(f789(f789(f241(a1),x55061),x55062))
% 21.40/21.36 [5507]E(f217(f789(f88(a1),x55071),f789(f88(a1),x55072)),f217(x55071,x55072))+~P1(f789(f789(f241(a1),x55072),f2(a1)))
% 21.40/21.36 [5519]E(x55191,x55192)+~E(f789(a5,f789(a121,f789(a22,x55191))),f789(a5,f789(a121,f789(a22,x55192))))
% 21.40/21.36 [5524]E(f61(x55241,x55242),f789(f789(f249(a1,a1),f2(a1)),x55241))+~P1(f789(f789(f240(a1),x55242),f2(a1)))
% 21.40/21.36 [5551]E(f59(a863,f789(f113(a863),x55511),f789(f113(a863),x55512)),f2(a863))+~P1(f789(a190,f789(f113(a1),x55511)))
% 21.40/21.36 [5566]P1(f789(f789(f240(a1),f2(a1)),f803(x55661)))+~P1(f789(x55661,f789(f109(a1),x55662)))
% 21.40/21.36 [5597]P38(f303(a1,x55971,x55972))+~P1(f789(f789(f240(a1),f2(a1)),x55971))
% 21.40/21.36 [5601]~P1(f789(f70(x56011),x56012))+P1(f789(f70(f870(x56011,a856)),f789(f309(x56011),x56012)))
% 21.40/21.36 [5614]E(f789(f789(f89(a1),x56141),f789(f109(a1),f810(x56142,x56141))),x56142)+~P1(f789(f789(f240(a1),x56141),x56142))
% 21.40/21.36 [5622]P1(f789(f789(f240(a863),x56221),x56222))+P1(f789(f789(f240(a863),f789(a121,x56222)),x56221))
% 21.40/21.36 [5667]E(f789(f789(f50(a863),f789(f113(a863),x56671)),f789(f113(a863),x56672)),f2(a863))+~P1(f789(a190,f789(f113(a1),x56671)))
% 21.40/21.36 [5668]E(f789(f789(f90(a863),f789(f113(a863),x56681)),f789(f113(a863),x56682)),f2(a863))+~P1(f789(f789(f241(a1),x56681),a92))
% 21.40/21.36 [5669]P1(f789(f789(f241(a863),x56691),f789(a121,x56692)))+~P1(f789(f789(f241(a863),x56691),x56692))
% 21.40/21.36 [5670]P1(f789(f789(f241(a863),x56701),f789(a121,x56702)))+~P1(f789(f789(f241(a863),x56701),x56702))
% 21.40/21.36 [5671]P1(f789(f789(f241(a863),x56711),f789(a121,x56712)))+~P1(f789(f789(f240(a863),x56711),x56712))
% 21.40/21.36 [5672]P1(f789(f789(f241(a863),x56721),f789(a121,x56722)))+~P1(f789(f789(f240(a863),x56721),x56722))
% 21.40/21.36 [5673]P1(f789(f789(f240(a863),x56731),f789(a121,x56732)))+~P1(f789(f789(f240(a863),x56731),x56732))
% 21.40/21.36 [5674]P1(f789(f789(f240(a863),x56741),f789(a121,x56742)))+~P1(f789(f789(f240(a863),x56741),x56742))
% 21.40/21.36 [5675]~E(x56751,x56752)+P1(f789(f789(f241(a1),x56751),f789(f789(f89(a1),x56752),f87(a1))))
% 21.40/21.36 [5678]E(f59(a1,x56781,x56782),f2(a1))+E(f789(f789(f3(a1),x56782),f59(a1,x56781,x56782)),f59(a1,f789(f88(a1),x56781),x56782))
% 21.40/21.36 [5686]E(x56861,f122(x56862))+P1(f789(f789(f342(x56862),f140(x56862,x56861)),f789(f163(x56862),x56861)))
% 21.40/21.36 [5697]E(f94(f869(a863,a863),f62(x56971,x56972)),f789(f789(f249(a863,a863),f2(a863)),x56971))+~P1(f789(f789(f241(a863),x56971),x56972))
% 21.40/21.36 [5698]E(f94(f869(a863,a863),f62(x56981,x56982)),f789(f789(f249(a863,a863),f2(a863)),x56981))+~P1(f789(f789(f241(a863),x56981),x56982))
% 21.40/21.36 [5738]E(f789(f789(f89(a863),f789(f113(a863),x57381)),f789(f113(a863),x57382)),f789(f113(a863),x57382))+~P1(f789(f789(f241(a1),x57381),a92))
% 21.40/21.36 [5739]E(f789(f789(f3(a863),f789(f113(a863),x57391)),f789(f113(a863),x57392)),f789(f113(a863),x57391))+~P1(f789(f789(f241(a1),x57392),a92))
% 21.40/21.36 [5744]E(f789(a121,f789(f789(f89(a863),x57441),f707(x57442,x57441))),x57442)+~P1(f789(f789(f241(a863),x57441),x57442))
% 21.40/21.36 [5745]E(f789(a121,f789(f789(f89(a863),x57451),f710(x57452,x57451))),x57452)+~P1(f789(f789(f241(a863),x57451),x57452))
% 21.40/21.36 [5752]~P1(f789(f789(f287(a1),x57521),x57522))+P1(f789(f789(f287(a1),x57521),f789(f88(a1),x57522)))
% 21.40/21.36 [5753]P1(f789(f789(f241(a863),f2(a863)),f742(x57531,x57532)))+~P1(f789(f789(f241(a863),x57532),x57531))
% 21.40/21.36 [5772]P1(f789(x57721,x57722))+~P1(f789(x57721,f789(a98,f614(x57722,x57721))))
% 21.40/21.36 [5780]~P1(f789(f789(f241(a863),x57801),f789(a121,x57802)))+P1(f789(f789(f240(a863),x57801),x57802))
% 21.40/21.36 [5828]E(f789(f789(f310(a863),x58281),f789(f302(a863,x58282),x58281)),f789(f302(a863,x58282),f789(a121,x58281)))+~P1(f789(f789(f240(a863),x58282),x58281))
% 21.40/21.36 [5833]E(x58331,f122(x58332))+E(f789(f789(f132(x58332),f123(x58332,x58331)),f789(f789(f146(x58332),f140(x58332,x58331)),f122(x58332))),x58331)
% 21.40/21.36 [5843]P1(f789(f70(x58431),x58432))+~P1(f789(f789(f241(a863),f2(a863)),f789(f49(x58431),x58432)))
% 21.40/21.36 [5844]P1(f789(f70(x58441),x58442))+~P1(f789(f789(f241(a863),f2(a863)),f789(f49(x58441),x58442)))
% 21.40/21.36 [5848]~E(x58481,f184(f870(x58482,a856)))+~P1(f789(f789(f241(a863),f2(a863)),f789(f49(x58482),x58481)))
% 21.40/21.36 [5856]~P1(f789(f789(f241(a863),x58561),x58562))+P1(f789(f789(f240(a863),f789(a121,x58561)),x58562))
% 21.40/21.36 [5857]~P1(f789(f789(f241(a863),x58571),x58572))+P1(f789(f789(f240(a863),f789(a121,x58571)),x58572))
% 21.40/21.36 [5858]~P1(f789(f789(f241(a863),x58581),x58582))+P1(f789(f789(f240(a863),f789(a121,x58581)),x58582))
% 21.40/21.36 [5866]E(x58661,f122(x58662))+P1(f789(f789(f342(x58662),f789(f137(x58662),x58661)),f789(f163(x58662),x58661)))
% 21.40/21.36 [5872]~P117(x58721)+P1(f789(f789(f241(x58721),x58722),f789(f789(f89(x58721),x58722),f87(x58721))))
% 21.40/21.36 [5874]~P80(x58741)+P1(f789(f789(f240(x58741),f789(f88(x58741),x58742)),f789(f84(x58741),x58742)))
% 21.40/21.36 [5886]P1(f789(f789(f287(a1),x58861),x58862))+~P1(f789(f789(f287(a1),x58861),f789(f88(a1),x58862)))
% 21.40/21.36 [5887]~E(x58871,x58872)+E(f290(a863,f287(a863),x58871,x58872),f789(f789(f310(a863),x58871),f184(f870(a863,a856))))
% 21.40/21.36 [5905]P1(f789(f70(a863),x59051))+~P1(f789(f789(f241(a863),f385(x59051,x59052)),x59052))
% 21.40/21.36 [5906]P1(f789(f70(a863),x59061))+~P1(f789(f789(f240(a863),f381(x59061,x59062)),x59062))
% 21.40/21.36 [5910]~P1(f789(f70(f869(x59101,x59101)),x59102))+P1(f789(f70(x59101),f789(f284(x59101),x59102)))
% 21.40/21.36 [5959]E(f290(a863,f287(a863),x59591,x59592),f184(f870(a863,a856)))+P1(f789(f789(f287(a863),x59591),x59592))
% 21.40/21.36 [5960]E(f290(a863,f287(a863),x59601,x59602),f184(f870(a863,a856)))+P1(f789(f789(f287(a863),x59601),x59602))
% 21.40/21.36 [5961]E(f167(f789(f113(a1),x59611),f789(f113(a1),x59612)),f122(a1))+P1(f789(f789(f240(a1),f789(f113(a1),x59611)),f789(f113(a1),x59612)))
% 21.40/21.36 [5966]~P1(f789(f789(f241(a863),x59662),f789(a121,x59661)))+~P1(f789(f789(f241(a863),x59661),x59662))
% 21.40/21.36 [5967]~P99(x59671)+E(f789(f789(f111(f870(x59671,a856)),f789(f301(x59671),x59672)),f789(f266(x59671),x59672)),f789(f789(f310(x59671),x59672),f184(f870(x59671,a856))))
% 21.40/21.36 [5969]E(f789(f789(f250(a863),f789(f113(a863),x59691)),f789(f113(a863),x59692)),f789(f789(f250(a863),f2(a863)),f789(f113(a863),x59692)))+~P1(f789(a190,f789(f113(a1),x59691)))
% 21.40/21.36 [5981]P1(f789(f70(x59811),x59812))+~P1(f789(f70(f870(x59811,a856)),f789(f309(x59811),x59812)))
% 21.40/21.36 [6004]P1(f789(f789(f241(a863),f789(a121,x60041)),f789(a121,x60042)))+~P1(f789(f789(f241(a863),x60041),x60042))
% 21.40/21.36 [6005]P1(f789(f789(f241(a863),f789(a121,x60051)),f789(a121,x60052)))+~P1(f789(f789(f241(a863),x60051),x60052))
% 21.40/21.36 [6006]P1(f789(f789(f241(a863),f789(a22,x60061)),f789(a22,x60062)))+~P1(f789(f789(f241(a108),x60061),x60062))
% 21.40/21.36 [6007]P1(f789(f789(f241(a108),f789(a5,x60071)),f789(a5,x60072)))+~P1(f789(f789(f241(a863),x60071),x60072))
% 21.40/21.36 [6008]P1(f789(f789(f240(a863),f789(a121,x60081)),f789(a121,x60082)))+~P1(f789(f789(f240(a863),x60081),x60082))
% 21.40/21.36 [6009]P1(f789(f789(f240(a863),f789(a22,x60091)),f789(a22,x60092)))+~P1(f789(f789(f240(a108),x60091),x60092))
% 21.40/21.36 [6010]P1(f789(f789(f240(a108),f789(a5,x60101)),f789(a5,x60102)))+~P1(f789(f789(f240(a863),x60101),x60102))
% 21.40/21.36 [6013]E(x60131,x60132)+~E(f789(f311(a863,a1,f109(a1)),x60131),f789(f311(a863,a1,f109(a1)),x60132))
% 21.40/21.36 [6030]P1(f789(f789(f241(a863),x60301),x60302))+~P1(f789(f789(f241(a863),f789(a121,x60301)),x60302))
% 21.40/21.36 [6031]P1(f789(f789(f241(a863),x60311),x60312))+~P1(f789(f789(f240(a863),f789(a121,x60311)),x60312))
% 21.40/21.36 [6032]P1(f789(f789(f241(a863),x60321),x60322))+~P1(f789(f789(f240(a863),f789(a121,x60321)),x60322))
% 21.40/21.36 [6033]P1(f789(f789(f241(a863),x60331),x60332))+~P1(f789(f789(f240(a863),f789(a121,x60331)),x60332))
% 21.40/21.36 [6034]P1(f789(f789(f240(a863),x60341),x60342))+~P1(f789(f789(f240(a863),f789(a121,x60341)),x60342))
% 21.40/21.36 [6051]E(f59(a1,x60511,x60512),f2(a1))+E(f789(f789(f3(a1),f59(a1,x60511,x60512)),x60512),f59(a1,x60511,f789(f88(a1),x60512)))
% 21.40/21.36 [6058]E(x60581,f122(x60582))+E(f789(f789(f132(x60582),f147(x60582,x60581)),f789(f789(f146(x60582),f789(f137(x60582),x60581)),f122(x60582))),f789(f148(x60582),x60581))
% 21.40/21.36 [6121]E(f789(f49(f870(x61211,a856)),f789(f309(x61211),x61212)),f789(f789(f250(a863),f789(a121,f789(a121,f2(a863)))),f789(f49(x61211),x61212)))+~P1(f789(f70(x61211),x61212))
% 21.40/21.36 [6124]E(x61241,f122(x61242))+E(f789(f789(f159(x61242),x61241),f789(f789(f3(a863),f789(f185(f864(x61242)),x61241)),f87(a863))),f140(x61242,x61241))
% 21.40/21.36 [6148]~P1(f789(f184(f870(x61481,a856)),x61482))+P1(f789(f789(f342(x61481),x61482),f184(f870(x61481,a856))))
% 21.40/21.36 [6178]~P1(f789(f70(x61781),f51(f870(x61781,a856),x61782)))+P1(f789(f70(f870(x61781,a856)),x61782))
% 21.40/21.36 [6199]P1(f789(f789(f240(a863),f789(f113(a863),x61991)),f789(f113(a863),x61992)))+~P1(f789(f789(f240(a1),x61991),a92))
% 21.40/21.36 [6219]~P1(f789(f789(f241(a1),x62191),x62192))+P1(f789(f789(f241(a1),x62191),f789(f789(f89(a1),x62192),f87(a1))))
% 21.40/21.36 [6220]~P1(f789(f789(f240(a1),x62201),x62202))+P1(f789(f789(f241(a1),x62201),f789(f789(f89(a1),x62202),f87(a1))))
% 21.40/21.36 [6221]~P1(f789(f789(f241(a1),x62211),x62212))+P1(f789(f789(f240(a1),x62211),f789(f789(f3(a1),x62212),f87(a1))))
% 21.40/21.36 [6223]~P1(f789(f789(f241(a863),x62231),x62232))+P1(f789(f789(f241(a1),f789(f109(a1),x62231)),f789(f109(a1),x62232)))
% 21.40/21.36 [6224]~P1(f789(f789(f241(a863),x62241),x62242))+P1(f789(f789(f241(a1),f789(f109(a1),x62241)),f789(f109(a1),x62242)))
% 21.40/21.36 [6225]~P1(f789(f789(f241(a1),x62251),x62252))+P1(f789(f789(f241(a1),f789(f113(a1),x62251)),f789(f113(a1),x62252)))
% 21.40/21.36 [6226]~P1(f789(f789(f240(a1),x62261),x62262))+P1(f789(f789(f240(a863),f789(f113(a863),x62261)),f789(f113(a863),x62262)))
% 21.40/21.36 [6227]~P1(f789(f789(f240(a863),x62271),x62272))+P1(f789(f789(f240(a1),f789(f109(a1),x62271)),f789(f109(a1),x62272)))
% 21.40/21.36 [6228]~P1(f789(f789(f240(a863),x62281),x62282))+P1(f789(f789(f240(a1),f789(f109(a1),x62281)),f789(f109(a1),x62282)))
% 21.40/21.36 [6229]~P1(f789(f789(f240(a1),x62291),x62292))+P1(f789(f789(f240(a1),f789(f113(a1),x62291)),f789(f113(a1),x62292)))
% 21.40/21.36 [6230]~P1(f789(f789(f287(a863),x62301),x62302))+P1(f789(f789(f287(a1),f789(f109(a1),x62301)),f789(f109(a1),x62302)))
% 21.40/21.36 [6231]~P1(f789(f789(f287(a863),x62311),x62312))+P1(f789(f789(f287(a1),f789(f109(a1),x62311)),f789(f109(a1),x62312)))
% 21.40/21.36 [6238]~E(x62382,f184(f870(x62381,a856)))+P1(f789(f789(f240(f870(x62381,a856)),x62382),f184(f870(x62381,a856))))
% 21.40/21.36 [6246]~P1(f789(f789(f240(a863),x62461),x62462))+~P1(f789(f789(f240(a863),f789(a121,x62462)),x62461))
% 21.40/21.36 [6292]~P1(f789(f789(f241(a863),f789(a121,x62921)),f789(a121,x62922)))+P1(f789(f789(f241(a863),x62921),x62922))
% 21.40/21.36 [6293]~P1(f789(f789(f241(a863),f789(a121,x62931)),f789(a121,x62932)))+P1(f789(f789(f241(a863),x62931),x62932))
% 21.40/21.36 [6294]~P1(f789(f789(f241(a108),f789(a5,x62941)),f789(a5,x62942)))+P1(f789(f789(f241(a863),x62941),x62942))
% 21.40/21.36 [6295]~P1(f789(f789(f241(a863),f789(a114,x62951)),f789(a114,x62952)))+P1(f789(f789(f241(a1),x62951),x62952))
% 21.40/21.36 [6296]~P1(f789(f789(f241(a863),f789(a22,x62961)),f789(a22,x62962)))+P1(f789(f789(f241(a108),x62961),x62962))
% 21.40/21.36 [6297]~P1(f789(f789(f240(a863),f789(a121,x62971)),f789(a121,x62972)))+P1(f789(f789(f240(a863),x62971),x62972))
% 21.40/21.36 [6298]~P1(f789(f789(f240(a108),f789(a5,x62981)),f789(a5,x62982)))+P1(f789(f789(f240(a863),x62981),x62982))
% 21.40/21.36 [6299]~P1(f789(f789(f240(a863),f789(a22,x62991)),f789(a22,x62992)))+P1(f789(f789(f240(a108),x62991),x62992))
% 21.40/21.36 [6316]~P1(f789(f789(f287(a863),x63162),x63161))+P1(f789(f789(f342(a863),x63161),f294(a863,f287(a863),x63162)))
% 21.40/21.36 [6317]~P1(f789(f789(f287(a863),x63171),x63172))+P1(f789(f789(f342(a863),x63171),f296(a863,f287(a863),x63172)))
% 21.40/21.36 [6322]~P1(f789(f789(f342(x63221),x63222),f184(f870(x63221,a856))))+P1(f789(f184(f870(x63221,a856)),x63222))
% 21.40/21.36 [6343]~P1(f789(f789(f241(a863),f789(a114,x63432)),f789(a114,x63431)))+P1(f789(f789(f241(a1),f2(a1)),x63431))
% 21.40/21.36 [6354]~E(f59(a1,f789(f113(a1),x63542),f789(f113(a1),x63541)),f2(a1))+P1(f789(f789(f287(a1),f789(f113(a1),x63541)),f789(f113(a1),x63542)))
% 21.40/21.36 [6372]P1(f789(f789(f240(a1),f2(a1)),f59(a1,x63721,x63722)))+~P1(f789(f789(f241(a1),f2(a1)),x63722))
% 21.40/21.36 [6373]P1(f789(f789(f240(a1),f2(a1)),f59(a1,x63731,x63732)))+~P1(f789(f789(f241(a1),f2(a1)),x63732))
% 21.40/21.36 [6540]P36(x65401,x65402)+~E(f789(f789(f289(x65401,x65401,x65401),x65402),x65402),f184(f870(f869(x65401,x65401),a856)))
% 21.40/21.36 [6556]~P36(x65561,x65562)+P36(x65561,f789(f789(f289(x65561,x65561,x65561),x65562),x65562))
% 21.40/21.36 [6568]P1(f789(f789(f241(a1),x65681),x65682))+~P1(f789(f789(f240(a1),x65681),f789(f789(f3(a1),x65682),f87(a1))))
% 21.40/21.36 [6569]P1(f789(f789(f240(a1),x65691),x65692))+~P1(f789(f789(f241(a1),x65691),f789(f789(f89(a1),x65692),f87(a1))))
% 21.40/21.36 [6571]P1(f789(f789(f241(a863),x65711),x65712))+~P1(f789(f789(f241(a1),f789(f109(a1),x65711)),f789(f109(a1),x65712)))
% 21.40/21.36 [6572]P1(f789(f789(f241(a863),x65721),x65722))+~P1(f789(f789(f241(a1),f789(f109(a1),x65721)),f789(f109(a1),x65722)))
% 21.40/21.36 [6573]P1(f789(f789(f241(a1),x65731),x65732))+~P1(f789(f789(f241(a863),f789(f113(a863),x65731)),f789(f113(a863),x65732)))
% 21.40/21.36 [6574]P1(f789(f789(f241(a1),x65741),x65742))+~P1(f789(f789(f241(a1),f789(f113(a1),x65741)),f789(f113(a1),x65742)))
% 21.40/21.36 [6575]P1(f789(f789(f240(a863),x65751),x65752))+~P1(f789(f789(f240(a1),f789(f109(a1),x65751)),f789(f109(a1),x65752)))
% 21.40/21.36 [6576]P1(f789(f789(f240(a863),x65761),x65762))+~P1(f789(f789(f240(a1),f789(f109(a1),x65761)),f789(f109(a1),x65762)))
% 21.40/21.36 [6577]P1(f789(f789(f240(a1),x65771),x65772))+~P1(f789(f789(f240(a1),f789(f113(a1),x65771)),f789(f113(a1),x65772)))
% 21.40/21.36 [6578]P1(f789(f789(f287(a863),x65781),x65782))+~P1(f789(f789(f287(a1),f789(f109(a1),x65781)),f789(f109(a1),x65782)))
% 21.40/21.36 [6579]P1(f789(f789(f287(a863),x65791),x65792))+~P1(f789(f789(f287(a1),f789(f109(a1),x65791)),f789(f109(a1),x65792)))
% 21.40/21.36 [6634]E(f59(a1,f789(f113(a1),x66341),f789(f113(a1),x66342)),f2(a1))+~P1(f789(f789(f287(a1),f789(f113(a1),x66342)),f789(f113(a1),x66341)))
% 21.40/21.36 [6648]~E(f290(a863,f287(a863),x66481,x66482),f184(f870(a863,a856)))+~P1(f789(f789(f287(a863),x66481),x66482))
% 21.40/21.36 [6649]~E(f290(a863,f287(a863),x66491,x66492),f184(f870(a863,a856)))+~P1(f789(f789(f287(a863),x66491),x66492))
% 21.40/21.36 [6675]P1(f789(f789(f287(a863),x66751),x66752))+~P1(f789(f789(f342(a863),x66752),f294(a863,f287(a863),x66751)))
% 21.40/21.36 [6676]P1(f789(f789(f287(a863),x66761),x66762))+~P1(f789(f789(f342(a863),x66761),f296(a863,f287(a863),x66762)))
% 21.40/21.36 [6677]~E(f782(x66772,x66771),f122(x66771))+E(f789(f138(f864(x66771),f864(x66771),f132(x66771),f122(x66771)),x66772),f122(x66771))
% 21.40/21.36 [6678]~E(f784(x66782,x66781),f122(x66781))+E(f789(f138(f864(x66781),f864(x66781),f132(x66781),f122(x66781)),x66782),f122(x66781))
% 21.40/21.36 [6685]~P9(x66851)+E(f789(f138(x66851,x66851,f111(x66851),f247(x66851)),x66852),f52(x66851,f789(f163(x66851),x66852)))
% 21.40/21.36 [6686]~P9(x66861)+E(f789(f138(x66861,x66861,f110(x66861),f184(x66861)),x66862),f51(x66861,f789(f163(x66861),x66862)))
% 21.40/21.36 [6698]E(x66981,f2(a108))+E(f789(f789(f89(a863),f789(a22,f789(f789(f3(a108),x66981),f87(a108)))),f789(a121,x66982)),f789(f789(f89(a863),f789(a22,x66981)),x66982))
% 21.40/21.36 [6750]P1(f789(f789(f241(a1),f789(f789(f3(a1),x67501),x67502)),f2(a1)))+~P1(f789(f789(f241(a1),x67501),x67502))
% 21.40/21.36 [6777]~P101(x67771)+E(f789(f789(f110(f870(x67771,a856)),f789(f789(f310(x67771),x67772),f184(f870(x67771,a856)))),f789(f304(x67771),x67772)),f789(f266(x67771),x67772))
% 21.40/21.36 [6859]~P58(x68591,x68592)+P36(x68591,f789(f264(f869(x68591,x68591)),f789(f259(x68591,x68591,a856),x68592)))
% 21.40/21.36 [6860]~P58(x68601,x68602)+P56(x68601,f789(f264(f869(x68601,x68601)),f789(f259(x68601,x68601,a856),x68602)))
% 21.40/21.36 [6861]E(x68611,f184(f870(x68612,a856)))+~P1(f789(f789(f240(f870(x68612,a856)),x68611),f184(f870(x68612,a856))))
% 21.40/21.36 [6945]~P1(f789(f789(f241(a863),f2(a863)),x69452))+P1(f789(f789(f241(a863),f59(a863,x69451,x69452)),x69452))
% 21.40/21.36 [6946]~P1(f789(f789(f241(a1),f2(a1)),x69462))+P1(f789(f789(f241(a1),f59(a1,x69461,x69462)),x69462))
% 21.40/21.36 [6947]~P1(f789(f789(f241(a1),f2(a1)),x69472))+P1(f789(f789(f241(a1),f59(a1,x69471,x69472)),x69472))
% 21.40/21.36 [6948]~P1(f789(f789(f241(a863),f2(a863)),x69482))+P1(f789(f789(f240(a863),f59(a863,x69481,x69482)),x69482))
% 21.40/21.36 [6949]~P1(f789(f789(f240(a1),f2(a1)),x69491))+P1(f789(f789(f240(a1),f59(a1,x69491,x69492)),x69491))
% 21.40/21.36 [7021]~P99(x70211)+E(f789(f789(f3(f870(x70211,a856)),f789(f789(f310(x70211),x70212),f184(f870(x70211,a856)))),f789(f265(x70211),x70212)),f789(f789(f310(x70211),x70212),f184(f870(x70211,a856))))
% 21.40/21.36 [7099]~P49(x70991,x70992)+P47(x70991,f247(f870(x70991,a856)),f789(f264(f869(x70991,x70991)),f789(f259(x70991,x70991,a856),x70992)))
% 21.40/21.36 [7100]P1(f789(x71001,x71002))+P1(f789(f789(f342(f870(f869(a863,a863),a856)),f614(x71002,x71001)),a107))
% 21.40/21.36 [7142]E(f789(f789(f132(a863),f136(a863,f789(f302(a863,x71421),x71422))),f789(f789(f146(a863),x71422),f122(a863))),f136(a863,f789(f302(a863,x71421),f789(a121,x71422))))+~P1(f789(f789(f240(a863),x71421),x71422))
% 21.40/21.36 [7143]E(f789(f789(f132(a863),f136(a863,f789(f302(a863,x71431),x71432))),f789(f789(f146(a863),x71432),f122(a863))),f136(a863,f789(f302(a863,x71431),f789(a121,x71432))))+~P1(f789(f789(f240(a863),x71431),x71432))
% 21.40/21.36 [7300]E(x73001,f2(a863))+~E(f789(f138(a863,a863,f89(a863),x73001),x73002),f2(a863))
% 21.40/21.36 [7329]~P1(f789(f789(f241(a1),f789(f789(f3(a1),x73291),x73292)),f2(a1)))+P1(f789(f789(f241(a1),x73291),x73292))
% 21.40/21.36 [7359]P36(x73591,x73592)+~P36(x73591,f789(f789(f289(x73591,x73591,x73591),x73592),x73592))
% 21.40/21.36 [7391]~P1(f789(f789(f240(a863),f789(a121,x73911)),x73912))+P1(f180(a856,a183,f789(f240(a863),x73911),x73912))
% 21.40/21.36 [7551]P29(a863,a863,f789(f789(f9(a863,a863,a863),f3(a863)),x75511),x75512)+P1(f789(f789(f342(a863),f616(x75511,x75512)),x75512))
% 21.40/21.36 [7609]E(f789(f789(f789(f74(a863,x76091,f89(a863)),f789(f18(a863,x76091),f87(a863))),f2(a863)),x76092),f789(f49(x76091),x76092))+~P1(f789(f70(x76091),x76092))
% 21.40/21.36 [7610]E(f789(f789(f789(f74(a863,x76101,f89(a863)),f789(f18(a863,x76101),f87(a863))),f2(a863)),x76102),f789(f49(x76101),x76102))+~P1(f789(f70(x76101),x76102))
% 21.40/21.36 [7653]P29(a863,a863,f789(f789(f9(a863,a863,a863),f3(a863)),x76531),x76532)+~P1(f789(f789(f240(a863),x76531),f616(x76531,x76532)))
% 21.40/21.36 [7709]P36(x77091,x77092)+P1(f789(f789(f240(f870(x77091,a856)),f612(x77092,x77091)),f789(f285(x77091,x77091,x77092),f612(x77092,x77091))))
% 21.40/21.36 [7713]P58(x77131,x77132)+~P36(x77131,f789(f264(f869(x77131,x77131)),f789(f259(x77131,x77131,a856),x77132)))
% 21.40/21.36 [7785]P1(f789(f789(f240(a863),f789(a121,x77851)),x77852))+~P1(f180(a856,a183,f789(f240(a863),x77851),x77852))
% 21.40/21.36 [7841]P1(f789(f789(f342(f869(a863,a863)),f789(f789(f249(a863,a863),x78411),x78412)),f308(a863,a331)))+~P1(f789(f789(f240(a863),x78411),x78412))
% 21.40/21.36 [7935]P49(x79351,x79352)+~P47(x79351,f247(f870(x79351,a856)),f789(f264(f869(x79351,x79351)),f789(f259(x79351,x79351,a856),x79352)))
% 21.40/21.36 [8188]~P36(x81881,f789(f286(x81881,x81881),x81882))+P36(x81881,f789(f286(x81881,x81881),f789(f789(f289(x81881,x81881,x81881),x81882),f308(x81881,x81882))))
% 21.40/21.36 [8306]P1(f789(f70(f869(x83061,x83061)),f789(f789(f289(x83061,x83061,x83061),x83062),f308(x83061,x83062))))+~P1(f789(f70(f869(x83061,x83061)),x83062))
% 21.40/21.36 [8336]E(x83361,f2(a1))+P1(f789(f63(x83362,x83361),f789(f789(f249(a1,a1),f789(f789(f50(a1),x83362),x83361)),f59(a1,x83362,x83361))))
% 21.40/21.36 [8350]~P1(f789(f789(f342(f869(a863,a863)),f789(f789(f249(a863,a863),x83501),x83502)),f308(a863,a331)))+P1(f789(f789(f240(a863),x83501),x83502))
% 21.40/21.36 [8371]~P71(x83711)+E(f789(f138(x83711,x83711,f789(f9(x83711,x83711,x83711),f89(x83711)),f2(x83711)),f789(f149(x83711),x83712)),f789(f138(x83711,x83711,f89(x83711),f2(x83711)),x83712))
% 21.40/21.36 [8646]P1(f789(f789(f342(f869(a863,a863)),f789(f789(f249(a863,a863),x86461),x86462)),f789(f789(f289(a863,a863,a863),a331),f308(a863,a331))))+~P1(f789(f789(f241(a863),x86461),x86462))
% 21.40/21.36 [8688]~P1(f789(f70(f869(x86881,x86881)),f789(f789(f289(x86881,x86881,x86881),x86882),f308(x86881,x86882))))+P1(f789(f70(f869(x86881,x86881)),x86882))
% 21.40/21.36 [8910]P56(x89101,x89102)+P1(f789(f789(f342(f869(x89101,x89101)),f789(f789(f249(x89101,x89101),f644(x89102,x89101)),f644(x89102,x89101))),f789(f789(f289(x89101,x89101,x89101),x89102),f308(x89101,x89102))))
% 21.40/21.36 [8911]P56(x89111,x89112)+P1(f789(f789(f342(f869(x89111,x89111)),f789(f789(f249(x89111,x89111),f686(x89112,x89111)),f686(x89112,x89111))),f789(f789(f289(x89111,x89111,x89111),x89112),f308(x89111,x89112))))
% 21.40/21.36 [9018]~P1(f789(f789(f342(f869(a863,a863)),f789(f789(f249(a863,a863),x90181),x90182)),f789(f789(f289(a863,a863,a863),a331),f308(a863,a331))))+P1(f789(f789(f241(a863),x90181),x90182))
% 21.40/21.36 [5011]~P88(x50111)+E(f789(f789(f89(x50111),f789(f113(x50111),a92)),x50112),x50112)
% 21.40/21.36 [5041]~P68(x50411)+E(f789(f789(f89(x50411),f789(f88(x50411),x50412)),x50412),f2(x50411))
% 21.40/21.36 [5042]~P6(x50421)+E(f789(f789(f89(x50421),f789(f88(x50421),x50422)),x50422),f2(x50421))
% 21.40/21.36 [5043]~P90(x50431)+E(f789(f789(f110(x50431),f789(f88(x50431),x50432)),x50432),f247(x50431))
% 21.40/21.36 [5044]~P90(x50441)+E(f789(f789(f111(x50441),f789(f88(x50441),x50442)),x50442),f184(x50441))
% 21.40/21.36 [5074]~P88(x50741)+E(f789(f789(f90(x50741),f789(f113(x50741),a106)),x50742),f789(f88(x50741),x50742))
% 21.40/21.36 [5233]~P104(x52331)+E(f789(f789(f90(x52331),f789(f88(x52331),f87(x52331))),x52332),f789(f88(x52331),x52332))
% 21.40/21.36 [5273]E(f789(f84(a1),x52731),f87(a1))+~E(f789(f84(a1),f789(f789(f90(a1),x52731),x52732)),f87(a1))
% 21.40/21.36 [5361]~P88(x53611)+E(f789(f789(f89(x53611),f87(x53611)),f789(f113(x53611),x53612)),f789(f113(x53611),f789(f789(f3(a1),x53612),a106)))
% 21.40/21.36 [5417]~P95(x54171)+E(f12(x54171,f789(f789(f310(x54171),x54172),f184(f870(x54171,a856)))),x54172)
% 21.40/21.36 [5418]~P95(x54181)+E(f15(x54181,f789(f789(f310(x54181),x54182),f184(f870(x54181,a856)))),x54182)
% 21.40/21.36 [5419]~P101(x54191)+E(f16(x54191,f789(f789(f310(x54191),x54192),f184(f870(x54191,a856)))),x54192)
% 21.40/21.36 [5420]~P101(x54201)+E(f17(x54201,f789(f789(f310(x54201),x54202),f184(f870(x54201,a856)))),x54202)
% 21.40/21.36 [5421]~P9(x54211)+E(f52(x54211,f789(f789(f310(x54211),x54212),f184(f870(x54211,a856)))),x54212)
% 21.40/21.36 [5422]~P9(x54221)+E(f51(x54221,f789(f789(f310(x54221),x54222),f184(f870(x54221,a856)))),x54222)
% 21.40/21.36 [5444]E(f789(f789(f89(a863),x54441),f789(f789(f3(a863),x54442),x54441)),x54442)+P1(f789(f789(f241(a863),x54442),x54441))
% 21.40/21.36 [5476]E(x54761,f122(x54762))+P1(f789(f789(f241(a863),f2(a863)),f789(f185(f864(x54762)),x54761)))
% 21.40/21.36 [5594]~P101(x55941)+E(f13(x55941,f239(x55941),f789(f789(f310(x55941),x55942),f184(f870(x55941,a856)))),x55942)
% 21.40/21.36 [5595]~P101(x55951)+E(f14(x55951,f244(x55951),f789(f789(f310(x55951),x55952),f184(f870(x55951,a856)))),x55952)
% 21.40/21.36 [5656]E(f789(f789(f89(a863),x56561),f789(f789(f3(a863),x56562),x56561)),x56562)+~P1(f789(f789(f240(a863),x56561),x56562))
% 21.40/21.36 [5657]E(f789(f789(f90(a1),x56571),f789(f789(f50(a1),x56572),x56571)),x56572)+~P1(f789(f789(f287(a1),x56571),x56572))
% 21.40/21.36 [5658]E(f789(f789(f3(a863),x56581),f789(f789(f3(a863),x56581),x56582)),x56582)+~P1(f789(f789(f240(a863),x56582),x56581))
% 21.40/21.36 [5676]E(f59(a863,f789(f789(f3(a863),x56761),x56762),x56762),f59(a863,x56761,x56762))+P1(f789(f789(f241(a863),x56761),x56762))
% 21.40/21.36 [5677]E(f59(a863,f789(f789(f3(a863),x56771),x56772),x56772),f59(a863,x56771,x56772))+P1(f789(f789(f241(a863),x56771),x56772))
% 21.40/21.36 [5687]E(f789(f88(a1),f789(f789(f50(a1),x56871),f789(f88(a1),x56872))),f293(x56871,x56872))+P1(f789(f789(f240(a1),f2(a1)),x56872))
% 21.40/21.36 [5689]~E(x56892,f2(a863))+P1(f789(f789(f241(a863),f2(a863)),f789(f789(f250(a863),x56891),x56892)))
% 21.40/21.36 [5749]~P88(x57491)+E(f789(f789(f89(x57491),f789(f88(x57491),f87(x57491))),f789(f113(x57491),x57492)),f789(f113(x57491),f789(f789(f89(a1),x57492),a106)))
% 21.40/21.36 [5750]E(f789(f789(f250(a863),f789(f113(a863),x57501)),x57502),f789(f789(f250(a863),f2(a863)),x57502))+~P1(f789(a190,f789(f113(a1),x57501)))
% 21.40/21.36 [5850]E(f789(f137(a863),f136(a863,f789(f302(a863,x58501),x58502))),x58501)+~P1(f789(f789(f241(a863),x58501),x58502))
% 21.40/21.36 [5867]E(f789(f789(f90(a863),f789(f113(a863),x58671)),f789(f113(a863),x58672)),f789(f113(a863),f789(f789(f90(a1),x58671),x58672)))+P1(f789(f789(f241(a1),x58671),a92))
% 21.40/21.36 [5873]~P119(x58731)+P1(f789(f789(f240(x58731),f2(x58731)),f789(f789(f90(x58731),x58732),x58732)))
% 21.40/21.36 [5885]E(f789(f789(f3(a863),f789(a121,x58851)),x58852),f789(a121,f789(f789(f3(a863),x58851),x58852)))+~P1(f789(f789(f240(a863),x58852),x58851))
% 21.40/21.36 [5888]E(f59(a863,f789(f789(f3(a863),x58881),x58882),x58882),f59(a863,x58881,x58882))+~P1(f789(f789(f240(a863),x58882),x58881))
% 21.40/21.36 [5939]E(f789(f789(f250(a863),f789(a114,x59391)),x59392),f789(a114,f789(f789(f250(a1),x59391),x59392)))+~P1(f789(f789(f240(a1),f2(a1)),x59391))
% 21.40/21.36 [5940]E(f789(f789(f250(a863),f789(a114,x59401)),x59402),f789(a114,f789(f789(f250(a1),x59401),x59402)))+~P1(f789(f789(f240(a1),f2(a1)),x59401))
% 21.40/21.36 [5955]P1(f789(f134(x59551),x59552))+P1(f789(f789(f241(a863),f736(x59552,x59551)),f789(f185(f864(x59551)),x59552)))
% 21.40/21.36 [5956]P1(f789(f134(x59561),x59562))+P1(f789(f789(f241(a863),f740(x59562,x59561)),f789(f185(f864(x59561)),x59562)))
% 21.40/21.36 [5972]~P1(f789(f789(f287(a1),x59721),x59722))+P1(f789(f789(f287(a1),f789(f88(a1),x59721)),x59722))
% 21.40/21.36 [5975]~E(x59751,f122(x59752))+~P1(f789(f789(f241(a863),f2(a863)),f789(f185(f864(x59752)),x59751)))
% 21.40/21.36 [5988]E(f140(a863,f136(a863,f789(f302(a863,x59881),x59882))),f789(f789(f3(a863),x59882),f87(a863)))+~P1(f789(f789(f241(a863),x59881),x59882))
% 21.40/21.36 [5991]E(f789(f789(f89(a1),x59911),f789(f109(a1),f789(a121,f711(x59912,x59911)))),x59912)+~P1(f789(f789(f241(a1),x59911),x59912))
% 21.40/21.36 [5997]E(x59971,f2(a863))+E(f789(f789(f90(a863),x59972),f789(f789(f250(a863),x59972),f789(f789(f3(a863),x59971),f87(a863)))),f789(f789(f250(a863),x59972),x59971))
% 21.40/21.36 [6023]E(f789(f789(f90(a863),f789(a114,x60231)),f789(a114,x60232)),f789(a114,f789(f789(f90(a1),x60231),x60232)))+~P1(f789(f789(f240(a1),f2(a1)),x60231))
% 21.40/21.36 [6024]E(f789(f789(f50(a863),f789(a114,x60241)),f789(a114,x60242)),f789(a114,f789(f789(f50(a1),x60241),x60242)))+~P1(f789(f789(f240(a1),f2(a1)),x60241))
% 21.40/21.36 [6039]~P70(x60391)+E(f789(f789(f89(x60391),x60392),x60392),f789(f789(f90(x60391),f789(f789(f89(x60391),f87(x60391)),f87(x60391))),x60392))
% 21.40/21.36 [6059]E(f789(f789(f50(a1),f789(f84(a1),x60591)),f789(f84(a1),x60592)),f789(f84(a1),f789(f789(f50(a1),x60591),x60592)))+~P1(f789(f789(f287(a1),x60592),x60591))
% 21.40/21.36 [6060]E(f789(f789(f3(a1),f789(f109(a1),x60601)),f789(f109(a1),x60602)),f789(f109(a1),f789(f789(f3(a863),x60601),x60602)))+~P1(f789(f789(f240(a863),x60602),x60601))
% 21.40/21.36 [6062]E(f789(f789(f249(a1,a1),f789(f113(a1),a106)),f789(f789(f89(a1),x60621),x60622)),f64(x60621,x60622))+~P1(f789(f789(f240(a1),x60622),f2(a1)))
% 21.40/21.36 [6100]E(f168(x61001,x61002),f122(f864(x61001)))+P1(f789(f789(f342(f864(x61001)),f735(x61002,x61001)),f789(f163(f864(x61001)),x61002)))
% 21.40/21.36 [6162]~P1(f789(f789(f287(a863),x61621),x61622))+P1(f789(f789(f287(a863),x61621),f789(f789(f89(a863),x61622),x61621)))
% 21.40/21.36 [6184]E(f789(f789(f146(a1),x61841),f167(f789(f789(f89(a1),x61841),f87(a1)),x61842)),f167(x61841,x61842))+~P1(f789(f789(f240(a1),x61841),x61842))
% 21.40/21.36 [6222]~P1(f789(f789(f241(a863),x62222),x62221))+P1(f789(f789(f241(a863),f2(a863)),f789(f789(f3(a863),x62221),x62222)))
% 21.40/21.36 [6253]~P1(f789(f789(f241(a863),x62531),f789(a114,x62532)))+P1(f789(f789(f241(a1),f789(f109(a1),x62531)),x62532))
% 21.40/21.36 [6254]P1(f789(f789(f287(a1),x62541),x62542))+~P1(f789(f789(f287(a1),f789(f88(a1),x62541)),x62542))
% 21.40/21.36 [6283]~P101(x62831)+E(f789(f789(f110(f870(x62831,a856)),f789(f265(x62831),x62832)),f789(f789(f310(x62831),x62832),f184(f870(x62831,a856)))),f789(f301(x62831),x62832))
% 21.40/21.36 [6284]~P1(f789(f789(f241(a863),f2(a863)),x62842))+P1(f789(f789(f241(a863),f2(a863)),f789(f789(f89(a863),x62841),x62842)))
% 21.40/21.36 [6285]~P1(f789(f789(f241(a863),f2(a863)),x62851))+P1(f789(f789(f241(a863),f2(a863)),f789(f789(f89(a863),x62851),x62852)))
% 21.40/21.36 [6286]~P1(f789(f789(f241(a863),f2(a863)),x62861))+P1(f789(f789(f241(a863),f2(a863)),f789(f789(f250(a863),x62861),x62862)))
% 21.40/21.36 [6287]~P1(f789(f789(f240(a1),f2(a1)),x62871))+P1(f789(f789(f240(a1),f2(a1)),f789(f789(f250(a1),x62871),x62872)))
% 21.40/21.36 [6315]~E(f789(x63151,f2(a863)),f2(a863))+E(f789(f789(f8(a863,a863),x63151),f303(a863,f789(a121,f2(a863)),x63152)),f789(f789(f8(a863,a863),x63151),f303(a863,f2(a863),x63152)))
% 21.40/21.36 [6381]~P88(x63811)+E(f789(f789(f90(x63811),f789(f789(f89(x63811),f87(x63811)),f87(x63811))),f789(f113(x63811),x63812)),f789(f113(x63811),f789(f789(f89(a1),x63812),x63812)))
% 21.40/21.36 [6403]E(f789(f789(f310(a1),x64031),f303(a1,f789(f789(f89(a1),x64031),f87(a1)),x64032)),f303(a1,x64031,x64032))+P1(f789(f789(f241(a1),x64032),x64031))
% 21.40/21.36 [6404]P1(f789(f789(f241(a863),x64041),f789(a114,x64042)))+~P1(f789(f789(f241(a1),f789(f109(a1),x64041)),x64042))
% 21.40/21.36 [6505]P1(f789(f789(f287(a863),x65051),x65052))+~P1(f789(f789(f287(a863),x65051),f789(f789(f89(a863),x65052),x65051)))
% 21.40/21.36 [6511]E(f789(a114,f789(f789(f50(a1),f789(f113(a1),x65111)),f789(f113(a1),x65112))),f789(f789(f50(a863),f789(f113(a863),x65111)),f789(f113(a863),x65112)))+P1(f789(a190,f789(f113(a1),x65111)))
% 21.40/21.36 [6512]E(f789(a114,f789(f789(f250(a1),f789(f113(a1),x65121)),f789(f113(a863),x65122))),f789(f789(f250(a863),f789(f113(a863),x65121)),f789(f113(a863),x65122)))+P1(f789(a190,f789(f113(a1),x65121)))
% 21.40/21.36 [6570]P1(f789(f789(f241(a863),x65701),x65702))+~P1(f789(f789(f241(a863),f2(a863)),f789(f789(f3(a863),x65702),x65701)))
% 21.40/21.36 [6613]P1(f789(f789(f241(a863),f2(a863)),x66131))+~P1(f789(f789(f241(a863),f2(a863)),f789(f789(f90(a863),x66132),x66131)))
% 21.40/21.36 [6614]P1(f789(f789(f241(a863),f2(a863)),x66141))+~P1(f789(f789(f241(a863),f2(a863)),f789(f789(f90(a863),x66141),x66142)))
% 21.40/21.36 [6628]E(f136(a863,f789(f302(a863,f789(f113(a863),x66281)),f789(f113(a863),x66282))),f122(a863))+P1(f789(f789(f241(a863),f789(f113(a863),x66281)),f789(f113(a863),x66282)))
% 21.40/21.36 [6630]~P1(f789(f789(f240(a1),x66301),f2(a1)))+E(f789(f789(f90(a863),f789(a114,f789(f88(a1),x66301))),f789(a114,f789(f88(a1),x66302))),f789(a114,f789(f789(f90(a1),x66301),x66302)))
% 21.40/21.36 [6696]~E(x66962,f184(f870(x66961,a856)))+P1(f789(f789(f240(f870(x66961,a856)),x66962),f789(f88(f870(x66961,a856)),x66962)))
% 21.40/21.36 [6759]~P88(x67591)+E(f789(f789(f89(x67591),f789(f789(f89(x67591),f2(x67591)),f789(f113(x67591),x67592))),f789(f113(x67591),x67592)),f789(f113(x67591),f789(f789(f89(a1),x67592),x67592)))
% 21.40/21.36 [6768]~P1(f789(f789(f287(a1),f789(f109(a1),x67681)),x67682))+P1(f789(f789(f287(a863),x67681),f789(a114,f789(f84(a1),x67682))))
% 21.40/21.36 [6818]~P1(f789(f789(f241(a1),x68181),x68182))+P1(f789(f789(f240(a1),f789(f789(f89(a1),x68181),f87(a1))),x68182))
% 21.40/21.36 [6819]~P1(f789(f789(f241(a1),x68191),x68192))+P1(f789(f789(f240(a1),f789(f789(f89(a1),x68191),f87(a1))),x68192))
% 21.40/21.36 [6858]P1(f789(f789(f287(a1),f789(f109(a1),x68581)),x68582))+~P1(f789(f789(f287(a863),x68581),f789(a114,f789(f84(a1),x68582))))
% 21.40/21.36 [6892]E(x68921,f2(a863))+~P1(f789(f789(f240(a1),f789(f109(a1),x68922)),f789(f88(a1),f789(f109(a1),x68921))))
% 21.40/21.36 [6893]E(x68931,f2(a863))+~P1(f789(f789(f240(a1),f789(f109(a1),x68931)),f789(f88(a1),f789(f109(a1),x68932))))
% 21.40/21.36 [6997]E(f789(f789(f249(a1,a1),f789(f113(a1),a106)),f789(f789(f89(a1),x69971),x69972)),f64(x69971,x69972))+~P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),x69971),x69972)))
% 21.40/21.36 [7034]~P30(x70341,x70342)+P36(x70341,f789(f248(f870(f869(x70341,x70341),a856),f870(f869(x70341,x70341),a856)),x70342))
% 21.40/21.36 [7055]~P1(f789(f789(f240(a863),f789(a121,f2(a863))),x70551))+P1(f789(f789(f240(a863),f789(a121,f2(a863))),f789(f789(f250(a863),x70551),x70552)))
% 21.40/21.36 [7224]~P1(f789(f789(f241(a1),x72241),x72242))+P1(f789(f789(f241(a1),f789(f789(f89(a1),x72241),x72241)),f789(f789(f89(a1),x72242),x72242)))
% 21.40/21.36 [7225]~P1(f789(f789(f241(a1),x72251),x72252))+P1(f789(f789(f241(a1),f789(f789(f89(a1),x72251),x72251)),f789(f789(f89(a1),x72252),x72252)))
% 21.40/21.36 [7236]~P1(f789(f789(f240(a1),x72361),x72362))+P1(f789(f789(f240(a1),f789(f789(f89(a1),x72361),x72361)),f789(f789(f89(a1),x72362),x72362)))
% 21.40/21.36 [7237]~P1(f789(f789(f240(a1),x72371),x72372))+P1(f789(f789(f240(a1),f789(f789(f89(a1),x72371),x72371)),f789(f789(f89(a1),x72372),x72372)))
% 21.40/21.36 [7304]~P1(f789(f789(f241(a863),f2(a863)),x73041))+P1(f789(f789(f241(a863),f789(f789(f3(a863),x73041),f789(a121,x73042))),x73041))
% 21.40/21.36 [7341]P1(f789(f789(f240(a863),f789(a121,f2(a863))),x73411))+~P1(f789(f789(f240(a863),f789(a121,f2(a863))),f789(f789(f90(a863),x73412),x73411)))
% 21.40/21.36 [7342]P1(f789(f789(f240(a863),f789(a121,f2(a863))),x73421))+~P1(f789(f789(f240(a863),f789(a121,f2(a863))),f789(f789(f90(a863),x73421),x73422)))
% 21.40/21.36 [7346]P1(f789(f789(f240(a863),f789(f789(f159(a863),x73461),x73462)),f789(f161(a863),x73461)))+~P1(f789(f789(f241(a863),x73462),f789(f185(f864(a863)),x73461)))
% 21.40/21.36 [7390]P1(f789(f789(f241(a1),x73901),x73902))+~P1(f789(f789(f240(a1),f789(f789(f89(a1),x73901),f87(a1))),x73902))
% 21.40/21.36 [7399]~P1(f789(f789(f342(a863),x73991),x73992))+P1(f789(f789(f342(a1),f789(f109(a1),x73991)),f789(f311(a863,a1,f109(a1)),x73992)))
% 21.40/21.36 [7436]P1(f789(f70(x74361),f247(f870(x74361,a856))))+~P1(f789(f70(f870(x74362,x74361)),f247(f870(f870(x74362,x74361),a856))))
% 21.40/21.36 [7437]P1(f789(f70(x74371),f247(f870(x74371,a856))))+~P1(f789(f70(f871(x74372,x74371)),f247(f870(f871(x74372,x74371),a856))))
% 21.40/21.36 [7438]P1(f789(f70(x74381),f247(f870(x74381,a856))))+~P1(f789(f70(f871(x74381,x74382)),f247(f870(f871(x74381,x74382),a856))))
% 21.40/21.36 [7477]E(x74771,f184(f870(x74772,a856)))+~P1(f789(f789(f240(f870(x74772,a856)),x74771),f789(f88(f870(x74772,a856)),x74771)))
% 21.40/21.36 [7620]E(f789(f138(f864(x76201),f864(x76201),f132(x76201),f122(x76201)),x76202),f122(x76201))+P1(f789(f789(f342(f864(x76201)),f782(x76202,x76201)),f789(f163(f864(x76201)),x76202)))
% 21.40/21.36 [7621]E(f789(f138(f864(x76211),f864(x76211),f132(x76211),f122(x76211)),x76212),f122(x76211))+P1(f789(f789(f342(f864(x76211)),f784(x76212,x76211)),f789(f163(f864(x76211)),x76212)))
% 21.40/21.36 [7756]E(f168(x77561,f789(f789(f146(f864(x77561)),f122(x77561)),x77562)),f168(x77561,x77562))+~P1(f789(f329(f864(f864(x77561)),f169(x77561)),f789(f789(f146(f864(x77561)),f122(x77561)),x77562)))
% 21.40/21.36 [7860]P1(f789(f789(f241(a1),x78601),x78602))+~P1(f789(f789(f241(a1),f789(f789(f89(a1),x78601),x78601)),f789(f789(f89(a1),x78602),x78602)))
% 21.40/21.36 [7861]P1(f789(f789(f241(a1),x78611),x78612))+~P1(f789(f789(f241(a1),f789(f789(f89(a1),x78611),x78611)),f789(f789(f89(a1),x78612),x78612)))
% 21.40/21.36 [7863]P1(f789(f789(f240(a1),x78631),x78632))+~P1(f789(f789(f240(a1),f789(f789(f89(a1),x78631),x78631)),f789(f789(f89(a1),x78632),x78632)))
% 21.40/21.36 [7864]P1(f789(f789(f240(a1),x78641),x78642))+~P1(f789(f789(f240(a1),f789(f789(f89(a1),x78641),x78641)),f789(f789(f89(a1),x78642),x78642)))
% 21.40/21.36 [7955]~P70(x79551)+E(f789(f789(f90(x79551),f789(f789(f89(x79551),f87(x79551)),f87(x79551))),f789(f789(f8(a863,x79551),f109(x79551)),f303(a863,f87(a863),x79552))),f789(f789(f90(x79551),f789(f109(x79551),x79552)),f789(f789(f89(x79551),f789(f109(x79551),x79552)),f87(x79551))))
% 21.40/21.36 [7995]E(f789(f789(f146(a1),f789(f113(a1),x79951)),f167(f789(f789(f89(a1),f789(f113(a1),x79951)),f87(a1)),f789(f113(a1),x79952))),f167(f789(f113(a1),x79951),f789(f113(a1),x79952)))+~P1(f789(f789(f240(a1),f789(f113(a1),x79951)),f789(f113(a1),x79952)))
% 21.40/21.36 [8010]P1(f789(f789(f342(a863),x80101),x80102))+~P1(f789(f789(f342(a1),f789(f109(a1),x80101)),f789(f311(a863,a1,f109(a1)),x80102)))
% 21.40/21.36 [8159]~P1(f789(f70(x81591),x81592))+E(f789(f311(a863,x81591,f591(x81592,x81591)),f789(f264(a863),f789(f789(f9(a863,a863,a856),f241(a863)),f592(x81592,x81591)))),x81592)
% 21.40/21.36 [8444]P48(x84441,x84442)+P1(f789(f789(f342(f869(x84441,x84441)),f789(f789(f249(x84441,x84441),f374(x84442,x84441)),f374(x84442,x84441))),x84442))
% 21.40/21.36 [8579]~P88(x85791)+E(f789(f789(f3(x85791),f87(x85791)),f789(f113(x85791),x85792)),f789(f113(x85791),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f88(a1),x85792))))
% 21.40/21.36 [8684]~P1(f789(f789(f241(f870(a863,a856)),x86841),x86842))+P1(f789(f789(f241(f870(a1,a856)),f789(f311(a863,a1,f109(a1)),x86841)),f789(f311(a863,a1,f109(a1)),x86842)))
% 21.40/21.36 [8685]~P1(f789(f789(f240(f870(a863,a856)),x86851),x86852))+P1(f789(f789(f240(f870(a1,a856)),f789(f311(a863,a1,f109(a1)),x86851)),f789(f311(a863,a1,f109(a1)),x86852)))
% 21.40/21.36 [8710]~P1(f789(f789(f241(a1),x87101),x87102))+P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),x87101),x87101)),a106)),f789(f789(f89(a1),x87102),x87102)))
% 21.40/21.36 [8711]~P1(f789(f789(f241(a1),x87111),x87112))+P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),x87111),x87111)),a106)),f789(f789(f89(a1),x87112),x87112)))
% 21.40/21.36 [8712]~P1(f789(f789(f241(a1),x87121),x87122))+P1(f789(f789(f240(a1),f789(f789(f3(a1),f789(f789(f89(a1),x87121),x87121)),a106)),f789(f789(f89(a1),x87122),x87122)))
% 21.40/21.36 [8713]~P1(f789(f789(f241(a1),x87131),x87132))+P1(f789(f789(f240(a1),f789(f789(f3(a1),f789(f789(f89(a1),x87131),x87131)),a106)),f789(f789(f89(a1),x87132),x87132)))
% 21.40/21.36 [8780]~P1(f789(f789(f342(a863),x87801),f789(f163(a863),x87802)))+P1(f789(f789(f240(a863),x87801),f789(f138(a863,a863,f89(a863),f2(a863)),x87802)))
% 21.40/21.36 [8855]P44(x88551,x88552)+~P1(f789(f789(f342(f869(x88551,x88551)),f789(f789(f249(x88551,x88551),f363(x88552,x88551)),f363(x88552,x88551))),x88552))
% 21.40/21.36 [8985]~P1(f789(f789(f241(f870(a1,a856)),f789(f311(a863,a1,f109(a1)),x89851)),f789(f311(a863,a1,f109(a1)),x89852)))+P1(f789(f789(f241(f870(a863,a856)),x89851),x89852))
% 21.40/21.36 [8986]~P1(f789(f789(f240(f870(a1,a856)),f789(f311(a863,a1,f109(a1)),x89861)),f789(f311(a863,a1,f109(a1)),x89862)))+P1(f789(f789(f240(f870(a863,a856)),x89861),x89862))
% 21.40/21.36 [9068]P1(f789(f789(f241(a1),x90681),x90682))+~P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),x90681),x90681)),a106)),f789(f789(f89(a1),x90682),x90682)))
% 21.40/21.36 [9069]P1(f789(f789(f241(a1),x90691),x90692))+~P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),x90691),x90691)),a106)),f789(f789(f89(a1),x90692),x90692)))
% 21.40/21.36 [9070]P1(f789(f789(f241(a1),x90701),x90702))+~P1(f789(f789(f240(a1),f789(f789(f3(a1),f789(f789(f89(a1),x90701),x90701)),a106)),f789(f789(f89(a1),x90702),x90702)))
% 21.40/21.36 [9071]P1(f789(f789(f241(a1),x90711),x90712))+~P1(f789(f789(f240(a1),f789(f789(f3(a1),f789(f789(f89(a1),x90711),x90711)),a106)),f789(f789(f89(a1),x90712),x90712)))
% 21.40/21.36 [9937]~P1(f789(f70(x99371),x99372))+E(f789(f185(f864(x99371)),f99(f864(x99371),f789(f789(f20(f864(x99371),a856,a856),f789(f789(f10(a856,f870(a856,a856),f864(x99371)),a339),f789(f789(f9(f864(x99371),f870(x99371,a856),a856),f789(f789(f10(f870(x99371,a856),f870(f870(x99371,a856),a856),f864(x99371)),a338),f163(x99371))),x99372))),f134(x99371)))),f216(x99371,x99372))
% 21.40/21.36 [5987]E(f789(f789(f89(a863),f789(f789(f3(a863),x59871),x59872)),x59872),x59871)+~P1(f789(f789(f240(a863),x59872),x59871))
% 21.40/21.36 [6054]E(f789(f789(f50(a863),f789(f789(f90(a863),x60541),x60542)),x60542),x60541)+~P1(f789(f789(f241(a863),f2(a863)),x60542))
% 21.40/21.36 [6055]E(f789(f789(f50(a863),f789(f789(f90(a863),x60551),x60552)),x60551),x60552)+~P1(f789(f789(f241(a863),f2(a863)),x60551))
% 21.40/21.36 [6061]~P4(x60611)+E(f789(f789(f8(a863,x60611),f789(f159(x60611),x60612)),f789(f302(a863,f2(a863)),f789(f185(f864(x60611)),x60612))),f789(f161(x60611),x60612))
% 21.40/21.36 [6176]E(f59(a863,f789(a121,f789(f789(f90(a863),x61761),x61762)),x61761),f87(a863))+~P1(f789(f789(f241(a863),f87(a863)),x61761))
% 21.40/21.36 [6182]E(f789(a121,f789(f789(f89(a863),f789(f113(a863),x61821)),x61822)),f789(f789(f89(a863),f87(a863)),x61822))+~P1(f789(a190,f789(f113(a1),x61821)))
% 21.40/21.36 [6208]E(f789(a114,f789(f789(f250(a1),f789(f113(a1),x62081)),x62082)),f789(f789(f250(a863),f789(f113(a863),x62081)),x62082))+P1(f789(a190,f789(f113(a1),x62081)))
% 21.40/21.36 [6458]E(f789(f789(f3(a863),x64581),f789(f113(a863),f789(f789(f89(a1),x64582),a106))),f789(f789(f3(a863),f789(a121,x64581)),f789(f113(a863),x64582)))+~P1(f789(f789(f241(a1),a92),x64582))
% 21.40/21.36 [6539]E(x65391,f2(a863))+E(f789(a121,f789(f789(f89(a863),f789(f789(f3(a863),x65391),f87(a863))),x65392)),f789(f789(f89(a863),x65391),x65392))
% 21.40/21.36 [6584]E(x65841,f2(a1))+P1(f789(f789(f241(a1),f2(a1)),f789(f789(f250(a1),f789(f84(a1),x65841)),x65842)))
% 21.40/21.36 [6599]~E(x65992,f2(a863))+P1(f789(f789(f241(a1),f2(a1)),f789(f789(f250(a1),f789(f84(a1),x65991)),x65992)))
% 21.40/21.36 [6635]E(x66351,f2(a863))+E(f789(f789(f89(a863),x66352),f789(f789(f90(a863),f789(f789(f3(a863),x66351),f87(a863))),x66352)),f789(f789(f90(a863),x66351),x66352))
% 21.40/21.36 [6690]~P1(f789(f789(f240(a1),x66901),x66902))+P1(f789(f789(f241(a1),f789(f789(f89(a1),x66901),a106)),x66902))
% 21.40/21.36 [6822]E(f789(f789(f146(a863),x68221),f136(a863,f789(f302(a863,f789(a121,x68221)),x68222))),f136(a863,f789(f302(a863,x68221),x68222)))+~P1(f789(f789(f241(a863),x68221),x68222))
% 21.40/21.36 [6823]E(f789(f789(f146(a863),x68231),f136(a863,f789(f302(a863,f789(a121,x68231)),x68232))),f136(a863,f789(f302(a863,x68231),x68232)))+~P1(f789(f789(f241(a863),x68231),x68232))
% 21.40/21.36 [6991]~P1(f789(f789(f287(a1),x69911),f789(f109(a1),x69912)))+P1(f789(f789(f287(a863),f789(a114,f789(f84(a1),x69911))),x69912))
% 21.40/21.36 [7025]E(x70251,x70252)+~E(f789(f789(f3(a1),f789(f789(f89(a1),x70251),x70251)),a106),f789(f789(f3(a1),f789(f789(f89(a1),x70252),x70252)),a106))
% 21.40/21.36 [7028]E(x70281,f122(x70282))+E(f271(x70282,f789(f789(f150(x70282,f869(a108,x70282)),f789(f249(a108,x70282),f87(a108))),x70281)),f278(x70282,x70281))
% 21.40/21.36 [7267]P1(f789(f789(f240(a1),x72671),x72672))+~P1(f789(f789(f241(a1),f789(f789(f89(a1),x72671),a106)),x72672))
% 21.40/21.36 [7409]P1(f789(f789(f287(a1),x74091),f789(f109(a1),x74092)))+~P1(f789(f789(f287(a863),f789(a114,f789(f84(a1),x74091))),x74092))
% 21.40/21.36 [7758]~P1(f789(f789(f241(a863),x77581),x77582))+P1(f789(f789(f342(f869(a863,a863)),f789(f789(f249(a863,a863),x77581),x77582)),a245))
% 21.40/21.36 [7984]~P1(f789(f789(f241(a108),f2(a108)),x79841))+P1(f789(f789(f241(a108),f789(f248(a108,f869(a108,a108)),f789(f272(x79841),x79842))),x79841))
% 21.40/21.36 [8285]~P80(x82851)+P1(f789(f789(f240(x82851),f789(f84(x82851),f789(f161(x82851),x82852))),f789(f161(x82851),f789(f789(f150(x82851,x82851),f84(x82851)),x82852))))
% 21.40/21.36 [8308]P1(f789(f789(f241(a863),x83081),x83082))+~P1(f789(f789(f342(f869(a863,a863)),f789(f789(f249(a863,a863),x83081),x83082)),a245))
% 21.40/21.36 [8467]E(f789(f789(f249(x84671,x84671),f704(x84672,x84671)),f704(x84672,x84671)),x84672)+~P1(f789(f789(f342(f869(x84671,x84671)),x84672),f308(x84671,f184(f870(f869(x84671,x84671),a856)))))
% 21.40/21.36 [8512]E(f789(f302(a863,x85121),f789(f789(f89(a863),x85121),f789(f49(a863),x85122))),x85122)+~P1(f789(f789(f240(f870(a863,a856)),x85122),f789(f302(a863,x85121),f789(f789(f89(a863),x85121),f789(f49(a863),x85122)))))
% 21.40/21.36 [8533]E(f789(f789(f146(a863),f789(f113(a863),x85331)),f136(a863,f789(f302(a863,f789(a121,f789(f113(a863),x85331))),f789(f113(a863),x85332)))),f136(a863,f789(f302(a863,f789(f113(a863),x85331)),f789(f113(a863),x85332))))+~P1(f789(f789(f241(a863),f789(f113(a863),x85331)),f789(f113(a863),x85332)))
% 21.40/21.36 [8813]E(f789(f789(f50(a1),f789(f113(a1),f789(f789(f3(a1),f789(f789(f89(a1),x88131),x88131)),a106))),f789(f113(a1),f789(f789(f89(a1),x88132),x88132))),f789(f789(f50(a1),f789(f113(a1),x88131)),f789(f113(a1),x88132)))+~P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x88132)))
% 21.40/21.36 [8922]E(f789(f789(f50(a1),f789(f113(a1),f789(f789(f3(a1),f789(f789(f89(a1),x89221),x89221)),a106))),f789(f113(a1),f789(f789(f89(a1),x89222),x89222))),f789(f789(f50(a1),f789(f789(f89(a1),f789(f113(a1),x89221)),f87(a1))),f789(f113(a1),x89222)))+P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x89222)))
% 21.40/21.36 [9703]P1(f789(a190,x97032))+E(f789(f789(f95(a1,a863),f789(f789(f3(a1),x97031),x97032)),f789(f789(f20(a1,a863,a863),f789(f789(f9(a1,a863,f870(a863,a863)),f789(f789(f10(a856,f870(a863,f870(a863,a863)),a1),f105(a863)),a190)),f2(a863))),a114)),f789(f789(f3(a863),f789(a114,x97031)),f789(a114,x97032)))
% 21.40/21.36 [9707]E(f789(f789(f95(a1,a863),f789(f113(a1),f789(f789(f89(a1),x97071),f789(f88(a1),x97072)))),f789(f789(f20(a1,a863,a863),f789(f789(f9(a1,a863,f870(a863,a863)),f789(f789(f10(a856,f870(a863,f870(a863,a863)),a1),f105(a863)),a190)),f2(a863))),a114)),f789(f789(f3(a863),f789(f113(a863),x97071)),f789(f113(a863),x97072)))+P1(f789(f789(f241(a1),x97072),a92))
% 21.40/21.36 [9708]~P30(x97081,x97082)+P1(f789(f789(f240(f870(f869(x97081,x97081),a856)),f789(f789(f289(x97081,x97081,x97081),f789(f248(f870(f869(x97081,x97081),a856),f870(f869(x97081,x97081),a856)),x97082)),f789(f258(f870(f869(x97081,x97081),a856),f870(f869(x97081,x97081),a856)),x97082))),f789(f248(f870(f869(x97081,x97081),a856),f870(f869(x97081,x97081),a856)),x97082)))
% 21.40/21.36 [9764]~E(f789(f49(a863),f789(f264(a863),f789(f789(f20(a863,a856,a856),f789(f789(f10(a856,f870(a856,a856),a863),a339),f789(f789(f9(a863,f870(a863,a856),a856),f342(a863)),x97641))),f789(f789(f9(a863,a863,a856),f241(a863)),f789(a121,x97642))))),f2(a863))+~P1(f789(f789(f342(a863),f2(a863)),x97641))
% 21.40/21.36 [9777]E(f299(a863,f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x97771,x97772),f184(f870(a863,a856)))+~P1(f789(f789(f287(a863),x97772),x97771))
% 21.40/21.36 [9783]E(f300(a863,f287(a863),f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x97831,x97832),f184(f870(a863,a856)))+P1(f789(f789(f287(a863),x97831),x97832))
% 21.40/21.36 [9784]E(f297(a863,f287(a863),f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x97841,x97842),f184(f870(a863,a856)))+P1(f789(f789(f287(a863),x97841),x97842))
% 21.40/21.36 [9785]E(f300(a863,f287(a863),f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x97851,x97852),f184(f870(a863,a856)))+P1(f789(f789(f287(a863),x97851),x97852))
% 21.40/21.36 [9786]E(f297(a863,f287(a863),f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x97861,x97862),f184(f870(a863,a856)))+P1(f789(f789(f287(a863),x97861),x97862))
% 21.40/21.36 [9787]E(f300(a863,f287(a863),f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x97871,x97872),f184(f870(a863,a856)))+~P1(f789(f789(f287(a863),x97872),x97871))
% 21.40/21.36 [9788]E(f297(a863,f287(a863),f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x97881,x97882),f184(f870(a863,a856)))+~P1(f789(f789(f287(a863),x97882),x97881))
% 21.40/21.36 [9789]E(f300(a863,f287(a863),f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x97891,x97892),f184(f870(a863,a856)))+~P1(f789(f789(f287(a863),x97892),x97891))
% 21.40/21.36 [9790]E(f300(a863,f287(a863),f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x97901,x97902),f184(f870(a863,a856)))+~P1(f789(f789(f287(a863),x97902),x97901))
% 21.40/21.36 [9791]E(f297(a863,f287(a863),f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x97911,x97912),f184(f870(a863,a856)))+~P1(f789(f789(f287(a863),x97912),x97911))
% 21.40/21.36 [9792]E(f297(a863,f287(a863),f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x97921,x97922),f184(f870(a863,a856)))+~P1(f789(f789(f287(a863),x97922),x97921))
% 21.40/21.36 [9835]E(f59(a1,f789(f113(a1),f789(f789(f3(a1),f789(f789(f89(a1),x98351),x98351)),a106)),f789(f113(a1),f789(f789(f89(a1),x98352),x98352))),f789(f789(f89(a1),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f59(a1,f789(f113(a1),x98351),f789(f113(a1),x98352)))),f87(a1)))+~P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x98352)))
% 21.40/21.36 [9844]E(f59(a1,f789(f113(a1),f789(f789(f3(a1),f789(f789(f89(a1),x98441),x98441)),a106)),f789(f113(a1),f789(f789(f89(a1),x98442),x98442))),f789(f789(f3(a1),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f59(a1,f789(f789(f89(a1),f789(f113(a1),x98441)),f87(a1)),f789(f113(a1),x98442)))),f87(a1)))+P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x98442)))
% 21.40/21.36 [9906]~P9(x99061)+E(f51(x99061,f789(f264(x99061),f789(f789(f10(f870(x99061,a856),a856,x99061),f97(x99061)),f789(f789(f10(f870(x99061,a856),f870(x99061,a856),x99061),f789(f20(x99061,a856,a856),f789(f789(f10(a856,f870(a856,a856),x99061),a343),f789(f789(f9(x99061,f870(x99061,a856),a856),f342(x99061)),x99062)))),f240(x99061))))),f52(x99061,x99062))
% 21.40/21.36 [9930]~P36(x99301,x99302)+P58(x99301,f789(f789(f9(x99301,f870(f869(x99301,x99301),a856),f870(x99301,a856)),f789(f789(f10(f870(x99301,f870(f870(f869(x99301,x99301),a856),a856)),f870(f870(f869(x99301,x99301),a856),f870(x99301,a856)),x99301),f9(x99301,f870(f869(x99301,x99301),a856),a856)),f789(f789(f10(f870(x99301,f869(x99301,x99301)),f870(x99301,f870(f870(f869(x99301,x99301),a856),a856)),x99301),f789(f10(f869(x99301,x99301),f870(f870(f869(x99301,x99301),a856),a856),x99301),f342(f869(x99301,x99301)))),f249(x99301,x99301)))),x99302))
% 21.40/21.36 [9931]~P12(x99311,f247(f870(x99311,a856)),x99312)+P11(x99311,f789(f789(f9(x99311,f870(f869(x99311,x99311),a856),f870(x99311,a856)),f789(f789(f10(f870(x99311,f870(f870(f869(x99311,x99311),a856),a856)),f870(f870(f869(x99311,x99311),a856),f870(x99311,a856)),x99311),f9(x99311,f870(f869(x99311,x99311),a856),a856)),f789(f789(f10(f870(x99311,f869(x99311,x99311)),f870(x99311,f870(f870(f869(x99311,x99311),a856),a856)),x99311),f789(f10(f869(x99311,x99311),f870(f870(f869(x99311,x99311),a856),a856),x99311),f342(f869(x99311,x99311)))),f249(x99311,x99311)))),x99312))
% 21.40/21.36 [9968]P36(x99681,x99682)+~P58(x99681,f789(f789(f9(x99681,f870(f869(x99681,x99681),a856),f870(x99681,a856)),f789(f789(f10(f870(x99681,f870(f870(f869(x99681,x99681),a856),a856)),f870(f870(f869(x99681,x99681),a856),f870(x99681,a856)),x99681),f9(x99681,f870(f869(x99681,x99681),a856),a856)),f789(f789(f10(f870(x99681,f869(x99681,x99681)),f870(x99681,f870(f870(f869(x99681,x99681),a856),a856)),x99681),f789(f10(f869(x99681,x99681),f870(f870(f869(x99681,x99681),a856),a856),x99681),f342(f869(x99681,x99681)))),f249(x99681,x99681)))),x99682))
% 21.40/21.36 [9969]P12(x99691,f247(f870(x99691,a856)),x99692)+~P11(x99691,f789(f789(f9(x99691,f870(f869(x99691,x99691),a856),f870(x99691,a856)),f789(f789(f10(f870(x99691,f870(f870(f869(x99691,x99691),a856),a856)),f870(f870(f869(x99691,x99691),a856),f870(x99691,a856)),x99691),f9(x99691,f870(f869(x99691,x99691),a856),a856)),f789(f789(f10(f870(x99691,f869(x99691,x99691)),f870(x99691,f870(f870(f869(x99691,x99691),a856),a856)),x99691),f789(f10(f869(x99691,x99691),f870(f870(f869(x99691,x99691),a856),a856),x99691),f342(f869(x99691,x99691)))),f249(x99691,x99691)))),x99692))
% 21.40/21.36 [7213]E(f789(f789(f89(a863),f789(f113(a863),f789(f789(f3(a1),x72131),a106))),x72132),f789(a121,f789(f789(f89(a863),f789(f113(a863),x72131)),x72132)))+P1(f789(a190,f789(f113(a1),x72131)))
% 21.40/21.36 [7678]~P88(x76781)+E(f789(f789(f89(x76781),f789(f789(f89(x76781),f87(x76781)),f789(f113(x76781),x76782))),f789(f113(x76781),x76782)),f789(f113(x76781),f789(f789(f3(a1),f789(f789(f89(a1),x76782),x76782)),a106)))
% 21.40/21.36 [8309]~P1(f789(f789(f240(a1),x83091),x83092))+P1(f789(f789(f241(a1),f789(f789(f89(a1),x83091),x83091)),f789(f789(f3(a1),f789(f789(f89(a1),x83092),x83092)),a106)))
% 21.40/21.36 [8310]~P1(f789(f789(f240(a1),x83101),x83102))+P1(f789(f789(f241(a1),f789(f789(f89(a1),x83101),x83101)),f789(f789(f3(a1),f789(f789(f89(a1),x83102),x83102)),a106)))
% 21.40/21.36 [8311]~P1(f789(f789(f240(a1),x83111),x83112))+P1(f789(f789(f240(a1),f789(f789(f89(a1),x83111),x83111)),f789(f789(f3(a1),f789(f789(f89(a1),x83112),x83112)),a106)))
% 21.40/21.36 [8312]~P1(f789(f789(f240(a1),x83121),x83122))+P1(f789(f789(f240(a1),f789(f789(f89(a1),x83121),x83121)),f789(f789(f3(a1),f789(f789(f89(a1),x83122),x83122)),a106)))
% 21.40/21.36 [8714]P1(f789(f789(f240(a1),x87141),x87142))+~P1(f789(f789(f241(a1),f789(f789(f89(a1),x87141),x87141)),f789(f789(f3(a1),f789(f789(f89(a1),x87142),x87142)),a106)))
% 21.40/21.36 [8715]P1(f789(f789(f240(a1),x87151),x87152))+~P1(f789(f789(f241(a1),f789(f789(f89(a1),x87151),x87151)),f789(f789(f3(a1),f789(f789(f89(a1),x87152),x87152)),a106)))
% 21.40/21.36 [8716]P1(f789(f789(f240(a1),x87161),x87162))+~P1(f789(f789(f240(a1),f789(f789(f89(a1),x87161),x87161)),f789(f789(f3(a1),f789(f789(f89(a1),x87162),x87162)),a106)))
% 21.40/21.36 [8717]P1(f789(f789(f240(a1),x87171),x87172))+~P1(f789(f789(f240(a1),f789(f789(f89(a1),x87171),x87171)),f789(f789(f3(a1),f789(f789(f89(a1),x87172),x87172)),a106)))
% 21.40/21.36 [8976]~P1(f789(f789(f241(a1),x89761),x89762))+P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),x89761),x89761)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),x89762),x89762)),a106)))
% 21.40/21.36 [8977]~P1(f789(f789(f241(a1),x89771),x89772))+P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),x89771),x89771)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),x89772),x89772)),a106)))
% 21.40/21.36 [8978]~P1(f789(f789(f240(a1),x89781),x89782))+P1(f789(f789(f240(a1),f789(f789(f3(a1),f789(f789(f89(a1),x89781),x89781)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),x89782),x89782)),a106)))
% 21.40/21.36 [8979]~P1(f789(f789(f240(a1),x89791),x89792))+P1(f789(f789(f240(a1),f789(f789(f3(a1),f789(f789(f89(a1),x89791),x89791)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),x89792),x89792)),a106)))
% 21.40/21.36 [9213]P1(f789(f789(f241(a1),x92131),x92132))+~P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),x92131),x92131)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),x92132),x92132)),a106)))
% 21.40/21.36 [9214]P1(f789(f789(f241(a1),x92141),x92142))+~P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),x92141),x92141)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),x92142),x92142)),a106)))
% 21.40/21.36 [9215]P1(f789(f789(f240(a1),x92151),x92152))+~P1(f789(f789(f240(a1),f789(f789(f3(a1),f789(f789(f89(a1),x92151),x92151)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),x92152),x92152)),a106)))
% 21.40/21.36 [9216]P1(f789(f789(f240(a1),x92161),x92162))+~P1(f789(f789(f240(a1),f789(f789(f3(a1),f789(f789(f89(a1),x92161),x92161)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),x92162),x92162)),a106)))
% 21.40/21.36 [9245]~P1(f789(f70(x92451),x92452))+P1(f789(f70(f870(x92451,a856)),f789(f264(f870(x92451,a856)),f789(f789(f9(f870(x92451,a856),f870(x92451,a856),a856),f240(f870(x92451,a856))),x92452))))
% 21.40/21.36 [9291]~E(f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),x92911),f184(f870(f869(a863,a863),a856)))),f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),x92912),f184(f870(f869(a863,a863),a856)))))+P1(f789(f789(f342(f869(f869(a863,a863),f869(a863,a863))),f789(f789(f249(f869(a863,a863),f869(a863,a863)),x92911),x92912)),a118))
% 21.40/21.36 [9379]E(f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),x93791),f184(f870(f869(a863,a863),a856)))),f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),x93792),f184(f870(f869(a863,a863),a856)))))+~P1(f789(f789(f342(f869(f869(a863,a863),f869(a863,a863))),f789(f789(f249(f869(a863,a863),f869(a863,a863)),x93791),x93792)),a118))
% 21.40/21.36 [9412]P1(f789(f789(f240(a1),f2(a1)),f709(x94121,x94122)))+E(f789(f264(a1),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f240(a1),f2(a1)))),x94121)),f789(f264(a1),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f240(a1),f2(a1)))),x94122)))
% 21.40/21.36 [9916]~P9(x99161)+E(f52(x99161,f789(f264(x99161),f789(f789(f10(f870(x99161,a856),a856,x99161),f97(x99161)),f789(f789(f10(f870(x99161,a856),f870(x99161,a856),x99161),f789(f20(x99161,a856,a856),f789(f789(f10(a856,f870(a856,a856),x99161),a343),f789(f789(f9(x99161,f870(x99161,a856),a856),f342(x99161)),x99162)))),f789(f9(x99161,x99161,a856),f240(x99161)))))),f51(x99161,x99162))
% 21.40/21.36 [9936]P1(f789(f789(f342(a863),f2(a863)),x99361))+E(f789(f49(a863),f789(f264(a863),f789(f789(f20(a863,a856,a856),f789(f789(f10(a856,f870(a856,a856),a863),a339),f789(f789(f9(a863,f870(a863,a856),a856),f789(f789(f10(a863,f870(f870(a863,a856),a856),a863),f342(a863)),a121)),x99361))),f789(f789(f9(a863,a863,a856),f241(a863)),x99362)))),f789(f49(a863),f789(f264(a863),f789(f789(f20(a863,a856,a856),f789(f789(f10(a856,f870(a856,a856),a863),a339),f789(f789(f9(a863,f870(a863,a856),a856),f342(a863)),x99361))),f789(f789(f9(a863,a863,a856),f241(a863)),f789(a121,x99362))))))
% 21.40/21.36 [9983]P1(f789(f789(f287(a863),x99831),x99832))+~P1(f789(f789(f342(a863),x99832),f295(a863,f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x99831)))
% 21.40/21.36 [9984]P1(f789(f789(f287(a863),x99841),x99842))+~P1(f789(f789(f342(a863),x99841),f298(a863,f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x99842)))
% 21.40/21.36 [9985]~P1(f789(f789(f287(a863),x99851),x99852))+~P1(f789(f789(f342(a863),x99852),f298(a863,f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x99851)))
% 21.40/21.36 [9986]~P1(f789(f789(f287(a863),x99861),x99862))+~P1(f789(f789(f342(a863),x99861),f295(a863,f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x99862)))
% 21.40/21.36 [7545]~P88(x75451)+E(f789(f789(f90(x75451),x75452),f789(f113(x75451),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),x75452)
% 21.40/21.36 [7811]~P88(x78111)+E(f789(f789(f89(x78111),f789(f113(x78111),x78112)),f87(x78111)),f789(f113(x78111),f789(f789(f89(a1),x78112),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))
% 21.40/21.36 [7954]P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x79542)))+E(f789(f789(f250(a1),x79541),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),x79542),x79542)),a106))),f87(a1))
% 21.40/21.36 [9269]~P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x92692)))+E(f789(f789(f250(a1),x92691),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),x92692),x92692)),a106))),f789(f789(f95(a1,a1),f789(f789(f250(a1),x92691),f789(f113(a863),x92692))),f789(f789(f20(a1,a1,a1),f789(f789(f10(a1,f870(a1,a1),a1),f90(a1)),f789(f90(a1),x92691))),f7(a1))))
% 21.40/21.36 [9754]~P1(f789(f789(f241(a863),f789(f113(a863),x97541)),f789(a121,x97542)))+P1(f789(f789(f95(a1,a856),f789(f113(a1),f789(f789(f89(a1),x97541),a106))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a343),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f9(a1,a863,a856),f789(f789(f10(a863,f870(a863,a856),a1),f241(a863)),a114)),x97542))))
% 21.40/21.36 [9755]~P1(f789(f789(f240(a863),f789(f113(a863),x97551)),f789(a121,x97552)))+P1(f789(f789(f95(a1,a856),f789(f113(a1),f789(f789(f89(a1),x97551),a106))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a343),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f9(a1,a863,a856),f789(f789(f10(a863,f870(a863,a856),a1),f240(a863)),a114)),x97552))))
% 21.40/21.36 [9819]P1(f789(f789(f241(a863),f789(f113(a863),x98191)),f789(a121,x98192)))+~P1(f789(f789(f95(a1,a856),f789(f113(a1),f789(f789(f89(a1),x98191),a106))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a343),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f9(a1,a863,a856),f789(f789(f10(a863,f870(a863,a856),a1),f241(a863)),a114)),x98192))))
% 21.40/21.36 [9820]P1(f789(f789(f240(a863),f789(f113(a863),x98201)),f789(a121,x98202)))+~P1(f789(f789(f95(a1,a856),f789(f113(a1),f789(f789(f89(a1),x98201),a106))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a343),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f9(a1,a863,a856),f789(f789(f10(a863,f870(a863,a856),a1),f240(a863)),a114)),x98202))))
% 21.40/21.36 [9850]~P1(f789(f789(f241(a863),f789(a121,x98502)),f789(f113(a863),x98501)))+P1(f789(f789(f95(a1,a856),f789(f113(a1),f789(f789(f89(a1),x98501),a106))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a343),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f10(a863,a856,a1),f789(f241(a863),x98502)),a114)))))
% 21.40/21.36 [9851]~P1(f789(f789(f240(a863),f789(a121,x98512)),f789(f113(a863),x98511)))+P1(f789(f789(f95(a1,a856),f789(f113(a1),f789(f789(f89(a1),x98511),a106))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a343),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f10(a863,a856,a1),f789(f240(a863),x98512)),a114)))))
% 21.40/21.36 [9904]P1(f789(f789(f241(a863),f789(a121,x99041)),f789(f113(a863),x99042)))+~P1(f789(f789(f95(a1,a856),f789(f113(a1),f789(f789(f89(a1),x99042),a106))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a343),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f10(a863,a856,a1),f789(f241(a863),x99041)),a114)))))
% 21.40/21.36 [9905]P1(f789(f789(f240(a863),f789(a121,x99051)),f789(f113(a863),x99052)))+~P1(f789(f789(f95(a1,a856),f789(f113(a1),f789(f789(f89(a1),x99052),a106))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a343),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f10(a863,a856,a1),f789(f240(a863),x99051)),a114)))))
% 21.40/21.36 [9976]~P1(f789(f789(f342(a863),f2(a863)),x99761))+E(f789(a121,f789(f49(a863),f789(f264(a863),f789(f789(f20(a863,a856,a856),f789(f789(f10(a856,f870(a856,a856),a863),a339),f789(f789(f9(a863,f870(a863,a856),a856),f789(f789(f10(a863,f870(f870(a863,a856),a856),a863),f342(a863)),a121)),x99761))),f789(f789(f9(a863,a863,a856),f241(a863)),x99762))))),f789(f49(a863),f789(f264(a863),f789(f789(f20(a863,a856,a856),f789(f789(f10(a856,f870(a856,a856),a863),a339),f789(f789(f9(a863,f870(a863,a856),a856),f342(a863)),x99761))),f789(f789(f9(a863,a863,a856),f241(a863)),f789(a121,x99762))))))
% 21.40/21.36 [8493]~P88(x84931)+E(f789(f789(f90(x84931),f789(f113(x84931),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),x84932),x84932)
% 21.40/21.36 [8553]~P88(x85531)+E(f789(f789(f89(x85531),f87(x85531)),f789(f113(x85531),x85532)),f789(f113(x85531),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),x85532)))
% 21.40/21.36 [8599]~P88(x85991)+E(f789(f789(f3(x85991),f789(f113(x85991),x85992)),f87(x85991)),f789(f113(x85991),f789(f789(f89(a1),x85992),f789(f88(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))
% 21.40/21.36 [8733]~P1(f789(f789(f241(a863),f789(f113(a863),a92)),x87332))+E(f789(f789(f3(a863),x87331),f789(f789(f3(a863),x87332),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f789(f3(a863),f789(a121,x87331)),x87332))
% 21.40/21.36 [9308]~P70(x93081)+E(f789(f789(f90(x93081),x93082),x93082),f789(f789(f250(x93081),x93082),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))
% 21.40/21.36 [9309]~P78(x93091)+E(f789(f789(f250(x93091),x93092),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f789(f90(x93091),x93092),x93092))
% 21.40/21.36 [9311]~P88(x93111)+E(f789(f789(f90(x93111),x93112),f789(f113(x93111),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f789(f89(x93111),x93112),x93112))
% 21.40/21.36 [9548]~P120(x95481)+E(f789(f789(f250(x95481),f789(f88(x95481),x95482)),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f789(f250(x95481),x95482),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))
% 21.40/21.36 [9549]~P110(x95491)+E(f789(f789(f250(x95491),f789(f84(x95491),x95492)),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f789(f250(x95491),x95492),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))
% 21.40/21.36 [9545]~P88(x95451)+E(f789(f789(f90(x95451),f789(f113(x95451),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x95452),f789(f789(f89(x95451),x95452),x95452))
% 21.40/21.36 [9666]~P110(x96661)+E(f789(f84(x96661),f789(f789(f250(x96661),x96662),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x96661),x96662),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))
% 21.40/21.36 [9715]~P110(x97151)+P1(f789(f789(f240(x97151),f2(x97151)),f789(f789(f250(x97151),x97152),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))
% 21.40/21.36 [9895]~E(f789(a121,x98952),f789(f113(a863),x98951))+P1(f789(f789(f95(a1,a856),f789(f113(a1),f789(f789(f89(a1),x98951),a106))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a343),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f9(a1,a863,a856),f789(f789(f10(a863,f870(a863,a856),a1),a338),a114)),x98952)))))
% 21.40/21.36 [9896]~E(f789(f113(a863),x98961),f789(a121,x98962))+P1(f789(f789(f95(a1,a856),f789(f113(a1),f789(f789(f89(a1),x98961),a106))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a343),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f9(a1,a863,a856),f789(f789(f10(a863,f870(a863,a856),a1),a338),a114)),x98962)))))
% 21.40/21.36 [9939]E(f789(a121,x99391),f789(f113(a863),x99392))+~P1(f789(f789(f95(a1,a856),f789(f113(a1),f789(f789(f89(a1),x99392),a106))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a343),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f9(a1,a863,a856),f789(f789(f10(a863,f870(a863,a856),a1),a338),a114)),x99391)))))
% 21.40/21.36 [9940]E(f789(f113(a863),x99401),f789(a121,x99402))+~P1(f789(f789(f95(a1,a856),f789(f113(a1),f789(f789(f89(a1),x99401),a106))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a343),f789(f789(f10(a856,a856,a1),a336),a190))),f789(f789(f9(a1,a863,a856),f789(f789(f10(a863,f870(a863,a856),a1),a338),a114)),x99402)))))
% 21.40/21.36 [9713]~P88(x97131)+E(f789(f789(f250(x97131),f789(f113(x97131),a106)),f789(f789(f90(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x97132)),f87(x97131))
% 21.40/21.36 [9714]~P120(x97141)+E(f789(f789(f250(x97141),f789(f88(x97141),f87(x97141))),f789(f789(f90(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x97142)),f87(x97141))
% 21.40/21.36 [9717]~P78(x97171)+E(f789(f789(f250(x97171),x97172),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),a106))),f789(f789(f90(x97171),f789(f789(f90(x97171),x97172),x97172)),x97172))
% 21.40/21.36 [9919]~P1(f789(f789(f240(a1),f2(a1)),x99192))+E(f59(a1,f789(f789(f89(a1),f87(a1)),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x99191)),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x99192)),f789(f789(f89(a1),f87(a1)),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f59(a1,x99191,x99192))))
% 21.40/21.36 [9942]~P1(f789(f789(f240(a1),f2(a1)),x99422))+E(f789(f789(f50(a1),f789(f789(f89(a1),f87(a1)),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x99421))),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x99422)),f789(f789(f50(a1),x99421),x99422))
% 21.40/21.36 [9944]~P1(f789(f789(f240(a1),x99442),f2(a1)))+E(f789(f789(f50(a1),f789(f789(f89(a1),f87(a1)),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x99441))),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x99442)),f789(f789(f50(a1),f789(f789(f89(a1),x99441),f87(a1))),x99442))
% 21.40/21.36 [9945]~P1(f789(f789(f240(a1),x99452),f2(a1)))+E(f59(a1,f789(f789(f89(a1),f87(a1)),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x99451)),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x99452)),f789(f789(f3(a1),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f59(a1,f789(f789(f89(a1),x99451),f87(a1)),x99452))),f87(a1)))
% 21.40/21.36 [9810]~P88(x98101)+E(f789(f789(f250(x98101),f789(f113(x98101),a106)),f789(a121,f789(f789(f90(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x98102))),f789(f113(x98101),a106))
% 21.40/21.36 [9812]~P120(x98121)+E(f789(f789(f250(x98121),f789(f88(x98121),f87(x98121))),f789(a121,f789(f789(f90(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x98122))),f789(f88(x98121),f87(x98121)))
% 21.40/21.36 [6040]E(x60401,x60402)+~P39(a25,x60401,x60403,x60402)
% 21.40/21.36 [5052]~P36(x50521,x50523)+P36(x50521,f335(x50521,x50522,x50523))
% 21.40/21.36 [5216]P31(x52161,x52162,x52163)+~P31(x52161,f789(a121,x52162),x52163)
% 21.40/21.36 [5297]~P12(x52971,x52972,x52973)+P12(f864(x52971),f156(x52971,x52972),f154(x52971,x52973))
% 21.40/21.36 [5298]~P47(x52981,x52982,x52983)+P47(f864(x52981),f156(x52981,x52982),f154(x52981,x52983))
% 21.40/21.36 [5409]P53(x54091,x54092,x54093)+~E(f655(x54093,x54092,x54091),f656(x54093,x54092,x54091))
% 21.40/21.36 [5410]P54(x54101,x54102,x54103)+~E(f661(x54103,x54102,x54101),f662(x54103,x54102,x54101))
% 21.40/21.36 [6358]P32(x63581,x63582,x63583)+~P31(x63581,f822(x63583,x63582,x63581),f830(x63583,x63582,x63581))
% 21.40/21.36 [4609]~E(x46091,f187(x46092))+~E(x46091,f789(f234(x46092),x46093))
% 21.40/21.36 [4610]~E(x46101,f187(x46102))+~E(x46101,f789(f234(x46102),x46103))
% 21.40/21.36 [4658]~E(f789(f149(x46582),x46581),x46583)+E(x46581,f789(f149(x46582),x46583))
% 21.40/21.36 [4659]~E(x46592,f789(f149(x46591),x46593))+E(f789(f149(x46591),x46592),x46593)
% 21.40/21.36 [4703]E(x47031,x47032)+~E(f789(f234(x47033),x47031),f789(f234(x47033),x47032))
% 21.40/21.36 [4704]E(x47041,x47042)+~E(f789(f149(x47043),x47041),f789(f149(x47043),x47042))
% 21.40/21.36 [4902]~P11(x49023,x49021)+P1(f789(f789(x49021,x49022),x49022))
% 21.40/21.36 [4903]~P49(x49033,x49031)+P1(f789(f789(x49031,x49032),x49032))
% 21.40/21.36 [4904]~P58(x49041,x49042)+P1(f789(f329(x49041,x49042),x49043))
% 21.40/21.36 [4905]~P58(x49051,x49052)+P1(f789(f329(x49051,x49052),x49053))
% 21.40/21.36 [4967]~P36(x49671,x49672)+P36(f864(x49671),f789(f139(x49671,x49672),x49673))
% 21.40/21.36 [4971]~P1(f789(x49712,x49713))+~E(f789(f264(x49711),x49712),f184(f870(x49711,a856)))
% 21.40/21.36 [4972]~P1(f789(x49722,x49723))+~E(f184(f870(x49721,a856)),f789(f264(x49721),x49722))
% 21.40/21.36 [5005]~P1(f789(x50051,x50053))+P1(f789(x50051,f99(x50052,x50051)))
% 21.40/21.36 [5006]~P1(f789(x50061,x50063))+P1(f789(x50061,f99(x50062,x50061)))
% 21.40/21.36 [5007]~P1(f789(x50071,x50073))+P1(f789(x50071,f99(x50072,x50071)))
% 21.40/21.36 [5008]~P1(f789(x50081,x50083))+P1(f789(x50081,f99(x50082,x50081)))
% 21.40/21.36 [5131]~E(x51312,x51313)+P1(f789(f789(f342(x51311),x51312),f789(a338,x51313)))
% 21.40/21.36 [5185]E(f789(f149(x51851),x51852),f789(f789(f146(x51851),x51853),f122(x51851)))+~E(x51852,f789(f789(f146(x51851),x51853),f122(x51851)))
% 21.40/21.36 [5186]~E(x51863,f789(f789(f146(x51861),x51862),f122(x51861)))+E(f789(f789(f146(x51861),x51862),f122(x51861)),f789(f149(x51861),x51863))
% 21.40/21.36 [5211]~E(x52113,f789(f18(f867(x52112),x52111),f187(x52112)))+E(f173(x52111,x52112,x52113),f184(f870(x52111,a856)))
% 21.40/21.36 [5232]E(f789(f49(x52321),f380(x52322,x52323,x52321)),x52322)+~E(f789(f49(x52321),x52323),f789(a121,x52322))
% 21.40/21.36 [5237]~P36(x52371,x52373)+P1(f789(f789(f342(x52371),x52372),f330(x52371,x52373)))
% 21.40/21.36 [5238]~P36(x52381,x52383)+P1(f789(f789(f342(x52381),x52382),f330(x52381,x52383)))
% 21.40/21.36 [5241]~E(f789(f149(x52412),x52411),f789(f789(f146(x52412),x52413),f122(x52412)))+E(x52411,f789(f789(f146(x52412),x52413),f122(x52412)))
% 21.40/21.36 [5242]~E(f789(f789(f146(x52422),x52423),f122(x52422)),f789(f149(x52422),x52421))+E(x52421,f789(f789(f146(x52422),x52423),f122(x52422)))
% 21.40/21.36 [5256]E(x52561,f789(f18(f867(x52562),x52563),f187(x52562)))+~E(f173(x52563,x52562,x52561),f184(f870(x52563,a856)))
% 21.40/21.36 [5262]E(f94(f869(a863,a863),f62(x52621,x52622)),x52623)+~P1(f789(f62(x52621,x52622),x52623))
% 21.40/21.36 [5269]~E(x52693,f789(f234(x52691),x52692))+P1(f789(f789(f342(x52691),x52692),f233(x52691,x52693)))
% 21.40/21.36 [5360]~E(x53602,f122(x53601))+P1(f789(f789(f342(f864(x53601)),x53602),f156(x53601,x53603)))
% 21.40/21.36 [5368]~P47(x53681,x53682,x53683)+P47(x53681,x53682,f789(f286(x53681,x53681),x53683))
% 21.40/21.36 [5369]~P54(x53691,x53692,x53693)+P54(x53691,x53692,f789(f286(x53691,x53691),x53693))
% 21.40/21.36 [5389]~P7(x53891)+E(f59(x53891,f59(x53891,x53892,x53893),x53893),f59(x53891,x53892,x53893))
% 21.40/21.36 [5487]E(x54871,x54872)+~P1(f789(f789(f342(x54873),x54871),f789(a338,x54872)))
% 21.40/21.36 [5529]~P2(x55291)+E(f186(x55291,x55292,f2(a863),x55293),x55293)
% 21.40/21.36 [5549]P47(x55491,x55492,x55493)+~P47(x55491,x55492,f789(f286(x55491,x55491),x55493))
% 21.40/21.36 [5550]P54(x55501,x55502,x55503)+~P54(x55501,x55502,f789(f286(x55501,x55501),x55503))
% 21.40/21.36 [5572]E(x55721,f789(f234(x55722),x55723))+~P1(f789(f789(f342(x55722),x55723),f233(x55722,x55721)))
% 21.40/21.36 [5653]~P1(f789(a26,x56533))+P1(f789(a26,f34(x56531,x56532,x56533)))
% 21.40/21.36 [5654]~P1(f789(a26,x56543))+P1(f789(a26,f34(x56541,x56542,x56543)))
% 21.40/21.36 [5666]E(f789(f133(x56661,x56662),x56663),f122(x56661))+P1(f789(x56662,f754(x56663,x56662,x56661)))
% 21.40/21.36 [5822]~P1(f789(f134(x58221),x58223))+P1(f789(f134(x58221),f158(x58221,x58222,x58223)))
% 21.40/21.36 [5823]~P1(f789(f134(x58231),x58232))+P1(f789(f134(x58231),f165(x58231,x58232,x58233)))
% 21.40/21.36 [5824]~P140(x58241,x58242,x58243)+P1(f789(x58241,f59(a1,x58242,x58243)))
% 21.40/21.36 [5922]P1(f789(a26,f33(x59221,x59222,x59223)))+~P1(f789(a26,f789(a29,x59222)))
% 21.40/21.36 [5923]P1(f789(a26,f33(x59231,x59232,x59233)))+~P1(f789(a26,f789(a29,x59232)))
% 21.40/21.36 [5935]~P99(x59351)+E(f789(f789(f111(f870(x59351,a856)),f789(f301(x59351),x59352)),f306(x59351,x59352,x59353)),f184(f870(x59351,a856)))
% 21.40/21.36 [5936]~P99(x59361)+E(f789(f789(f111(f870(x59361,a856)),f789(f301(x59361),x59362)),f305(x59361,x59362,x59363)),f184(f870(x59361,a856)))
% 21.40/21.36 [5937]~P99(x59371)+E(f789(f789(f111(f870(x59371,a856)),f789(f265(x59371),x59372)),f303(x59371,x59372,x59373)),f184(f870(x59371,a856)))
% 21.40/21.36 [6088]P1(f789(a26,x60881))+~P1(f789(a26,f34(x60882,x60883,x60881)))
% 21.40/21.36 [6089]P1(f789(a26,x60891))+~P1(f789(a26,f34(x60892,x60893,x60891)))
% 21.40/21.36 [6090]P1(f789(a26,x60901))+~P1(f789(a26,f35(x60902,x60903,x60901)))
% 21.40/21.36 [6091]P1(f789(a26,x60911))+~P1(f789(a26,f35(x60912,x60913,x60911)))
% 21.40/21.36 [6092]P1(f789(a26,x60921))+~P1(f789(a26,f35(x60922,x60921,x60923)))
% 21.40/21.36 [6093]P1(f789(a26,x60931))+~P1(f789(a26,f35(x60932,x60931,x60933)))
% 21.40/21.36 [6171]E(f789(f133(x61711,x61712),x61713),x61713)+~P1(f789(x61712,f773(x61713,x61712,x61711)))
% 21.40/21.36 [6173]E(f789(f789(f310(x61731),f389(x61732,x61733,x61731)),f380(x61732,x61733,x61731)),x61733)+~E(f789(f49(x61731),x61733),f789(a121,x61732))
% 21.40/21.36 [6188]P140(x61881,x61882,x61883)+~P1(f789(x61881,f59(a1,x61882,x61883)))
% 21.40/21.36 [6278]~P1(f789(a26,f33(x62782,x62781,x62783)))+P1(f789(a26,f789(a29,x62781)))
% 21.40/21.36 [6279]~P1(f789(a26,f33(x62792,x62791,x62793)))+P1(f789(a26,f789(a29,x62791)))
% 21.40/21.36 [6327]~P1(f789(x63272,f347(x63273,x63272,x63271)))+P1(f789(f253(x63271,x63272),x63273))
% 21.40/21.36 [6585]~P1(f789(f329(x65851,x65852),f840(x65853,x65852,x65851)))+P1(f789(f329(x65851,x65852),x65853))
% 21.40/21.36 [6586]~P1(f789(f329(x65861,x65862),f841(x65863,x65862,x65861)))+P1(f789(f329(x65861,x65862),x65863))
% 21.40/21.36 [7214]~P7(x72141)+E(f789(f789(f89(x72141),f789(f789(f90(x72141),x72142),f789(f789(f50(x72141),x72143),x72142))),f59(x72141,x72143,x72142)),x72143)
% 21.40/21.36 [7702]E(f789(f789(f249(x77021,x77021),f435(x77022,x77023,x77021)),f435(x77022,x77023,x77021)),x77023)+~P1(f789(f789(f342(f869(x77021,x77021)),x77023),f268(x77021,x77022)))
% 21.40/21.36 [7820]~P1(f789(f789(f342(x78201),f361(x78203,x78202,x78201)),f330(x78201,x78203)))+P1(f789(f789(f342(x78201),x78202),f330(x78201,x78203)))
% 21.40/21.36 [7821]~P1(f789(f789(f342(x78211),f631(x78213,x78212,x78211)),f330(x78211,x78213)))+P1(f789(f789(f342(x78211),x78212),f330(x78211,x78213)))
% 21.40/21.36 [7822]~P1(f789(f789(f342(x78221),f633(x78223,x78222,x78221)),f330(x78221,x78223)))+P1(f789(f789(f342(x78221),x78222),f330(x78221,x78223)))
% 21.40/21.36 [8005]~P7(x80051)+E(f789(f789(f89(x80051),f789(f789(f90(x80051),f789(f789(f50(x80051),x80052),x80053)),x80053)),f59(x80051,x80052,x80053)),x80052)
% 21.40/21.36 [8006]~P7(x80061)+E(f789(f789(f89(x80061),f789(f789(f90(x80061),f789(f789(f50(x80061),x80062),x80063)),x80063)),f59(x80061,x80062,x80063)),x80062)
% 21.40/21.36 [8047]~E(f789(f49(x80471),x80472),f789(a121,x80473))+~P1(f789(f789(f342(x80471),f389(x80473,x80472,x80471)),f380(x80473,x80472,x80471)))
% 21.40/21.36 [8648]P1(f789(f789(f240(f870(f869(x86481,x86481),a856)),f308(x86481,x86482)),f308(x86481,x86483)))+~P1(f789(f789(f240(f870(f869(x86481,x86481),a856)),x86482),f308(x86481,x86483)))
% 21.40/21.36 [8888]E(x88881,f122(x88882))+~P1(f789(f789(f342(f869(f864(x88882),f864(x88882))),f789(f789(f249(f864(x88882),f864(x88882)),x88881),f122(x88882))),f154(x88882,x88883)))
% 21.40/21.36 [8914]E(x89141,f122(x89142))+~P1(f789(f789(f342(f869(f864(x89142),f864(x89142))),f789(f789(f249(f864(x89142),f864(x89142)),f122(x89142)),x89141)),f154(x89142,x89143)))
% 21.40/21.36 [9039]E(f789(f789(f146(x90391),f763(x90392,x90393,x90391)),f764(x90392,x90393,x90391)),x90393)+~P1(f789(f789(f342(f869(f864(x90391),f864(x90391))),f789(f789(f249(f864(x90391),f864(x90391)),f122(x90391)),x90393)),f143(x90391,x90392)))
% 21.40/21.36 [9238]~P119(x92381)+~P1(f789(f789(f241(x92381),f789(f789(f89(x92381),f789(f789(f90(x92381),x92382),x92382)),f789(f789(f90(x92381),x92383),x92383))),f2(x92381)))
% 21.40/21.36 [9286]P1(f789(f70(x92861),x92862))+~P1(f789(f789(f342(f869(f870(x92861,a856),f870(x92861,a856))),f789(f789(f249(f870(x92861,a856),f870(x92861,a856)),x92863),x92862)),f307(x92861)))
% 21.40/21.36 [9570]~P45(x95701,x95702,x95703)+P1(f789(f789(f241(a1),f789(f789(f82(f869(a1,a1),a1,x95701,f248(a1,a1)),f214(x95701)),f231(x95701,x95702,f228(x95701,x95703)))),f2(a1)))
% 21.40/21.36 [9571]~P46(x95711,x95712,x95713)+P1(f789(f789(f240(a1),f789(f789(f82(f869(a1,a1),a1,x95711,f248(a1,a1)),f214(x95711)),f231(x95711,x95712,f228(x95711,x95713)))),f2(a1)))
% 21.40/21.36 [9691]P45(x96911,x96912,x96913)+~P1(f789(f789(f241(a1),f789(f789(f82(f869(a1,a1),a1,x96911,f248(a1,a1)),f214(x96911)),f231(x96911,x96912,f228(x96911,x96913)))),f2(a1)))
% 21.40/21.36 [9692]P46(x96921,x96922,x96923)+~P1(f789(f789(f240(a1),f789(f789(f82(f869(a1,a1),a1,x96921,f248(a1,a1)),f214(x96921)),f231(x96921,x96922,f228(x96921,x96923)))),f2(a1)))
% 21.40/21.36 [10027]~P110(x100271)+~P1(f789(f789(f241(x100271),f789(f789(f89(x100271),f789(f789(f250(x100271),x100272),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x100271),x100273),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))),f2(x100271)))
% 21.40/21.36 [4685]~E(x46853,f122(x46851))+E(f789(f789(f132(x46851),x46852),x46853),x46852)
% 21.40/21.36 [4686]~E(x46862,f122(x46861))+E(f789(f789(f132(x46861),x46862),x46863),x46863)
% 21.40/21.36 [4687]~E(x46873,f122(x46871))+E(f789(f789(f132(x46871),x46872),x46873),x46872)
% 21.40/21.36 [4688]~E(x46882,f122(x46881))+E(f789(f789(f132(x46881),x46882),x46883),x46883)
% 21.40/21.36 [4694]~E(x46942,f2(a863))+E(f789(f789(f164(x46941),x46942),x46943),f122(x46941))
% 21.40/21.36 [4698]~E(x46983,f122(x46981))+E(f789(f789(f164(x46981),x46982),x46983),f122(x46981))
% 21.40/21.36 [4737]~E(x47371,x47373)+E(x47371,f789(f789(f132(x47372),f122(x47372)),x47373))
% 21.40/21.36 [4818]~P102(x48182)+E(f789(f184(f870(x48181,x48182)),x48183),f184(x48182))
% 21.40/21.36 [4819]~P102(x48192)+E(f789(f184(f870(x48191,x48192)),x48193),f184(x48192))
% 21.40/21.36 [4820]~P107(x48202)+E(f789(f247(f870(x48201,x48202)),x48203),f247(x48202))
% 21.40/21.36 [4837]E(x48371,f122(x48372))+~E(f789(f789(f132(x48372),x48371),x48373),x48373)
% 21.40/21.36 [4838]E(x48381,f122(x48382))+~E(f789(f789(f132(x48382),x48383),x48381),x48383)
% 21.40/21.36 [4839]E(x48391,f122(x48392))+~E(f789(f789(f132(x48392),x48393),x48391),x48393)
% 21.40/21.36 [4840]E(x48401,f122(x48402))+~E(f789(f789(f132(x48402),x48401),x48403),x48403)
% 21.40/21.36 [4846]E(x48461,f122(x48462))+~E(f789(f789(f132(x48462),x48463),x48461),f122(x48462))
% 21.40/21.36 [4847]E(x48471,f122(x48472))+~E(f789(f789(f132(x48472),x48471),x48473),f122(x48472))
% 21.40/21.36 [4848]E(x48481,f122(x48482))+~E(f789(f789(f132(x48482),x48483),x48481),f122(x48482))
% 21.40/21.36 [4849]E(x48491,f122(x48492))+~E(f789(f789(f132(x48492),x48491),x48493),f122(x48492))
% 21.40/21.36 [4874]~E(x48742,f2(a863))+E(f789(f789(f90(a863),x48741),x48742),f789(f789(f90(a863),x48743),x48742))
% 21.40/21.36 [4875]~E(x48751,f2(a863))+E(f789(f789(f90(a863),x48751),x48752),f789(f789(f90(a863),x48751),x48753))
% 21.40/21.36 [4876]~E(x48761,f2(a863))+E(f789(f789(f90(a863),x48761),x48762),f789(f789(f90(a863),x48761),x48763))
% 21.40/21.36 [4929]~P70(x49291)+E(f789(f789(f89(x49291),x49292),x49293),f789(f789(f89(x49291),x49293),x49292))
% 21.40/21.36 [4930]~P70(x49301)+E(f789(f789(f90(x49301),x49302),x49303),f789(f789(f90(x49301),x49303),x49302))
% 21.40/21.36 [4931]~P101(x49311)+E(f789(f789(f244(x49311),x49312),x49313),f789(f789(f244(x49311),x49313),x49312))
% 21.40/21.36 [4932]~P101(x49321)+E(f789(f789(f244(x49321),x49322),x49323),f789(f789(f244(x49321),x49323),x49322))
% 21.40/21.36 [4933]~P101(x49331)+E(f789(f789(f239(x49331),x49332),x49333),f789(f789(f239(x49331),x49333),x49332))
% 21.40/21.36 [4934]~P101(x49341)+E(f789(f789(f239(x49341),x49342),x49343),f789(f789(f239(x49341),x49343),x49342))
% 21.40/21.36 [4935]~P94(x49351)+E(f789(f789(f110(x49351),x49352),x49353),f789(f789(f110(x49351),x49353),x49352))
% 21.40/21.36 [4936]~P94(x49361)+E(f789(f789(f110(x49361),x49362),x49363),f789(f789(f110(x49361),x49363),x49362))
% 21.40/21.36 [4937]~P95(x49371)+E(f789(f789(f110(x49371),x49372),x49373),f789(f789(f110(x49371),x49373),x49372))
% 21.40/21.36 [4938]~P95(x49381)+E(f789(f789(f111(x49381),x49382),x49383),f789(f789(f111(x49381),x49383),x49382))
% 21.40/21.36 [4939]~P98(x49391)+E(f789(f789(f111(x49391),x49392),x49393),f789(f789(f111(x49391),x49393),x49392))
% 21.40/21.36 [4940]~P98(x49401)+E(f789(f789(f111(x49401),x49402),x49403),f789(f789(f111(x49401),x49403),x49402))
% 21.40/21.36 [5003]E(f59(a863,x50031,x50032),f2(a863))+~E(x50031,f789(f789(f90(a863),x50032),x50033))
% 21.40/21.36 [5004]E(f59(a1,x50041,x50042),f2(a1))+~E(x50041,f789(f789(f90(a1),x50042),x50043))
% 21.40/21.36 [5064]E(x50641,x50642)+~E(f789(f789(f89(a863),x50643),x50641),f789(f789(f89(a863),x50643),x50642))
% 21.40/21.36 [5065]E(x50651,x50652)+~E(f789(f789(f89(a863),x50651),x50653),f789(f789(f89(a863),x50652),x50653))
% 21.40/21.36 [5075]~P68(x50751)+E(f789(f789(f89(x50751),x50752),f789(f88(x50751),x50753)),f789(f789(f3(x50751),x50752),x50753))
% 21.40/21.36 [5076]~P6(x50761)+E(f789(f789(f89(x50761),x50762),f789(f88(x50761),x50763)),f789(f789(f3(x50761),x50762),x50763))
% 21.40/21.36 [5077]~P104(x50771)+E(f789(f789(f89(x50771),x50772),f789(f88(x50771),x50773)),f789(f789(f3(x50771),x50772),x50773))
% 21.40/21.36 [5078]~P90(x50781)+E(f789(f789(f111(x50781),x50782),f789(f88(x50781),x50783)),f789(f789(f3(x50781),x50782),x50783))
% 21.40/21.36 [5079]~P68(x50791)+E(f789(f789(f3(x50791),x50792),f789(f88(x50791),x50793)),f789(f789(f89(x50791),x50792),x50793))
% 21.40/21.36 [5125]~P1(f789(x51253,x51252))+P1(f789(f789(f342(x51251),x51252),x51253))
% 21.40/21.36 [5126]~P69(x51262)+E(f789(f789(f11(x51261,x51262),x51263),f184(f870(x51261,a856))),f87(x51262))
% 21.40/21.36 [5127]~P69(x51272)+E(f789(f789(f11(x51271,x51272),x51273),f184(f870(x51271,a856))),f87(x51272))
% 21.40/21.36 [5128]~P4(x51282)+E(f789(f789(f8(x51281,x51282),x51283),f184(f870(x51281,a856))),f2(x51282))
% 21.40/21.36 [5129]~P4(x51292)+E(f789(f789(f8(x51291,x51292),x51293),f184(f870(x51291,a856))),f2(x51292))
% 21.40/21.36 [5174]~E(x51742,f789(f789(f89(a863),x51741),x51743))+P1(f789(f789(f240(a863),x51741),x51742))
% 21.40/21.36 [5176]~E(x51762,f184(f870(x51761,a856)))+E(f789(f789(f68(x51761),x51762),x51763),f184(f870(f870(x51761,a856),a856)))
% 21.40/21.36 [5177]~E(x51772,f184(f870(x51771,a856)))+E(f184(f870(f870(x51771,a856),a856)),f789(f789(f68(x51771),x51772),x51773))
% 21.40/21.36 [5245]~E(f789(f267(x52452,x52453),x52451),f184(f870(x52453,a856)))+E(x52451,f184(f870(f869(x52452,x52453),a856)))
% 21.40/21.36 [5246]~E(f789(f269(x52462,x52463),x52461),f184(f870(x52462,a856)))+E(x52461,f184(f870(f869(x52462,x52463),a856)))
% 21.40/21.36 [5275]E(f789(f267(x52751,x52752),x52753),f184(f870(x52752,a856)))+~E(x52753,f184(f870(f869(x52751,x52752),a856)))
% 21.40/21.36 [5276]E(f789(f269(x52761,x52762),x52763),f184(f870(x52761,a856)))+~E(x52763,f184(f870(f869(x52761,x52762),a856)))
% 21.40/21.36 [5279]E(f277(x52791,x52792,x52793),f789(f789(f3(a108),x52792),x52793))+P1(f789(f789(f241(a108),x52792),x52793))
% 21.40/21.36 [5295]P1(f789(x52951,x52952))+~P1(f789(f789(f342(x52953),x52952),x52951))
% 21.40/21.36 [5331]E(x53311,x53312)+~E(f789(f88(f870(x53313,a856)),x53311),f789(f88(f870(x53313,a856)),x53312))
% 21.40/21.36 [5336]E(f315(x53361,x53362,x53363),f187(f864(a854)))+~P1(f789(f789(f241(a1),x53362),x53363))
% 21.40/21.36 [5339]~E(x53391,f184(f870(x53392,a856)))+~P1(f789(f789(f342(x53392),x53393),x53391))
% 21.40/21.36 [5340]~E(x53401,f184(f870(x53402,a856)))+~P1(f789(f789(f342(x53402),x53403),x53401))
% 21.40/21.36 [5341]~E(x53411,f184(f870(x53412,a856)))+~P1(f789(f789(f342(x53412),x53413),x53411))
% 21.40/21.36 [5370]~E(x53702,f789(f789(f89(a1),x53701),f789(f109(a1),x53703)))+P1(f789(f789(f240(a1),x53701),x53702))
% 21.40/21.36 [5386]E(f789(f789(f310(x53861),x53862),x53863),x53863)+~P1(f789(f789(f342(x53861),x53862),x53863))
% 21.40/21.36 [5398]E(x53981,f184(f870(x53982,a856)))+~E(f789(f789(f68(x53982),x53981),x53983),f184(f870(f870(x53982,a856),a856)))
% 21.40/21.36 [5399]E(x53991,f184(f870(x53992,a856)))+~E(f184(f870(f870(x53992,a856),a856)),f789(f789(f68(x53992),x53991),x53993))
% 21.40/21.36 [5406]~P121(x54061)+E(f789(f789(f90(x54061),f789(f88(x54061),x54062)),f789(f88(x54061),x54063)),f789(f789(f90(x54061),x54062),x54063))
% 21.40/21.36 [5408]~P60(x54081)+E(f789(f789(f291(x54081),f789(f88(x54081),x54082)),f789(f88(x54081),x54083)),f789(f789(f291(x54081),x54082),x54083))
% 21.40/21.36 [5439]~P1(f789(x54393,x54392))+P1(f789(f789(f342(x54391),x54392),f789(f264(x54391),x54393)))
% 21.40/21.36 [5440]~P1(f789(x54403,x54402))+P1(f789(f789(f342(x54401),x54402),f789(f264(x54401),x54403)))
% 21.40/21.36 [5480]E(f158(x54801,x54802,x54803),x54803)+P1(f789(f789(f342(x54801),x54802),f789(f163(x54801),x54803)))
% 21.40/21.36 [5558]~P1(f789(f134(x55581),x55583))+P1(f789(f134(x55581),f789(f133(x55581,x55582),x55583)))
% 21.40/21.36 [5600]~P7(x56001)+E(f789(f789(f50(x56001),f59(x56001,x56002,x56003)),x56003),f2(x56001))
% 21.40/21.36 [5618]E(f165(x56181,f789(f789(f146(x56181),x56182),f122(x56181)),x56183),f122(x56181))+P1(f789(f789(f342(a863),f2(a863)),x56183))
% 21.40/21.36 [5683]E(x56831,x56832)+~E(f789(f789(f90(a863),f789(a121,x56833)),x56831),f789(f789(f90(a863),f789(a121,x56833)),x56832))
% 21.40/21.36 [5684]~E(x56842,f789(f789(f89(a1),x56841),f789(f109(a1),f789(a121,x56843))))+P1(f789(f789(f241(a1),x56841),x56842))
% 21.40/21.36 [5802]~E(x58023,f122(x58021))+E(f789(f789(f789(f178(f864(x58021),f864(x58021)),x58022),f148(x58021)),x58023),f122(x58021))
% 21.40/21.36 [5804]P1(f789(x58041,x58042))+~P1(f789(f789(f342(x58043),x58042),f789(f264(x58043),x58041)))
% 21.40/21.36 [5805]P1(f789(x58051,x58052))+~P1(f789(f789(f342(x58053),x58052),f789(f264(x58053),x58051)))
% 21.40/21.36 [5806]P1(f789(x58061,x58062))+~P1(f789(f789(f342(x58063),x58062),f789(f264(x58063),x58061)))
% 21.40/21.36 [5839]E(x58391,x58392)+~E(f789(f789(f310(x58393),x58391),f184(f870(x58393,a856))),f789(f789(f310(x58393),x58392),f184(f870(x58393,a856))))
% 21.40/21.36 [5849]~P99(x58491)+E(f789(f789(f111(f870(x58491,a856)),f789(f265(x58491),x58492)),f789(f302(x58491,x58492),x58493)),f184(f870(x58491,a856)))
% 21.40/21.36 [5909]~P76(x59091)+E(f789(f311(x59091,x59091,f88(x59091)),f789(f302(x59091,x59092),x59093)),f305(x59091,f789(f88(x59091),x59093),f789(f88(x59091),x59092)))
% 21.40/21.36 [5917]E(f789(f185(f864(x59171)),f158(x59171,x59172,x59173)),f789(f185(f864(x59171)),x59173))+P1(f789(f789(f342(x59171),x59172),f789(f163(x59171),x59173)))
% 21.40/21.36 [5938]P1(f789(x59381,x59382))+~P1(f789(f789(f342(x59383),x59382),f184(f870(x59383,a856))))
% 21.40/21.36 [5974]~P99(x59741)+E(f789(f789(f111(f870(x59741,a856)),f789(f302(x59741,x59742),x59743)),f789(f266(x59741),x59743)),f184(f870(x59741,a856)))
% 21.40/21.36 [5995]~P76(x59951)+E(f789(f311(x59951,x59951,f88(x59951)),f306(x59951,x59952,x59953)),f306(x59951,f789(f88(x59951),x59953),f789(f88(x59951),x59952)))
% 21.40/21.36 [5996]~P76(x59961)+E(f789(f311(x59961,x59961,f88(x59961)),f303(x59961,x59962,x59963)),f303(x59961,f789(f88(x59961),x59963),f789(f88(x59961),x59962)))
% 21.40/21.36 [6028]E(x60281,f122(x60282))+E(f789(f789(f146(x60282),f789(f137(x60282),x60281)),f789(f789(f164(x60282),x60283),f147(x60282,x60281))),f789(f789(f164(x60282),f789(a121,x60283)),x60281))
% 21.40/21.36 [6056]E(f165(x60561,f789(f789(f146(x60561),x60562),f122(x60561)),x60563),f789(f789(f146(x60561),x60562),f122(x60561)))+~P1(f789(f789(f342(a863),f2(a863)),x60563))
% 21.40/21.36 [6065]~P76(x60651)+E(f789(f311(x60651,x60651,f88(x60651)),f305(x60651,x60652,x60653)),f789(f302(x60651,f789(f88(x60651),x60653)),f789(f88(x60651),x60652)))
% 21.40/21.36 [6084]~P8(x60841)+E(f59(x60841,f789(f88(x60841),f59(x60841,x60842,x60843)),x60843),f59(x60841,f789(f88(x60841),x60842),x60843))
% 21.40/21.36 [6186]~P1(f789(f70(f869(x61862,x61861)),x61863))+P1(f789(f70(x61861),f789(f267(x61862,x61861),x61863)))
% 21.40/21.36 [6187]~P1(f789(f70(f869(x61871,x61872)),x61873))+P1(f789(f70(x61871),f789(f269(x61871,x61872),x61873)))
% 21.40/21.36 [6192]~P99(x61921)+E(f789(f789(f111(f870(x61921,a856)),f306(x61921,x61922,x61923)),f789(f266(x61921),x61923)),f184(f870(x61921,a856)))
% 21.40/21.36 [6193]~P99(x61931)+E(f789(f789(f111(f870(x61931,a856)),f305(x61931,x61932,x61933)),f789(f304(x61931),x61933)),f184(f870(x61931,a856)))
% 21.40/21.36 [6194]~P99(x61941)+E(f789(f789(f111(f870(x61941,a856)),f303(x61941,x61942,x61943)),f789(f304(x61941),x61943)),f184(f870(x61941,a856)))
% 21.40/21.36 [6261]E(f789(f789(f159(x62611),x62612),f743(x62612,x62613,x62611)),x62613)+~P1(f789(f789(f342(x62611),x62613),f789(f163(x62611),x62612)))
% 21.40/21.36 [6413]E(x64131,f122(x64132))+~E(f789(f789(f789(f178(f864(x64132),f864(x64132)),x64133),f148(x64132)),x64131),f122(x64132))
% 21.40/21.36 [6491]P39(x64911,x64912,f411(x64913,x64912,x64911),x64913)+~P1(f789(f789(f191(x64911),x64912),x64913))
% 21.40/21.36 [6492]P39(x64921,x64922,f630(x64923,x64922,x64921),x64923)+~P1(f789(f789(f191(x64921),x64922),x64923))
% 21.40/21.36 [6521]~P1(f789(f70(f869(x65212,x65211)),x65213))+P1(f789(f70(f869(x65211,x65212)),f789(f286(x65212,x65211),x65213)))
% 21.40/21.36 [6543]E(x65431,x65432)+~E(f290(a863,f287(a863),x65433,x65431),f789(f789(f310(a863),x65432),f184(f870(a863,a856))))
% 21.40/21.36 [6544]E(x65441,x65442)+~E(f290(a863,f287(a863),x65441,x65442),f789(f789(f310(a863),x65443),f184(f870(a863,a856))))
% 21.40/21.36 [6679]P54(x66791,x66792,x66793)+P1(f789(f789(f342(x66791),f662(x66793,x66792,x66791)),x66792))
% 21.40/21.36 [6680]P54(x66801,x66802,x66803)+P1(f789(f789(f342(x66801),f661(x66803,x66802,x66801)),x66802))
% 21.40/21.36 [6692]P1(f789(f329(x66921,x66922),x66923))+P1(f789(f789(x66922,f840(x66923,x66922,x66921)),x66923))
% 21.40/21.36 [6693]P1(f789(f329(x66931,x66932),x66933))+P1(f789(f789(x66932,f841(x66933,x66932,x66931)),x66933))
% 21.40/21.36 [6724]E(f789(f185(f864(x67241)),f158(x67241,x67242,x67243)),f789(f789(f3(a863),f789(f185(f864(x67241)),x67243)),f87(a863)))+~P1(f789(f789(f342(x67241),x67242),f789(f163(x67241),x67243)))
% 21.40/21.36 [6764]P1(f789(f253(x67641,x67642),x67643))+P1(f789(f789(f342(x67641),f347(x67643,x67642,x67641)),x67643))
% 21.40/21.36 [6776]~P1(f789(f70(f869(x67762,x67761)),f789(f286(x67761,x67762),x67763)))+P1(f789(f70(f869(x67761,x67762)),x67763))
% 21.40/21.36 [6837]~P1(f789(f789(f342(x68371),x68372),f789(f163(x68371),f123(x68371,x68373))))+P1(f789(f789(f342(x68371),x68372),f789(f163(x68371),x68373)))
% 21.40/21.36 [6844]P32(x68441,x68442,x68443)+P1(f789(f789(f342(f862(x68441)),f830(x68443,x68442,x68441)),x68443))
% 21.40/21.36 [6873]E(f789(f133(x68731,x68732),x68733),x68733)+P1(f789(f789(f342(x68731),f773(x68733,x68732,x68731)),f789(f163(x68731),x68733)))
% 21.40/21.36 [6890]E(f789(f133(x68901,x68902),x68903),f122(x68901))+P1(f789(f789(f342(x68901),f754(x68903,x68902,x68901)),f789(f163(x68901),x68903)))
% 21.40/21.36 [7038]P1(f789(f789(f342(x70381),x70382),f712(x70383,x70382,x70381)))+~P1(f789(f789(f342(x70381),x70382),f51(f870(x70381,a856),x70383)))
% 21.40/21.36 [7040]~P4(x70401)+E(f789(f789(f89(x70401),f789(f789(f8(a863,x70401),x70402),f789(f265(a863),x70403))),f789(x70402,x70403)),f789(f789(f8(a863,x70401),x70402),f789(f265(a863),f789(a121,x70403))))
% 21.40/21.36 [7144]~P1(f789(f789(f342(x71441),x71442),f702(x71442,x71443,x71441)))+P1(f789(f789(f342(x71441),x71442),f52(f870(x71441,a856),x71443)))
% 21.40/21.36 [7173]~P4(x71731)+E(f789(f789(f89(x71731),f789(f789(f8(a863,x71731),x71732),f789(f301(a863),x71733))),f789(x71732,f789(a121,x71733))),f789(f789(f8(a863,x71731),x71732),f789(f301(a863),f789(a121,x71733))))
% 21.40/21.36 [7327]P1(f789(f789(f342(f864(x73271)),x73272),f156(x73271,x73273)))+P1(f789(f789(f342(x73271),f762(x73273,x73272,x73271)),f789(f163(x73271),x73272)))
% 21.40/21.36 [7344]~P1(f789(f789(f342(f864(x73441)),x73442),f156(x73441,f330(x73441,x73443))))+P1(f789(f789(f342(f864(x73441)),x73442),f330(f864(x73441),f153(x73441,x73443))))
% 21.40/21.36 [7372]~P1(f789(f789(f342(f864(x73721)),x73722),f330(f864(x73721),f153(x73721,x73723))))+P1(f789(f789(f342(f864(x73721)),x73722),f156(x73721,f330(x73721,x73723))))
% 21.40/21.36 [7412]E(f789(f789(f789(f178(f864(x74121),f864(x74121)),x74122),f148(x74121)),x74123),x74123)+~P1(f789(f789(f240(a863),f789(f185(f864(x74121)),x74123)),f87(a863)))
% 21.40/21.36 [7465]~P29(x74651,x74652,x74653,f247(f870(x74651,a856)))+P29(f864(x74651),f864(x74652),f789(f150(x74651,x74652),x74653),f247(f870(f864(x74651),a856)))
% 21.40/21.36 [7466]~P29(x74661,x74662,x74663,f247(f870(x74661,a856)))+P29(f864(x74661),f864(x74662),f789(f150(x74661,x74662),x74663),f247(f870(f864(x74661),a856)))
% 21.40/21.36 [7623]E(x76231,f789(f789(f89(a863),f789(f789(f90(a863),f789(f248(a863,a863),x76232)),x76233)),f789(f258(a863,a863),x76232)))+~P1(f789(f62(x76231,x76233),x76232))
% 21.40/21.36 [7630]P29(x76301,x76302,x76303,f247(f870(x76301,a856)))+~P29(f864(x76301),f864(x76302),f789(f150(x76301,x76302),x76303),f247(f870(f864(x76301),a856)))
% 21.40/21.36 [7631]P29(x76311,x76312,x76313,f247(f870(x76311,a856)))+~P29(f864(x76311),f864(x76312),f789(f150(x76311,x76312),x76313),f247(f870(f864(x76311),a856)))
% 21.40/21.36 [7674]P1(f789(f789(f342(f870(x76741,a856)),f702(x76742,x76743,x76741)),x76743))+P1(f789(f789(f342(x76741),x76742),f52(f870(x76741,a856),x76743)))
% 21.40/21.36 [7762]P1(f789(f789(f342(f864(x77621)),x77622),f156(x77621,x77623)))+~P1(f789(f789(f342(x77621),f762(x77623,x77622,x77621)),x77623))
% 21.40/21.36 [7893]E(x78931,x78932)+~E(f789(f789(f9(x78933,f870(x78933,a856),a856),f342(x78933)),x78931),f789(f789(f9(x78933,f870(x78933,a856),a856),f342(x78933)),x78932))
% 21.40/21.36 [7899]~P1(f789(f789(f342(f869(x78991,x78991)),x78993),f268(x78991,x78992)))+P1(f789(f789(f342(x78991),f435(x78992,x78993,x78991)),x78992))
% 21.40/21.36 [7901]~P1(f789(f789(f342(x79011),x79013),f51(f870(x79011,a856),x79012)))+P1(f789(f789(f342(f870(x79011,a856)),f712(x79012,x79013,x79011)),x79012))
% 21.40/21.36 [8158]E(f789(f236(f867(f864(a854)),f864(a854),f315(x81581,x81582,f789(f789(f89(a1),x81583),f87(a1))),f234(f864(a854))),f789(x81581,x81583)),f315(x81581,x81582,x81583))+P1(f789(f789(f241(a1),x81582),x81583))
% 21.40/21.36 [8257]E(x82571,f122(x82572))+P1(f789(f789(f342(x82572),f789(f248(x82572,f869(a108,a108)),f789(f278(x82572,x82571),x82573))),f789(f163(x82572),x82571)))
% 21.40/21.36 [8356]~P5(x83561)+E(f789(f138(x83561,x83561,f789(f9(x83561,x83561,x83561),f89(x83561)),x83562),f789(f149(x83561),x83563)),f789(f138(x83561,x83561,f89(x83561),x83562),x83563))
% 21.40/21.36 [8817]~P101(x88171)+E(f789(f163(x88171),f145(x88171,x88171,f7(x88171),x88172,x88173)),f789(f789(f310(x88171),x88172),f789(f163(x88171),x88173)))
% 21.40/21.36 [8826]P1(f789(f789(f241(a863),f2(a863)),f664(x88261,x88262,x88263)))+~P1(f789(f789(f342(f869(x88263,x88263)),x88262),f789(f789(f289(x88263,x88263,x88263),x88261),f308(x88263,x88261))))
% 21.40/21.36 [9091]~P56(x90911,x90912)+~P1(f789(f789(f342(f869(x90911,x90911)),f789(f789(f249(x90911,x90911),x90913),x90913)),f789(f789(f289(x90911,x90911,x90911),x90912),f308(x90911,x90912))))
% 21.40/21.36 [9202]~E(f789(f789(f111(f870(f869(x92021,x92021),a856)),f789(f286(x92021,x92021),x92022)),f308(x92021,x92022)),f184(f870(f869(x92021,x92021),a856)))+~P1(f789(f789(f342(f869(x92021,x92021)),f789(f789(f249(x92021,x92021),x92023),x92023)),f789(f789(f289(x92021,x92021,x92021),x92022),f308(x92021,x92022))))
% 21.40/21.36 [9375]~P1(f789(f70(x93751),x93752))+P1(f789(f789(f240(a863),f789(f49(x93751),f789(f789(f3(f870(x93751,a856)),x93752),f789(f789(f310(x93751),x93753),f184(f870(x93751,a856)))))),f789(f49(x93751),x93752)))
% 21.40/21.36 [4986]~E(x49863,f122(x49861))+E(f140(x49861,f789(f789(f146(x49861),x49862),x49863)),x49862)
% 21.40/21.36 [4987]~E(x49873,f122(x49871))+E(f140(x49871,f789(f789(f146(x49871),x49872),x49873)),x49872)
% 21.40/21.36 [5000]~E(x50003,f122(x50001))+E(f123(x50001,f789(f789(f146(x50001),x50002),x50003)),f122(x50001))
% 21.40/21.36 [5028]E(x50281,f122(x50282))+E(f140(x50282,f789(f789(f146(x50282),x50283),x50281)),f140(x50282,x50281))
% 21.40/21.36 [5029]E(x50291,f122(x50292))+E(f140(x50292,f789(f789(f146(x50292),x50293),x50291)),f140(x50292,x50291))
% 21.40/21.36 [5030]E(x50301,f122(x50302))+E(f140(x50302,f789(f789(f132(x50302),x50303),x50301)),f140(x50302,x50301))
% 21.40/21.36 [5031]E(x50311,f122(x50312))+E(f140(x50312,f789(f789(f132(x50312),x50313),x50311)),f140(x50312,x50311))
% 21.40/21.36 [5037]~E(x50373,f122(x50371))+E(f140(x50371,f789(f789(f132(x50371),x50372),x50373)),f140(x50371,x50372))
% 21.40/21.36 [5038]~E(x50383,f122(x50381))+E(f140(x50381,f789(f789(f132(x50381),x50382),x50383)),f140(x50381,x50382))
% 21.40/21.36 [5039]~E(x50393,f122(x50391))+E(f123(x50391,f789(f789(f132(x50391),x50392),x50393)),f123(x50391,x50392))
% 21.40/21.36 [5068]E(x50681,f122(x50682))+E(f789(f137(x50682),f789(f789(f132(x50682),x50681),x50683)),f789(f137(x50682),x50681))
% 21.40/21.36 [5069]E(x50691,f122(x50692))+E(f789(f137(x50692),f789(f789(f132(x50692),x50691),x50693)),f789(f137(x50692),x50691))
% 21.40/21.36 [5100]~E(x51002,f122(x51001))+E(f789(f137(x51001),f789(f789(f132(x51001),x51002),x51003)),f789(f137(x51001),x51003))
% 21.40/21.36 [5151]~P101(x51511)+E(f789(f789(f244(x51511),x51512),f789(f789(f239(x51511),x51512),x51513)),x51512)
% 21.40/21.36 [5152]~P101(x51521)+E(f789(f789(f239(x51521),x51522),f789(f789(f244(x51521),x51522),x51523)),x51522)
% 21.40/21.36 [5153]~P95(x51531)+E(f789(f789(f110(x51531),x51532),f789(f789(f111(x51531),x51532),x51533)),x51532)
% 21.40/21.36 [5154]~P95(x51541)+E(f789(f789(f111(x51541),x51542),f789(f789(f110(x51541),x51542),x51543)),x51542)
% 21.40/21.36 [5172]~P7(x51721)+E(f59(x51721,f789(f789(f90(x51721),x51722),x51723),x51723),f2(x51721))
% 21.40/21.36 [5173]~P7(x51731)+E(f59(x51731,f789(f789(f90(x51731),x51732),x51733),x51732),f2(x51731))
% 21.40/21.36 [5240]~P6(x52401)+E(f789(f88(x52401),f789(f789(f3(x52401),x52402),x52403)),f789(f789(f3(x52401),x52403),x52402))
% 21.40/21.36 [5299]E(x52991,f122(x52992))+E(f123(x52992,f789(f789(f146(x52992),x52993),x52991)),f789(f789(f146(x52992),x52993),f123(x52992,x52991)))
% 21.40/21.36 [5300]E(x53001,f122(x53002))+E(f123(x53002,f789(f789(f132(x53002),x53003),x53001)),f789(f789(f132(x53002),x53003),f123(x53002,x53001)))
% 21.40/21.36 [5301]~P9(x53011)+E(f52(x53011,f789(f789(f310(x53011),x53012),x53013)),f789(f789(f111(x53011),x53012),f52(x53011,x53013)))
% 21.40/21.36 [5302]~P9(x53021)+E(f51(x53021,f789(f789(f310(x53021),x53022),x53023)),f789(f789(f110(x53021),x53022),f51(x53021,x53023)))
% 21.40/21.36 [5345]~P91(x53451)+E(f789(f789(f90(x53451),x53452),f789(f789(f90(x53451),x53452),x53453)),f789(f789(f90(x53451),x53452),x53453))
% 21.40/21.36 [5346]~P101(x53461)+E(f789(f789(f244(x53461),x53462),f789(f789(f244(x53461),x53462),x53463)),f789(f789(f244(x53461),x53462),x53463))
% 21.40/21.36 [5347]~P101(x53471)+E(f789(f789(f244(x53471),x53472),f789(f789(f244(x53471),x53472),x53473)),f789(f789(f244(x53471),x53472),x53473))
% 21.40/21.36 [5348]~P101(x53481)+E(f789(f789(f239(x53481),x53482),f789(f789(f239(x53481),x53482),x53483)),f789(f789(f239(x53481),x53482),x53483))
% 21.40/21.36 [5349]~P101(x53491)+E(f789(f789(f239(x53491),x53492),f789(f789(f239(x53491),x53492),x53493)),f789(f789(f239(x53491),x53492),x53493))
% 21.40/21.36 [5350]~P94(x53501)+E(f789(f789(f110(x53501),x53502),f789(f789(f110(x53501),x53502),x53503)),f789(f789(f110(x53501),x53502),x53503))
% 21.40/21.36 [5351]~P94(x53511)+E(f789(f789(f110(x53511),x53512),f789(f789(f110(x53511),x53512),x53513)),f789(f789(f110(x53511),x53512),x53513))
% 21.40/21.36 [5352]~P95(x53521)+E(f789(f789(f110(x53521),x53522),f789(f789(f110(x53521),x53522),x53523)),f789(f789(f110(x53521),x53522),x53523))
% 21.40/21.36 [5353]~P95(x53531)+E(f789(f789(f111(x53531),x53532),f789(f789(f111(x53531),x53532),x53533)),f789(f789(f111(x53531),x53532),x53533))
% 21.40/21.36 [5354]~P98(x53541)+E(f789(f789(f111(x53541),x53542),f789(f789(f111(x53541),x53542),x53543)),f789(f789(f111(x53541),x53542),x53543))
% 21.40/21.36 [5355]~P98(x53551)+E(f789(f789(f111(x53551),x53552),f789(f789(f111(x53551),x53552),x53553)),f789(f789(f111(x53551),x53552),x53553))
% 21.40/21.36 [5363]~P7(x53631)+E(f59(x53631,f789(f789(f89(x53631),x53632),x53633),x53633),f59(x53631,x53632,x53633))
% 21.40/21.36 [5364]~P7(x53641)+E(f59(x53641,f789(f789(f89(x53641),x53642),x53643),x53642),f59(x53641,x53643,x53642))
% 21.40/21.36 [5371]~P121(x53711)+E(f789(f789(f90(x53711),x53712),f789(f88(x53711),x53713)),f789(f88(x53711),f789(f789(f90(x53711),x53712),x53713)))
% 21.40/21.36 [5372]~P60(x53721)+E(f789(f789(f291(x53721),x53722),f789(f88(x53721),x53723)),f789(f88(x53721),f789(f789(f291(x53721),x53722),x53723)))
% 21.40/21.36 [5373]~P71(x53731)+E(f789(f789(f89(x53731),x53732),f789(f161(x53731),x53733)),f789(f161(x53731),f789(f789(f146(x53731),x53732),x53733)))
% 21.40/21.36 [5404]E(x54041,f122(x54042))+E(f147(x54042,f789(f789(f132(x54042),x54041),x54043)),f789(f789(f132(x54042),f147(x54042,x54041)),x54043))
% 21.40/21.36 [5405]~P121(x54051)+E(f789(f789(f90(x54051),f789(f88(x54051),x54052)),x54053),f789(f789(f90(x54051),x54052),f789(f88(x54051),x54053)))
% 21.40/21.36 [5411]~P12(x54111,x54112,x54113)+E(f51(f870(x54111,a856),f789(f789(f68(x54111),x54112),x54113)),x54112)
% 21.40/21.36 [5471]~P70(x54711)+E(f789(f789(f90(x54711),x54712),f789(f789(f250(x54711),x54712),x54713)),f789(f789(f250(x54711),x54712),f789(a121,x54713)))
% 21.40/21.36 [5472]~P106(x54721)+E(f789(f789(f90(x54721),x54722),f789(f789(f250(x54721),x54722),x54723)),f789(f789(f250(x54721),x54722),f789(a121,x54723)))
% 21.40/21.36 [5473]~P70(x54731)+E(f789(f789(f90(x54731),x54732),f789(f789(f250(x54731),x54732),x54733)),f789(f789(f250(x54731),x54732),f789(a121,x54733)))
% 21.40/21.36 [5483]~P68(x54831)+E(f789(f789(f89(x54831),f789(f88(x54831),x54832)),f789(f789(f89(x54831),x54832),x54833)),x54833)
% 21.40/21.36 [5502]~P2(x55021)+E(f789(f789(f250(x55021),f789(f109(x55021),x55022)),x55023),f789(f109(x55021),f789(f789(f250(a863),x55022),x55023)))
% 21.40/21.36 [5503]~P120(x55031)+E(f789(f789(f250(x55031),f789(f112(x55031),x55032)),x55033),f789(f112(x55031),f789(f789(f250(a1),x55032),x55033)))
% 21.40/21.36 [5508]~P80(x55081)+E(f789(f84(x55081),f789(f789(f3(x55081),x55082),x55083)),f789(f84(x55081),f789(f789(f3(x55081),x55083),x55082)))
% 21.40/21.36 [5511]~P110(x55111)+E(f789(f789(f90(x55111),f91(x55111,x55112)),f91(x55111,x55113)),f91(x55111,f789(f789(f90(x55111),x55112),x55113)))
% 21.40/21.36 [5520]~E(x55202,f789(a121,f789(f789(f89(a863),x55201),x55203)))+P1(f789(f789(f241(a863),x55201),x55202))
% 21.40/21.36 [5521]~P121(x55211)+E(f789(f789(f90(x55211),f789(f88(x55211),x55212)),x55213),f789(f88(x55211),f789(f789(f90(x55211),x55212),x55213)))
% 21.40/21.36 [5522]~P113(x55221)+E(f789(f789(f291(x55221),f789(f88(x55221),x55222)),x55223),f789(f88(x55221),f789(f789(f291(x55221),x55222),x55223)))
% 21.40/21.36 [5523]~P110(x55231)+E(f789(f789(f250(x55231),f789(f84(x55231),x55232)),x55233),f789(f84(x55231),f789(f789(f250(x55231),x55232),x55233)))
% 21.40/21.36 [5617]E(f387(x56171,x56172,x56173),f388(x56171,x56172,x56173))+E(f789(f789(f111(f870(x56173,a856)),x56172),x56171),f184(f870(x56173,a856)))
% 21.40/21.36 [5631]~P69(x56312)+E(f789(f789(f11(x56311,x56312),f789(f18(x56312,x56311),f87(x56312))),x56313),f87(x56312))
% 21.40/21.36 [5632]~P4(x56322)+E(f789(f789(f8(x56321,x56322),f789(f18(x56322,x56321),f2(x56322))),x56323),f2(x56322))
% 21.40/21.36 [5634]~P2(x56341)+E(f789(f789(f89(x56341),f789(f109(x56341),x56342)),f789(f109(x56341),x56343)),f789(f109(x56341),f789(f789(f89(a863),x56342),x56343)))
% 21.40/21.36 [5635]~P2(x56351)+E(f789(f789(f90(x56351),f789(f109(x56351),x56352)),f789(f109(x56351),x56353)),f789(f109(x56351),f789(f789(f90(a863),x56352),x56353)))
% 21.40/21.36 [5636]~P120(x56361)+E(f789(f789(f89(x56361),f789(f112(x56361),x56362)),f789(f112(x56361),x56363)),f789(f112(x56361),f789(f789(f89(a1),x56362),x56363)))
% 21.40/21.36 [5637]~P120(x56371)+E(f789(f789(f90(x56371),f789(f112(x56371),x56372)),f789(f112(x56371),x56373)),f789(f112(x56371),f789(f789(f90(a1),x56372),x56373)))
% 21.40/21.36 [5638]~P120(x56381)+E(f789(f789(f3(x56381),f789(f112(x56381),x56382)),f789(f112(x56381),x56383)),f789(f112(x56381),f789(f789(f3(a1),x56382),x56383)))
% 21.40/21.36 [5639]~P88(x56391)+E(f789(f789(f89(x56391),f789(f113(x56391),x56392)),f789(f113(x56391),x56393)),f789(f113(x56391),f789(f789(f89(a1),x56392),x56393)))
% 21.40/21.36 [5640]~P88(x56401)+E(f789(f789(f90(x56401),f789(f113(x56401),x56402)),f789(f113(x56401),x56403)),f789(f113(x56401),f789(f789(f90(a1),x56402),x56403)))
% 21.40/21.36 [5641]~P88(x56411)+E(f789(f789(f3(x56411),f789(f113(x56411),x56412)),f789(f113(x56411),x56413)),f789(f113(x56411),f789(f789(f3(a1),x56412),x56413)))
% 21.40/21.36 [5642]~P88(x56421)+E(f789(f789(f89(x56421),f789(f113(x56421),x56422)),f789(f113(x56421),x56423)),f789(f113(x56421),f789(f789(f89(a1),x56422),x56423)))
% 21.40/21.36 [5643]~P88(x56431)+E(f789(f789(f90(x56431),f789(f113(x56431),x56432)),f789(f113(x56431),x56433)),f789(f113(x56431),f789(f789(f90(a1),x56432),x56433)))
% 21.40/21.36 [5690]~E(x56903,x56902)+P1(f789(f789(f240(f870(x56901,a856)),x56902),x56903))
% 21.40/21.36 [5691]~E(x56912,x56913)+P1(f789(f789(f240(f870(x56911,a856)),x56912),x56913))
% 21.40/21.36 [5692]~E(x56922,x56923)+P1(f789(f789(f240(f870(x56921,a856)),x56922),x56923))
% 21.40/21.36 [5693]~E(x56932,x56933)+P1(f789(f789(f240(f870(x56931,a856)),x56932),x56933))
% 21.40/21.36 [5694]~E(x56942,x56943)+P1(f789(f789(f240(f870(x56941,a856)),x56942),x56943))
% 21.40/21.36 [5695]~E(x56952,x56953)+P1(f789(f789(f240(f870(x56951,a856)),x56952),x56953))
% 21.40/21.36 [5696]~E(x56962,x56963)+P1(f789(f789(f240(f870(x56961,a856)),x56962),x56963))
% 21.40/21.36 [5701]~P68(x57011)+E(f789(f789(f89(x57011),f789(f88(x57011),x57012)),f789(f88(x57011),x57013)),f789(f88(x57011),f789(f789(f89(x57011),x57013),x57012)))
% 21.40/21.36 [5702]~P6(x57021)+E(f789(f789(f89(x57021),f789(f88(x57021),x57022)),f789(f88(x57021),x57023)),f789(f88(x57021),f789(f789(f89(x57021),x57022),x57023)))
% 21.40/21.36 [5703]~P3(x57031)+E(f789(f789(f239(x57031),f789(f88(x57031),x57032)),f789(f88(x57031),x57033)),f789(f88(x57031),f789(f789(f244(x57031),x57032),x57033)))
% 21.40/21.36 [5704]~P3(x57041)+E(f789(f789(f244(x57041),f789(f88(x57041),x57042)),f789(f88(x57041),x57043)),f789(f88(x57041),f789(f789(f239(x57041),x57042),x57043)))
% 21.40/21.36 [5705]~P90(x57051)+E(f789(f789(f111(x57051),f789(f88(x57051),x57052)),f789(f88(x57051),x57053)),f789(f88(x57051),f789(f789(f110(x57051),x57052),x57053)))
% 21.40/21.36 [5706]~P90(x57061)+E(f789(f789(f110(x57061),f789(f88(x57061),x57062)),f789(f88(x57061),x57063)),f789(f88(x57061),f789(f789(f111(x57061),x57062),x57063)))
% 21.40/21.36 [5707]~P110(x57071)+E(f789(f789(f90(x57071),f789(f84(x57071),x57072)),f789(f84(x57071),x57073)),f789(f84(x57071),f789(f789(f90(x57071),x57072),x57073)))
% 21.40/21.36 [5708]~P62(x57081)+E(f789(f789(f291(x57081),f789(f84(x57081),x57082)),f789(f84(x57081),x57083)),f789(f84(x57081),f789(f789(f291(x57081),x57082),x57083)))
% 21.40/21.36 [5709]~P71(x57091)+E(f789(f789(f89(x57091),f789(f161(x57091),x57092)),f789(f161(x57091),x57093)),f789(f161(x57091),f789(f789(f132(x57091),x57092),x57093)))
% 21.40/21.36 [5710]E(x57101,f184(f870(x57102,a856)))+~E(f789(f789(f110(f870(x57102,a856)),x57103),x57101),f184(f870(x57102,a856)))
% 21.40/21.36 [5711]E(x57111,f184(f870(x57112,a856)))+~E(f789(f789(f110(f870(x57112,a856)),x57111),x57113),f184(f870(x57112,a856)))
% 21.40/21.36 [5712]~P141(x57121,x57122,x57123)+P1(f789(x57121,f789(f789(f50(a1),x57122),x57123)))
% 21.40/21.36 [5773]~P1(f789(f70(x57731),x57733))+P1(f789(f70(x57731),f789(f789(f310(x57731),x57732),x57733)))
% 21.40/21.36 [5774]~P1(f789(f70(x57741),x57743))+P1(f789(f70(x57741),f789(f789(f310(x57741),x57742),x57743)))
% 21.40/21.36 [5775]~P1(f789(f134(x57751),x57753))+P1(f789(f134(x57751),f789(f789(f164(x57751),x57752),x57753)))
% 21.40/21.36 [5776]~P1(f789(f134(x57761),x57763))+P1(f789(f134(x57761),f789(f789(f135(x57761),x57762),x57763)))
% 21.40/21.36 [5807]~P101(x58071)+P1(f789(f789(f240(x58071),x58072),f789(f789(f239(x58071),x58073),x58072)))
% 21.40/21.36 [5808]~P101(x58081)+P1(f789(f789(f240(x58081),x58082),f789(f789(f239(x58081),x58082),x58083)))
% 21.40/21.36 [5809]~P94(x58091)+P1(f789(f789(f240(x58091),x58092),f789(f789(f110(x58091),x58093),x58092)))
% 21.40/21.36 [5810]~P95(x58101)+P1(f789(f789(f240(x58101),x58102),f789(f789(f110(x58101),x58103),x58102)))
% 21.40/21.36 [5811]~P94(x58111)+P1(f789(f789(f240(x58111),x58112),f789(f789(f110(x58111),x58112),x58113)))
% 21.40/21.36 [5812]~P95(x58121)+P1(f789(f789(f240(x58121),x58122),f789(f789(f110(x58121),x58122),x58123)))
% 21.40/21.36 [5813]~P70(x58131)+P1(f789(f789(f287(x58131),x58132),f789(f789(f90(x58131),x58133),x58132)))
% 21.40/21.36 [5814]~P70(x58141)+P1(f789(f789(f287(x58141),x58142),f789(f789(f90(x58141),x58142),x58143)))
% 21.40/21.36 [5826]~E(x58261,f2(a863))+E(f789(f789(f50(a863),f789(f789(f90(a863),x58261),x58262)),f789(f789(f90(a863),x58261),x58263)),f2(a863))
% 21.40/21.36 [5889]P1(f789(x58891,x58892))+P1(f789(f789(f191(f37(x58891,x58893)),x58892),x58892))
% 21.40/21.36 [5890]P1(f789(x58901,x58902))+P1(f789(f789(f191(f37(x58901,x58903)),x58902),x58902))
% 21.40/21.36 [5902]~P88(x59021)+E(f789(f789(f3(x59021),f789(f113(x59021),x59022)),f789(f113(x59021),x59023)),f789(f113(x59021),f789(f789(f89(a1),x59022),f789(f88(a1),x59023))))
% 21.40/21.36 [5957]E(x59571,f2(a863))+E(f789(f789(f50(a863),f789(f789(f90(a863),x59571),x59572)),f789(f789(f90(a863),x59571),x59573)),f789(f789(f50(a863),x59572),x59573))
% 21.40/21.36 [6027]P141(x60271,x60272,x60273)+~P1(f789(x60271,f789(f789(f50(a1),x60272),x60273)))
% 21.40/21.36 [6112]E(f789(f789(f3(f870(x61121,a856)),x61122),x61123),x61122)+~E(f789(f789(f111(f870(x61121,a856)),x61122),x61123),f184(f870(x61121,a856)))
% 21.40/21.36 [6154]~P1(f789(f789(f241(a863),x61541),x61543))+P1(f789(f789(f241(a863),x61541),f789(f789(f89(a863),x61542),x61543)))
% 21.40/21.36 [6155]~P1(f789(f789(f241(a863),x61551),x61553))+P1(f789(f789(f241(a863),x61551),f789(f789(f89(a863),x61552),x61553)))
% 21.40/21.36 [6156]~P1(f789(f789(f241(a863),x61561),x61562))+P1(f789(f789(f241(a863),x61561),f789(f789(f89(a863),x61562),x61563)))
% 21.40/21.36 [6157]~P1(f789(f789(f241(a863),x61571),x61572))+P1(f789(f789(f241(a863),x61571),f789(f789(f89(a863),x61572),x61573)))
% 21.40/21.36 [6158]~P1(f789(f789(f240(a863),x61581),x61583))+P1(f789(f789(f240(a863),x61581),f789(f789(f89(a863),x61582),x61583)))
% 21.40/21.36 [6159]~P1(f789(f789(f240(a863),x61591),x61593))+P1(f789(f789(f240(a863),x61591),f789(f789(f89(a863),x61592),x61593)))
% 21.40/21.36 [6160]~P1(f789(f789(f240(a863),x61601),x61602))+P1(f789(f789(f240(a863),x61601),f789(f789(f89(a863),x61602),x61603)))
% 21.40/21.36 [6161]~P1(f789(f789(f240(a863),x61611),x61612))+P1(f789(f789(f240(a863),x61611),f789(f789(f89(a863),x61612),x61613)))
% 21.40/21.36 [6200]P1(f789(f70(x62001),x62002))+~P1(f789(f70(x62001),f789(f789(f310(x62001),x62003),x62002)))
% 21.40/21.36 [6201]P1(f789(f134(x62011),x62012))+~P1(f789(f134(x62011),f789(f789(f146(x62011),x62013),x62012)))
% 21.40/21.36 [6202]P1(f789(f134(x62021),x62022))+~P1(f789(f134(x62021),f789(f789(f132(x62021),x62023),x62022)))
% 21.40/21.36 [6203]P1(f789(f134(x62031),x62032))+~P1(f789(f134(x62031),f789(f789(f132(x62031),x62032),x62033)))
% 21.40/21.36 [6247]~E(f59(a1,x62472,x62471),f59(a1,x62473,x62471))+P1(f789(f789(f287(a1),x62471),f789(f789(f3(a1),x62472),x62473)))
% 21.40/21.36 [6252]~P70(x62521)+E(f789(f789(f89(x62521),x62522),f789(f789(f90(x62521),x62523),x62522)),f789(f789(f90(x62521),f789(f789(f89(x62521),x62523),f87(x62521))),x62522))
% 21.40/21.36 [6300]~E(x63001,x63002)+~P1(f789(f789(f241(f870(x63003,a856)),x63001),x63002))
% 21.40/21.36 [6347]P1(f789(f789(f342(x63471),x63472),x63473))+P1(f789(f789(f342(x63471),x63472),f789(f88(f870(x63471,a856)),x63473)))
% 21.40/21.36 [6348]P1(f789(f789(f342(x63481),x63482),x63483))+P1(f789(f789(f342(x63481),x63482),f789(f88(f870(x63481,a856)),x63483)))
% 21.40/21.36 [6355]E(f140(x63551,f789(f789(f135(x63551),x63552),x63553)),f140(x63551,x63553))+~P1(f789(f789(f241(a863),x63552),f789(f185(f864(x63551)),x63553)))
% 21.40/21.36 [6356]E(f789(f789(f164(x63561),x63562),f123(x63561,x63563)),f789(f789(f164(x63561),x63562),x63563))+~P1(f789(f789(f241(a863),x63562),f789(f185(f864(x63561)),x63563)))
% 21.40/21.36 [6415]E(f789(f789(f789(f178(f864(x64151),f864(x64151)),x64152),f148(x64151)),x64153),x64153)+~E(f59(a863,x64152,f789(f185(f864(x64151)),x64153)),f2(a863))
% 21.40/21.36 [6424]~P12(x64241,x64243,x64242)+E(f789(f789(f289(x64241,x64241,x64241),f789(f286(x64241,x64241),x64242)),x64242),x64242)
% 21.40/21.36 [6466]~E(f789(f789(f110(f870(x64661,a856)),x64662),x64663),x64663)+P1(f789(f789(f240(f870(x64661,a856)),x64662),x64663))
% 21.40/21.36 [6471]~P53(x64711,x64711,x64713)+P53(x64711,x64711,f789(f789(f178(f869(x64711,x64711),a856),x64712),x64713))
% 21.40/21.36 [6473]~P1(f789(f789(f342(x64731),x64733),f789(f163(x64731),x64732)))+P1(f789(f789(f241(a863),f2(a863)),f789(f185(f864(x64731)),x64732)))
% 21.40/21.36 [6490]~E(x64902,x64903)+P1(f789(f789(f342(x64901),x64902),f789(f789(f310(x64901),x64903),f184(f870(x64901,a856)))))
% 21.40/21.36 [6503]~P80(x65031)+E(f789(f84(x65031),f789(f789(f89(x65031),f789(f84(x65031),x65032)),f789(f84(x65031),x65033))),f789(f789(f89(x65031),f789(f84(x65031),x65032)),f789(f84(x65031),x65033)))
% 21.40/21.36 [6514]E(f789(f789(f50(a863),f789(f789(f90(a863),x65141),x65142)),f789(f789(f90(a863),x65141),x65143)),f789(f789(f50(a863),x65142),x65143))+~P1(f789(f789(f241(a863),f2(a863)),x65141))
% 21.40/21.36 [6541]E(f59(a1,x65411,x65412),f59(a1,x65413,x65412))+~P1(f789(f789(f287(a1),x65412),f789(f789(f3(a1),x65411),x65413)))
% 21.40/21.36 [6654]~P1(f789(f70(x66541),x66543))+E(f789(f789(f73(x66541,f870(x66541,a856),f310(x66541)),x66542),x66543),f789(f789(f110(f870(x66541,a856)),x66543),x66542))
% 21.40/21.36 [6717]E(f789(f789(f110(f870(x67171,a856)),x67172),x67173),x67172)+~P1(f789(f789(f240(f870(x67171,a856)),x67173),x67172))
% 21.40/21.36 [6718]E(f789(f789(f110(f870(x67181,a856)),x67182),x67183),x67183)+~P1(f789(f789(f240(f870(x67181,a856)),x67182),x67183))
% 21.40/21.36 [6719]E(f789(f789(f110(f870(x67191,a856)),x67192),x67193),x67193)+~P1(f789(f789(f240(f870(x67191,a856)),x67192),x67193))
% 21.40/21.36 [6720]E(f789(f789(f111(f870(x67201,a856)),x67202),x67203),x67203)+~P1(f789(f789(f240(f870(x67201,a856)),x67203),x67202))
% 21.40/21.36 [6721]E(f789(f789(f111(f870(x67211,a856)),x67212),x67213),x67212)+~P1(f789(f789(f240(f870(x67211,a856)),x67212),x67213))
% 21.40/21.36 [6774]~P1(f789(f134(x67741),x67742))+E(f789(f789(f3(f870(x67741,a856)),f789(f163(x67741),x67742)),f789(f789(f310(x67741),x67743),f184(f870(x67741,a856)))),f789(f163(x67741),f158(x67741,x67743,x67742)))
% 21.40/21.36 [6832]P36(x68321,x68322)+~P36(x68321,f789(f789(f178(f869(x68321,x68321),a856),x68323),x68322))
% 21.40/21.36 [6848]~E(x68481,f2(a863))+P1(f789(f789(f287(a863),f789(f789(f90(a863),x68481),x68482)),f789(f789(f90(a863),x68481),x68483)))
% 21.40/21.36 [6902]P1(f789(f63(x69021,x69022),f789(a65,x69023)))+~P1(f789(f63(f789(f88(a1),x69021),f789(f88(a1),x69022)),x69023))
% 21.40/21.36 [6907]E(f789(f789(f3(f870(x69071,a856)),f789(f789(f310(x69071),x69072),x69073)),f789(f789(f310(x69071),x69072),f184(f870(x69071,a856)))),x69073)+P1(f789(f789(f342(x69071),x69072),x69073))
% 21.40/21.36 [6925]E(f789(f789(f111(f870(x69251,a856)),f789(f163(x69251),x69252)),f789(f163(x69251),x69253)),f184(f870(x69251,a856)))+~P1(f789(f134(x69251),f789(f789(f132(x69251),x69252),x69253)))
% 21.40/21.36 [6942]~P1(f789(f789(f342(x69421),x69422),f789(f163(x69421),x69423)))+~P1(f789(f134(x69421),f789(f789(f146(x69421),x69422),x69423)))
% 21.40/21.36 [7019]E(f789(f789(f111(f870(x70191,a856)),x70192),x70193),f184(f870(x70191,a856)))+P1(f789(f789(f342(x70191),f387(x70193,x70192,x70191)),x70192))
% 21.40/21.36 [7020]E(f789(f789(f111(f870(x70201,a856)),x70202),x70203),f184(f870(x70201,a856)))+P1(f789(f789(f342(x70201),f388(x70203,x70202,x70201)),x70203))
% 21.40/21.36 [7024]E(f123(x70241,f789(f789(f164(x70241),x70242),x70243)),f789(f789(f164(x70241),f789(f789(f3(a863),x70242),f87(a863))),x70243))+~P1(f789(f789(f240(a863),x70242),f789(f185(f864(x70241)),x70243)))
% 21.40/21.36 [7106]P1(f789(f789(f241(a863),f2(a863)),x71061))+P1(f789(f789(f240(a863),f789(f789(f90(a863),x71062),x71061)),f789(f789(f90(a863),x71063),x71061)))
% 21.40/21.36 [7107]P1(f789(f789(f241(a863),f2(a863)),x71071))+P1(f789(f789(f240(a863),f789(f789(f90(a863),x71071),x71072)),f789(f789(f90(a863),x71071),x71073)))
% 21.40/21.36 [7108]~P1(f789(f789(f342(x71081),x71082),x71083))+~P1(f789(f789(f342(x71081),x71082),f789(f88(f870(x71081,a856)),x71083)))
% 21.40/21.36 [7109]~P1(f789(f789(f342(x71091),x71092),x71093))+~P1(f789(f789(f342(x71091),x71092),f789(f88(f870(x71091,a856)),x71093)))
% 21.40/21.36 [7110]~P1(f789(f789(f342(x71101),x71102),x71103))+~P1(f789(f789(f342(x71101),x71102),f789(f88(f870(x71101,a856)),x71103)))
% 21.40/21.36 [7114]~P1(f789(f789(f241(f870(x71141,a856)),x71142),x71143))+P1(f789(f789(f240(f870(x71141,a856)),x71142),x71143))
% 21.40/21.36 [7115]~P1(f789(f789(f241(f870(x71151,a856)),x71152),x71153))+P1(f789(f789(f240(f870(x71151,a856)),x71152),x71153))
% 21.40/21.36 [7116]~P1(f789(f789(f241(f870(x71161,a856)),x71162),x71163))+P1(f789(f789(f240(f870(x71161,a856)),x71162),x71163))
% 21.40/21.36 [7221]~P1(f789(f789(f241(a863),x72212),x72213))+P1(f789(f789(f241(a863),f789(f789(f89(a863),x72211),x72212)),f789(f789(f89(a863),x72211),x72213)))
% 21.40/21.36 [7222]~P1(f789(f789(f241(a863),x72221),x72223))+P1(f789(f789(f241(a863),f789(f789(f89(a863),x72221),x72222)),f789(f789(f89(a863),x72223),x72222)))
% 21.40/21.36 [7223]~P1(f789(f789(f241(a1),x72231),x72233))+P1(f789(f789(f241(a1),f789(f789(f89(a1),x72231),x72232)),f789(f789(f89(a1),x72233),x72232)))
% 21.40/21.36 [7226]~P1(f789(f789(f240(a863),x72262),x72263))+P1(f789(f789(f240(a863),f789(f789(f89(a863),x72261),x72262)),f789(f789(f89(a863),x72261),x72263)))
% 21.40/21.36 [7227]~P1(f789(f789(f240(a863),x72271),x72273))+P1(f789(f789(f240(a863),f789(f789(f89(a863),x72271),x72272)),f789(f789(f89(a863),x72273),x72272)))
% 21.40/21.36 [7228]~P1(f789(f789(f240(a863),x72282),x72283))+P1(f789(f789(f240(a863),f789(f789(f90(a863),x72281),x72282)),f789(f789(f90(a863),x72281),x72283)))
% 21.40/21.36 [7229]~P1(f789(f789(f240(a863),x72292),x72293))+P1(f789(f789(f240(a863),f789(f789(f90(a863),x72291),x72292)),f789(f789(f90(a863),x72291),x72293)))
% 21.40/21.36 [7230]~P1(f789(f789(f240(a863),x72301),x72303))+P1(f789(f789(f240(a863),f789(f789(f90(a863),x72301),x72302)),f789(f789(f90(a863),x72303),x72302)))
% 21.40/21.36 [7231]~P1(f789(f789(f240(a863),x72311),x72313))+P1(f789(f789(f240(a863),f789(f789(f90(a863),x72311),x72312)),f789(f789(f90(a863),x72313),x72312)))
% 21.40/21.36 [7232]~P1(f789(f789(f240(a863),x72321),x72323))+P1(f789(f789(f240(a863),f789(f789(f50(a863),x72321),x72322)),f789(f789(f50(a863),x72323),x72322)))
% 21.40/21.36 [7233]~P1(f789(f789(f240(a863),x72333),x72332))+P1(f789(f789(f240(a863),f789(f789(f3(a863),x72331),x72332)),f789(f789(f3(a863),x72331),x72333)))
% 21.40/21.36 [7234]~P1(f789(f789(f240(a863),x72341),x72343))+P1(f789(f789(f240(a863),f789(f789(f3(a863),x72341),x72342)),f789(f789(f3(a863),x72343),x72342)))
% 21.40/21.36 [7235]~P1(f789(f789(f240(a1),x72352),x72353))+P1(f789(f789(f240(a1),f789(f789(f89(a1),x72351),x72352)),f789(f789(f89(a1),x72351),x72353)))
% 21.40/21.36 [7238]~P1(f789(f789(f287(a863),x72382),x72383))+P1(f789(f789(f287(a863),f789(f789(f90(a863),x72381),x72382)),f789(f789(f90(a863),x72381),x72383)))
% 21.40/21.36 [7325]E(x73251,x73252)+~P1(f789(f789(f342(x73253),x73251),f789(f789(f310(x73253),x73252),f184(f870(x73253,a856)))))
% 21.40/21.36 [7326]E(x73261,x73262)+~P1(f789(f789(f342(x73263),x73261),f789(f789(f310(x73263),x73262),f184(f870(x73263,a856)))))
% 21.40/21.36 [7328]~E(f789(f789(f111(f870(x73281,a856)),x73282),x73283),f184(f870(x73281,a856)))+P1(f789(f789(f240(f870(x73281,a856)),x73282),f789(f88(f870(x73281,a856)),x73283)))
% 21.40/21.36 [7334]P1(f789(f789(f342(f870(x73341,a856)),x73342),f789(f309(x73341),x73343)))+~P1(f789(f789(f240(f870(x73341,a856)),x73342),x73343))
% 21.40/21.36 [7335]P1(f789(f789(f342(f870(x73351,a856)),x73352),f789(f309(x73351),x73353)))+~P1(f789(f789(f240(f870(x73351,a856)),x73352),x73353))
% 21.40/21.36 [7392]E(f789(f789(f146(x73921),f789(f789(f159(x73921),x73922),x73923)),f789(f789(f135(x73921),f789(a121,x73923)),x73922)),f789(f789(f135(x73921),x73923),x73922))+~P1(f789(f789(f241(a863),x73923),f789(f185(f864(x73921)),x73922)))
% 21.40/21.36 [7422]P1(f789(f789(f342(f869(x74221,x74221)),x74222),f308(x74221,x74223)))+~P1(f789(f789(f342(f869(x74221,x74221)),x74222),x74223))
% 21.40/21.36 [7431]~P1(f789(f789(f342(f870(x74311,a856)),x74312),f789(f309(x74311),x74313)))+P1(f789(f789(f240(f870(x74311,a856)),x74312),x74313))
% 21.40/21.36 [7432]~P1(f789(f789(f342(f870(x74321,a856)),x74322),f789(f309(x74321),x74323)))+P1(f789(f789(f240(f870(x74321,a856)),x74322),x74323))
% 21.40/21.36 [7474]P1(f789(f789(f240(f870(x74741,a856)),x74742),f51(f870(x74741,a856),x74743)))+~P1(f789(f789(f342(f870(x74741,a856)),x74742),x74743))
% 21.40/21.36 [7502]~P120(x75021)+E(f789(f789(f90(x75021),f789(f789(f250(x75021),f789(f88(x75021),f87(x75021))),x75022)),f789(f789(f250(x75021),x75023),x75022)),f789(f789(f250(x75021),f789(f88(x75021),x75023)),x75022))
% 21.40/21.36 [7524]E(f789(f789(f159(x75241),x75242),f789(f789(f3(a863),f789(f185(f864(x75241)),x75242)),f789(a121,x75243))),f789(f789(f159(x75241),f789(f149(x75241),x75242)),x75243))+~P1(f789(f789(f241(a863),x75243),f789(f185(f864(x75241)),x75242)))
% 21.40/21.36 [7541]~E(f789(f789(f111(f870(x75411,a856)),f675(x75413,x75412,x75411)),x75413),f184(f870(x75411,a856)))+E(f789(f789(f111(f870(x75411,a856)),f51(f870(x75411,a856),x75412)),x75413),f184(f870(x75411,a856)))
% 21.40/21.36 [7605]~P1(f789(f789(f342(x76053),x76052),f789(f163(x76053),x76051)))+P1(f789(f789(f241(a863),f743(x76051,x76052,x76053)),f789(f185(f864(x76053)),x76051)))
% 21.40/21.36 [7613]P1(f789(f789(f342(x76131),f789(f789(f159(x76131),x76132),x76133)),f789(f163(x76131),x76132)))+~P1(f789(f789(f241(a863),x76133),f789(f185(f864(x76131)),x76132)))
% 21.40/21.36 [7721]P1(f789(f789(f240(f870(f864(x77211),a856)),f156(x77211,x77212)),f156(x77211,x77213)))+~P1(f789(f789(f240(f870(x77211,a856)),x77212),x77213))
% 21.40/21.36 [7750]E(f789(f789(f111(f870(x77501,a856)),f51(f870(x77501,a856),x77502)),x77503),f184(f870(x77501,a856)))+P1(f789(f789(f342(f870(x77501,a856)),f675(x77503,x77502,x77501)),x77502))
% 21.40/21.36 [7752]~P1(f789(f789(f342(f870(x77521,a856)),x77523),x77522))+P1(f789(f789(f240(f870(x77521,a856)),f52(f870(x77521,a856),x77522)),x77523))
% 21.40/21.36 [7754]E(f789(f789(f111(f870(x77541,a856)),x77542),x77543),f184(f870(x77541,a856)))+~P1(f789(f789(f240(f870(x77541,a856)),x77542),f789(f88(f870(x77541,a856)),x77543)))
% 21.40/21.37 [7807]E(f789(f789(f3(a863),f789(f789(f89(a863),f789(f161(a863),x78071)),x78072)),f789(f789(f159(a863),x78071),x78073)),f789(f161(a863),f789(f789(f155(a863,x78071),x78073),x78072)))+~P1(f789(f789(f241(a863),x78073),f789(f185(f864(a863)),x78071)))
% 21.40/21.37 [7857]P1(f789(f789(f241(a863),x78571),x78572))+~P1(f789(f789(f241(a863),f789(f789(f89(a863),x78573),x78571)),f789(f789(f89(a863),x78573),x78572)))
% 21.40/21.37 [7858]P1(f789(f789(f241(a863),x78581),x78582))+~P1(f789(f789(f241(a863),f789(f789(f90(a863),x78583),x78581)),f789(f789(f90(a863),x78583),x78582)))
% 21.40/21.37 [7859]P1(f789(f789(f241(a863),x78591),x78592))+~P1(f789(f789(f241(a863),f789(f789(f90(a863),x78591),x78593)),f789(f789(f90(a863),x78592),x78593)))
% 21.40/21.37 [7862]P1(f789(f789(f240(a863),x78621),x78622))+~P1(f789(f789(f240(a863),f789(f789(f89(a863),x78623),x78621)),f789(f789(f89(a863),x78623),x78622)))
% 21.40/21.37 [7891]P1(f789(f789(f241(a863),f2(a863)),x78911))+~P1(f789(f789(f241(a863),f789(f789(f90(a863),x78912),x78911)),f789(f789(f90(a863),x78913),x78911)))
% 21.40/21.37 [7892]P1(f789(f789(f241(a863),f2(a863)),x78921))+~P1(f789(f789(f241(a863),f789(f789(f90(a863),x78921),x78922)),f789(f789(f90(a863),x78921),x78923)))
% 21.40/21.37 [7963]E(f252(x79631,x79632,x79633),x79632)+~P1(f789(f789(f240(f870(x79631,a856)),x79633),f789(f789(f310(x79631),x79632),f184(f870(x79631,a856)))))
% 21.40/21.37 [8042]E(f789(f789(f132(x80421),f789(f789(f164(x80421),x80422),x80423)),f789(f789(f146(x80421),f789(f789(f159(x80421),x80423),x80422)),f122(x80421))),f789(f789(f164(x80421),f789(a121,x80422)),x80423))+~P1(f789(f789(f241(a863),x80422),f789(f185(f864(x80421)),x80423)))
% 21.40/21.37 [8111]P1(f789(f789(f240(f870(f870(x81111,a856),a856)),f253(x81111,x81112)),f253(x81111,x81113)))+~P1(f789(f789(f240(f870(x81111,a856)),x81112),x81113))
% 21.40/21.37 [8150]~P1(f789(f134(x81501),x81503))+P1(f789(f134(x81501),f789(f789(f789(f178(f864(x81501),f864(x81501)),x81502),f148(x81501)),x81503)))
% 21.40/21.37 [8155]~P1(f789(f789(f241(a863),x81552),x81553))+P1(f789(f789(f241(a863),f789(f789(f90(a863),f789(a121,x81551)),x81552)),f789(f789(f90(a863),f789(a121,x81551)),x81553)))
% 21.40/21.37 [8156]~P1(f789(f789(f240(a863),x81562),x81563))+P1(f789(f789(f240(a863),f789(f789(f90(a863),f789(a121,x81561)),x81562)),f789(f789(f90(a863),f789(a121,x81561)),x81563)))
% 21.40/21.37 [8177]P1(f789(f789(f240(f870(f870(x81771,a856),a856)),f789(f309(x81771),x81772)),f789(f309(x81771),x81773)))+~P1(f789(f789(f240(f870(x81771,a856)),x81772),x81773))
% 21.40/21.37 [8334]~P1(f789(f789(f240(f870(x83341,a856)),x83343),x83342))+P1(f789(f789(f240(f870(x83341,a856)),f789(f88(f870(x83341,a856)),x83342)),f789(f88(f870(x83341,a856)),x83343)))
% 21.40/21.37 [8335]~P1(f789(f789(f240(f870(x83351,a856)),x83353),x83352))+P1(f789(f789(f240(f870(x83351,a856)),f789(f88(f870(x83351,a856)),x83352)),f789(f88(f870(x83351,a856)),x83353)))
% 21.40/21.37 [8374]E(f789(f311(a863,a863,f789(f789(f9(a863,a863,a863),f3(a863)),x83741)),f789(f302(a863,x83742),x83743)),f789(f302(a863,f789(f789(f3(a863),x83742),x83741)),f789(f789(f3(a863),x83743),x83741)))+~P1(f789(f789(f241(a863),x83741),x83743))
% 21.40/21.37 [8400]~P71(x84001)+E(f789(f789(f89(x84001),x84002),f789(f138(x84001,x84001,f89(x84001),f2(x84001)),x84003)),f789(f138(x84001,x84001,f89(x84001),x84002),x84003))
% 21.40/21.37 [8480]~P80(x84801)+P1(f789(f789(f240(x84801),f789(f84(x84801),f789(f789(f89(x84801),x84802),x84803))),f789(f789(f89(x84801),f789(f84(x84801),x84802)),f789(f84(x84801),x84803))))
% 21.40/21.37 [8481]~P80(x84811)+P1(f789(f789(f240(x84811),f789(f84(x84811),f789(f789(f3(x84811),x84812),x84813))),f789(f789(f89(x84811),f789(f84(x84811),x84812)),f789(f84(x84811),x84813))))
% 21.40/21.37 [8491]E(f789(f789(f89(a1),f789(f789(f90(a1),x84911),f59(a1,f789(f789(f50(a1),x84912),x84911),x84913))),f59(a1,x84912,x84911)),f59(a1,x84912,f789(f789(f90(a1),x84911),x84913)))+~P1(f789(f789(f241(a1),f2(a1)),x84913))
% 21.40/21.37 [8500]E(f789(f789(f132(x85001),f789(f789(f164(x85001),x85002),x85003)),f789(f789(f146(x85001),f789(f137(x85001),f789(f789(f135(x85001),x85002),x85003))),f122(x85001))),f789(f789(f164(x85001),f789(a121,x85002)),x85003))+~P1(f789(f789(f241(a863),x85002),f789(f185(f864(x85001)),x85003)))
% 21.40/21.37 [8519]E(f789(f273(x85191,f789(f789(f150(x85191,f869(a108,x85191)),f789(f249(a108,x85191),f87(a108))),x85192)),f789(a5,x85193)),f789(f789(f159(x85191),x85192),x85193))+~P1(f789(f789(f241(a863),x85193),f789(f185(f864(x85191)),x85192)))
% 21.40/21.37 [8576]P1(f789(f789(f342(f869(x85761,x85761)),x85762),f789(f789(f289(x85761,x85761,x85761),x85763),f308(x85761,x85763))))+~P1(f789(f789(f342(f869(x85761,x85761)),x85762),x85763))
% 21.40/21.37 [8592]P1(f789(f789(f241(a863),x85921),x85922))+~P1(f789(f789(f241(a863),f789(f789(f90(a863),f789(a121,x85923)),x85921)),f789(f789(f90(a863),f789(a121,x85923)),x85922)))
% 21.40/21.37 [8593]P1(f789(f789(f240(a863),x85931),x85932))+~P1(f789(f789(f240(a863),f789(f789(f90(a863),f789(a121,x85933)),x85931)),f789(f789(f90(a863),f789(a121,x85933)),x85932)))
% 21.40/21.37 [8604]P1(f789(f789(f240(f870(x86041,a856)),x86042),x86043))+~P1(f789(f789(f240(f870(x86041,a856)),f789(f88(f870(x86041,a856)),x86043)),f789(f88(f870(x86041,a856)),x86042)))
% 21.40/21.37 [8623]P1(f789(f134(x86231),x86232))+~P1(f789(f134(x86231),f789(f789(f789(f178(f864(x86231),f864(x86231)),x86233),f148(x86231)),x86232)))
% 21.40/21.37 [8689]E(f789(f285(x86891,x86891,f308(x86891,x86892)),x86893),x86893)+~P1(f789(f789(f240(f870(x86891,a856)),f789(f285(x86891,x86891,x86892),x86893)),x86893))
% 21.40/21.37 [8691]E(f789(f311(f869(x86911,x86912),x86912,f258(x86911,x86912)),f789(f163(f869(x86911,x86912)),x86913)),f175(x86911,x86912,f170(x86911,x86912,x86913)))+~P1(f789(f134(x86911),f789(f789(f150(f869(x86911,x86912),x86911),f248(x86911,x86912)),x86913)))
% 21.40/21.37 [8730]~P101(x87301)+P18(x87301,f789(f133(x87301,f789(f789(f9(x87301,x87301,a856),a338),f789(x87302,x87303))),x87303))
% 21.40/21.37 [8735]~P1(f789(f789(f240(a863),x87351),x87352))+P1(f789(f789(f240(a863),x87351),f789(f138(a863,a863,f89(a863),x87352),x87353)))
% 21.40/21.37 [8806]~P1(f789(f789(f342(f869(x88061,x88061)),x88062),f308(x88061,x88063)))+P1(f789(f789(f342(f869(x88061,x88061)),x88062),f789(f789(f178(f869(x88061,x88061),a856),f663(x88063,x88062,x88061)),x88063)))
% 21.40/21.37 [8877]~P71(x88771)+E(f789(f789(f89(x88771),x88772),f789(f138(x88771,x88771,f789(f9(x88771,x88771,x88771),f89(x88771)),f2(x88771)),f789(f149(x88771),x88773))),f789(f138(x88771,x88771,f89(x88771),x88772),x88773))
% 21.40/21.37 [9136]P53(x91361,x91362,x91363)+P1(f789(f789(f342(f869(x91361,x91362)),f789(f789(f249(x91361,x91362),f657(x91363,x91362,x91361)),f656(x91363,x91362,x91361))),x91363))
% 21.40/21.37 [9137]P53(x91371,x91372,x91373)+P1(f789(f789(f342(f869(x91371,x91372)),f789(f789(f249(x91371,x91372),f657(x91373,x91372,x91371)),f655(x91373,x91372,x91371))),x91373))
% 21.40/21.37 [9193]~P1(f789(f789(f342(f869(x91931,x91931)),x91932),f789(f789(f289(x91931,x91931,x91931),x91933),f308(x91931,x91933))))+P1(f789(f789(f342(f869(x91931,x91931)),x91932),f789(f789(f178(f869(x91931,x91931),a856),f664(x91933,x91932,x91931)),x91933)))
% 21.40/21.37 [9267]~P1(f789(f789(f240(f870(x92671,a856)),x92672),x92673))+P1(f789(f789(f240(f870(x92671,a856)),f789(f789(f9(x92671,f870(x92671,a856),a856),f342(x92671)),x92672)),f789(f789(f9(x92671,f870(x92671,a856),a856),f342(x92671)),x92673)))
% 21.40/21.37 [9323]~P1(f789(f789(f342(f869(f870(x93231,a856),f870(x93231,a856))),f789(f789(f249(f870(x93231,a856),f870(x93231,a856)),x93232),x93233)),f307(x93231)))+P1(f789(f789(f241(f870(x93231,a856)),x93232),x93233))
% 21.40/21.37 [9350]P54(x93501,x93502,x93503)+~P1(f789(f789(f342(f869(x93501,x93501)),f789(f789(f249(x93501,x93501),f662(x93503,x93502,x93501)),f661(x93503,x93502,x93501))),x93503))
% 21.40/21.37 [9351]P54(x93511,x93512,x93513)+~P1(f789(f789(f342(f869(x93511,x93511)),f789(f789(f249(x93511,x93511),f661(x93513,x93512,x93511)),f662(x93513,x93512,x93511))),x93513))
% 21.40/21.37 [9385]~P1(f789(f789(f342(f869(f864(x93851),f864(x93851))),f789(f789(f249(f864(x93851),f864(x93851)),x93852),x93852)),f143(x93851,x93853)))+P1(f789(f789(f342(f869(x93851,x93851)),f789(f789(f249(x93851,x93851),f766(x93852,x93853,x93851)),f766(x93852,x93853,x93851))),x93853))
% 21.40/21.37 [9429]P1(f789(f789(f240(f870(x94291,a856)),x94292),x94293))+~P1(f789(f789(f240(f870(x94291,a856)),f789(f789(f9(x94291,f870(x94291,a856),a856),f342(x94291)),x94292)),f789(f789(f9(x94291,f870(x94291,a856),a856),f342(x94291)),x94293)))
% 21.40/21.37 [9518]E(f789(f789(f3(a863),f789(f789(f8(a863,a863),x95181),f789(f265(a863),x95182))),f789(f789(f8(a863,a863),x95183),f789(f265(a863),x95182))),f789(f789(f8(a863,a863),f789(f789(f20(a863,a863,a863),f789(f789(f10(a863,f870(a863,a863),a863),f3(a863)),x95181)),x95183)),f789(f265(a863),x95182)))+~P1(f789(f789(f240(a863),f789(x95183,f529(x95182,x95181,x95183))),f789(x95181,f529(x95182,x95181,x95183))))
% 21.40/21.37 [9807]E(f789(f264(f869(x98071,x98072)),f789(f259(x98071,x98072,a856),f789(f789(f9(x98071,f870(x98072,f867(x98072)),f870(x98072,a856)),f789(f789(f10(f870(f867(x98072),a856),f870(f870(x98072,f867(x98072)),f870(x98072,a856)),x98071),f10(f867(x98072),a856,x98072)),f789(f789(f10(f867(x98072),f870(f867(x98072),a856),x98071),a338),f170(x98071,x98072,x98073)))),f234(x98072)))),f789(f163(f869(x98071,x98072)),x98073))+~P1(f789(f134(x98071),f789(f789(f150(f869(x98071,x98072),x98071),f248(x98071,x98072)),x98073)))
% 21.40/21.37 [5555]~P68(x55551)+E(f789(f789(f89(x55551),f789(f789(f3(x55551),x55552),x55553)),x55553),x55552)
% 21.40/21.37 [5556]~P68(x55561)+E(f789(f789(f3(x55561),f789(f789(f89(x55561),x55562),x55563)),x55563),x55562)
% 21.40/21.37 [5782]~P68(x57821)+E(f789(f789(f89(x57821),x57822),f789(f789(f89(x57821),f789(f88(x57821),x57822)),x57823)),x57823)
% 21.40/21.37 [5864]~P78(x58641)+E(f789(f789(f90(x58641),f789(f789(f250(x58641),x58642),x58643)),x58642),f789(f789(f250(x58641),x58642),f789(a121,x58643)))
% 21.40/21.37 [5865]~P70(x58651)+E(f789(f789(f90(x58651),f789(f789(f250(x58651),x58652),x58653)),x58652),f789(f789(f250(x58651),x58652),f789(a121,x58653)))
% 21.40/21.37 [6082]~P110(x60821)+E(f789(f84(x60821),f789(f789(f250(x60821),f789(f88(x60821),x60822)),x60823)),f789(f84(x60821),f789(f789(f250(x60821),x60822),x60823)))
% 21.40/21.37 [6132]~P78(x61321)+E(f789(f789(f90(x61321),f789(f789(f250(x61321),x61322),x61323)),x61322),f789(f789(f90(x61321),x61322),f789(f789(f250(x61321),x61322),x61323)))
% 21.40/21.37 [6191]E(f789(f789(f3(a108),f789(f789(f89(a108),x61911),x61912)),x61913),f277(x61911,x61912,x61913))+~P1(f789(f789(f241(a108),x61912),x61913))
% 21.40/21.37 [6213]~E(f789(f789(f135(x62131),x62133),x62132),f122(x62131))+P1(f789(f789(f240(a863),f789(f185(f864(x62131)),x62132)),x62133))
% 21.40/21.37 [6353]E(f789(f789(f90(a863),f789(f113(a863),x63531)),f789(f789(f90(a863),f789(f113(a863),x63532)),x63533)),f2(a863))+~P1(f789(f789(f241(a1),x63531),a92))
% 21.40/21.37 [6369]~P60(x63691)+E(f789(f789(f250(x63691),f789(f789(f291(x63691),f87(x63691)),x63692)),x63693),f789(f789(f291(x63691),f87(x63691)),f789(f789(f250(x63691),x63692),x63693)))
% 21.40/21.37 [6452]E(f789(f789(f3(a863),f789(f789(f89(a863),x64521),x64522)),x64523),f789(f789(f89(a863),x64521),f789(f789(f3(a863),x64522),x64523)))+~P1(f789(f789(f240(a863),x64523),x64522))
% 21.40/21.37 [6453]E(f789(f789(f3(a863),f789(f789(f89(a863),x64531),x64532)),x64533),f789(f789(f3(a863),x64531),f789(f789(f3(a863),x64533),x64532)))+~P1(f789(f789(f240(a863),x64532),x64533))
% 21.40/21.37 [6454]E(f789(f789(f3(a863),f789(f789(f89(a863),x64541),x64542)),x64543),f789(f789(f89(a863),x64541),f789(f789(f3(a863),x64542),x64543)))+~P1(f789(f789(f240(a863),x64543),x64542))
% 21.40/21.37 [6494]~P101(x64941)+P1(f789(f789(f240(x64941),f789(f789(f244(x64941),x64942),x64943)),x64943))
% 21.40/21.37 [6495]~P101(x64951)+P1(f789(f789(f240(x64951),f789(f789(f244(x64951),x64952),x64953)),x64952))
% 21.40/21.37 [6496]~P95(x64961)+P1(f789(f789(f240(x64961),f789(f789(f111(x64961),x64962),x64963)),x64963))
% 21.40/21.37 [6497]~P98(x64971)+P1(f789(f789(f240(x64971),f789(f789(f111(x64971),x64972),x64973)),x64973))
% 21.40/21.37 [6498]~P95(x64981)+P1(f789(f789(f240(x64981),f789(f789(f111(x64981),x64982),x64983)),x64982))
% 21.40/21.37 [6499]~P98(x64991)+P1(f789(f789(f240(x64991),f789(f789(f111(x64991),x64992),x64993)),x64992))
% 21.40/21.37 [6513]E(f789(f789(f50(a1),f789(f789(f50(a1),x65131),x65132)),x65133),f789(f789(f50(a1),x65131),f789(f789(f90(a1),x65132),x65133)))+~P1(f789(f789(f241(a1),f2(a1)),x65133))
% 21.40/21.37 [6566]~P70(x65661)+E(f789(f789(f89(x65661),f789(f789(f90(x65661),x65662),x65663)),x65663),f789(f789(f90(x65661),f789(f789(f89(x65661),x65662),f87(x65661))),x65663))
% 21.40/21.37 [6567]~P88(x65671)+E(f789(f789(f90(x65671),f789(f88(x65671),f789(f113(x65671),x65672))),x65673),f789(f789(f90(x65671),f789(f113(x65671),f789(f88(a1),x65672))),x65673))
% 21.40/21.37 [6639]~P71(x66391)+E(f789(f161(x66391),f789(f789(f150(x66392,x66391),f789(f18(x66391,x66392),f2(x66391))),x66393)),f2(x66391))
% 21.40/21.37 [6658]E(f789(f789(f89(a863),f789(f113(a863),x66581)),f789(f789(f89(a863),f789(f113(a863),x66582)),x66583)),f789(f789(f89(a863),f789(f113(a863),x66582)),x66583))+~P1(f789(a190,f789(f113(a1),x66581)))
% 21.40/21.37 [6673]~P9(x66731)+E(f52(x66731,f789(f789(f310(x66731),x66732),f789(f789(f310(x66731),x66733),f184(f870(x66731,a856))))),f789(f789(f111(x66731),x66732),x66733))
% 21.40/21.37 [6674]~P9(x66741)+E(f51(x66741,f789(f789(f310(x66741),x66742),f789(f789(f310(x66741),x66743),f184(f870(x66741,a856))))),f789(f789(f110(x66741),x66742),x66743))
% 21.40/21.37 [6699]E(f789(f789(f164(x66991),x66992),x66993),x66993)+~P1(f789(f789(f240(a863),f789(f185(f864(x66991)),x66993)),x66992))
% 21.40/21.37 [6710]E(f789(f789(f135(x67101),x67102),x67103),f122(x67101))+~P1(f789(f789(f240(a863),f789(f185(f864(x67101)),x67103)),x67102))
% 21.40/21.37 [6711]E(f789(f789(f135(x67111),x67112),x67113),f122(x67111))+~P1(f789(f789(f240(a863),f789(f185(f864(x67111)),x67113)),x67112))
% 21.40/21.37 [6722]E(f789(f789(f3(a863),f789(f789(f89(a863),x67221),x67222)),x67223),f789(f789(f89(a863),f789(f789(f3(a863),x67221),x67223)),x67222))+~P1(f789(f789(f240(a863),x67223),x67221))
% 21.40/21.37 [6723]E(f789(f789(f3(a863),f789(f789(f89(a863),x67231),x67232)),x67233),f789(f789(f89(a863),f789(f789(f3(a863),x67231),x67233)),x67232))+~P1(f789(f789(f240(a863),x67233),x67231))
% 21.40/21.37 [6737]~P1(f789(f789(f241(a863),x67371),x67373))+P1(f789(f789(f241(a863),f789(f789(f3(a863),x67371),x67372)),x67373))
% 21.40/21.37 [6765]~P101(x67651)+E(f158(x67651,x67652,f789(f789(f144(x67651,x67651,f7(x67651)),x67652),x67653)),x67653)
% 21.40/21.37 [6862]E(f789(f789(f3(a863),f789(f789(f89(a863),x68621),x68622)),f789(a121,x68623)),f789(f789(f3(a863),x68621),f789(a121,f789(f789(f3(a863),x68623),x68622))))+~P1(f789(f789(f240(a863),x68622),x68623))
% 21.40/21.37 [6863]~P110(x68631)+P1(f789(f789(f240(x68631),f2(x68631)),f789(f789(f250(x68631),f789(f84(x68631),x68632)),x68633)))
% 21.40/21.37 [6914]P28(x69141,x69142,x69143)+~P1(f789(f789(f240(f870(f862(x69141),a856)),x69143),x69142))
% 21.40/21.37 [6954]~P1(f789(f70(x69541),x69542))+P1(f789(f70(x69541),f789(f789(f3(f870(x69541,a856)),x69542),x69543)))
% 21.40/21.37 [6955]~P1(f789(f70(x69551),x69553))+P1(f789(f70(x69551),f789(f789(f111(f870(x69551,a856)),x69552),x69553)))
% 21.40/21.37 [6956]~P1(f789(f70(x69561),x69562))+P1(f789(f70(x69561),f789(f789(f111(f870(x69561,a856)),x69562),x69563)))
% 21.40/21.37 [7095]~P36(x70951,x70953)+P36(x70951,f789(f789(f111(f870(f869(x70951,x70951),a856)),x70952),x70953))
% 21.40/21.37 [7096]~P36(x70961,x70962)+P36(x70961,f789(f789(f111(f870(f869(x70961,x70961),a856)),x70962),x70963))
% 21.40/21.37 [7216]~P95(x72161)+E(f12(x72161,f789(f163(x72161),f789(f789(f146(x72161),x72162),x72163))),f789(f138(x72161,x72161,f111(x72161),x72162),x72163))
% 21.40/21.37 [7217]~P95(x72171)+E(f15(x72171,f789(f163(x72171),f789(f789(f146(x72171),x72172),x72173))),f789(f138(x72171,x72171,f110(x72171),x72172),x72173))
% 21.40/21.37 [7218]~P101(x72181)+E(f16(x72181,f789(f163(x72181),f789(f789(f146(x72181),x72182),x72183))),f789(f138(x72181,x72181,f239(x72181),x72182),x72183))
% 21.40/21.37 [7219]~P101(x72191)+E(f17(x72191,f789(f163(x72191),f789(f789(f146(x72191),x72192),x72193))),f789(f138(x72191,x72191,f244(x72191),x72192),x72193))
% 21.40/21.37 [7220]~P1(f789(f789(f287(a1),x72201),x72202))+P1(f789(f789(f287(a1),x72201),f789(f789(f89(a1),x72202),f789(f789(f90(a1),x72201),x72203))))
% 21.40/21.37 [7290]~P1(f789(f70(x72901),x72902))+P1(f789(f789(f240(a863),f789(f49(x72901),x72902)),f789(f49(x72901),f789(f789(f310(x72901),x72903),x72902))))
% 21.40/21.37 [7297]E(f789(f789(f110(f870(a863,a856)),f789(f302(a863,x72971),x72972)),f789(f302(a863,x72972),f789(f789(f89(a863),x72972),x72973))),f789(f302(a863,x72971),f789(f789(f89(a863),x72972),x72973)))+~P1(f789(f789(f240(a863),x72971),x72972))
% 21.40/21.37 [7307]P1(f789(f789(f241(a863),x73071),x73072))+~P1(f789(f789(f241(a863),f789(f789(f89(a863),x73071),x73073)),x73072))
% 21.40/21.37 [7308]P1(f789(f789(f240(a863),x73081),x73082))+~P1(f789(f789(f240(a863),f789(f789(f89(a863),x73083),x73081)),x73082))
% 21.40/21.37 [7309]P1(f789(f789(f240(a863),x73091),x73092))+~P1(f789(f789(f240(a863),f789(f789(f89(a863),x73091),x73093)),x73092))
% 21.40/21.37 [7310]P1(f789(f789(f240(a863),x73101),x73102))+~P1(f789(f789(f240(a863),f789(f789(f89(a863),x73103),x73101)),x73102))
% 21.40/21.37 [7311]P1(f789(f789(f240(a863),x73111),x73112))+~P1(f789(f789(f240(a863),f789(f789(f89(a863),x73111),x73113)),x73112))
% 21.40/21.37 [7353]~P101(x73531)+E(f13(x73531,f239(x73531),f789(f163(x73531),f789(f789(f146(x73531),x73532),x73533))),f789(f138(x73531,x73531,f239(x73531),x73532),x73533))
% 21.40/21.37 [7354]~P101(x73541)+E(f14(x73541,f244(x73541),f789(f163(x73541),f789(f789(f146(x73541),x73542),x73543))),f789(f138(x73541,x73541,f244(x73541),x73542),x73543))
% 21.40/21.37 [7358]~E(x73582,f184(f870(f869(x73581,x73581),a856)))+P1(f789(f789(f240(f870(f869(x73581,x73581),a856)),x73582),x73583))
% 21.40/21.37 [7467]E(f789(f789(f110(f870(x74671,a856)),x74672),f789(f789(f3(f870(x74671,a856)),x74673),x74672)),x74673)+~P1(f789(f789(f240(f870(x74671,a856)),x74672),x74673))
% 21.40/21.37 [7470]~P1(f789(f789(f241(a863),x74701),f789(f789(f3(a863),x74703),x74702)))+P1(f789(f789(f241(a863),f789(f789(f89(a863),x74701),x74702)),x74703))
% 21.40/21.37 [7471]~P1(f789(f789(f240(a863),x74711),f789(f789(f89(a863),x74713),x74712)))+P1(f789(f789(f240(a863),f789(f789(f3(a863),x74711),x74712)),x74713))
% 21.40/21.37 [7531]E(x75311,f122(x75312))+E(f789(f137(x75312),f789(f789(f789(f178(f864(x75312),f864(x75312)),x75313),f148(x75312)),x75311)),f789(f789(f159(x75312),x75311),f59(a863,x75313,f789(f185(f864(x75312)),x75311))))
% 21.40/21.37 [7540]E(f789(f789(f310(x75401),x75402),f789(f789(f3(f870(x75401,a856)),x75403),f789(f789(f310(x75401),x75402),f184(f870(x75401,a856))))),x75403)+~P1(f789(f789(f342(x75401),x75402),x75403))
% 21.40/21.37 [7704]P1(f789(f789(f241(a863),x77041),f789(f789(f3(a863),x77042),x77043)))+~P1(f789(f789(f241(a863),f789(f789(f89(a863),x77041),x77043)),x77042))
% 21.40/21.37 [7705]P1(f789(f789(f240(a863),x77051),f789(f789(f89(a863),x77052),x77053)))+~P1(f789(f789(f240(a863),f789(f789(f3(a863),x77051),x77053)),x77052))
% 21.40/21.37 [7724]P1(f789(f70(x77241),x77242))+~P1(f789(f70(x77241),f789(f789(f110(f870(x77241,a856)),x77243),x77242)))
% 21.40/21.37 [7725]P1(f789(f70(x77251),x77252))+~P1(f789(f70(x77251),f789(f789(f110(f870(x77251,a856)),x77252),x77253)))
% 21.40/21.37 [7806]~P44(x78061,x78063)+P1(f789(f789(f342(f869(x78061,x78061)),f789(f789(f249(x78061,x78061),x78062),x78062)),x78063))
% 21.40/21.37 [7856]P1(f789(f789(f287(a1),x78561),x78562))+~P1(f789(f789(f287(a1),x78561),f789(f789(f89(a1),x78562),f789(f789(f90(a1),x78561),x78563))))
% 21.40/21.37 [7936]E(f789(f789(f159(a863),f136(a863,f789(f302(a863,x79361),x79362))),x79363),f789(f789(f89(a863),x79361),x79363))+~P1(f789(f789(f241(a863),f789(f789(f89(a863),x79361),x79363)),x79362))
% 21.40/21.37 [8003]~P1(f789(f789(f191(f789(a29,x80031)),x80032),x80033))+P1(f789(f789(f191(f789(f238(a857),f789(a32,x80031))),x80032),x80033))
% 21.40/21.37 [8004]~P1(f789(f789(f191(f789(a29,x80041)),x80042),x80043))+P1(f789(f789(f191(f789(f238(a857),f789(a32,x80041))),x80042),x80043))
% 21.40/21.37 [8008]E(f789(f789(f164(a863),x80081),f136(a863,f789(f302(a863,x80082),x80083))),f136(a863,f789(f302(a863,x80082),f789(f789(f89(a863),x80082),x80081))))+~P1(f789(f789(f240(a863),f789(f789(f89(a863),x80082),x80081)),x80083))
% 21.40/21.37 [8057]~P88(x80571)+E(f789(f789(f250(x80571),x80572),f789(f113(a863),f789(f789(f89(a1),x80573),x80573))),f789(f789(f95(x80571,x80571),f789(f789(f250(x80571),x80572),f789(f113(a863),x80573))),f789(f789(f20(x80571,x80571,x80571),f90(x80571)),f7(x80571))))
% 21.40/21.37 [8255]P1(f789(f789(f191(f789(a29,x82551)),x82552),x82553))+~P1(f789(f789(f191(f789(f238(a857),f789(a32,x82551))),x82552),x82553))
% 21.40/21.37 [8256]P1(f789(f789(f191(f789(a29,x82561)),x82562),x82563))+~P1(f789(f789(f191(f789(f238(a857),f789(a32,x82561))),x82562),x82563))
% 21.40/21.37 [8314]E(f789(f789(f132(x83141),f789(f789(f164(x83141),x83142),x83143)),f789(f789(f146(x83141),f789(f789(f159(x83141),x83143),x83142)),f789(f789(f135(x83141),f789(a121,x83142)),x83143))),x83143)+~P1(f789(f789(f241(a863),x83142),f789(f185(f864(x83141)),x83143)))
% 21.40/21.37 [8321]P1(f789(f789(f240(f870(x83211,a856)),f329(x83211,x83212)),f329(x83211,x83213)))+~P1(f789(f789(f240(f870(x83211,f870(x83211,a856))),x83213),x83212))
% 21.40/21.37 [8322]~P54(x83221,x83222,x83223)+P54(x83221,x83222,f789(f789(f3(f870(f869(x83221,x83221),a856)),x83223),f308(x83221,f184(f870(f869(x83221,x83221),a856)))))
% 21.40/21.37 [8344]P1(f789(f789(f240(f870(x83441,a856)),f330(x83441,x83442)),f330(x83441,x83443)))+~P1(f789(f789(f240(f870(f869(x83441,x83441),a856)),x83443),x83442))
% 21.40/21.37 [8351]~P119(x83511)+P1(f789(f789(f240(x83511),f2(x83511)),f789(f789(f89(x83511),f789(f789(f90(x83511),x83512),x83512)),f789(f789(f90(x83511),x83513),x83513))))
% 21.40/21.37 [8383]~P88(x83831)+E(f789(f789(f250(x83831),f789(f113(x83831),x83832)),f789(f113(a863),f789(f789(f89(a1),x83833),x83833))),f789(f789(f95(x83831,x83831),f789(f789(f250(x83831),f789(f113(x83831),x83832)),f789(f113(a863),x83833))),f789(f789(f20(x83831,x83831,x83831),f90(x83831)),f7(x83831))))
% 21.40/21.37 [8388]P1(f789(f789(f240(f870(x83881,a856)),f789(f284(x83881),x83882)),f789(f284(x83881),x83883)))+~P1(f789(f789(f240(f870(f869(x83881,x83881),a856)),x83882),x83883))
% 21.40/21.37 [8420]~P48(x84201,x84202)+~P1(f789(f789(f342(f869(x84201,x84201)),f789(f789(f249(x84201,x84201),x84203),x84203)),x84202))
% 21.40/21.37 [8421]~P36(x84211,x84212)+~P1(f789(f789(f342(f869(x84211,x84211)),f789(f789(f249(x84211,x84211),x84213),x84213)),x84212))
% 21.40/21.37 [8422]~P36(x84221,x84222)+~P1(f789(f789(f342(f869(x84221,x84221)),f789(f789(f249(x84221,x84221),x84223),x84223)),x84222))
% 21.40/21.37 [8461]~E(x84612,x84613)+P1(f789(f789(f342(f869(x84611,x84611)),f789(f789(f249(x84611,x84611),x84612),x84613)),f308(x84611,f184(f870(f869(x84611,x84611),a856)))))
% 21.40/21.37 [8482]P1(f789(f789(f240(f870(x84821,a856)),f52(f870(x84821,a856),x84822)),f52(f870(x84821,a856),x84823)))+~P1(f789(f789(f240(f870(f870(x84821,a856),a856)),x84823),x84822))
% 21.40/21.37 [8483]P1(f789(f789(f240(f870(x84831,a856)),f51(f870(x84831,a856),x84832)),f51(f870(x84831,a856),x84833)))+~P1(f789(f789(f240(f870(f870(x84831,a856),a856)),x84832),x84833))
% 21.40/21.37 [8538]~P12(x85381,x85383,x85382)+P1(f789(f789(f240(f870(f869(x85381,x85381),a856)),x85382),f789(f789(f256(x85381,x85381),x85383),f789(f18(f870(x85381,a856),x85381),x85383))))
% 21.40/21.37 [8539]~P47(x85391,x85393,x85392)+P1(f789(f789(f240(f870(f869(x85391,x85391),a856)),x85392),f789(f789(f256(x85391,x85391),x85393),f789(f18(f870(x85391,a856),x85391),x85393))))
% 21.40/21.37 [8577]~P80(x85771)+P1(f789(f789(f240(x85771),f789(f789(f3(x85771),f789(f84(x85771),x85772)),f789(f84(x85771),x85773))),f789(f84(x85771),f789(f789(f3(x85771),x85773),x85772))))
% 21.40/21.37 [8578]~P80(x85781)+P1(f789(f789(f240(x85781),f789(f789(f3(x85781),f789(f84(x85781),x85782)),f789(f84(x85781),x85783))),f789(f84(x85781),f789(f789(f3(x85781),x85782),x85783))))
% 21.40/21.37 [8602]P1(f789(f789(f240(f870(f869(x86021,x86021),a856)),f308(x86021,x86022)),f308(x86021,x86023)))+~P1(f789(f789(f240(f870(f869(x86021,x86021),a856)),x86022),x86023))
% 21.40/21.37 [8749]P54(x87491,x87492,x87493)+~P54(x87491,x87492,f789(f789(f3(f870(f869(x87491,x87491),a856)),x87493),f308(x87491,f184(f870(f869(x87491,x87491),a856)))))
% 21.40/21.37 [8768]P1(f789(f789(f240(f870(f869(f864(x87681),f864(x87681)),a856)),f154(x87681,x87682)),f154(x87681,x87683)))+~P1(f789(f789(f240(f870(f869(x87681,x87681),a856)),x87682),x87683))
% 21.40/21.37 [8769]P1(f789(f789(f240(f870(f869(f864(x87691),f864(x87691)),a856)),f153(x87691,x87692)),f153(x87691,x87693)))+~P1(f789(f789(f240(f870(f869(x87691,x87691),a856)),x87692),x87693))
% 21.40/21.37 [8786]~P47(x87861,x87863,x87862)+P1(f789(f789(f240(f870(f869(x87861,x87861),a856)),x87862),f789(f789(f289(x87861,x87861,x87861),f789(f286(x87861,x87861),x87862)),x87862)))
% 21.40/21.37 [8827]~P1(f789(f134(x88271),x88272))+E(f789(f133(x88271,f789(f789(f9(x88271,f870(x88271,a856),a856),f342(x88271)),f789(f163(x88271),f165(x88271,x88272,x88273)))),x88272),f165(x88271,x88272,x88273))
% 21.40/21.37 [8875]E(x88751,x88752)+~P1(f789(f789(f342(f869(x88753,x88753)),f789(f789(f249(x88753,x88753),x88751),x88752)),f308(x88753,f184(f870(f869(x88753,x88753),a856)))))
% 21.40/21.37 [8956]P1(f789(f789(f342(x89561),x89562),f330(x89561,x89563)))+P1(f789(f789(f342(f869(x89561,x89561)),f789(f789(f249(x89561,x89561),f361(x89563,x89562,x89561)),x89562)),x89563))
% 21.40/21.37 [8957]P1(f789(f789(f342(x89571),x89572),f330(x89571,x89573)))+P1(f789(f789(f342(f869(x89571,x89571)),f789(f789(f249(x89571,x89571),f631(x89573,x89572,x89571)),x89572)),x89573))
% 21.40/21.37 [8958]P1(f789(f789(f342(x89581),x89582),f330(x89581,x89583)))+P1(f789(f789(f342(f869(x89581,x89581)),f789(f789(f249(x89581,x89581),f633(x89583,x89582,x89581)),x89582)),x89583))
% 21.40/21.37 [9062]P1(f789(x90623,x90622))+E(f789(f264(x90621),f789(f789(f20(x90621,a856,a856),f789(f789(f10(a856,f870(a856,a856),x90621),a339),f789(a338,x90622))),x90623)),f184(f870(x90621,a856)))
% 21.40/21.37 [9082]~P80(x90821)+P1(f789(f789(f240(x90821),f789(f84(x90821),f789(f789(f3(x90821),f789(f84(x90821),x90822)),f789(f84(x90821),x90823)))),f789(f84(x90821),f789(f789(f3(x90821),x90822),x90823))))
% 21.40/21.37 [9095]~P1(f789(x90953,x90952))+E(f789(f264(x90951),f789(f789(f20(x90951,a856,a856),f789(f789(f10(a856,f870(a856,a856),x90951),a339),f789(a338,x90952))),x90953)),f789(f789(f310(x90951),x90952),f184(f870(x90951,a856))))
% 21.40/21.37 [9101]~P1(f789(f789(f342(f870(x91011,a856)),x91013),f789(f309(x91011),x91012)))+P1(f789(f253(x91011,f789(f789(f9(x91011,f870(x91011,a856),a856),f342(x91011)),x91012)),x91013))
% 21.40/21.37 [9135]P36(x91351,x91352)+P1(f789(f789(f342(f869(x91351,x91351)),f789(f789(f249(x91351,x91351),f789(f597(x91352,x91351),f789(a121,x91353))),f789(f597(x91352,x91351),x91353))),x91352))
% 21.40/21.37 [9259]P1(f789(f789(f342(f870(x92591,a856)),x92592),f789(f309(x92591),x92593)))+~P1(f789(f253(x92591,f789(f789(f9(x92591,f870(x92591,a856),a856),f342(x92591)),x92593)),x92592))
% 21.40/21.37 [9319]P1(f789(f789(f342(x93191),f789(f273(x93191,x93192),x93193)),f789(f163(x93191),f789(f789(f150(f869(a108,x93191),x93191),f258(a108,x93191)),x93192))))+~P1(f789(f789(f241(a108),x93193),f789(f161(a108),f789(f789(f150(f869(a108,x93191),a108),f248(a108,x93191)),x93192))))
% 21.40/21.37 [9368]P1(f789(f789(f240(f870(f869(f864(x93681),f864(x93681)),a856)),f154(x93681,x93682)),f789(f789(f256(f864(x93681),f864(x93681)),f156(x93681,x93683)),f789(f18(f870(f864(x93681),a856),f864(x93681)),f156(x93681,x93683)))))+~P1(f789(f789(f240(f870(f869(x93681,x93681),a856)),x93682),f789(f789(f256(x93681,x93681),x93683),f789(f18(f870(x93681,a856),x93681),x93683))))
% 21.40/21.37 [9388]P1(f789(f789(f342(x93881),f789(f248(x93881,f869(a108,a108)),f789(f271(x93881,x93882),x93883))),f789(f163(x93881),f789(f789(f150(f869(a108,x93881),x93881),f258(a108,x93881)),x93882))))+~P1(f789(f789(f241(a108),f2(a108)),f789(f161(a108),f789(f789(f150(f869(a108,x93881),a108),f248(a108,x93881)),x93882))))
% 21.40/21.37 [9402]~P1(f789(f789(f240(f870(f869(x94021,x94021),a856)),x94022),f789(f789(f256(x94021,x94021),x94023),f789(f18(f870(x94021,a856),x94021),x94023))))+P1(f789(f789(f240(f870(f869(x94021,x94021),a856)),f789(f789(f289(x94021,x94021,x94021),x94022),f308(x94021,x94022))),f789(f789(f256(x94021,x94021),x94023),f789(f18(f870(x94021,a856),x94021),x94023))))
% 21.40/21.37 [9694]~P36(x96941,x96942)+~P1(f789(f789(f342(f869(x96941,x96941)),f789(f789(f249(x96941,x96941),f789(x96943,f789(a121,f598(x96942,x96941,x96943)))),f789(x96943,f598(x96942,x96941,x96943)))),x96942))
% 21.40/21.37 [9695]~P36(x96951,x96952)+~P1(f789(f789(f342(f869(x96951,x96951)),f789(f789(f249(x96951,x96951),f789(x96953,f789(a121,f641(x96953,x96952,x96951)))),f789(x96953,f641(x96953,x96952,x96951)))),x96952))
% 21.40/21.37 [9953]P1(f789(f789(f240(f870(f869(f870(x99531,a856),f870(x99531,a856)),a856)),f789(f789(f289(f870(x99531,a856),f870(x99531,a856),f870(x99531,a856)),f334(x99531,x99532)),f789(f789(f110(f870(f869(f870(x99531,a856),f870(x99531,a856)),a856)),f334(x99531,x99533)),f789(f789(f310(f869(f870(x99531,a856),f870(x99531,a856))),f789(f789(f249(f870(x99531,a856),f870(x99531,a856)),f184(f870(x99531,a856))),f184(f870(x99531,a856)))),f184(f870(f869(f870(x99531,a856),f870(x99531,a856)),a856)))))),f334(x99531,x99532)))+~P1(f789(f789(f240(f870(f869(x99531,x99531),a856)),f789(f789(f289(x99531,x99531,x99531),x99532),x99533)),x99532))
% 21.40/21.37 [9954]P1(f789(f789(f240(f870(f869(f870(x99541,a856),f870(x99541,a856)),a856)),f789(f789(f289(f870(x99541,a856),f870(x99541,a856),f870(x99541,a856)),f332(x99541,x99542)),f789(f789(f110(f870(f869(f870(x99541,a856),f870(x99541,a856)),a856)),f332(x99541,x99543)),f789(f789(f310(f869(f870(x99541,a856),f870(x99541,a856))),f789(f789(f249(f870(x99541,a856),f870(x99541,a856)),f184(f870(x99541,a856))),f184(f870(x99541,a856)))),f184(f870(f869(f870(x99541,a856),f870(x99541,a856)),a856)))))),f332(x99541,x99542)))+~P1(f789(f789(f240(f870(f869(x99541,x99541),a856)),f789(f789(f289(x99541,x99541,x99541),x99542),x99543)),x99542))
% 21.40/21.37 [7215]~P1(f789(f789(f240(a863),x72152),x72151))+E(f789(f789(f3(a863),f789(a121,f789(f789(f3(a863),x72151),x72152))),x72153),f789(f789(f3(a863),f789(a121,x72151)),f789(f789(f89(a863),x72152),x72153)))
% 21.40/21.37 [7255]~P7(x72551)+E(f789(f789(f89(x72551),f59(x72551,x72552,x72553)),f789(f789(f90(x72551),f789(f789(f50(x72551),x72552),x72553)),x72553)),x72552)
% 21.40/21.37 [7475]E(f789(f789(f90(a863),f789(f113(a863),x74751)),f789(f789(f90(a863),f789(f113(a863),x74752)),x74753)),f789(f789(f90(a863),f789(f113(a863),f789(f789(f90(a1),x74751),x74752))),x74753))+P1(f789(f789(f241(a1),x74751),a92))
% 21.40/21.37 [7946]~P1(f789(f789(f240(a863),x79463),x79462))+P1(f789(f789(f240(a863),x79461),f789(f789(f3(a863),f789(f789(f89(a863),x79462),x79461)),x79463)))
% 21.40/21.37 [8140]~P1(f789(f789(f240(a863),x81401),x81402))+E(f789(f789(f132(a863),f136(a863,f789(f302(a863,x81401),x81402))),f136(a863,f789(f302(a863,x81402),f789(f789(f89(a863),x81402),x81403)))),f136(a863,f789(f302(a863,x81401),f789(f789(f89(a863),x81402),x81403))))
% 21.40/21.37 [8397]~P1(f789(f70(x83971),x83972))+E(f789(a121,f789(f49(x83971),f789(f789(f3(f870(x83971,a856)),x83972),f789(f789(f310(x83971),x83973),f184(f870(x83971,a856)))))),f789(f49(x83971),f789(f789(f310(x83971),x83973),x83972)))
% 21.40/21.37 [8441]~P1(f789(f70(x84411),x84412))+E(f789(f789(f89(a863),f87(a863)),f789(f49(x84411),f789(f789(f3(f870(x84411,a856)),x84412),f789(f789(f310(x84411),x84413),f184(f870(x84411,a856)))))),f789(f49(x84411),f789(f789(f310(x84411),x84413),x84412)))
% 21.40/21.37 [8611]E(f789(f789(f3(a863),f789(f49(x86111),x86112)),f789(f49(x86111),f789(f789(f111(f870(x86111,a856)),x86112),x86113))),f789(f49(x86111),f789(f789(f3(f870(x86111,a856)),x86112),x86113)))+~P1(f789(f70(x86111),f789(f789(f111(f870(x86111,a856)),x86112),x86113)))
% 21.40/21.37 [8824]~P10(f789(x88242,f417(x88242,x88243,x88241)))+E(f789(f109(a1),f789(f789(f11(x88241,a863),f789(f789(f10(a1,a863,x88241),a114),x88242)),x88243)),f789(f789(f11(x88241,a1),x88242),x88243))
% 21.40/21.37 [8825]~P10(f789(x88252,f525(x88252,x88253,x88251)))+E(f789(f109(a1),f789(f789(f8(x88251,a863),f789(f789(f10(a1,a863,x88251),a114),x88252)),x88253)),f789(f789(f8(x88251,a1),x88252),x88253))
% 21.40/21.37 [8860]~P1(f789(f70(x88601),x88603))+P1(f789(f789(f240(a863),f789(f789(f3(a863),f789(f49(x88601),x88602)),f789(f49(x88601),x88603))),f789(f49(x88601),f789(f789(f3(f870(x88601,a856)),x88602),x88603))))
% 21.40/21.37 [8883]P1(f789(f789(f342(x88831),f417(x88832,x88833,x88831)),x88833))+E(f789(f109(a1),f789(f789(f11(x88831,a863),f789(f789(f10(a1,a863,x88831),a114),x88832)),x88833)),f789(f789(f11(x88831,a1),x88832),x88833))
% 21.40/21.37 [8884]P1(f789(f789(f342(x88841),f525(x88842,x88843,x88841)),x88843))+E(f789(f109(a1),f789(f789(f8(x88841,a863),f789(f789(f10(a1,a863,x88841),a114),x88842)),x88843)),f789(f789(f8(x88841,a1),x88842),x88843))
% 21.40/21.37 [8950]E(f94(x89501,f789(f789(f9(x89501,f870(x89501,a856),a856),f342(x89501)),f789(f789(f3(f870(x89501,a856)),x89502),f789(f789(f310(x89501),x89503),f184(f870(x89501,a856)))))),f252(x89501,x89503,x89502))+P1(f789(f789(f240(f870(x89501,a856)),x89502),f789(f789(f310(x89501),x89503),f184(f870(x89501,a856)))))
% 21.40/21.37 [9260]E(f789(f789(f150(f864(x92601),x92601),f789(f789(f9(f864(x92601),a863,x92601),f159(x92601)),x92602)),f789(f133(f864(x92601),f789(f789(f10(a863,a856,f864(x92601)),f789(f241(a863),x92602)),f185(f864(x92601)))),x92603)),f789(f789(f159(f864(x92601)),f168(x92601,x92603)),x92602))+~P1(f789(f789(f241(a863),x92602),f789(f185(f864(f864(x92601))),f168(x92601,x92603))))
% 21.40/21.37 [9563]~P1(f789(f789(f342(f869(x95631,x95631)),x95632),f308(x95631,x95633)))+P1(f789(f789(f342(f869(x95631,x95631)),x95632),f789(f789(f53(a863,f870(f869(x95631,x95631),a856)),f247(f870(a863,a856))),f789(f789(f9(a863,f870(f869(x95631,x95631),a856),f870(f869(x95631,x95631),a856)),f178(f869(x95631,x95631),a856)),x95633))))
% 21.40/21.37 [9620]~P1(f789(f789(f240(f870(x96201,a856)),f789(f789(f53(a863,f870(x96201,a856)),f789(f302(a863,f2(a863)),f544(x96203,x96202,x96201))),x96202)),x96203))+P1(f789(f789(f240(f870(x96201,a856)),f789(f789(f53(a863,f870(x96201,a856)),f247(f870(a863,a856))),x96202)),x96203))
% 21.40/21.37 [9671]~P1(f789(f789(f241(a1),f2(a1)),x96713))+P1(f789(f789(f241(a1),x96711),f789(f789(f89(a1),x96712),f789(f789(f90(a1),f789(f789(f89(a1),f789(f84(a1),f789(f789(f3(a1),x96712),x96711))),f87(a1))),x96713))))
% 21.40/21.37 [9681]~P36(x96811,f789(f789(f110(f870(f869(x96811,x96811),a856)),x96812),x96813))+P36(x96811,f789(f789(f110(f870(f869(x96811,x96811),a856)),f789(f789(f110(f870(f869(x96811,x96811),a856)),f789(f789(f289(x96811,x96811,x96811),x96812),x96812)),f789(f789(f289(x96811,x96811,x96811),x96813),x96812))),x96813))
% 21.40/21.37 [9745]P36(x97451,f789(f789(f110(f870(f869(x97451,x97451),a856)),x97452),x97453))+~P36(x97451,f789(f789(f110(f870(f869(x97451,x97451),a856)),f789(f789(f110(f870(f869(x97451,x97451),a856)),f789(f789(f289(x97451,x97451,x97451),x97452),x97452)),f789(f789(f289(x97451,x97451,x97451),x97453),x97452))),x97453))
% 21.40/21.37 [9342]~P120(x93421)+E(f789(f112(x93421),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x93422),x93423)),f184(f870(f869(a863,a863),a856)))))),f789(f789(f3(x93421),f789(f109(x93421),x93422)),f789(f109(x93421),x93423)))
% 21.40/21.37 [9420]P1(f789(x94203,x94202))+E(f789(f264(x94201),f789(f789(f20(x94201,a856,a856),f789(f789(f10(a856,f870(a856,a856),x94201),a339),f789(f789(f9(x94201,x94201,a856),a338),x94202))),x94203)),f184(f870(x94201,a856)))
% 21.40/21.37 [9422]~P1(f789(x94223,x94222))+E(f789(f264(x94221),f789(f789(f20(x94221,a856,a856),f789(f789(f10(a856,f870(a856,a856),x94221),a339),f789(f789(f9(x94221,x94221,a856),a338),x94222))),x94223)),f789(f789(f310(x94221),x94222),f184(f870(x94221,a856))))
% 21.40/21.37 [9737]~P1(f789(f70(x97371),x97373))+E(f789(f789(f73(x97371,f870(x97371,a856),f789(f789(f10(f870(x97371,a856),f870(f870(x97371,a856),f870(x97371,a856)),x97371),f789(f9(f870(x97371,a856),f870(x97371,a856),f870(x97371,a856)),f3(f870(x97371,a856)))),f789(f789(f9(x97371,f870(x97371,a856),f870(x97371,a856)),f310(x97371)),f184(f870(x97371,a856))))),x97372),x97373),f789(f789(f3(f870(x97371,a856)),x97372),x97373))
% 21.40/21.37 [9771]~P1(f789(f789(f241(a1),f2(a1)),x97713))+P1(f789(f789(f241(a1),f789(f789(f3(a1),x97711),f789(f789(f90(a1),f789(f789(f89(a1),f789(f84(a1),f789(f789(f3(a1),x97711),x97712))),f87(a1))),x97713))),x97712))
% 21.40/21.37 [10023]~P1(f789(f789(f342(x100231),x100233),f330(x100231,x100232)))+P1(f789(f329(x100231,f789(f789(f9(x100231,f870(f869(x100231,x100231),a856),f870(x100231,a856)),f789(f789(f10(f870(x100231,f870(f870(f869(x100231,x100231),a856),a856)),f870(f870(f869(x100231,x100231),a856),f870(x100231,a856)),x100231),f9(x100231,f870(f869(x100231,x100231),a856),a856)),f789(f789(f10(f870(x100231,f869(x100231,x100231)),f870(x100231,f870(f870(f869(x100231,x100231),a856),a856)),x100231),f789(f10(f869(x100231,x100231),f870(f870(f869(x100231,x100231),a856),a856),x100231),f342(f869(x100231,x100231)))),f249(x100231,x100231)))),x100232)),x100233))
% 21.40/21.37 [10035]P1(f789(f789(f342(x100351),x100352),f330(x100351,x100353)))+~P1(f789(f329(x100351,f789(f789(f9(x100351,f870(f869(x100351,x100351),a856),f870(x100351,a856)),f789(f789(f10(f870(x100351,f870(f870(f869(x100351,x100351),a856),a856)),f870(f870(f869(x100351,x100351),a856),f870(x100351,a856)),x100351),f9(x100351,f870(f869(x100351,x100351),a856),a856)),f789(f789(f10(f870(x100351,f869(x100351,x100351)),f870(x100351,f870(f870(f869(x100351,x100351),a856),a856)),x100351),f789(f10(f869(x100351,x100351),f870(f870(f869(x100351,x100351),a856),a856),x100351),f342(f869(x100351,x100351)))),f249(x100351,x100351)))),x100353)),x100352))
% 21.40/21.37 [9618]~P1(f789(f70(x96181),f789(f264(x96181),x96183)))+P1(f789(f70(x96181),f789(f264(x96181),f789(f789(f20(x96181,a856,a856),f789(f789(f10(a856,f870(a856,a856),x96181),a339),x96182)),x96183))))
% 21.40/21.37 [9619]~P1(f789(f70(x96191),f789(f264(x96191),x96192)))+P1(f789(f70(x96191),f789(f264(x96191),f789(f789(f20(x96191,a856,a856),f789(f789(f10(a856,f870(a856,a856),x96191),a339),x96192)),x96193))))
% 21.40/21.37 [9705]P1(f789(f70(x97051),f789(f264(x97051),x97052)))+~P1(f789(f70(x97051),f789(f264(x97051),f789(f789(f20(x97051,a856,a856),f789(f789(f10(a856,f870(a856,a856),x97051),a340),x97053)),x97052))))
% 21.40/21.37 [9706]P1(f789(f70(x97061),f789(f264(x97061),x97062)))+~P1(f789(f70(x97061),f789(f264(x97061),f789(f789(f20(x97061,a856,a856),f789(f789(f10(a856,f870(a856,a856),x97061),a340),x97062)),x97063))))
% 21.40/21.37 [10008]~P1(f789(f70(x100081),x100082))+P1(f789(f70(f864(x100081)),f789(f264(f864(x100081)),f789(f789(f20(f864(x100081),a856,a856),f789(f789(f10(a856,f870(a856,a856),f864(x100081)),a339),f789(f789(f9(f864(x100081),f870(x100081,a856),a856),f789(f789(f10(f870(x100081,a856),f870(f870(x100081,a856),a856),f864(x100081)),f240(f870(x100081,a856))),f163(x100081))),x100082))),f789(f789(f9(f864(x100081),a863,a856),f789(f789(f10(a863,f870(a863,a856),f864(x100081)),a338),f185(f864(x100081)))),x100083)))))
% 21.40/21.37 [10009]~P1(f789(f70(x100091),x100092))+P1(f789(f70(f864(x100091)),f789(f264(f864(x100091)),f789(f789(f20(f864(x100091),a856,a856),f789(f789(f10(a856,f870(a856,a856),f864(x100091)),a339),f789(f789(f9(f864(x100091),f870(x100091,a856),a856),f789(f789(f10(f870(x100091,a856),f870(f870(x100091,a856),a856),f864(x100091)),f240(f870(x100091,a856))),f163(x100091))),x100092))),f789(f789(f9(f864(x100091),a863,a856),f789(f789(f10(a863,f870(a863,a856),f864(x100091)),f240(a863)),f185(f864(x100091)))),x100093)))))
% 21.40/21.37 [9719]~P70(x97191)+E(f789(f789(f250(x97191),x97192),f789(f789(f90(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x97193)),f789(f789(f90(x97191),f789(f789(f250(x97191),x97192),x97193)),f789(f789(f250(x97191),x97192),x97193)))
% 21.40/21.37 [9750]~P78(x97501)+E(f789(f789(f250(x97501),f789(f789(f250(x97501),x97502),x97503)),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f789(f250(x97501),x97502),f789(f789(f90(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x97503)))
% 21.40/21.37 [9811]~P120(x98111)+E(f789(f789(f250(x98111),f789(f88(x98111),x98112)),f789(f789(f90(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x98113)),f789(f789(f250(x98111),x98112),f789(f789(f90(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x98113)))
% 21.40/21.37 [9958]~P110(x99581)+P1(f789(f789(f240(x99581),f2(x99581)),f789(f789(f89(x99581),f789(f789(f250(x99581),x99582),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x99581),x99583),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))))
% 21.40/21.37 [9821]~P70(x98211)+E(f789(f789(f250(x98211),x98212),f789(a121,f789(f789(f90(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x98213))),f789(f789(f90(x98211),x98212),f789(f789(f90(x98211),f789(f789(f250(x98211),x98212),x98213)),f789(f789(f250(x98211),x98212),x98213))))
% 21.40/21.37 [9873]~P78(x98731)+E(f789(f789(f90(x98731),x98732),f789(f789(f250(x98731),f789(f789(f250(x98731),x98732),x98733)),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x98731),x98732),f789(a121,f789(f789(f90(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x98733))))
% 21.40/21.37 [9918]~P110(x99181)+P1(f789(f789(f240(x99181),f2(x99181)),f789(f789(f250(x99181),x99182),f789(f789(f90(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x99183))))
% 21.40/21.37 [9987]~P88(x99871)+E(f789(f789(f89(x99871),f789(f789(f89(x99871),f789(f789(f250(x99871),x99872),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x99871),x99873),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))),f789(f789(f90(x99871),f789(f789(f90(x99871),f789(f113(x99871),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x99872)),x99873)),f789(f789(f250(x99871),f789(f789(f89(x99871),x99872),x99873)),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))
% 21.40/21.37 [9988]~P88(x99881)+E(f789(f789(f3(x99881),f789(f789(f89(x99881),f789(f789(f250(x99881),x99882),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x99881),x99883),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))),f789(f789(f90(x99881),f789(f789(f90(x99881),f789(f113(x99881),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x99882)),x99883)),f789(f789(f250(x99881),f789(f789(f3(x99881),x99882),x99883)),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))
% 21.40/21.37 [4625]E(x46251,x46252)+~E(f38(x46253,x46251),f38(x46254,x46252))
% 21.40/21.37 [4626]E(x46261,x46262)+~E(f38(x46261,x46263),f38(x46262,x46264))
% 21.40/21.37 [4627]E(x46271,x46272)+~E(f30(x46273,x46271),f30(x46274,x46272))
% 21.40/21.37 [4628]E(x46281,x46282)+~E(f30(x46281,x46283),f30(x46282,x46284))
% 21.40/21.37 [4629]E(x46291,x46292)+~E(f37(x46293,x46291),f37(x46294,x46292))
% 21.40/21.37 [4630]E(x46301,x46302)+~E(f37(x46301,x46303),f37(x46302,x46304))
% 21.40/21.37 [5746]P39(f37(x57461,x57463),x57462,x57464,x57462)+P1(f789(x57461,x57462))
% 21.40/21.37 [5747]P39(f37(x57471,x57473),x57472,x57474,x57472)+P1(f789(x57471,x57472))
% 21.40/21.37 [6901]~P39(x69011,x69012,x69013,x69014)+P39(x69011,x69012,f789(a121,x69013),x69014)
% 21.40/21.37 [7744]P29(x77441,x77442,x77443,x77444)+~E(f462(x77444,x77443,x77442,x77441),f464(x77444,x77443,x77442,x77441))
% 21.40/21.37 [8241]~P29(x82411,f867(x82412),x82414,f173(x82411,x82412,x82414))+P29(x82411,f867(x82412),f174(x82411,x82412,x82413,x82414),f173(x82411,x82412,x82414))
% 21.40/21.37 [8455]~P29(x84551,f867(x84552),f174(x84551,x84552,x84554,x84553),f173(x84551,x84552,x84553))+P29(x84551,f867(x84552),x84553,f173(x84551,x84552,x84553))
% 21.40/21.37 [4992]~P21(x49923,x49921,x49924)+E(f789(f789(x49921,x49922),x49922),x49922)
% 21.40/21.37 [4994]E(x49941,x49942)+~E(f789(f312(x49943,x49944),x49941),f789(f312(x49943,x49944),x49942))
% 21.40/21.37 [4995]E(x49951,x49952)+~E(f789(f312(x49953,x49954),x49951),f789(f312(x49953,x49954),x49952))
% 21.40/21.37 [4996]E(x49961,x49962)+~E(f789(f321(x49963,x49964),x49961),f789(f321(x49963,x49964),x49962))
% 21.40/21.37 [4997]E(x49971,x49972)+~E(f789(f321(x49973,x49974),x49971),f789(f321(x49973,x49974),x49972))
% 21.40/21.37 [5271]~E(x52714,f184(f870(x52711,a856)))+E(f789(f311(x52711,x52712,x52713),x52714),f184(f870(x52712,a856)))
% 21.40/21.37 [5272]~E(x52724,f184(f870(x52721,a856)))+E(f789(f311(x52721,x52722,x52723),x52724),f184(f870(x52722,a856)))
% 21.40/21.37 [5535]~E(f789(f311(x55352,x55353,x55354),x55351),f184(f870(x55353,a856)))+E(x55351,f184(f870(x55352,a856)))
% 21.40/21.37 [5536]~E(f789(f311(x55362,x55363,x55364),x55361),f184(f870(x55363,a856)))+E(x55361,f184(f870(x55362,a856)))
% 21.40/21.37 [5827]~P101(x58272)+E(f789(f789(f144(x58271,x58272,x58273),x58274),f122(x58271)),f789(f789(f146(x58271),x58274),f122(x58271)))
% 21.40/21.37 [5862]E(f789(x58621,x58622),f187(x58623))+P1(f789(f789(f342(x58624),x58622),f173(x58624,x58623,x58621)))
% 21.40/21.37 [6185]~E(x61851,f184(f870(x61852,a856)))+~P1(f789(f71(x61852,x61853,x61851),x61854))
% 21.40/21.37 [6206]~P57(x62061,x62063,x62064,x62062)+P1(f789(f70(x62061),x62062))
% 21.40/21.37 [6207]~P57(x62071,x62073,x62072,x62074)+P1(f789(f70(x62071),x62072))
% 21.40/21.37 [6214]~P57(x62142,x62143,x62144,x62141)+~E(x62141,f184(f870(x62142,a856)))
% 21.40/21.37 [6245]~P99(x62451)+E(f789(f789(f111(f870(x62451,a856)),f789(f302(x62451,x62452),x62453)),f303(x62451,x62453,x62454)),f184(f870(x62451,a856)))
% 21.40/21.37 [6273]~P1(f789(f789(x62733,x62734),x62732))+P1(f789(f789(f342(x62731),x62732),f295(x62731,x62733,x62734)))
% 21.40/21.37 [6274]~P1(f789(f789(x62743,x62744),x62742))+P1(f789(f789(f342(x62741),x62742),f294(x62741,x62743,x62744)))
% 21.40/21.37 [6275]~P1(f789(f789(x62753,x62752),x62754))+P1(f789(f789(f342(x62751),x62752),f298(x62751,x62753,x62754)))
% 21.40/21.37 [6276]~P1(f789(f789(x62763,x62762),x62764))+P1(f789(f789(f342(x62761),x62762),f296(x62761,x62763,x62764)))
% 21.40/21.37 [6428]~P99(x64281)+E(f789(f789(f111(f870(x64281,a856)),f306(x64281,x64282,x64283)),f303(x64281,x64283,x64284)),f184(f870(x64281,a856)))
% 21.40/21.37 [6429]~P99(x64291)+E(f789(f789(f111(f870(x64291,a856)),f305(x64291,x64292,x64293)),f306(x64291,x64293,x64294)),f184(f870(x64291,a856)))
% 21.40/21.37 [6430]~P99(x64301)+E(f789(f789(f111(f870(x64301,a856)),f305(x64301,x64302,x64303)),f305(x64301,x64303,x64304)),f184(f870(x64301,a856)))
% 21.40/21.37 [6431]~P99(x64311)+E(f789(f789(f111(f870(x64311,a856)),f303(x64311,x64312,x64313)),f306(x64311,x64313,x64314)),f184(f870(x64311,a856)))
% 21.40/21.37 [6432]~P99(x64321)+E(f789(f789(f111(f870(x64321,a856)),f303(x64321,x64322,x64323)),f305(x64321,x64323,x64324)),f184(f870(x64321,a856)))
% 21.40/21.37 [6469]P1(f789(f789(x64691,x64692),f606(x64692,x64691)))+~P1(f789(f254(x64693,x64694,x64691),x64692))
% 21.40/21.37 [6522]~E(f789(x65221,x65222),f187(x65223))+~P1(f789(f789(f342(x65224),x65222),f173(x65224,x65223,x65221)))
% 21.40/21.37 [6604]~P2(x66041)+E(f186(x66041,x66042,f789(a121,x66043),x66044),f186(x66041,x66042,x66043,f789(x66042,x66044)))
% 21.40/21.37 [6667]~P1(f789(f789(f342(x66674),x66673),f295(x66674,x66671,x66672)))+P1(f789(f789(x66671,x66672),x66673))
% 21.40/21.37 [6668]~P1(f789(f789(f342(x66684),x66683),f294(x66684,x66681,x66682)))+P1(f789(f789(x66681,x66682),x66683))
% 21.40/21.37 [6669]~P1(f789(f789(f342(x66694),x66692),f298(x66694,x66691,x66693)))+P1(f789(f789(x66691,x66692),x66693))
% 21.40/21.37 [6670]~P1(f789(f789(f342(x66704),x66702),f296(x66704,x66701,x66703)))+P1(f789(f789(x66701,x66702),x66703))
% 21.40/21.37 [6752]E(f789(f49(f871(x67521,x67522)),f322(x67521,x67522,x67523,x67524)),f2(a863))+P1(f789(f70(x67522),x67524))
% 21.40/21.37 [6753]E(f789(f49(f871(x67531,x67532)),f322(x67531,x67532,x67533,x67534)),f2(a863))+P1(f789(f70(x67531),x67533))
% 21.40/21.37 [6962]~P19(x69624,x69621,x69622)+E(f789(f82(x69621,x69621,x69621,f789(x69622,x69623)),f789(x69622,x69623)),f789(x69622,x69623))
% 21.40/21.37 [7200]E(f280(x72001,x72002,x72003,x72004),f789(f249(f870(a108,f870(a856,f867(f865(x72001)))),f869(a108,a108)),f55(x72001)))+~P1(f789(f789(f240(a108),x72003),f2(a108)))
% 21.40/21.37 [7266]~P39(f789(a29,x72661),x72662,f789(a121,x72663),x72664)+P39(f789(f238(a857),f789(a32,x72661)),x72662,x72663,x72664)
% 21.40/21.37 [7302]P39(f789(a29,x73021),x73022,f789(a121,x73023),x73024)+~P39(f789(f238(a857),f789(a32,x73021)),x73022,x73023,x73024)
% 21.40/21.37 [7303]P39(f789(a29,x73031),x73032,f789(a121,x73033),x73034)+~P39(f789(f238(a857),f789(a32,x73031)),x73032,x73033,x73034)
% 21.40/21.37 [7603]~P39(f789(a29,x76034),x76033,x76032,x76031)+E(f789(a121,f473(x76031,x76032,x76033,x76034)),x76032)
% 21.40/21.37 [7872]~E(x78722,x78723)+P1(f789(f789(f342(f869(x78721,x78721)),f789(f789(f249(x78721,x78721),x78722),x78723)),f308(x78721,x78724)))
% 21.40/21.37 [7898]~P29(x78981,x78982,x78983,f247(f870(x78981,a856)))+E(f789(f86(x78981,x78982,f247(f870(x78981,a856)),x78983),f789(x78983,x78984)),x78984)
% 21.40/21.37 [7988]~P1(f789(f789(f342(f864(x79881)),f789(f789(f146(x79881),x79884),x79882)),f156(x79881,x79883)))+P1(f789(f789(f342(f864(x79881)),x79882),f156(x79881,x79883)))
% 21.40/21.37 [7989]~P1(f789(f789(f342(f864(x79891)),f789(f789(f132(x79891),x79894),x79892)),f156(x79891,x79893)))+P1(f789(f789(f342(f864(x79891)),x79892),f156(x79891,x79893)))
% 21.40/21.37 [7990]~P1(f789(f789(f342(f864(x79901)),f789(f789(f132(x79901),x79902),x79904)),f156(x79901,x79903)))+P1(f789(f789(f342(f864(x79901)),x79902),f156(x79901,x79903)))
% 21.40/21.37 [8064]~P39(f789(a29,x80641),x80642,x80644,x80643)+P39(f789(f238(a857),f789(a32,x80641)),x80642,f473(x80643,x80644,x80642,x80641),x80643)
% 21.40/21.37 [8101]P29(x81014,x81013,x81011,x81012)+E(f789(x81011,f462(x81012,x81011,x81013,x81014)),f789(x81011,f464(x81012,x81011,x81013,x81014)))
% 21.40/21.37 [8110]E(f174(x81101,x81102,x81103,x81104),f174(x81101,x81102,x81104,x81103))+~E(f789(f789(f111(f870(x81101,a856)),f173(x81101,x81102,x81103)),f173(x81101,x81102,x81104)),f184(f870(x81101,a856)))
% 21.40/21.37 [8206]~P29(x82062,x82061,x82064,x82063)+P29(x82061,x82062,f86(x82062,x82061,x82063,x82064),f789(f311(x82062,x82061,x82064),x82063))
% 21.40/21.37 [8342]P36(f869(x83422,x83424),f283(x83422,x83424,x83421,x83423))+P1(f789(x83421,f602(x83422,x83423,x83424,x83421)))
% 21.40/21.37 [8462]E(x84621,x84622)+~P1(f789(f789(f342(f869(x84623,x84623)),f789(f789(f249(x84623,x84623),x84621),x84622)),f268(x84623,x84624)))
% 21.40/21.37 [8496]~E(f789(x84961,f523(x84963,x84962,x84964,x84961)),f789(f179(x84964,x84962,x84963),f523(x84963,x84962,x84964,x84961)))+E(f789(x84961,f2(a863)),x84962)
% 21.40/21.37 [8528]~P1(f789(f70(f871(x85283,x85281)),f322(x85283,x85281,x85284,x85282)))+P1(f789(f70(x85281),x85282))
% 21.40/21.37 [8529]~P1(f789(f70(f871(x85291,x85293)),f322(x85291,x85293,x85292,x85294)))+P1(f789(f70(x85291),x85292))
% 21.40/21.37 [8530]~P1(f789(f70(f871(x85303,x85301)),f322(x85303,x85301,x85304,x85302)))+P1(f789(f70(x85301),x85302))
% 21.40/21.37 [8531]~P1(f789(f70(f871(x85311,x85313)),f322(x85311,x85313,x85312,x85314)))+P1(f789(f70(x85311),x85312))
% 21.40/21.37 [8693]P36(f869(x86931,x86932),f283(x86931,x86932,x86933,x86934))+~P36(x86932,f789(x86934,f602(x86931,x86934,x86932,x86933)))
% 21.40/21.37 [9196]E(f789(f789(f155(x91961,x91962),f756(x91963,x91964,x91962,x91961)),f750(x91963,x91964,x91962,x91961)),x91964)+~P1(f789(f789(f342(f869(f864(x91961),f864(x91961))),f789(f789(f249(f864(x91961),f864(x91961)),x91962),x91964)),f153(x91961,x91963)))
% 21.40/21.37 [9200]~P1(f789(f789(f342(f869(f864(x92001),f864(x92001))),f789(f789(f249(f864(x92001),f864(x92001)),x92002),x92003)),f141(x92001,x92004)))+P1(f789(f789(f342(f869(f864(x92001),f864(x92001))),f789(f789(f249(f864(x92001),f864(x92001)),x92002),x92003)),f143(x92001,x92004)))
% 21.40/21.37 [9294]P1(f789(f70(x92941),x92942))+~P1(f789(f789(f342(f869(f870(x92941,a856),f870(x92941,a856))),f789(f789(f249(f870(x92941,a856),f870(x92941,a856)),x92943),x92942)),f332(x92941,x92944)))
% 21.40/21.37 [9295]P1(f789(f70(x92951),x92952))+~P1(f789(f789(f342(f869(f870(x92951,a856),f870(x92951,a856))),f789(f789(f249(f870(x92951,a856),f870(x92951,a856)),x92952),x92953)),f332(x92951,x92954)))
% 21.40/21.37 [9298]~E(x92981,f184(f870(x92982,a856)))+~P1(f789(f789(f342(f869(f870(x92982,a856),f870(x92982,a856))),f789(f789(f249(f870(x92982,a856),f870(x92982,a856)),x92983),x92981)),f332(x92982,x92984)))
% 21.40/21.37 [9929]P16(x99291,x99292,x99293,x99294)+~P1(f789(f789(f259(x99291,x99291,a856),f789(f789(f9(x99291,f870(x99291,x99292),f870(x99291,a856)),f789(f789(f10(f870(x99292,a856),f870(f870(x99291,x99292),f870(x99291,a856)),x99291),f10(x99292,a856,x99291)),f789(f789(f10(x99292,f870(x99292,a856),x99291),a338),x99294))),x99294)),f416(x99294,x99293,x99292,x99291)))
% 21.40/21.37 [4894]~E(x48944,f122(x48941))+E(f789(f789(f150(x48941,x48942),x48943),x48944),f122(x48942))
% 21.40/21.37 [4895]~E(x48954,f122(x48951))+E(f789(f789(f150(x48951,x48952),x48953),x48954),f122(x48952))
% 21.40/21.37 [4896]~E(x48964,f187(x48961))+E(f789(f789(f203(x48961,x48962),x48963),x48964),f187(x48962))
% 21.40/21.37 [4897]~E(x48972,f122(x48971))+E(f789(f789(f155(x48971,x48972),x48973),x48974),f122(x48971))
% 21.40/21.37 [5132]E(x51321,f122(x51322))+~E(f789(f789(f150(x51322,x51323),x51324),x51321),f122(x51323))
% 21.40/21.37 [5133]E(x51331,f187(x51332))+~E(f789(f789(f203(x51332,x51333),x51334),x51331),f187(x51333))
% 21.40/21.37 [5134]E(x51341,f122(x51342))+~E(f789(f789(f150(x51342,x51343),x51344),x51341),f122(x51343))
% 21.40/21.37 [5135]E(x51351,f122(x51352))+~E(f789(f789(f155(x51352,x51351),x51353),x51354),f122(x51352))
% 21.40/21.37 [5165]E(x51651,x51652)+~E(f789(f789(f132(x51653),x51654),x51651),f789(f789(f132(x51653),x51654),x51652))
% 21.40/21.37 [5166]E(x51661,x51662)+~E(f789(f789(f132(x51663),x51661),x51664),f789(f789(f132(x51663),x51662),x51664))
% 21.40/21.37 [5307]P1(f789(x53073,x53072))+E(f158(x53071,x53072,f789(f133(x53071,x53073),x53074)),f789(f133(x53071,x53073),x53074))
% 21.40/21.37 [5318]E(x53181,x53182)+~E(f136(a863,f789(f302(a863,x53181),x53183)),f789(f789(f146(a863),x53182),x53184))
% 21.40/21.37 [5366]~P30(x53662,x53663)+P30(x53661,f789(f789(f83(x53662,x53661),x53663),x53664))
% 21.40/21.37 [5367]~P36(x53672,x53673)+P36(x53671,f789(f789(f288(x53672,x53671),x53673),x53674))
% 21.40/21.37 [5577]~E(x55771,f122(x55772))+~E(f789(f789(f132(x55772),x55773),f789(f789(f146(x55772),x55774),f122(x55772))),x55771)
% 21.40/21.37 [5610]E(f140(x56101,x56102),x56103)+~E(f789(f789(f132(x56101),x56104),f789(f789(f146(x56101),x56103),f122(x56101))),x56102)
% 21.40/21.37 [5611]E(f123(x56111,x56112),x56113)+~E(f789(f789(f132(x56111),x56113),f789(f789(f146(x56111),x56114),f122(x56111))),x56112)
% 21.40/21.37 [5719]~E(f136(a863,f789(f302(a863,x57191),x57192)),f789(f789(f146(a863),x57193),x57194))+P1(f789(f789(f241(a863),x57191),x57192))
% 21.40/21.37 [5818]~E(f789(f113(a863),x58184),f2(a863))+E(f789(f789(f159(x58181),f789(f789(f146(x58181),x58182),x58183)),f789(f113(a863),x58184)),x58182)
% 21.40/21.37 [5925]E(x59251,f789(f789(f132(x59252),f789(f149(x59252),x59253)),f789(f789(f146(x59252),x59254),f122(x59252))))+~E(f789(f149(x59252),x59251),f789(f789(f146(x59252),x59254),x59253))
% 21.40/21.37 [6108]~P99(x61081)+E(f789(f789(f111(f870(x61081,a856)),f789(f302(x61081,x61082),x61083)),f789(f302(x61081,x61083),x61084)),f184(f870(x61081,a856)))
% 21.40/21.37 [6143]~P4(x61431)+E(f789(f161(x61431),f789(f789(f150(a1,x61431),x61432),f167(x61433,x61434))),f789(f789(f8(a1,x61431),x61432),f789(f163(a1),f167(x61433,x61434))))
% 21.40/21.37 [6144]~P4(x61441)+E(f789(f789(f8(a1,x61441),x61442),f789(f163(a1),f167(x61443,x61444))),f789(f161(x61441),f789(f789(f150(a1,x61441),x61442),f167(x61443,x61444))))
% 21.40/21.37 [6288]~E(x62882,f789(f789(f132(x62881),f789(f149(x62881),x62884)),f789(f789(f146(x62881),x62883),f122(x62881))))+E(f789(f149(x62881),x62882),f789(f789(f146(x62881),x62883),x62884))
% 21.40/21.37 [6304]~P23(x63042,x63043,x63044,x63041)+E(f789(x63041,f184(f870(x63042,a856))),f41(x63043))
% 21.40/21.37 [6334]~P99(x63341)+E(f789(f789(f111(f870(x63341,a856)),f306(x63341,x63342,x63343)),f789(f302(x63341,x63343),x63344)),f184(f870(x63341,a856)))
% 21.40/21.37 [6420]~P39(x64201,x64202,x64204,x64203)+P1(f789(f789(f191(x64201),x64202),x64203))
% 21.40/21.37 [6421]~P39(x64211,x64212,x64214,x64213)+P1(f789(f789(f191(x64211),x64212),x64213))
% 21.40/21.37 [6553]E(x65531,f184(f870(x65532,a856)))+~E(f322(x65533,x65532,x65534,x65531),f184(f870(f871(x65533,x65532),a856)))
% 21.40/21.37 [6554]E(x65541,f184(f870(x65542,a856)))+~E(f322(x65542,x65543,x65541,x65544),f184(f870(f871(x65542,x65543),a856)))
% 21.40/21.37 [6633]~P1(f789(f255(x66333,x66334,x66331),x66332))+P1(f789(f789(x66331,f601(x66332,x66331)),x66332))
% 21.40/21.37 [6663]E(f789(f113(a863),x66631),f2(a863))+E(f789(f789(f159(x66632),f789(f789(f146(x66632),x66633),x66634)),f789(f113(a863),x66631)),f789(f789(f159(x66632),x66634),f789(f789(f3(a863),f789(f113(a863),x66631)),f87(a863))))
% 21.40/21.37 [6681]~P1(f789(f70(x66812),x66814))+P1(f789(f70(x66811),f789(f311(x66812,x66811,x66813),x66814)))
% 21.40/21.37 [6921]~P29(x69212,x69211,x69213,x69214)+E(f789(f49(x69211),f789(f311(x69212,x69211,x69213),x69214)),f789(f49(x69212),x69214))
% 21.40/21.37 [6941]E(f789(f311(x69411,x69412,x69413),f789(f313(x69411,x69412,x69413),x69414)),x69414)+~E(f789(f311(x69411,x69412,x69413),f247(f870(x69411,a856))),f247(f870(x69412,a856)))
% 21.40/21.37 [7367]~P29(x73671,x73672,x73673,f247(f870(x73671,a856)))+E(f789(f313(x73671,x73672,x73673),f789(f311(x73671,x73672,x73673),x73674)),x73674)
% 21.40/21.37 [7816]~P1(f789(f789(f342(f864(x78161)),f789(f789(f146(x78161),x78162),x78164)),f156(x78161,x78163)))+P1(f789(f789(f342(x78161),x78162),x78163))
% 21.40/21.37 [7943]~P1(f789(f789(f342(x79431),x79432),f789(f163(x79431),f158(x79431,x79434,x79433))))+P1(f789(f789(f342(x79431),x79432),f789(f163(x79431),x79433)))
% 21.40/21.37 [7944]~P1(f789(f789(f342(x79441),x79442),f789(f163(x79441),f165(x79441,x79443,x79444))))+P1(f789(f789(f342(x79441),x79442),f789(f163(x79441),x79443)))
% 21.40/21.37 [7945]~P1(f789(f789(f342(x79451),x79452),f789(f163(x79451),f165(x79451,x79453,x79454))))+P1(f789(f789(f342(x79451),x79452),f789(f163(x79451),x79453)))
% 21.40/21.37 [8239]~P4(x82391)+E(f789(f789(f8(a863,x82391),f789(f789(f10(a863,x82391,a863),x82392),a121)),f789(f302(a863,x82393),x82394)),f789(f789(f8(a863,x82391),x82392),f789(f302(a863,f789(a121,x82393)),f789(a121,x82394))))
% 21.40/21.37 [8248]~P4(x82481)+E(f789(f789(f8(a863,x82481),f789(f789(f10(a863,x82481,a863),x82482),a121)),f303(a863,x82483,x82484)),f789(f789(f8(a863,x82481),x82482),f303(a863,f789(a121,x82483),f789(a121,x82484))))
% 21.40/21.37 [8381]~P29(x83811,x83813,x83814,f247(f870(x83811,a856)))+P29(x83811,f870(x83812,x83813),f789(f789(f10(x83813,f870(x83812,x83813),x83811),f18(x83813,x83812)),x83814),f247(f870(x83811,a856)))
% 21.40/21.37 [8471]~P29(x84712,x84711,x84714,x84713)+E(f789(f311(x84711,x84712,f86(x84712,x84711,x84713,x84714)),f789(f311(x84712,x84711,x84714),x84713)),x84713)
% 21.40/21.37 [8532]~P1(f789(f789(f342(f869(x85321,x85321)),f789(f789(f249(x85321,x85321),x85322),x85324)),f268(x85321,x85323)))+P1(f789(f789(f342(x85321),x85322),x85323))
% 21.40/21.37 [8607]E(f789(f789(f789(f81(x86071,f867(x86072)),f789(f18(f867(x86072),x86071),f187(x86072))),x86073),f789(f234(x86072),f534(x86073,x86074,x86072,x86071))),x86074)+~E(f173(x86071,x86072,x86074),f789(f789(f310(x86071),x86073),f184(f870(x86071,a856))))
% 21.40/21.37 [8726]~E(f789(f789(f8(x87261,a863),x87264),x87263),f789(a121,x87262))+P1(f789(f789(f342(x87261),f624(x87262,x87263,x87264,x87261)),x87263))
% 21.40/21.37 [8742]~E(f789(f789(f8(x87424,a863),x87421),x87423),f789(a121,x87422))+P1(f789(f789(f241(a863),f2(a863)),f789(x87421,f624(x87422,x87423,x87421,x87424))))
% 21.40/21.37 [8752]~P1(f789(f70(x87522),x87524))+P1(f789(f789(f240(a863),f789(f49(x87521),f789(f311(x87522,x87521,x87523),x87524))),f789(f49(x87522),x87524)))
% 21.40/21.37 [8753]E(f789(f789(f249(x87531,x87532),f714(x87533,x87534,x87532,x87531)),f715(x87533,x87534,x87532,x87531)),x87534)+~P1(f789(f789(f342(f869(x87531,x87532)),x87534),f789(f286(x87532,x87531),x87533)))
% 21.40/21.37 [8762]P29(x87621,x87622,x87623,x87624)+P1(f789(f789(f342(x87621),f462(x87624,x87623,x87622,x87621)),x87624))
% 21.40/21.37 [8763]P29(x87631,x87632,x87633,x87634)+P1(f789(f789(f342(x87631),f464(x87634,x87633,x87632,x87631)),x87634))
% 21.40/21.37 [8816]P16(x88161,x88162,x88163,x88164)+P1(f789(f789(f342(f869(x88161,x88161)),f416(x88164,x88163,x88162,x88161)),x88163))
% 21.40/21.37 [8866]P1(f789(x88661,x88662))+~P1(f789(x88661,f789(f789(f249(x88663,x88664),f849(x88664,x88663,x88661)),f850(x88664,x88663,x88661))))
% 21.40/21.37 [8878]E(f789(f185(f864(x88781)),x88782),f789(f185(f864(x88781)),x88783))+~P1(f789(f789(f342(f869(f864(x88781),f864(x88781))),f789(f789(f249(f864(x88781),f864(x88781)),x88782),x88783)),f141(x88781,x88784)))
% 21.40/21.37 [8879]E(f789(f185(f864(x88791)),x88792),f789(f185(f864(x88791)),x88793))+~P1(f789(f789(f342(f869(f864(x88791),f864(x88791))),f789(f789(f249(f864(x88791),f864(x88791)),x88792),x88793)),f154(x88791,x88794)))
% 21.40/21.37 [8880]E(f789(f185(f864(x88801)),x88802),f789(f185(f864(x88801)),x88803))+~P1(f789(f789(f342(f869(f864(x88801),f864(x88801))),f789(f789(f249(f864(x88801),f864(x88801)),x88802),x88803)),f154(x88801,x88804)))
% 21.40/21.37 [8881]E(f789(f185(f864(x88811)),x88812),f789(f185(f864(x88811)),x88813))+~P1(f789(f789(f342(f869(f864(x88811),f864(x88811))),f789(f789(f249(f864(x88811),f864(x88811)),x88812),x88813)),f154(x88811,x88814)))
% 21.40/21.37 [8882]E(f789(f185(f864(x88821)),x88822),f789(f185(f864(x88821)),x88823))+~P1(f789(f789(f342(f869(f864(x88821),f864(x88821))),f789(f789(f249(f864(x88821),f864(x88821)),x88822),x88823)),f153(x88821,x88824)))
% 21.40/21.37 [8954]P1(f789(f789(f240(a863),f151(x89541,x89542,x89543)),f151(x89541,x89544,x89543)))+P1(f789(f789(f342(x89541),f772(x89544,x89542,x89543,x89541)),f789(f163(x89541),x89543)))
% 21.40/21.37 [8955]E(f789(f185(f864(x89551)),x89552),f789(f185(f864(x89551)),x89553))+~P1(f789(f789(f342(f869(f864(x89551),f864(x89551))),f789(f789(f249(f864(x89551),f864(x89551)),x89552),x89553)),f308(f864(x89551),f153(x89551,x89554))))
% 21.40/21.37 [9067]P1(f789(f789(f287(a863),x90671),x90672))+P1(f789(f789(f240(f870(a863,a856)),f290(a863,f287(a863),x90671,x90672)),f290(a863,f287(a863),x90673,x90674)))
% 21.40/21.37 [9177]~P29(x91771,x91772,x91773,x91774)+~P1(f789(f789(f241(a863),f789(f49(x91772),f789(f311(x91771,x91772,x91773),x91774))),f789(f49(x91771),x91774)))
% 21.40/21.37 [9206]~P1(f789(f789(f342(f869(f864(x92061),f864(x92061))),f789(f789(f249(f864(x92061),f864(x92061)),x92062),x92063)),f153(x92061,x92064)))+P1(f789(f789(f342(f869(f864(x92061),f864(x92061))),f789(f789(f249(f864(x92061),f864(x92061)),x92062),x92063)),f154(x92061,f308(x92061,x92064))))
% 21.40/21.37 [9209]~P1(f789(f789(f342(f869(f864(x92091),f864(x92091))),f789(f789(f249(f864(x92091),f864(x92091)),x92092),x92093)),f154(x92091,x92094)))+P1(f789(f789(f342(f869(f864(x92091),f864(x92091))),f789(f789(f249(f864(x92091),f864(x92091)),x92092),x92093)),f308(f864(x92091),f153(x92091,x92094))))
% 21.40/21.37 [9223]P1(f789(f789(f342(f869(x92231,x92231)),f789(f789(f249(x92231,x92231),x92232),x92233)),f308(x92231,x92234)))+~P1(f789(f789(f342(f869(x92231,x92231)),f789(f789(f249(x92231,x92231),x92232),x92233)),f789(f789(f289(x92231,x92231,x92231),x92234),f308(x92231,x92234))))
% 21.40/21.37 [9290]P1(f789(f789(f287(a863),x92901),x92902))+~P1(f789(f789(f241(f870(a863,a856)),f290(a863,f287(a863),x92903,x92904)),f290(a863,f287(a863),x92901,x92902)))
% 21.40/21.37 [9403]E(f789(f789(f132(x94031),f757(x94032,x94033,x94034,x94031)),f789(f789(f146(x94031),f758(x94032,x94033,x94034,x94031)),f760(x94032,x94033,x94034,x94031))),x94034)+~P1(f789(f789(f342(f869(f864(x94031),f864(x94031))),f789(f789(f249(f864(x94031),f864(x94031)),x94034),x94033)),f153(x94031,x94032)))
% 21.40/21.37 [9404]E(f789(f789(f132(x94041),f757(x94042,x94043,x94044,x94041)),f789(f789(f146(x94041),f759(x94042,x94043,x94044,x94041)),f760(x94042,x94043,x94044,x94041))),x94043)+~P1(f789(f789(f342(f869(f864(x94041),f864(x94041))),f789(f789(f249(f864(x94041),f864(x94041)),x94044),x94043)),f153(x94041,x94042)))
% 21.40/21.37 [9478]P1(f789(f789(f342(f869(x94781,x94781)),f789(f789(f249(x94781,x94781),x94782),f698(x94783,x94784,x94782,x94781))),f308(x94781,x94783)))+~P1(f789(f789(f342(f869(x94781,x94781)),f789(f789(f249(x94781,x94781),x94782),x94784)),f789(f789(f289(x94781,x94781,x94781),x94783),f308(x94781,x94783))))
% 21.40/21.37 [9546]P1(f789(f789(f240(a863),f151(x95461,x95462,x95463)),f151(x95461,x95464,x95463)))+~P1(f789(f789(f241(a863),f789(x95462,f772(x95464,x95462,x95463,x95461))),f789(x95464,f772(x95464,x95462,x95463,x95461))))
% 21.40/21.37 [9615]P1(f789(f789(f342(f869(x96151,x96151)),f789(f789(f249(x96151,x96151),f690(x96152,x96153,x96154,x96151)),x96153)),f308(x96151,x96152)))+~P1(f789(f789(f342(f869(x96151,x96151)),f789(f789(f249(x96151,x96151),x96154),x96153)),f789(f789(f289(x96151,x96151,x96151),x96152),f308(x96151,x96152))))
% 21.40/21.37 [5145]~E(x51452,x51453)+E(f158(x51451,x51452,f789(f789(f146(x51451),x51453),x51454)),x51454)
% 21.40/21.37 [5159]~E(x51592,f2(a863))+E(f789(f789(f164(x51591),x51592),f789(f789(f146(x51591),x51593),x51594)),f122(x51591))
% 21.40/21.37 [5329]~P83(x53292)+E(f789(f789(f88(f870(x53291,x53292)),x53293),x53294),f789(f88(x53292),f789(x53293,x53294)))
% 21.40/21.37 [5330]~P83(x53302)+E(f789(f789(f88(f870(x53301,x53302)),x53303),x53304),f789(f88(x53302),f789(x53303,x53304)))
% 21.40/21.37 [5342]~E(x53422,f2(a863))+E(f789(f789(f135(x53421),x53422),f789(f789(f146(x53421),x53423),x53424)),f789(f789(f146(x53421),x53423),x53424))
% 21.40/21.37 [5343]P1(f789(x53432,x53433))+E(f789(f133(x53431,x53432),f789(f789(f146(x53431),x53433),x53434)),f789(f133(x53431,x53432),x53434))
% 21.40/21.37 [5478]~E(x54782,x54784)+P1(f789(f789(f789(f310(x54781),x54782),x54783),x54784))
% 21.40/21.37 [5486]E(x54861,f122(x54862))+E(f140(x54863,f789(f789(f150(x54862,x54863),x54864),x54861)),f789(x54864,f140(x54862,x54861)))
% 21.40/21.37 [5497]~E(x54971,f72(x54972,x54974))+E(f789(x54971,f789(f789(f310(x54972),x54973),f184(f870(x54972,a856)))),x54973)
% 21.40/21.37 [5512]~E(f789(f113(a863),x55122),f2(a863))+E(f789(f789(f164(x55121),f789(f113(a863),x55122)),f789(f789(f146(x55121),x55123),x55124)),f122(x55121))
% 21.40/21.37 [5531]E(x55311,f122(x55312))+E(f789(f137(x55313),f789(f789(f150(x55312,x55313),x55314),x55311)),f789(x55314,f789(f137(x55312),x55311)))
% 21.40/21.37 [5629]~P1(f789(x56293,x56294))+P1(f789(f789(f789(f310(x56291),x56292),x56293),x56294))
% 21.40/21.37 [5736]~E(f789(f113(a863),x57362),f2(a863))+E(f789(f789(f135(x57361),f789(f113(a863),x57362)),f789(f789(f146(x57361),x57363),x57364)),f789(f789(f146(x57361),x57363),x57364))
% 21.40/21.37 [5754]~P22(x57542,x57544,x57541)+E(f789(x57541,f789(f789(f310(x57542),x57543),f184(f870(x57542,a856)))),x57543)
% 21.40/21.37 [5778]~E(x57782,x57783)+P1(f789(f789(f342(x57781),x57782),f789(f789(f310(x57781),x57783),x57784)))
% 21.40/21.37 [5779]~E(x57792,x57793)+P1(f789(f789(f342(x57791),x57792),f789(f789(f310(x57791),x57793),x57794)))
% 21.40/21.37 [5783]~P70(x57831)+E(f789(f789(f89(x57831),x57832),f789(f789(f89(x57831),x57833),x57834)),f789(f789(f89(x57831),x57833),f789(f789(f89(x57831),x57832),x57834)))
% 21.40/21.37 [5784]~P70(x57841)+E(f789(f789(f90(x57841),x57842),f789(f789(f90(x57841),x57843),x57844)),f789(f789(f90(x57841),x57843),f789(f789(f90(x57841),x57842),x57844)))
% 21.40/21.37 [5785]~P101(x57851)+E(f789(f789(f244(x57851),x57852),f789(f789(f244(x57851),x57853),x57854)),f789(f789(f244(x57851),x57853),f789(f789(f244(x57851),x57852),x57854)))
% 21.40/21.37 [5786]~P101(x57861)+E(f789(f789(f244(x57861),x57862),f789(f789(f244(x57861),x57863),x57864)),f789(f789(f244(x57861),x57863),f789(f789(f244(x57861),x57862),x57864)))
% 21.40/21.37 [5787]~P101(x57871)+E(f789(f789(f239(x57871),x57872),f789(f789(f239(x57871),x57873),x57874)),f789(f789(f239(x57871),x57873),f789(f789(f239(x57871),x57872),x57874)))
% 21.40/21.37 [5788]~P101(x57881)+E(f789(f789(f239(x57881),x57882),f789(f789(f239(x57881),x57883),x57884)),f789(f789(f239(x57881),x57883),f789(f789(f239(x57881),x57882),x57884)))
% 21.40/21.37 [5789]~P94(x57891)+E(f789(f789(f110(x57891),x57892),f789(f789(f110(x57891),x57893),x57894)),f789(f789(f110(x57891),x57893),f789(f789(f110(x57891),x57892),x57894)))
% 21.40/21.37 [5790]~P94(x57901)+E(f789(f789(f110(x57901),x57902),f789(f789(f110(x57901),x57903),x57904)),f789(f789(f110(x57901),x57903),f789(f789(f110(x57901),x57902),x57904)))
% 21.40/21.37 [5791]~P95(x57911)+E(f789(f789(f110(x57911),x57912),f789(f789(f110(x57911),x57913),x57914)),f789(f789(f110(x57911),x57913),f789(f789(f110(x57911),x57912),x57914)))
% 21.40/21.37 [5792]~P95(x57921)+E(f789(f789(f111(x57921),x57922),f789(f789(f111(x57921),x57923),x57924)),f789(f789(f111(x57921),x57923),f789(f789(f111(x57921),x57922),x57924)))
% 21.40/21.37 [5793]~P98(x57931)+E(f789(f789(f111(x57931),x57932),f789(f789(f111(x57931),x57933),x57934)),f789(f789(f111(x57931),x57933),f789(f789(f111(x57931),x57932),x57934)))
% 21.40/21.37 [5794]~P98(x57941)+E(f789(f789(f111(x57941),x57942),f789(f789(f111(x57941),x57943),x57944)),f789(f789(f111(x57941),x57943),f789(f789(f111(x57941),x57942),x57944)))
% 21.40/21.37 [5801]E(x58011,x58012)+E(f158(x58013,x58011,f789(f789(f146(x58013),x58012),x58014)),f789(f789(f146(x58013),x58012),f158(x58013,x58011,x58014)))
% 21.40/21.37 [5816]~P1(f789(x58162,x58163))+E(f789(f133(x58161,x58162),f789(f789(f146(x58161),x58163),x58164)),f789(f789(f146(x58161),x58163),f789(f133(x58161,x58162),x58164)))
% 21.40/21.37 [5901]~E(x59014,f184(f870(x59011,a856)))+E(f789(f311(x59011,x59012,f789(f18(x59012,x59011),x59013)),x59014),f184(f870(x59012,a856)))
% 21.40/21.37 [5998]P28(x59981,x59982,x59983)+~P28(x59981,x59982,f789(f789(f310(f862(x59981)),x59984),x59983))
% 21.40/21.37 [6011]E(x60111,f184(f870(x60112,a856)))+E(f789(f789(f53(x60112,f870(x60113,a856)),x60111),f789(f18(f870(x60113,a856),x60112),x60114)),x60114)
% 21.40/21.37 [6012]E(x60121,f184(f870(x60122,a856)))+E(f789(f789(f54(x60122,f870(x60123,a856)),x60121),f789(f18(f870(x60123,a856),x60122),x60124)),x60124)
% 21.40/21.37 [6021]~E(x60214,f184(f870(x60212,a856)))+E(f789(f789(f256(x60211,x60212),x60213),f789(f18(f870(x60212,a856),x60211),x60214)),f184(f870(f869(x60211,x60212),a856)))
% 21.40/21.37 [6022]~E(x60223,f184(f870(x60221,a856)))+E(f789(f789(f256(x60221,x60222),x60223),f789(f18(f870(x60222,a856),x60221),x60224)),f184(f870(f869(x60221,x60222),a856)))
% 21.40/21.37 [6075]E(x60751,f2(a863))+E(f789(f789(f135(x60752),x60751),f789(f789(f146(x60752),x60753),x60754)),f789(f789(f135(x60752),f789(f789(f3(a863),x60751),f87(a863))),x60754))
% 21.40/21.37 [6101]E(x61011,f184(f870(x61012,a856)))+E(f789(f311(x61012,x61013,f789(f18(x61013,x61012),x61014)),x61011),f789(f789(f310(x61013),x61014),f184(f870(x61013,a856))))
% 21.40/21.37 [6104]E(f789(f313(x61041,x61042,f789(f18(x61042,x61041),x61043)),x61044),f184(f870(x61041,a856)))+P1(f789(f789(f342(x61042),x61043),x61044))
% 21.40/21.37 [6169]~E(x61693,f184(f870(x61691,a856)))+E(f789(f789(f53(x61691,f870(x61692,a856)),x61693),f789(f18(f870(x61692,a856),x61691),x61694)),f184(f870(x61692,a856)))
% 21.40/21.37 [6170]~E(x61703,f184(f870(x61701,a856)))+E(f789(f789(f54(x61701,f870(x61702,a856)),x61703),f789(f18(f870(x61702,a856),x61701),x61704)),f247(f870(x61702,a856)))
% 21.40/21.37 [6172]~P7(x61721)+E(f59(x61721,f789(f789(f90(x61721),x61722),x61723),f789(f789(f90(x61721),x61722),x61724)),f789(f789(f90(x61721),x61722),f59(x61721,x61723,x61724)))
% 21.40/21.37 [6344]E(f789(f313(x63441,x63442,f789(f18(x63442,x63441),x63443)),x63444),f247(f870(x63441,a856)))+~P1(f789(f789(f342(x63442),x63443),x63444))
% 21.40/21.37 [6365]~P1(f789(f789(f342(x63651),x63652),x63654))+P1(f789(f789(f342(x63651),x63652),f789(f789(f310(x63651),x63653),x63654)))
% 21.40/21.37 [6366]~P1(f789(f789(f342(x63661),x63662),x63664))+P1(f789(f789(f342(x63661),x63662),f789(f789(f310(x63661),x63663),x63664)))
% 21.40/21.37 [6367]~P1(f789(f789(f342(x63671),x63672),x63674))+P1(f789(f789(f342(x63671),x63672),f789(f789(f310(x63671),x63673),x63674)))
% 21.40/21.37 [6380]~E(x63803,f789(f789(f3(a863),f789(f185(f864(x63801)),x63802)),f87(a863)))+E(f123(x63801,f789(f789(f155(x63801,x63802),x63803),x63804)),f123(x63801,x63802))
% 21.40/21.37 [6405]~P101(x64051)+E(f789(f789(f111(f870(x64051,a856)),f789(f301(x64051),x64052)),f303(x64051,x64053,x64054)),f303(x64051,x64053,f789(f789(f244(x64051),x64052),x64054)))
% 21.40/21.37 [6406]~P101(x64061)+E(f789(f789(f111(f870(x64061,a856)),f789(f266(x64061),x64062)),f303(x64061,x64063,x64064)),f303(x64061,f789(f789(f239(x64061),x64062),x64063),x64064))
% 21.40/21.37 [6422]E(f789(f789(f111(f870(x64221,a856)),x64222),f789(f789(f310(x64221),x64223),x64224)),f789(f789(f111(f870(x64221,a856)),x64222),x64224))+P1(f789(f789(f342(x64221),x64223),x64222))
% 21.40/21.37 [6423]E(f789(f789(f111(f870(x64231,a856)),x64232),f789(f789(f310(x64231),x64233),x64234)),f789(f789(f111(f870(x64231,a856)),x64232),x64234))+P1(f789(f789(f342(x64231),x64233),x64232))
% 21.40/21.37 [6435]E(f158(x64351,x64352,f789(f789(f132(x64351),x64353),x64354)),f789(f789(f132(x64351),x64353),f158(x64351,x64352,x64354)))+P1(f789(f789(f342(x64351),x64352),f789(f163(x64351),x64353)))
% 21.40/21.37 [6439]~P78(x64391)+E(f789(f789(f90(x64391),f789(f789(f250(x64391),x64392),x64393)),f789(f789(f250(x64391),x64392),x64394)),f789(f789(f250(x64391),x64392),f789(f789(f89(a863),x64393),x64394)))
% 21.40/21.37 [6440]~P70(x64401)+E(f789(f789(f90(x64401),f789(f789(f250(x64401),x64402),x64403)),f789(f789(f250(x64401),x64402),x64404)),f789(f789(f250(x64401),x64402),f789(f789(f89(a863),x64403),x64404)))
% 21.40/21.37 [6476]~P70(x64761)+E(f789(f789(f89(x64761),f789(f789(f90(x64761),x64762),x64763)),f789(f789(f90(x64761),x64762),x64764)),f789(f789(f90(x64761),x64762),f789(f789(f89(x64761),x64763),x64764)))
% 21.40/21.37 [6477]~P101(x64771)+E(f789(f789(f239(x64771),f789(f789(f244(x64771),x64772),x64773)),f789(f789(f244(x64771),x64772),x64774)),f789(f789(f244(x64771),x64772),f789(f789(f239(x64771),x64773),x64774)))
% 21.40/21.37 [6478]~P101(x64781)+E(f789(f789(f244(x64781),f789(f789(f239(x64781),x64782),x64783)),f789(f789(f239(x64781),x64782),x64784)),f789(f789(f239(x64781),x64782),f789(f789(f244(x64781),x64783),x64784)))
% 21.40/21.37 [6479]~P96(x64791)+E(f789(f789(f111(x64791),f789(f789(f110(x64791),x64792),x64793)),f789(f789(f110(x64791),x64792),x64794)),f789(f789(f110(x64791),x64792),f789(f789(f111(x64791),x64793),x64794)))
% 21.40/21.37 [6480]~P96(x64801)+E(f789(f789(f110(x64801),f789(f789(f111(x64801),x64802),x64803)),f789(f789(f111(x64801),x64802),x64804)),f789(f789(f111(x64801),x64802),f789(f789(f110(x64801),x64803),x64804)))
% 21.40/21.37 [6516]~P7(x65161)+E(f59(x65161,f789(f789(f90(x65161),x65162),x65163),f789(f789(f90(x65161),x65164),x65163)),f789(f789(f90(x65161),f59(x65161,x65162,x65164)),x65163))
% 21.40/21.37 [6519]~E(f789(f185(f864(x65191)),x65193),f789(f185(f864(x65192)),x65194))+E(f789(f789(f150(f869(x65191,x65192),x65192),f258(x65191,x65192)),f789(f789(f171(x65191,x65192),x65193),x65194)),x65194)
% 21.40/21.37 [6520]~E(f789(f185(f864(x65201)),x65203),f789(f185(f864(x65202)),x65204))+E(f789(f789(f150(f869(x65201,x65202),x65201),f248(x65201,x65202)),f789(f789(f171(x65201,x65202),x65203),x65204)),x65203)
% 21.40/21.37 [6530]~P7(x65301)+E(f59(x65301,f789(f789(f89(x65301),x65302),f59(x65301,x65303,x65304)),x65304),f59(x65301,f789(f789(f89(x65301),x65302),x65303),x65304))
% 21.40/21.37 [6531]~P7(x65311)+E(f59(x65311,f789(f789(f90(x65311),x65312),f59(x65311,x65313,x65314)),x65314),f59(x65311,f789(f789(f90(x65311),x65312),x65313),x65314))
% 21.40/21.37 [6532]~P8(x65321)+E(f59(x65321,f789(f789(f3(x65321),x65322),f59(x65321,x65323,x65324)),x65324),f59(x65321,f789(f789(f3(x65321),x65322),x65323),x65324))
% 21.40/21.37 [6533]~P7(x65331)+E(f59(x65331,f789(f789(f89(x65331),x65332),f59(x65331,x65333,x65334)),x65334),f59(x65331,f789(f789(f89(x65331),x65332),x65333),x65334))
% 21.40/21.37 [6616]~P101(x66161)+E(f789(f789(f111(f870(x66161,a856)),f303(x66161,x66162,x66163)),f789(f301(x66161),x66164)),f303(x66161,x66162,f789(f789(f244(x66161),x66163),x66164)))
% 21.40/21.37 [6617]~P101(x66171)+E(f789(f789(f111(f870(x66171,a856)),f303(x66171,x66172,x66173)),f789(f266(x66171),x66174)),f303(x66171,f789(f789(f239(x66171),x66172),x66174),x66173))
% 21.40/21.37 [6620]~E(f789(f185(f864(x66201)),x66203),f789(f185(f864(x66202)),x66204))+E(f789(f789(f171(x66201,x66202),f789(f149(x66201),x66203)),f789(f149(x66202),x66204)),f789(f149(f869(x66201,x66202)),f789(f789(f171(x66201,x66202),x66203),x66204)))
% 21.40/21.37 [6629]E(x66291,f789(f789(f3(a863),f789(f185(f864(x66292)),x66293)),f87(a863)))+E(f123(x66292,f789(f789(f155(x66292,x66293),x66291),x66294)),f789(f789(f155(x66292,f123(x66292,x66293)),x66291),x66294))
% 21.40/21.37 [6646]~P1(f789(f134(x66462),x66464))+P1(f789(f134(f869(x66461,x66462)),f789(f789(f171(x66461,x66462),x66463),x66464)))
% 21.40/21.37 [6647]~P1(f789(f134(x66471),x66473))+P1(f789(f134(f869(x66471,x66472)),f789(f789(f171(x66471,x66472),x66473),x66474)))
% 21.40/21.37 [6745]E(x67451,f789(f789(f789(a193,x67452),x67453),f789(x67454,x67452)))+~P1(f789(f789(f191(f30(x67453,x67454)),x67452),x67451))
% 21.40/21.37 [6924]E(f789(f789(f50(a863),x69241),x69242),x69243)+~P1(f789(f62(x69241,x69242),f789(f789(f249(a863,a863),x69243),x69244)))
% 21.40/21.37 [6950]E(f59(a863,x69501,x69502),x69503)+~P1(f789(f62(x69501,x69502),f789(f789(f249(a863,a863),x69504),x69503)))
% 21.40/21.37 [6953]P1(f789(f134(x69531),x69532))+~P1(f789(f134(x69533),f789(f789(f150(x69531,x69533),x69534),x69532)))
% 21.40/21.37 [6961]~P28(x69611,x69612,f789(f789(f310(f862(x69611)),x69613),x69614))+P28(x69611,x69612,f789(f789(f310(f862(x69611)),x69613),f184(f870(f862(x69611),a856))))
% 21.40/21.37 [7033]E(f158(x70331,x70332,f789(f789(f132(x70331),x70333),x70334)),f789(f789(f132(x70331),f158(x70331,x70332,x70333)),x70334))+~P1(f789(f789(f342(x70331),x70332),f789(f163(x70331),x70333)))
% 21.40/21.37 [7101]E(f789(f113(a863),x71011),f2(a863))+E(f789(f789(f135(x71012),f789(f113(a863),x71011)),f789(f789(f146(x71012),x71013),x71014)),f789(f789(f135(x71012),f789(f789(f3(a863),f789(f113(a863),x71011)),f87(a863))),x71014))
% 21.40/21.37 [7127]~P7(x71271)+E(f59(x71271,f789(f789(f89(x71271),f59(x71271,x71272,x71273)),x71274),x71273),f59(x71271,f789(f789(f89(x71271),x71272),x71274),x71273))
% 21.40/21.37 [7128]~P7(x71281)+E(f59(x71281,f789(f789(f90(x71281),f59(x71281,x71282,x71283)),x71284),x71283),f59(x71281,f789(f789(f90(x71281),x71282),x71284),x71283))
% 21.40/21.37 [7129]~P8(x71291)+E(f59(x71291,f789(f789(f3(x71291),f59(x71291,x71292,x71293)),x71294),x71293),f59(x71291,f789(f789(f3(x71291),x71292),x71294),x71293))
% 21.40/21.37 [7130]~P7(x71301)+E(f59(x71301,f789(f789(f89(x71301),f59(x71301,x71302,x71303)),x71304),x71303),f59(x71301,f789(f789(f89(x71301),x71302),x71304),x71303))
% 21.40/21.37 [7131]~P7(x71311)+E(f59(x71311,f789(f789(f90(x71311),f59(x71311,x71312,x71313)),x71314),x71313),f59(x71311,f789(f789(f90(x71311),x71312),x71314),x71313))
% 21.40/21.37 [7337]~E(x73371,f789(f789(f146(x73372),x73373),x73374))+~P1(f789(f789(f240(a863),f789(f185(f864(x73372)),x73371)),f789(f185(f864(x73372)),x73374)))
% 21.40/21.37 [7509]~E(f170(x75091,x75092,x75093),f170(x75091,x75092,x75094))+E(f789(f311(f869(x75091,x75092),x75091,f248(x75091,x75092)),f789(f163(f869(x75091,x75092)),x75093)),f789(f311(f869(x75091,x75092),x75091,f248(x75091,x75092)),f789(f163(f869(x75091,x75092)),x75094)))
% 21.40/21.37 [7552]P29(x75521,x75522,x75523,f789(f163(x75521),x75524))+~P1(f789(f134(x75522),f789(f789(f150(x75521,x75522),x75523),x75524)))
% 21.40/21.37 [7629]~P1(f789(f789(f240(f870(x76291,a856)),x76292),x76294))+P1(f789(f789(f240(f870(x76291,a856)),x76292),f789(f789(f310(x76291),x76293),x76294)))
% 21.40/21.37 [7664]~P7(x76641)+E(f59(x76641,f789(f789(f89(x76641),f59(x76641,x76642,x76643)),f59(x76641,x76644,x76643)),x76643),f59(x76641,f789(f789(f89(x76641),x76642),x76644),x76643))
% 21.40/21.37 [7665]~P7(x76651)+E(f59(x76651,f789(f789(f90(x76651),f59(x76651,x76652,x76653)),f59(x76651,x76654,x76653)),x76653),f59(x76651,f789(f789(f90(x76651),x76652),x76654),x76653))
% 21.40/21.37 [7666]~P8(x76661)+E(f59(x76661,f789(f789(f3(x76661),f59(x76661,x76662,x76663)),f59(x76661,x76664,x76663)),x76663),f59(x76661,f789(f789(f3(x76661),x76662),x76664),x76663))
% 21.40/21.37 [7766]~E(f789(x77664,f414(x77664,x77663,x77661,x77662)),f184(f870(x77662,a856)))+E(f789(f789(f53(x77661,f870(x77662,a856)),x77663),x77664),f184(f870(x77662,a856)))
% 21.40/21.37 [7767]~E(f789(x77674,f643(x77674,x77673,x77671,x77672)),f247(f870(x77672,a856)))+E(f789(f789(f54(x77671,f870(x77672,a856)),x77673),x77674),f247(f870(x77672,a856)))
% 21.40/21.37 [7768]~E(f789(x77684,f415(x77684,x77683,x77682,x77681)),f184(f870(x77682,a856)))+E(f789(f789(f53(x77681,f870(x77682,a856)),x77683),x77684),f184(f870(x77682,a856)))
% 21.40/21.37 [7769]~E(f789(x77694,f650(x77694,x77693,x77692,x77691)),f247(f870(x77692,a856)))+E(f789(f789(f54(x77691,f870(x77692,a856)),x77693),x77694),f247(f870(x77692,a856)))
% 21.40/21.37 [8157]P1(f789(x81571,x81572))+~P1(f789(f789(f342(x81573),x81572),f789(f789(f111(f870(x81573,a856)),x81574),f789(f264(x81573),x81571))))
% 21.40/21.37 [8196]~P1(f789(f789(f240(f870(x81961,a856)),x81963),x81964))+P1(f789(f789(f240(f870(x81961,a856)),f789(f789(f310(x81961),x81962),x81963)),f789(f789(f310(x81961),x81962),x81964)))
% 21.40/21.37 [8237]P1(f789(f789(f342(x82371),x82372),x82373))+~P1(f789(f789(f342(x82371),x82372),f789(f789(f111(f870(x82371,a856)),x82373),f789(f264(x82371),x82374))))
% 21.40/21.37 [8364]P1(f789(f789(f191(x83641),x83642),f470(x83643,x83642,x83644,x83641)))+~P1(f789(f789(f191(f38(x83641,x83644)),x83642),x83643))
% 21.40/21.37 [8365]P1(f789(f789(f191(x83651),x83652),f509(x83653,x83652,x83654,x83651)))+~P1(f789(f789(f191(f38(x83651,x83654)),x83652),x83653))
% 21.40/21.37 [8485]~P1(f789(f789(f241(a863),f789(x84854,x84852)),f789(x84854,x84853)))+P1(f789(f789(f342(f869(x84851,x84851)),f789(f789(f249(x84851,x84851),x84852),x84853)),f789(f789(f288(a863,x84851),a245),x84854)))
% 21.40/21.37 [8633]P29(f864(x86331),f864(x86332),f789(f150(x86331,x86332),x86333),x86334)+~P29(x86331,x86332,x86333,f51(f870(x86331,a856),f789(f311(f864(x86331),f870(x86331,a856),f163(x86331)),x86334)))
% 21.40/21.37 [8743]E(f789(f789(f53(x87431,f870(x87432,a856)),x87433),x87434),f184(f870(x87432,a856)))+P1(f789(f789(f342(x87431),f414(x87434,x87433,x87431,x87432)),x87433))
% 21.40/21.37 [8744]E(f789(f789(f54(x87441,f870(x87442,a856)),x87443),x87444),f247(f870(x87442,a856)))+P1(f789(f789(f342(x87441),f643(x87444,x87443,x87441,x87442)),x87443))
% 21.40/21.37 [8745]E(f789(f789(f53(x87451,f870(x87452,a856)),x87453),x87454),f184(f870(x87452,a856)))+P1(f789(f789(f342(x87451),f415(x87454,x87453,x87452,x87451)),x87453))
% 21.40/21.37 [8746]E(f789(f789(f54(x87461,f870(x87462,a856)),x87463),x87464),f247(f870(x87462,a856)))+P1(f789(f789(f342(x87461),f650(x87464,x87463,x87462,x87461)),x87463))
% 21.40/21.37 [8781]P1(f789(f789(f241(a863),f789(x87811,x87812)),f789(x87811,x87813)))+~P1(f789(f789(f342(f869(x87814,x87814)),f789(f789(f249(x87814,x87814),x87812),x87813)),f789(f789(f288(a863,x87814),a245),x87811)))
% 21.40/21.37 [8830]P1(f789(f789(f191(x88301),f470(x88302,x88303,x88301,x88304)),x88302))+~P1(f789(f789(f191(f38(x88304,x88301)),x88303),x88302))
% 21.40/21.37 [8831]P1(f789(f789(f191(x88311),f509(x88312,x88313,x88311,x88314)),x88312))+~P1(f789(f789(f191(f38(x88314,x88311)),x88313),x88312))
% 21.40/21.37 [8943]P1(f789(f789(f342(x89431),f391(x89432,x89433,x89434,x89431)),x89433))+~P1(f789(f789(f342(f870(x89431,a856)),x89434),f789(f789(f68(x89431),x89433),x89432)))
% 21.40/21.37 [8946]E(x89461,x89462)+~P1(f789(f789(f342(f869(x89463,x89463)),f789(f789(f249(x89463,x89463),x89461),x89462)),f789(f789(f178(f869(x89463,x89463),a856),f2(a863)),x89464)))
% 21.40/21.37 [9017]E(f789(f285(x90171,x90171,x90172),f789(f789(f310(x90171),f391(x90172,x90173,x90174,x90171)),f184(f870(x90171,a856)))),x90174)+~P1(f789(f789(f342(f870(x90171,a856)),x90174),f789(f789(f68(x90171),x90173),x90172)))
% 21.40/21.37 [9028]~P1(f789(f789(f342(f869(x90281,x90281)),f789(f789(f249(x90281,x90281),x90283),x90282)),f308(x90281,x90284)))+P1(f789(f789(f342(f869(x90281,x90281)),f789(f789(f249(x90281,x90281),x90282),x90283)),f308(x90281,f789(f286(x90281,x90281),x90284))))
% 21.40/21.37 [9041]~P7(x90411)+E(f789(f789(f89(x90411),f789(f789(f89(x90411),f789(f789(f90(x90411),x90412),f789(f789(f50(x90411),x90413),x90412))),f59(x90411,x90413,x90412))),x90414),f789(f789(f89(x90411),x90413),x90414))
% 21.40/21.37 [9049]~P1(f789(f789(f342(x90491),x90493),x90494))+P1(f789(f789(f342(f870(x90491,a856)),f789(f285(x90491,x90491,x90492),f789(f789(f310(x90491),x90493),f184(f870(x90491,a856))))),f789(f789(f68(x90491),x90494),x90492)))
% 21.40/21.37 [9059]P1(f789(f789(f342(f869(x90591,x90591)),f789(f789(f249(x90591,x90591),x90592),x90593)),f308(x90591,x90594)))+~P1(f789(f789(f342(f869(x90591,x90591)),f789(f789(f249(x90591,x90591),x90593),x90592)),f308(x90591,f789(f286(x90591,x90591),x90594))))
% 21.40/21.37 [9143]E(f789(f789(f155(x91431,f789(f149(x91431),x91432)),f789(f789(f3(a863),f789(f789(f3(a863),f789(f185(f864(x91431)),x91432)),x91433)),f87(a863))),x91434),f789(f149(x91431),f789(f789(f155(x91431,x91432),x91433),x91434)))+~P1(f789(f789(f241(a863),x91433),f789(f185(f864(x91431)),x91432)))
% 21.40/21.37 [9181]~P29(x91812,x91811,x91813,f247(f870(x91812,a856)))+P1(f789(f789(f240(f870(x91811,a856)),f789(f311(x91812,x91811,x91813),f789(f88(f870(x91812,a856)),x91814))),f789(f88(f870(x91811,a856)),f789(f311(x91812,x91811,x91813),x91814))))
% 21.40/21.37 [9189]~P9(x91891)+E(f789(f138(x91891,x91892,f789(f9(x91892,x91891,x91891),f789(f789(f10(x91891,f870(x91891,x91891),x91892),f110(x91891)),x91893)),f184(x91891)),x91894),f789(f789(f53(x91892,x91891),f789(f163(x91892),x91894)),x91893))
% 21.40/21.37 [9190]~P9(x91901)+E(f789(f138(x91901,x91902,f789(f9(x91902,x91901,x91901),f789(f789(f10(x91901,f870(x91901,x91901),x91902),f111(x91901)),x91903)),f247(x91901)),x91904),f789(f789(f54(x91902,x91901),f789(f163(x91902),x91904)),x91903))
% 21.40/21.37 [9253]~P1(f789(f789(f342(f869(f864(x92534),f864(x92534))),f789(f789(f249(f864(x92534),f864(x92534)),x92533),x92532)),f153(x92534,x92531)))+P1(f789(f789(f241(a863),f756(x92531,x92532,x92533,x92534)),f789(f185(f864(x92534)),x92533)))
% 21.40/21.37 [9254]~P7(x92541)+E(f789(f789(f89(x92541),f789(f789(f89(x92541),f789(f789(f90(x92541),f789(f789(f50(x92541),x92542),x92543)),x92543)),f59(x92541,x92542,x92543))),x92544),f789(f789(f89(x92541),x92542),x92544))
% 21.40/21.37 [9282]~P1(f789(f789(f342(f869(f864(x92821),f864(x92821))),f789(f789(f249(f864(x92821),f864(x92821)),x92822),x92823)),f789(f286(f864(x92821),f864(x92821)),f153(x92821,x92824))))+P1(f789(f789(f342(f869(f864(x92821),f864(x92821))),f789(f789(f249(f864(x92821),f864(x92821)),x92822),x92823)),f153(x92821,f789(f286(x92821,x92821),x92824))))
% 21.40/21.37 [9283]P1(f789(f789(f342(f869(f864(x92831),f864(x92831))),f789(f789(f249(f864(x92831),f864(x92831)),x92832),x92833)),f789(f286(f864(x92831),f864(x92831)),f153(x92831,x92834))))+~P1(f789(f789(f342(f869(f864(x92831),f864(x92831))),f789(f789(f249(f864(x92831),f864(x92831)),x92832),x92833)),f153(x92831,f789(f286(x92831,x92831),x92834))))
% 21.40/21.37 [9321]~P1(f789(f789(f342(x93211),x93213),f789(f269(x93211,x93212),x93214)))+P1(f789(f789(f342(f869(x93211,x93212)),f789(f789(f249(x93211,x93212),x93213),f607(x93214,x93212,x93213,x93211))),x93214))
% 21.40/21.37 [9322]~P1(f789(f789(f342(x93221),x93223),f789(f269(x93221,x93222),x93224)))+P1(f789(f789(f342(f869(x93221,x93222)),f789(f789(f249(x93221,x93222),x93223),f608(x93224,x93222,x93223,x93221))),x93224))
% 21.40/21.37 [9449]~P1(f789(f70(f867(x94491)),f789(f311(x94492,f867(x94491),x94493),f247(f870(x94492,a856)))))+P1(f789(f70(f867(x94491)),f789(f311(x94492,f867(x94491),f174(x94492,x94491,x94493,f170(x94492,x94491,x94494))),f247(f870(x94492,a856)))))
% 21.40/21.37 [9473]~P1(f789(f789(f342(f869(x94731,x94731)),f789(f789(f249(x94731,x94731),x94732),x94734)),f789(f789(f289(x94731,x94731,x94731),x94733),f308(x94731,x94733))))+P1(f789(f789(f342(f869(x94731,x94731)),f789(f789(f249(x94731,x94731),x94732),f690(x94733,x94734,x94732,x94731))),x94733))
% 21.40/21.37 [9640]~P1(f789(f789(f342(f869(x96402,x96401)),x96404),f789(f286(x96401,x96402),x96403)))+P1(f789(f789(f342(f869(x96401,x96402)),f789(f789(f249(x96401,x96402),f715(x96403,x96404,x96401,x96402)),f714(x96403,x96404,x96401,x96402))),x96403))
% 21.40/21.37 [9664]~P1(f789(f789(f342(f869(f864(x96641),f864(x96641))),f789(f789(f249(f864(x96641),f864(x96641)),x96644),x96643)),f153(x96641,x96642)))+P1(f789(f789(f342(f869(x96641,x96641)),f789(f789(f249(x96641,x96641),f758(x96642,x96643,x96644,x96641)),f759(x96642,x96643,x96644,x96641))),x96642))
% 21.40/21.37 [9739]~P1(f789(f789(f342(f869(f864(x97391),f864(x97391))),f789(f789(f249(f864(x97391),f864(x97391)),x97392),x97394)),f153(x97391,x97393)))+P1(f789(f789(f342(f869(x97391,x97391)),f789(f789(f249(x97391,x97391),f789(f789(f159(x97391),x97392),f756(x97393,x97394,x97392,x97391))),f750(x97393,x97394,x97392,x97391))),x97393))
% 21.40/21.37 [9761]~P1(f789(f70(x97612),x97614))+E(f789(f789(f789(f74(f870(x97611,a856),x97612,f110(f870(x97611,a856))),f789(f789(f9(x97612,f870(x97611,a856),f870(x97611,a856)),f789(f789(f10(x97611,f870(f870(x97611,a856),f870(x97611,a856)),x97612),f310(x97611)),x97613)),f184(f870(x97611,a856)))),f184(f870(x97611,a856))),x97614),f789(f311(x97612,x97611,x97613),x97614))
% 21.40/21.37 [9881]~P29(x98811,x98812,x98813,f247(f870(x98811,a856)))+P1(f789(f789(f240(f870(x98811,a856)),f789(f313(x98811,x98812,x98813),f789(f789(f310(x98812),x98814),f184(f870(x98812,a856))))),f789(f789(f310(x98811),f94(x98811,f789(f789(f9(x98811,x98812,a856),f789(f789(f10(x98812,f870(x98812,a856),x98811),a338),x98813)),x98814))),f184(f870(x98811,a856)))))
% 21.40/21.37 [5540]~E(f789(f789(f132(x55401),x55402),x55404),x55403)+E(f789(f789(f164(x55401),f789(f185(f864(x55401)),x55402)),x55403),x55402)
% 21.40/21.37 [5541]~E(f789(f789(f132(x55412),x55413),x55411),x55414)+E(x55411,f789(f789(f135(x55412),f789(f185(f864(x55412)),x55413)),x55414))
% 21.40/21.37 [5552]~E(x55524,f2(a863))+E(f789(f789(f159(x55521),f789(f789(f146(x55521),x55522),x55523)),x55524),x55522)
% 21.40/21.37 [6085]~P70(x60851)+E(f789(f789(f250(x60851),f789(f789(f250(x60851),x60852),x60853)),x60854),f789(f789(f250(x60851),x60852),f789(f789(f90(a863),x60853),x60854)))
% 21.40/21.37 [6086]~P78(x60861)+E(f789(f789(f250(x60861),f789(f789(f250(x60861),x60862),x60863)),x60864),f789(f789(f250(x60861),x60862),f789(f789(f90(a863),x60863),x60864)))
% 21.40/21.37 [6102]E(x61021,f2(a863))+E(f789(f789(f159(x61022),f789(f789(f146(x61022),x61023),x61024)),x61021),f789(f789(f159(x61022),x61024),f789(f789(f3(a863),x61021),f87(a863))))
% 21.40/21.37 [6125]~P70(x61251)+E(f789(f789(f89(x61251),f789(f789(f89(x61251),x61252),x61253)),x61254),f789(f789(f89(x61251),x61252),f789(f789(f89(x61251),x61253),x61254)))
% 21.40/21.37 [6126]~P70(x61261)+E(f789(f789(f90(x61261),f789(f789(f90(x61261),x61262),x61263)),x61264),f789(f789(f90(x61261),x61262),f789(f789(f90(x61261),x61263),x61264)))
% 21.40/21.37 [6127]~P113(x61271)+E(f789(f789(f291(x61271),f789(f789(f90(x61271),x61272),x61273)),x61274),f789(f789(f90(x61271),x61272),f789(f789(f291(x61271),x61273),x61274)))
% 21.40/21.37 [6128]~P70(x61281)+E(f789(f789(f89(x61281),f789(f789(f89(x61281),x61282),x61283)),x61284),f789(f789(f89(x61281),x61282),f789(f789(f89(x61281),x61283),x61284)))
% 21.40/21.37 [6129]~P5(x61291)+E(f789(f789(f89(x61291),f789(f789(f89(x61291),x61292),x61293)),x61294),f789(f789(f89(x61291),x61292),f789(f789(f89(x61291),x61293),x61294)))
% 21.40/21.37 [6130]~P70(x61301)+E(f789(f789(f90(x61301),f789(f789(f90(x61301),x61302),x61303)),x61304),f789(f789(f90(x61301),x61302),f789(f789(f90(x61301),x61303),x61304)))
% 21.40/21.37 [6131]~P66(x61311)+E(f789(f789(f90(x61311),f789(f789(f90(x61311),x61312),x61313)),x61314),f789(f789(f90(x61311),x61312),f789(f789(f90(x61311),x61313),x61314)))
% 21.40/21.37 [6133]~P101(x61331)+E(f789(f789(f244(x61331),f789(f789(f244(x61331),x61332),x61333)),x61334),f789(f789(f244(x61331),x61332),f789(f789(f244(x61331),x61333),x61334)))
% 21.40/21.37 [6134]~P101(x61341)+E(f789(f789(f244(x61341),f789(f789(f244(x61341),x61342),x61343)),x61344),f789(f789(f244(x61341),x61342),f789(f789(f244(x61341),x61343),x61344)))
% 21.40/21.37 [6135]~P101(x61351)+E(f789(f789(f239(x61351),f789(f789(f239(x61351),x61352),x61353)),x61354),f789(f789(f239(x61351),x61352),f789(f789(f239(x61351),x61353),x61354)))
% 21.40/21.37 [6136]~P101(x61361)+E(f789(f789(f239(x61361),f789(f789(f239(x61361),x61362),x61363)),x61364),f789(f789(f239(x61361),x61362),f789(f789(f239(x61361),x61363),x61364)))
% 21.40/21.37 [6137]~P94(x61371)+E(f789(f789(f110(x61371),f789(f789(f110(x61371),x61372),x61373)),x61374),f789(f789(f110(x61371),x61372),f789(f789(f110(x61371),x61373),x61374)))
% 21.40/21.37 [6138]~P94(x61381)+E(f789(f789(f110(x61381),f789(f789(f110(x61381),x61382),x61383)),x61384),f789(f789(f110(x61381),x61382),f789(f789(f110(x61381),x61383),x61384)))
% 21.40/21.37 [6139]~P95(x61391)+E(f789(f789(f110(x61391),f789(f789(f110(x61391),x61392),x61393)),x61394),f789(f789(f110(x61391),x61392),f789(f789(f110(x61391),x61393),x61394)))
% 21.40/21.37 [6140]~P95(x61401)+E(f789(f789(f111(x61401),f789(f789(f111(x61401),x61402),x61403)),x61404),f789(f789(f111(x61401),x61402),f789(f789(f111(x61401),x61403),x61404)))
% 21.40/21.37 [6141]~P98(x61411)+E(f789(f789(f111(x61411),f789(f789(f111(x61411),x61412),x61413)),x61414),f789(f789(f111(x61411),x61412),f789(f789(f111(x61411),x61413),x61414)))
% 21.40/21.37 [6142]~P98(x61421)+E(f789(f789(f111(x61421),f789(f789(f111(x61421),x61422),x61423)),x61424),f789(f789(f111(x61421),x61422),f789(f789(f111(x61421),x61423),x61424)))
% 21.40/21.37 [6152]~P7(x61521)+E(f59(x61521,f789(f789(f89(x61521),x61522),f789(f789(f90(x61521),x61523),x61524)),x61524),f59(x61521,x61522,x61524))
% 21.40/21.37 [6153]~P7(x61531)+E(f59(x61531,f789(f789(f89(x61531),x61532),f789(f789(f90(x61531),x61533),x61534)),x61533),f59(x61531,x61532,x61533))
% 21.40/21.37 [6289]E(f789(f789(f159(x62891),f789(f789(f164(x62891),x62892),x62893)),x62894),f789(f789(f159(x62891),x62893),x62894))+~P1(f789(f789(f241(a863),x62894),x62892))
% 21.40/21.37 [6474]~P70(x64741)+E(f789(f789(f89(x64741),f789(f789(f89(x64741),x64742),x64743)),x64744),f789(f789(f89(x64741),f789(f789(f89(x64741),x64742),x64744)),x64743))
% 21.40/21.37 [6475]~P70(x64751)+E(f789(f789(f90(x64751),f789(f789(f90(x64751),x64752),x64753)),x64754),f789(f789(f90(x64751),f789(f789(f90(x64751),x64752),x64754)),x64753))
% 21.40/21.37 [6536]~P2(x65362)+E(f789(f789(f8(x65361,x65362),f789(f18(x65362,x65361),x65363)),x65364),f789(f789(f90(x65362),f789(f109(x65362),f789(f49(x65361),x65364))),x65363))
% 21.40/21.37 [6713]E(f789(f789(f111(f870(x67131,a856)),f789(f789(f310(x67131),x67132),x67133)),x67134),f789(f789(f111(f870(x67131,a856)),x67133),x67134))+P1(f789(f789(f342(x67131),x67132),x67134))
% 21.40/21.37 [6714]E(f789(f789(f111(f870(x67141,a856)),f789(f789(f310(x67141),x67142),x67143)),x67144),f789(f789(f111(f870(x67141,a856)),x67143),x67144))+P1(f789(f789(f342(x67141),x67142),x67144))
% 21.40/21.37 [6788]~P75(x67881)+E(f789(f789(f244(x67881),f789(f789(f89(x67881),x67882),x67883)),f789(f789(f89(x67881),x67884),x67883)),f789(f789(f89(x67881),f789(f789(f244(x67881),x67882),x67884)),x67883))
% 21.40/21.37 [6789]~P75(x67891)+E(f789(f789(f239(x67891),f789(f789(f89(x67891),x67892),x67893)),f789(f789(f89(x67891),x67894),x67893)),f789(f789(f89(x67891),f789(f789(f239(x67891),x67892),x67894)),x67893))
% 21.40/21.37 [6790]~P70(x67901)+E(f789(f789(f89(x67901),f789(f789(f90(x67901),x67902),x67903)),f789(f789(f90(x67901),x67904),x67903)),f789(f789(f90(x67901),f789(f789(f89(x67901),x67902),x67904)),x67903))
% 21.40/21.37 [6791]~P103(x67911)+E(f789(f789(f89(x67911),f789(f789(f90(x67911),x67912),x67913)),f789(f789(f90(x67911),x67914),x67913)),f789(f789(f90(x67911),f789(f789(f89(x67911),x67912),x67914)),x67913))
% 21.40/21.37 [6792]~P76(x67921)+E(f789(f789(f244(x67921),f789(f789(f3(x67921),x67922),x67923)),f789(f789(f3(x67921),x67924),x67923)),f789(f789(f3(x67921),f789(f789(f244(x67921),x67922),x67924)),x67923))
% 21.40/21.37 [6793]~P76(x67931)+E(f789(f789(f239(x67931),f789(f789(f3(x67931),x67932),x67933)),f789(f789(f3(x67931),x67934),x67933)),f789(f789(f3(x67931),f789(f789(f239(x67931),x67932),x67934)),x67933))
% 21.40/21.37 [6794]~P70(x67941)+E(f789(f789(f90(x67941),f789(f789(f250(x67941),x67942),x67943)),f789(f789(f250(x67941),x67944),x67943)),f789(f789(f250(x67941),f789(f789(f90(x67941),x67942),x67944)),x67943))
% 21.40/21.37 [6795]~P69(x67951)+E(f789(f789(f90(x67951),f789(f789(f250(x67951),x67952),x67953)),f789(f789(f250(x67951),x67954),x67953)),f789(f789(f250(x67951),f789(f789(f90(x67951),x67952),x67954)),x67953))
% 21.40/21.37 [6796]~P60(x67961)+E(f789(f789(f291(x67961),f789(f789(f250(x67961),x67962),x67963)),f789(f789(f250(x67961),x67964),x67963)),f789(f789(f250(x67961),f789(f789(f291(x67961),x67962),x67964)),x67963))
% 21.40/21.37 [6797]~P113(x67971)+E(f789(f789(f89(x67971),f789(f789(f291(x67971),x67972),x67973)),f789(f789(f291(x67971),x67974),x67973)),f789(f789(f291(x67971),f789(f789(f89(x67971),x67972),x67974)),x67973))
% 21.40/21.37 [6798]~P113(x67981)+E(f789(f789(f3(x67981),f789(f789(f291(x67981),x67982),x67983)),f789(f789(f291(x67981),x67984),x67983)),f789(f789(f291(x67981),f789(f789(f3(x67981),x67982),x67984)),x67983))
% 21.40/21.37 [6799]~P101(x67991)+E(f789(f789(f239(x67991),f789(f789(f244(x67991),x67992),x67993)),f789(f789(f244(x67991),x67994),x67993)),f789(f789(f244(x67991),f789(f789(f239(x67991),x67992),x67994)),x67993))
% 21.40/21.37 [6800]~P101(x68001)+E(f789(f789(f244(x68001),f789(f789(f239(x68001),x68002),x68003)),f789(f789(f239(x68001),x68004),x68003)),f789(f789(f239(x68001),f789(f789(f244(x68001),x68002),x68004)),x68003))
% 21.40/21.37 [6801]~P96(x68011)+E(f789(f789(f111(x68011),f789(f789(f110(x68011),x68012),x68013)),f789(f789(f110(x68011),x68014),x68013)),f789(f789(f110(x68011),f789(f789(f111(x68011),x68012),x68014)),x68013))
% 21.40/21.37 [6802]~P96(x68021)+E(f789(f789(f110(x68021),f789(f789(f111(x68021),x68022),x68023)),f789(f789(f111(x68021),x68024),x68023)),f789(f789(f111(x68021),f789(f789(f110(x68021),x68022),x68024)),x68023))
% 21.40/21.37 [6803]~P70(x68031)+E(f789(f789(f89(x68031),f789(f789(f90(x68031),x68032),x68033)),f789(f789(f90(x68031),x68034),x68033)),f789(f789(f90(x68031),f789(f789(f89(x68031),x68032),x68034)),x68033))
% 21.40/21.37 [6838]E(f789(f789(f155(x68381,x68382),x68383),x68384),x68382)+~P1(f789(f789(f240(a863),f789(f185(f864(x68381)),x68382)),x68383))
% 21.40/21.37 [6864]~P1(f789(x68643,x68644))+P1(f789(f789(f789(f110(f870(x68641,a856)),x68642),x68643),x68644))
% 21.40/21.37 [6865]~P1(f789(x68653,x68654))+P1(f789(f789(f789(f110(f870(x68651,a856)),x68652),x68653),x68654))
% 21.40/21.37 [6866]~P1(f789(x68662,x68664))+P1(f789(f789(f789(f110(f870(x68661,a856)),x68662),x68663),x68664))
% 21.40/21.37 [6867]~P1(f789(x68672,x68674))+P1(f789(f789(f789(f110(f870(x68671,a856)),x68672),x68673),x68674))
% 21.40/21.37 [6889]E(f789(f789(f159(x68891),f789(f789(f132(x68891),x68892),x68893)),x68894),f789(f789(f159(x68891),x68892),x68894))+~P1(f789(f789(f241(a863),x68894),f789(f185(f864(x68891)),x68892)))
% 21.40/21.37 [6898]E(f789(f789(f3(f870(x68981,a856)),f789(f789(f310(x68981),x68982),x68983)),x68984),f789(f789(f3(f870(x68981,a856)),x68983),x68984))+~P1(f789(f789(f342(x68981),x68982),x68984))
% 21.40/21.37 [6899]E(f789(f789(f3(f870(x68991,a856)),f789(f789(f310(x68991),x68992),x68993)),x68994),f789(f789(f3(f870(x68991,a856)),x68993),x68994))+~P1(f789(f789(f342(x68991),x68992),x68994))
% 21.40/21.37 [6939]~E(f136(a863,f789(f302(a863,x69391),x69392)),f789(f789(f146(a863),x69394),x69393))+E(f136(a863,f789(f302(a863,f789(f789(f89(a863),x69391),f87(a863))),x69392)),x69393)
% 21.40/21.37 [7008]E(x70081,f2(a863))+E(f789(f789(f146(x70082),x70083),f789(f789(f164(x70082),f789(f789(f3(a863),x70081),f87(a863))),x70084)),f789(f789(f164(x70082),x70081),f789(f789(f146(x70082),x70083),x70084)))
% 21.40/21.37 [7112]E(f789(f789(f159(x71121),x71122),f789(f789(f3(a863),x71123),f789(f185(f864(x71121)),x71124))),f789(f789(f159(x71121),f789(f789(f132(x71121),x71124),x71122)),x71123))+P1(f789(f789(f241(a863),x71123),f789(f185(f864(x71121)),x71124)))
% 21.40/21.37 [7139]E(f789(f789(f111(f870(x71391,a856)),x71392),f789(f789(f310(x71391),x71393),x71394)),f789(f789(f310(x71391),x71393),f789(f789(f111(f870(x71391,a856)),x71392),x71394)))+~P1(f789(f789(f342(x71391),x71393),x71392))
% 21.40/21.37 [7140]E(f789(f789(f111(f870(x71401,a856)),x71402),f789(f789(f310(x71401),x71403),x71404)),f789(f789(f310(x71401),x71403),f789(f789(f111(f870(x71401,a856)),x71402),x71404)))+~P1(f789(f789(f342(x71401),x71403),x71402))
% 21.40/21.37 [7174]E(f789(f789(f159(x71741),f789(f789(f155(x71741,x71742),x71743),x71744)),x71743),x71744)+~P1(f789(f789(f241(a863),x71743),f789(f185(f864(x71741)),x71742)))
% 21.40/21.37 [7195]E(x71951,f184(f870(x71952,a856)))+E(f789(f311(f869(x71953,x71952),x71953,f248(x71953,x71952)),f789(f789(f256(x71953,x71952),x71954),f789(f18(f870(x71952,a856),x71953),x71951))),x71954)
% 21.40/21.37 [7196]E(x71961,f184(f870(x71962,a856)))+E(f789(f311(f869(x71962,x71963),x71963,f258(x71962,x71963)),f789(f789(f256(x71962,x71963),x71961),f789(f18(f870(x71963,a856),x71962),x71964))),x71964)
% 21.40/21.37 [7280]E(f789(f789(f3(f870(x72801,a856)),f789(f789(f310(x72801),x72802),x72803)),x72804),f789(f789(f310(x72801),x72802),f789(f789(f3(f870(x72801,a856)),x72803),x72804)))+P1(f789(f789(f342(x72801),x72802),x72804))
% 21.40/21.37 [7321]~E(x73214,f184(f870(x73212,a856)))+E(f789(f311(f869(x73211,x73212),x73211,f248(x73211,x73212)),f789(f789(f256(x73211,x73212),x73213),f789(f18(f870(x73212,a856),x73211),x73214))),f184(f870(x73211,a856)))
% 21.40/21.37 [7322]~E(x73223,f184(f870(x73221,a856)))+E(f789(f311(f869(x73221,x73222),x73222,f258(x73221,x73222)),f789(f789(f256(x73221,x73222),x73223),f789(f18(f870(x73222,a856),x73221),x73224))),f184(f870(x73222,a856)))
% 21.40/21.37 [7379]~P1(f789(f789(f342(x73791),x73792),x73794))+P1(f789(f789(f342(x73791),x73792),f789(f789(f110(f870(x73791,a856)),x73793),x73794)))
% 21.40/21.37 [7380]~P1(f789(f789(f342(x73801),x73802),x73804))+P1(f789(f789(f342(x73801),x73802),f789(f789(f110(f870(x73801,a856)),x73803),x73804)))
% 21.40/21.37 [7381]~P1(f789(f789(f342(x73811),x73812),x73814))+P1(f789(f789(f342(x73811),x73812),f789(f789(f110(f870(x73811,a856)),x73813),x73814)))
% 21.40/21.37 [7382]~P1(f789(f789(f342(x73821),x73822),x73823))+P1(f789(f789(f342(x73821),x73822),f789(f789(f110(f870(x73821,a856)),x73823),x73824)))
% 21.40/21.37 [7383]~P1(f789(f789(f342(x73831),x73832),x73833))+P1(f789(f789(f342(x73831),x73832),f789(f789(f110(f870(x73831,a856)),x73833),x73834)))
% 21.40/21.37 [7384]~P1(f789(f789(f342(x73841),x73842),x73843))+P1(f789(f789(f342(x73841),x73842),f789(f789(f110(f870(x73841,a856)),x73843),x73844)))
% 21.40/21.37 [7405]E(f789(f789(f111(f870(x74051,a856)),f789(f789(f310(x74051),x74052),x74053)),x74054),f789(f789(f310(x74051),x74052),f789(f789(f111(f870(x74051,a856)),x74053),x74054)))+~P1(f789(f789(f342(x74051),x74052),x74054))
% 21.40/21.37 [7406]E(f789(f789(f111(f870(x74061,a856)),f789(f789(f310(x74061),x74062),x74063)),x74064),f789(f789(f310(x74061),x74062),f789(f789(f111(f870(x74061,a856)),x74063),x74064)))+~P1(f789(f789(f342(x74061),x74062),x74064))
% 21.40/21.37 [7683]P1(f789(x76831,x76832))+~P1(f789(f789(f789(f111(f870(x76833,a856)),x76834),x76831),x76832))
% 21.40/21.37 [7684]P1(f789(x76841,x76842))+~P1(f789(f789(f789(f111(f870(x76843,a856)),x76841),x76844),x76842))
% 21.40/21.37 [7685]P1(f789(x76851,x76852))+~P1(f789(f789(f789(f111(f870(x76853,a856)),x76854),x76851),x76852))
% 21.40/21.37 [7686]P1(f789(x76861,x76862))+~P1(f789(f789(f789(f111(f870(x76863,a856)),x76861),x76864),x76862))
% 21.40/21.37 [7689]E(f789(f789(f8(x76891,a863),x76892),f789(f789(f3(f870(x76891,a856)),x76893),f789(f789(f310(x76891),x76894),f184(f870(x76891,a856))))),f789(f789(f8(x76891,a863),x76892),x76893))+P1(f789(f789(f342(x76891),x76894),x76893))
% 21.40/21.37 [7695]~P4(x76951)+E(f789(f161(x76951),f789(f789(f150(a863,x76951),x76952),f136(a863,f789(f302(a863,x76953),x76954)))),f789(f789(f8(a863,x76951),x76952),f789(f163(a863),f136(a863,f789(f302(a863,x76953),x76954)))))
% 21.40/21.37 [7696]~P4(x76961)+E(f789(f789(f8(a863,x76961),x76962),f789(f163(a863),f136(a863,f789(f302(a863,x76963),x76964)))),f789(f161(x76961),f789(f789(f150(a863,x76961),x76962),f136(a863,f789(f302(a863,x76963),x76964)))))
% 21.40/21.37 [7809]~E(x78093,x78094)+P1(f789(f71(x78091,x78092,f789(f789(f310(x78091),x78093),f184(f870(x78091,a856)))),x78094))
% 21.40/21.37 [7905]P1(f789(f789(f342(x79051),x79052),f789(f163(x79051),x79053)))+~P1(f789(f789(f342(x79051),x79052),f789(f163(x79051),f789(f789(f164(x79051),x79054),x79053))))
% 21.40/21.37 [7906]P1(f789(f789(f342(x79061),x79062),f789(f163(x79061),x79063)))+~P1(f789(f789(f342(x79061),x79062),f789(f163(x79061),f789(f789(f135(x79061),x79064),x79063))))
% 21.40/21.37 [7975]P1(f789(f789(f342(x79751),x79752),x79753))+~P1(f789(f789(f342(x79751),x79752),f789(f789(f111(f870(x79751,a856)),x79754),x79753)))
% 21.40/21.37 [7976]P1(f789(f789(f342(x79761),x79762),x79763))+~P1(f789(f789(f342(x79761),x79762),f789(f789(f3(f870(x79761,a856)),x79763),x79764)))
% 21.40/21.37 [7977]P1(f789(f789(f342(x79771),x79772),x79773))+~P1(f789(f789(f342(x79771),x79772),f789(f789(f3(f870(x79771,a856)),x79773),x79774)))
% 21.40/21.37 [7978]P1(f789(f789(f342(x79781),x79782),x79783))+~P1(f789(f789(f342(x79781),x79782),f789(f789(f3(f870(x79781,a856)),x79783),x79784)))
% 21.40/21.37 [7979]P1(f789(f789(f342(x79791),x79792),x79793))+~P1(f789(f789(f342(x79791),x79792),f789(f789(f111(f870(x79791,a856)),x79794),x79793)))
% 21.40/21.37 [7980]P1(f789(f789(f342(x79801),x79802),x79803))+~P1(f789(f789(f342(x79801),x79802),f789(f789(f111(f870(x79801,a856)),x79804),x79803)))
% 21.40/21.37 [7981]P1(f789(f789(f342(x79811),x79812),x79813))+~P1(f789(f789(f342(x79811),x79812),f789(f789(f111(f870(x79811,a856)),x79813),x79814)))
% 21.40/21.37 [7982]P1(f789(f789(f342(x79821),x79822),x79823))+~P1(f789(f789(f342(x79821),x79822),f789(f789(f111(f870(x79821,a856)),x79823),x79824)))
% 21.40/21.37 [7983]P1(f789(f789(f342(x79831),x79832),x79833))+~P1(f789(f789(f342(x79831),x79832),f789(f789(f111(f870(x79831,a856)),x79833),x79834)))
% 21.40/21.37 [8000]E(f789(f789(f132(x80001),f789(f789(f164(x80001),x80002),x80003)),f789(f789(f146(x80001),x80004),f789(f789(f135(x80001),f789(a121,x80002)),x80003))),f789(f789(f155(x80001,x80003),x80002),x80004))+~P1(f789(f789(f241(a863),x80002),f789(f185(f864(x80001)),x80003)))
% 21.40/21.37 [8023]P1(f789(f789(f342(x80231),x80232),x80233))+~P1(f789(f789(f240(f870(x80231,a856)),f789(f789(f310(x80231),x80232),x80234)),x80233))
% 21.40/21.37 [8051]~P1(f789(f789(f342(x80511),x80512),x80513))+~P1(f789(f789(f342(x80511),x80512),f789(f789(f3(f870(x80511,a856)),x80514),x80513)))
% 21.40/21.37 [8052]~P1(f789(f789(f342(x80521),x80522),x80523))+~P1(f789(f789(f342(x80521),x80522),f789(f789(f3(f870(x80521,a856)),x80524),x80523)))
% 21.40/21.37 [8053]~P1(f789(f789(f342(x80531),x80532),x80533))+~P1(f789(f789(f342(x80531),x80532),f789(f789(f3(f870(x80531,a856)),x80534),x80533)))
% 21.40/21.37 [8086]~P1(f789(f789(f241(a863),x80864),f789(f185(f864(x80861)),x80863)))+P1(f789(f789(f342(x80861),x80862),f789(f163(x80861),f789(f789(f155(x80861,x80863),x80864),x80862))))
% 21.40/21.37 [8127]E(f789(f113(a863),x81271),f2(a863))+E(f789(f789(f146(x81272),x81273),f789(f789(f164(x81272),f789(f789(f3(a863),f789(f113(a863),x81271)),f87(a863))),x81274)),f789(f789(f164(x81272),f789(f113(a863),x81271)),f789(f789(f146(x81272),x81273),x81274)))
% 21.40/21.37 [8136]E(f789(f789(f159(x81361),f789(f789(f135(x81361),x81362),x81363)),x81364),f789(f789(f159(x81361),x81363),f789(f789(f89(a863),x81362),x81364)))+~P1(f789(f789(f240(a863),f789(f789(f89(a863),x81362),x81364)),f789(f185(f864(x81361)),x81363)))
% 21.40/21.37 [8145]~P2(x81452)+E(f789(f789(f8(x81451,x81452),f789(f789(f10(a863,x81452,x81451),f109(x81452)),x81453)),x81454),f789(f109(x81452),f789(f789(f8(x81451,a863),x81453),x81454)))
% 21.40/21.37 [8146]~P120(x81462)+E(f789(f789(f8(x81461,x81462),f789(f789(f10(a1,x81462,x81461),f112(x81462)),x81463)),x81464),f789(f112(x81462),f789(f789(f8(x81461,a1),x81463),x81464)))
% 21.40/21.37 [8198]~P63(x81982)+E(f789(f789(f11(x81981,x81982),f789(f789(f10(x81982,x81982,x81981),f84(x81982)),x81983)),x81984),f789(f84(x81982),f789(f789(f11(x81981,x81982),x81983),x81984)))
% 21.40/21.37 [8199]~P6(x81992)+E(f789(f789(f8(x81991,x81992),f789(f789(f10(x81992,x81992,x81991),f88(x81992)),x81993)),x81994),f789(f88(x81992),f789(f789(f8(x81991,x81992),x81993),x81994)))
% 21.40/21.37 [8201]E(f789(f789(f8(x82011,a863),x82012),f789(f789(f3(f870(x82011,a856)),x82013),f789(f789(f310(x82011),x82014),f184(f870(x82011,a856))))),f789(f789(f3(a863),f789(f789(f8(x82011,a863),x82012),x82013)),f789(x82012,x82014)))+~P1(f789(f789(f342(x82011),x82014),x82013))
% 21.40/21.37 [8220]P1(f789(f789(f240(f870(x82201,a856)),x82202),x82203))+~P1(f789(f789(f240(f870(x82201,a856)),f789(f789(f310(x82201),x82204),x82202)),x82203))
% 21.40/21.37 [8429]P36(x84291,x84292)+~P36(x84291,f789(f789(f310(f869(x84291,x84291)),f789(f789(f249(x84291,x84291),x84293),x84294)),x84292))
% 21.40/21.37 [8430]P56(x84301,x84302)+~P56(x84301,f789(f789(f310(f869(x84301,x84301)),f789(f789(f249(x84301,x84301),x84303),x84304)),x84302))
% 21.40/21.37 [8438]~P101(x84381)+E(f789(f789(f144(x84381,x84381,f7(x84381)),x84382),f789(f789(f144(x84381,x84381,f7(x84381)),x84383),x84384)),f789(f789(f144(x84381,x84381,f7(x84381)),x84383),f789(f789(f144(x84381,x84381,f7(x84381)),x84382),x84384)))
% 21.40/21.37 [8448]E(x84481,x84482)+~P1(f789(f71(x84483,x84484,f789(f789(f310(x84483),x84481),f184(f870(x84483,a856)))),x84482))
% 21.40/21.37 [8452]E(f789(f170(x84521,x84522,x84523),x84524),f187(x84522))+P1(f789(f789(f342(x84521),x84524),f789(f311(f869(x84521,x84522),x84521,f248(x84521,x84522)),f789(f163(f869(x84521,x84522)),x84523))))
% 21.40/21.37 [8458]E(f789(f789(f132(x84581),f789(f789(f164(x84581),x84582),x84583)),f789(f789(f164(x84581),x84584),f789(f789(f135(x84581),x84582),x84583))),f789(f789(f164(x84581),f789(f789(f89(a863),x84582),x84584)),x84583))+~P1(f789(f789(f240(a863),f789(f789(f89(a863),x84582),x84584)),f789(f185(f864(x84581)),x84583)))
% 21.40/21.37 [8501]P1(f789(f70(x85011),x85012))+~E(x85012,f789(f311(a863,x85011,x85013),f789(f264(a863),f789(f789(f9(a863,a863,a856),f241(a863)),x85014))))
% 21.40/21.37 [8502]P1(f789(f70(x85021),x85022))+~E(x85022,f789(f311(a863,x85021,x85023),f789(f264(a863),f789(f789(f9(a863,a863,a856),f241(a863)),x85024))))
% 21.40/21.37 [8522]~P85(x85221)+E(f789(f138(x85221,x85221,f89(x85221),f789(f789(f89(x85221),x85222),x85223)),x85224),f789(f789(f89(x85221),x85222),f789(f138(x85221,x85221,f89(x85221),x85223),x85224)))
% 21.40/21.37 [8554]P1(f789(f789(f240(f870(x85541,a856)),f789(f269(x85541,x85542),x85543)),f789(f269(x85541,x85542),x85544)))+~P1(f789(f789(f240(f870(f869(x85541,x85542),a856)),x85543),x85544))
% 21.40/21.37 [8565]~P1(f789(f789(f240(a863),x85652),x85654))+P1(f789(f789(f240(f870(x85651,a856)),f789(f163(x85651),f789(f789(f164(x85651),x85652),x85653))),f789(f163(x85651),f789(f789(f164(x85651),x85654),x85653))))
% 21.40/21.37 [8566]~P1(f789(f789(f240(a863),x85664),x85662))+P1(f789(f789(f240(f870(x85661,a856)),f789(f163(x85661),f789(f789(f135(x85661),x85662),x85663))),f789(f163(x85661),f789(f789(f135(x85661),x85664),x85663))))
% 21.40/21.37 [8609]~P1(f789(f70(x86091),f789(f789(f3(f870(x86091,a856)),x86092),x86094)))+P1(f789(f70(x86091),f789(f789(f3(f870(x86091,a856)),x86092),f789(f789(f310(x86091),x86093),x86094))))
% 21.40/21.37 [8643]P1(f789(f789(f342(f869(x86431,x86431)),x86432),f308(x86431,x86433)))+~P1(f789(f789(f342(f869(x86431,x86431)),x86432),f789(f789(f178(f869(x86431,x86431),a856),x86434),x86433)))
% 21.40/21.37 [8644]P1(f789(f789(f342(f869(x86441,x86441)),x86442),f308(x86441,x86443)))+~P1(f789(f789(f342(f869(x86441,x86441)),x86442),f789(f789(f178(f869(x86441,x86441),a856),x86444),x86443)))
% 21.40/21.37 [8719]~P1(f789(f70(x87191),f789(f789(f3(f870(x87191,a856)),x87192),f789(f789(f310(x87191),x87194),x87193))))+P1(f789(f70(x87191),f789(f789(f3(f870(x87191,a856)),x87192),x87193)))
% 21.40/21.37 [8785]P1(f789(f789(f342(f869(x87851,x87852)),f789(f789(f249(x87851,x87852),x87853),x87854)),f184(f870(f869(x87851,x87852),a856))))+~P1(f789(f789(f184(f870(x87851,f870(x87852,a856))),x87853),x87854))
% 21.40/21.37 [8865]~E(f789(f170(x88651,x88652,x88653),x88654),f187(x88652))+~P1(f789(f789(f342(x88651),x88654),f789(f311(f869(x88651,x88652),x88651,f248(x88651,x88652)),f789(f163(f869(x88651,x88652)),x88653))))
% 21.40/21.37 [8901]~P101(x89011)+P1(f789(f789(f240(x89011),f789(f789(f239(x89011),x89012),f789(f789(f244(x89011),x89013),x89014))),f789(f789(f244(x89011),f789(f789(f239(x89011),x89012),x89013)),f789(f789(f239(x89011),x89012),x89014))))
% 21.40/21.37 [8902]~P95(x89021)+P1(f789(f789(f240(x89021),f789(f789(f110(x89021),x89022),f789(f789(f111(x89021),x89023),x89024))),f789(f789(f111(x89021),f789(f789(f110(x89021),x89022),x89023)),f789(f789(f110(x89021),x89022),x89024))))
% 21.40/21.37 [8920]~P1(f789(f789(f342(f869(x89201,x89202)),f789(f789(f249(x89201,x89202),x89203),x89204)),f184(f870(f869(x89201,x89202),a856))))+P1(f789(f789(f184(f870(x89201,f870(x89202,a856))),x89203),x89204))
% 21.40/21.37 [9044]E(x90441,x90442)+~P1(f789(f789(f342(f869(x90443,x90443)),f789(f789(f249(x90443,x90443),x90441),x90442)),f789(f163(f869(x90443,x90443)),f789(f789(f171(x90443,x90443),x90444),x90444))))
% 21.40/21.37 [9076]~P1(f789(f789(f342(f869(x90761,x90761)),f789(f789(f249(x90761,x90761),x90763),x90762)),f308(x90761,x90764)))+~P36(x90761,f789(f789(f310(f869(x90761,x90761)),f789(f789(f249(x90761,x90761),x90762),x90763)),x90764))
% 21.40/21.37 [9077]~P1(f789(f789(f342(f869(x90771,x90771)),f789(f789(f249(x90771,x90771),x90773),x90772)),f308(x90771,x90774)))+~P56(x90771,f789(f789(f310(f869(x90771,x90771)),f789(f789(f249(x90771,x90771),x90772),x90773)),x90774))
% 21.40/21.37 [9090]P1(f789(f789(f342(x90901),x90902),f789(f163(x90901),x90903)))+~P1(f789(f789(f342(f869(x90901,x90901)),f789(f789(f249(x90901,x90901),x90902),x90904)),f789(f163(f869(x90901,x90901)),f789(f789(f171(x90901,x90901),x90903),x90903))))
% 21.40/21.37 [9122]~P101(x91221)+P1(f789(f789(f240(x91221),f789(f789(f239(x91221),f789(f789(f244(x91221),x91222),x91223)),f789(f789(f244(x91221),x91222),x91224))),f789(f789(f244(x91221),x91222),f789(f789(f239(x91221),x91223),x91224))))
% 21.40/21.37 [9123]~P95(x91231)+P1(f789(f789(f240(x91231),f789(f789(f110(x91231),f789(f789(f111(x91231),x91232),x91233)),f789(f789(f111(x91231),x91232),x91234))),f789(f789(f111(x91231),x91232),f789(f789(f110(x91231),x91233),x91234))))
% 21.40/21.37 [9158]P1(f789(f789(f342(f869(x91581,x91581)),f789(f789(f249(x91581,x91581),x91582),x91583)),f789(f789(f289(x91581,x91581,x91581),x91584),f308(x91581,x91584))))+~P1(f789(f789(f342(f869(x91581,x91581)),f789(f789(f249(x91581,x91581),x91582),x91583)),x91584))
% 21.40/21.37 [9186]~E(f789(f311(x91862,x91861,x91863),f247(f870(x91862,a856))),f247(f870(x91861,a856)))+P1(f789(f789(f240(f870(x91861,a856)),f789(f88(f870(x91861,a856)),f789(f311(x91862,x91861,x91863),x91864))),f789(f311(x91862,x91861,x91863),f789(f88(f870(x91862,a856)),x91864))))
% 21.40/21.37 [9488]P1(f789(f789(f342(f869(x94881,x94881)),f789(f789(f249(x94881,x94881),x94882),x94883)),f789(f286(x94881,x94881),f789(f789(f289(x94881,x94881,x94881),x94884),f308(x94881,x94884)))))+~P1(f789(f789(f342(f869(x94881,x94881)),f789(f789(f249(x94881,x94881),x94882),x94883)),f789(f789(f289(x94881,x94881,x94881),f789(f286(x94881,x94881),x94884)),f308(x94881,f789(f286(x94881,x94881),x94884)))))
% 21.40/21.37 [9489]~P1(f789(f789(f342(f869(x94891,x94891)),f789(f789(f249(x94891,x94891),x94892),x94893)),f789(f286(x94891,x94891),f789(f789(f289(x94891,x94891,x94891),x94894),f308(x94891,x94894)))))+P1(f789(f789(f342(f869(x94891,x94891)),f789(f789(f249(x94891,x94891),x94892),x94893)),f789(f789(f289(x94891,x94891,x94891),f789(f286(x94891,x94891),x94894)),f308(x94891,f789(f286(x94891,x94891),x94894)))))
% 21.40/21.37 [9515]~P1(f789(f789(f342(x95152),x95154),f789(f267(x95151,x95152),x95153)))+P1(f789(f789(f342(f869(x95151,x95152)),f789(f789(f249(x95151,x95152),f604(x95153,x95151,x95154,x95152)),x95154)),x95153))
% 21.40/21.37 [9516]~P1(f789(f789(f342(x95162),x95164),f789(f267(x95161,x95162),x95163)))+P1(f789(f789(f342(f869(x95161,x95162)),f789(f789(f249(x95161,x95162),f605(x95163,x95161,x95164,x95162)),x95164)),x95163))
% 21.40/21.37 [9536]~P1(f789(f789(f342(x95361),x95364),f789(f789(f110(f870(x95361,a856)),x95362),x95363)))+P1(f789(f789(f789(f110(f870(x95361,a856)),f789(f789(f9(x95361,f870(x95361,a856),a856),f342(x95361)),x95362)),f789(f789(f9(x95361,f870(x95361,a856),a856),f342(x95361)),x95363)),x95364))
% 21.40/21.37 [9537]~P1(f789(f789(f342(x95371),x95374),f789(f789(f111(f870(x95371,a856)),x95372),x95373)))+P1(f789(f789(f789(f111(f870(x95371,a856)),f789(f789(f9(x95371,f870(x95371,a856),a856),f342(x95371)),x95372)),f789(f789(f9(x95371,f870(x95371,a856),a856),f342(x95371)),x95373)),x95374))
% 21.40/21.37 [9613]~P1(f789(f789(f342(f869(x96131,x96131)),f789(f789(f249(x96131,x96131),x96134),x96133)),f789(f789(f289(x96131,x96131,x96131),x96132),f308(x96131,x96132))))+P1(f789(f789(f342(f869(x96131,x96131)),f789(f789(f249(x96131,x96131),f698(x96132,x96133,x96134,x96131)),x96133)),x96132))
% 21.40/21.37 [9651]P1(f789(f789(f342(x96511),x96512),f789(f789(f110(f870(x96511,a856)),x96513),x96514)))+~P1(f789(f789(f789(f110(f870(x96511,a856)),f789(f789(f9(x96511,f870(x96511,a856),a856),f342(x96511)),x96513)),f789(f789(f9(x96511,f870(x96511,a856),a856),f342(x96511)),x96514)),x96512))
% 21.40/21.37 [9652]P1(f789(f789(f342(x96521),x96522),f789(f789(f111(f870(x96521,a856)),x96523),x96524)))+~P1(f789(f789(f789(f111(f870(x96521,a856)),f789(f789(f9(x96521,f870(x96521,a856),a856),f342(x96521)),x96523)),f789(f789(f9(x96521,f870(x96521,a856),a856),f342(x96521)),x96524)),x96522))
% 21.40/21.37 [9934]P34(x99341,f789(f789(f9(x99341,f870(f869(x99341,x99341),a856),f870(x99341,a856)),f789(f789(f10(f870(x99341,f870(f870(f869(x99341,x99341),a856),a856)),f870(f870(f869(x99341,x99341),a856),f870(x99341,a856)),x99341),f9(x99341,f870(f869(x99341,x99341),a856),a856)),f789(f789(f10(f870(x99341,f869(x99341,x99341)),f870(x99341,f870(f870(f869(x99341,x99341),a856),a856)),x99341),f789(f10(f869(x99341,x99341),f870(f870(f869(x99341,x99341),a856),a856),x99341),f342(f869(x99341,x99341)))),f249(x99341,x99341)))),x99342),x99343,x99344)+~P1(f789(f789(f342(f869(f864(x99341),f864(x99341))),f789(f789(f249(f864(x99341),f864(x99341)),x99343),x99344)),f154(x99341,x99342)))
% 21.40/21.37 [9938]P57(x99381,f789(f789(f9(x99381,f870(f869(x99381,x99381),a856),f870(x99381,a856)),f789(f789(f10(f870(x99381,f870(f870(f869(x99381,x99381),a856),a856)),f870(f870(f869(x99381,x99381),a856),f870(x99381,a856)),x99381),f9(x99381,f870(f869(x99381,x99381),a856),a856)),f789(f789(f10(f870(x99381,f869(x99381,x99381)),f870(x99381,f870(f870(f869(x99381,x99381),a856),a856)),x99381),f789(f10(f869(x99381,x99381),f870(f870(f869(x99381,x99381),a856),a856),x99381),f342(f869(x99381,x99381)))),f249(x99381,x99381)))),x99382),x99383,x99384)+~P1(f789(f789(f342(f869(f870(x99381,a856),f870(x99381,a856))),f789(f789(f249(f870(x99381,a856),f870(x99381,a856)),x99383),x99384)),f332(x99381,x99382)))
% 21.40/21.37 [9967]E(x99671,x99672)+~E(f789(f789(f9(x99673,f870(f869(x99673,x99674),a856),f870(x99674,a856)),f789(f789(f10(f870(x99674,f870(f870(f869(x99673,x99674),a856),a856)),f870(f870(f869(x99673,x99674),a856),f870(x99674,a856)),x99673),f9(x99674,f870(f869(x99673,x99674),a856),a856)),f789(f789(f10(f870(x99674,f869(x99673,x99674)),f870(x99674,f870(f870(f869(x99673,x99674),a856),a856)),x99673),f789(f10(f869(x99673,x99674),f870(f870(f869(x99673,x99674),a856),a856),x99674),f342(f869(x99673,x99674)))),f249(x99673,x99674)))),x99671),f789(f789(f9(x99673,f870(f869(x99673,x99674),a856),f870(x99674,a856)),f789(f789(f10(f870(x99674,f870(f870(f869(x99673,x99674),a856),a856)),f870(f870(f869(x99673,x99674),a856),f870(x99674,a856)),x99673),f9(x99674,f870(f869(x99673,x99674),a856),a856)),f789(f789(f10(f870(x99674,f869(x99673,x99674)),f870(x99674,f870(f870(f869(x99673,x99674),a856),a856)),x99673),f789(f10(f869(x99673,x99674),f870(f870(f869(x99673,x99674),a856),a856),x99674),f342(f869(x99673,x99674)))),f249(x99673,x99674)))),x99672))
% 21.40/21.37 [9970]~P34(x99701,f789(f789(f9(x99701,f870(f869(x99701,x99701),a856),f870(x99701,a856)),f789(f789(f10(f870(x99701,f870(f870(f869(x99701,x99701),a856),a856)),f870(f870(f869(x99701,x99701),a856),f870(x99701,a856)),x99701),f9(x99701,f870(f869(x99701,x99701),a856),a856)),f789(f789(f10(f870(x99701,f869(x99701,x99701)),f870(x99701,f870(f870(f869(x99701,x99701),a856),a856)),x99701),f789(f10(f869(x99701,x99701),f870(f870(f869(x99701,x99701),a856),a856),x99701),f342(f869(x99701,x99701)))),f249(x99701,x99701)))),x99704),x99702,x99703)+P1(f789(f789(f342(f869(f864(x99701),f864(x99701))),f789(f789(f249(f864(x99701),f864(x99701)),x99702),x99703)),f154(x99701,x99704)))
% 21.40/21.37 [9971]~P57(x99711,f789(f789(f9(x99711,f870(f869(x99711,x99711),a856),f870(x99711,a856)),f789(f789(f10(f870(x99711,f870(f870(f869(x99711,x99711),a856),a856)),f870(f870(f869(x99711,x99711),a856),f870(x99711,a856)),x99711),f9(x99711,f870(f869(x99711,x99711),a856),a856)),f789(f789(f10(f870(x99711,f869(x99711,x99711)),f870(x99711,f870(f870(f869(x99711,x99711),a856),a856)),x99711),f789(f10(f869(x99711,x99711),f870(f870(f869(x99711,x99711),a856),a856),x99711),f342(f869(x99711,x99711)))),f249(x99711,x99711)))),x99714),x99712,x99713)+P1(f789(f789(f342(f869(f870(x99711,a856),f870(x99711,a856))),f789(f789(f249(f870(x99711,a856),f870(x99711,a856)),x99712),x99713)),f332(x99711,x99714)))
% 21.40/21.37 [7454]~P88(x74541)+E(f789(f789(f89(x74541),f789(f113(x74541),x74542)),f789(f789(f89(x74541),f789(f113(x74541),x74543)),x74544)),f789(f789(f89(x74541),f789(f113(x74541),f789(f789(f89(a1),x74542),x74543))),x74544))
% 21.40/21.37 [7455]~P88(x74551)+E(f789(f789(f89(x74551),f789(f113(x74551),x74552)),f789(f789(f3(x74551),f789(f113(x74551),x74553)),x74554)),f789(f789(f3(x74551),f789(f113(x74551),f789(f789(f89(a1),x74552),x74553))),x74554))
% 21.40/21.37 [7456]~P88(x74561)+E(f789(f789(f90(x74561),f789(f113(x74561),x74562)),f789(f789(f90(x74561),f789(f113(x74561),x74563)),x74564)),f789(f789(f90(x74561),f789(f113(x74561),f789(f789(f90(a1),x74562),x74563))),x74564))
% 21.40/21.37 [7503]~P2(x75031)+E(f789(f161(x75031),f789(f789(f150(x75032,x75031),f789(f18(x75031,x75032),x75033)),x75034)),f789(f789(f90(x75031),f789(f109(x75031),f789(f185(f864(x75032)),x75034))),x75033))
% 21.40/21.37 [7738]E(f789(f273(x77381,f789(f789(f146(f869(a108,x77381)),x77382),x77383)),x77384),f789(f258(a108,x77381),x77382))+~P1(f789(f789(f241(a108),x77384),f789(f248(a108,x77381),x77382)))
% 21.40/21.37 [7786]~P88(x77861)+E(f789(f789(f89(x77861),f789(f113(x77861),x77862)),f789(f789(f3(x77861),x77863),f789(f113(x77861),x77864))),f789(f789(f89(x77861),f789(f113(x77861),f789(f789(f89(a1),x77862),f789(f88(a1),x77864)))),x77863))
% 21.40/21.37 [7917]E(f789(f273(x79171,x79172),f789(f789(f3(a108),x79173),f789(f248(a108,x79171),x79174))),f789(f273(x79171,f789(f789(f146(f869(a108,x79171)),x79174),x79172)),x79173))+P1(f789(f789(f241(a108),x79173),f789(f248(a108,x79171),x79174)))
% 21.40/21.37 [8346]~P1(f789(f789(f342(x83461),x83462),f789(f163(x83461),f123(x83461,x83464))))+P1(f789(f789(f342(x83461),x83462),f789(f163(x83461),f123(x83461,f789(f789(f132(x83461),x83463),x83464)))))
% 21.40/21.37 [8347]~P1(f789(f789(f342(x83471),x83472),f789(f163(x83471),f123(x83471,x83473))))+P1(f789(f789(f342(x83471),x83472),f789(f163(x83471),f123(x83471,f789(f789(f132(x83471),x83473),x83474)))))
% 21.40/21.37 [8370]E(f789(f789(f110(f870(x83701,a856)),f789(f789(f111(f870(x83701,a856)),x83702),x83703)),x83704),f789(f789(f111(f870(x83701,a856)),x83702),f789(f789(f110(f870(x83701,a856)),x83703),x83704)))+~P1(f789(f789(f240(f870(x83701,a856)),x83704),x83702))
% 21.40/21.37 [8657]~E(f789(f789(f110(f870(x86571,a856)),f789(f789(f111(f870(x86571,a856)),x86573),x86574)),x86572),f789(f789(f111(f870(x86571,a856)),x86573),f789(f789(f110(f870(x86571,a856)),x86574),x86572)))+P1(f789(f789(f240(f870(x86571,a856)),x86572),x86573))
% 21.40/21.37 [8908]~P1(f789(f789(f240(f870(x89081,a856)),x89082),f789(f789(f110(f870(x89081,a856)),x89083),x89084)))+P1(f789(f789(f240(f870(x89081,a856)),f789(f789(f3(f870(x89081,a856)),x89082),x89083)),x89084))
% 21.40/21.37 [9025]P1(f789(f789(f240(f870(x90251,a856)),x90252),f789(f789(f110(f870(x90251,a856)),x90253),x90254)))+~P1(f789(f789(f240(f870(x90251,a856)),f789(f789(f3(f870(x90251,a856)),x90252),x90253)),x90254))
% 21.40/21.37 [9104]~P80(x91041)+E(f789(f84(x91041),f789(f789(f8(x91042,x91041),f789(f789(f10(x91041,x91041,x91042),f84(x91041)),x91043)),x91044)),f789(f789(f8(x91042,x91041),f789(f789(f10(x91041,x91041,x91042),f84(x91041)),x91043)),x91044))
% 21.40/21.37 [9246]~P80(x92461)+P1(f789(f789(f240(x92461),f2(x92461)),f789(f789(f8(x92462,x92461),f789(f789(f10(x92461,x92461,x92462),f84(x92461)),x92463)),x92464)))
% 21.40/21.37 [9249]~P6(x92491)+E(f789(f161(x92491),f789(f789(f150(x92492,x92491),f789(f82(x92491,x92491,x92492,f88(x92491)),x92493)),x92494)),f789(f88(x92491),f789(f161(x92491),f789(f789(f150(x92492,x92491),x92493),x92494))))
% 21.40/21.37 [9387]~P80(x93871)+P1(f789(f789(f240(x93871),f789(f84(x93871),f789(f789(f8(x93872,x93871),x93873),x93874))),f789(f789(f8(x93872,x93871),f789(f789(f10(x93871,x93871,x93872),f84(x93871)),x93873)),x93874)))
% 21.40/21.37 [9414]~E(f789(f789(f89(a863),x94141),x94144),f789(f789(f89(a863),x94143),x94142))+P1(f789(f789(f342(f869(f869(a863,a863),f869(a863,a863))),f789(f789(f249(f869(a863,a863),f869(a863,a863)),f789(f789(f249(a863,a863),x94141),x94142)),f789(f789(f249(a863,a863),x94143),x94144))),a118))
% 21.40/21.37 [9415]~P1(f789(f789(f241(a863),x94151),x94153))+P1(f789(f789(f342(f869(f869(a863,a863),f869(a863,a863))),f789(f789(f249(f869(a863,a863),f869(a863,a863)),f789(f789(f249(a863,a863),x94151),x94152)),f789(f789(f249(a863,a863),x94153),x94154))),a47))
% 21.40/21.37 [9416]~P1(f789(f789(f241(a863),x94161),x94163))+P1(f789(f789(f342(f869(f869(a863,a863),f869(a863,a863))),f789(f789(f249(f869(a863,a863),f869(a863,a863)),f789(f789(f249(a863,a863),x94161),x94162)),f789(f789(f249(a863,a863),x94163),x94164))),a79))
% 21.40/21.37 [9559]E(f789(f789(f89(a863),x95591),x95592),f789(f789(f89(a863),x95593),x95594))+~P1(f789(f789(f342(f869(f869(a863,a863),f869(a863,a863))),f789(f789(f249(f869(a863,a863),f869(a863,a863)),f789(f789(f249(a863,a863),x95591),x95594)),f789(f789(f249(a863,a863),x95593),x95592))),a118))
% 21.40/21.37 [9606]~P1(f789(f789(f342(x96062),x96064),f789(f789(f53(x96061,f870(x96062,a856)),f247(f870(x96061,a856))),x96063)))+P1(f789(f789(f789(f53(x96061,f870(x96062,a856)),f247(f870(x96061,a856))),f789(f789(f10(f870(x96062,a856),f870(x96062,a856),x96061),f789(f9(x96062,f870(x96062,a856),a856),f342(x96062))),x96063)),x96064))
% 21.40/21.37 [9607]~P1(f789(f789(f342(x96072),x96074),f789(f789(f54(x96071,f870(x96072,a856)),f247(f870(x96071,a856))),x96073)))+P1(f789(f789(f789(f54(x96071,f870(x96072,a856)),f247(f870(x96071,a856))),f789(f789(f10(f870(x96072,a856),f870(x96072,a856),x96071),f789(f9(x96072,f870(x96072,a856),a856),f342(x96072))),x96073)),x96074))
% 21.40/21.37 [9677]~P1(f789(f63(x96771,x96772),f789(f789(f249(a1,a1),x96774),x96773)))+P1(f789(f63(f789(f88(a1),x96771),x96772),f789(f789(f249(a1,a1),f789(f789(f789(f105(a1),f789(f789(a338,x96773),f2(a1))),f789(f88(a1),x96774)),f789(f789(f3(a1),f789(f88(a1),x96774)),f87(a1)))),f789(f789(f789(f105(a1),f789(f789(a338,x96773),f2(a1))),f2(a1)),f789(f789(f3(a1),x96772),x96773)))))
% 21.40/21.37 [9686]P1(f789(f789(f342(x96861),x96862),f789(f789(f53(x96863,f870(x96861,a856)),f247(f870(x96863,a856))),x96864)))+~P1(f789(f789(f789(f53(x96863,f870(x96861,a856)),f247(f870(x96863,a856))),f789(f789(f10(f870(x96861,a856),f870(x96861,a856),x96863),f789(f9(x96861,f870(x96861,a856),a856),f342(x96861))),x96864)),x96862))
% 21.40/21.37 [9687]P1(f789(f789(f342(x96871),x96872),f789(f789(f54(x96873,f870(x96871,a856)),f247(f870(x96873,a856))),x96874)))+~P1(f789(f789(f789(f54(x96873,f870(x96871,a856)),f247(f870(x96873,a856))),f789(f789(f10(f870(x96871,a856),f870(x96871,a856),x96873),f789(f9(x96871,f870(x96871,a856),a856),f342(x96871))),x96874)),x96872))
% 21.40/21.37 [9698]E(f789(f789(f53(a863,f870(x96981,a856)),f247(f870(a863,a856))),x96982),f789(f789(f53(a863,f870(x96981,a856)),f247(f870(a863,a856))),x96983))+~E(f789(f789(f53(a863,f870(x96981,a856)),f789(f302(a863,f2(a863)),f546(x96982,x96984,x96983,x96981))),x96983),f789(f789(f53(a863,f870(x96981,a856)),f789(f302(a863,f2(a863)),f789(f789(f89(a863),f546(x96982,x96984,x96983,x96981)),x96984))),x96982))
% 21.40/21.37 [10033]~P1(f789(f789(f240(f870(f869(x100331,x100332),a856)),x100333),x100334))+P1(f789(f789(f240(f870(x100331,f870(x100332,a856))),f789(f789(f9(x100331,f870(f869(x100331,x100332),a856),f870(x100332,a856)),f789(f789(f10(f870(x100332,f870(f870(f869(x100331,x100332),a856),a856)),f870(f870(f869(x100331,x100332),a856),f870(x100332,a856)),x100331),f9(x100332,f870(f869(x100331,x100332),a856),a856)),f789(f789(f10(f870(x100332,f869(x100331,x100332)),f870(x100332,f870(f870(f869(x100331,x100332),a856),a856)),x100331),f789(f10(f869(x100331,x100332),f870(f870(f869(x100331,x100332),a856),a856),x100332),f342(f869(x100331,x100332)))),f249(x100331,x100332)))),x100333)),f789(f789(f9(x100331,f870(f869(x100331,x100332),a856),f870(x100332,a856)),f789(f789(f10(f870(x100332,f870(f870(f869(x100331,x100332),a856),a856)),f870(f870(f869(x100331,x100332),a856),f870(x100332,a856)),x100331),f9(x100332,f870(f869(x100331,x100332),a856),a856)),f789(f789(f10(f870(x100332,f869(x100331,x100332)),f870(x100332,f870(f870(f869(x100331,x100332),a856),a856)),x100331),f789(f10(f869(x100331,x100332),f870(f870(f869(x100331,x100332),a856),a856),x100332),f342(f869(x100331,x100332)))),f249(x100331,x100332)))),x100334)))
% 21.40/21.37 [10049]P1(f789(f789(f240(f870(f869(x100491,x100492),a856)),x100493),x100494))+~P1(f789(f789(f240(f870(x100491,f870(x100492,a856))),f789(f789(f9(x100491,f870(f869(x100491,x100492),a856),f870(x100492,a856)),f789(f789(f10(f870(x100492,f870(f870(f869(x100491,x100492),a856),a856)),f870(f870(f869(x100491,x100492),a856),f870(x100492,a856)),x100491),f9(x100492,f870(f869(x100491,x100492),a856),a856)),f789(f789(f10(f870(x100492,f869(x100491,x100492)),f870(x100492,f870(f870(f869(x100491,x100492),a856),a856)),x100491),f789(f10(f869(x100491,x100492),f870(f870(f869(x100491,x100492),a856),a856),x100492),f342(f869(x100491,x100492)))),f249(x100491,x100492)))),x100493)),f789(f789(f9(x100491,f870(f869(x100491,x100492),a856),f870(x100492,a856)),f789(f789(f10(f870(x100492,f870(f870(f869(x100491,x100492),a856),a856)),f870(f870(f869(x100491,x100492),a856),f870(x100492,a856)),x100491),f9(x100492,f870(f869(x100491,x100492),a856),a856)),f789(f789(f10(f870(x100492,f869(x100491,x100492)),f870(x100492,f870(f870(f869(x100491,x100492),a856),a856)),x100491),f789(f10(f869(x100491,x100492),f870(f870(f869(x100491,x100492),a856),a856),x100492),f342(f869(x100491,x100492)))),f249(x100491,x100492)))),x100494)))
% 21.40/21.37 [9148]~P1(f789(f789(f342(f869(x91481,x91481)),x91482),f308(x91481,x91484)))+P1(f789(f789(f342(f869(x91481,x91481)),x91482),f308(x91481,f789(f789(f110(f870(f869(x91481,x91481),a856)),x91483),x91484))))
% 21.40/21.37 [9149]~P1(f789(f789(f342(f869(x91491,x91491)),x91492),f308(x91491,x91493)))+P1(f789(f789(f342(f869(x91491,x91491)),x91492),f308(x91491,f789(f789(f110(f870(f869(x91491,x91491),a856)),x91493),x91494))))
% 21.40/21.37 [9479]~E(f789(f163(x94791),x94794),f173(x94791,x94792,x94793))+E(f170(x94791,x94792,f789(f789(f150(x94791,f869(x94791,x94792)),f789(f789(f20(x94791,x94792,f869(x94791,x94792)),f249(x94791,x94792)),f789(f789(f10(f867(x94792),x94792,x94791),f238(x94792)),x94793))),x94794)),x94793)
% 21.40/21.37 [9779]~P1(f789(f789(f241(a863),f789(f789(f89(a863),x97791),x97794)),f789(f789(f89(a863),x97793),x97792)))+P1(f789(f789(f241(a1),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x97791),x97792)),f184(f870(f869(a863,a863),a856)))))),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x97793),x97794)),f184(f870(f869(a863,a863),a856)))))))
% 21.40/21.37 [9780]~P1(f789(f789(f240(a863),f789(f789(f89(a863),x97801),x97804)),f789(f789(f89(a863),x97803),x97802)))+P1(f789(f789(f240(a1),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x97801),x97802)),f184(f870(f869(a863,a863),a856)))))),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x97803),x97804)),f184(f870(f869(a863,a863),a856)))))))
% 21.40/21.37 [9871]P1(f789(f789(f241(a863),f789(f789(f89(a863),x98711),x98712)),f789(f789(f89(a863),x98713),x98714)))+~P1(f789(f789(f241(a1),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x98711),x98714)),f184(f870(f869(a863,a863),a856)))))),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x98713),x98712)),f184(f870(f869(a863,a863),a856)))))))
% 21.40/21.37 [9872]P1(f789(f789(f240(a863),f789(f789(f89(a863),x98721),x98722)),f789(f789(f89(a863),x98723),x98724)))+~P1(f789(f789(f240(a1),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x98721),x98724)),f184(f870(f869(a863,a863),a856)))))),f789(a98,f789(f285(f869(a863,a863),f869(a863,a863),a118),f789(f789(f310(f869(a863,a863)),f789(f789(f249(a863,a863),x98723),x98722)),f184(f870(f869(a863,a863),a856)))))))
% 21.40/21.37 [9920]P1(f789(f789(f240(f870(x99201,a856)),f789(f789(f53(a863,f870(x99201,a856)),f247(f870(a863,a856))),x99202)),f789(f789(f53(a863,f870(x99201,a856)),f247(f870(a863,a856))),x99203)))+~P1(f789(f789(f240(f870(x99201,a856)),f789(f789(f53(a863,f870(x99201,a856)),f789(f302(a863,f2(a863)),f547(x99203,x99204,x99202,x99201))),x99202)),f789(f789(f53(a863,f870(x99201,a856)),f789(f302(a863,f2(a863)),f789(f789(f89(a863),f547(x99203,x99204,x99202,x99201)),x99204))),x99203)))
% 21.40/21.37 [9973]P1(f789(f789(f240(a108),x99734),f2(a108)))+E(f789(f789(f261(f869(a108,a108),f869(x99731,f870(a866,a854)),f869(a108,a108),f869(f870(a108,f870(a856,f867(f865(x99731)))),f869(a108,a108))),f789(x99732,x99733)),f789(f789(f10(f870(f870(a108,f870(a856,f867(f865(x99731)))),f870(f869(a108,a108),f869(f870(a108,f870(a856,f867(f865(x99731)))),f869(a108,a108)))),f870(f869(a108,a108),f869(f870(a108,f870(a856,f867(f865(x99731)))),f869(a108,a108))),f869(x99731,f870(a866,a854))),f789(f261(f869(a108,a108),f870(a108,f870(a856,f867(f865(x99731)))),f869(a108,a108),f869(f870(a108,f870(a856,f867(f865(x99731)))),f869(a108,a108))),f280(x99731,x99732,f789(f789(f3(a108),x99734),f87(a108)),x99733))),f789(f789(f10(f870(f870(a108,f870(a856,f867(f865(x99731)))),f870(a108,f870(a856,f867(f865(x99731))))),f870(f870(a108,f870(a856,f867(f865(x99731)))),f870(f869(a108,a108),f869(f870(a108,f870(a856,f867(f865(x99731)))),f869(a108,a108)))),f869(x99731,f870(a866,a854))),f789(f10(f870(a108,f870(a856,f867(f865(x99731)))),f870(f869(a108,a108),f869(f870(a108,f870(a856,f867(f865(x99731)))),f869(a108,a108))),f870(a108,f870(a856,f867(f865(x99731))))),f249(f870(a108,f870(a856,f867(f865(x99731)))),f869(a108,a108)))),f789(f789(f10(f870(a108,f870(a856,f867(f865(x99731)))),f870(f870(a108,f870(a856,f867(f865(x99731)))),f870(a108,f870(a856,f867(f865(x99731))))),f869(x99731,f870(a866,a854))),f58(x99731)),f789(f789(f10(x99731,f870(a108,f870(a856,f867(f865(x99731)))),f869(x99731,f870(a866,a854))),f56(x99731)),f248(x99731,f870(a866,a854))))))),f280(x99731,x99732,x99734,x99733))
% 21.40/21.37 [10024]~P1(f789(f789(f342(x100242),x100244),f789(f267(x100241,x100242),x100243)))+P1(f789(f255(x100241,x100242,f789(f789(f9(x100241,f870(f869(x100241,x100242),a856),f870(x100242,a856)),f789(f789(f10(f870(x100242,f870(f870(f869(x100241,x100242),a856),a856)),f870(f870(f869(x100241,x100242),a856),f870(x100242,a856)),x100241),f9(x100242,f870(f869(x100241,x100242),a856),a856)),f789(f789(f10(f870(x100242,f869(x100241,x100242)),f870(x100242,f870(f870(f869(x100241,x100242),a856),a856)),x100241),f789(f10(f869(x100241,x100242),f870(f870(f869(x100241,x100242),a856),a856),x100242),f342(f869(x100241,x100242)))),f249(x100241,x100242)))),x100243)),x100244))
% 21.40/21.37 [10025]~P1(f789(f789(f342(x100251),x100254),f789(f269(x100251,x100252),x100253)))+P1(f789(f254(x100251,x100252,f789(f789(f9(x100251,f870(f869(x100251,x100252),a856),f870(x100252,a856)),f789(f789(f10(f870(x100252,f870(f870(f869(x100251,x100252),a856),a856)),f870(f870(f869(x100251,x100252),a856),f870(x100252,a856)),x100251),f9(x100252,f870(f869(x100251,x100252),a856),a856)),f789(f789(f10(f870(x100252,f869(x100251,x100252)),f870(x100252,f870(f870(f869(x100251,x100252),a856),a856)),x100251),f789(f10(f869(x100251,x100252),f870(f870(f869(x100251,x100252),a856),a856),x100252),f342(f869(x100251,x100252)))),f249(x100251,x100252)))),x100253)),x100254))
% 21.40/21.37 [10036]P1(f789(f789(f342(x100361),x100362),f789(f267(x100363,x100361),x100364)))+~P1(f789(f255(x100363,x100361,f789(f789(f9(x100363,f870(f869(x100363,x100361),a856),f870(x100361,a856)),f789(f789(f10(f870(x100361,f870(f870(f869(x100363,x100361),a856),a856)),f870(f870(f869(x100363,x100361),a856),f870(x100361,a856)),x100363),f9(x100361,f870(f869(x100363,x100361),a856),a856)),f789(f789(f10(f870(x100361,f869(x100363,x100361)),f870(x100361,f870(f870(f869(x100363,x100361),a856),a856)),x100363),f789(f10(f869(x100363,x100361),f870(f870(f869(x100363,x100361),a856),a856),x100361),f342(f869(x100363,x100361)))),f249(x100363,x100361)))),x100364)),x100362))
% 21.40/21.37 [10037]P1(f789(f789(f342(x100371),x100372),f789(f269(x100371,x100373),x100374)))+~P1(f789(f254(x100371,x100373,f789(f789(f9(x100371,f870(f869(x100371,x100373),a856),f870(x100373,a856)),f789(f789(f10(f870(x100373,f870(f870(f869(x100371,x100373),a856),a856)),f870(f870(f869(x100371,x100373),a856),f870(x100373,a856)),x100371),f9(x100373,f870(f869(x100371,x100373),a856),a856)),f789(f789(f10(f870(x100373,f869(x100371,x100373)),f870(x100373,f870(f870(f869(x100371,x100373),a856),a856)),x100371),f789(f10(f869(x100371,x100373),f870(f870(f869(x100371,x100373),a856),a856),x100373),f342(f869(x100371,x100373)))),f249(x100371,x100373)))),x100374)),x100372))
% 21.40/21.37 [9793]~P70(x97931)+E(f789(f789(f90(x97931),f789(f789(f89(x97931),f87(x97931)),f87(x97931))),f789(f789(f8(a863,x97931),f789(f789(f10(x97931,x97931,a863),f789(f89(x97931),x97932)),f789(f789(f9(a863,x97931,x97931),f789(f789(f10(x97931,f870(x97931,x97931),a863),f90(x97931)),f109(x97931))),x97933))),f789(f265(a863),x97934))),f789(f789(f90(x97931),f789(f109(x97931),x97934)),f789(f789(f89(x97931),x97932),f789(f789(f89(x97931),x97932),f789(f789(f90(x97931),f789(f109(x97931),f789(f789(f3(a863),x97934),f87(a863)))),x97933)))))
% 21.40/21.37 [9941]P1(f789(x99411,f603(x99412,x99413,x99414,x99411)))+P36(x99412,f789(f264(f869(x99412,x99412)),f789(f259(x99412,x99412,a856),f789(f789(f10(f870(x99412,a856),f870(x99412,a856),x99412),f789(f20(x99412,a856,a856),f789(f789(f10(a856,f870(a856,a856),x99412),a339),x99411))),f789(f789(f9(x99412,f870(x99412,x99412),f870(x99412,a856)),f789(f789(f10(f870(x99412,a856),f870(f870(x99412,x99412),f870(x99412,a856)),x99412),f10(x99412,a856,x99412)),a338)),x99413)))))
% 21.40/21.37 [9955]~P1(f789(f789(f241(a863),f789(x99554,f789(x99553,f603(x99551,x99553,x99554,x99552)))),f789(x99554,f603(x99551,x99553,x99554,x99552))))+P36(x99551,f789(f264(f869(x99551,x99551)),f789(f259(x99551,x99551,a856),f789(f789(f10(f870(x99551,a856),f870(x99551,a856),x99551),f789(f20(x99551,a856,a856),f789(f789(f10(a856,f870(a856,a856),x99551),a339),x99552))),f789(f789(f9(x99551,f870(x99551,x99551),f870(x99551,a856)),f789(f789(f10(f870(x99551,a856),f870(f870(x99551,x99551),f870(x99551,a856)),x99551),f10(x99551,a856,x99551)),a338)),x99553)))))
% 21.40/21.37 [10062]~P1(f789(f789(f342(f869(x100621,x100621)),f789(f789(f249(x100621,x100621),x100623),x100624)),f789(f789(f110(f870(f869(x100621,x100621),a856)),x100622),f308(x100621,f184(f870(f869(x100621,x100621),a856))))))+P1(f789(f789(f789(f789(f110(f870(x100621,f870(x100621,a856))),f789(f789(f9(x100621,f870(f869(x100621,x100621),a856),f870(x100621,a856)),f789(f789(f10(f870(x100621,f870(f870(f869(x100621,x100621),a856),a856)),f870(f870(f869(x100621,x100621),a856),f870(x100621,a856)),x100621),f9(x100621,f870(f869(x100621,x100621),a856),a856)),f789(f789(f10(f870(x100621,f869(x100621,x100621)),f870(x100621,f870(f870(f869(x100621,x100621),a856),a856)),x100621),f789(f10(f869(x100621,x100621),f870(f870(f869(x100621,x100621),a856),a856),x100621),f342(f869(x100621,x100621)))),f249(x100621,x100621)))),x100622)),a338),x100623),x100624))
% 21.40/21.37 [10071]P1(f789(f789(f342(f869(x100711,x100711)),f789(f789(f249(x100711,x100711),x100712),x100713)),f789(f789(f110(f870(f869(x100711,x100711),a856)),x100714),f308(x100711,f184(f870(f869(x100711,x100711),a856))))))+~P1(f789(f789(f789(f789(f110(f870(x100711,f870(x100711,a856))),f789(f789(f9(x100711,f870(f869(x100711,x100711),a856),f870(x100711,a856)),f789(f789(f10(f870(x100711,f870(f870(f869(x100711,x100711),a856),a856)),f870(f870(f869(x100711,x100711),a856),f870(x100711,a856)),x100711),f9(x100711,f870(f869(x100711,x100711),a856),a856)),f789(f789(f10(f870(x100711,f869(x100711,x100711)),f870(x100711,f870(f870(f869(x100711,x100711),a856),a856)),x100711),f789(f10(f869(x100711,x100711),f870(f870(f869(x100711,x100711),a856),a856),x100711),f342(f869(x100711,x100711)))),f249(x100711,x100711)))),x100714)),a338),x100712),x100713))
% 21.40/21.37 [10021]E(f789(f789(f146(f864(x100211)),f789(f789(f146(x100211),x100212),f789(f138(f864(x100211),f864(x100211),f132(x100211),f122(x100211)),f789(f789(f150(f864(x100211),f864(x100211)),f152(f864(x100211),x100211,f122(x100211),f789(f789(f10(f864(x100211),f870(f864(x100211),f864(x100211)),x100211),f18(f864(x100211),f864(x100211))),f789(f789(f9(x100211,f864(x100211),f864(x100211)),f146(x100211)),f122(x100211))))),x100213)))),f168(x100211,f789(f789(f146(f864(x100211)),x100214),f789(f138(f864(f864(x100211)),f864(f864(x100211)),f132(f864(x100211)),f122(f864(x100211))),f789(f789(f150(f864(x100211),f864(f864(x100211))),f152(f864(f864(x100211)),x100211,f122(f864(x100211)),f789(f18(f870(f864(x100211),f864(f864(x100211))),x100211),f789(f789(f9(f864(x100211),f864(f864(x100211)),f864(f864(x100211))),f146(f864(x100211))),f122(f864(x100211)))))),x100213))))),f168(x100211,f789(f789(f146(f864(x100211)),f789(f789(f146(x100211),x100212),x100214)),x100213)))+~P1(f789(f329(f864(f864(x100211)),f169(x100211)),f789(f789(f146(f864(x100211)),f789(f789(f146(x100211),x100212),x100214)),x100213)))
% 21.40/21.37 [10061]~P1(f789(f70(x100612),f789(f264(x100612),x100614)))+P1(f789(f70(x100611),f789(f264(x100611),f789(f789(f10(f870(x100612,a856),a856,x100611),f96(x100612)),f789(f789(f9(x100611,f870(x100612,a856),f870(x100612,a856)),f789(f789(f10(f870(x100612,f870(a856,a856)),f870(f870(x100612,a856),f870(x100612,a856)),x100611),f20(x100612,a856,a856)),f789(f789(f10(f870(x100612,a856),f870(x100612,f870(a856,a856)),x100611),f789(f10(a856,f870(a856,a856),x100612),a339)),f789(f789(f9(x100611,f870(x100612,x100611),f870(x100612,a856)),f789(f789(f10(f870(x100611,a856),f870(f870(x100612,x100611),f870(x100612,a856)),x100611),f10(x100611,a856,x100612)),a338)),x100613)))),x100614)))))
% 21.40/21.37 [7209]E(x72091,x72092)+~E(f324(x72093,x72094,x72095,x72091),f324(x72093,x72094,x72095,x72092))
% 21.40/21.37 [7210]E(x72101,x72102)+~E(f325(x72103,x72104,x72105,x72101),f325(x72103,x72104,x72105,x72102))
% 21.40/21.37 [9019]~P39(f38(x90191,x90195),x90192,x90193,x90194)+P39(x90191,x90192,x90193,f853(x90194,x90193,x90192,x90195,x90191))
% 21.40/21.37 [9020]~P39(f38(x90201,x90205),x90202,x90203,x90204)+P39(x90201,x90202,x90203,f353(x90204,x90203,x90202,x90205,x90201))
% 21.40/21.37 [9021]~P39(f38(x90215,x90211),x90214,x90213,x90212)+P39(x90211,f853(x90212,x90213,x90214,x90211,x90215),x90213,x90212)
% 21.40/21.37 [9022]~P39(f38(x90225,x90221),x90224,x90223,x90222)+P39(x90221,f353(x90222,x90223,x90224,x90221,x90225),x90223,x90222)
% 21.40/21.37 [5565]E(f789(f789(f310(x55651),x55652),f173(x55651,x55653,x55654)),f173(x55651,x55653,x55654))+~E(f789(x55654,x55652),f789(f234(x55653),x55655))
% 21.40/21.37 [5977]P1(f789(f255(x59771,x59772,x59773),x59774))+~P1(f789(f789(x59773,x59775),x59774))
% 21.40/21.37 [5978]P1(f789(f255(x59781,x59782,x59783),x59784))+~P1(f789(f789(x59783,x59785),x59784))
% 21.40/21.37 [5979]P1(f789(f254(x59791,x59792,x59793),x59794))+~P1(f789(f789(x59793,x59794),x59795))
% 21.40/21.37 [5980]P1(f789(f254(x59801,x59802,x59803),x59804))+~P1(f789(f789(x59803,x59804),x59805))
% 21.40/21.37 [5983]~E(f789(x59834,x59832),f789(f234(x59833),x59835))+P1(f789(f789(f342(x59831),x59832),f173(x59831,x59833,x59834)))
% 21.40/21.37 [5984]~E(f789(x59844,x59845),f789(f234(x59841),x59842))+P1(f789(f789(f342(x59841),x59842),f175(x59843,x59841,x59844)))
% 21.40/21.37 [6464]~E(x64645,f2(a108))+E(f789(f200(x64641,x64642,x64643,x64644),x64645),f124(x64642))
% 21.40/21.37 [6465]~E(x64655,f2(a108))+E(f789(f198(x64651,x64652,x64653,x64654),x64655),f131(x64652))
% 21.40/21.37 [6560]~P39(f30(x65603,x65604),x65602,x65605,x65601)+E(x65601,f789(f789(f789(a193,x65602),x65603),f789(x65604,x65602)))
% 21.40/21.37 [6605]~E(x66053,f2(a108))+E(f789(f276(x66051,x66052,x66053,x66054),x66055),f789(f249(x66051,x66052),x66055))
% 21.40/21.37 [6683]~E(f789(x66834,x66835),f187(x66832))+E(f789(f236(f867(x66831),x66832,f187(x66831),x66833),f789(x66834,x66835)),f187(x66831))
% 21.40/21.37 [6684]~E(f789(x66844,x66845),f187(x66842))+E(f789(f236(f867(x66841),x66842,f187(x66841),x66843),f789(x66844,x66845)),f187(x66841))
% 21.40/21.37 [7332]E(f789(x73321,x73322),f187(x73323))+~E(f789(f174(x73324,x73323,x73325,x73321),x73322),f187(x73323))
% 21.40/21.37 [7333]E(f789(x73331,x73332),f187(x73333))+~E(f789(f174(x73334,x73333,x73331,x73335),x73332),f187(x73333))
% 21.40/21.37 [7373]E(f789(f174(x73731,x73732,x73733,x73734),x73735),f789(x73733,x73735))+P1(f789(f789(f342(x73731),x73735),f173(x73731,x73732,x73734)))
% 21.40/21.37 [7374]E(f789(f174(x73741,x73742,x73743,x73744),x73745),f789(x73744,x73745))+P1(f789(f789(f342(x73741),x73745),f173(x73741,x73742,x73743)))
% 21.40/21.37 [7700]~P24(x77004,x77001,x77002,x77005)+E(f789(f82(x77001,x77001,x77001,f789(x77002,x77003)),f789(x77002,x77003)),f789(x77002,x77003))
% 21.40/21.37 [7742]E(f789(f174(x77421,x77422,x77423,x77424),x77425),f789(x77424,x77425))+~P1(f789(f789(f342(x77421),x77425),f173(x77421,x77422,x77424)))
% 21.40/21.37 [8087]~P20(x80875,x80871,x80872)+E(f789(f82(x80871,x80871,x80871,f789(x80872,x80873)),f789(x80872,x80874)),f789(f82(x80871,x80871,x80871,f789(x80872,x80874)),f789(x80872,x80873)))
% 21.40/21.37 [8409]P1(f789(f789(f342(f869(x84091,x84091)),f789(f789(f249(x84091,x84091),x84092),x84093)),f335(x84091,x84094,x84095)))+~P1(f789(f789(f241(a863),f789(x84094,x84092)),f789(x84094,x84093)))
% 21.40/21.37 [8508]~P1(f789(f789(f342(x85084),x85083),f299(x85084,x85081,x85082,x85085)))+P1(f789(f789(x85081,x85082),x85083))
% 21.40/21.37 [8509]~P1(f789(f789(f342(x85094),x85093),f290(x85094,x85091,x85092,x85095)))+P1(f789(f789(x85091,x85092),x85093))
% 21.40/21.37 [8510]~P1(f789(f789(f342(x85104),x85102),f299(x85104,x85101,x85105,x85103)))+P1(f789(f789(x85101,x85102),x85103))
% 21.40/21.37 [8511]~P1(f789(f789(f342(x85114),x85112),f290(x85114,x85111,x85115,x85113)))+P1(f789(f789(x85111,x85112),x85113))
% 21.40/21.37 [8634]~P55(x86342,x86341,x86345,x86343,x86344)+E(f789(f311(x86341,x86342,x86343),x86344),f247(f870(x86342,a856)))
% 21.40/21.37 [9405]P1(f789(f789(f342(f869(f864(x94051),f864(x94051))),f789(f789(f249(f864(x94051),f864(x94051)),f789(f789(f146(x94051),x94052),x94053)),f789(f789(f146(x94051),x94052),x94054))),f153(x94051,x94055)))+~P1(f789(f789(f342(f869(f864(x94051),f864(x94051))),f789(f789(f249(f864(x94051),f864(x94051)),x94053),x94054)),f153(x94051,x94055)))
% 21.40/21.37 [9406]P1(f789(f789(f342(f869(f864(x94061),f864(x94061))),f789(f789(f249(f864(x94061),f864(x94061)),f789(f789(f132(x94061),x94062),x94063)),f789(f789(f132(x94061),x94062),x94064))),f143(x94061,x94065)))+~P1(f789(f789(f342(f869(f864(x94061),f864(x94061))),f789(f789(f249(f864(x94061),f864(x94061)),x94063),x94064)),f143(x94061,x94065)))
% 21.40/21.37 [9458]~E(f789(x94583,f395(x94582,x94581,x94584,x94585,x94583)),f789(f179(x94585,x94584,x94581),f395(x94582,x94581,x94584,x94585,x94583)))+E(f789(f789(x94581,x94582),f789(x94583,x94582)),f789(x94583,f789(a121,x94582)))
% 21.40/21.37 [9587]E(f789(f789(f146(x95871),f732(x95872,x95873,x95874,x95875,x95871)),f734(x95872,x95873,x95874,x95875,x95871)),x95875)+~P1(f789(f789(f342(f869(f864(x95871),f864(x95871))),f789(f789(f249(f864(x95871),f864(x95871)),x95875),f789(f789(f146(x95871),x95874),x95873))),f154(x95871,x95872)))
% 21.40/21.37 [9616]E(f789(f789(f146(x96161),f731(x96162,x96163,x96164,x96165,x96161)),f733(x96162,x96163,x96164,x96165,x96161)),x96163)+~P1(f789(f789(f342(f869(f864(x96161),f864(x96161))),f789(f789(f249(f864(x96161),f864(x96161)),f789(f789(f146(x96161),x96165),x96164)),x96163)),f154(x96161,x96162)))
% 21.40/21.37 [9751]~P1(f789(f789(f342(f869(f864(x97511),f864(x97511))),f789(f789(f249(f864(x97511),f864(x97511)),f789(f789(f146(x97511),x97515),x97512)),x97514)),f154(x97511,x97513)))+P1(f789(f789(f342(f869(f864(x97511),f864(x97511))),f789(f789(f249(f864(x97511),f864(x97511)),x97512),f733(x97513,x97514,x97512,x97515,x97511))),f154(x97511,x97513)))
% 21.40/21.37 [9836]~P1(f789(f789(f342(f869(f864(x98361),f864(x98361))),f789(f789(f249(f864(x98361),f864(x98361)),x98365),f789(f789(f146(x98361),x98364),x98363))),f154(x98361,x98362)))+P1(f789(f789(f342(f869(f864(x98361),f864(x98361))),f789(f789(f249(f864(x98361),f864(x98361)),f734(x98362,x98363,x98364,x98365,x98361)),x98363)),f154(x98361,x98362)))
% 21.40/21.37 [10015]P1(f789(f789(f342(f869(x100151,x100151)),f789(f789(f249(x100151,x100151),f789(x100152,f789(f789(f89(a863),x100153),x100154))),f789(x100152,x100153))),f308(x100151,x100155)))+~P1(f789(f789(f342(f869(x100151,x100151)),f789(f789(f249(x100151,x100151),f789(x100152,f789(a121,f652(x100154,x100153,x100155,x100152,x100151)))),f789(x100152,f652(x100154,x100153,x100155,x100152,x100151)))),f308(x100151,x100155)))
% 21.40/21.37 [10039]E(x100391,f2(a108))+E(f789(f236(f869(f864(x100392),x100393),f869(x100392,x100393),f789(f789(f249(f864(x100392),x100393),f122(x100392)),x100394),f789(f259(x100392,x100393,f869(f864(x100392),x100393)),f789(f789(f9(x100392,f870(x100393,f869(f864(x100392),x100393)),f870(x100393,f869(f864(x100392),x100393))),f789(f789(f10(f870(f869(f864(x100392),x100393),f869(f864(x100392),x100393)),f870(f870(x100393,f869(f864(x100392),x100393)),f870(x100393,f869(f864(x100392),x100393))),x100392),f10(f869(f864(x100392),x100393),f869(f864(x100392),x100393),x100393)),f789(f789(f10(f870(f864(x100392),f870(x100393,f869(f864(x100392),x100393))),f870(f869(f864(x100392),x100393),f869(f864(x100392),x100393)),x100392),f259(f864(x100392),x100393,f869(f864(x100392),x100393))),f789(f789(f10(f870(f864(x100392),f864(x100392)),f870(f864(x100392),f870(x100393,f869(f864(x100392),x100393))),x100392),f789(f10(f864(x100392),f870(x100393,f869(f864(x100392),x100393)),f864(x100392)),f249(f864(x100392),x100393))),f146(x100392))))),f126(x100393,x100392,x100395,f789(f789(f3(a108),x100391),f87(a108)))))),f789(x100395,x100394)),f789(f126(x100393,x100392,x100395,x100391),x100394))
% 21.40/21.37 [5167]E(x51671,x51672)+~E(f789(f789(f146(x51673),x51674),x51671),f789(f789(f146(x51673),x51675),x51672))
% 21.40/21.37 [5168]E(x51681,x51682)+~E(f789(f789(f146(x51683),x51681),x51684),f789(f789(f146(x51683),x51682),x51685))
% 21.40/21.37 [5362]~E(f789(f789(f135(x53621),x53623),x53622),f789(f789(f146(x53621),x53624),x53625))+E(f789(f789(f159(x53621),x53622),x53623),x53624)
% 21.40/21.37 [5496]~P19(x54964,x54965,x54961)+E(f789(f789(x54961,x54962),f789(f789(x54961,x54962),x54963)),f789(f789(x54961,x54962),x54963))
% 21.40/21.37 [5860]~E(f789(x58603,x58604),f789(f234(x58602),x58605))+E(f789(f789(f789(f81(x58601,f867(x58602)),x58603),x58604),f789(f234(x58602),x58605)),x58603)
% 21.40/21.37 [6111]~P101(x61112)+~E(f789(f789(f144(x61111,x61112,x61113),x61114),x61115),f122(x61111))
% 21.40/21.37 [6506]E(x65061,x65062)+~E(f789(f789(f132(x65063),x65064),f789(f789(f146(x65063),x65061),f122(x65063))),f789(f789(f132(x65063),x65065),f789(f789(f146(x65063),x65062),f122(x65063))))
% 21.40/21.37 [6507]E(x65071,x65072)+~E(f789(f789(f132(x65073),x65071),f789(f789(f146(x65073),x65074),f122(x65073))),f789(f789(f132(x65073),x65072),f789(f789(f146(x65073),x65075),f122(x65073))))
% 21.40/21.37 [6766]E(f789(f177(x67661,x67662,x67663,x67664),x67665),f187(x67662))+P1(f789(f789(f342(x67661),x67665),x67664))
% 21.40/21.37 [6767]E(f789(f177(x67671,x67672,x67673,x67674),x67675),f187(x67672))+P1(f789(f789(f342(x67671),x67675),x67674))
% 21.40/21.37 [6836]E(f789(f789(f310(x68361),f789(x68362,x68363)),f789(f311(x68364,x68361,x68362),x68365)),f789(f311(x68364,x68361,x68362),x68365))+~P1(f789(f789(f342(x68364),x68363),x68365))
% 21.40/21.37 [6845]~P1(f789(x68454,f789(x68453,x68455)))+P1(f789(f789(f313(x68451,x68452,x68453),x68454),x68455))
% 21.40/21.37 [6850]~E(x68504,f2(a108))+E(f789(f126(x68501,x68502,x68503,x68504),x68505),f789(f789(f249(f864(x68502),x68501),f122(x68502)),x68505))
% 21.40/21.37 [6943]~E(f789(f311(x69431,x69432,x69433),x69434),x69435)+E(f789(f311(f870(x69431,a856),f870(x69432,a856),f311(x69431,x69432,x69433)),f789(f309(x69431),x69434)),f789(f309(x69432),x69435))
% 21.40/21.37 [6973]E(f789(f177(x69731,x69732,x69733,x69734),x69735),f789(x69733,x69735))+~P1(f789(f789(f342(x69731),x69735),x69734))
% 21.40/21.37 [6974]E(f789(f177(x69741,x69742,x69743,x69744),x69745),f789(x69743,x69745))+~P1(f789(f789(f342(x69741),x69745),x69744))
% 21.40/21.37 [7289]P29(x72891,x72892,x72893,x72894)+~P29(x72891,x72892,x72893,f789(f789(f310(x72891),x72895),x72894))
% 21.40/21.37 [7360]P1(f789(x73601,x73602))+~P1(f789(f789(f101(x73603,x73604,x73601),x73605),x73602))
% 21.40/21.37 [7411]~P1(f789(f789(f342(x74114),x74113),x74115))+P1(f789(f789(f342(x74111),f789(x74112,x74113)),f789(f311(x74114,x74111,x74112),x74115)))
% 21.40/21.37 [7463]P1(f789(x74631,f789(x74632,x74633)))+~P1(f789(f789(f313(x74634,x74635,x74632),x74631),x74633))
% 21.40/21.37 [7464]P1(f789(f789(x74641,x74642),x74643))+~P1(f789(f789(f101(x74644,x74641,x74645),x74642),x74643))
% 21.40/21.37 [7532]~P1(f789(f789(f342(x75323),f789(x75324,x75322)),x75325))+P1(f789(f789(f342(x75321),x75322),f789(f313(x75321,x75323,x75324),x75325)))
% 21.40/21.37 [7533]~P1(f789(f789(f342(x75333),f789(x75334,x75332)),x75335))+P1(f789(f789(f342(x75331),x75332),f789(f313(x75331,x75333,x75334),x75335)))
% 21.40/21.37 [7930]~P1(f789(f789(f342(x79305),x79303),f789(f313(x79305,x79301,x79302),x79304)))+P1(f789(f789(f342(x79301),f789(x79302,x79303)),x79304))
% 21.40/21.37 [7931]~P1(f789(f789(f342(x79315),x79313),f789(f313(x79315,x79311,x79312),x79314)))+P1(f789(f789(f342(x79311),f789(x79312,x79313)),x79314))
% 21.40/21.37 [8147]~E(x81473,f789(f789(f789(f81(x81471,f867(x81472)),f789(f18(f867(x81472),x81471),f187(x81472))),x81474),f789(f234(x81472),x81475)))+E(f173(x81471,x81472,x81473),f789(f789(f310(x81471),x81474),f184(f870(x81471,a856))))
% 21.40/21.37 [8242]E(f789(x82421,f368(x82422,x82421,x82423,x82424)),x82424)+~P1(f789(f789(f342(x82425),x82424),f789(f311(x82423,x82425,x82421),x82422)))
% 21.40/21.37 [8494]P1(f789(f789(f342(f871(x84941,x84942)),f789(f321(x84942,x84941),x84943)),f322(x84941,x84942,x84944,x84945)))+~P1(f789(f789(f342(x84942),x84943),x84945))
% 21.40/21.37 [8495]P1(f789(f789(f342(f871(x84951,x84952)),f789(f312(x84951,x84952),x84953)),f322(x84951,x84952,x84954,x84955)))+~P1(f789(f789(f342(x84951),x84953),x84954))
% 21.40/21.37 [8552]~E(x85522,f789(f789(f146(x85521),x85524),x85525))+P1(f789(f789(f342(f869(f864(x85521),f864(x85521))),f789(f789(f249(f864(x85521),f864(x85521)),f122(x85521)),x85522)),f143(x85521,x85523)))
% 21.40/21.37 [8603]P1(f789(f789(f240(f870(x86031,a856)),f789(f789(f54(x86032,f870(x86031,a856)),x86033),x86034)),f789(x86034,x86035)))+~P1(f789(f789(f342(x86032),x86035),x86033))
% 21.40/21.37 [8650]~P55(x86501,x86502,x86503,x86505,x86504)+E(f789(f311(x86501,x86502,x86503),f247(f870(x86501,a856))),x86504)
% 21.40/21.37 [8839]E(f789(f789(f789(f81(x88391,f867(x88392)),f177(x88391,x88392,x88393,x88394)),x88395),f187(x88392)),f177(x88391,x88392,x88393,x88394))+P1(f789(f789(f342(x88391),x88395),x88394))
% 21.40/21.37 [8842]E(f789(x88421,f723(x88422,x88423,x88421,x88424,x88425)),x88422)+~E(f789(f789(f203(x88425,x88424),x88421),x88423),f789(f234(x88424),x88422))
% 21.40/21.37 [8845]E(f789(f234(x88451),f723(x88452,x88453,x88454,x88455,x88451)),x88453)+~E(f789(f789(f203(x88451,x88455),x88454),x88453),f789(f234(x88455),x88452))
% 21.40/21.37 [8930]E(f789(f185(f864(x89301)),x89302),x89303)+~P1(f789(f789(f342(f869(f864(x89301),f864(x89301))),f789(f789(f249(f864(x89301),f864(x89301)),x89304),x89302)),f789(f139(x89301,x89305),x89303)))
% 21.40/21.37 [8931]E(f789(f185(f864(x89311)),x89312),x89313)+~P1(f789(f789(f342(f869(f864(x89311),f864(x89311))),f789(f789(f249(f864(x89311),f864(x89311)),x89312),x89314)),f789(f139(x89311,x89315),x89313)))
% 21.40/21.37 [8991]P1(f789(f789(f342(x89911),f368(x89912,x89913,x89911,x89914)),x89912))+~P1(f789(f789(f342(x89915),x89914),f789(f311(x89911,x89915,x89913),x89912)))
% 21.40/21.37 [9146]E(f789(f311(x91461,x91462,x91463),f371(x91464,x91463,x91461,x91465,x91462)),x91465)+~P1(f789(f789(f240(f870(x91462,a856)),x91465),f789(f311(x91461,x91462,x91463),x91464)))
% 21.40/21.37 [9378]E(f789(x93781,f539(x93782,x93781,x93783,x93784,x93785)),f789(f234(x93785),x93784))+~P1(f789(f789(f342(x93785),x93784),f175(x93783,x93785,f177(x93783,x93785,x93781,x93782))))
% 21.40/21.37 [9421]P1(f789(f789(f342(f869(f864(x94211),f864(x94211))),f789(f789(f249(f864(x94211),f864(x94211)),f789(f789(f146(x94211),x94212),x94213)),f789(f789(f146(x94211),x94212),x94214))),f308(f864(x94211),f153(x94211,x94215))))+~P1(f789(f789(f342(f869(f864(x94211),f864(x94211))),f789(f789(f249(f864(x94211),f864(x94211)),x94213),x94214)),f308(f864(x94211),f153(x94211,x94215))))
% 21.40/21.37 [9451]~E(f789(x94513,f724(x94515,x94514,x94513,x94512,x94511)),f789(x94515,f724(x94515,x94514,x94513,x94512,x94511)))+E(f789(f789(f150(x94511,x94512),x94513),x94514),f789(f789(f150(x94511,x94512),x94515),x94514))
% 21.40/21.37 [9532]E(f789(f789(f150(x95321,x95322),x95323),x95324),f789(f789(f150(x95321,x95322),x95325),x95324))+P1(f789(f789(f342(x95321),f724(x95323,x95324,x95325,x95322,x95321)),f789(f163(x95321),x95324)))
% 21.40/21.37 [9560]~P1(f789(f789(f342(x95605),x95604),f789(f285(x95601,x95605,x95603),x95602)))+P1(f789(f789(f342(x95601),f375(x95602,x95603,x95601,x95604,x95605)),x95602))
% 21.40/21.37 [9561]~P1(f789(f789(f342(x95615),x95614),f789(f285(x95611,x95615,x95613),x95612)))+P1(f789(f789(f342(x95611),f383(x95612,x95613,x95611,x95614,x95615)),x95612))
% 21.40/21.37 [9585]~P1(f789(f789(f240(f870(x95855,a856)),x95854),f789(f311(x95851,x95855,x95853),x95852)))+P1(f789(f789(f240(f870(x95851,a856)),f371(x95852,x95853,x95851,x95854,x95855)),x95852))
% 21.40/21.37 [9634]~P1(f789(f789(f342(x96345),x96344),f175(x96341,x96345,f177(x96341,x96345,x96343,x96342))))+P1(f789(f789(f342(x96341),f539(x96342,x96343,x96341,x96344,x96345)),x96342))
% 21.40/21.37 [5375]~E(f789(x53753,x53754),x53755)+E(f789(f789(f789(f81(x53751,x53752),x53753),x53754),x53755),x53753)
% 21.40/21.37 [5376]~E(f789(x53763,x53764),x53765)+E(f789(f789(f789(f81(x53761,x53762),x53763),x53764),x53765),x53763)
% 21.40/21.37 [5825]E(f789(x58251,x58252),x58253)+~E(f789(f789(f789(f81(x58254,x58255),x58251),x58252),x58253),x58251)
% 21.40/21.37 [5914]E(x59141,x59142)+~E(f789(f258(x59143,x59144),f789(f789(f249(x59143,x59144),x59145),x59141)),x59142)
% 21.40/21.37 [5915]E(x59151,x59152)+~E(f789(f248(x59153,x59154),f789(f789(f249(x59153,x59154),x59151),x59155)),x59152)
% 21.40/21.37 [6593]E(f789(f311(x65931,x65932,f789(f18(x65932,x65931),x65933)),x65934),f789(f789(f310(x65932),x65933),f184(f870(x65932,a856))))+~P1(f789(f789(f342(x65931),x65935),x65934))
% 21.40/21.37 [6666]E(f789(f789(f110(f870(x66661,a856)),f789(f163(x66661),x66662)),f789(f163(x66661),x66663)),f789(f163(x66661),x66664))+~E(f162(x66661,x66665,x66664),f789(f789(f249(f864(x66661),f864(x66661)),x66662),x66663))
% 21.40/21.37 [6773]~P101(x67732)+E(f789(f185(f864(x67731)),f789(f789(f144(x67731,x67732,x67733),x67734),x67735)),f789(a121,f789(f185(f864(x67731)),x67735)))
% 21.40/21.37 [6787]~P101(x67872)+E(f789(f163(x67871),f789(f789(f144(x67871,x67872,x67873),x67874),x67875)),f789(f789(f310(x67871),x67874),f789(f163(x67871),x67875)))
% 21.40/21.37 [7065]~P70(x70651)+E(f789(f789(f89(x70651),f789(f789(f89(x70651),x70652),x70653)),f789(f789(f89(x70651),x70654),x70655)),f789(f789(f89(x70651),f789(f789(f89(x70651),x70652),x70654)),f789(f789(f89(x70651),x70653),x70655)))
% 21.40/21.37 [7066]~P70(x70661)+E(f789(f789(f90(x70661),f789(f789(f90(x70661),x70662),x70663)),f789(f789(f90(x70661),x70664),x70665)),f789(f789(f90(x70661),f789(f789(f90(x70661),x70662),x70664)),f789(f789(f90(x70661),x70663),x70665)))
% 21.40/21.37 [7067]~P60(x70671)+E(f789(f789(f291(x70671),f789(f789(f90(x70671),x70672),x70673)),f789(f789(f90(x70671),x70674),x70675)),f789(f789(f90(x70671),f789(f789(f291(x70671),x70672),x70674)),f789(f789(f291(x70671),x70673),x70675)))
% 21.40/21.37 [7081]~P101(x70811)+E(f306(x70811,f789(f789(f239(x70811),x70812),x70813),f789(f789(f244(x70811),x70814),x70815)),f789(f789(f111(f870(x70811,a856)),f306(x70811,x70812,x70814)),f306(x70811,x70813,x70815)))
% 21.40/21.37 [7082]~P101(x70821)+E(f305(x70821,f789(f789(f239(x70821),x70822),x70823),f789(f789(f244(x70821),x70824),x70825)),f789(f789(f111(f870(x70821,a856)),f305(x70821,x70822,x70824)),f305(x70821,x70823,x70825)))
% 21.40/21.37 [7083]~P101(x70831)+E(f303(x70831,f789(f789(f239(x70831),x70832),x70833),f789(f789(f244(x70831),x70834),x70835)),f789(f789(f111(f870(x70831,a856)),f303(x70831,x70832,x70834)),f303(x70831,x70833,x70835)))
% 21.40/21.37 [7084]~P101(x70841)+E(f789(f789(f111(f870(x70841,a856)),f789(f302(x70841,x70842),x70843)),f789(f302(x70841,x70844),x70845)),f789(f302(x70841,f789(f789(f239(x70841),x70842),x70844)),f789(f789(f244(x70841),x70843),x70845)))
% 21.40/21.37 [7201]~P1(f789(x72011,f843(x72013,x72012,x72011)))+P1(f789(x72011,f789(f789(f249(x72012,x72013),x72014),x72015)))
% 21.40/21.37 [7301]~E(f789(x73013,x73014),f187(x73012))+E(f175(x73011,x73012,f789(f789(f789(f81(x73011,f867(x73012)),x73013),x73014),f789(f234(x73012),x73015))),f789(f789(f310(x73012),x73015),f175(x73011,x73012,x73013)))
% 21.40/21.37 [7324]~E(x73242,f789(x73244,x73245))+P1(f789(f789(f342(x73241),x73242),f789(f311(x73243,x73241,x73244),f247(f870(x73243,a856)))))
% 21.40/21.37 [7385]~E(f789(x73853,x73854),f187(x73852))+E(f789(f789(f3(f870(x73851,a856)),f173(x73851,x73852,x73853)),f789(f789(f310(x73851),x73854),x73855)),f789(f789(f3(f870(x73851,a856)),f173(x73851,x73852,x73853)),x73855))
% 21.40/21.37 [7407]~P19(x74073,x74072,x74074)+P19(x74071,x74072,f789(f789(f10(x74073,f870(x74072,x74072),x74071),x74074),x74075))
% 21.40/21.37 [7408]~P20(x74083,x74082,x74084)+P20(x74081,x74082,f789(f789(f10(x74083,f870(x74082,x74082),x74081),x74084),x74085))
% 21.40/21.37 [7549]~P29(x75491,x75492,x75493,x75494)+P29(x75491,x75492,x75493,f789(f789(f3(f870(x75491,a856)),x75494),x75495))
% 21.40/21.37 [7707]~P1(f789(f789(x77073,x77074),x77075))+P1(f789(f789(f259(x77071,x77072,a856),x77073),f789(f789(f249(x77071,x77072),x77074),x77075)))
% 21.40/21.37 [7708]~P1(f789(f789(x77083,x77084),x77085))+P1(f789(f789(f259(x77081,x77082,a856),x77083),f789(f789(f249(x77081,x77082),x77084),x77085)))
% 21.40/21.37 [7842]P29(x78421,x78422,x78423,x78424)+~P29(x78421,x78422,x78423,f789(f789(f110(f870(x78421,a856)),x78425),x78424))
% 21.40/21.37 [7843]P29(x78431,x78432,x78433,x78434)+~P29(x78431,x78432,x78433,f789(f789(f110(f870(x78431,a856)),x78434),x78435))
% 21.40/21.37 [8046]~P31(x80461,f789(a121,x80462),f789(f789(f789(f100(x80461),x80463),f789(a29,x80464)),x80465))+P31(x80461,x80462,f789(f789(f789(f100(x80461),x80463),f789(f238(a857),f789(a32,x80464))),x80465))
% 21.40/21.37 [8173]P31(x81731,f789(a121,x81732),f789(f789(f789(f100(x81731),x81733),f789(a29,x81734)),x81735))+~P31(x81731,x81732,f789(f789(f789(f100(x81731),x81733),f789(f238(a857),f789(a32,x81734))),x81735))
% 21.40/21.37 [8202]~P19(x82022,x82021,x82023)+E(f789(f138(x82021,x82022,f789(f9(x82022,x82021,x82021),x82023),x82024),x82025),f789(f789(f73(x82022,x82021,x82023),x82024),f789(f163(x82022),x82025)))
% 21.40/21.37 [8252]P1(f789(f789(x82521,x82522),x82523))+~P1(f789(f789(f259(x82524,x82525,a856),x82521),f789(f789(f249(x82524,x82525),x82522),x82523)))
% 21.40/21.37 [8324]P39(x83244,f680(x83245,x83244,x83243,x83242),x83242,f786(x83245,x83244,x83243,x83242))+P31(x83241,x83242,f789(f789(f789(f100(x83241),x83243),x83244),x83245))
% 21.40/21.37 [8339]~E(f789(f170(x83391,x83392,x83395),x83393),f789(f234(x83392),x83394))+P1(f789(f789(f342(f869(x83391,x83392)),f789(f789(f249(x83391,x83392),x83393),x83394)),f789(f163(f869(x83391,x83392)),x83395)))
% 21.40/21.37 [8340]~E(f789(f170(x83401,x83402,x83405),x83403),f789(f234(x83402),x83404))+P1(f789(f789(f342(f869(x83401,x83402)),f789(f789(f249(x83401,x83402),x83403),x83404)),f789(f163(f869(x83401,x83402)),x83405)))
% 21.40/21.37 [8703]P1(f789(f789(f240(f870(x87031,a856)),f789(f311(x87032,x87031,x87033),x87034)),f789(f311(x87032,x87031,x87033),x87035)))+~P1(f789(f789(f240(f870(x87032,a856)),x87034),x87035))
% 21.40/21.37 [8704]P1(f789(f789(f240(f870(x87041,a856)),f789(f313(x87041,x87042,x87043),x87044)),f789(f313(x87041,x87042,x87043),x87045)))+~P1(f789(f789(f240(f870(x87042,a856)),x87044),x87045))
% 21.40/21.37 [8775]E(x87751,f2(a108))+E(f789(f789(f261(x87752,x87753,x87752,f869(x87753,x87752)),f789(x87754,x87755)),f276(x87753,x87752,f789(f789(f3(a108),x87751),f87(a108)),x87754)),f789(f276(x87753,x87752,x87751,x87754),x87755))
% 21.40/21.37 [8864]P1(f789(f789(f257(x88641,x88642,a856,x88643),x88644),x88645))+~P1(f789(x88643,f789(f789(f249(x88641,x88642),x88644),x88645)))
% 21.40/21.37 [9063]P31(x90631,x90632,f789(f789(f789(f100(x90631),x90633),x90634),x90635))+P1(f789(f789(x90633,f568(x90635,x90634,x90633,x90632)),f680(x90635,x90634,x90633,x90632)))
% 21.40/21.37 [9073]~P1(f789(f789(f191(x90733),f789(f789(f789(a193,x90734),f42(x90731)),f789(x90732,x90734))),x90735))+P1(f789(f789(f191(f34(x90731,x90732,x90733)),x90734),f789(f789(f789(a193,x90735),f42(x90731)),f789(f789(a194,x90734),x90731))))
% 21.40/21.37 [9125]~P1(f789(f789(f257(x91252,x91253,a856,x91251),x91254),x91255))+P1(f789(x91251,f789(f789(f249(x91252,x91253),x91254),x91255)))
% 21.40/21.37 [9126]~P1(f789(f789(f257(x91262,x91263,a856,x91261),x91264),x91265))+P1(f789(x91261,f789(f789(f249(x91262,x91263),x91264),x91265)))
% 21.40/21.37 [9233]E(f789(f234(x92331),f728(x92332,x92333,x92334,x92331,x92335)),f789(f170(x92335,x92331,x92332),x92334))+~P1(f789(f789(f342(f869(x92335,x92331)),f789(f789(f249(x92335,x92331),x92334),x92333)),f789(f163(f869(x92335,x92331)),x92332)))
% 21.40/21.37 [9275]P31(x92751,x92752,f789(f789(f789(f100(x92751),x92753),x92754),x92755))+~P1(f789(f789(x92755,f568(x92755,x92754,x92753,x92752)),f786(x92755,x92754,x92753,x92752)))
% 21.40/21.37 [9343]~P28(x93431,x93432,f789(f789(f310(f862(x93431)),f789(f789(f789(f100(x93431),x93433),f789(f238(a857),f789(a32,x93434))),x93435)),f184(f870(f862(x93431),a856))))+P28(x93431,x93432,f789(f789(f310(f862(x93431)),f789(f789(f789(f100(x93431),x93433),f789(a29,x93434)),x93435)),f184(f870(f862(x93431),a856))))
% 21.40/21.37 [9370]~P1(f789(f70(x93703),f789(f311(x93702,x93703,x93705),f247(f870(x93702,a856)))))+P1(f789(f70(x93701),f789(f311(x93702,x93701,f789(f789(f10(x93703,x93701,x93702),x93704),x93705)),f247(f870(x93702,a856)))))
% 21.40/21.37 [9391]P1(f789(f789(f240(f870(f870(x93911,a856),a856)),f789(f311(f870(x93912,a856),f870(x93911,a856),f311(x93912,x93911,x93913)),f789(f309(x93912),x93914))),f789(f309(x93911),x93915)))+~P1(f789(f789(f240(f870(x93911,a856)),f789(f311(x93912,x93911,x93913),x93914)),x93915))
% 21.40/21.37 [9401]~P1(f789(f70(f867(x94011)),f789(f311(x94012,f867(x94011),x94013),f247(f870(x94012,a856)))))+P1(f789(f70(f867(x94011)),f789(f311(x94012,f867(x94011),f789(f789(f789(f81(x94012,f867(x94011)),x94013),x94014),f789(f234(x94011),x94015))),f247(f870(x94012,a856)))))
% 21.40/21.37 [9432]P1(f789(f789(f191(x94321),f789(f789(f789(a193,x94322),f42(x94323)),f789(x94324,x94322))),f495(x94325,x94322,x94321,x94324,x94323)))+~P1(f789(f789(f191(f34(x94323,x94324,x94321)),x94322),x94325))
% 21.40/21.37 [9461]E(x94611,x94612)+~P1(f789(f75(x94613,x94614,x94615,x94611,f184(f870(x94613,a856))),x94612))
% 21.40/21.37 [9474]E(f789(f789(f249(x94741,x94742),f579(x94743,x94744,x94745,x94742,x94741)),f580(x94743,x94744,x94745,x94742,x94741)),x94745)+~P1(f789(f789(f342(f869(x94741,x94742)),x94745),f789(f789(f256(x94741,x94742),x94744),x94743)))
% 21.40/21.37 [9485]P1(f789(f789(f191(x94851),f789(f789(f789(a193,x94852),f42(x94853)),f789(x94854,x94852))),f424(x94855,x94852,x94851,x94854,x94853)))+~P1(f789(f789(f191(f34(x94853,x94854,x94851)),x94852),f789(f789(f789(a193,x94855),f42(x94853)),f789(f789(a194,x94852),x94853))))
% 21.40/21.37 [9491]~P1(f789(f789(f191(f789(a29,x94912)),f789(f789(f789(a193,f789(f789(a195,x94914),a196)),f42(a28)),f789(x94913,x94914))),x94915))+P1(f789(f789(f191(f33(x94911,x94912,x94913)),x94914),f789(f789(f789(a193,f789(f789(a195,x94915),f789(a194,x94914))),x94911),f789(f789(a194,x94915),a27))))
% 21.40/21.37 [9525]P1(f789(f789(f191(f789(a29,x95251)),f789(f789(f789(a193,f789(f789(a195,x95252),a196)),f42(a28)),f789(x95253,x95252))),f570(x95254,x95252,x95253,x95251,x95255)))+~P1(f789(f789(f191(f33(x95255,x95251,x95253)),x95252),x95254))
% 21.40/21.37 [9565]P1(f789(f789(f342(x95651),f579(x95652,x95653,x95654,x95655,x95651)),x95653))+~P1(f789(f789(f342(f869(x95651,x95655)),x95654),f789(f789(f256(x95651,x95655),x95653),x95652)))
% 21.40/21.37 [9591]E(f789(f789(f789(a193,f495(x95911,x95912,x95913,x95914,x95915)),f42(x95915)),f789(f789(a194,x95912),x95915)),x95911)+~P1(f789(f789(f191(f34(x95915,x95914,x95913)),x95912),x95911))
% 21.40/21.37 [9617]E(f789(f789(f789(a193,f424(x96171,x96172,x96173,x96174,x96175)),f42(x96175)),f789(f789(a194,x96172),x96175)),f789(f789(f789(a193,x96171),f42(x96175)),f789(f789(a194,x96172),x96175)))+~P1(f789(f789(f191(f34(x96175,x96174,x96173)),x96172),f789(f789(f789(a193,x96171),f42(x96175)),f789(f789(a194,x96172),x96175))))
% 21.40/21.37 [9641]P1(f789(f789(f191(f789(a29,x96411)),f789(f789(f789(a193,f789(f789(a195,x96412),a196)),f42(a28)),f789(x96413,x96412))),f545(x96414,x96412,x96413,x96411,x96415)))+~P1(f789(f789(f191(f33(x96415,x96411,x96413)),x96412),f789(f789(f789(a193,f789(f789(a195,x96414),f789(a194,x96412))),x96415),f789(f789(a194,x96414),a27))))
% 21.40/21.37 [9668]P28(x96685,x96684,f789(f789(f310(f862(x96685)),f789(f789(f789(f100(x96685),x96681),x96683),x96682)),f184(f870(f862(x96685),a856))))+P1(f789(f789(x96681,f354(x96682,x96683,x96684,x96685,x96681)),f355(x96682,x96683,x96684,x96685,x96681)))
% 21.40/21.37 [9709]P1(f789(f789(f342(x97091),f580(x97092,x97093,x97094,x97091,x97095)),f789(x97092,f579(x97092,x97093,x97094,x97091,x97095))))+~P1(f789(f789(f342(f869(x97095,x97091)),x97094),f789(f789(f256(x97095,x97091),x97093),x97092)))
% 21.40/21.37 [9727]P1(f789(f789(f342(f869(x97271,x97271)),f789(f789(f249(x97271,x97271),x97272),f695(x97273,x97274,x97275,x97272,x97271))),x97273))+~P1(f789(f789(f342(f869(x97271,x97271)),f789(f789(f249(x97271,x97271),x97272),x97275)),f789(f789(f178(f869(x97271,x97271),a856),f789(a121,x97274)),x97273)))
% 21.40/21.37 [9728]P1(f789(f789(f342(f869(x97281,x97281)),f789(f789(f249(x97281,x97281),x97282),f697(x97283,x97284,x97285,x97282,x97281))),x97283))+~P1(f789(f789(f342(f869(x97281,x97281)),f789(f789(f249(x97281,x97281),x97282),x97285)),f789(f789(f178(f869(x97281,x97281),a856),f789(a121,x97284)),x97283)))
% 21.40/21.37 [9746]~P1(f789(f789(f342(f869(f864(x97461),f864(x97461))),f789(f789(f249(f864(x97461),f864(x97461)),f789(f789(f146(x97461),x97462),x97465)),x97464)),f154(x97461,x97463)))+P1(f789(f789(f342(f869(x97461,x97461)),f789(f789(f249(x97461,x97461),x97462),f731(x97463,x97464,x97465,x97462,x97461))),x97463))
% 21.40/21.37 [9748]~P32(x97481,x97482,f789(f789(f310(f862(x97481)),f789(f789(f789(f100(x97481),f101(x97481,x97483,x97484)),x97485),x97483)),f184(f870(f862(x97481),a856))))+P32(x97481,x97482,f789(f789(f310(f862(x97481)),f789(f789(f789(f100(x97481),x97483),f37(x97484,x97485)),f101(x97481,x97483,f789(f82(a856,a856,a861,a336),x97484)))),f184(f870(f862(x97481),a856))))
% 21.40/21.37 [9749]~P28(x97491,x97492,f789(f789(f310(f862(x97491)),f789(f789(f789(f100(x97491),f101(x97491,x97493,x97494)),x97495),x97493)),f184(f870(f862(x97491),a856))))+P28(x97491,x97492,f789(f789(f310(f862(x97491)),f789(f789(f789(f100(x97491),x97493),f37(x97494,x97495)),f101(x97491,x97493,f789(f82(a856,a856,a861,a336),x97494)))),f184(f870(f862(x97491),a856))))
% 21.40/21.37 [9868]E(f789(f789(f789(a193,f789(f789(a195,f570(x98681,x98682,x98683,x98684,x98685)),f789(a194,x98682))),x98685),f789(f789(a194,f570(x98681,x98682,x98683,x98684,x98685)),a27)),x98681)+~P1(f789(f789(f191(f33(x98685,x98684,x98683)),x98682),x98681))
% 21.40/21.37 [9880]E(f789(f789(f789(a193,f789(f789(a195,f545(x98801,x98802,x98803,x98804,x98805)),f789(a194,x98802))),x98805),f789(f789(a194,f545(x98801,x98802,x98803,x98804,x98805)),a27)),f789(f789(f789(a193,f789(f789(a195,x98801),f789(a194,x98802))),x98805),f789(f789(a194,x98801),a27)))+~P1(f789(f789(f191(f33(x98805,x98804,x98803)),x98802),f789(f789(f789(a193,f789(f789(a195,x98801),f789(a194,x98802))),x98805),f789(f789(a194,x98801),a27))))
% 21.40/21.37 [10040]P28(x100401,x100402,f789(f789(f310(f862(x100401)),f789(f789(f789(f100(x100401),x100403),x100404),x100405)),f184(f870(f862(x100401),a856))))+~P28(x100401,x100402,f789(f789(f310(f862(x100401)),f789(f789(f789(f100(x100401),f789(f18(f870(a861,a856),x100401),f789(f789(f9(a861,a861,a856),a338),f355(x100405,x100404,x100402,x100401,x100403)))),x100404),f789(f18(f870(a861,a856),x100401),f789(x100405,f354(x100405,x100404,x100402,x100401,x100403))))),f184(f870(f862(x100401),a856))))
% 21.40/21.37 [6308]~P72(x63082)+E(f789(f789(f789(f3(f870(x63081,x63082)),x63083),x63084),x63085),f789(f789(f3(x63082),f789(x63083,x63085)),f789(x63084,x63085)))
% 21.40/21.37 [6309]~P72(x63092)+E(f789(f789(f789(f3(f870(x63091,x63092)),x63093),x63094),x63095),f789(f789(f3(x63092),f789(x63093,x63095)),f789(x63094,x63095)))
% 21.40/21.37 [6310]~P95(x63102)+E(f789(f789(f789(f110(f870(x63101,x63102)),x63103),x63104),x63105),f789(f789(f110(x63102),f789(x63103,x63105)),f789(x63104,x63105)))
% 21.40/21.37 [6311]~P95(x63112)+E(f789(f789(f789(f110(f870(x63111,x63112)),x63113),x63114),x63115),f789(f789(f110(x63112),f789(x63113,x63115)),f789(x63114,x63115)))
% 21.40/21.37 [6312]~P95(x63122)+E(f789(f789(f789(f111(f870(x63121,x63122)),x63123),x63124),x63125),f789(f789(f111(x63122),f789(x63123,x63125)),f789(x63124,x63125)))
% 21.40/21.37 [6313]~P95(x63132)+E(f789(f789(f789(f111(f870(x63131,x63132)),x63133),x63134),x63135),f789(f789(f111(x63132),f789(x63133,x63135)),f789(x63134,x63135)))
% 21.40/21.37 [6335]E(x63351,x63352)+E(f789(f789(f159(x63353),f789(f789(f155(x63353,x63354),x63351),x63355)),x63352),f789(f789(f159(x63353),x63354),x63352))
% 21.40/21.37 [6610]~E(x66104,f184(f870(x66103,a856)))+E(f789(f789(f3(f870(x66101,a856)),x66102),f789(f789(f53(x66103,f870(x66101,a856)),x66104),x66105)),x66102)
% 21.40/21.37 [6611]~E(x66114,f184(f870(x66113,a856)))+E(f789(f789(f110(f870(x66111,a856)),x66112),f789(f789(f53(x66113,f870(x66111,a856)),x66114),x66115)),x66112)
% 21.40/21.37 [6612]~E(x66124,f184(f870(x66123,a856)))+E(f789(f789(f111(f870(x66121,a856)),x66122),f789(f789(f54(x66123,f870(x66121,a856)),x66124),x66125)),x66122)
% 21.40/21.37 [6625]~E(x66254,f184(f870(x66253,a856)))+E(f789(f789(f310(x66251),x66252),f789(f789(f53(x66253,f870(x66251,a856)),x66254),x66255)),f789(f789(f310(x66251),x66252),f184(f870(x66251,a856))))
% 21.40/21.37 [7064]~P70(x70641)+E(f789(f789(f90(x70641),f789(f789(f90(x70641),x70642),x70643)),f789(f789(f90(x70641),x70644),x70645)),f789(f789(f90(x70641),x70642),f789(f789(f90(x70641),x70643),f789(f789(f90(x70641),x70644),x70645))))
% 21.40/21.37 [7452]E(f789(f789(f159(x74521),f789(f789(f150(x74522,x74521),x74523),x74524)),x74525),f789(x74523,f789(f789(f159(x74522),x74524),x74525)))+~P1(f789(f789(f241(a863),x74525),f789(f185(f864(x74522)),x74524)))
% 21.40/21.37 [7521]E(f789(f789(f110(f870(x75211,a856)),f789(x75212,x75213)),f789(f789(f53(x75214,f870(x75211,a856)),x75215),x75212)),f789(f789(f53(x75214,f870(x75211,a856)),x75215),x75212))+~P1(f789(f789(f342(x75214),x75213),x75215))
% 21.40/21.37 [7522]E(f789(f789(f111(f870(x75221,a856)),f789(x75222,x75223)),f789(f789(f54(x75224,f870(x75221,a856)),x75225),x75222)),f789(f789(f54(x75224,f870(x75221,a856)),x75225),x75222))+~P1(f789(f789(f342(x75224),x75223),x75225))
% 21.40/21.37 [8122]~E(x81223,f184(f870(x81221,a856)))+E(f789(f789(f53(x81221,f870(x81222,a856)),x81223),f789(f789(f10(f870(x81222,a856),f870(x81222,a856),x81221),f789(f310(x81222),x81224)),x81225)),f184(f870(x81222,a856)))
% 21.40/21.37 [8128]~P1(f789(f789(f342(x81284),x81283),x81285))+P1(f789(f789(f240(f870(x81281,a856)),f789(x81282,x81283)),f789(f789(f53(x81284,f870(x81281,a856)),x81285),x81282)))
% 21.40/21.37 [8251]~E(f789(x82514,x82512),x82515)+P1(f789(f789(f342(x82511),x82512),f789(f313(x82511,x82513,x82514),f789(f789(f310(x82513),x82515),f184(f870(x82513,a856))))))
% 21.40/21.37 [8298]~P53(x82981,x82982,f789(f286(x82982,x82981),x82983))+E(f789(f789(f111(f870(x82981,a856)),f789(f285(x82982,x82981,x82983),x82984)),f789(f285(x82982,x82981,x82983),x82985)),f789(f285(x82982,x82981,x82983),f789(f789(f111(f870(x82982,a856)),x82984),x82985)))
% 21.40/21.37 [8323]E(x83231,f2(a108))+E(f125(x83232,x83233,f789(x83234,f789(f789(f3(a108),x83231),f87(a108))),f789(f789(f9(x83232,a108,f865(x83233)),x83235),x83231)),f789(f200(x83232,x83233,x83234,x83235),x83231))
% 21.40/21.37 [8418]E(x84181,f184(f870(x84182,a856)))+E(f789(f789(f53(x84182,f870(x84183,a856)),x84181),f789(f789(f10(f870(x84183,a856),f870(x84183,a856),x84182),f789(f310(x84183),x84184)),x84185)),f789(f789(f310(x84183),x84184),f789(f789(f53(x84182,f870(x84183,a856)),x84181),x84185)))
% 21.40/21.37 [8419]E(x84191,f184(f870(x84192,a856)))+E(f789(f789(f53(x84192,f870(x84193,a856)),x84191),f789(f789(f10(f870(x84193,a856),f870(x84193,a856),x84192),f789(f310(x84193),x84194)),x84195)),f789(f789(f310(x84193),x84194),f789(f789(f53(x84192,f870(x84193,a856)),x84191),x84195)))
% 21.40/21.37 [8472]~P29(x84722,x84721,x84723,f247(f870(x84722,a856)))+E(f789(f789(f3(f870(x84721,a856)),f789(f311(x84722,x84721,x84723),x84724)),f789(f311(x84722,x84721,x84723),x84725)),f789(f311(x84722,x84721,x84723),f789(f789(f3(f870(x84722,a856)),x84724),x84725)))
% 21.40/21.37 [8473]~P29(x84732,x84731,x84733,f247(f870(x84732,a856)))+E(f789(f789(f111(f870(x84731,a856)),f789(f311(x84732,x84731,x84733),x84734)),f789(f311(x84732,x84731,x84733),x84735)),f789(f311(x84732,x84731,x84733),f789(f789(f111(f870(x84732,a856)),x84734),x84735)))
% 21.40/21.37 [8540]~P1(f789(f789(f76(x85401,x85402,x85405),x85403),x85404))+P1(f789(f789(f342(f869(x85401,x85402)),f789(f789(f249(x85401,x85402),x85403),x85404)),x85405))
% 21.40/21.37 [8567]P1(f789(f789(f342(x85671),x85672),f789(f267(x85673,x85671),x85674)))+~P1(f789(f789(f342(f869(x85673,x85671)),f789(f789(f249(x85673,x85671),x85675),x85672)),x85674))
% 21.40/21.37 [8568]P1(f789(f789(f342(x85681),x85682),f789(f267(x85683,x85681),x85684)))+~P1(f789(f789(f342(f869(x85683,x85681)),f789(f789(f249(x85683,x85681),x85685),x85682)),x85684))
% 21.40/21.37 [8569]P1(f789(f789(f342(x85691),x85692),f789(f269(x85691,x85693),x85694)))+~P1(f789(f789(f342(f869(x85691,x85693)),f789(f789(f249(x85691,x85693),x85692),x85695)),x85694))
% 21.40/21.37 [8570]P1(f789(f789(f342(x85701),x85702),f789(f269(x85701,x85703),x85704)))+~P1(f789(f789(f342(f869(x85701,x85703)),f789(f789(f249(x85701,x85703),x85702),x85705)),x85704))
% 21.40/21.37 [8692]P1(f789(f789(f76(x86921,x86922,x86923),x86924),x86925))+~P1(f789(f789(f342(f869(x86921,x86922)),f789(f789(f249(x86921,x86922),x86924),x86925)),x86923))
% 21.40/21.37 [8725]E(f789(x87251,x87252),x87253)+~P1(f789(f789(f342(x87254),x87252),f789(f313(x87254,x87255,x87251),f789(f789(f310(x87255),x87253),f184(f870(x87255,a856))))))
% 21.40/21.37 [8926]P1(f789(f789(f342(f869(x89261,x89262)),f789(f789(f249(x89261,x89262),x89263),x89264)),f789(f286(x89262,x89261),x89265)))+~P1(f789(f789(f342(f869(x89262,x89261)),f789(f789(f249(x89262,x89261),x89264),x89263)),x89265))
% 21.40/21.37 [8927]P1(f789(f789(f342(f869(x89271,x89272)),f789(f789(f249(x89271,x89272),x89273),x89274)),f789(f286(x89272,x89271),x89275)))+~P1(f789(f789(f342(f869(x89272,x89271)),f789(f789(f249(x89272,x89271),x89274),x89273)),x89275))
% 21.40/21.37 [8945]~P1(f789(f789(x89451,x89455),x89454))+P1(f789(f789(x89451,f789(f258(x89452,x89453),f789(f789(f249(x89452,x89453),x89454),x89455))),f789(f248(x89452,x89453),f789(f789(f249(x89452,x89453),x89454),x89455))))
% 21.40/21.37 [8971]~P1(f789(f789(f342(f869(x89712,x89711)),f789(f789(f249(x89712,x89711),x89714),x89713)),f789(f286(x89711,x89712),x89715)))+P1(f789(f789(f342(f869(x89711,x89712)),f789(f789(f249(x89711,x89712),x89713),x89714)),x89715))
% 21.40/21.37 [8972]~P1(f789(f789(f342(f869(x89722,x89721)),f789(f789(f249(x89722,x89721),x89724),x89723)),f789(f286(x89721,x89722),x89725)))+P1(f789(f789(f342(f869(x89721,x89722)),f789(f789(f249(x89721,x89722),x89723),x89724)),x89725))
% 21.40/21.37 [8999]~P1(f789(f789(f342(f869(x89993,x89991)),f789(f789(f249(x89993,x89991),x89995),x89992)),x89994))+P1(f789(f789(f342(x89991),x89992),f789(f285(x89993,x89991,x89994),f789(f789(f310(x89993),x89995),f184(f870(x89993,a856))))))
% 21.40/21.37 [9046]P1(f789(f789(f342(f869(x90461,x90462)),f789(f789(f249(x90461,x90462),x90463),x90464)),x90465))+~P1(f789(f789(f342(x90462),x90464),f789(f285(x90461,x90462,x90465),f789(f789(f310(x90461),x90463),f184(f870(x90461,a856))))))
% 21.40/21.37 [9066]E(f789(f789(f789(f81(x90661,f867(x90662)),f177(x90661,x90662,x90663,x90664)),x90665),f187(x90662)),f177(x90661,x90662,x90663,f789(f789(f3(f870(x90661,a856)),x90664),f789(f789(f310(x90661),x90665),f184(f870(x90661,a856))))))+~P1(f789(f789(f342(x90661),x90665),x90664))
% 21.40/21.37 [9132]~P4(x91321)+E(f789(f789(f8(a863,x91321),x91322),f303(a863,f789(f789(f89(a863),x91323),x91324),f789(f789(f89(a863),x91325),x91324))),f789(f789(f8(a863,x91321),f789(f789(f10(a863,x91321,a863),x91322),f789(f789(f9(a863,a863,a863),f89(a863)),x91324))),f303(a863,x91323,x91325)))
% 21.40/21.37 [9150]~P4(x91501)+E(f789(f789(f8(a863,x91501),x91502),f789(f302(a863,f789(f789(f89(a863),x91503),x91504)),f789(f789(f89(a863),x91505),x91504))),f789(f789(f8(a863,x91501),f789(f789(f10(a863,x91501,a863),x91502),f789(f789(f9(a863,a863,a863),f89(a863)),x91504))),f789(f302(a863,x91503),x91505)))
% 21.40/21.37 [9358]P1(f789(f789(f342(f869(f864(x93581),f864(x93581))),f789(f789(f249(f864(x93581),f864(x93581)),f789(f789(f146(x93581),x93582),x93583)),f789(f789(f146(x93581),x93584),x93583))),f153(x93581,x93585)))+~P1(f789(f789(f342(f869(x93581,x93581)),f789(f789(f249(x93581,x93581),x93582),x93584)),x93585))
% 21.40/21.37 [9459]P28(x94591,x94592,f789(f789(f310(f862(x94591)),f789(f789(f789(f100(x94591),x94593),f789(a29,x94594)),x94595)),f184(f870(f862(x94591),a856))))+~P28(x94591,f789(f789(f310(f862(x94591)),f789(f789(f789(f100(x94591),x94593),f789(a29,x94594)),x94595)),x94592),f789(f789(f310(f862(x94591)),f789(f789(f789(f100(x94591),x94593),f789(f238(a857),f789(a32,x94594))),x94595)),f184(f870(f862(x94591),a856))))
% 21.40/21.37 [9470]E(f789(f789(f310(x94701),f556(x94702,x94703,x94704,x94705,x94701)),f557(x94702,x94703,x94704,x94705,x94701)),f789(f789(f310(x94701),x94704),x94703))+~P1(f789(f71(x94701,x94705,f789(f789(f310(x94701),x94704),x94703)),x94702))
% 21.40/21.37 [9471]E(f789(f789(f310(x94711),f558(x94712,x94713,x94714,x94715,x94711)),f560(x94712,x94713,x94714,x94715,x94711)),f789(f789(f310(x94711),x94714),x94713))+~P1(f789(f71(x94711,x94715,f789(f789(f310(x94711),x94714),x94713)),x94712))
% 21.40/21.37 [9551]P1(f789(f789(f342(x95511),f658(x95512,x95513,x95514,x95515,x95511)),x95514))+P1(f789(f789(f789(f54(x95511,f870(x95515,a856)),x95514),x95513),x95512))
% 21.40/21.37 [9556]P1(f789(f789(f342(x95561),f649(x95562,x95563,x95561,x95564,x95565)),x95563))+P1(f789(f789(f342(x95565),x95564),f789(f789(f54(x95561,f870(x95565,a856)),x95563),x95562)))
% 21.40/21.37 [9564]P1(f789(f789(f342(x95641),f647(x95642,x95643,x95641,x95644,x95645)),x95643))+P1(f789(f789(f240(f870(x95645,a856)),x95644),f789(f789(f54(x95641,f870(x95645,a856)),x95643),x95642)))
% 21.40/21.37 [9567]P1(f789(f789(x95671,f423(x95672,x95671,x95673,x95674,x95675)),x95672))+~P1(f789(f789(f789(f53(x95675,f870(x95674,a856)),x95673),x95671),x95672))
% 21.40/21.37 [9569]P1(f789(f789(f342(x95691),f423(x95692,x95693,x95694,x95695,x95691)),x95694))+~P1(f789(f789(f789(f53(x95691,f870(x95695,a856)),x95694),x95693),x95692))
% 21.40/21.37 [9579]P1(f789(f789(f342(x95791),f429(x95792,x95793,x95791,x95794,x95795)),x95793))+~P1(f789(f789(f342(x95795),x95794),f789(f789(f53(x95791,f870(x95795,a856)),x95793),x95792)))
% 21.40/21.37 [9584]P1(f789(f789(f342(x95841),x95842),f789(x95843,f429(x95843,x95844,x95845,x95842,x95841))))+~P1(f789(f789(f342(x95841),x95842),f789(f789(f53(x95845,f870(x95841,a856)),x95844),x95843)))
% 21.40/21.37 [9672]~P1(f789(f789(x96724,f658(x96725,x96724,x96723,x96722,x96721)),x96725))+P1(f789(f789(f789(f54(x96721,f870(x96722,a856)),x96723),x96724),x96725))
% 21.40/21.37 [9675]~P1(f789(f789(f342(x96751),x96752),f789(x96755,f649(x96755,x96754,x96753,x96752,x96751))))+P1(f789(f789(f342(x96751),x96752),f789(f789(f54(x96753,f870(x96751,a856)),x96754),x96755)))
% 21.40/21.37 [9678]~P1(f789(f789(f240(f870(x96781,a856)),x96782),f789(x96785,f647(x96785,x96784,x96783,x96782,x96781))))+P1(f789(f789(f240(f870(x96781,a856)),x96782),f789(f789(f54(x96783,f870(x96781,a856)),x96784),x96785)))
% 21.40/21.37 [9731]~P1(f789(f789(f342(x97311),f556(x97315,x97314,x97313,x97312,x97311)),f557(x97315,x97314,x97313,x97312,x97311)))+~P1(f789(f71(x97311,x97312,f789(f789(f310(x97311),x97313),x97314)),x97315))
% 21.40/21.37 [9732]~P1(f789(f789(f342(x97321),f558(x97325,x97324,x97323,x97322,x97321)),f560(x97325,x97324,x97323,x97322,x97321)))+~P1(f789(f71(x97321,x97322,f789(f789(f310(x97321),x97323),x97324)),x97325))
% 21.40/21.37 [9733]~P1(f789(f789(f342(f869(x97331,x97331)),f789(f789(f249(x97331,x97331),x97332),x97335)),f789(f789(f178(f869(x97331,x97331),a856),f789(a121,x97334)),x97333)))+P1(f789(f789(f342(f869(x97331,x97331)),f789(f789(f249(x97331,x97331),x97332),f696(x97333,x97334,x97335,x97332,x97331))),f789(f789(f178(f869(x97331,x97331),a856),x97334),x97333)))
% 21.40/21.37 [9740]P1(f789(f75(x97401,x97401,x97402,f556(x97403,x97404,x97405,x97402,x97401),f557(x97403,x97404,x97405,x97402,x97401)),x97403))+~P1(f789(f71(x97401,x97402,f789(f789(f310(x97401),x97405),x97404)),x97403))
% 21.40/21.37 [9741]P1(f789(f75(x97411,x97411,x97412,f558(x97413,x97414,x97415,x97412,x97411),f560(x97413,x97414,x97415,x97412,x97411)),x97413))+~P1(f789(f71(x97411,x97412,f789(f789(f310(x97411),x97415),x97414)),x97413))
% 21.40/21.37 [9753]~P101(x97531)+P18(x97531,f789(f789(f150(x97532,x97531),x97533),f789(f133(x97532,f789(f789(f9(x97532,x97531,a856),f789(f789(f10(x97531,f870(x97531,a856),x97532),a338),x97533)),f789(x97534,x97535))),x97535)))
% 21.40/21.37 [9808]~P1(f789(f789(f342(x98082),x98085),f789(f285(x98081,x98082,x98084),x98083)))+P1(f789(f789(f342(f869(x98081,x98082)),f789(f789(f249(x98081,x98082),f375(x98083,x98084,x98081,x98085,x98082)),x98085)),x98084))
% 21.40/21.37 [9809]~P1(f789(f789(f342(x98092),x98095),f789(f285(x98091,x98092,x98094),x98093)))+P1(f789(f789(f342(f869(x98091,x98092)),f789(f789(f249(x98091,x98092),f383(x98093,x98094,x98091,x98095,x98092)),x98095)),x98094))
% 21.40/21.37 [9829]~P1(f789(f789(f342(f869(x98291,x98291)),f789(f789(f249(x98291,x98291),x98295),x98294)),f789(f789(f178(f869(x98291,x98291),a856),f789(a121,x98293)),x98292)))+P1(f789(f789(f342(f869(x98291,x98291)),f789(f789(f249(x98291,x98291),f696(x98292,x98293,x98294,x98295,x98291)),x98294)),x98292))
% 21.40/21.37 [9832]~P1(f789(f789(f342(f869(x98321,x98321)),f789(f789(f249(x98321,x98321),x98325),x98324)),f789(f789(f178(f869(x98321,x98321),a856),f789(a121,x98323)),x98322)))+P1(f789(f789(f342(f869(x98321,x98321)),f789(f789(f249(x98321,x98321),f695(x98322,x98323,x98324,x98325,x98321)),x98324)),f789(f789(f178(f869(x98321,x98321),a856),x98323),x98322)))
% 21.40/21.37 [9833]~P1(f789(f789(f342(f869(x98331,x98331)),f789(f789(f249(x98331,x98331),x98335),x98334)),f789(f789(f178(f869(x98331,x98331),a856),f789(a121,x98333)),x98332)))+P1(f789(f789(f342(f869(x98331,x98331)),f789(f789(f249(x98331,x98331),f697(x98332,x98333,x98334,x98335,x98331)),x98334)),f789(f789(f178(f869(x98331,x98331),a856),x98333),x98332)))
% 21.40/21.37 [9834]~P1(f789(f789(f342(f869(f864(x98341),f864(x98341))),f789(f789(f249(f864(x98341),f864(x98341)),x98345),f789(f789(f146(x98341),x98344),x98343))),f154(x98341,x98342)))+P1(f789(f789(f342(f869(x98341,x98341)),f789(f789(f249(x98341,x98341),f732(x98342,x98343,x98344,x98345,x98341)),x98344)),x98342))
% 21.40/21.37 [7023]E(x70231,f187(x70232))+E(f173(x70233,x70232,f789(f789(f789(f81(x70233,f867(x70232)),x70234),x70235),x70231)),f789(f789(f310(x70233),x70235),f173(x70233,x70232,x70234)))
% 21.40/21.37 [7542]~E(x75423,f184(f870(x75422,a856)))+E(f789(f789(f110(f870(x75421,a856)),f789(f789(f53(x75422,f870(x75421,a856)),x75423),x75424)),x75425),x75425)
% 21.40/21.37 [7543]~E(x75433,f184(f870(x75432,a856)))+E(f789(f789(f111(f870(x75431,a856)),f789(f789(f54(x75432,f870(x75431,a856)),x75433),x75434)),x75435),x75435)
% 21.40/21.37 [7595]~P70(x75951)+E(f789(f789(f90(x75951),f789(f789(f90(x75951),x75952),x75953)),f789(f789(f90(x75951),x75954),x75955)),f789(f789(f90(x75951),x75954),f789(f789(f90(x75951),f789(f789(f90(x75951),x75952),x75953)),x75955)))
% 21.40/21.37 [7904]~E(x79045,f187(x79042))+E(f173(x79041,x79042,f789(f789(f789(f81(x79041,f867(x79042)),x79043),x79044),x79045)),f789(f789(f3(f870(x79041,a856)),f173(x79041,x79042,x79043)),f789(f789(f310(x79041),x79044),f184(f870(x79041,a856)))))
% 21.40/21.37 [7972]~E(x79723,f184(f870(x79722,a856)))+E(f789(f789(f3(f870(x79721,a856)),f789(f789(f54(x79722,f870(x79721,a856)),x79723),x79724)),x79725),f789(f789(f3(f870(x79721,a856)),f247(f870(x79721,a856))),x79725))
% 21.40/21.37 [8099]E(f789(f789(f155(x80991,f789(f789(f132(x80991),x80992),x80993)),x80994),x80995),f789(f789(f132(x80991),f789(f789(f155(x80991,x80992),x80994),x80995)),x80993))+~P1(f789(f789(f241(a863),x80994),f789(f185(f864(x80991)),x80992)))
% 21.40/21.37 [8100]E(f789(f789(f155(x81001,f789(f789(f132(x81001),x81002),x81003)),x81004),x81005),f789(f789(f132(x81001),f789(f789(f155(x81001,x81002),x81004),x81005)),x81003))+~P1(f789(f789(f241(a863),x81004),f789(f185(f864(x81001)),x81002)))
% 21.40/21.37 [8229]P1(f789(f789(f342(x82291),x82295),f789(f163(x82291),x82293)))+E(f789(f170(x82291,x82292,f789(f789(f171(x82291,x82292),x82293),f789(f789(f150(x82291,x82292),x82294),x82293))),x82295),f187(x82292))
% 21.40/21.37 [8338]~P1(f789(f789(f342(x83381),x83385),f789(f163(x83381),x83383)))+E(f789(f170(x83381,x83382,f789(f789(f171(x83381,x83382),x83383),f789(f789(f150(x83381,x83382),x83384),x83383))),x83385),f789(f234(x83382),f789(x83384,x83385)))
% 21.40/21.37 [8369]E(f789(f789(f159(x83691),f789(f789(f150(a863,x83691),x83692),f136(a863,f789(f302(a863,x83693),x83694)))),x83695),f789(x83692,f789(f789(f89(a863),x83693),x83695)))+~P1(f789(f789(f241(a863),x83695),f789(f789(f3(a863),x83694),x83693)))
% 21.40/21.37 [8382]E(x83821,f2(a108))+E(f129(x83822,x83823,f789(x83824,f789(f789(f3(a108),x83821),f87(a108))),f789(f789(f9(x83822,a108,f865(f867(x83823))),x83825),x83821)),f789(f198(x83822,x83823,x83824,x83825),x83821))
% 21.40/21.37 [8406]~E(x84063,f184(f870(x84061,a856)))+E(f789(f789(f53(x84061,f870(x84062,a856)),x84063),f789(f789(f10(f870(x84062,a856),f870(x84062,a856),x84061),f789(f110(f870(x84062,a856)),x84064)),x84065)),f184(f870(x84062,a856)))
% 21.40/21.37 [8407]~E(x84073,f184(f870(x84071,a856)))+E(f789(f789(f54(x84071,f870(x84072,a856)),x84073),f789(f789(f10(f870(x84072,a856),f870(x84072,a856),x84071),f789(f3(f870(x84072,a856)),x84074)),x84075)),f247(f870(x84072,a856)))
% 21.40/21.37 [8408]~E(x84083,f184(f870(x84081,a856)))+E(f789(f789(f54(x84081,f870(x84082,a856)),x84083),f789(f789(f10(f870(x84082,a856),f870(x84082,a856),x84081),f789(f111(f870(x84082,a856)),x84084)),x84085)),f247(f870(x84082,a856)))
% 21.40/21.37 [8413]~P136(x84132)+E(f789(f789(f8(x84131,x84132),f789(f789(f10(x84132,x84132,x84131),f789(f90(x84132),x84133)),x84134)),x84135),f789(f789(f90(x84132),x84133),f789(f789(f8(x84131,x84132),x84134),x84135)))
% 21.40/21.37 [8674]E(x86741,f184(f870(x86742,a856)))+E(f789(f789(f54(x86742,f870(x86743,a856)),x86741),f789(f789(f10(f870(x86743,a856),f870(x86743,a856),x86742),f789(f3(f870(x86743,a856)),x86744)),x86745)),f789(f789(f3(f870(x86743,a856)),x86744),f789(f789(f53(x86742,f870(x86743,a856)),x86741),x86745)))
% 21.40/21.37 [8675]E(x86751,f184(f870(x86752,a856)))+E(f789(f789(f53(x86752,f870(x86753,a856)),x86751),f789(f789(f10(f870(x86753,a856),f870(x86753,a856),x86752),f789(f110(f870(x86753,a856)),x86754)),x86755)),f789(f789(f110(f870(x86753,a856)),x86754),f789(f789(f53(x86752,f870(x86753,a856)),x86751),x86755)))
% 21.40/21.37 [8676]E(x86761,f184(f870(x86762,a856)))+E(f789(f789(f54(x86762,f870(x86763,a856)),x86761),f789(f789(f10(f870(x86763,a856),f870(x86763,a856),x86762),f789(f111(f870(x86763,a856)),x86764)),x86765)),f789(f789(f111(f870(x86763,a856)),x86764),f789(f789(f54(x86762,f870(x86763,a856)),x86761),x86765)))
% 21.40/21.37 [8677]E(x86771,f184(f870(x86772,a856)))+E(f789(f789(f53(x86772,f870(x86773,a856)),x86771),f789(f789(f10(f870(x86773,a856),f870(x86773,a856),x86772),f789(f110(f870(x86773,a856)),x86774)),x86775)),f789(f789(f110(f870(x86773,a856)),x86774),f789(f789(f53(x86772,f870(x86773,a856)),x86771),x86775)))
% 21.40/21.37 [8678]E(x86781,f184(f870(x86782,a856)))+E(f789(f789(f54(x86782,f870(x86783,a856)),x86781),f789(f789(f10(f870(x86783,a856),f870(x86783,a856),x86782),f789(f3(f870(x86783,a856)),x86784)),x86785)),f789(f789(f3(f870(x86783,a856)),x86784),f789(f789(f53(x86782,f870(x86783,a856)),x86781),x86785)))
% 21.40/21.37 [8679]E(x86791,f184(f870(x86792,a856)))+E(f789(f789(f54(x86792,f870(x86793,a856)),x86791),f789(f789(f10(f870(x86793,a856),f870(x86793,a856),x86792),f789(f111(f870(x86793,a856)),x86794)),x86795)),f789(f789(f111(f870(x86793,a856)),x86794),f789(f789(f54(x86792,f870(x86793,a856)),x86791),x86795)))
% 21.40/21.37 [9100]~P29(x91002,x91001,x91003,f789(f789(f110(f870(x91002,a856)),x91004),x91005))+E(f789(f789(f111(f870(x91001,a856)),f789(f311(x91002,x91001,x91003),f789(f789(f3(f870(x91002,a856)),x91004),x91005))),f789(f311(x91002,x91001,x91003),f789(f789(f3(f870(x91002,a856)),x91005),x91004))),f184(f870(x91001,a856)))
% 21.40/21.37 [9354]~P1(f789(f789(f240(f870(x93543,a856)),f789(f285(x93541,x93543,x93544),x93542)),x93545))+P1(f789(f789(f240(f870(x93541,a856)),x93542),f789(f88(f870(x93541,a856)),f789(f285(x93543,x93541,f789(f286(x93541,x93543),x93544)),f789(f88(f870(x93543,a856)),x93545)))))
% 21.40/21.37 [9377]~P29(x93771,x93772,x93773,f789(f789(f310(x93771),x93774),x93775))+~P1(f789(f789(f342(x93772),f789(x93773,x93774)),f789(f311(x93771,x93772,x93773),f789(f789(f3(f870(x93771,a856)),x93775),f789(f789(f310(x93771),x93774),f184(f870(x93771,a856)))))))
% 21.40/21.37 [9425]P1(f789(f789(f240(f870(x94251,a856)),f789(f285(x94252,x94251,x94253),x94254)),x94255))+~P1(f789(f789(f240(f870(x94252,a856)),x94254),f789(f88(f870(x94252,a856)),f789(f285(x94251,x94252,f789(f286(x94252,x94251),x94253)),f789(f88(f870(x94251,a856)),x94255)))))
% 21.40/21.37 [9501]~P80(x95011)+P1(f789(f789(f240(x95011),f789(f84(x95011),f789(f789(f3(x95011),f789(f789(f89(x95011),x95012),x95013)),f789(f789(f89(x95011),x95014),x95015)))),f789(f789(f89(x95011),f789(f84(x95011),f789(f789(f3(x95011),x95012),x95014))),f789(f84(x95011),f789(f789(f3(x95011),x95013),x95015)))))
% 21.40/21.37 [9597]P1(f789(f789(f342(x95971),f430(x95972,x95973,x95974,x95971,x95975)),x95974))+P1(f789(f789(f240(f870(x95975,a856)),f789(f789(f53(x95971,f870(x95975,a856)),x95974),x95973)),x95972))
% 21.40/21.37 [9773]~P1(f789(f789(f240(f870(x97731,a856)),f789(x97734,f430(x97735,x97734,x97733,x97732,x97731))),x97735))+P1(f789(f789(f240(f870(x97731,a856)),f789(f789(f53(x97732,f870(x97731,a856)),x97733),x97734)),x97735))
% 21.40/21.37 [8521]E(f789(f789(f132(x85211),x85212),f789(f789(f155(x85211,x85213),f789(f789(f3(a863),x85214),f789(f185(f864(x85211)),x85212))),x85215)),f789(f789(f155(x85211,f789(f789(f132(x85211),x85212),x85213)),x85214),x85215))+P1(f789(f789(f241(a863),x85214),f789(f185(f864(x85211)),x85212)))
% 21.40/21.37 [8546]~P135(x85461)+E(f789(f789(f89(x85461),f789(f789(f90(x85461),x85462),x85463)),f789(f789(f89(x85461),f789(f789(f90(x85461),x85464),x85463)),x85465)),f789(f789(f89(x85461),f789(f789(f90(x85461),f789(f789(f89(x85461),x85462),x85464)),x85463)),x85465))
% 21.40/21.37 [9056]~P136(x90561)+E(f789(f161(x90561),f789(f789(f150(x90562,x90561),f789(f789(f10(x90561,x90561,x90562),f789(f90(x90561),x90563)),x90564)),x90565)),f789(f789(f90(x90561),x90563),f789(f161(x90561),f789(f789(f150(x90562,x90561),x90564),x90565))))
% 21.40/21.37 [9433]~P136(x94332)+E(f789(f789(f8(x94331,x94332),f789(f789(f9(x94331,x94332,x94332),f789(f789(f10(x94332,f870(x94332,x94332),x94331),f90(x94332)),x94333)),x94334)),x94335),f789(f789(f90(x94332),f789(f789(f8(x94331,x94332),x94333),x94335)),x94334))
% 21.40/21.37 [9434]~P61(x94342)+E(f789(f789(f8(x94341,x94342),f789(f789(f9(x94341,x94342,x94342),f789(f789(f10(x94342,f870(x94342,x94342),x94341),f291(x94342)),x94343)),x94344)),x94345),f789(f789(f291(x94342),f789(f789(f8(x94341,x94342),x94343),x94345)),x94344))
% 21.40/21.37 [9441]~P69(x94412)+E(f789(f789(f11(x94411,x94412),f789(f789(f20(x94411,x94412,x94412),f789(f789(f10(x94412,f870(x94412,x94412),x94411),f90(x94412)),x94413)),x94414)),x94415),f789(f789(f90(x94412),f789(f789(f11(x94411,x94412),x94413),x94415)),f789(f789(f11(x94411,x94412),x94414),x94415)))
% 21.40/21.37 [9442]~P4(x94422)+E(f789(f789(f8(x94421,x94422),f789(f789(f20(x94421,x94422,x94422),f789(f789(f10(x94422,f870(x94422,x94422),x94421),f89(x94422)),x94423)),x94424)),x94425),f789(f789(f89(x94422),f789(f789(f8(x94421,x94422),x94423),x94425)),f789(f789(f8(x94421,x94422),x94424),x94425)))
% 21.40/21.37 [9443]~P6(x94432)+E(f789(f789(f8(x94431,x94432),f789(f789(f20(x94431,x94432,x94432),f789(f789(f10(x94432,f870(x94432,x94432),x94431),f3(x94432)),x94433)),x94434)),x94435),f789(f789(f3(x94432),f789(f789(f8(x94431,x94432),x94433),x94435)),f789(f789(f8(x94431,x94432),x94434),x94435)))
% 21.40/21.37 [9482]~E(x94823,f184(f870(x94821,a856)))+E(f789(f789(f53(x94821,f870(x94822,a856)),x94823),f789(f789(f9(x94821,f870(x94822,a856),f870(x94822,a856)),f789(f789(f10(f870(x94822,a856),f870(f870(x94822,a856),f870(x94822,a856)),x94821),f110(f870(x94822,a856))),x94824)),x94825)),f184(f870(x94822,a856)))
% 21.40/21.37 [9483]~E(x94833,f184(f870(x94831,a856)))+E(f789(f789(f54(x94831,f870(x94832,a856)),x94833),f789(f789(f9(x94831,f870(x94832,a856),f870(x94832,a856)),f789(f789(f10(f870(x94832,a856),f870(f870(x94832,a856),f870(x94832,a856)),x94831),f3(f870(x94832,a856))),x94834)),x94835)),f247(f870(x94832,a856)))
% 21.40/21.37 [9484]~E(x94843,f184(f870(x94841,a856)))+E(f789(f789(f54(x94841,f870(x94842,a856)),x94843),f789(f789(f9(x94841,f870(x94842,a856),f870(x94842,a856)),f789(f789(f10(f870(x94842,a856),f870(f870(x94842,a856),f870(x94842,a856)),x94841),f111(f870(x94842,a856))),x94844)),x94845)),f247(f870(x94842,a856)))
% 21.40/21.37 [9508]E(x95081,f184(f870(x95082,a856)))+E(f789(f789(f54(x95082,f870(x95083,a856)),x95081),f789(f789(f9(x95082,f870(x95083,a856),f870(x95083,a856)),f789(f789(f10(f870(x95083,a856),f870(f870(x95083,a856),f870(x95083,a856)),x95082),f3(f870(x95083,a856))),x95084)),x95085)),f789(f789(f3(f870(x95083,a856)),f789(f789(f54(x95082,f870(x95083,a856)),x95081),x95084)),x95085))
% 21.40/21.37 [9509]E(x95091,f184(f870(x95092,a856)))+E(f789(f789(f53(x95092,f870(x95093,a856)),x95091),f789(f789(f9(x95092,f870(x95093,a856),f870(x95093,a856)),f789(f789(f10(f870(x95093,a856),f870(f870(x95093,a856),f870(x95093,a856)),x95092),f110(f870(x95093,a856))),x95094)),x95095)),f789(f789(f110(f870(x95093,a856)),f789(f789(f53(x95092,f870(x95093,a856)),x95091),x95094)),x95095))
% 21.40/21.37 [9510]E(x95101,f184(f870(x95102,a856)))+E(f789(f789(f54(x95102,f870(x95103,a856)),x95101),f789(f789(f9(x95102,f870(x95103,a856),f870(x95103,a856)),f789(f789(f10(f870(x95103,a856),f870(f870(x95103,a856),f870(x95103,a856)),x95102),f111(f870(x95103,a856))),x95104)),x95105)),f789(f789(f111(f870(x95103,a856)),f789(f789(f54(x95102,f870(x95103,a856)),x95101),x95104)),x95105))
% 21.40/21.37 [9511]E(x95111,f184(f870(x95112,a856)))+E(f789(f789(f53(x95112,f870(x95113,a856)),x95111),f789(f789(f9(x95112,f870(x95113,a856),f870(x95113,a856)),f789(f789(f10(f870(x95113,a856),f870(f870(x95113,a856),f870(x95113,a856)),x95112),f110(f870(x95113,a856))),x95114)),x95115)),f789(f789(f110(f870(x95113,a856)),f789(f789(f53(x95112,f870(x95113,a856)),x95111),x95114)),x95115))
% 21.40/21.37 [9512]E(x95121,f184(f870(x95122,a856)))+E(f789(f789(f54(x95122,f870(x95123,a856)),x95121),f789(f789(f9(x95122,f870(x95123,a856),f870(x95123,a856)),f789(f789(f10(f870(x95123,a856),f870(f870(x95123,a856),f870(x95123,a856)),x95122),f3(f870(x95123,a856))),x95124)),x95125)),f789(f789(f3(f870(x95123,a856)),f789(f789(f54(x95122,f870(x95123,a856)),x95121),x95124)),x95125))
% 21.40/21.37 [9513]E(x95131,f184(f870(x95132,a856)))+E(f789(f789(f54(x95132,f870(x95133,a856)),x95131),f789(f789(f9(x95132,f870(x95133,a856),f870(x95133,a856)),f789(f789(f10(f870(x95133,a856),f870(f870(x95133,a856),f870(x95133,a856)),x95132),f111(f870(x95133,a856))),x95134)),x95135)),f789(f789(f111(f870(x95133,a856)),f789(f789(f54(x95132,f870(x95133,a856)),x95131),x95134)),x95135))
% 21.40/21.37 [9105]~P1(f789(f789(f240(a863),x91051),x91054))+E(f789(f789(f3(a863),f789(f789(f89(a863),f789(f789(f90(a863),x91051),x91052)),x91053)),f789(f789(f89(a863),f789(f789(f90(a863),x91054),x91052)),x91055)),f789(f789(f3(a863),x91053),f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f3(a863),x91054),x91051)),x91052)),x91055)))
% 21.40/21.37 [9654]~P136(x96541)+E(f789(f161(x96541),f789(f789(f150(x96542,x96541),f789(f789(f9(x96542,x96541,x96541),f789(f789(f10(x96541,f870(x96541,x96541),x96542),f90(x96541)),x96543)),x96544)),x96545)),f789(f789(f90(x96541),f789(f161(x96541),f789(f789(f150(x96542,x96541),x96543),x96545))),x96544))
% 21.40/21.37 [9660]~P4(x96601)+E(f789(f161(x96601),f789(f789(f150(x96602,x96601),f789(f789(f20(x96602,x96601,x96601),f789(f789(f10(x96601,f870(x96601,x96601),x96602),f89(x96601)),x96603)),x96604)),x96605)),f789(f789(f89(x96601),f789(f161(x96601),f789(f789(f150(x96602,x96601),x96603),x96605))),f789(f161(x96601),f789(f789(f150(x96602,x96601),x96604),x96605))))
% 21.40/21.37 [9661]~P6(x96611)+E(f789(f161(x96611),f789(f789(f150(x96612,x96611),f789(f789(f20(x96612,x96611,x96611),f789(f789(f10(x96611,f870(x96611,x96611),x96612),f3(x96611)),x96613)),x96614)),x96615)),f789(f789(f3(x96611),f789(f161(x96611),f789(f789(f150(x96612,x96611),x96613),x96615))),f789(f161(x96611),f789(f789(f150(x96612,x96611),x96614),x96615))))
% 21.40/21.37 [9320]~P1(f789(f789(f240(a863),x93204),x93201))+E(f789(f789(f3(a863),f789(f789(f89(a863),f789(f789(f90(a863),x93201),x93202)),x93203)),f789(f789(f89(a863),f789(f789(f90(a863),x93204),x93202)),x93205)),f789(f789(f3(a863),f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f3(a863),x93201),x93204)),x93202)),x93203)),x93205))
% 21.40/21.37 [10065]P32(x100651,x100652,f789(f311(a859,f862(x100651),f789(f789(f20(a859,f870(x100651,f870(a861,a856)),f862(x100651)),f789(f789(f20(a859,a857,f870(f870(x100651,f870(a861,a856)),f862(x100651))),f789(f789(f10(f870(x100651,f870(a861,a856)),f870(a857,f870(f870(x100651,f870(a861,a856)),f862(x100651))),a859),f100(x100651)),x100653)),a29)),x100654)),x100655))+~P32(x100651,f789(f789(f110(f870(f862(x100651),a856)),x100652),f789(f311(a859,f862(x100651),f789(f789(f20(a859,f870(x100651,f870(a861,a856)),f862(x100651)),f789(f789(f20(a859,a857,f870(f870(x100651,f870(a861,a856)),f862(x100651))),f789(f789(f10(f870(x100651,f870(a861,a856)),f870(a857,f870(f870(x100651,f870(a861,a856)),f862(x100651))),a859),f100(x100651)),x100653)),a29)),x100654)),x100655)),f789(f311(a859,f862(x100651),f789(f789(f20(a859,f870(x100651,f870(a861,a856)),f862(x100651)),f789(f789(f20(a859,a857,f870(f870(x100651,f870(a861,a856)),f862(x100651))),f789(f789(f10(f870(x100651,f870(a861,a856)),f870(a857,f870(f870(x100651,f870(a861,a856)),f862(x100651))),a859),f100(x100651)),x100653)),f789(f789(f10(f867(a857),a857,a859),f238(a857)),a32))),x100654)),x100655))
% 21.40/21.37 [10066]P28(x100661,x100662,f789(f311(a859,f862(x100661),f789(f789(f20(a859,f870(x100661,f870(a861,a856)),f862(x100661)),f789(f789(f20(a859,a857,f870(f870(x100661,f870(a861,a856)),f862(x100661))),f789(f789(f10(f870(x100661,f870(a861,a856)),f870(a857,f870(f870(x100661,f870(a861,a856)),f862(x100661))),a859),f100(x100661)),x100663)),a29)),x100664)),x100665))+~P28(x100661,f789(f789(f110(f870(f862(x100661),a856)),x100662),f789(f311(a859,f862(x100661),f789(f789(f20(a859,f870(x100661,f870(a861,a856)),f862(x100661)),f789(f789(f20(a859,a857,f870(f870(x100661,f870(a861,a856)),f862(x100661))),f789(f789(f10(f870(x100661,f870(a861,a856)),f870(a857,f870(f870(x100661,f870(a861,a856)),f862(x100661))),a859),f100(x100661)),x100663)),a29)),x100664)),x100665)),f789(f311(a859,f862(x100661),f789(f789(f20(a859,f870(x100661,f870(a861,a856)),f862(x100661)),f789(f789(f20(a859,a857,f870(f870(x100661,f870(a861,a856)),f862(x100661))),f789(f789(f10(f870(x100661,f870(a861,a856)),f870(a857,f870(f870(x100661,f870(a861,a856)),f862(x100661))),a859),f100(x100661)),x100663)),f789(f789(f10(f867(a857),a857,a859),f238(a857)),a32))),x100664)),x100665))
% 21.40/21.37 [5193]E(x51931,x51932)+~E(f35(x51933,x51934,x51931),f35(x51935,x51936,x51932))
% 21.40/21.37 [5194]E(x51941,x51942)+~E(f35(x51943,x51941,x51944),f35(x51945,x51942,x51946))
% 21.40/21.37 [5195]E(x51951,x51952)+~E(f35(x51951,x51953,x51954),f35(x51952,x51955,x51956))
% 21.40/21.37 [5196]E(x51961,x51962)+~E(f34(x51963,x51964,x51961),f34(x51965,x51966,x51962))
% 21.40/21.37 [5197]E(x51971,x51972)+~E(f34(x51973,x51971,x51974),f34(x51975,x51972,x51976))
% 21.40/21.37 [5198]E(x51981,x51982)+~E(f34(x51981,x51983,x51984),f34(x51982,x51985,x51986))
% 21.40/21.37 [5199]E(x51991,x51992)+~E(f33(x51993,x51994,x51991),f33(x51995,x51996,x51992))
% 21.40/21.37 [5200]E(x52001,x52002)+~E(f33(x52003,x52001,x52004),f33(x52005,x52002,x52006))
% 21.40/21.37 [5201]E(x52011,x52012)+~E(f33(x52011,x52013,x52014),f33(x52012,x52015,x52016))
% 21.40/21.37 [7211]E(x72111,x72112)+~E(f222(x72113,x72114,x72115,x72111),f222(x72113,x72114,x72116,x72112))
% 21.40/21.37 [7212]E(x72121,x72122)+~E(f222(x72123,x72124,x72121,x72125),f222(x72123,x72124,x72122,x72126))
% 21.40/21.37 [6655]E(f789(f174(x66551,x66552,x66553,x66554),x66555),f789(f234(x66552),x66556))+~E(f789(x66554,x66555),f789(f234(x66552),x66556))
% 21.40/21.37 [6656]E(f789(f174(x66561,x66562,x66563,x66564),x66565),f789(f234(x66562),x66566))+~E(f789(x66564,x66565),f789(f234(x66562),x66566))
% 21.40/21.37 [6807]E(f789(f236(f867(x68071),x68072,f187(x68071),x68073),f789(x68074,x68075)),f789(x68073,x68076))+~E(f789(x68074,x68075),f789(f234(x68072),x68076))
% 21.40/21.37 [8349]~P23(x83495,x83491,x83492,x83496)+E(f789(f82(x83491,x83491,x83491,f789(x83492,x83493)),f789(x83492,x83494)),f789(f82(x83491,x83491,x83491,f789(x83492,x83494)),f789(x83492,x83493)))
% 21.40/21.37 [8581]~P55(x85814,x85815,x85812,x85811,x85816)+E(f789(x85811,f789(x85812,x85813)),x85813)
% 21.40/21.37 [8723]P29(x87231,x87232,x87233,x87234)+~P29(x87231,x87235,f789(f82(x87232,x87235,x87231,x87236),x87233),x87234)
% 21.40/21.37 [8800]~P29(x88004,x88002,f789(f82(x88001,x88002,x88004,x88003),x88005),x88006)+P29(x88001,x88002,x88003,f789(f311(x88004,x88001,x88005),x88006))
% 21.40/21.37 [9444]P1(f789(f70(x94441),x94442))+~P1(f789(f75(x94441,x94443,x94444,x94445,x94442),x94446))
% 21.40/21.37 [9454]~P1(f789(f789(f342(x94544),x94543),f300(x94544,x94545,x94541,x94542,x94546)))+P1(f789(f789(x94541,x94542),x94543))
% 21.40/21.37 [9455]~P1(f789(f789(f342(x94554),x94553),f297(x94554,x94551,x94555,x94552,x94556)))+P1(f789(f789(x94551,x94552),x94553))
% 21.40/21.37 [9456]~P1(f789(f789(f342(x94564),x94562),f300(x94564,x94561,x94565,x94566,x94563)))+P1(f789(f789(x94561,x94562),x94563))
% 21.40/21.37 [9457]~P1(f789(f789(f342(x94574),x94572),f297(x94574,x94575,x94571,x94576,x94573)))+P1(f789(f789(x94571,x94572),x94573))
% 21.40/21.37 [9628]~P39(f34(x96283,x96284,x96281),x96282,x96285,x96286)+P39(x96281,f789(f789(f789(a193,x96282),f42(x96283)),f789(x96284,x96282)),x96285,f505(x96286,x96285,x96282,x96281,x96284,x96283))
% 21.40/21.37 [9639]~P39(f33(x96396,x96391,x96393),x96392,x96394,x96395)+P39(f789(a29,x96391),f789(f789(f789(a193,f789(f789(a195,x96392),a196)),f42(a28)),f789(x96393,x96392)),x96394,f581(x96395,x96394,x96392,x96393,x96391,x96396))
% 21.40/21.37 [5679]E(x56791,x56792)+~E(f789(f789(f249(x56793,x56794),x56795),x56791),f789(f789(f249(x56793,x56794),x56796),x56792))
% 21.40/21.37 [5680]E(x56801,x56802)+~E(f789(f789(f249(x56803,x56804),x56805),x56801),f789(f789(f249(x56803,x56804),x56806),x56802))
% 21.40/21.37 [5681]E(x56811,x56812)+~E(f789(f789(f249(x56813,x56814),x56811),x56815),f789(f789(f249(x56813,x56814),x56812),x56816))
% 21.40/21.37 [5682]E(x56821,x56822)+~E(f789(f789(f249(x56823,x56824),x56821),x56825),f789(f789(f249(x56823,x56824),x56822),x56826))
% 21.40/21.37 [5821]~P20(x58215,x58216,x58211)+E(f789(f789(x58211,x58212),f789(f789(x58211,x58213),x58214)),f789(f789(x58211,x58213),f789(f789(x58211,x58212),x58214)))
% 21.40/21.37 [7282]~P34(x72824,x72821,f789(f789(f146(x72824),x72822),x72825),f789(f789(f146(x72824),x72823),x72826))+P1(f789(f789(x72821,x72822),x72823))
% 21.40/21.37 [7661]P34(x76611,x76612,x76613,x76614)+~P34(x76611,x76612,f789(f789(f146(x76611),x76615),x76613),f789(f789(f146(x76611),x76616),x76614))
% 21.40/21.37 [8284]~P39(x82843,f789(f789(f789(a193,x82844),f42(x82841)),f789(x82842,x82844)),x82845,x82846)+P39(f34(x82841,x82842,x82843),x82844,x82845,f789(f789(f789(a193,x82846),f42(x82841)),f789(f789(a194,x82844),x82841)))
% 21.40/21.37 [8668]~P55(x86685,x86681,x86682,x86686,x86684)+P1(f789(f789(f342(x86681),f789(x86682,x86683)),x86684))
% 21.40/21.37 [8821]E(f789(f85(x88211,x88212,x88213,x88214,x88215),x88216),f789(x88213,x88216))+P1(f789(f789(f342(x88211),x88216),x88215))
% 21.40/21.37 [8822]E(f789(f85(x88221,x88222,x88223,x88224,x88225),x88226),f789(x88223,x88226))+P1(f789(f789(f342(x88221),x88226),x88225))
% 21.40/21.37 [8840]~E(x88403,f789(f789(f146(x88401),x88405),x88406))+P1(f789(f789(f342(f869(f864(x88401),f864(x88401))),f789(f789(f249(f864(x88401),f864(x88401)),x88402),f789(f789(f132(x88401),x88402),x88403))),f143(x88401,x88404)))
% 21.40/21.37 [8843]E(f789(f85(x88431,x88432,x88433,x88434,x88435),x88436),f789(x88434,x88436))+~P1(f789(f789(f342(x88431),x88436),x88435))
% 21.40/21.37 [8844]E(f789(f85(x88441,x88442,x88443,x88444,x88445),x88446),f789(x88444,x88446))+~P1(f789(f789(f342(x88441),x88446),x88445))
% 21.40/21.37 [8848]E(f789(f176(x88481,x88482,x88483,x88484,x88485),x88486),f789(x88483,x88486))+P1(f789(f789(f342(x88481),x88486),f789(f163(x88481),x88484)))
% 21.40/21.37 [9047]~P39(f789(a29,x90472),f789(f789(f789(a193,f789(f789(a195,x90474),a196)),f42(a28)),f789(x90473,x90474)),x90475,x90476)+P39(f33(x90471,x90472,x90473),x90474,x90475,f789(f789(f789(a193,f789(f789(a195,x90476),f789(a194,x90474))),x90471),f789(f789(a194,x90476),a27)))
% 21.40/21.37 [9523]~P27(x95234,x95232,x95235,x95233,x95236,x95231)+E(f789(x95231,f184(f870(x95232,a856))),x95233)
% 21.40/21.37 [9637]P39(x96371,f789(f789(f789(a193,x96372),f42(x96373)),f789(x96374,x96372)),x96375,f413(x96376,x96375,x96372,x96371,x96374,x96373))+~P39(f34(x96373,x96374,x96371),x96372,x96375,f789(f789(f789(a193,x96376),f42(x96373)),f789(f789(a194,x96372),x96373)))
% 21.40/21.37 [9665]P39(f789(a29,x96651),f789(f789(f789(a193,f789(f789(a195,x96652),a196)),f42(a28)),f789(x96653,x96652)),x96654,f559(x96655,x96654,x96652,x96653,x96651,x96656))+~P39(f33(x96656,x96651,x96653),x96652,x96654,f789(f789(f789(a193,f789(f789(a195,x96655),f789(a194,x96652))),x96656),f789(f789(a194,x96655),a27)))
% 21.40/21.37 [9734]~E(f789(x97344,f789(f248(x97341,x97343),x97345)),f789(x97346,f789(f248(x97341,x97343),x97345)))+E(f789(f260(x97341,x97342,x97343,x97343,x97344,f41(x97343)),x97345),f789(f260(x97341,x97342,x97343,x97343,x97346,f41(x97343)),x97345))
% 21.40/21.37 [9735]~E(f789(x97354,f789(f258(x97351,x97352),x97355)),f789(x97356,f789(f258(x97351,x97352),x97355)))+E(f789(f260(x97351,x97351,x97352,x97353,f41(x97351),x97354),x97355),f789(f260(x97351,x97351,x97352,x97353,f41(x97351),x97356),x97355))
% 21.40/21.37 [9796]~E(f789(f260(x97962,x97966,x97963,x97963,x97961,f41(x97963)),x97964),f789(f260(x97962,x97966,x97963,x97963,x97965,f41(x97963)),x97964))+E(f789(x97961,f789(f248(x97962,x97963),x97964)),f789(x97965,f789(f248(x97962,x97963),x97964)))
% 21.40/21.37 [9797]~E(f789(f260(x97972,x97972,x97973,x97976,f41(x97972),x97971),x97974),f789(f260(x97972,x97972,x97973,x97976,f41(x97972),x97975),x97974))+E(f789(x97971,f789(f258(x97972,x97973),x97974)),f789(x97975,f789(f258(x97972,x97973),x97974)))
% 21.40/21.37 [9858]~P39(f34(x98586,x98585,x98584),x98583,x98582,x98581)+E(f789(f789(f789(a193,f505(x98581,x98582,x98583,x98584,x98585,x98586)),f42(x98586)),f789(f789(a194,x98583),x98586)),x98581)
% 21.40/21.37 [9865]~P39(f34(x98656,x98655,x98654),x98653,x98652,f789(f789(f789(a193,x98651),f42(x98656)),f789(f789(a194,x98653),x98656)))+E(f789(f789(f789(a193,f413(x98651,x98652,x98653,x98654,x98655,x98656)),f42(x98656)),f789(f789(a194,x98653),x98656)),f789(f789(f789(a193,x98651),f42(x98656)),f789(f789(a194,x98653),x98656)))
% 21.40/21.37 [8755]P1(f789(f789(f342(x87551),x87552),x87553))+~P1(f789(f789(f342(f869(x87551,x87554)),f789(f789(f249(x87551,x87554),x87552),x87555)),f789(f789(f256(x87551,x87554),x87553),x87556)))
% 21.40/21.37 [8756]P1(f789(f789(f342(x87561),x87562),x87563))+~P1(f789(f789(f342(f869(x87561,x87564)),f789(f789(f249(x87561,x87564),x87562),x87565)),f789(f789(f256(x87561,x87564),x87563),x87566)))
% 21.40/21.37 [8757]P1(f789(f789(f342(x87571),x87572),x87573))+~P1(f789(f789(f342(f869(x87571,x87574)),f789(f789(f249(x87571,x87574),x87572),x87575)),f789(f789(f256(x87571,x87574),x87573),x87576)))
% 21.40/21.37 [8770]P1(f789(f789(f342(x87701),x87702),f789(x87703,x87704)))+~P1(f789(f789(f342(f869(x87705,x87701)),f789(f789(f249(x87705,x87701),x87704),x87702)),f789(f789(f256(x87705,x87701),x87706),x87703)))
% 21.40/21.37 [8771]P1(f789(f789(f342(x87711),x87712),f789(x87713,x87714)))+~P1(f789(f789(f342(f869(x87715,x87711)),f789(f789(f249(x87715,x87711),x87714),x87712)),f789(f789(f256(x87715,x87711),x87716),x87713)))
% 21.40/21.37 [8772]P1(f789(f789(f342(x87721),x87722),f789(x87723,x87724)))+~P1(f789(f789(f342(f869(x87725,x87721)),f789(f789(f249(x87725,x87721),x87724),x87722)),f789(f789(f256(x87725,x87721),x87726),x87723)))
% 21.40/21.37 [8846]~E(f789(f185(f864(x88461)),x88464),f789(f185(f864(x88462)),x88465))+E(f176(x88461,x88462,x88463,x88464,f789(f789(f132(x88462),x88465),x88466)),f176(x88461,x88462,x88463,x88464,x88465))
% 21.40/21.37 [8847]~E(f789(f185(f864(x88471)),x88474),f789(f185(f864(x88472)),x88476))+E(f176(x88471,x88472,x88473,f789(f789(f132(x88471),x88474),x88475),x88476),f176(x88471,x88472,x88473,x88474,x88476))
% 21.40/21.37 [9080]P1(f789(f789(f342(x90801),x90804),f173(x90801,x90802,x90806)))+E(f174(x90801,x90802,f789(f789(f789(f81(x90801,f867(x90802)),x90803),x90804),f789(f234(x90802),x90805)),x90806),f789(f789(f789(f81(x90801,f867(x90802)),f174(x90801,x90802,x90803,x90806)),x90804),f789(f234(x90802),x90805)))
% 21.40/21.37 [9171]P1(f789(f789(f342(f869(x91711,x91711)),f789(f789(f249(x91711,x91711),f789(x91712,x91713)),f789(x91712,x91714))),x91715))+~P1(f789(f789(f342(f869(x91716,x91716)),f789(f789(f249(x91716,x91716),x91713),x91714)),f789(f789(f288(x91711,x91716),x91715),x91712)))
% 21.40/21.37 [9184]~P1(f789(f789(f342(f869(x91844,x91844)),f789(f789(f249(x91844,x91844),f789(x91846,x91842)),f789(x91846,x91843))),x91845))+P1(f789(f789(f342(f869(x91841,x91841)),f789(f789(f249(x91841,x91841),x91842),x91843)),f789(f789(f288(x91844,x91841),x91845),x91846)))
% 21.40/21.37 [9799]E(f789(f789(f249(x97991,x97992),f716(x97993,x97994,x97995,x97996,x97992,x97991)),f717(x97993,x97994,x97995,x97996,x97992,x97991)),x97996)+~P1(f789(f789(f342(f869(x97991,x97992)),x97996),f789(f789(f289(x97991,x97995,x97992),x97994),x97993)))
% 21.40/21.37 [9997]~P39(f33(x99976,x99975,x99974),x99973,x99972,x99971)+E(f789(f789(f789(a193,f789(f789(a195,f581(x99971,x99972,x99973,x99974,x99975,x99976)),f789(a194,x99973))),x99976),f789(f789(a194,f581(x99971,x99972,x99973,x99974,x99975,x99976)),a27)),x99971)
% 21.40/21.37 [10002]~P39(f33(x100026,x100025,x100024),x100023,x100022,f789(f789(f789(a193,f789(f789(a195,x100021),f789(a194,x100023))),x100026),f789(f789(a194,x100021),a27)))+E(f789(f789(f789(a193,f789(f789(a195,f559(x100021,x100022,x100023,x100024,x100025,x100026)),f789(a194,x100023))),x100026),f789(f789(a194,f559(x100021,x100022,x100023,x100024,x100025,x100026)),a27)),f789(f789(f789(a193,f789(f789(a195,x100021),f789(a194,x100023))),x100026),f789(f789(a194,x100021),a27)))
% 21.40/21.37 [10013]~P1(f789(f789(f342(f869(x100131,x100136)),x100135),f789(f789(f289(x100131,x100132,x100136),x100134),x100133)))+P1(f789(f789(f342(f869(x100131,x100132)),f789(f789(f249(x100131,x100132),f716(x100133,x100134,x100132,x100135,x100136,x100131)),f718(x100133,x100134,x100132,x100135,x100136,x100131))),x100134))
% 21.40/21.37 [10014]~P1(f789(f789(f342(f869(x100146,x100142)),x100145),f789(f789(f289(x100146,x100141,x100142),x100144),x100143)))+P1(f789(f789(f342(f869(x100141,x100142)),f789(f789(f249(x100141,x100142),f718(x100143,x100144,x100141,x100145,x100142,x100146)),f717(x100143,x100144,x100141,x100145,x100142,x100146))),x100143))
% 21.40/21.37 [6098]~E(x60986,x60984)+E(f789(f789(f789(f789(f81(x60981,x60982),x60983),x60984),x60985),x60986),x60985)
% 21.40/21.37 [6099]~E(x60996,x60994)+E(f789(f789(f789(f789(f81(x60991,x60992),x60993),x60994),x60995),x60996),x60995)
% 21.40/21.37 [6145]E(x61451,x61452)+E(f789(f789(f789(f789(f81(x61453,x61454),x61455),x61452),x61456),x61451),f789(x61455,x61451))
% 21.40/21.37 [6146]E(x61461,x61462)+E(f789(f789(f789(f789(f81(x61463,x61464),x61465),x61462),x61466),x61461),f789(x61465,x61461))
% 21.40/21.37 [6147]E(x61471,x61472)+E(f789(f789(f789(f789(f81(x61473,x61474),x61475),x61472),x61476),x61471),f789(x61475,x61471))
% 21.40/21.37 [7726]~P9(x77262)+E(f789(f789(f53(x77261,x77262),x77263),f789(f789(f9(x77261,x77264,x77262),x77265),x77266)),f789(f789(f789(f53(x77261,f870(x77264,x77262)),x77263),x77265),x77266))
% 21.40/21.37 [7727]~P9(x77272)+E(f789(f789(f54(x77271,x77272),x77273),f789(f789(f9(x77271,x77274,x77272),x77275),x77276)),f789(f789(f789(f54(x77271,f870(x77274,x77272)),x77273),x77275),x77276))
% 21.40/21.37 [8313]E(f789(f311(x83131,f867(x83132),f789(f789(f789(f81(x83131,f867(x83132)),x83133),x83134),f789(f234(x83132),x83135))),x83136),f789(f311(x83131,f867(x83132),x83133),x83136))+P1(f789(f789(f342(x83131),x83134),x83136))
% 21.40/21.37 [8503]E(f789(f789(f53(x85031,f870(x85032,a856)),x85033),f789(f789(f10(f870(x85032,a856),f870(x85032,a856),x85031),f789(f310(x85032),x85034)),x85035)),f789(f789(f310(x85032),x85034),f789(f789(f53(x85031,f870(x85032,a856)),x85033),x85035)))+~P1(f789(f789(f342(x85031),x85036),x85033))
% 21.40/21.37 [8504]E(f789(f789(f54(x85041,f870(x85042,a856)),x85043),f789(f789(f10(f870(x85042,a856),f870(x85042,a856),x85041),f789(f310(x85042),x85044)),x85045)),f789(f789(f310(x85042),x85044),f789(f789(f54(x85041,f870(x85042,a856)),x85043),x85045)))+~P1(f789(f789(f342(x85041),x85046),x85043))
% 21.40/21.37 [8886]~P9(x88862)+E(f789(f789(f53(x88861,x88862),x88863),f789(f789(f10(f870(x88864,x88862),x88862,x88861),f789(f53(x88864,x88862),x88865)),f789(f9(x88864,x88861,x88862),x88866))),f789(f789(f53(x88864,x88862),x88865),f789(f789(f10(f870(x88861,x88862),x88862,x88864),f789(f53(x88861,x88862),x88863)),x88866)))
% 21.40/21.37 [8887]~P9(x88872)+E(f789(f789(f54(x88871,x88872),x88873),f789(f789(f10(f870(x88874,x88872),x88872,x88871),f789(f54(x88874,x88872),x88875)),f789(f9(x88874,x88871,x88872),x88876))),f789(f789(f54(x88874,x88872),x88875),f789(f789(f10(f870(x88871,x88872),x88872,x88874),f789(f54(x88871,x88872),x88873)),x88876)))
% 21.40/21.37 [9086]P1(f789(f789(f342(x90861),x90862),f789(f163(x90861),x90863)))+~P1(f789(f789(f342(f869(x90864,x90861)),f789(f789(f249(x90864,x90861),x90865),x90862)),f789(f163(f869(x90864,x90861)),f789(f789(f171(x90864,x90861),x90866),x90863))))
% 21.40/21.37 [9087]P1(f789(f789(f342(x90871),x90872),f789(f163(x90871),x90873)))+~P1(f789(f789(f342(f869(x90871,x90874)),f789(f789(f249(x90871,x90874),x90872),x90875)),f789(f163(f869(x90871,x90874)),f789(f789(f171(x90871,x90874),x90873),x90876))))
% 21.40/21.37 [9088]P1(f789(f789(f342(x90881),x90882),f789(f163(x90881),x90883)))+~P1(f789(f789(f342(f869(x90884,x90881)),f789(f789(f249(x90884,x90881),x90885),x90882)),f789(f163(f869(x90884,x90881)),f789(f789(f171(x90884,x90881),x90886),x90883))))
% 21.40/21.37 [9089]P1(f789(f789(f342(x90891),x90892),f789(f163(x90891),x90893)))+~P1(f789(f789(f342(f869(x90891,x90894)),f789(f789(f249(x90891,x90894),x90892),x90895)),f789(f163(f869(x90891,x90894)),f789(f789(f171(x90891,x90894),x90893),x90896))))
% 21.40/21.37 [9182]P1(f789(f789(f240(f870(x91821,a856)),f789(f285(x91822,x91821,x91823),x91824)),x91825))+~P1(f789(f789(f240(f870(f869(x91822,x91821),a856)),x91823),f789(f789(f256(x91822,x91821),x91826),f789(f18(f870(x91821,a856),x91822),x91825))))
% 21.40/21.37 [9357]P1(f789(f789(f342(f869(f864(x93571),f864(x93571))),f789(f789(f249(f864(x93571),f864(x93571)),f789(f789(f146(x93571),x93572),x93573)),f789(f789(f146(x93571),x93574),x93575))),f143(x93571,x93576)))+~P1(f789(f789(f342(f869(x93571,x93571)),f789(f789(f249(x93571,x93571),x93572),x93574)),x93576))
% 21.40/21.37 [9795]E(f789(f789(f249(x97951,x97952),f625(x97953,x97954,x97955,x97952,x97951,x97956)),f628(x97953,x97954,x97955,x97952,x97951,x97956)),x97956)+P1(f789(f789(f342(x97955),x97954),f789(f789(f259(x97951,x97952,f870(x97955,a856)),x97953),x97956)))
% 21.40/21.37 [9800]E(f789(f789(f249(x98001,x98002),f626(x98003,x98004,x98002,x98001,x98005,x98006)),f627(x98003,x98004,x98002,x98001,x98005,x98006)),x98003)+~P1(f789(f789(f342(x98006),x98005),f789(f789(f259(x98001,x98002,f870(x98006,a856)),x98004),x98003)))
% 21.40/21.37 [9966]P1(f789(f789(f342(x99661),x99662),f789(f789(x99663,f626(x99664,x99663,x99665,x99666,x99662,x99661)),f627(x99664,x99663,x99665,x99666,x99662,x99661))))+~P1(f789(f789(f342(x99661),x99662),f789(f789(f259(x99666,x99665,f870(x99661,a856)),x99663),x99664)))
% 21.40/21.37 [9990]~P1(f789(f789(f342(x99901),x99902),f789(f789(x99905,f625(x99905,x99902,x99901,x99904,x99903,x99906)),f628(x99905,x99902,x99901,x99904,x99903,x99906))))+P1(f789(f789(f342(x99901),x99902),f789(f789(f259(x99903,x99904,f870(x99901,a856)),x99905),x99906)))
% 21.40/21.37 [7851]P1(f789(f789(f342(x78511),x78514),x78516))+E(f177(x78511,x78512,f789(f789(f789(f81(x78511,f867(x78512)),x78513),x78514),x78515),x78516),f177(x78511,x78512,x78513,x78516))
% 21.40/21.37 [7926]P1(f789(f789(f342(x79261),x79264),x79266))+E(f789(f311(x79261,x79262,f789(f789(f789(f81(x79261,x79262),x79263),x79264),x79265)),x79266),f789(f311(x79261,x79262,x79263),x79266))
% 21.40/21.37 [7953]P1(f789(f789(f342(x79531),x79534),f789(f163(x79531),x79536)))+E(f789(f789(f150(x79531,x79532),f789(f789(f789(f81(x79531,x79532),x79533),x79534),x79535)),x79536),f789(f789(f150(x79531,x79532),x79533),x79536))
% 21.40/21.37 [8399]E(x83991,x83992)+E(f789(f789(f155(x83993,f789(f789(f155(x83993,x83994),x83991),x83995)),x83992),x83996),f789(f789(f155(x83993,f789(f789(f155(x83993,x83994),x83992),x83996)),x83991),x83995))
% 21.40/21.37 [8892]~P1(f789(f789(f342(x88923),x88926),x88925))+E(f789(f789(f310(x88921),x88922),f789(f311(x88923,x88921,x88924),f789(f789(f3(f870(x88923,a856)),x88925),f789(f789(f310(x88923),x88926),f184(f870(x88923,a856)))))),f789(f311(x88923,x88921,f789(f789(f789(f81(x88923,x88921),x88924),x88926),x88922)),x88925))
% 21.40/21.37 [9621]E(f176(x96211,x96212,x96213,f789(f789(f132(x96211),x96214),f789(f789(f146(x96211),x96215),f122(x96211))),x96216),f789(f789(f789(f81(x96211,f867(x96212)),f176(x96211,x96212,x96213,x96214,x96216)),x96215),f789(f234(x96212),f789(f789(f159(x96212),x96216),f789(f185(f864(x96211)),x96214)))))+~P1(f789(f789(f241(a863),f789(f185(f864(x96211)),x96214)),f789(f185(f864(x96212)),x96216)))
% 21.40/21.37 [8718]~E(x87183,x87186)+E(f789(f170(x87181,x87182,f789(f789(f146(f869(x87181,x87182)),f789(f789(f249(x87181,x87182),x87183),x87184)),x87185)),x87186),f789(f234(x87182),x87184))
% 21.40/21.37 [8759]E(x87591,x87592)+E(f789(f170(x87593,x87594,f789(f789(f146(f869(x87593,x87594)),f789(f789(f249(x87593,x87594),x87591),x87595)),x87596)),x87592),f789(f170(x87593,x87594,x87596),x87592))
% 21.40/21.37 [8965]~P1(f789(f789(x89654,x89655),x89656))+P1(f789(f789(f789(f789(f110(f870(x89651,f870(x89652,a856))),x89653),x89654),x89655),x89656))
% 21.40/21.37 [8966]~P1(f789(f789(x89664,x89665),x89666))+P1(f789(f789(f789(f789(f110(f870(x89661,f870(x89662,a856))),x89663),x89664),x89665),x89666))
% 21.40/21.37 [8967]~P1(f789(f789(x89673,x89675),x89676))+P1(f789(f789(f789(f789(f110(f870(x89671,f870(x89672,a856))),x89673),x89674),x89675),x89676))
% 21.40/21.37 [8968]~P1(f789(f789(x89683,x89685),x89686))+P1(f789(f789(f789(f789(f110(f870(x89681,f870(x89682,a856))),x89683),x89684),x89685),x89686))
% 21.40/21.37 [9219]P1(f789(f789(x92191,x92192),x92193))+~P1(f789(f789(f789(f789(f111(f870(x92194,f870(x92195,a856))),x92196),x92191),x92192),x92193))
% 21.40/21.37 [9220]P1(f789(f789(x92201,x92202),x92203))+~P1(f789(f789(f789(f789(f111(f870(x92204,f870(x92205,a856))),x92201),x92206),x92202),x92203))
% 21.40/21.37 [9221]P1(f789(f789(x92211,x92212),x92213))+~P1(f789(f789(f789(f789(f111(f870(x92214,f870(x92215,a856))),x92216),x92211),x92212),x92213))
% 21.40/21.37 [9222]P1(f789(f789(x92221,x92222),x92223))+~P1(f789(f789(f789(f789(f111(f870(x92224,f870(x92225,a856))),x92221),x92226),x92222),x92223))
% 21.40/21.37 [9644]~P69(x96442)+E(f789(f789(f11(x96441,x96442),f789(f789(f9(x96441,f870(x96443,a856),x96442),f789(f789(f10(f870(x96443,x96442),f870(f870(x96443,a856),x96442),x96441),f11(x96443,x96442)),x96444)),x96445)),x96446),f789(f789(f11(f869(x96441,x96443),x96442),f789(f259(x96441,x96443,x96442),x96444)),f789(f789(f256(x96441,x96443),x96446),f789(f18(f870(x96443,a856),x96441),x96445))))
% 21.40/21.37 [9645]~P4(x96452)+E(f789(f789(f8(x96451,x96452),f789(f789(f9(x96451,f870(x96453,a856),x96452),f789(f789(f10(f870(x96453,x96452),f870(f870(x96453,a856),x96452),x96451),f8(x96453,x96452)),x96454)),x96455)),x96456),f789(f789(f8(f869(x96451,x96453),x96452),f789(f259(x96451,x96453,x96452),x96454)),f789(f789(f256(x96451,x96453),x96456),f789(f18(f870(x96453,a856),x96451),x96455))))
% 21.40/21.37 [9762]~P4(x97622)+E(f789(f789(f8(x97621,x97622),f789(f789(f9(x97621,f870(x97623,a856),x97622),f789(f789(f10(f870(x97623,x97622),f870(f870(x97623,a856),x97622),x97621),f8(x97623,x97622)),f789(f9(x97623,x97621,x97622),x97624))),x97625)),x97626),f789(f789(f8(x97623,x97622),f789(f789(f9(x97623,f870(x97621,a856),x97622),f789(f789(f10(f870(x97621,x97622),f870(f870(x97621,a856),x97622),x97623),f8(x97621,x97622)),x97624)),x97626)),x97625))
% 21.40/21.37 [9487]~P1(f789(f789(f342(x94871),x94875),x94874))+E(f789(f789(f789(f81(x94871,f867(x94872)),f177(x94871,x94872,x94873,f789(f789(f3(f870(x94871,a856)),x94874),f789(f789(f310(x94871),x94875),f184(f870(x94871,a856)))))),x94875),x94876),f177(x94871,x94872,f789(f789(f789(f81(x94871,f867(x94872)),x94873),x94875),x94876),x94874))
% 21.40/21.37 [9541]~P1(f789(f789(f342(x95411),x95415),x95414))+E(f789(f789(f789(f81(x95411,f867(x95412)),f177(x95411,x95412,x95413,f789(f789(f3(f870(x95411,a856)),x95414),f789(f789(f310(x95411),x95415),f184(f870(x95411,a856)))))),x95415),x95416),f789(f789(f789(f81(x95411,f867(x95412)),f177(x95411,x95412,x95413,x95414)),x95415),x95416))
% 21.40/21.37 [10069]~P1(f789(f789(f342(f869(x100691,x100692)),f789(f789(f249(x100691,x100692),x100695),x100696)),f789(f789(f110(f870(f869(x100691,x100692),a856)),x100693),x100694)))+P1(f789(f789(f789(f789(f110(f870(x100691,f870(x100692,a856))),f789(f789(f9(x100691,f870(f869(x100691,x100692),a856),f870(x100692,a856)),f789(f789(f10(f870(x100692,f870(f870(f869(x100691,x100692),a856),a856)),f870(f870(f869(x100691,x100692),a856),f870(x100692,a856)),x100691),f9(x100692,f870(f869(x100691,x100692),a856),a856)),f789(f789(f10(f870(x100692,f869(x100691,x100692)),f870(x100692,f870(f870(f869(x100691,x100692),a856),a856)),x100691),f789(f10(f869(x100691,x100692),f870(f870(f869(x100691,x100692),a856),a856),x100692),f342(f869(x100691,x100692)))),f249(x100691,x100692)))),x100693)),f789(f789(f9(x100691,f870(f869(x100691,x100692),a856),f870(x100692,a856)),f789(f789(f10(f870(x100692,f870(f870(f869(x100691,x100692),a856),a856)),f870(f870(f869(x100691,x100692),a856),f870(x100692,a856)),x100691),f9(x100692,f870(f869(x100691,x100692),a856),a856)),f789(f789(f10(f870(x100692,f869(x100691,x100692)),f870(x100692,f870(f870(f869(x100691,x100692),a856),a856)),x100691),f789(f10(f869(x100691,x100692),f870(f870(f869(x100691,x100692),a856),a856),x100692),f342(f869(x100691,x100692)))),f249(x100691,x100692)))),x100694)),x100695),x100696))
% 21.40/21.37 [10070]~P1(f789(f789(f342(f869(x100701,x100702)),f789(f789(f249(x100701,x100702),x100705),x100706)),f789(f789(f111(f870(f869(x100701,x100702),a856)),x100703),x100704)))+P1(f789(f789(f789(f789(f111(f870(x100701,f870(x100702,a856))),f789(f789(f9(x100701,f870(f869(x100701,x100702),a856),f870(x100702,a856)),f789(f789(f10(f870(x100702,f870(f870(f869(x100701,x100702),a856),a856)),f870(f870(f869(x100701,x100702),a856),f870(x100702,a856)),x100701),f9(x100702,f870(f869(x100701,x100702),a856),a856)),f789(f789(f10(f870(x100702,f869(x100701,x100702)),f870(x100702,f870(f870(f869(x100701,x100702),a856),a856)),x100701),f789(f10(f869(x100701,x100702),f870(f870(f869(x100701,x100702),a856),a856),x100702),f342(f869(x100701,x100702)))),f249(x100701,x100702)))),x100703)),f789(f789(f9(x100701,f870(f869(x100701,x100702),a856),f870(x100702,a856)),f789(f789(f10(f870(x100702,f870(f870(f869(x100701,x100702),a856),a856)),f870(f870(f869(x100701,x100702),a856),f870(x100702,a856)),x100701),f9(x100702,f870(f869(x100701,x100702),a856),a856)),f789(f789(f10(f870(x100702,f869(x100701,x100702)),f870(x100702,f870(f870(f869(x100701,x100702),a856),a856)),x100701),f789(f10(f869(x100701,x100702),f870(f870(f869(x100701,x100702),a856),a856),x100702),f342(f869(x100701,x100702)))),f249(x100701,x100702)))),x100704)),x100705),x100706))
% 21.40/21.37 [10074]P1(f789(f789(f342(f869(x100741,x100742)),f789(f789(f249(x100741,x100742),x100743),x100744)),f789(f789(f110(f870(f869(x100741,x100742),a856)),x100745),x100746)))+~P1(f789(f789(f789(f789(f110(f870(x100741,f870(x100742,a856))),f789(f789(f9(x100741,f870(f869(x100741,x100742),a856),f870(x100742,a856)),f789(f789(f10(f870(x100742,f870(f870(f869(x100741,x100742),a856),a856)),f870(f870(f869(x100741,x100742),a856),f870(x100742,a856)),x100741),f9(x100742,f870(f869(x100741,x100742),a856),a856)),f789(f789(f10(f870(x100742,f869(x100741,x100742)),f870(x100742,f870(f870(f869(x100741,x100742),a856),a856)),x100741),f789(f10(f869(x100741,x100742),f870(f870(f869(x100741,x100742),a856),a856),x100742),f342(f869(x100741,x100742)))),f249(x100741,x100742)))),x100745)),f789(f789(f9(x100741,f870(f869(x100741,x100742),a856),f870(x100742,a856)),f789(f789(f10(f870(x100742,f870(f870(f869(x100741,x100742),a856),a856)),f870(f870(f869(x100741,x100742),a856),f870(x100742,a856)),x100741),f9(x100742,f870(f869(x100741,x100742),a856),a856)),f789(f789(f10(f870(x100742,f869(x100741,x100742)),f870(x100742,f870(f870(f869(x100741,x100742),a856),a856)),x100741),f789(f10(f869(x100741,x100742),f870(f870(f869(x100741,x100742),a856),a856),x100742),f342(f869(x100741,x100742)))),f249(x100741,x100742)))),x100746)),x100743),x100744))
% 21.40/21.37 [10075]P1(f789(f789(f342(f869(x100751,x100752)),f789(f789(f249(x100751,x100752),x100753),x100754)),f789(f789(f111(f870(f869(x100751,x100752),a856)),x100755),x100756)))+~P1(f789(f789(f789(f789(f111(f870(x100751,f870(x100752,a856))),f789(f789(f9(x100751,f870(f869(x100751,x100752),a856),f870(x100752,a856)),f789(f789(f10(f870(x100752,f870(f870(f869(x100751,x100752),a856),a856)),f870(f870(f869(x100751,x100752),a856),f870(x100752,a856)),x100751),f9(x100752,f870(f869(x100751,x100752),a856),a856)),f789(f789(f10(f870(x100752,f869(x100751,x100752)),f870(x100752,f870(f870(f869(x100751,x100752),a856),a856)),x100751),f789(f10(f869(x100751,x100752),f870(f870(f869(x100751,x100752),a856),a856),x100752),f342(f869(x100751,x100752)))),f249(x100751,x100752)))),x100755)),f789(f789(f9(x100751,f870(f869(x100751,x100752),a856),f870(x100752,a856)),f789(f789(f10(f870(x100752,f870(f870(f869(x100751,x100752),a856),a856)),f870(f870(f869(x100751,x100752),a856),f870(x100752,a856)),x100751),f9(x100752,f870(f869(x100751,x100752),a856),a856)),f789(f789(f10(f870(x100752,f869(x100751,x100752)),f870(x100752,f870(f870(f869(x100751,x100752),a856),a856)),x100751),f789(f10(f869(x100751,x100752),f870(f870(f869(x100751,x100752),a856),a856),x100752),f342(f869(x100751,x100752)))),f249(x100751,x100752)))),x100756)),x100753),x100754))
% 21.40/21.37 [10063]~P1(f789(f789(f342(f869(x100632,x100633)),f789(f789(f249(x100632,x100633),x100635),x100636)),f789(f789(f53(x100631,f870(f869(x100632,x100633),a856)),f247(f870(x100631,a856))),x100634)))+P1(f789(f789(f789(f789(f53(x100631,f870(x100632,f870(x100633,a856))),f247(f870(x100631,a856))),f789(f789(f10(f870(f869(x100632,x100633),a856),f870(x100632,f870(x100633,a856)),x100631),f789(f9(x100632,f870(f869(x100632,x100633),a856),f870(x100633,a856)),f789(f789(f10(f870(x100633,f870(f870(f869(x100632,x100633),a856),a856)),f870(f870(f869(x100632,x100633),a856),f870(x100633,a856)),x100632),f9(x100633,f870(f869(x100632,x100633),a856),a856)),f789(f789(f10(f870(x100633,f869(x100632,x100633)),f870(x100633,f870(f870(f869(x100632,x100633),a856),a856)),x100632),f789(f10(f869(x100632,x100633),f870(f870(f869(x100632,x100633),a856),a856),x100633),f342(f869(x100632,x100633)))),f249(x100632,x100633))))),x100634)),x100635),x100636))
% 21.40/21.37 [10064]~P1(f789(f789(f342(f869(x100642,x100643)),f789(f789(f249(x100642,x100643),x100645),x100646)),f789(f789(f54(x100641,f870(f869(x100642,x100643),a856)),f247(f870(x100641,a856))),x100644)))+P1(f789(f789(f789(f789(f54(x100641,f870(x100642,f870(x100643,a856))),f247(f870(x100641,a856))),f789(f789(f10(f870(f869(x100642,x100643),a856),f870(x100642,f870(x100643,a856)),x100641),f789(f9(x100642,f870(f869(x100642,x100643),a856),f870(x100643,a856)),f789(f789(f10(f870(x100643,f870(f870(f869(x100642,x100643),a856),a856)),f870(f870(f869(x100642,x100643),a856),f870(x100643,a856)),x100642),f9(x100643,f870(f869(x100642,x100643),a856),a856)),f789(f789(f10(f870(x100643,f869(x100642,x100643)),f870(x100643,f870(f870(f869(x100642,x100643),a856),a856)),x100642),f789(f10(f869(x100642,x100643),f870(f870(f869(x100642,x100643),a856),a856),x100643),f342(f869(x100642,x100643)))),f249(x100642,x100643))))),x100644)),x100645),x100646))
% 21.40/21.37 [10072]P1(f789(f789(f342(f869(x100721,x100722)),f789(f789(f249(x100721,x100722),x100723),x100724)),f789(f789(f53(x100725,f870(f869(x100721,x100722),a856)),f247(f870(x100725,a856))),x100726)))+~P1(f789(f789(f789(f789(f53(x100725,f870(x100721,f870(x100722,a856))),f247(f870(x100725,a856))),f789(f789(f10(f870(f869(x100721,x100722),a856),f870(x100721,f870(x100722,a856)),x100725),f789(f9(x100721,f870(f869(x100721,x100722),a856),f870(x100722,a856)),f789(f789(f10(f870(x100722,f870(f870(f869(x100721,x100722),a856),a856)),f870(f870(f869(x100721,x100722),a856),f870(x100722,a856)),x100721),f9(x100722,f870(f869(x100721,x100722),a856),a856)),f789(f789(f10(f870(x100722,f869(x100721,x100722)),f870(x100722,f870(f870(f869(x100721,x100722),a856),a856)),x100721),f789(f10(f869(x100721,x100722),f870(f870(f869(x100721,x100722),a856),a856),x100722),f342(f869(x100721,x100722)))),f249(x100721,x100722))))),x100726)),x100723),x100724))
% 21.40/21.37 [10073]P1(f789(f789(f342(f869(x100731,x100732)),f789(f789(f249(x100731,x100732),x100733),x100734)),f789(f789(f54(x100735,f870(f869(x100731,x100732),a856)),f247(f870(x100735,a856))),x100736)))+~P1(f789(f789(f789(f789(f54(x100735,f870(x100731,f870(x100732,a856))),f247(f870(x100735,a856))),f789(f789(f10(f870(f869(x100731,x100732),a856),f870(x100731,f870(x100732,a856)),x100735),f789(f9(x100731,f870(f869(x100731,x100732),a856),f870(x100732,a856)),f789(f789(f10(f870(x100732,f870(f870(f869(x100731,x100732),a856),a856)),f870(f870(f869(x100731,x100732),a856),f870(x100732,a856)),x100731),f9(x100732,f870(f869(x100731,x100732),a856),a856)),f789(f789(f10(f870(x100732,f869(x100731,x100732)),f870(x100732,f870(f870(f869(x100731,x100732),a856),a856)),x100731),f789(f10(f869(x100731,x100732),f870(f870(f869(x100731,x100732),a856),a856),x100732),f342(f869(x100731,x100732)))),f249(x100731,x100732))))),x100736)),x100733),x100734))
% 21.40/21.37 [9156]E(x91561,x91562)+~E(f327(x91563,x91564,x91565,x91566,x91561),f327(x91563,x91564,x91565,x91567,x91562))
% 21.40/21.37 [9157]E(x91571,x91572)+~E(f327(x91573,x91574,x91575,x91571,x91576),f327(x91573,x91574,x91575,x91572,x91577))
% 21.40/21.37 [7400]E(f789(x74001,f789(x74002,x74003)),f789(x74004,x74003))+~E(f789(f82(x74005,x74006,x74007,x74001),x74002),x74004)
% 21.40/21.37 [9522]~P26(x95223,x95224,x95221,x95225,x95226,x95227)+E(f789(f789(x95221,x95222),x95222),x95222)
% 21.40/21.37 [9855]~P51(x98555,x98556,x98557,x98551,x98554,x98552,x98553)+P1(f789(f789(x98551,x98552),f596(x98553,x98552,x98554,x98551)))
% 21.40/21.37 [9884]~E(f789(f236(f867(x98847),x98841,f187(x98847),x98845),f789(x98844,x98843)),f789(f234(x98847),x98842))+E(f789(f234(x98841),f726(x98842,x98843,x98844,x98845,x98846,x98847,x98841)),f789(x98844,x98843))
% 21.40/21.37 [9885]~E(f789(f236(f867(x98856),x98857,f187(x98856),x98851),f789(x98854,x98853)),f789(f234(x98856),x98852))+E(f789(x98851,f726(x98852,x98853,x98854,x98851,x98855,x98856,x98857)),f789(f234(x98856),x98852))
% 21.40/21.37 [5916]~E(f789(f789(f150(x59161,x59165),x59166),x59162),f789(f789(f150(x59163,x59165),x59167),x59164))+E(f789(f185(f864(x59161)),x59162),f789(f185(f864(x59163)),x59164))
% 21.40/21.37 [7476]E(x74761,x74762)+~E(f789(f789(f789(f81(x74763,f867(x74764)),x74765),x74766),f789(f234(x74764),x74761)),f789(f789(f789(f81(x74763,f867(x74764)),x74767),x74766),f789(f234(x74764),x74762)))
% 21.40/21.37 [8434]E(f789(x84341,f789(x84342,x84343)),f789(x84344,x84343))+~E(f789(f82(x84345,x84346,x84347,x84341),x84342),f789(f82(x84346,x84346,x84347,f41(x84346)),x84344))
% 21.40/21.37 [9861]~P51(x98615,x98616,x98617,x98614,x98611,x98613,x98612)+P1(f789(f789(x98611,f596(x98612,x98613,x98611,x98614)),x98612))
% 21.40/21.37 [5962]E(x59621,x59622)+~E(f789(f789(f789(f100(x59623),x59624),x59625),x59621),f789(f789(f789(f100(x59623),x59626),x59627),x59622))
% 21.40/21.37 [5963]E(x59631,x59632)+~E(f789(f789(f789(f100(x59633),x59634),x59631),x59635),f789(f789(f789(f100(x59633),x59636),x59632),x59637))
% 21.40/21.37 [5964]E(x59641,x59642)+~E(f789(f789(f789(f100(x59643),x59641),x59644),x59645),f789(f789(f789(f100(x59643),x59642),x59646),x59647))
% 21.40/21.37 [8850]~P24(x88506,x88501,x88503,x88507)+E(f789(f82(x88501,x88501,x88502,f789(x88503,x88504)),f789(f82(x88501,x88501,x88502,f789(x88503,x88504)),x88505)),f789(f82(x88501,x88501,x88502,f789(x88503,x88504)),x88505))
% 21.40/21.37 [9603]E(f176(x96031,x96032,f789(f789(f789(f81(x96031,f867(x96032)),x96033),x96034),f789(f234(x96032),x96035)),x96036,x96037),f789(f789(f789(f81(x96031,f867(x96032)),f176(x96031,x96032,x96033,x96036,x96037)),x96034),f789(f234(x96032),x96035)))+P1(f789(f789(f342(x96031),x96034),f789(f163(x96031),x96036)))
% 21.40/21.37 [8849]~P1(f789(f789(f342(x88491),x88492),f789(f789(x88495,x88496),x88497)))+P1(f789(f789(f342(x88491),x88492),f789(f789(f259(x88493,x88494,f870(x88491,a856)),x88495),f789(f789(f249(x88493,x88494),x88496),x88497))))
% 21.40/21.37 [9116]P1(f789(f789(f789(x91161,x91162),x91163),x91164))+~P1(f789(f789(f789(f259(x91165,x91166,f870(x91167,a856)),x91161),f789(f789(f249(x91165,x91166),x91162),x91163)),x91164))
% 21.40/21.37 [9234]P1(f789(f789(f342(x92341),f789(f789(x92342,x92343),x92344)),f789(f311(f869(x92345,x92346),x92341,f789(f259(x92345,x92346,x92341),x92342)),x92347)))+~P1(f789(f789(f342(f869(x92345,x92346)),f789(f789(f249(x92345,x92346),x92343),x92344)),x92347))
% 21.40/21.37 [9562]P1(f789(f789(f342(f869(f864(x95621),f864(x95621))),f789(f789(f249(f864(x95621),f864(x95621)),f789(f789(f132(x95621),x95622),f789(f789(f146(x95621),x95623),x95624))),f789(f789(f132(x95621),x95622),f789(f789(f146(x95621),x95625),x95626)))),f143(x95621,x95627)))+~P1(f789(f789(f342(f869(x95621,x95621)),f789(f789(f249(x95621,x95621),x95623),x95625)),x95627))
% 21.40/21.37 [9989]P51(x99891,x99892,x99893,f789(f789(f9(x99891,f870(f869(x99891,x99892),a856),f870(x99892,a856)),f789(f789(f10(f870(x99892,f870(f870(f869(x99891,x99892),a856),a856)),f870(f870(f869(x99891,x99892),a856),f870(x99892,a856)),x99891),f9(x99892,f870(f869(x99891,x99892),a856),a856)),f789(f789(f10(f870(x99892,f869(x99891,x99892)),f870(x99892,f870(f870(f869(x99891,x99892),a856),a856)),x99891),f789(f10(f869(x99891,x99892),f870(f870(f869(x99891,x99892),a856),a856),x99892),f342(f869(x99891,x99892)))),f249(x99891,x99892)))),x99894),f789(f789(f9(x99892,f870(f869(x99892,x99893),a856),f870(x99893,a856)),f789(f789(f10(f870(x99893,f870(f870(f869(x99892,x99893),a856),a856)),f870(f870(f869(x99892,x99893),a856),f870(x99893,a856)),x99892),f9(x99893,f870(f869(x99892,x99893),a856),a856)),f789(f789(f10(f870(x99893,f869(x99892,x99893)),f870(x99893,f870(f870(f869(x99892,x99893),a856),a856)),x99892),f789(f10(f869(x99892,x99893),f870(f870(f869(x99892,x99893),a856),a856),x99893),f342(f869(x99892,x99893)))),f249(x99892,x99893)))),x99895),x99896,x99897)+~P1(f789(f789(f342(f869(x99891,x99893)),f789(f789(f249(x99891,x99893),x99896),x99897)),f789(f789(f289(x99891,x99892,x99893),x99894),x99895)))
% 21.40/21.37 [10020]~P51(x100201,x100205,x100202,f789(f789(f9(x100201,f870(f869(x100201,x100205),a856),f870(x100205,a856)),f789(f789(f10(f870(x100205,f870(f870(f869(x100201,x100205),a856),a856)),f870(f870(f869(x100201,x100205),a856),f870(x100205,a856)),x100201),f9(x100205,f870(f869(x100201,x100205),a856),a856)),f789(f789(f10(f870(x100205,f869(x100201,x100205)),f870(x100205,f870(f870(f869(x100201,x100205),a856),a856)),x100201),f789(f10(f869(x100201,x100205),f870(f870(f869(x100201,x100205),a856),a856),x100205),f342(f869(x100201,x100205)))),f249(x100201,x100205)))),x100206),f789(f789(f9(x100205,f870(f869(x100205,x100202),a856),f870(x100202,a856)),f789(f789(f10(f870(x100202,f870(f870(f869(x100205,x100202),a856),a856)),f870(f870(f869(x100205,x100202),a856),f870(x100202,a856)),x100205),f9(x100202,f870(f869(x100205,x100202),a856),a856)),f789(f789(f10(f870(x100202,f869(x100205,x100202)),f870(x100202,f870(f870(f869(x100205,x100202),a856),a856)),x100205),f789(f10(f869(x100205,x100202),f870(f870(f869(x100205,x100202),a856),a856),x100202),f342(f869(x100205,x100202)))),f249(x100205,x100202)))),x100207),x100203,x100204)+P1(f789(f789(f342(f869(x100201,x100202)),f789(f789(f249(x100201,x100202),x100203),x100204)),f789(f789(f289(x100201,x100205,x100202),x100206),x100207)))
% 21.40/21.37 [9111]E(x91111,x91112)+E(f789(f789(f789(f81(x91113,x91114),f789(f789(f789(f81(x91113,x91114),x91115),x91111),x91116)),x91112),x91117),f789(f789(f789(f81(x91113,x91114),f789(f789(f789(f81(x91113,x91114),x91115),x91112),x91117)),x91111),x91116))
% 21.40/21.37 [9330]E(f176(x93301,x93302,f789(f789(f789(f81(x93301,f867(x93302)),x93303),x93304),f789(f234(x93302),x93305)),x93306,x93307),f176(x93301,x93302,x93303,x93306,x93307))+~P1(f789(f789(f342(x93301),x93304),f789(f163(x93301),f789(f789(f164(x93301),f789(f185(f864(x93302)),x93307)),x93306))))
% 21.40/21.37 [9631]E(f176(x96311,x96312,f789(f789(f789(f81(x96311,f867(x96312)),x96313),x96314),f789(f234(x96312),x96315)),x96316,x96317),f789(f789(f789(f81(x96311,f867(x96312)),f176(x96311,x96312,x96313,x96316,x96317)),x96314),f789(f234(x96312),x96315)))+P1(f789(f789(f342(x96311),x96314),f789(f163(x96311),f789(f789(f164(x96311),f789(f185(f864(x96312)),x96317)),x96316))))
% 21.40/21.37 [10001]P1(f789(f789(f342(x100011),f659(x100012,x100013,x100014,x100015,x100016,x100017,x100011)),x100015))+P1(f789(f789(f789(f789(f54(x100011,f870(x100017,f870(x100016,a856))),x100015),x100014),x100013),x100012))
% 21.40/21.37 [10003]P1(f789(f789(f342(x100031),f440(x100032,x100033,x100034,x100035,x100036,x100037,x100031)),x100035))+~P1(f789(f789(f789(f789(f53(x100031,f870(x100037,f870(x100036,a856))),x100035),x100034),x100033),x100032))
% 21.40/21.37 [10030]P1(f789(f789(f789(x100301,f440(x100302,x100303,x100301,x100304,x100305,x100306,x100307)),x100303),x100302))+~P1(f789(f789(f789(f789(f53(x100307,f870(x100306,f870(x100305,a856))),x100304),x100301),x100303),x100302))
% 21.40/21.37 [10047]~P1(f789(f789(f789(x100475,f659(x100477,x100476,x100475,x100474,x100473,x100472,x100471)),x100476),x100477))+P1(f789(f789(f789(f789(f54(x100471,f870(x100472,f870(x100473,a856))),x100474),x100475),x100476),x100477))
% 21.40/21.37 [10012]~P136(x100122)+E(f789(f789(f8(x100121,x100122),f789(f789(f9(x100121,f870(x100123,a856),x100122),f789(f789(f10(f870(x100123,x100122),f870(f870(x100123,a856),x100122),x100121),f8(x100123,x100122)),f789(f789(f9(x100121,f870(x100123,x100122),f870(x100123,x100122)),f789(f789(f10(f870(x100122,x100122),f870(f870(x100123,x100122),f870(x100123,x100122)),x100121),f10(x100122,x100122,x100123)),f789(f789(f10(x100122,f870(x100122,x100122),x100121),f90(x100122)),x100124))),x100125))),x100126)),x100127),f789(f789(f90(x100122),f789(f789(f8(x100121,x100122),x100124),x100127)),f789(f789(f8(x100123,x100122),x100125),x100126)))
% 21.40/21.37 [9147]~P23(x91477,x91471,x91473,x91478)+E(f789(f82(x91471,x91471,x91472,f789(x91473,x91474)),f789(f82(x91471,x91471,x91472,f789(x91473,x91475)),x91476)),f789(f82(x91471,x91471,x91472,f789(x91473,x91475)),f789(f82(x91471,x91471,x91472,f789(x91473,x91474)),x91476)))
% 21.40/21.37 [10058]P28(x100581,x100582,f789(f789(f310(f862(x100581)),f789(f789(f789(f100(x100581),f789(f789(f10(f870(a861,a856),f870(a861,a856),x100581),f789(f20(a861,a856,a856),f789(f789(f10(a856,f870(a856,a856),a861),a339),f789(a338,x100583)))),f789(f789(f9(x100581,f870(a861,a861),f870(a861,a856)),f789(f789(f10(f870(a861,a856),f870(f870(a861,a861),f870(a861,a856)),x100581),f10(a861,a856,a861)),x100584)),f789(f789(f20(a861,a863,a861),f789(f789(f9(a861,a858,f870(a863,a861)),a193),f42(x100585))),x100586)))),f34(x100585,x100586,x100587)),x100588)),f184(f870(f862(x100581),a856))))+~P28(x100581,x100582,f789(f789(f310(f862(x100581)),f789(f789(f789(f100(x100581),x100584),x100587),f789(f789(f9(x100581,f870(a861,a861),f870(a861,a856)),f789(f789(f10(f870(a861,a856),f870(f870(a861,a861),f870(a861,a856)),x100581),f10(a861,a856,a861)),x100588)),f789(f789(f9(a861,a863,a861),f789(f789(f9(a861,a858,f870(a863,a861)),a193),f42(x100585))),f789(f789(a194,x100583),x100585))))),f184(f870(f862(x100581),a856))))
% 21.40/21.37 [10067]E(f789(f789(f249(x100671,x100672),f789(x100673,f582(x100674,x100675,x100673,x100676,x100677,x100678,x100672,x100671))),f789(x100675,f583(x100674,x100675,x100673,x100676,x100677,x100678,x100672,x100671))),x100678)+~P1(f789(f789(f342(f869(x100671,x100672)),x100678),f789(f311(f869(x100677,x100676),f869(x100671,x100672),f260(x100677,x100671,x100676,x100672,x100673,x100675)),x100674)))
% 21.40/21.37 [10079]P28(x100791,x100792,f789(f789(f310(f862(x100791)),f789(f789(f789(f100(x100791),f789(f789(f10(f870(a861,a856),f870(a861,a856),x100791),f789(f20(a861,a856,a856),f789(f789(f10(a856,f870(a856,a856),a861),a339),f789(a338,x100793)))),f789(f789(f9(x100791,f870(a861,a861),f870(a861,a856)),f789(f789(f10(f870(a861,a856),f870(f870(a861,a861),f870(a861,a856)),x100791),f10(a861,a856,a861)),x100794)),f789(f789(f20(a861,a863,a861),f789(f789(f9(a861,a858,f870(a863,a861)),f789(f789(f10(a861,f870(a858,f870(a863,a861)),a861),a193),f789(f789(f9(a861,f870(a860,a863),a861),a195),a196))),f42(a28))),x100795)))),f33(x100796,x100797,x100795)),x100798)),f184(f870(f862(x100791),a856))))+~P28(x100791,x100792,f789(f789(f310(f862(x100791)),f789(f789(f789(f100(x100791),x100794),f789(a29,x100797)),f789(f789(f9(x100791,f870(a861,a861),f870(a861,a856)),f789(f789(f10(f870(a861,a856),f870(f870(a861,a861),f870(a861,a856)),x100791),f10(a861,a856,a861)),x100798)),f789(f789(f20(a861,a863,a861),f789(f789(f9(a861,a858,f870(a863,a861)),f789(f789(f10(a861,f870(a858,f870(a863,a861)),a861),a193),f789(f789(f9(a861,f870(a860,a863),a861),a195),f789(a194,x100793)))),x100796)),f789(f789(f9(a861,a860,a863),a194),a27))))),f184(f870(f862(x100791),a856))))
% 21.40/21.37 [10080]~P1(f789(f789(f342(f869(x100808,x100807)),x100806),f789(f311(f869(x100801,x100802),f869(x100808,x100807),f260(x100801,x100808,x100802,x100807,x100805,x100804)),x100803)))+P1(f789(f789(f342(f869(x100801,x100802)),f789(f789(f249(x100801,x100802),f582(x100803,x100804,x100805,x100802,x100801,x100806,x100807,x100808)),f583(x100803,x100804,x100805,x100802,x100801,x100806,x100807,x100808))),x100803))
% 21.40/21.37 [9552]P1(f789(f789(f342(f869(f869(x95521,x95522),f869(x95521,x95522))),f789(f789(f249(f869(x95521,x95522),f869(x95521,x95522)),f789(f789(f249(x95521,x95522),x95523),x95524)),f789(f789(f249(x95521,x95522),x95525),x95526))),f333(x95521,x95522,x95527,x95528)))+~P1(f789(f789(f342(f869(x95521,x95521)),f789(f789(f249(x95521,x95521),x95523),x95525)),x95527))
% 21.40/21.37 [8439]E(f789(x84391,f789(x84392,x84393)),f789(x84394,f789(x84395,x84393)))+~E(f789(f82(x84396,x84397,x84398,x84391),x84392),f789(f82(x84399,x84397,x84398,x84394),x84395))
% 21.40/21.37 [8440]E(f789(x84401,f789(x84402,x84403)),f789(x84404,f789(x84405,x84403)))+~E(f789(f82(x84406,x84407,x84408,x84401),x84402),f789(f82(x84409,x84407,x84408,x84404),x84405))
% 21.40/21.37 [9935]P1(f789(f789(f342(f869(x99351,x99352)),f789(f789(f249(x99351,x99352),f789(x99353,x99354)),f789(x99355,x99356))),f789(f311(f869(x99357,x99358),f869(x99351,x99352),f260(x99357,x99351,x99358,x99352,x99353,x99355)),x99359)))+~P1(f789(f789(f342(f869(x99357,x99358)),f789(f789(f249(x99357,x99358),x99354),x99356)),x99359))
% 21.40/21.37 [8699]~E(f789(x86994,f789(x86995,x86996)),f789(x86999,f789(x869910,x869911)))+E(f789(f789(f82(x86991,x86992,x86993,x86994),x86995),x86996),f789(f789(f82(x86997,x86992,x86998,x86999),x869910),x869911))
% 21.40/21.37 [9208]~P23(x92088,x92089,x920810,x920811)+E(f789(f82(x92081,x92082,x92083,x92084),f789(f82(x92085,x92081,x92083,x92086),x92087)),f789(f82(x92085,x92082,x92083,f789(f82(x92081,x92082,x92085,x92084),x92086)),x92087))
% 21.40/21.37 [4540]~P101(x45401)+~P94(x45401)+E(f239(x45401),f110(x45401))
% 21.40/21.37 [4541]~P101(x45411)+~P98(x45411)+E(f244(x45411),f111(x45411))
% 21.40/21.37 [4775]~P110(x47751)+~P88(x47751)+E(f789(f84(x47751),f789(f113(x47751),a106)),f87(x47751))
% 21.40/21.37 [5049]E(x50491,f2(a1))+E(f91(a1,x50491),f789(f88(a1),f87(a1)))+P1(f789(f789(f241(a1),f2(a1)),x50491))
% 21.40/21.37 [5250]E(x52501,f2(a1))+E(f91(a1,x52501),f87(a1))+~P1(f789(f789(f241(a1),f2(a1)),x52501))
% 21.40/21.37 [6563]~P38(x65631)+~P1(f789(f70(a1),x65631))+P1(f789(f70(a863),f789(f311(a1,a863,a114),x65631)))
% 21.40/21.37 [6940]E(f61(f87(a1),f789(f113(a1),x69401)),f789(f789(f249(a1,a1),f2(a1)),f87(a1)))+~P1(f789(f789(f241(a1),f2(a1)),f789(f113(a1),x69401)))+~P1(f789(f789(f241(a1),f87(a1)),f789(f113(a1),x69401)))
% 21.40/21.37 [7287]~P38(x72871)+P1(f789(f70(a1),x72871))+~P1(f789(f70(a863),f789(f311(a1,a863,a114),x72871)))
% 21.40/21.37 [8138]E(f789(f789(f249(a1,a1),f789(f113(a1),a106)),f789(f789(f89(a1),f87(a1)),f789(f113(a1),x81381))),f64(f87(a1),f789(f113(a1),x81381)))+~P1(f789(f789(f241(a1),f2(a1)),f789(f113(a1),x81381)))+~P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),f87(a1)),f789(f113(a1),x81381))))
% 21.40/21.37 [8545]~P13(a500)+~P1(f789(f789(f342(f869(a859,a857)),x85451),f789(f163(f869(a859,a857)),a31)))+P1(f789(f789(f259(a859,a857,a856),f789(f18(f870(a857,a856),a859),a26)),x85451))
% 21.40/21.37 [9818]E(f789(f57(f789(f113(a1),x98181)),f61(f87(a1),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f113(a1),x98181)))),f61(f87(a1),f789(f113(a1),x98181)))+~P1(f789(f789(f241(a1),f2(a1)),f789(f113(a1),x98181)))+P1(f789(f789(f241(a1),f87(a1)),f789(f113(a1),x98181)))
% 21.40/21.37 [9824]E(f789(f57(f789(f113(a1),x98241)),f64(f87(a1),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f113(a1),x98241)))),f64(f87(a1),f789(f113(a1),x98241)))+~P1(f789(f789(f241(a1),f2(a1)),f789(f113(a1),x98241)))+P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),f87(a1)),f789(f113(a1),x98241))))
% 21.40/21.37 [9521]E(x95211,f184(f870(f869(a863,a863),a856)))+~P1(f789(f70(f869(a863,a863)),x95211))+P1(f789(f789(f342(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f249(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),f184(f870(f869(a863,a863),a856))),x95211)),a48))
% 21.40/21.37 [9676]E(x96761,f2(a863))+E(x96761,f789(a121,f2(a863)))+~P1(f789(f789(f241(a863),x96761),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))
% 21.40/21.37 [9961]E(x99611,f2(a108))+E(f789(f789(f89(a1),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(a23,f789(f789(f50(a108),x99611),f789(f113(a108),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))),f87(a1)),f789(a23,x99611))+E(f59(a108,x99611,f789(f113(a108),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f2(a108))
% 21.40/21.37 [9804]E(x98041,f2(a108))+~E(f59(a108,x98041,f789(f113(a108),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f2(a108))+E(f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(a23,f789(f789(f50(a108),x98041),f789(f113(a108),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))),f789(a23,x98041))
% 21.40/21.37 [4611]~P56(x46111,x46112)+P42(x46111,x46112)+~P43(a856)
% 21.40/21.37 [4551]~P2(x45511)+P33(x45511,x45512)+~E(x45512,f2(x45511))
% 21.40/21.37 [4560]~P110(x45601)+~E(x45602,f2(x45601))+E(f91(x45601,x45602),f2(x45601))
% 21.40/21.37 [4561]~P84(x45611)+~E(x45612,f2(x45611))+E(f91(x45611,x45612),f2(x45611))
% 21.40/21.37 [4567]~P2(x45672)+~P33(x45672,x45671)+E(x45671,f2(x45672))
% 21.40/21.37 [4601]~P110(x46012)+~E(f91(x46012,x46011),f2(x46012))+E(x46011,f2(x46012))
% 21.40/21.37 [4618]~P10(x46182)+~P10(x46181)+P10(f192(x46181,x46182))
% 21.40/21.37 [4619]~P59(x46192)+~P59(x46191)+P59(f871(x46191,x46192))
% 21.40/21.37 [4620]~P59(x46202)+~P59(x46201)+P59(f870(x46201,x46202))
% 21.40/21.37 [4621]~P59(x46212)+~P59(x46211)+P59(f869(x46211,x46212))
% 21.40/21.37 [4622]~P139(x46222)+~P139(x46221)+P139(f869(x46221,x46222))
% 21.40/21.37 [4747]~P101(x47471)+~P18(x47471,x47472)+P18(x47471,f147(x47471,x47472))
% 21.40/21.37 [4977]~P10(x49772)+~P10(x49771)+P10(f59(a1,x49771,x49772))
% 21.40/21.37 [4568]~P3(x45681)+~E(x45682,f2(x45681))+E(f789(f88(x45681),x45682),x45682)
% 21.40/21.37 [4569]~P3(x45691)+~E(x45692,f2(x45691))+E(f789(f88(x45691),x45692),x45692)
% 21.40/21.37 [4572]~P87(x45721)+~E(x45722,f2(a1))+E(f789(f112(x45721),x45722),f2(x45721))
% 21.40/21.37 [4573]~P120(x45731)+~E(x45732,f2(a1))+E(f789(f112(x45731),x45732),f2(x45731))
% 21.40/21.37 [4574]~P87(x45741)+~E(x45742,f2(a1))+E(f789(f112(x45741),x45742),f2(x45741))
% 21.40/21.37 [4598]~P68(x45981)+~E(f2(x45981),x45982)+E(f789(f88(x45981),x45982),f2(x45981))
% 21.40/21.37 [4599]~P68(x45991)+~E(x45992,f2(x45991))+E(f789(f88(x45991),x45992),f2(x45991))
% 21.40/21.37 [4600]~P80(x46001)+~E(x46002,f2(x46001))+E(f789(f84(x46001),x46002),f2(x46001))
% 21.40/21.37 [4623]~P3(x46232)+E(x46231,f2(x46232))+~E(f789(f88(x46232),x46231),x46231)
% 21.40/21.37 [4624]~P3(x46242)+E(x46241,f2(x46242))+~E(f789(f88(x46242),x46241),x46241)
% 21.40/21.37 [4632]E(x46321,f789(a114,x46322))+~E(x46321,f2(a863))+~E(x46322,f789(f109(a1),x46321))
% 21.40/21.37 [4633]E(f789(a114,x46331),x46332)+~E(x46332,f2(a863))+~E(x46331,f789(f109(a1),x46332))
% 21.40/21.37 [4636]~P87(x46362)+E(x46361,f2(a1))+~E(f789(f112(x46362),x46361),f2(x46362))
% 21.40/21.37 [4637]~P87(x46372)+E(x46371,f2(a1))+~E(f789(f112(x46372),x46371),f2(x46372))
% 21.40/21.37 [4642]~P68(x46422)+E(x46421,f2(x46422))+~E(f789(f88(x46422),x46421),f2(x46422))
% 21.40/21.37 [4643]~P80(x46432)+E(x46431,f2(x46432))+~E(f789(f84(x46432),x46431),f2(x46432))
% 21.40/21.37 [4644]~P68(x46441)+E(f2(x46441),x46442)+~E(f789(f88(x46441),x46442),f2(x46441))
% 21.40/21.37 [4779]~P13(a500)+~E(f789(a32,x47792),f789(f234(a857),x47791))+P1(f789(a26,x47791))
% 21.40/21.37 [4843]~P1(x48432)+~P1(x48431)+P1(f789(f789(a339,x48431),x48432))
% 21.40/21.37 [4877]~E(f87(a863),f2(a863))+E(f789(f49(x48771),x48772),f2(a863))+~P1(f789(f70(x48771),x48772))
% 21.40/21.37 [4908]~P106(x49081)+~P136(x49081)+E(f789(f789(f250(x49081),f2(x49081)),f789(a121,x49082)),f2(x49081))
% 21.40/21.37 [4948]~P101(x49481)+P18(x49481,f136(x49481,x49482))+~P1(f789(f70(x49481),x49482))
% 21.40/21.37 [4968]~P101(x49681)+E(f789(f163(x49681),f136(x49681,x49682)),x49682)+~P1(f789(f70(x49681),x49682))
% 21.40/21.37 [5002]P1(x50021)+P1(x50022)+~P1(f789(f789(a340,x50022),x50021))
% 21.40/21.37 [5014]E(x50141,f184(f870(x50142,a856)))+~E(f789(f49(x50142),x50141),f2(a863))+~P1(f789(f70(x50142),x50141))
% 21.40/21.37 [5019]P1(x50191)+~P1(x50192)+~P1(f789(f789(a343,x50192),x50191))
% 21.40/21.37 [5067]~P67(x50671)+E(f789(f84(x50671),x50672),x50672)+P1(f789(f789(f241(x50671),x50672),f2(x50671)))
% 21.40/21.37 [5162]~P1(f789(a26,x51622))+~P1(f789(a26,x51621))+P1(f789(a26,f38(x51621,x51622)))
% 21.40/21.37 [5163]~P1(f789(a26,x51632))+~P1(f789(a26,x51631))+P1(f789(a26,f38(x51631,x51632)))
% 21.40/21.37 [5170]E(x51701,f122(x51702))+P1(f789(f134(x51702),f123(x51702,x51701)))+~P1(f789(f134(x51702),x51701))
% 21.40/21.37 [5175]~P101(x51751)+~P1(f789(f70(x51751),x51752))+P1(f789(f134(x51751),f136(x51751,x51752)))
% 21.40/21.37 [5180]P1(f789(x51801,x51802))+P1(f789(x51801,f654(x51802,x51801)))+~P1(f789(x51801,f2(a863)))
% 21.40/21.37 [5182]~P120(x51821)+E(f789(f109(x51821),f789(a114,x51822)),f789(f112(x51821),x51822))+P1(f789(f789(f241(a1),x51822),f2(a1)))
% 21.40/21.37 [5208]P11(x52082,x52081)+E(f789(x52081,f522(x52081)),f789(x52081,f548(x52081)))+P1(f789(f789(x52081,f522(x52081)),f548(x52081)))
% 21.40/21.37 [5221]E(f789(f109(a1),f774(x52211,x52212)),x52211)+P1(f789(x52212,f789(a114,x52211)))+~P1(f789(x52212,f2(a863)))
% 21.40/21.37 [5260]~P110(x52601)+~E(f91(x52601,x52602),f789(f88(x52601),f87(x52601)))+P1(f789(f789(f241(x52601),x52602),f2(x52601)))
% 21.40/21.37 [5332]~E(x53322,f2(a1))+E(f217(x53321,x53322),f789(f789(f249(a1,a1),f2(a1)),f87(a1)))+P1(f789(f789(f241(a1),x53322),f2(a1)))
% 21.40/21.37 [5333]~E(x53331,f2(a1))+E(f217(x53331,x53332),f789(f789(f249(a1,a1),f2(a1)),f87(a1)))+P1(f789(f789(f241(a1),x53332),f2(a1)))
% 21.40/21.37 [5356]~P1(f789(x53561,x53562))+~P1(f789(x53561,f666(x53562,x53561)))+P1(f789(x53561,f2(a863)))
% 21.40/21.37 [5385]E(f789(f109(a1),f774(x53851,x53852)),x53851)+P1(f789(x53852,f789(a114,x53851)))+P1(f789(f789(f241(a1),x53851),f2(a1)))
% 21.40/21.37 [5451]~P110(x54511)+E(f91(x54511,x54512),f789(f88(x54511),f87(x54511)))+~P1(f789(f789(f241(x54511),x54512),f2(x54511)))
% 21.40/21.37 [5452]~P110(x54521)+E(f91(x54521,x54522),f789(f88(x54521),f87(x54521)))+~P1(f789(f789(f241(x54521),x54522),f2(x54521)))
% 21.40/21.37 [5453]~P80(x54531)+E(f789(f84(x54531),x54532),f789(f88(x54531),x54532))+~P1(f789(f789(f241(x54531),x54532),f2(x54531)))
% 21.40/21.37 [5454]~P80(x54541)+E(f789(f84(x54541),x54542),f789(f88(x54541),x54542))+~P1(f789(f789(f240(x54541),x54542),f2(x54541)))
% 21.40/21.37 [5455]~P67(x54551)+E(f789(f84(x54551),x54552),f789(f88(x54551),x54552))+~P1(f789(f789(f241(x54551),x54552),f2(x54551)))
% 21.40/21.37 [5546]~P1(f789(x55461,f774(x55462,x55461)))+P1(f789(x55461,f789(a114,x55462)))+~P1(f789(x55461,f2(a863)))
% 21.40/21.37 [5553]E(x55531,f2(a863))+E(f789(a121,f677(x55532,x55531)),x55531)+~P1(f789(f789(f241(a863),x55531),f789(a121,x55532)))
% 21.40/21.37 [5557]P11(x55571,x55572)+~E(f789(x55572,f522(x55572)),f789(x55572,f548(x55572)))+~P1(f789(f789(x55572,f522(x55572)),f548(x55572)))
% 21.40/21.37 [5576]~P101(x55761)+P18(x55761,x55762)+P1(f789(f789(f240(a863),f776(x55762,x55761)),f777(x55762,x55761)))
% 21.40/21.37 [5662]~P80(x56621)+~E(x56622,f2(x56621))+P1(f789(f789(f240(x56621),f789(f84(x56621),x56622)),f2(x56621)))
% 21.40/21.37 [5751]~P1(f789(x57511,f774(x57512,x57511)))+P1(f789(x57511,f789(a114,x57512)))+P1(f789(f789(f241(a1),x57512),f2(a1)))
% 21.40/21.37 [5777]~P1(f789(x57771,f789(a114,x57772)))+P1(f789(x57771,f2(a863)))+~P1(f789(f789(f241(a1),x57772),f2(a1)))
% 21.40/21.37 [6120]~P110(x61201)+~P1(f789(f789(f241(x61201),x61202),f2(x61201)))+P1(f789(f789(f241(x61201),f91(x61201,x61202)),f2(x61201)))
% 21.40/21.37 [6236]~P110(x62361)+P1(f789(f789(f241(x62361),f789(f112(x62361),x62362)),f2(x62361)))+~P1(f789(f789(f241(a1),x62362),f2(a1)))
% 21.40/21.37 [6237]~P110(x62371)+P1(f789(f789(f240(x62371),f789(f112(x62371),x62372)),f2(x62371)))+~P1(f789(f789(f240(a1),x62372),f2(a1)))
% 21.40/21.37 [6241]~P80(x62412)+E(x62411,f2(x62412))+~P1(f789(f789(f240(x62412),f789(f84(x62412),x62411)),f2(x62412)))
% 21.40/21.37 [6325]~P120(x63251)+~P1(f789(f789(f342(x63251),x63252),f119(x63251)))+P1(f789(f789(f342(x63251),f789(f88(x63251),x63252)),f119(x63251)))
% 21.40/21.37 [6357]~P110(x63571)+~P1(f789(f789(f241(x63571),f91(x63571,x63572)),f2(x63571)))+P1(f789(f789(f241(x63571),x63572),f2(x63571)))
% 21.40/21.37 [6534]~P110(x65342)+~P1(f789(f789(f241(x65342),f789(f112(x65342),x65341)),f2(x65342)))+P1(f789(f789(f241(a1),x65341),f2(a1)))
% 21.40/21.37 [6535]~P110(x65352)+~P1(f789(f789(f240(x65352),f789(f112(x65352),x65351)),f2(x65352)))+P1(f789(f789(f240(a1),x65351),f2(a1)))
% 21.40/21.37 [7057]~P3(x70571)+~P1(f789(f789(f241(x70571),x70572),f2(x70571)))+P1(f789(f789(f241(x70571),f789(f789(f89(x70571),x70572),x70572)),f2(x70571)))
% 21.40/21.37 [7058]~P110(x70581)+~P1(f789(f789(f241(x70581),x70582),f2(x70581)))+P1(f789(f789(f241(x70581),f789(f789(f89(x70581),x70582),x70582)),f2(x70581)))
% 21.40/21.37 [7059]~P3(x70591)+~P1(f789(f789(f240(x70591),x70592),f2(x70591)))+P1(f789(f789(f240(x70591),f789(f789(f89(x70591),x70592),x70592)),f2(x70591)))
% 21.40/21.37 [7654]~P3(x76541)+~P1(f789(f789(f241(x76541),f789(f789(f89(x76541),x76542),x76542)),f2(x76541)))+P1(f789(f789(f241(x76541),x76542),f2(x76541)))
% 21.40/21.37 [7655]~P110(x76551)+~P1(f789(f789(f241(x76551),f789(f789(f89(x76551),x76552),x76552)),f2(x76551)))+P1(f789(f789(f241(x76551),x76552),f2(x76551)))
% 21.40/21.37 [7656]~P3(x76561)+~P1(f789(f789(f240(x76561),f789(f789(f89(x76561),x76562),x76562)),f2(x76561)))+P1(f789(f789(f240(x76561),x76562),f2(x76561)))
% 21.40/21.37 [4680]~E(x46802,f87(a863))+~E(x46801,f87(a863))+E(f789(f789(f90(a863),x46801),x46802),f87(a863))
% 21.40/21.37 [4681]~E(x46812,f2(a863))+~E(x46811,f2(a863))+E(f789(f789(f89(a863),x46811),x46812),f2(a863))
% 21.40/21.37 [4682]~E(x46822,f87(a863))+~E(x46821,f87(a863))+E(f789(f789(f90(a863),x46821),x46822),f87(a863))
% 21.40/21.37 [4683]~E(x46832,f87(a1))+~E(x46831,f87(a1))+E(f789(f789(f90(a1),x46831),x46832),f87(a1))
% 21.40/21.37 [4733]~P7(x47332)+E(x47331,f2(x47332))+E(f789(f789(f50(x47332),x47331),x47331),f87(x47332))
% 21.40/21.37 [4734]~P113(x47342)+E(x47341,f2(x47342))+E(f789(f789(f291(x47342),x47341),x47341),f87(x47342))
% 21.40/21.37 [4735]~P114(x47352)+E(x47351,f2(x47352))+E(f789(f789(f291(x47352),x47351),x47351),f87(x47352))
% 21.40/21.37 [4750]~P3(x47501)+~E(x47502,f2(x47501))+E(f789(f789(f89(x47501),x47502),x47502),f2(x47501))
% 21.40/21.37 [4751]~P3(x47511)+~E(x47512,f2(x47511))+E(f789(f789(f89(x47511),x47512),x47512),f2(x47511))
% 21.40/21.37 [4754]~P134(x47541)+~E(x47542,f87(x47541))+E(f789(f789(f90(x47541),x47542),x47542),f87(x47541))
% 21.40/21.37 [4755]~P114(x47551)+~E(x47552,f2(x47551))+E(f789(f789(f291(x47551),x47552),x47552),f2(x47551))
% 21.40/21.37 [4799]~E(x47992,f2(a863))+~E(x47991,f2(a863))+E(f789(f88(a1),f789(f109(a1),x47991)),f789(f109(a1),x47992))
% 21.40/21.37 [4817]E(x48171,f87(a863))+E(x48172,f2(a863))+~E(f789(f789(f90(a863),x48172),x48171),x48172)
% 21.40/21.37 [4824]E(x48241,f2(a863))+E(x48242,f2(a863))+~E(f789(f789(f90(a863),x48242),x48241),f2(a863))
% 21.40/21.37 [4850]~E(x48502,f2(a863))+~E(x48501,f789(a121,f2(a863)))+E(f789(f789(f89(a863),x48501),x48502),f789(a121,f2(a863)))
% 21.40/21.37 [4851]~E(x48511,f2(a863))+~E(x48512,f789(a121,f2(a863)))+E(f789(f789(f89(a863),x48511),x48512),f789(a121,f2(a863)))
% 21.40/21.37 [4852]~E(x48522,f2(a863))+~E(x48521,f789(a121,f2(a863)))+E(f789(f789(f89(a863),x48521),x48522),f789(a121,f2(a863)))
% 21.40/21.37 [4853]~E(x48531,f2(a863))+~E(x48532,f789(a121,f2(a863)))+E(f789(f789(f89(a863),x48531),x48532),f789(a121,f2(a863)))
% 21.40/21.37 [4858]E(x48581,f87(a1))+E(x48582,f789(f113(a1),a106))+~E(f789(f789(f90(a1),x48581),x48582),f87(a1))
% 21.40/21.37 [4859]E(x48591,f87(a1))+E(x48592,f789(f113(a1),a106))+~E(f789(f789(f90(a1),x48592),x48591),f87(a1))
% 21.40/21.37 [4860]E(x48601,f87(a1))+E(x48601,f789(f113(a1),a106))+~E(f789(f789(f90(a1),x48602),x48601),f87(a1))
% 21.40/21.37 [4861]E(x48611,f87(a1))+E(x48611,f789(f113(a1),a106))+~E(f789(f789(f90(a1),x48611),x48612),f87(a1))
% 21.40/21.37 [4862]E(x48621,f87(a1))+E(x48621,f789(f113(a1),a106))+~E(f789(f789(f90(a1),x48621),x48622),f87(a1))
% 21.40/21.37 [4880]~P3(x48802)+E(x48801,f2(x48802))+~E(f789(f789(f89(x48802),x48801),x48801),f2(x48802))
% 21.40/21.37 [4881]~P3(x48812)+E(x48811,f2(x48812))+~E(f789(f789(f89(x48812),x48811),x48811),f2(x48812))
% 21.40/21.37 [4887]~E(x48871,f789(f113(a1),a106))+~E(x48872,f789(f113(a1),a106))+E(f789(f789(f90(a1),x48871),x48872),f87(a1))
% 21.40/21.37 [4898]E(x48981,f2(a863))+E(x48982,f2(a863))+~E(f789(f789(f89(a863),x48982),x48981),f789(a121,f2(a863)))
% 21.40/21.37 [4899]E(x48991,f2(a863))+E(x48992,f2(a863))+~E(f789(f789(f89(a863),x48992),x48991),f789(a121,f2(a863)))
% 21.40/21.37 [4907]~P88(x49071)+~P60(x49071)+E(f789(f789(f291(x49071),x49072),f789(f113(x49071),a92)),f2(x49071))
% 21.40/21.37 [4914]~P134(x49141)+~E(x49142,f789(f88(x49141),f87(x49141)))+E(f789(f789(f90(x49141),x49142),x49142),f87(x49141))
% 21.40/21.37 [4919]~P10(x49192)+~P10(x49191)+P10(f789(f789(f89(a1),x49191),x49192))
% 21.40/21.37 [4920]~P10(x49202)+~P10(x49201)+P10(f789(f789(f90(a1),x49201),x49202))
% 21.40/21.37 [4921]~P10(x49212)+~P10(x49211)+P10(f789(f789(f50(a1),x49211),x49212))
% 21.40/21.37 [4922]~E(x49222,f2(a1))+E(x49221,f2(a1))+E(f60(x49221,x49222),f789(f789(f249(a1,a1),f2(a1)),x49221))
% 21.40/21.37 [4923]~E(x49232,f2(a1))+E(x49231,f2(a1))+E(f60(x49231,x49232),f789(f789(f249(a1,a1),f2(a1)),x49231))
% 21.40/21.37 [4946]~E(x49462,f789(a121,f2(a863)))+~E(x49461,f789(a121,f2(a863)))+E(f789(f789(f90(a863),x49461),x49462),f789(a121,f2(a863)))
% 21.40/21.37 [4957]E(x49571,f2(a863))+E(x49571,f789(a121,f2(a863)))+~E(f789(f789(f89(a863),x49572),x49571),f789(a121,f2(a863)))
% 21.40/21.37 [4958]E(x49581,f2(a863))+E(x49581,f789(a121,f2(a863)))+~E(f789(f789(f89(a863),x49581),x49582),f789(a121,f2(a863)))
% 21.40/21.37 [4959]E(x49591,f2(a863))+E(x49592,f789(a121,f2(a863)))+~E(f789(f789(f250(a863),x49592),x49591),f789(a121,f2(a863)))
% 21.40/21.37 [4960]E(x49601,f2(a863))+E(x49601,f789(a121,f2(a863)))+~E(f789(f789(f89(a863),x49602),x49601),f789(a121,f2(a863)))
% 21.40/21.37 [4961]E(x49611,f2(a863))+E(x49611,f789(a121,f2(a863)))+~E(f789(f789(f89(a863),x49611),x49612),f789(a121,f2(a863)))
% 21.40/21.37 [4969]~P88(x49691)+~P60(x49691)+E(f789(f789(f291(x49691),x49692),f789(f113(x49691),a106)),f789(f88(x49691),x49692))
% 21.40/21.37 [4990]E(x49901,f789(a114,x49902))+~E(x49901,f2(a863))+P1(f789(f789(f240(a1),f2(a1)),x49902))
% 21.40/21.37 [4991]E(f789(a114,x49911),x49912)+~E(x49912,f2(a863))+P1(f789(f789(f240(a1),f2(a1)),x49911))
% 21.40/21.37 [5009]E(x50091,f789(a121,f2(a863)))+E(x50092,f789(a121,f2(a863)))+~E(f789(f789(f89(a863),x50091),x50092),f789(a121,f2(a863)))
% 21.40/21.37 [5010]E(x50101,f789(a121,f2(a863)))+E(x50102,f789(a121,f2(a863)))+~E(f789(f789(f89(a863),x50101),x50102),f789(a121,f2(a863)))
% 21.40/21.37 [5021]~E(x50211,f789(a114,x50212))+E(x50211,f2(a863))+P1(f789(f789(f240(a1),f2(a1)),x50212))
% 21.40/21.37 [5022]~E(f789(a114,x50222),x50221)+E(x50221,f2(a863))+P1(f789(f789(f240(a1),f2(a1)),x50222))
% 21.40/21.37 [5045]~P95(x50451)+E(f789(f72(x50451,f111(x50451)),x50452),f12(x50451,x50452))+~P1(f789(f70(x50451),x50452))
% 21.40/21.37 [5046]~P95(x50461)+E(f789(f72(x50461,f110(x50461)),x50462),f15(x50461,x50462))+~P1(f789(f70(x50461),x50462))
% 21.40/21.37 [5047]~P101(x50471)+E(f789(f72(x50471,f239(x50471)),x50472),f16(x50471,x50472))+~P1(f789(f70(x50471),x50472))
% 21.40/21.37 [5048]~P101(x50481)+E(f789(f72(x50481,f244(x50481)),x50482),f17(x50481,x50482))+~P1(f789(f70(x50481),x50482))
% 21.40/21.37 [5130]E(x51301,x51302)+~E(f789(f789(f3(a863),x51302),x51301),f2(a863))+~E(f789(f789(f3(a863),x51301),x51302),f2(a863))
% 21.40/21.37 [5140]P10(x51401)+~P38(x51402)+~P1(f789(f789(f342(a1),x51401),x51402))
% 21.40/21.37 [5171]~P110(x51711)+~E(f91(x51711,x51712),f87(x51711))+P1(f789(f789(f241(x51711),f2(x51711)),x51712))
% 21.40/21.37 [5183]~P88(x51831)+E(f789(f109(x51831),f789(f113(a863),x51832)),f789(f113(x51831),x51832))+P1(f789(a190,f789(f113(a1),x51832)))
% 21.40/21.37 [5188]~P42(x51881,x51882)+P43(a856)+P1(f789(f70(f869(x51881,x51881)),x51882))
% 21.40/21.37 [5252]~P101(x52521)+E(f789(f72(x52521,f239(x52521)),x52522),f13(x52521,f239(x52521),x52522))+~P1(f789(f70(x52521),x52522))
% 21.40/21.37 [5253]~P101(x52531)+E(f789(f72(x52531,f244(x52531)),x52532),f14(x52531,f244(x52531),x52532))+~P1(f789(f70(x52531),x52532))
% 21.40/21.37 [5265]E(x52651,x52652)+P1(f789(f789(f241(a863),x52652),x52651))+P1(f789(f789(f241(a863),x52651),x52652))
% 21.40/21.37 [5266]E(x52661,x52662)+P1(f789(f789(f241(a863),x52662),x52661))+P1(f789(f789(f241(a863),x52661),x52662))
% 21.40/21.37 [5267]E(x52671,x52672)+P1(f789(f789(f241(a1),x52672),x52671))+P1(f789(f789(f241(a1),x52671),x52672))
% 21.40/21.37 [5319]~P88(x53191)+E(f789(f109(x53191),f789(f113(a863),x53192)),f2(x53191))+~P1(f789(a190,f789(f113(a1),x53192)))
% 21.40/21.37 [5322]~E(x53222,f789(a114,x53221))+E(x53221,f789(f109(a1),x53222))+~P1(f789(f789(f240(a1),f2(a1)),x53221))
% 21.40/21.37 [5323]~E(f789(a114,x53231),x53232)+E(x53231,f789(f109(a1),x53232))+~P1(f789(f789(f240(a1),f2(a1)),x53231))
% 21.40/21.37 [5324]~E(x53241,f789(a114,x53242))+E(f789(f109(a1),x53241),x53242)+~P1(f789(f789(f240(a1),f2(a1)),x53242))
% 21.40/21.37 [5334]E(x53341,f789(a114,x53342))+~E(x53342,f789(f109(a1),x53341))+~P1(f789(f789(f240(a1),f2(a1)),x53342))
% 21.40/21.37 [5335]E(f789(a114,x53351),x53352)+~E(x53351,f789(f109(a1),x53352))+~P1(f789(f789(f240(a1),f2(a1)),x53351))
% 21.40/21.37 [5365]~P70(x53652)+E(x53651,f2(x53652))+~P1(f789(f789(f287(x53652),f2(x53652)),x53651))
% 21.40/21.37 [5374]~P80(x53742)+E(x53741,f2(x53742))+P1(f789(f789(f241(x53742),f2(x53742)),f789(f84(x53742),x53741)))
% 21.40/21.37 [5442]~P110(x54421)+E(f91(x54421,x54422),f87(x54421))+~P1(f789(f789(f241(x54421),f2(x54421)),x54422))
% 21.40/21.37 [5443]~P110(x54431)+E(f91(x54431,x54432),f87(x54431))+~P1(f789(f789(f241(x54431),f2(x54431)),x54432))
% 21.40/21.37 [5449]~P88(x54491)+E(f789(f109(x54491),f789(f113(a863),x54492)),f2(x54491))+P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x54492)))
% 21.40/21.37 [5456]~P80(x54561)+E(f789(f84(x54561),x54562),x54562)+~P1(f789(f789(f241(x54561),f2(x54561)),x54562))
% 21.40/21.37 [5457]~P80(x54571)+E(f789(f84(x54571),x54572),x54572)+~P1(f789(f789(f240(x54571),f2(x54571)),x54572))
% 21.40/21.37 [5464]E(x54641,f2(a863))+~E(f136(a863,f789(f302(a863,x54642),x54641)),f122(a863))+P1(f789(f789(f240(a863),x54641),x54642))
% 21.40/21.37 [5474]~P4(x54741)+E(f789(f789(f8(x54741,x54741),f7(x54741)),f789(f163(x54741),x54742)),f789(f161(x54741),x54742))+~P1(f789(f134(x54741),x54742))
% 21.40/21.37 [5477]~P120(x54771)+E(f789(f109(x54771),f789(a114,x54772)),f789(f112(x54771),x54772))+~P1(f789(f789(f240(a1),f2(a1)),x54772))
% 21.40/21.37 [5479]~E(x54791,x54792)+P1(f789(f789(f241(a863),x54791),f789(a121,x54792)))+P1(f789(f789(f241(a863),x54791),x54792))
% 21.40/21.37 [5498]E(x54981,x54982)+P1(f789(f789(f241(a863),x54981),x54982))+~P1(f789(f789(f240(a863),x54981),x54982))
% 21.40/21.37 [5499]E(x54991,x54992)+P1(f789(f789(f241(a863),x54991),x54992))+~P1(f789(f789(f240(a863),x54991),x54992))
% 21.40/21.37 [5500]E(x55001,x55002)+P1(f789(f789(f241(a863),x55001),x55002))+~P1(f789(f789(f240(a863),x55001),x55002))
% 21.40/21.37 [5501]E(x55011,x55012)+P1(f789(f789(f241(a1),x55011),x55012))+~P1(f789(f789(f240(a1),x55011),x55012))
% 21.40/21.37 [5504]E(x55041,f87(a1))+~E(f789(f789(f90(a1),x55042),x55041),f87(a1))+~P1(f789(f789(f241(a1),f2(a1)),x55042))
% 21.40/21.37 [5505]E(x55051,f87(a1))+~E(f789(f789(f90(a1),x55051),x55052),f87(a1))+~P1(f789(f789(f241(a1),f2(a1)),x55051))
% 21.40/21.37 [5542]~P38(x55422)+P1(f789(f789(f240(a1),f2(a1)),x55421))+~P1(f789(f789(f342(a1),x55421),x55422))
% 21.40/21.37 [5543]~P38(x55432)+P1(f789(f789(f240(a1),f2(a1)),x55431))+~P1(f789(f789(f342(a1),x55431),x55432))
% 21.40/21.37 [5554]~P1(f789(x55541,x55542))+P1(f789(x55541,f2(a863)))+P1(f789(x55541,f789(a121,f666(x55542,x55541))))
% 21.40/21.37 [5561]~P56(x55611,x55612)+P36(x55611,x55612)+~P1(f789(f70(f869(x55611,x55611)),x55612))
% 21.40/21.37 [5562]~P56(x55621,x55622)+P36(x55621,x55622)+~P1(f789(f70(f869(x55621,x55621)),x55622))
% 21.40/21.37 [5563]~P36(x55631,x55632)+P56(x55631,x55632)+~P1(f789(f70(f869(x55631,x55631)),x55632))
% 21.40/21.37 [5564]~P56(x55641,x55642)+P42(x55641,x55642)+~P1(f789(f70(f869(x55641,x55641)),x55642))
% 21.40/21.37 [5604]E(x56041,f184(f870(x56042,a856)))+~P1(f789(f70(x56042),x56041))+P1(f789(f789(f241(a863),f2(a863)),f789(f49(x56042),x56041)))
% 21.40/21.37 [5630]~P1(f789(x56301,x56302))+P1(f789(x56301,f2(a863)))+P1(f789(f789(f241(a863),f813(x56302,x56301)),x56302))
% 21.40/21.37 [5655]E(x56551,f2(a863))+~E(f789(f161(a863),x56552),f2(a863))+~P1(f789(f789(f342(a863),x56551),f789(f163(a863),x56552)))
% 21.40/21.37 [5688]~E(x56881,x56882)+P1(f789(f789(f241(a863),x56881),f789(a121,x56882)))+~P1(f789(f789(f240(a863),x56882),x56881))
% 21.40/21.37 [5717]~E(x57172,f2(a863))+P1(f789(f789(f240(a1),f2(a1)),x57171))+P1(f789(f789(f287(a863),f789(a114,x57171)),x57172))
% 21.40/21.37 [5720]E(x57201,x57202)+~P1(f789(f789(f240(a863),x57202),x57201))+~P1(f789(f789(f240(a863),x57201),x57202))
% 21.40/21.37 [5721]E(x57211,x57212)+~P1(f789(f789(f240(a1),x57212),x57211))+~P1(f789(f789(f240(a1),x57211),x57212))
% 21.40/21.37 [5722]E(x57221,x57222)+~P1(f789(f789(f287(a863),x57222),x57221))+~P1(f789(f789(f287(a863),x57221),x57222))
% 21.40/21.37 [5723]E(x57231,x57232)+~P1(f789(f789(f287(a863),x57232),x57231))+~P1(f789(f789(f287(a863),x57231),x57232))
% 21.40/21.37 [5724]E(x57241,x57242)+~P1(f789(f789(f287(a863),x57242),x57241))+~P1(f789(f789(f287(a863),x57241),x57242))
% 21.40/21.37 [5725]E(x57251,x57252)+~P1(f789(f789(f287(a863),x57252),x57251))+~P1(f789(f789(f287(a863),x57251),x57252))
% 21.40/21.37 [5726]E(x57261,x57262)+~P1(f789(f789(f287(a863),x57262),x57261))+~P1(f789(f789(f287(a863),x57261),x57262))
% 21.40/21.37 [5727]E(x57271,x57272)+~P1(f789(f789(f287(a863),x57272),x57271))+~P1(f789(f789(f287(a863),x57271),x57272))
% 21.40/21.37 [5728]E(x57281,x57282)+~P1(f789(f789(f287(a863),x57282),x57281))+~P1(f789(f789(f287(a863),x57281),x57282))
% 21.40/21.37 [5729]E(x57291,x57292)+~P1(f789(f789(f287(a863),x57292),x57291))+~P1(f789(f789(f287(a863),x57291),x57292))
% 21.40/21.37 [5730]E(x57301,x57302)+~P1(f789(f789(f287(a863),x57302),x57301))+~P1(f789(f789(f287(a863),x57301),x57302))
% 21.40/21.37 [5731]E(f789(f49(x57311),x57312),f2(a863))+~P1(f789(f70(x57311),x57312))+P1(f789(f789(f342(x57311),f629(x57312,x57311)),x57312))
% 21.40/21.37 [5737]E(f64(x57371,x57372),f60(x57371,x57372))+P1(f789(f789(f240(a1),f2(a1)),x57371))+~P1(f789(f789(f241(a1),f2(a1)),x57372))
% 21.40/21.37 [5766]~P1(f789(x57661,f806(x57661)))+P1(f789(x57661,f789(a114,x57662)))+~P1(f789(f789(f240(a1),f2(a1)),x57662))
% 21.40/21.37 [5768]P1(f789(f789(f241(a863),x57681),f386(x57682)))+~P1(f789(f70(a863),x57682))+~P1(f789(f789(f342(a863),x57681),x57682))
% 21.40/21.37 [5769]P1(f789(f789(f240(a863),x57691),f382(x57692)))+~P1(f789(f70(a863),x57692))+~P1(f789(f789(f342(a863),x57691),x57692))
% 21.40/21.37 [5795]E(x57951,x57952)+~P1(f789(f789(f241(a863),x57951),f789(a121,x57952)))+P1(f789(f789(f241(a863),x57951),x57952))
% 21.40/21.37 [5796]E(x57961,x57962)+~P1(f789(f789(f241(a863),x57961),f789(a121,x57962)))+P1(f789(f789(f241(a863),x57961),x57962))
% 21.40/21.37 [5797]E(x57971,x57972)+~P1(f789(f789(f241(a863),x57971),f789(a121,x57972)))+P1(f789(f789(f241(a863),x57971),x57972))
% 21.40/21.37 [5798]E(x57981,x57982)+~P1(f789(f789(f241(a863),x57981),f789(a121,x57982)))+P1(f789(f789(f241(a863),x57981),x57982))
% 21.40/21.37 [5834]E(x58341,f789(a121,x58342))+~P1(f789(f789(f240(a863),x58341),f789(a121,x58342)))+P1(f789(f789(f240(a863),x58341),x58342))
% 21.40/21.37 [5835]E(x58351,f789(a121,x58352))+~P1(f789(f789(f240(a863),x58351),f789(a121,x58352)))+P1(f789(f789(f240(a863),x58351),x58352))
% 21.40/21.37 [5845]P1(f789(x58451,f811(x58451)))+~P1(f789(x58451,f789(a114,x58452)))+~P1(f789(f789(f240(a1),f2(a1)),x58452))
% 21.40/21.37 [5847]E(f789(f84(a1),x58471),f789(f84(a1),x58472))+~P1(f789(f789(f287(a1),x58472),x58471))+~P1(f789(f789(f287(a1),x58471),x58472))
% 21.40/21.37 [5859]~P1(f789(x58591,x58592))+~P1(f789(f789(f240(a1),f2(a1)),x58592))+P1(f789(x58591,f789(f109(a1),f804(x58591))))
% 21.40/21.37 [5871]~P80(x58712)+~E(x58711,f2(x58712))+~P1(f789(f789(f241(x58712),f2(x58712)),f789(f84(x58712),x58711)))
% 21.40/21.37 [5896]~P56(x58961,x58962)+P36(x58961,f789(f286(x58961,x58961),x58962))+~P1(f789(f70(f869(x58961,x58961)),x58962))
% 21.40/21.37 [5904]~P88(x59041)+E(f789(f109(x59041),f789(f113(a863),x59042)),f789(f113(x59041),x59042))+~P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x59042)))
% 21.40/21.37 [5908]E(f789(a121,x59081),x59082)+~P1(f789(f789(f241(a863),x59081),x59082))+P1(f789(f789(f241(a863),f789(a121,x59081)),x59082))
% 21.40/21.37 [5920]E(f789(f789(f50(a1),x59201),x59202),f2(a1))+~P1(f789(f789(f240(a1),x59201),f2(a1)))+~P1(f789(f789(f241(a1),x59202),x59201))
% 21.40/21.37 [5921]E(f789(f789(f50(a1),x59211),x59212),f2(a1))+~P1(f789(f789(f240(a1),x59211),f2(a1)))+~P1(f789(f789(f241(a1),x59212),x59211))
% 21.40/21.37 [5934]E(f59(a1,x59341,x59342),x59341)+~P1(f789(f789(f240(a1),x59341),f2(a1)))+~P1(f789(f789(f241(a1),x59342),x59341))
% 21.40/21.37 [5946]E(f61(x59461,x59462),f60(x59461,x59462))+~P1(f789(f789(f240(a1),f2(a1)),x59461))+~P1(f789(f789(f240(a1),f2(a1)),x59462))
% 21.40/21.37 [5952]E(f789(f789(f50(a863),x59521),x59522),f2(a863))+~P1(f789(f789(f241(a863),f2(a863)),x59522))+~P1(f789(f789(f241(a863),x59521),x59522))
% 21.40/21.37 [5953]E(f789(f789(f50(a1),x59531),x59532),f2(a1))+~P1(f789(f789(f240(a1),f2(a1)),x59531))+~P1(f789(f789(f241(a1),x59531),x59532))
% 21.40/21.37 [5954]E(f789(f789(f50(a1),x59541),x59542),f2(a1))+~P1(f789(f789(f240(a1),f2(a1)),x59541))+~P1(f789(f789(f241(a1),x59541),x59542))
% 21.40/21.37 [5968]E(f59(a863,f789(f113(a863),x59681),f789(f113(a863),x59682)),f789(f113(a863),x59681))+P1(f789(a190,f789(f113(a1),x59681)))+~P1(f789(a190,f789(f113(a1),x59682)))
% 21.40/21.37 [5970]E(f59(a1,x59701,x59702),x59701)+~P1(f789(f789(f240(a1),f2(a1)),x59701))+~P1(f789(f789(f241(a1),x59701),x59702))
% 21.40/21.37 [5971]P1(f789(x59711,x59712))+~P1(f789(x59711,f2(a863)))+~P1(f789(x59711,f789(a121,f654(x59712,x59711))))
% 21.40/21.37 [5973]E(x59731,x59732)+~P1(f789(f789(f241(a863),x59731),f789(a121,x59732)))+~P1(f789(f789(f240(a863),x59732),x59731))
% 21.40/21.37 [5985]E(f789(f113(a1),x59851),f789(f109(a1),x59852))+~E(x59852,f789(a114,f789(f113(a1),x59851)))+~P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x59851)))
% 21.40/21.37 [5989]~P110(x59891)+~P1(f789(f789(f241(x59891),x59892),f2(x59891)))+P1(f789(f789(f241(x59891),x59892),f789(f88(x59891),x59892)))
% 21.40/21.37 [5990]~P3(x59901)+~P1(f789(f789(f240(x59901),x59902),f2(x59901)))+P1(f789(f789(f240(x59901),x59902),f789(f88(x59901),x59902)))
% 21.40/21.37 [5999]~P9(x59991)+E(f789(f789(f73(x59991,x59991,f111(x59991)),f247(x59991)),x59992),f52(x59991,x59992))+~P1(f789(f70(x59991),x59992))
% 21.40/21.37 [6000]~P9(x60001)+E(f789(f789(f73(x60001,x60001,f110(x60001)),f184(x60001)),x60002),f51(x60001,x60002))+~P1(f789(f70(x60001),x60002))
% 21.40/21.37 [6014]~P117(x60141)+~P1(f789(f789(f241(a863),f2(a863)),x60142))+P1(f789(f789(f241(x60141),f2(x60141)),f789(f109(x60141),x60142)))
% 21.40/21.37 [6015]~P110(x60151)+~P1(f789(f789(f241(a1),f2(a1)),x60152))+P1(f789(f789(f241(x60151),f2(x60151)),f789(f112(x60151),x60152)))
% 21.40/21.37 [6016]~P110(x60161)+~P1(f789(f789(f240(a1),f2(a1)),x60162))+P1(f789(f789(f240(x60161),f2(x60161)),f789(f112(x60161),x60162)))
% 21.40/21.37 [6019]~P10(x60192)+~P10(x60191)+E(f789(f311(a863,a1,f109(a1)),f303(a863,f789(a114,x60191),f789(a114,x60192))),f303(a1,x60191,x60192))
% 21.40/21.37 [6025]P1(f789(x60251,x60252))+~P1(f789(f789(f240(a1),f2(a1)),x60252))+~P1(f789(x60251,f789(f109(a1),f805(x60251))))
% 21.40/21.37 [6053]E(f789(f789(f89(a863),f789(f113(a863),x60531)),f789(f113(a863),x60532)),f789(f113(a863),x60531))+P1(f789(f789(f241(a1),x60531),a92))+~P1(f789(f789(f241(a1),x60532),a92))
% 21.40/21.37 [6057]~P110(x60571)+P1(f789(f789(f241(x60571),f2(x60571)),f91(x60571,x60572)))+~P1(f789(f789(f241(x60571),f2(x60571)),x60572))
% 21.40/21.37 [6072]~P76(x60721)+~P1(f789(f789(f241(x60721),x60722),f2(x60721)))+P1(f789(f789(f241(x60721),f2(x60721)),f789(f88(x60721),x60722)))
% 21.40/21.37 [6073]~P76(x60731)+~P1(f789(f789(f240(x60731),x60732),f2(x60731)))+P1(f789(f789(f240(x60731),f2(x60731)),f789(f88(x60731),x60732)))
% 21.40/21.37 [6076]E(x60761,f2(a863))+P1(f789(f789(f240(a1),f2(a1)),x60762))+~P1(f789(f789(f287(a863),f789(a114,x60762)),x60761))
% 21.40/21.37 [6077]E(x60771,f247(f870(x60772,a856)))+~E(f789(f49(x60772),x60771),f789(f49(x60772),f247(f870(x60772,a856))))+~P1(f789(f70(x60772),f247(f870(x60772,a856))))
% 21.40/21.37 [6106]~P1(f789(f789(f241(a863),f2(a863)),x61062))+~P1(f789(f789(f287(a863),x61061),x61062))+P1(f789(f789(f240(a863),x61061),x61062))
% 21.40/21.37 [6107]~P1(f789(f789(f241(a1),f2(a1)),x61072))+~P1(f789(f789(f287(a1),x61071),x61072))+P1(f789(f789(f240(a1),x61071),x61072))
% 21.40/21.37 [6113]~P110(x61131)+P1(f789(f789(f241(x61131),x61132),f2(x61131)))+~P1(f789(f789(f241(x61131),x61132),f789(f88(x61131),x61132)))
% 21.40/21.37 [6114]~P3(x61141)+P1(f789(f789(f240(x61141),x61142),f2(x61141)))+~P1(f789(f789(f240(x61141),x61142),f789(f88(x61141),x61142)))
% 21.40/21.37 [6119]E(f61(x61191,x61192),f789(f789(f249(a1,a1),f2(a1)),x61191))+~P1(f789(f789(f241(a1),f2(a1)),x61192))+~P1(f789(f789(f241(a1),x61191),x61192))
% 21.40/21.37 [6122]~P88(x61221)+P1(f789(f789(f342(x61221),f789(f113(x61221),x61222)),f181(x61221)))+~P1(f789(f789(f240(a1),a92),x61222))
% 21.40/21.37 [6151]E(x61511,f2(a863))+~P1(f789(f789(f241(a863),x61511),f789(a121,x61512)))+P1(f789(f789(f241(a863),f677(x61512,x61511)),x61512))
% 21.40/21.37 [6175]~P110(x61751)+~P1(f789(f789(f241(x61751),f2(x61751)),f91(x61751,x61752)))+P1(f789(f789(f241(x61751),f2(x61751)),x61752))
% 21.40/21.37 [6177]~E(f789(f113(a863),x61772),f789(f113(a863),x61771))+P1(f789(f789(f240(a1),f789(f113(a1),x61771)),f2(a1)))+~P1(f789(a190,f789(f113(a1),x61772)))
% 21.40/21.37 [6205]E(f789(f248(a1,a1),f64(x62051,x62052)),f789(f789(f50(a1),x62051),x62052))+~P1(f789(f789(f241(a1),x62051),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x62052))
% 21.40/21.37 [6239]E(f789(f258(a1,a1),f64(x62391,x62392)),f59(a1,x62391,x62392))+~P1(f789(f789(f241(a1),x62391),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x62392))
% 21.40/21.37 [6240]E(x62401,f2(a1))+~P1(f789(f789(f287(a1),x62402),x62401))+P1(f789(f789(f240(a1),f789(f84(a1),x62402)),f789(f84(a1),x62401)))
% 21.40/21.37 [6242]~P117(x62422)+~P1(f789(f789(f241(x62422),f2(x62422)),f789(f109(x62422),x62421)))+P1(f789(f789(f241(a863),f2(a863)),x62421))
% 21.40/21.37 [6243]~P110(x62432)+~P1(f789(f789(f241(x62432),f2(x62432)),f789(f112(x62432),x62431)))+P1(f789(f789(f241(a1),f2(a1)),x62431))
% 21.40/21.37 [6244]~P110(x62442)+~P1(f789(f789(f240(x62442),f2(x62442)),f789(f112(x62442),x62441)))+P1(f789(f789(f240(a1),f2(a1)),x62441))
% 21.40/21.37 [6248]~E(x62482,f2(a863))+P1(f789(f789(f287(a863),f789(a114,x62481)),x62482))+~P1(f789(f789(f287(a1),x62481),f789(f109(a1),x62482)))
% 21.40/21.37 [6249]E(f789(f248(a1,a1),f61(x62491,x62492)),f789(f789(f50(a1),x62491),x62492))+~P1(f789(f789(f241(a1),f2(a1)),x62491))+~P1(f789(f789(f240(a1),f2(a1)),x62492))
% 21.40/21.37 [6262]E(f789(f258(a1,a1),f61(x62621,x62622)),f59(a1,x62621,x62622))+~P1(f789(f789(f241(a1),f2(a1)),x62621))+~P1(f789(f789(f240(a1),f2(a1)),x62622))
% 21.40/21.37 [6280]~P76(x62801)+P1(f789(f789(f241(x62801),x62802),f2(x62801)))+~P1(f789(f789(f241(x62801),f2(x62801)),f789(f88(x62801),x62802)))
% 21.40/21.37 [6281]~P76(x62811)+P1(f789(f789(f240(x62811),x62812),f2(x62811)))+~P1(f789(f789(f240(x62811),f2(x62811)),f789(f88(x62811),x62812)))
% 21.40/21.37 [6307]P1(f789(f63(x63071,x63072),f64(x63071,x63072)))+~P1(f789(f789(f241(a1),x63071),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x63072))
% 21.40/21.37 [6323]~P1(f789(f789(f241(a863),f2(a863)),x63231))+~P1(f789(f789(f287(a863),x63232),x63231))+~P1(f789(f789(f241(a863),x63231),x63232))
% 21.40/21.37 [6324]~P1(f789(f789(f241(a1),f2(a1)),x63241))+~P1(f789(f789(f287(a1),x63242),x63241))+~P1(f789(f789(f241(a1),x63241),x63242))
% 21.40/21.37 [6336]P1(f789(f63(x63361,x63362),f61(x63361,x63362)))+~P1(f789(f789(f241(a1),f2(a1)),x63362))+~P1(f789(f789(f240(a1),f2(a1)),x63361))
% 21.40/21.37 [6378]~P76(x63781)+P1(f789(f789(f241(x63781),f789(f88(x63781),x63782)),f2(x63781)))+~P1(f789(f789(f241(x63781),f2(x63781)),x63782))
% 21.40/21.37 [6379]~P76(x63791)+P1(f789(f789(f240(x63791),f789(f88(x63791),x63792)),f2(x63791)))+~P1(f789(f789(f240(x63791),f2(x63791)),x63792))
% 21.40/21.37 [6401]E(f789(f789(f3(a863),f789(a114,x64011)),f789(a114,x64012)),f789(a114,f192(x64011,x64012)))+~P1(f789(f789(f240(a1),f2(a1)),x64012))+~P1(f789(f789(f240(a1),f2(a1)),x64011))
% 21.40/21.37 [6419]P1(f789(f789(f240(a1),f2(a1)),f192(x64191,x64192)))+~P1(f789(f789(f240(a1),f2(a1)),x64192))+~P1(f789(f789(f240(a1),f2(a1)),x64191))
% 21.40/21.37 [6457]~P1(f789(x64571,x64572))+P1(f789(x64571,f2(a863)))+P1(f789(x64571,f789(f789(f89(a863),f813(x64572,x64571)),f87(a863))))
% 21.40/21.37 [6463]E(f290(a863,f287(a863),x64631,x64632),f184(f870(a863,a856)))+P1(f789(f789(f287(a863),x64631),x64632))+~P1(f789(f789(f287(a863),x64632),x64631))
% 21.40/21.37 [6542]E(f789(f113(a863),x65421),f789(f113(a863),x65422))+~P1(f789(f789(f240(a1),f789(f113(a1),x65422)),f2(a1)))+~P1(f789(a190,f789(f113(a1),x65421)))
% 21.40/21.37 [6555]~E(x65551,f2(a863))+~E(f755(x65552,x65551),f2(a863))+E(f789(f138(a863,a863,f89(a863),x65551),x65552),f2(a863))
% 21.40/21.37 [6581]~P1(f789(f70(x65811),f678(x65812,x65811)))+~P1(f789(f70(f870(x65811,a856)),x65812))+P1(f789(f70(x65811),f51(f870(x65811,a856),x65812)))
% 21.40/21.37 [6587]E(x65871,x65872)+P1(f789(f789(f241(a1),x65871),x65872))+~P1(f789(f789(f241(a1),x65871),f789(f789(f89(a1),x65872),f87(a1))))
% 21.40/21.37 [6588]P1(f789(f789(f241(a863),f789(a114,x65881)),f789(a114,x65882)))+~P1(f789(f789(f241(a1),f2(a1)),x65882))+~P1(f789(f789(f241(a1),x65881),x65882))
% 21.40/21.37 [6589]P1(f789(f789(f241(a863),f789(a114,x65891)),f789(a114,x65892)))+~P1(f789(f789(f241(a1),f2(a1)),x65892))+~P1(f789(f789(f241(a1),x65891),x65892))
% 21.40/21.37 [6590]P1(f789(f789(f241(a863),f789(a114,x65901)),f789(a114,x65902)))+~P1(f789(f789(f240(a1),f2(a1)),x65901))+~P1(f789(f789(f241(a1),x65901),x65902))
% 21.40/21.37 [6591]P1(f789(f789(f240(a863),f789(a114,x65911)),f789(a114,x65912)))+~P1(f789(f789(f241(a1),f2(a1)),x65911))+~P1(f789(f789(f240(a1),x65911),x65912))
% 21.40/21.37 [6592]P1(f789(f789(f240(a863),f789(a114,x65921)),f789(a114,x65922)))+~P1(f789(f789(f240(a1),f2(a1)),x65922))+~P1(f789(f789(f240(a1),x65921),x65922))
% 21.40/21.37 [6602]E(f59(a863,f789(a114,x66021),f789(a114,x66022)),f789(a114,f59(a1,x66021,x66022)))+~P1(f789(f789(f240(a1),f2(a1)),x66022))+~P1(f789(f789(f240(a1),f2(a1)),x66021))
% 21.40/21.37 [6603]E(f59(a863,f789(a114,x66031),f789(a114,x66032)),f789(a114,f59(a1,x66031,x66032)))+~P1(f789(f789(f240(a1),f2(a1)),x66032))+~P1(f789(f789(f240(a1),f2(a1)),x66031))
% 21.40/21.37 [6623]~P76(x66231)+~P1(f789(f789(f241(x66231),f789(f88(x66231),x66232)),f2(x66231)))+P1(f789(f789(f241(x66231),f2(x66231)),x66232))
% 21.40/21.37 [6624]~P76(x66241)+~P1(f789(f789(f240(x66241),f789(f88(x66241),x66242)),f2(x66241)))+P1(f789(f789(f240(x66241),f2(x66241)),x66242))
% 21.40/21.37 [6641]~P1(f789(f789(f241(a1),a92),x66412))+~P1(f789(f789(f241(a1),x66411),x66412))+P1(f789(f789(f241(a863),f789(f113(a863),x66411)),f789(f113(a863),x66412)))
% 21.40/21.37 [6738]~P1(f789(f789(f240(a1),f2(a1)),x67381))+P1(f789(f789(f241(a863),f789(a114,x67381)),x67382))+~P1(f789(f789(f241(a1),x67381),f789(f109(a1),x67382)))
% 21.40/21.37 [6739]~P1(f789(f789(f240(a1),f2(a1)),x67391))+P1(f789(f789(f287(a863),f789(a114,x67391)),x67392))+~P1(f789(f789(f287(a1),x67391),f789(f109(a1),x67392)))
% 21.40/21.37 [6755]E(x67551,f2(a1))+E(f59(a1,x67552,x67551),f2(a1))+E(f789(f789(f3(a1),f789(f88(a1),f789(f789(f50(a1),x67552),x67551))),f87(a1)),f789(f789(f50(a1),x67552),f789(f88(a1),x67551)))
% 21.40/21.37 [6771]~P1(f789(f789(f240(a1),f2(a1)),x67711))+~P1(f789(f789(f241(a863),f789(a114,x67711)),x67712))+P1(f789(f789(f241(a1),x67711),f789(f109(a1),x67712)))
% 21.40/21.37 [6772]~P1(f789(f789(f240(a1),f2(a1)),x67721))+~P1(f789(f789(f287(a863),f789(a114,x67721)),x67722))+P1(f789(f789(f287(a1),x67721),f789(f109(a1),x67722)))
% 21.40/21.37 [6809]~P1(f789(f789(f241(a863),f789(a114,x68091)),f789(a114,x68092)))+~P1(f789(f789(f241(a1),f2(a1)),x68092))+P1(f789(f789(f241(a1),x68091),x68092))
% 21.40/21.37 [6810]~P1(f789(f789(f241(a863),f789(a114,x68101)),f789(a114,x68102)))+~P1(f789(f789(f240(a1),f2(a1)),x68101))+P1(f789(f789(f241(a1),x68101),x68102))
% 21.40/21.37 [6811]~P1(f789(f789(f240(a863),f789(a114,x68111)),f789(a114,x68112)))+~P1(f789(f789(f241(a1),f2(a1)),x68111))+P1(f789(f789(f240(a1),x68111),x68112))
% 21.40/21.37 [6812]~P1(f789(f789(f240(a863),f789(a114,x68121)),f789(a114,x68122)))+~P1(f789(f789(f240(a1),f2(a1)),x68122))+P1(f789(f789(f240(a1),x68121),x68122))
% 21.40/21.37 [6843]P1(f789(f789(f240(a1),x68431),x68432))+~P1(f789(f789(f240(a863),f789(f113(a863),x68431)),f789(f113(a863),x68432)))+P1(f789(f789(f240(a1),x68431),a92))
% 21.40/21.37 [6870]P1(f789(f789(f240(a1),f2(a1)),f59(a1,x68701,x68702)))+~P1(f789(f789(f240(a1),f2(a1)),x68702))+~P1(f789(f789(f240(a1),f2(a1)),x68701))
% 21.40/21.37 [6968]P1(f789(f789(f241(a1),a92),x69681))+~P1(f789(f789(f241(a1),x69682),x69681))+~P1(f789(f789(f241(a863),f789(f113(a863),x69682)),f789(f113(a863),x69681)))
% 21.40/21.37 [7016]E(f789(f789(f249(a1,a1),f789(f789(f50(a1),x70161),x70162)),f59(a1,x70161,x70162)),f64(x70161,x70162))+~P1(f789(f789(f241(a1),x70161),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x70162))
% 21.40/21.37 [7037]E(f789(f789(f249(a1,a1),f789(f789(f50(a1),x70371),x70372)),f59(a1,x70371,x70372)),f61(x70371,x70372))+~P1(f789(f789(f240(a1),f2(a1)),x70372))+~P1(f789(f789(f240(a1),f2(a1)),x70371))
% 21.40/21.37 [7061]~P91(x70612)+E(x70611,f122(x70612))+E(f789(f138(x70612,x70612,f90(x70612),f789(f137(x70612),x70611)),f147(x70612,x70611)),f789(f72(x70612,f90(x70612)),f789(f163(x70612),x70611)))
% 21.40/21.37 [7206]~E(x72061,f2(a863))+E(f789(f138(a863,a863,f89(a863),x72061),x72062),f2(a863))+P1(f789(f789(f342(a863),f755(x72062,x72061)),f789(f163(a863),x72062)))
% 21.40/21.37 [7260]~P1(f789(f789(f241(a1),x72602),f2(a1)))+P1(f789(f789(f241(a1),f789(f789(f50(a1),x72601),x72602)),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x72601))
% 21.40/21.37 [7261]~P1(f789(f789(f241(a1),x72611),f2(a1)))+P1(f789(f789(f241(a1),f789(f789(f50(a1),x72611),x72612)),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x72612))
% 21.40/21.37 [7262]~P1(f789(f789(f241(a1),x72621),f2(a1)))+P1(f789(f789(f241(a1),f789(f789(f50(a1),x72621),x72622)),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x72622))
% 21.40/21.37 [7263]~P1(f789(f789(f241(a1),x72632),f2(a1)))+P1(f789(f789(f240(a1),f789(f789(f50(a1),x72631),x72632)),f2(a1)))+~P1(f789(f789(f240(a1),f2(a1)),x72631))
% 21.40/21.37 [7264]~P1(f789(f789(f240(a1),x72641),f2(a1)))+P1(f789(f789(f240(a1),f789(f789(f50(a1),x72641),x72642)),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x72642))
% 21.40/21.37 [7273]P1(f789(f789(f342(f870(x72731,a856)),f678(x72732,x72731)),x72732))+~P1(f789(f70(f870(x72731,a856)),x72732))+P1(f789(f70(x72731),f51(f870(x72731,a856),x72732)))
% 21.40/21.37 [7378]P29(x73781,x73781,x73782,f247(f870(x73781,a856)))+~E(f789(f311(x73781,x73781,x73782),f247(f870(x73781,a856))),f247(f870(x73781,a856)))+~P1(f789(f70(x73781),f247(f870(x73781,a856))))
% 21.40/21.37 [7507]~P29(x75071,x75071,x75072,f247(f870(x75071,a856)))+E(f789(f311(x75071,x75071,x75072),f247(f870(x75071,a856))),f247(f870(x75071,a856)))+~P1(f789(f70(x75071),f247(f870(x75071,a856))))
% 21.40/21.37 [7530]E(f61(f789(f113(a1),x75301),f789(f113(a1),x75302)),f789(f789(f249(a1,a1),f2(a1)),f789(f113(a1),x75301)))+~P1(f789(f789(f241(a1),f2(a1)),f789(f113(a1),x75302)))+~P1(f789(f789(f241(a1),f789(f113(a1),x75301)),f789(f113(a1),x75302)))
% 21.40/21.37 [7648]E(f789(f789(f50(a1),x76481),x76482),f789(f113(a1),a106))+~P1(f789(f789(f240(a1),f789(f789(f89(a1),x76481),x76482)),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x76481))
% 21.40/21.37 [7706]~P1(f789(f789(f241(a1),x77062),f2(a1)))+~P1(f789(f789(f241(a1),f789(f789(f50(a1),x77061),x77062)),f2(a1)))+P1(f789(f789(f241(a1),f2(a1)),x77061))
% 21.40/21.37 [7710]E(f789(f789(f89(a1),x77101),x77102),f59(a1,x77101,x77102))+~P1(f789(f789(f240(a1),f789(f789(f89(a1),x77101),x77102)),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x77101))
% 21.40/21.37 [7712]P1(f789(f789(f241(a1),x77121),f2(a1)))+~P1(f789(f789(f241(a1),f789(f789(f50(a1),x77121),x77122)),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x77122))
% 21.40/21.37 [8404]~P101(x84041)+P18(x84041,x84042)+~P1(f789(f789(f240(x84041),f789(f789(f159(x84041),x84042),f776(x84042,x84041))),f789(f789(f159(x84041),x84042),f777(x84042,x84041))))
% 21.40/21.37 [5598]E(x55981,f2(a1))+~E(f59(a1,x55982,x55981),f2(a1))+E(f789(f789(f50(a1),x55982),f789(f88(a1),x55981)),f789(f88(a1),f789(f789(f50(a1),x55982),x55981)))
% 21.40/21.37 [5615]~P38(x56152)+~P38(x56151)+P38(f789(f789(f110(f870(a1,a856)),x56151),x56152))
% 21.40/21.37 [5616]~P38(x56162)+~P38(x56161)+P38(f789(f789(f111(f870(a1,a856)),x56161),x56162))
% 21.40/21.37 [5633]~P88(x56331)+~P60(x56331)+E(f789(f88(x56331),f789(f789(f291(x56331),f87(x56331)),x56332)),f789(f789(f291(x56331),f789(f113(x56331),a106)),x56332))
% 21.40/21.37 [5758]E(x57581,f2(a1))+~E(f59(a1,x57582,x57581),f2(a1))+E(f789(f789(f50(a1),f789(f88(a1),x57582)),x57581),f789(f88(a1),f789(f789(f50(a1),x57582),x57581)))
% 21.40/21.37 [5891]~P101(x58911)+P18(x58911,x58912)+P1(f789(f789(f241(a863),f777(x58912,x58911)),f789(f185(f864(x58911)),x58912)))
% 21.40/21.37 [6049]~P88(x60491)+~E(f789(f113(x60491),x60492),f2(x60491))+P33(x60491,f789(f113(x60491),f789(f789(f89(a1),x60492),f789(f88(a1),a92))))
% 21.40/21.37 [6050]~P88(x60501)+~E(f789(f113(x60501),x60502),f2(x60501))+P33(x60501,f789(f113(x60501),f789(f789(f89(a1),a92),f789(f88(a1),x60502))))
% 21.40/21.37 [6052]E(f789(a65,f61(f789(f88(a1),x60521),f789(f88(a1),x60522))),f60(x60521,x60522))+P1(f789(f789(f241(a1),f2(a1)),x60522))+P1(f789(f789(f240(a1),f2(a1)),x60521))
% 21.40/21.37 [6183]~E(x61832,f2(a863))+~E(x61831,f2(a863))+P1(f789(f789(f240(a1),f789(f109(a1),x61831)),f789(f88(a1),f789(f109(a1),x61832))))
% 21.40/21.37 [6209]E(f789(f789(f89(a863),f789(f113(a863),x62091)),f789(f113(a863),x62092)),f789(f113(a863),f789(f789(f89(a1),x62091),x62092)))+P1(f789(f789(f241(a1),x62091),a92))+P1(f789(f789(f241(a1),x62092),a92))
% 21.40/21.37 [6345]~P3(x63451)+~P1(f789(f789(f241(x63451),f2(x63451)),x63452))+P1(f789(f789(f241(x63451),f789(f88(x63451),x63452)),x63452))
% 21.40/21.37 [6346]~P3(x63461)+~P1(f789(f789(f240(x63461),f2(x63461)),x63462))+P1(f789(f789(f240(x63461),f789(f88(x63461),x63462)),x63462))
% 21.40/21.37 [6527]E(f789(f789(f3(a863),f789(a114,x65271)),f789(a114,x65272)),f789(a114,f789(f789(f3(a1),x65271),x65272)))+~P1(f789(f789(f240(a1),f2(a1)),x65272))+~P1(f789(f789(f240(a1),x65272),x65271))
% 21.40/21.37 [6564]E(f789(a114,f59(a1,f789(f113(a1),x65641),f789(f113(a1),x65642))),f59(a863,f789(f113(a863),x65641),f789(f113(a863),x65642)))+P1(f789(a190,f789(f113(a1),x65641)))+P1(f789(a190,f789(f113(a1),x65642)))
% 21.40/21.37 [6582]~P3(x65821)+P1(f789(f789(f241(x65821),f2(x65821)),x65822))+~P1(f789(f789(f241(x65821),f789(f88(x65821),x65822)),x65822))
% 21.40/21.37 [6583]~P3(x65831)+P1(f789(f789(f240(x65831),f2(x65831)),x65832))+~P1(f789(f789(f240(x65831),f789(f88(x65831),x65832)),x65832))
% 21.40/21.37 [6594]~P3(x65941)+~P1(f789(f789(f241(x65941),f2(x65941)),x65942))+P1(f789(f789(f241(x65941),f2(x65941)),f789(f789(f89(x65941),x65942),x65942)))
% 21.40/21.37 [6596]~P3(x65961)+~P1(f789(f789(f240(x65961),f2(x65961)),x65962))+P1(f789(f789(f240(x65961),f2(x65961)),f789(f789(f89(x65961),x65962),x65962)))
% 21.40/21.37 [6606]E(f789(f789(f89(a863),f789(a114,x66061)),f789(a114,x66062)),f789(a114,f789(f789(f89(a1),x66061),x66062)))+~P1(f789(f789(f240(a1),f2(a1)),x66062))+~P1(f789(f789(f240(a1),f2(a1)),x66061))
% 21.40/21.37 [6607]E(f789(f789(f89(a863),f789(a114,x66071)),f789(a114,x66072)),f789(a114,f789(f789(f89(a1),x66071),x66072)))+~P1(f789(f789(f240(a1),f2(a1)),x66072))+~P1(f789(f789(f240(a1),f2(a1)),x66071))
% 21.40/21.37 [6608]E(f789(f789(f90(a863),f789(a114,x66081)),f789(a114,x66082)),f789(a114,f789(f789(f90(a1),x66081),x66082)))+~P1(f789(f789(f240(a1),f2(a1)),x66082))+~P1(f789(f789(f240(a1),f2(a1)),x66081))
% 21.40/21.37 [6609]E(f789(f789(f50(a863),f789(a114,x66091)),f789(a114,x66092)),f789(a114,f789(f789(f50(a1),x66091),x66092)))+~P1(f789(f789(f240(a1),f2(a1)),x66092))+~P1(f789(f789(f240(a1),f2(a1)),x66091))
% 21.40/21.37 [6619]E(x66191,f2(a863))+P1(f789(f789(f241(a863),f2(a863)),x66192))+~P1(f789(f789(f241(a863),f2(a863)),f789(f789(f250(a863),x66192),x66191)))
% 21.40/21.37 [6652]~P88(x66521)+E(f789(f113(x66521),x66522),f2(x66521))+~P33(x66521,f789(f113(x66521),f789(f789(f89(a1),a92),f789(f88(a1),x66522))))
% 21.40/21.37 [6653]~P88(x66531)+E(f789(f113(x66531),x66532),f2(x66531))+~P33(x66531,f789(f113(x66531),f789(f789(f89(a1),x66532),f789(f88(a1),a92))))
% 21.40/21.37 [6715]~P1(f789(f70(x67151),x67152))+~P1(f789(f70(x67151),f247(f870(x67151,a856))))+P1(f789(f70(x67151),f789(f88(f870(x67151,a856)),x67152)))
% 21.40/21.37 [6740]~P1(f789(f789(f241(a1),f2(a1)),x67402))+~P1(f789(f789(f240(a1),x67402),x67401))+P1(f789(f789(f241(a1),f2(a1)),f789(f789(f50(a1),x67401),x67402)))
% 21.40/21.37 [6741]~P1(f789(f789(f241(a1),x67412),f2(a1)))+~P1(f789(f789(f240(a1),x67411),f2(a1)))+P1(f789(f789(f240(a1),f2(a1)),f789(f789(f50(a1),x67411),x67412)))
% 21.40/21.37 [6782]~P1(f789(f789(f241(a863),f2(a863)),x67822))+~P1(f789(f789(f241(a863),f2(a863)),x67821))+P1(f789(f789(f241(a863),f2(a863)),f789(f789(f90(a863),x67821),x67822)))
% 21.40/21.37 [6783]~P1(f789(f789(f240(a1),f2(a1)),x67832))+~P1(f789(f789(f240(a1),f2(a1)),x67831))+P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),x67831),x67832)))
% 21.40/21.37 [6784]~P1(f789(f789(f240(a1),f2(a1)),x67842))+~P1(f789(f789(f240(a1),f2(a1)),x67841))+P1(f789(f789(f240(a1),f2(a1)),f789(f789(f90(a1),x67841),x67842)))
% 21.40/21.37 [6785]~P1(f789(f789(f241(a1),f2(a1)),x67852))+~P1(f789(f789(f240(a1),f2(a1)),x67851))+P1(f789(f789(f240(a1),f2(a1)),f789(f789(f50(a1),x67851),x67852)))
% 21.40/21.37 [6786]~P1(f789(f789(f240(a1),f2(a1)),x67862))+~P1(f789(f789(f240(a1),f2(a1)),x67861))+P1(f789(f789(f240(a1),f2(a1)),f789(f789(f50(a1),x67861),x67862)))
% 21.40/21.37 [6855]E(x68551,f2(a1))+E(f59(a1,x68552,x68551),f2(a1))+E(f789(f789(f3(a1),f789(f88(a1),f789(f789(f50(a1),x68552),x68551))),f87(a1)),f789(f789(f50(a1),f789(f88(a1),x68552)),x68551))
% 21.40/21.37 [6915]P1(f789(f789(f241(a863),f2(a863)),x69151))+P1(f789(f789(f241(a863),f2(a863)),x69152))+~P1(f789(f789(f241(a863),f2(a863)),f789(f789(f89(a863),x69152),x69151)))
% 21.40/21.37 [6916]~P3(x69161)+P1(f789(f789(f241(x69161),f2(x69161)),x69162))+~P1(f789(f789(f241(x69161),f2(x69161)),f789(f789(f89(x69161),x69162),x69162)))
% 21.40/21.37 [6917]~P3(x69171)+P1(f789(f789(f240(x69171),f2(x69171)),x69172))+~P1(f789(f789(f240(x69171),f2(x69171)),f789(f789(f89(x69171),x69172),x69172)))
% 21.40/21.37 [6969]~P1(f789(f70(x69691),x69692))+P1(f789(f70(x69691),f247(f870(x69691,a856))))+~P1(f789(f70(x69691),f789(f88(f870(x69691,a856)),x69692)))
% 21.40/21.37 [7029]P1(f789(f789(f240(a1),x70291),f2(a1)))+~P1(f789(f789(f241(a1),x70292),f2(a1)))+~P1(f789(f789(f240(a1),f2(a1)),f789(f789(f50(a1),x70291),x70292)))
% 21.40/21.37 [7035]~P1(f789(f789(f241(a1),f2(a1)),x70351))+P1(f789(f789(f240(a1),x70351),x70352))+~P1(f789(f789(f241(a1),f2(a1)),f789(f789(f50(a1),x70352),x70351)))
% 21.40/21.37 [7036]~P1(f789(f789(f240(a1),f2(a1)),x70362))+P1(f789(f789(f240(a1),x70361),x70362))+~P1(f789(f789(f241(a1),f2(a1)),f789(f789(f50(a1),x70362),x70361)))
% 21.40/21.37 [7069]P1(f789(f789(f241(a1),f2(a1)),x70691))+~P1(f789(f789(f240(a1),f2(a1)),x70692))+~P1(f789(f789(f241(a1),f2(a1)),f789(f789(f50(a1),x70692),x70691)))
% 21.40/21.37 [7070]P1(f789(f789(f240(a1),f2(a1)),x70701))+~P1(f789(f789(f241(a1),f2(a1)),x70702))+~P1(f789(f789(f240(a1),f2(a1)),f789(f789(f50(a1),x70701),x70702)))
% 21.40/21.37 [7169]E(f218(x71691,x71692),x71691)+~E(x71692,f2(a863))+~P1(f789(f329(f869(a863,a863),a221),f789(f789(f249(a863,a863),x71691),x71692)))
% 21.40/21.37 [7398]E(f167(x73981,x73982),f122(a1))+P1(f789(f789(f240(a1),x73981),x73982))+~P1(f789(f329(f869(a1,a1),a172),f789(f789(f249(a1,a1),x73981),x73982)))
% 21.40/21.37 [7423]E(f789(f789(f249(a1,a1),f789(f113(a1),a106)),f789(f789(f89(a1),x74231),x74232)),f64(x74231,x74232))+~P1(f789(f789(f241(a1),f2(a1)),x74232))+~P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),x74231),x74232)))
% 21.40/21.37 [7450]E(x74501,f2(a863))+E(f218(x74501,f59(a863,x74502,x74501)),f218(x74502,x74501))+~P1(f789(f329(f869(a863,a863),a221),f789(f789(f249(a863,a863),x74502),x74501)))
% 21.40/21.37 [7538]~P1(f789(f70(x75382),f247(f870(x75382,a856))))+~P1(f789(f70(x75381),f247(f870(x75381,a856))))+P1(f789(f70(f871(x75381,x75382)),f247(f870(f871(x75381,x75382),a856))))
% 21.40/21.37 [7539]~P1(f789(f70(x75392),f247(f870(x75392,a856))))+~P1(f789(f70(x75391),f247(f870(x75391,a856))))+P1(f789(f70(f869(x75391,x75392)),f247(f870(f869(x75391,x75392),a856))))
% 21.40/21.37 [7611]~P1(f789(f789(f241(a863),f789(a121,f2(a863))),x76111))+~P1(f789(f789(f241(a863),f789(a121,f2(a863))),x76112))+P1(f789(f789(f241(a863),x76111),f789(f789(f90(a863),x76112),x76111)))
% 21.40/21.37 [7612]~P1(f789(f789(f241(a863),f789(a121,f2(a863))),x76121))+~P1(f789(f789(f241(a863),f789(a121,f2(a863))),x76122))+P1(f789(f789(f241(a863),x76121),f789(f789(f90(a863),x76121),x76122)))
% 21.40/21.37 [7647]E(f789(f49(x76471),f247(f870(x76471,a856))),f789(a121,f2(a863)))+P1(f789(f70(x76472),f247(f870(x76472,a856))))+~P1(f789(f70(f870(x76472,x76471)),f247(f870(f870(x76472,x76471),a856))))
% 21.40/21.37 [7699]E(f61(x76991,x76992),f789(f789(f249(a1,a1),f2(a1)),x76991))+~P1(f789(f789(f241(a1),x76991),x76992))+~P1(f789(f329(f869(a1,a1),a69),f789(f789(f249(a1,a1),x76991),x76992)))
% 21.40/21.37 [7703]E(f217(f789(f88(a1),x77031),f789(f88(a1),x77032)),f217(x77031,x77032))+~P1(f789(f789(f241(a1),x77032),f2(a1)))+~P1(f789(f329(f869(a1,a1),a223),f789(f789(f249(a1,a1),x77031),x77032)))
% 21.40/21.37 [7719]E(f61(x77191,x77192),f789(f789(f249(a1,a1),f2(a1)),x77191))+~P1(f789(f789(f240(a1),x77192),f2(a1)))+~P1(f789(f329(f869(a1,a1),a69),f789(f789(f249(a1,a1),x77191),x77192)))
% 21.40/21.37 [7771]~P1(f789(f789(f241(a863),f789(a121,f2(a863))),x77712))+~P1(f789(f789(f241(a863),f789(a121,f2(a863))),x77711))+P1(f789(f789(f241(a863),f789(a121,f2(a863))),f789(f789(f90(a863),x77711),x77712)))
% 21.40/21.37 [7772]~P1(f789(f789(f240(a863),f789(a121,f2(a863))),x77721))+~P1(f789(f789(f240(a863),f789(a121,f2(a863))),x77722))+P1(f789(f789(f240(a863),f789(a121,f2(a863))),f789(f789(f90(a863),x77721),x77722)))
% 21.40/21.37 [7934]E(f789(f789(f249(a1,a1),f789(f113(a1),a106)),f789(f789(f89(a1),x79341),x79342)),f64(x79341,x79342))+~P1(f789(f789(f240(a1),x79342),f2(a1)))+~P1(f789(f329(f869(a1,a1),a66),f789(f789(f249(a1,a1),x79341),x79342)))
% 21.40/21.37 [7973]E(f789(f789(f146(a1),x79731),f167(f789(f789(f89(a1),x79731),f87(a1)),x79732)),f167(x79731,x79732))+~P1(f789(f789(f240(a1),x79731),x79732))+~P1(f789(f329(f869(a1,a1),a172),f789(f789(f249(a1,a1),x79731),x79732)))
% 21.40/21.37 [8244]E(f789(f789(f249(a1,a1),f789(f113(a1),a106)),f789(f789(f89(a1),x82441),x82442)),f64(x82441,x82442))+~P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),x82441),x82442)))+~P1(f789(f329(f869(a1,a1),a66),f789(f789(f249(a1,a1),x82441),x82442)))
% 21.40/21.37 [8527]E(f789(f789(f249(a1,a1),f789(f113(a1),a106)),f789(f789(f89(a1),f789(f113(a1),x85271)),f789(f113(a1),x85272))),f64(f789(f113(a1),x85271),f789(f113(a1),x85272)))+~P1(f789(f789(f241(a1),f2(a1)),f789(f113(a1),x85272)))+~P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),f789(f113(a1),x85271)),f789(f113(a1),x85272))))
% 21.40/21.37 [8548]~P38(x85482)+~P38(x85481)+E(f789(f311(a863,a1,f109(a1)),f789(f789(f110(f870(a863,a856)),f789(f311(a1,a863,a114),x85481)),f789(f311(a1,a863,a114),x85482))),f789(f789(f110(f870(a1,a856)),x85481),x85482))
% 21.40/21.37 [8549]~P38(x85492)+~P38(x85491)+E(f789(f311(a863,a1,f109(a1)),f789(f789(f111(f870(a863,a856)),f789(f311(a1,a863,a114),x85491)),f789(f311(a1,a863,a114),x85492))),f789(f789(f111(f870(a1,a856)),x85491),x85492))
% 21.40/21.37 [9141]~P88(x91411)+~E(f789(f113(x91411),x91412),f87(x91411))+P33(x91411,f789(f113(x91411),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f88(a1),x91412))))
% 21.40/21.37 [9355]~P88(x93551)+E(f789(f113(x93551),x93552),f87(x93551))+~P33(x93551,f789(f113(x93551),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f88(a1),x93552))))
% 21.40/21.37 [9778]~P99(x97782)+P52(a863,x97782,f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x97781)+P1(f789(f789(f287(a863),f621(x97781,x97782)),f622(x97781,x97782)))
% 21.40/21.37 [9781]~P99(x97811)+P52(a863,x97811,f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x97812)+~P1(f789(f789(f287(a863),f622(x97812,x97811)),f621(x97812,x97811)))
% 21.40/21.37 [9782]~P99(x97821)+P52(a863,x97821,f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x97822)+~P1(f789(f789(f241(x97821),f789(x97822,f621(x97822,x97821))),f789(x97822,f622(x97822,x97821))))
% 21.40/21.37 [9874]~P99(x98741)+P50(a863,x98741,f287(a863),x98742)+~P52(a863,x98741,f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x98742)
% 21.40/21.37 [10077]E(x100771,f2(a1))+E(x100772,f2(a1))+E(f789(f260(a1,a1,a1,a1,f41(a1),f789(f90(a1),f91(a1,x100772))),f789(f789(f789(f105(f869(a1,a1)),f789(f789(a338,f91(a1,x100771)),f91(a1,x100772))),f67(x100771,x100772)),f789(f789(f259(a1,a1,f869(a1,a1)),f789(f789(f20(a1,f870(a1,f869(a1,a1)),f870(a1,f869(a1,a1))),f789(f789(f10(f870(a1,f870(f869(a1,a1),f869(a1,a1))),f870(f870(a1,f869(a1,a1)),f870(a1,f869(a1,a1))),a1),f20(a1,f869(a1,a1),f869(a1,a1))),f789(f789(f10(f869(a1,a1),f870(a1,f870(f869(a1,a1),f869(a1,a1))),a1),f789(f9(a1,f869(a1,a1),f870(f869(a1,a1),f869(a1,a1))),f789(f789(f10(a856,f870(f869(a1,a1),f870(f869(a1,a1),f869(a1,a1))),a1),f105(f869(a1,a1))),f789(f789(f9(a1,a1,a856),a338),f2(a1))))),f789(f789(f9(a1,a1,f869(a1,a1)),f789(f789(f10(a1,f870(a1,f869(a1,a1)),a1),f249(a1,a1)),f88(a1))),f2(a1))))),f789(f789(f9(a1,f870(a1,a1),f870(a1,f869(a1,a1))),f789(f789(f10(f870(a1,f869(a1,a1)),f870(f870(a1,a1),f870(a1,f869(a1,a1))),a1),f10(a1,f869(a1,a1),a1)),f789(f789(f10(a1,f870(a1,f869(a1,a1)),a1),f249(a1,a1)),f789(f789(f9(a1,a1,a1),f789(f789(f10(a1,f870(a1,a1),a1),f3(a1)),f88(a1))),f87(a1))))),f789(f3(a1),f789(f84(a1),x100772))))),f67(x100771,x100772)))),f60(x100771,x100772))
% 21.40/21.37 [10078]E(x100781,f2(a1))+E(x100782,f2(a1))+E(f789(f260(a1,a1,a1,a1,f41(a1),f789(f90(a1),f91(a1,x100782))),f789(f789(f789(f105(f869(a1,a1)),f789(f789(a340,f789(f789(a339,f789(f789(f241(a1),f2(a1)),x100782)),f789(f789(f240(a1),f2(a1)),x100781))),f789(f789(a339,f789(f789(f241(a1),x100782),f2(a1))),f789(f789(f241(a1),x100781),f2(a1))))),f67(x100781,x100782)),f789(f789(f259(a1,a1,f869(a1,a1)),f789(f789(f20(a1,f870(a1,f869(a1,a1)),f870(a1,f869(a1,a1))),f789(f789(f10(f870(a1,f870(f869(a1,a1),f869(a1,a1))),f870(f870(a1,f869(a1,a1)),f870(a1,f869(a1,a1))),a1),f20(a1,f869(a1,a1),f869(a1,a1))),f789(f789(f10(f869(a1,a1),f870(a1,f870(f869(a1,a1),f869(a1,a1))),a1),f789(f9(a1,f869(a1,a1),f870(f869(a1,a1),f869(a1,a1))),f789(f789(f10(a856,f870(f869(a1,a1),f870(f869(a1,a1),f869(a1,a1))),a1),f105(f869(a1,a1))),f789(f789(f9(a1,a1,a856),a338),f2(a1))))),f789(f789(f9(a1,a1,f869(a1,a1)),f789(f789(f10(a1,f870(a1,f869(a1,a1)),a1),f249(a1,a1)),f88(a1))),f2(a1))))),f789(f789(f9(a1,f870(a1,a1),f870(a1,f869(a1,a1))),f789(f789(f10(f870(a1,f869(a1,a1)),f870(f870(a1,a1),f870(a1,f869(a1,a1))),a1),f10(a1,f869(a1,a1),a1)),f789(f789(f10(a1,f870(a1,f869(a1,a1)),a1),f249(a1,a1)),f789(f789(f9(a1,a1,a1),f789(f789(f10(a1,f870(a1,a1),a1),f3(a1)),f88(a1))),f87(a1))))),f789(f3(a1),f789(f84(a1),x100782))))),f67(x100781,x100782)))),f60(x100781,x100782))
% 21.40/21.37 [5623]~P110(x56231)+~P88(x56231)+E(f789(f84(x56231),f789(f789(f250(x56231),f789(f113(x56231),a106)),x56232)),f87(x56231))
% 21.40/21.37 [6123]~P120(x61231)+~P1(f789(f789(f241(a1),x61232),f2(a1)))+E(f789(f88(x61231),f789(f109(x61231),f789(a114,f789(f88(a1),x61232)))),f789(f112(x61231),x61232))
% 21.40/21.37 [6329]P1(f789(f789(f240(a108),x63291),f87(a108)))+E(f789(f789(f89(a108),f87(a108)),f275(x63291,f789(f789(f50(a108),x63292),x63291))),f275(x63291,x63292))+P1(f789(f789(f241(a108),x63292),x63291))
% 21.40/21.37 [6402]E(x64021,f2(a1))+~E(f789(f84(a1),x64022),f87(a1))+P1(f789(f789(f287(a1),f789(f789(f90(a1),x64021),x64022)),x64021))
% 21.40/21.37 [6824]~E(x68242,f87(a863))+~P1(f789(f789(f241(a863),f2(a863)),x68241))+P1(f789(f789(f287(a863),f789(f789(f90(a863),x68241),x68242)),x68241))
% 21.40/21.37 [6825]~E(x68251,f87(a863))+~P1(f789(f789(f241(a863),f2(a863)),x68252))+P1(f789(f789(f287(a863),f789(f789(f90(a863),x68251),x68252)),x68252))
% 21.40/21.37 [6957]~P87(x69571)+~P1(f789(f789(f342(x69571),x69572),f119(x69571)))+~E(f789(f789(f89(x69571),f789(f789(f89(x69571),f87(x69571)),x69572)),x69572),f2(x69571))
% 21.40/21.37 [7071]~P1(f789(f789(f241(a1),x70711),f2(a1)))+~P1(f789(f789(f240(a1),x70712),f2(a1)))+E(f789(f248(a1,a1),f789(a65,f61(f789(f88(a1),x70711),f789(f88(a1),x70712)))),f789(f789(f50(a1),x70711),x70712))
% 21.40/21.37 [7087]~P1(f789(f789(f241(a1),x70871),f2(a1)))+~P1(f789(f789(f240(a1),x70872),f2(a1)))+E(f789(f258(a1,a1),f789(a65,f61(f789(f88(a1),x70871),f789(f88(a1),x70872)))),f59(a1,x70871,x70872))
% 21.40/21.37 [7094]~P1(f789(f789(f241(a1),x70942),f2(a1)))+E(f789(f248(a1,a1),f789(a65,f64(f789(f88(a1),x70941),f789(f88(a1),x70942)))),f789(f789(f50(a1),x70941),x70942))+~P1(f789(f789(f241(a1),f2(a1)),x70941))
% 21.40/21.37 [7098]E(x70981,f2(a1))+E(f789(f84(a1),x70982),f87(a1))+~P1(f789(f789(f287(a1),f789(f789(f90(a1),x70981),x70982)),x70981))
% 21.40/21.37 [7113]~P1(f789(f789(f241(a1),x71132),f2(a1)))+E(f789(f258(a1,a1),f789(a65,f64(f789(f88(a1),x71131),f789(f88(a1),x71132)))),f59(a1,x71131,x71132))+~P1(f789(f789(f241(a1),f2(a1)),x71131))
% 21.40/21.37 [7164]E(f789(f789(f50(a1),f789(f789(f250(a1),x71641),x71642)),x71641),f789(f789(f250(a1),x71641),f789(f789(f3(a863),x71642),f789(a121,f2(a863)))))+~P1(f789(f789(f241(a863),f2(a863)),x71642))+~P1(f789(f789(f241(a1),f2(a1)),x71641))
% 21.40/21.37 [7269]~P1(f789(f789(f241(a863),f2(a863)),x72691))+~P1(f789(f789(f241(a863),f87(a863)),x72692))+P1(f789(f789(f241(a863),f789(f789(f50(a863),x72691),x72692)),x72691))
% 21.40/21.37 [7270]~P1(f789(f789(f241(a863),f2(a863)),x72701))+~P1(f789(f789(f241(a863),f2(a863)),x72702))+P1(f789(f789(f241(a863),f789(f789(f3(a863),x72701),x72702)),x72701))
% 21.40/21.37 [7271]~P1(f789(f789(f241(a1),f2(a1)),x72711))+~P1(f789(f789(f241(a1),f87(a1)),x72712))+P1(f789(f789(f241(a1),f789(f789(f50(a1),x72711),x72712)),x72711))
% 21.40/21.37 [7430]E(x74301,f2(a863))+~E(x74302,f2(a1))+~P1(f789(f789(f241(a1),f2(a1)),f789(f789(f250(a1),f789(f84(a1),x74302)),x74301)))
% 21.40/21.37 [7468]E(x74681,f87(a863))+~P1(f789(f789(f241(a863),f2(a863)),x74682))+~P1(f789(f789(f287(a863),f789(f789(f90(a863),x74682),x74681)),x74682))
% 21.40/21.37 [7469]E(x74691,f87(a863))+~P1(f789(f789(f241(a863),f2(a863)),x74692))+~P1(f789(f789(f287(a863),f789(f789(f90(a863),x74691),x74692)),x74692))
% 21.40/21.37 [7854]~E(x78542,f122(f864(x78541)))+E(f789(f185(f864(f864(x78541))),f168(x78541,x78542)),f2(a863))+~P18(a863,f789(f149(a863),f789(f789(f150(f864(x78541),a863),f185(f864(x78541))),x78542)))
% 21.40/21.37 [8102]P1(f789(x81021,x81022))+~P1(f789(x81021,f789(a117,f584(x81021,x81022))))+~P1(f789(f789(f342(f870(f869(a863,a863),a856)),x81022),a107))
% 21.40/21.37 [8116]E(x81161,f122(f864(x81162)))+E(f789(f185(f864(x81162)),f789(f789(f159(f864(x81162)),x81161),f2(a863))),f789(f185(f864(f864(x81162))),f168(x81162,x81161)))+~P18(a863,f789(f149(a863),f789(f789(f150(f864(x81162),a863),f185(f864(x81162))),x81161)))
% 21.40/21.37 [8788]~P1(f789(f70(x87881),f789(f264(x87881),x87882)))+~P1(f789(f70(x87881),f247(f870(x87881,a856))))+P1(f789(f70(x87881),f789(f264(x87881),f789(f789(f10(a856,a856,x87881),a336),x87882))))
% 21.40/21.37 [8841]E(f789(f789(f249(a863,a863),f789(a121,f789(f789(f50(a863),f789(f789(f3(a863),x88411),x88412)),x88412))),f59(a863,f789(f789(f3(a863),x88411),x88412),x88412)),f94(f869(a863,a863),f62(x88411,x88412)))+~P1(f789(f789(f241(a863),f2(a863)),x88412))+~P1(f789(f789(f240(a863),x88412),x88411))
% 21.40/21.37 [9109]~P1(f789(f70(x91091),f789(f264(x91091),x91092)))+P1(f789(f70(x91091),f247(f870(x91091,a856))))+~P1(f789(f70(x91091),f789(f264(x91091),f789(f789(f10(a856,a856,x91091),a336),x91092))))
% 21.40/21.37 [9775]P30(x97751,x97752)+~P36(x97751,f789(f248(f870(f869(x97751,x97751),a856),f870(f869(x97751,x97751),a856)),x97752))+~P1(f789(f789(f240(f870(f869(x97751,x97751),a856)),f789(f789(f289(x97751,x97751,x97751),f789(f248(f870(f869(x97751,x97751),a856),f870(f869(x97751,x97751),a856)),x97752)),f789(f258(f870(f869(x97751,x97751),a856),f870(f869(x97751,x97751),a856)),x97752))),f789(f248(f870(f869(x97751,x97751),a856),f870(f869(x97751,x97751),a856)),x97752)))
% 21.40/21.37 [9822]E(f789(f57(f789(f113(a1),x98221)),f61(f789(f113(a1),x98222),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f113(a1),x98221)))),f61(f789(f113(a1),x98222),f789(f113(a1),x98221)))+~P1(f789(f789(f241(a1),f2(a1)),f789(f113(a1),x98221)))+P1(f789(f789(f241(a1),f789(f113(a1),x98222)),f789(f113(a1),x98221)))
% 21.40/21.37 [9828]E(f789(f57(f789(f113(a1),x98281)),f64(f789(f113(a1),x98282),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f113(a1),x98281)))),f64(f789(f113(a1),x98282),f789(f113(a1),x98281)))+~P1(f789(f789(f241(a1),f2(a1)),f789(f113(a1),x98281)))+P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),f789(f113(a1),x98282)),f789(f113(a1),x98281))))
% 21.40/21.37 [9876]~E(f300(a863,f287(a863),f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x98762,x98761),f184(f870(a863,a856)))+~P1(f789(f789(f287(a863),x98762),x98761))+P1(f789(f789(f287(a863),x98761),x98762))
% 21.40/21.37 [9877]~E(f297(a863,f287(a863),f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x98772,x98771),f184(f870(a863,a856)))+~P1(f789(f789(f287(a863),x98772),x98771))+P1(f789(f789(f287(a863),x98771),x98772))
% 21.40/21.37 [9878]~E(f300(a863,f287(a863),f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x98782,x98781),f184(f870(a863,a856)))+~P1(f789(f789(f287(a863),x98782),x98781))+P1(f789(f789(f287(a863),x98781),x98782))
% 21.40/21.37 [9879]~E(f297(a863,f287(a863),f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x98792,x98791),f184(f870(a863,a856)))+~P1(f789(f789(f287(a863),x98792),x98791))+P1(f789(f789(f287(a863),x98791),x98792))
% 21.40/21.37 [7187]~P1(f789(f789(f241(a863),f2(a863)),x71872))+P1(f789(f789(f241(a863),x71871),x71872))+E(f789(a121,f789(f789(f50(a863),f789(f789(f3(a863),x71871),x71872)),x71872)),f789(f789(f50(a863),x71871),x71872))
% 21.40/21.37 [7188]~P1(f789(f789(f241(a863),f2(a863)),x71882))+P1(f789(f789(f241(a863),x71881),x71882))+E(f789(a121,f789(f789(f50(a863),f789(f789(f3(a863),x71881),x71882)),x71882)),f789(f789(f50(a863),x71881),x71882))
% 21.40/21.37 [7345]~P1(f789(f789(f241(a863),f2(a863)),x73452))+~P1(f789(f789(f240(a863),x73452),x73451))+E(f789(a121,f789(f789(f50(a863),f789(f789(f3(a863),x73451),x73452)),x73452)),f789(f789(f50(a863),x73451),x73452))
% 21.40/21.37 [8315]~P88(x83151)+~P87(x83151)+~P33(x83151,f789(f113(x83151),f789(f789(f3(a1),f789(f789(f89(a1),x83152),x83152)),a106)))
% 21.40/21.37 [9016]E(x90161,f2(a863))+E(f789(f789(f259(a863,a863,f869(a863,a863)),f789(f789(f10(a863,f870(a863,f869(a863,a863)),a863),f249(a863,a863)),a121)),f94(f869(a863,a863),f62(f789(f789(f3(a863),x90162),x90161),x90161))),f94(f869(a863,a863),f62(x90162,x90161)))+P1(f789(f789(f241(a863),x90162),x90161))
% 21.40/21.37 [9413]P1(f789(x94132,f709(x94132,x94131)))+P1(f789(x94131,f709(x94132,x94131)))+E(f789(f264(a1),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f240(a1),f2(a1)))),x94131)),f789(f264(a1),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f240(a1),f2(a1)))),x94132)))
% 21.40/21.37 [9417]~P1(f789(x94172,f709(x94172,x94171)))+~P1(f789(x94171,f709(x94172,x94171)))+E(f789(f264(a1),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f240(a1),f2(a1)))),x94171)),f789(f264(a1),f789(f789(f20(a1,a856,a856),f789(f789(f10(a856,f870(a856,a856),a1),a339),f789(f240(a1),f2(a1)))),x94172)))
% 21.40/21.37 [9962]~P1(f789(f789(f287(a863),x99622),x99621))+P1(f789(f789(f287(a863),x99621),x99622))+P1(f789(f789(f342(a863),x99621),f295(a863,f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x99622)))
% 21.40/21.37 [9963]~P1(f789(f789(f287(a863),x99632),x99631))+P1(f789(f789(f287(a863),x99631),x99632))+P1(f789(f789(f342(a863),x99632),f298(a863,f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x99631)))
% 21.40/21.37 [7567]~P88(x75671)+~P61(x75671)+E(f789(f789(f291(x75671),x75672),f789(f113(x75671),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),x75672)
% 21.40/21.37 [7568]~P88(x75681)+~P61(x75681)+E(f789(f789(f291(x75681),x75682),f789(f113(x75681),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))),x75682)
% 21.40/21.37 [9140]~P88(x91401)+~E(f789(f113(x91401),x91402),f87(x91401))+P33(x91401,f789(f113(x91401),f789(f789(f89(a1),x91402),f789(f88(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))
% 21.40/21.37 [9292]~P134(x92921)+~E(x92922,f2(x92921))+E(f789(f789(f250(x92921),x92922),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f2(x92921))
% 21.40/21.37 [9293]~P134(x92931)+~E(x92932,f87(x92931))+E(f789(f789(f250(x92931),x92932),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f87(x92931))
% 21.40/21.37 [9307]~P134(x93071)+~E(x93072,f789(f88(x93071),f87(x93071)))+E(f789(f789(f250(x93071),x93072),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f87(x93071))
% 21.40/21.37 [9327]~P78(x93271)+~P89(x93271)+E(f789(f789(f250(x93271),f789(f113(x93271),x93272)),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f789(f90(x93271),f789(f113(x93271),x93272)),f789(f113(x93271),x93272)))
% 21.40/21.37 [9356]~P88(x93561)+E(f789(f113(x93561),x93562),f87(x93561))+~P33(x93561,f789(f113(x93561),f789(f789(f89(a1),x93562),f789(f88(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))
% 21.40/21.37 [9466]~P134(x94662)+E(x94661,f2(x94662))+~E(f789(f789(f250(x94662),x94661),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f2(x94662))
% 21.40/21.37 [9716]~P110(x97162)+E(x97161,f2(x97162))+P1(f789(f789(f241(x97162),f2(x97162)),f789(f789(f250(x97162),x97161),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))
% 21.40/21.37 [9774]~P110(x97742)+~E(x97741,f2(x97742))+~P1(f789(f789(f241(x97742),f2(x97742)),f789(f789(f250(x97742),x97741),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))
% 21.40/21.37 [9813]P1(f789(f789(f240(a1),x98131),f2(a1)))+P1(f789(f789(f241(a1),x98132),x98131))+E(f789(f57(x98131),f61(x98132,f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x98131))),f61(x98132,x98131))
% 21.40/21.37 [9814]~P1(f789(f789(f241(a1),f2(a1)),x98141))+P1(f789(f789(f241(a1),x98142),x98141))+E(f789(f57(x98141),f61(x98142,f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x98141))),f61(x98142,x98141))
% 21.40/21.37 [9815]P1(f789(f789(f240(a1),x98151),f2(a1)))+P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),x98152),x98151)))+E(f789(f57(x98151),f64(x98152,f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x98151))),f64(x98152,x98151))
% 21.40/21.37 [9816]~P1(f789(f789(f241(a1),f2(a1)),x98161))+P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),x98162),x98161)))+E(f789(f57(x98161),f64(x98162,f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x98161))),f64(x98162,x98161))
% 21.40/21.37 [9817]~P2(x98171)+~P1(f789(f789(f240(a1),f2(a1)),x98172))+E(f789(f109(x98171),f789(a114,f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x98172))),f789(f789(f89(x98171),f789(f109(x98171),f789(a114,x98172))),f789(f109(x98171),f789(a114,x98172))))
% 21.40/21.37 [4978]~P140(x49781,x49782,x49783)+~E(x49783,f2(a1))+P1(f789(x49781,x49782))
% 21.40/21.37 [5104]~P101(x51041)+~P18(x51041,x51043)+P18(x51041,f158(x51041,x51042,x51043))
% 21.40/21.37 [4690]~P68(x46902)+~E(x46903,f789(f88(x46902),x46901))+E(x46901,f789(f88(x46902),x46903))
% 21.40/21.37 [4691]~P68(x46912)+~E(x46913,f789(f88(x46912),x46911))+E(x46911,f789(f88(x46912),x46913))
% 21.40/21.37 [4692]~P68(x46921)+~E(f789(f88(x46921),x46923),x46922)+E(f789(f88(x46921),x46922),x46923)
% 21.40/21.37 [4693]~P68(x46931)+~E(f789(f88(x46931),x46933),x46932)+E(f789(f88(x46931),x46932),x46933)
% 21.40/21.37 [4765]~P86(x47653)+E(x47651,x47652)+~E(f789(f109(x47653),x47651),f789(f109(x47653),x47652))
% 21.40/21.37 [4766]~P87(x47663)+E(x47661,x47662)+~E(f789(f112(x47663),x47661),f789(f112(x47663),x47662))
% 21.40/21.37 [4767]~P68(x47673)+E(x47671,x47672)+~E(f789(f88(x47673),x47671),f789(f88(x47673),x47672))
% 21.40/21.37 [4768]~P90(x47683)+E(x47681,x47682)+~E(f789(f88(x47683),x47681),f789(f88(x47683),x47682))
% 21.40/21.37 [4769]~P101(x47693)+E(x47691,x47692)+~E(f789(f301(x47693),x47691),f789(f301(x47693),x47692))
% 21.40/21.37 [4770]~P101(x47703)+E(x47701,x47702)+~E(f789(f265(x47703),x47701),f789(f265(x47703),x47702))
% 21.40/21.37 [4771]~P101(x47713)+E(x47711,x47712)+~E(f789(f266(x47713),x47711),f789(f266(x47713),x47712))
% 21.40/21.37 [4772]~P101(x47723)+E(x47721,x47722)+~E(f789(f304(x47723),x47721),f789(f304(x47723),x47722))
% 21.40/21.37 [5001]~P141(x50011,x50013,x50012)+~E(x50012,f2(a1))+P1(f789(x50011,f2(a1)))
% 21.40/21.37 [5040]~E(x50401,f2(a863))+E(f380(x50401,x50402,x50403),f184(f870(x50403,a856)))+~E(f789(f49(x50403),x50402),f789(a121,x50401))
% 21.40/21.37 [5187]~E(x51872,f2(a863))+E(f789(f248(a863,a863),x51871),f2(a863))+~P1(f789(f62(x51873,x51872),x51871))
% 21.40/21.37 [5231]P1(f789(x52311,x52312))+~E(x52313,f789(f109(a1),x52312))+~P1(f789(x52311,f789(a114,x52313)))
% 21.40/21.37 [5685]~E(x56853,f2(a863))+~P1(f789(x56851,x56852))+P1(f789(x56851,f59(a863,x56852,x56853)))
% 21.40/21.37 [5830]~P1(f789(a26,x58303))+~P1(f789(a26,x58302))+P1(f789(a26,f35(x58301,x58302,x58303)))
% 21.40/21.37 [5831]~P1(f789(a26,x58313))+~P1(f789(a26,x58312))+P1(f789(a26,f35(x58311,x58312,x58313)))
% 21.40/21.37 [6105]~E(x61053,f2(a863))+P1(f789(x61051,x61052))+~P1(f789(x61051,f59(a863,x61052,x61053)))
% 21.40/21.37 [6808]E(x68081,f2(a863))+~P1(f789(x68082,f824(x68081,x68083,x68082)))+P1(f789(x68082,f59(a863,x68083,x68081)))
% 21.40/21.37 [6920]~P9(x69201)+~P1(f789(f789(f240(x69201),x69202),f668(x69203,x69202,x69201)))+P1(f789(f789(f240(x69201),x69202),f52(x69201,x69203)))
% 21.40/21.37 [6922]~P1(f789(x69221,x69222))+~P1(f789(x69221,f824(x69223,x69222,x69221)))+P1(f789(x69221,f59(a863,x69222,x69223)))
% 21.40/21.37 [7022]E(x70221,f122(x70222))+E(f789(f789(f146(x70222),f761(x70223,x70221,x70222)),f770(x70223,x70221,x70222)),x70221)+~P1(f789(f789(f342(f864(x70222)),x70221),f156(x70222,x70223)))
% 21.40/21.37 [7056]~P120(x70561)+~P1(f789(f789(f342(x70561),x70562),f119(x70561)))+P1(f789(f789(f342(x70561),f789(f789(f250(x70561),x70562),x70563)),f119(x70561)))
% 21.40/21.37 [7397]P36(x73971,x73972)+~P1(f789(f789(f342(x73971),x73973),f700(x73972,x73971)))+P1(f789(f789(f342(x73971),f708(x73972,x73971,x73973)),f700(x73972,x73971)))
% 21.40/21.37 [7673]E(x76731,f122(x76732))+~P1(f789(f789(f342(f864(x76732)),x76731),f156(x76732,x76733)))+P1(f789(f789(f342(f864(x76732)),f770(x76733,x76731,x76732)),f156(x76732,x76733)))
% 21.40/21.37 [7722]E(x77221,f2(a863))+E(f789(f789(f89(a863),f789(f789(f90(a863),x77221),f826(x77221,x77222,x77223))),f824(x77221,x77222,x77223)),x77222)+P1(f789(x77223,f59(a863,x77222,x77221)))
% 21.40/21.37 [7765]~P1(f789(x77653,x77652))+E(f789(f789(f89(a863),f789(f789(f90(a863),x77651),f826(x77651,x77652,x77653))),f824(x77651,x77652,x77653)),x77652)+P1(f789(x77653,f59(a863,x77652,x77651)))
% 21.40/21.37 [7909]P1(f789(f789(f241(a1),x79091),f816(x79092,x79093,x79091)))+P1(f789(f789(x79093,f789(f789(f50(a1),x79092),x79091)),f59(a1,x79092,x79091)))+~P1(f789(f789(f241(a1),x79091),f2(a1)))
% 21.40/21.37 [8172]P1(f789(f789(x81722,f789(f789(f50(a1),x81721),x81723)),f59(a1,x81721,x81723)))+~P1(f789(f789(f241(a1),x81723),f2(a1)))+P1(f789(f789(f240(a1),f816(x81721,x81722,x81723)),f2(a1)))
% 21.40/21.37 [8352]E(f789(f789(f89(a1),f789(f789(f90(a1),x83521),f817(x83522,x83523,x83521))),f816(x83522,x83523,x83521)),x83522)+P1(f789(f789(x83523,f789(f789(f50(a1),x83522),x83521)),f59(a1,x83522,x83521)))+~P1(f789(f789(f241(a1),x83521),f2(a1)))
% 21.40/21.37 [8586]~P1(f789(f789(x85861,f817(x85862,x85861,x85863)),f816(x85862,x85861,x85863)))+P1(f789(f789(x85861,f789(f789(f50(a1),x85862),x85863)),f59(a1,x85862,x85863)))+~P1(f789(f789(f241(a1),x85863),f2(a1)))
% 21.40/21.37 [8798]~P101(x87981)+~P18(x87981,x87983)+P18(x87981,f145(x87981,x87981,f7(x87981),x87982,x87983))
% 21.40/21.37 [9243]~P118(x92432)+E(x92431,f2(x92432))+~P1(f789(f789(f240(x92432),f789(f789(f89(x92432),f789(f789(f90(x92432),x92433),x92433)),f789(f789(f90(x92432),x92431),x92431))),f2(x92432)))
% 21.40/21.37 [9244]~P118(x92442)+E(x92441,f2(x92442))+~P1(f789(f789(f240(x92442),f789(f789(f89(x92442),f789(f789(f90(x92442),x92441),x92441)),f789(f789(f90(x92442),x92443),x92443))),f2(x92442)))
% 21.40/21.37 [10018]~P110(x100181)+~P1(f789(f789(f241(x100181),x100182),f2(x100181)))+P1(f789(f789(f241(x100181),f789(f789(f250(x100181),x100182),f789(a121,f789(f789(f90(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x100183)))),f2(x100181)))
% 21.40/21.37 [10028]~P110(x100282)+E(x100281,f2(x100282))+~P1(f789(f789(f240(x100282),f789(f789(f89(x100282),f789(f789(f250(x100282),x100283),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x100282),x100281),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))),f2(x100282)))
% 21.40/21.37 [10029]~P110(x100292)+E(x100291,f2(x100292))+~P1(f789(f789(f240(x100292),f789(f789(f89(x100292),f789(f789(f250(x100292),x100291),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x100292),x100293),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))),f2(x100292)))
% 21.40/21.37 [4722]~E(x47222,x47223)+~P68(x47221)+E(f789(f789(f3(x47221),x47222),x47223),f2(x47221))
% 21.40/21.37 [4723]~E(x47232,x47233)+~P6(x47231)+E(f789(f789(f3(x47231),x47232),x47233),f2(x47231))
% 21.40/21.37 [4736]~P137(x47361)+~E(x47363,f2(x47361))+E(f789(f789(f89(x47361),x47362),x47363),x47362)
% 21.40/21.37 [4752]~P133(x47521)+~E(x47523,f2(x47521))+E(f789(f789(f90(x47521),x47522),x47523),f2(x47521))
% 21.40/21.37 [4753]~P133(x47531)+~E(x47532,f2(x47531))+E(f789(f789(f90(x47531),x47532),x47533),f2(x47531))
% 21.40/21.37 [4773]~E(x47733,f122(x47731))+~E(x47732,f122(x47731))+E(f789(f789(f132(x47731),x47732),x47733),f122(x47731))
% 21.40/21.37 [4774]~E(x47743,f122(x47741))+~E(x47742,f122(x47741))+E(f789(f789(f132(x47741),x47742),x47743),f122(x47741))
% 21.40/21.37 [4856]~P137(x48562)+E(x48561,f2(x48562))+~E(f789(f789(f89(x48562),x48563),x48561),x48563)
% 21.40/21.37 [4857]~P68(x48571)+~E(x48572,f789(f88(x48571),x48573))+E(f789(f789(f89(x48571),x48572),x48573),f2(x48571))
% 21.40/21.37 [4864]E(x48641,f122(x48642))+E(x48643,f2(a863))+~E(f789(f789(f164(x48642),x48643),x48641),f122(x48642))
% 21.40/21.37 [4872]~P68(x48723)+E(x48721,x48722)+~E(f789(f789(f3(x48723),x48721),x48722),f2(x48723))
% 21.40/21.37 [4873]~P6(x48733)+E(x48731,x48732)+~E(f789(f789(f3(x48733),x48731),x48732),f2(x48733))
% 21.40/21.37 [4882]~P134(x48822)+E(x48821,f2(x48822))+~E(f789(f789(f250(x48822),x48821),x48823),f2(x48822))
% 21.40/21.37 [4883]~P92(x48832)+E(x48831,f184(x48832))+~E(f789(f789(f110(x48832),x48833),x48831),f184(x48832))
% 21.40/21.37 [4884]~P92(x48842)+E(x48841,f184(x48842))+~E(f789(f789(f110(x48842),x48841),x48843),f184(x48842))
% 21.40/21.37 [4885]~P97(x48852)+E(x48851,f247(x48852))+~E(f789(f789(f111(x48852),x48853),x48851),f247(x48852))
% 21.40/21.37 [4886]~P97(x48862)+E(x48861,f247(x48862))+~E(f789(f789(f111(x48862),x48861),x48863),f247(x48862))
% 21.40/21.37 [4951]~P68(x49512)+E(x49511,f789(f88(x49512),x49513))+~E(f789(f789(f89(x49512),x49511),x49513),f2(x49512))
% 21.40/21.37 [4952]~P68(x49521)+E(f789(f88(x49521),x49522),x49523)+~E(f789(f789(f89(x49521),x49522),x49523),f2(x49521))
% 21.40/21.37 [4953]~E(x49532,x49533)+~P99(x49531)+P1(f789(f789(f240(x49531),x49532),x49533))
% 21.40/21.37 [4954]~E(x49542,x49543)+~P99(x49541)+P1(f789(f789(f240(x49541),x49542),x49543))
% 21.40/21.37 [4955]~E(x49552,x49553)+~P99(x49551)+P1(f789(f789(f240(x49551),x49552),x49553))
% 21.40/21.37 [4956]~E(x49562,x49563)+~P105(x49561)+P1(f789(f789(f240(x49561),x49562),x49563))
% 21.40/21.37 [5054]~P111(x50541)+~E(x50542,f789(f88(x50541),x50543))+E(f789(f789(f90(x50541),x50542),x50542),f789(f789(f90(x50541),x50543),x50543))
% 21.40/21.37 [5062]~P101(x50621)+~P18(x50621,x50623)+P18(x50621,f789(f789(f164(x50621),x50622),x50623))
% 21.40/21.37 [5063]~P101(x50631)+~P18(x50631,x50633)+P18(x50631,f789(f789(f135(x50631),x50632),x50633))
% 21.40/21.37 [5101]E(x51011,x51012)+E(x51013,f2(a863))+~E(f789(f789(f90(a863),x51013),x51011),f789(f789(f90(a863),x51013),x51012))
% 21.40/21.37 [5102]E(x51021,x51022)+E(x51023,f2(a863))+~E(f789(f789(f90(a863),x51023),x51021),f789(f789(f90(a863),x51023),x51022))
% 21.40/21.37 [5103]E(x51031,x51032)+E(x51033,f2(a863))+~E(f789(f789(f90(a863),x51031),x51033),f789(f789(f90(a863),x51032),x51033))
% 21.40/21.37 [5178]~E(x51782,x51783)+~P99(x51781)+E(f303(x51781,x51782,x51783),f789(f789(f310(x51781),x51782),f184(f870(x51781,a856))))
% 21.40/21.37 [5219]~P110(x52191)+~E(f789(f84(x52191),x52192),f789(f84(x52191),x52193))+P1(f789(f789(f287(x52191),x52192),x52193))
% 21.40/21.37 [5223]~E(x52231,x52232)+~P99(x52233)+~P1(f789(f789(f241(x52233),x52231),x52232))
% 21.40/21.37 [5224]~E(x52241,x52242)+~P99(x52243)+~P1(f789(f789(f241(x52243),x52241),x52242))
% 21.40/21.37 [5225]~E(x52251,x52252)+~P99(x52253)+~P1(f789(f789(f241(x52253),x52251),x52252))
% 21.40/21.37 [5226]~E(x52261,x52262)+~P101(x52263)+~P1(f789(f789(f241(x52263),x52261),x52262))
% 21.40/21.37 [5227]~E(x52271,x52272)+~P101(x52273)+~P1(f789(f789(f241(x52273),x52271),x52272))
% 21.40/21.37 [5228]~E(x52281,x52282)+~P99(x52283)+~P1(f789(f789(f241(x52283),x52281),x52282))
% 21.40/21.37 [5229]~E(x52291,x52292)+~P101(x52293)+~P1(f789(f789(f241(x52293),x52291),x52292))
% 21.40/21.37 [5235]~P99(x52351)+E(f789(f302(x52351,x52352),x52353),f184(f870(x52351,a856)))+P1(f789(f789(f241(x52351),x52352),x52353))
% 21.40/21.37 [5236]~P99(x52361)+E(f789(f302(x52361,x52362),x52363),f184(f870(x52361,a856)))+P1(f789(f789(f241(x52361),x52362),x52363))
% 21.40/21.37 [5280]~P99(x52801)+E(f305(x52801,x52802,x52803),f184(f870(x52801,a856)))+P1(f789(f789(f241(x52801),x52802),x52803))
% 21.40/21.37 [5281]~P99(x52811)+E(f303(x52811,x52812,x52813),f184(f870(x52811,a856)))+P1(f789(f789(f240(x52811),x52812),x52813))
% 21.40/21.37 [5282]~P99(x52821)+E(f184(f870(x52821,a856)),f305(x52821,x52822,x52823))+P1(f789(f789(f241(x52821),x52822),x52823))
% 21.40/21.37 [5283]~P99(x52831)+E(f184(f870(x52831,a856)),f303(x52831,x52832,x52833))+P1(f789(f789(f240(x52831),x52832),x52833))
% 21.40/21.37 [5291]~P101(x52911)+~E(f789(f789(f244(x52911),x52912),x52913),x52912)+P1(f789(f789(f240(x52911),x52912),x52913))
% 21.40/21.37 [5292]~P101(x52921)+~E(f789(f789(f239(x52921),x52922),x52923),x52923)+P1(f789(f789(f240(x52921),x52922),x52923))
% 21.40/21.37 [5293]~P94(x52931)+~E(f789(f789(f110(x52931),x52932),x52933),x52933)+P1(f789(f789(f240(x52931),x52932),x52933))
% 21.40/21.37 [5294]~P98(x52941)+~E(f789(f789(f111(x52941),x52942),x52943),x52942)+P1(f789(f789(f240(x52941),x52942),x52943))
% 21.40/21.37 [5309]~P101(x53091)+P18(x53091,x53092)+~P18(x53091,f789(f789(f146(x53091),x53093),x53092))
% 21.40/21.37 [5310]~P101(x53101)+P18(x53101,x53102)+~P18(x53101,f789(f789(f146(x53101),x53103),x53102))
% 21.40/21.37 [5311]~P101(x53111)+P18(x53111,x53112)+~P18(x53111,f789(f789(f132(x53111),x53113),x53112))
% 21.40/21.37 [5312]~P101(x53121)+P18(x53121,x53122)+~P18(x53121,f789(f789(f132(x53121),x53122),x53123))
% 21.40/21.37 [5317]~P7(x53171)+~E(f59(x53171,x53173,x53172),f2(x53171))+P1(f789(f789(f287(x53171),x53172),x53173))
% 21.40/21.37 [5377]~P101(x53771)+P1(f789(f789(f240(x53771),x53773),x53772))+P1(f789(f789(f241(x53771),x53772),x53773))
% 21.40/21.37 [5378]~P101(x53781)+P1(f789(f789(f240(x53781),x53783),x53782))+P1(f789(f789(f241(x53781),x53782),x53783))
% 21.40/21.37 [5379]~P101(x53791)+P1(f789(f789(f240(x53791),x53793),x53792))+P1(f789(f789(f241(x53791),x53792),x53793))
% 21.40/21.37 [5380]~P101(x53801)+P1(f789(f789(f240(x53801),x53803),x53802))+P1(f789(f789(f241(x53801),x53802),x53803))
% 21.40/21.37 [5381]~P101(x53811)+P1(f789(f789(f240(x53811),x53813),x53812))+P1(f789(f789(f241(x53811),x53812),x53813))
% 21.40/21.37 [5382]~P101(x53821)+P1(f789(f789(f240(x53821),x53823),x53822))+P1(f789(f789(f240(x53821),x53822),x53823))
% 21.40/21.37 [5383]~P101(x53831)+P1(f789(f789(f240(x53831),x53833),x53832))+P1(f789(f789(f240(x53831),x53832),x53833))
% 21.40/21.37 [5423]~P101(x54231)+E(f789(f789(f244(x54231),x54232),x54233),x54233)+~P1(f789(f789(f240(x54231),x54233),x54232))
% 21.40/21.37 [5424]~P101(x54241)+E(f789(f789(f244(x54241),x54242),x54243),x54242)+~P1(f789(f789(f240(x54241),x54242),x54243))
% 21.40/21.37 [5425]~P101(x54251)+E(f789(f789(f244(x54251),x54252),x54253),x54252)+~P1(f789(f789(f240(x54251),x54252),x54253))
% 21.40/21.37 [5426]~P101(x54261)+E(f789(f789(f239(x54261),x54262),x54263),x54262)+~P1(f789(f789(f240(x54261),x54263),x54262))
% 21.40/21.37 [5427]~P101(x54271)+E(f789(f789(f239(x54271),x54272),x54273),x54273)+~P1(f789(f789(f240(x54271),x54272),x54273))
% 21.40/21.37 [5428]~P101(x54281)+E(f789(f789(f239(x54281),x54282),x54283),x54283)+~P1(f789(f789(f240(x54281),x54282),x54283))
% 21.40/21.37 [5429]~P94(x54291)+E(f789(f789(f110(x54291),x54292),x54293),x54292)+~P1(f789(f789(f240(x54291),x54293),x54292))
% 21.40/21.37 [5430]~P94(x54301)+E(f789(f789(f110(x54301),x54302),x54303),x54303)+~P1(f789(f789(f240(x54301),x54302),x54303))
% 21.40/21.37 [5431]~P94(x54311)+E(f789(f789(f110(x54311),x54312),x54313),x54313)+~P1(f789(f789(f240(x54311),x54312),x54313))
% 21.40/21.37 [5432]~P98(x54321)+E(f789(f789(f111(x54321),x54322),x54323),x54323)+~P1(f789(f789(f240(x54321),x54323),x54322))
% 21.40/21.37 [5433]~P98(x54331)+E(f789(f789(f111(x54331),x54332),x54333),x54332)+~P1(f789(f789(f240(x54331),x54332),x54333))
% 21.40/21.37 [5434]~P98(x54341)+E(f789(f789(f111(x54341),x54342),x54343),x54342)+~P1(f789(f789(f240(x54341),x54342),x54343))
% 21.40/21.37 [5441]~P113(x54412)+E(x54411,f2(x54412))+E(f789(f789(f291(x54412),f789(f88(x54412),x54413)),f789(f88(x54412),x54411)),f789(f789(f291(x54412),x54413),x54411))
% 21.40/21.37 [5447]~P7(x54471)+E(f59(x54471,x54472,x54473),f2(x54471))+~P1(f789(f789(f287(x54471),x54473),x54472))
% 21.40/21.37 [5448]~P7(x54481)+E(f59(x54481,x54482,x54483),f2(x54481))+~P1(f789(f789(f287(x54481),x54483),x54482))
% 21.40/21.37 [5488]~P99(x54881)+E(f789(f302(x54881,x54882),x54883),f184(f870(x54881,a856)))+~P1(f789(f789(f240(x54881),x54883),x54882))
% 21.40/21.37 [5516]~P99(x55161)+E(f306(x55161,x55162,x55163),f184(f870(x55161,a856)))+~P1(f789(f789(f240(x55161),x55163),x55162))
% 21.40/21.37 [5517]~P99(x55171)+E(f305(x55171,x55172,x55173),f184(f870(x55171,a856)))+~P1(f789(f789(f240(x55171),x55173),x55172))
% 21.40/21.37 [5518]~P99(x55181)+E(f303(x55181,x55182,x55183),f184(f870(x55181,a856)))+~P1(f789(f789(f241(x55181),x55183),x55182))
% 21.40/21.37 [5568]~E(f789(f789(f3(a863),x55681),x55683),x55682)+E(x55681,f789(f789(f89(a863),x55682),x55683))+~P1(f789(f789(f240(a863),x55683),x55681))
% 21.40/21.37 [5569]~E(x55691,f789(f789(f89(a863),x55693),x55692))+E(f789(f789(f3(a863),x55691),x55692),x55693)+~P1(f789(f789(f240(a863),x55692),x55691))
% 21.40/21.37 [5612]~P1(f789(x56121,x56123))+P1(f789(x56121,f457(x56121,x56122)))+~P1(f789(f789(f240(a863),x56123),x56122))
% 21.40/21.37 [5613]~P1(f789(x56131,x56133))+P1(f789(x56131,f466(x56131,x56132)))+~P1(f789(f789(f241(a863),x56133),x56132))
% 21.40/21.37 [5620]~P99(x56201)+~E(f789(f302(x56201,x56202),x56203),f184(f870(x56201,a856)))+~P1(f789(f789(f241(x56201),x56202),x56203))
% 21.40/21.37 [5621]~P99(x56211)+~E(f789(f302(x56211,x56212),x56213),f184(f870(x56211,a856)))+~P1(f789(f789(f241(x56211),x56212),x56213))
% 21.40/21.37 [5624]~P99(x56241)+~P1(f789(f789(f241(x56241),x56242),x56243))+P1(f789(f789(f240(x56241),x56242),x56243))
% 21.40/21.37 [5625]~P99(x56251)+~P1(f789(f789(f241(x56251),x56252),x56253))+P1(f789(f789(f240(x56251),x56252),x56253))
% 21.40/21.37 [5626]~P105(x56261)+~P1(f789(f789(f241(x56261),x56262),x56263))+P1(f789(f789(f240(x56261),x56262),x56263))
% 21.40/21.37 [5627]~P105(x56271)+~P1(f789(f789(f241(x56271),x56272),x56273))+P1(f789(f789(f240(x56271),x56272),x56273))
% 21.40/21.37 [5740]~P99(x57401)+~E(f305(x57401,x57402,x57403),f184(f870(x57401,a856)))+~P1(f789(f789(f241(x57401),x57402),x57403))
% 21.40/21.37 [5741]~P99(x57411)+~E(f303(x57411,x57412,x57413),f184(f870(x57411,a856)))+~P1(f789(f789(f240(x57411),x57412),x57413))
% 21.40/21.37 [5742]~P99(x57421)+~E(f184(f870(x57421,a856)),f305(x57421,x57422,x57423))+~P1(f789(f789(f241(x57421),x57422),x57423))
% 21.40/21.37 [5743]~P99(x57431)+~E(f184(f870(x57431,a856)),f303(x57431,x57432,x57433))+~P1(f789(f789(f240(x57431),x57432),x57433))
% 21.40/21.37 [5756]P1(f789(x57561,x57562))+~P1(f789(x57561,f467(x57561,x57563)))+~P1(f789(f789(f240(a863),x57562),x57563))
% 21.40/21.37 [5757]P1(f789(x57571,x57572))+~P1(f789(x57571,f471(x57571,x57573)))+~P1(f789(f789(f241(a863),x57572),x57573))
% 21.40/21.37 [5765]~E(x57651,f789(a121,x57653))+P1(f789(f789(f241(a863),x57651),f789(a121,x57652)))+~P1(f789(f789(f241(a863),x57653),x57652))
% 21.40/21.37 [5781]E(x57811,x57812)+~E(f789(f789(f90(a863),x57813),x57811),f789(f789(f90(a863),x57813),x57812))+~P1(f789(f789(f241(a863),f2(a863)),x57813))
% 21.40/21.37 [5841]E(f789(x58411,f506(x58411,x58412,x58413)),f87(a863))+~E(f789(f789(f8(x58413,a863),x58411),x58412),f87(a863))+~P1(f789(f70(x58413),x58412))
% 21.40/21.37 [5851]~P9(x58511)+P1(f789(f789(f240(x58511),x58512),f51(x58511,x58513)))+~P1(f789(f789(f342(x58511),x58512),x58513))
% 21.40/21.37 [5875]~P99(x58751)+~P1(f789(f789(f241(x58751),x58753),x58752))+~P1(f789(f789(f241(x58751),x58752),x58753))
% 21.40/21.37 [5876]~P105(x58761)+~P1(f789(f789(f241(x58761),x58763),x58762))+~P1(f789(f789(f241(x58761),x58762),x58763))
% 21.40/21.37 [5877]~P105(x58771)+~P1(f789(f789(f241(x58771),x58773),x58772))+~P1(f789(f789(f241(x58771),x58772),x58773))
% 21.40/21.37 [5878]~P105(x58781)+~P1(f789(f789(f241(x58781),x58783),x58782))+~P1(f789(f789(f241(x58781),x58782),x58783))
% 21.40/21.37 [5879]~P105(x58791)+~P1(f789(f789(f241(x58791),x58793),x58792))+~P1(f789(f789(f241(x58791),x58792),x58793))
% 21.40/21.37 [5880]~P105(x58801)+~P1(f789(f789(f240(x58801),x58803),x58802))+~P1(f789(f789(f241(x58801),x58802),x58803))
% 21.40/21.37 [5881]~P101(x58811)+~P1(f789(f789(f241(x58811),x58813),x58812))+~P1(f789(f789(f241(x58811),x58812),x58813))
% 21.40/21.37 [5882]~P101(x58821)+~P1(f789(f789(f240(x58821),x58823),x58822))+~P1(f789(f789(f241(x58821),x58822),x58823))
% 21.40/21.37 [5883]~P101(x58831)+~P1(f789(f789(f240(x58831),x58833),x58832))+~P1(f789(f789(f241(x58831),x58832),x58833))
% 21.40/21.37 [5884]~P101(x58841)+~P1(f789(f789(f240(x58841),x58843),x58842))+~P1(f789(f789(f241(x58841),x58842),x58843))
% 21.40/21.37 [5903]~E(x59032,x59033)+~E(x59031,x59032)+E(f290(a863,f287(a863),x59031,x59032),f789(f789(f310(a863),x59033),f184(f870(a863,a856))))
% 21.40/21.37 [5911]~E(f789(x59112,f408(x59112,x59113,x59111)),f87(a863))+E(f789(f789(f11(x59111,a863),x59112),x59113),f87(a863))+~P1(f789(f70(x59111),x59113))
% 21.40/21.37 [5912]~E(f789(x59122,f507(x59122,x59123,x59121)),f2(a863))+E(f789(f789(f8(x59121,a863),x59122),x59123),f2(a863))+~P1(f789(f70(x59121),x59123))
% 21.40/21.37 [5926]~P100(x59261)+~P1(f789(f789(f240(x59261),x59263),x59262))+P1(f789(f789(f342(x59261),x59262),f789(f266(x59261),x59263)))
% 21.40/21.37 [5927]~P100(x59271)+~P1(f789(f789(f241(x59271),x59273),x59272))+P1(f789(f789(f342(x59271),x59272),f789(f304(x59271),x59273)))
% 21.40/21.37 [5928]~P100(x59281)+~P1(f789(f789(f240(x59281),x59282),x59283))+P1(f789(f789(f342(x59281),x59282),f789(f301(x59281),x59283)))
% 21.40/21.37 [5929]~P100(x59291)+~P1(f789(f789(f241(x59291),x59292),x59293))+P1(f789(f789(f342(x59291),x59292),f789(f265(x59291),x59293)))
% 21.40/21.37 [5930]~P104(x59301)+~P1(f789(f789(f287(x59301),x59302),x59303))+P1(f789(f789(f287(x59301),x59302),f789(f88(x59301),x59303)))
% 21.40/21.37 [5931]~P110(x59311)+~P1(f789(f789(f287(x59311),x59312),x59313))+P1(f789(f789(f287(x59311),x59312),f789(f84(x59311),x59313)))
% 21.40/21.37 [5942]E(f789(x59421,f519(x59421,x59422,x59423)),f789(a121,f2(a863)))+~E(f789(f789(f8(x59423,a863),x59421),x59422),f789(a121,f2(a863)))+~P1(f789(f70(x59423),x59422))
% 21.40/21.37 [6026]~P9(x60261)+~P1(f789(f789(f342(x60261),x60263),x60262))+P1(f789(f789(f240(x60261),f52(x60261,x60262)),x60263))
% 21.40/21.37 [6045]~P1(f789(f789(f240(a863),x60451),x60453))+P1(f789(f789(f240(a863),x60451),x60452))+~P1(f789(f789(f240(a863),x60453),x60452))
% 21.40/21.37 [6046]~P1(f789(f789(f240(a1),x60461),x60463))+P1(f789(f789(f240(a1),x60461),x60462))+~P1(f789(f789(f240(a1),x60463),x60462))
% 21.40/21.37 [6047]~P1(f789(f789(f287(a863),x60471),x60473))+P1(f789(f789(f287(a863),x60471),x60472))+~P1(f789(f789(f287(a863),x60473),x60472))
% 21.40/21.37 [6066]~P100(x60661)+~P1(f789(f789(f342(x60661),x60663),f789(f304(x60661),x60662)))+P1(f789(f789(f241(x60661),x60662),x60663))
% 21.40/21.37 [6067]~P100(x60671)+~P1(f789(f789(f342(x60671),x60672),f789(f265(x60671),x60673)))+P1(f789(f789(f241(x60671),x60672),x60673))
% 21.40/21.37 [6068]~P100(x60681)+~P1(f789(f789(f342(x60681),x60683),f789(f266(x60681),x60682)))+P1(f789(f789(f240(x60681),x60682),x60683))
% 21.40/21.37 [6069]~P100(x60691)+~P1(f789(f789(f342(x60691),x60692),f789(f301(x60691),x60693)))+P1(f789(f789(f240(x60691),x60692),x60693))
% 21.40/21.37 [6070]~P110(x60701)+~P1(f789(f789(f287(x60701),x60702),f789(f84(x60701),x60703)))+P1(f789(f789(f287(x60701),x60702),x60703))
% 21.40/21.37 [6071]~P104(x60711)+~P1(f789(f789(f287(x60711),x60712),f789(f88(x60711),x60713)))+P1(f789(f789(f287(x60711),x60712),x60713))
% 21.40/21.37 [6290]~P62(x62901)+P1(f789(f789(f241(x62901),f2(x62901)),f821(x62903,x62902,x62901)))+P1(f789(f789(f240(x62901),x62902),x62903))
% 21.40/21.37 [6291]~P63(x62911)+P1(f789(f789(f241(x62911),f2(x62911)),f829(x62913,x62912,x62911)))+P1(f789(f789(f240(x62911),x62912),x62913))
% 21.40/21.37 [6361]~P76(x63611)+~P1(f789(f789(f241(x63611),x63613),f789(f88(x63611),x63612)))+P1(f789(f789(f241(x63611),x63612),f789(f88(x63611),x63613)))
% 21.40/21.37 [6362]~P76(x63621)+~P1(f789(f789(f241(x63621),x63623),f789(f88(x63621),x63622)))+P1(f789(f789(f241(x63621),x63622),f789(f88(x63621),x63623)))
% 21.40/21.37 [6363]~P76(x63631)+~P1(f789(f789(f240(x63631),x63633),f789(f88(x63631),x63632)))+P1(f789(f789(f240(x63631),x63632),f789(f88(x63631),x63633)))
% 21.40/21.37 [6364]~P76(x63641)+~P1(f789(f789(f240(x63641),x63643),f789(f88(x63641),x63642)))+P1(f789(f789(f240(x63641),x63642),f789(f88(x63641),x63643)))
% 21.40/21.37 [6375]~P1(f789(f789(f241(a863),x63751),x63753))+~P1(f789(f789(f241(a863),x63753),x63752))+P1(f789(f789(f241(a863),f789(a121,x63751)),x63752))
% 21.40/21.37 [6407]~P117(x64071)+P1(f789(f789(f241(x64071),f789(f109(x64071),x64072)),f789(f109(x64071),x64073)))+~P1(f789(f789(f241(a863),x64072),x64073))
% 21.40/21.37 [6408]~P110(x64081)+P1(f789(f789(f241(x64081),f789(f112(x64081),x64082)),f789(f112(x64081),x64083)))+~P1(f789(f789(f241(a1),x64082),x64083))
% 21.40/21.37 [6409]~P117(x64091)+P1(f789(f789(f241(x64091),f789(f109(x64091),x64092)),f789(f109(x64091),x64093)))+~P1(f789(f789(f241(a863),x64092),x64093))
% 21.40/21.37 [6410]~P117(x64101)+P1(f789(f789(f240(x64101),f789(f109(x64101),x64102)),f789(f109(x64101),x64103)))+~P1(f789(f789(f240(a863),x64102),x64103))
% 21.40/21.37 [6411]~P110(x64111)+P1(f789(f789(f240(x64111),f789(f112(x64111),x64112)),f789(f112(x64111),x64113)))+~P1(f789(f789(f240(a1),x64112),x64113))
% 21.40/21.37 [6417]~P101(x64171)+E(f789(f789(f110(f870(x64171,a856)),f789(f265(x64171),x64172)),f789(f302(x64171,x64172),x64173)),f789(f265(x64171),x64173))+~P1(f789(f789(f240(x64171),x64172),x64173))
% 21.40/21.37 [6447]~P76(x64471)+~P1(f789(f789(f241(x64471),x64473),x64472))+P1(f789(f789(f241(x64471),f789(f88(x64471),x64472)),f789(f88(x64471),x64473)))
% 21.40/21.37 [6448]~P76(x64481)+~P1(f789(f789(f240(x64481),x64483),x64482))+P1(f789(f789(f240(x64481),f789(f88(x64481),x64482)),f789(f88(x64481),x64483)))
% 21.40/21.37 [6449]~P76(x64491)+~P1(f789(f789(f240(x64491),x64493),x64492))+P1(f789(f789(f240(x64491),f789(f88(x64491),x64492)),f789(f88(x64491),x64493)))
% 21.40/21.37 [6450]~P90(x64501)+~P1(f789(f789(f240(x64501),x64503),x64502))+P1(f789(f789(f240(x64501),f789(f88(x64501),x64502)),f789(f88(x64501),x64503)))
% 21.40/21.37 [6451]~P90(x64511)+~P1(f789(f789(f240(x64511),x64513),x64512))+P1(f789(f789(f240(x64511),f789(f88(x64511),x64512)),f789(f88(x64511),x64513)))
% 21.40/21.37 [6486]~P101(x64861)+E(f789(f789(f110(f870(x64861,a856)),f789(f301(x64861),x64862)),f306(x64861,x64862,x64863)),f789(f265(x64861),x64863))+~P1(f789(f789(f241(x64861),x64862),x64863))
% 21.40/21.37 [6487]~P101(x64871)+E(f789(f789(f110(f870(x64871,a856)),f789(f301(x64871),x64872)),f305(x64871,x64872,x64873)),f789(f301(x64871),x64873))+~P1(f789(f789(f240(x64871),x64872),x64873))
% 21.40/21.37 [6488]~P101(x64881)+E(f789(f789(f110(f870(x64881,a856)),f789(f265(x64881),x64882)),f303(x64881,x64882,x64883)),f789(f301(x64881),x64883))+~P1(f789(f789(f240(x64881),x64882),x64883))
% 21.40/21.37 [6525]~P101(x65251)+E(f789(f789(f110(f870(x65251,a856)),f789(f302(x65251,x65252),x65253)),f789(f266(x65251),x65253)),f789(f266(x65251),x65252))+~P1(f789(f789(f240(x65251),x65252),x65253))
% 21.40/21.37 [6687]~P101(x66871)+E(f789(f789(f110(f870(x66871,a856)),f306(x66871,x66872,x66873)),f789(f266(x66871),x66873)),f789(f304(x66871),x66872))+~P1(f789(f789(f241(x66871),x66872),x66873))
% 21.40/21.37 [6688]~P101(x66881)+E(f789(f789(f110(f870(x66881,a856)),f305(x66881,x66882,x66883)),f789(f304(x66881),x66883)),f789(f304(x66881),x66882))+~P1(f789(f789(f240(x66881),x66882),x66883))
% 21.40/21.37 [6689]~P101(x66891)+E(f789(f789(f110(f870(x66891,a856)),f303(x66891,x66892,x66893)),f789(f304(x66891),x66893)),f789(f266(x66891),x66892))+~P1(f789(f789(f240(x66891),x66892),x66893))
% 21.40/21.37 [6706]P1(f789(x67061,x67062))+~P1(f789(f789(f240(a863),x67062),x67063))+P1(f789(f789(f342(a863),f467(x67061,x67063)),f303(a863,f2(a863),x67063)))
% 21.40/21.37 [6716]P1(f789(f789(f287(a1),x67161),f59(a1,x67162,x67163)))+~P1(f789(f789(f287(a1),x67161),x67162))+~P1(f789(f789(f287(a1),x67161),x67163))
% 21.40/21.37 [6742]E(x67421,x67422)+~E(f789(f789(f159(x67423),x67421),f737(x67423,x67422,x67421)),f789(f789(f159(x67423),x67422),f737(x67423,x67422,x67421)))+~E(f789(f185(f864(x67423)),x67421),f789(f185(f864(x67423)),x67422))
% 21.40/21.37 [6748]~E(x67483,f789(f789(f50(a863),x67481),x67482))+~P1(f789(f789(f241(a863),f2(a863)),x67482))+P1(f789(f789(f241(a863),x67481),f789(f789(f90(a863),x67482),f789(a121,x67483))))
% 21.40/21.37 [6763]~P1(f789(x67631,x67633))+~P1(f789(f789(f240(a863),x67633),x67632))+P1(f789(f789(f342(a863),f457(x67631,x67632)),f303(a863,f2(a863),x67632)))
% 21.40/21.37 [6805]~P1(f789(x68051,x68053))+P1(f789(x68051,f468(x68051,x68052)))+~P1(f789(f789(f342(a863),x68053),f303(a863,f2(a863),x68052)))
% 21.40/21.37 [6827]~P117(x68273)+~P1(f789(f789(f241(x68273),f789(f109(x68273),x68271)),f789(f109(x68273),x68272)))+P1(f789(f789(f241(a863),x68271),x68272))
% 21.40/21.37 [6828]~P117(x68283)+~P1(f789(f789(f241(x68283),f789(f109(x68283),x68281)),f789(f109(x68283),x68282)))+P1(f789(f789(f241(a863),x68281),x68282))
% 21.40/21.37 [6829]~P110(x68293)+~P1(f789(f789(f241(x68293),f789(f112(x68293),x68291)),f789(f112(x68293),x68292)))+P1(f789(f789(f241(a1),x68291),x68292))
% 21.40/21.37 [6830]~P117(x68303)+~P1(f789(f789(f240(x68303),f789(f109(x68303),x68301)),f789(f109(x68303),x68302)))+P1(f789(f789(f240(a863),x68301),x68302))
% 21.40/21.37 [6831]~P110(x68313)+~P1(f789(f789(f240(x68313),f789(f112(x68313),x68311)),f789(f112(x68313),x68312)))+P1(f789(f789(f240(a1),x68311),x68312))
% 21.40/21.37 [6847]~P117(x68471)+~P1(f789(f789(f241(x68471),f87(x68471)),x68472))+P1(f789(f789(f241(x68471),f87(x68471)),f789(f789(f250(x68471),x68472),f789(a121,x68473))))
% 21.40/21.37 [6851]~P76(x68511)+~P1(f789(f789(f241(x68511),f789(f88(x68511),x68513)),f789(f88(x68511),x68512)))+P1(f789(f789(f241(x68511),x68512),x68513))
% 21.40/21.37 [6852]~P76(x68521)+~P1(f789(f789(f240(x68521),f789(f88(x68521),x68523)),f789(f88(x68521),x68522)))+P1(f789(f789(f240(x68521),x68522),x68523))
% 21.40/21.37 [6853]~P90(x68531)+~P1(f789(f789(f240(x68531),f789(f88(x68531),x68533)),f789(f88(x68531),x68532)))+P1(f789(f789(f240(x68531),x68532),x68533))
% 21.40/21.37 [6879]P1(f789(x68791,x68792))+~P1(f789(x68791,f469(x68791,x68793)))+~P1(f789(f789(f342(a863),x68792),f303(a863,f2(a863),x68793)))
% 21.40/21.37 [6900]~P62(x69001)+P1(f789(f789(f241(x69001),f821(x69003,x69002,x69001)),f87(x69001)))+P1(f789(f789(f240(x69001),x69002),x69003))
% 21.40/21.37 [6918]~E(f59(a863,x69183,x69182),f59(a863,x69181,x69182))+E(f789(f789(f89(a863),x69181),f789(f789(f90(a863),x69182),f831(x69181,x69182,x69183))),x69183)+~P1(f789(f789(f240(a863),x69181),x69183))
% 21.40/21.37 [6936]E(f789(x69361,f615(x69361,x69362,x69363)),f187(x69362))+~P1(f789(f70(x69363),f173(x69363,x69362,x69361)))+P1(f789(f70(x69363),f247(f870(x69363,a856))))
% 21.40/21.37 [6977]E(f789(f789(f11(x69771,a863),x69772),x69773),f87(a863))+~P1(f789(f70(x69771),x69773))+P1(f789(f789(f342(x69771),f408(x69772,x69773,x69771)),x69773))
% 21.40/21.37 [6978]E(f789(f789(f8(x69781,a863),x69782),x69783),f2(a863))+~P1(f789(f70(x69781),x69783))+P1(f789(f789(f342(x69781),f507(x69782,x69783,x69781)),x69783))
% 21.40/21.37 [7000]~P101(x70001)+~P1(f789(f789(f241(x70001),x70002),x70003))+P1(f789(f789(f241(f870(x70001,a856)),f789(f265(x70001),x70002)),f789(f265(x70001),x70003)))
% 21.40/21.37 [7001]~P99(x70011)+~P1(f789(f789(f240(x70011),x70012),x70013))+P1(f789(f789(f240(f870(x70011,a856)),f789(f301(x70011),x70012)),f789(f301(x70011),x70013)))
% 21.40/21.37 [7002]~P101(x70021)+~P1(f789(f789(f240(x70021),x70022),x70023))+P1(f789(f789(f240(f870(x70021,a856)),f789(f265(x70021),x70022)),f789(f265(x70021),x70023)))
% 21.40/21.37 [7003]~P99(x70031)+~P1(f789(f789(f240(x70031),x70033),x70032))+P1(f789(f789(f240(f870(x70031,a856)),f789(f266(x70031),x70032)),f789(f266(x70031),x70033)))
% 21.40/21.37 [7004]~P101(x70041)+~P1(f789(f789(f240(x70041),x70043),x70042))+P1(f789(f789(f240(f870(x70041,a856)),f789(f304(x70041),x70042)),f789(f304(x70041),x70043)))
% 21.40/21.37 [7009]~P9(x70091)+P1(f789(f789(f240(x70091),x70092),f52(x70091,x70093)))+P1(f789(f789(f342(x70091),f668(x70093,x70092,x70091)),x70093))
% 21.40/21.37 [7014]~P76(x70141)+P1(f789(f789(f241(x70141),f789(f789(f3(x70141),x70142),x70143)),f2(x70141)))+~P1(f789(f789(f241(x70141),x70142),x70143))
% 21.40/21.37 [7015]~P76(x70151)+P1(f789(f789(f240(x70151),f789(f789(f3(x70151),x70152),x70153)),f2(x70151)))+~P1(f789(f789(f240(x70151),x70152),x70153))
% 21.40/21.37 [7053]~P1(f789(f789(f287(a1),x70531),f59(a1,x70532,x70533)))+~P1(f789(f789(f287(a1),x70531),x70533))+P1(f789(f789(f287(a1),x70531),x70532))
% 21.40/21.37 [7060]P1(f789(x70601,x70602))+P1(f789(f789(f240(a863),f469(x70601,x70603)),x70603))+~P1(f789(f789(f342(a863),x70602),f303(a863,f2(a863),x70603)))
% 21.40/21.37 [7102]~E(f789(f789(f8(x71021,a863),x71022),x71023),f87(a863))+~P1(f789(f70(x71021),x71023))+P1(f789(f789(f342(x71021),f506(x71022,x71023,x71021)),x71023))
% 21.40/21.37 [7103]~P1(f789(x71031,x71033))+P1(f789(f789(f240(a863),f468(x71031,x71032)),x71032))+~P1(f789(f789(f342(a863),x71033),f303(a863,f2(a863),x71032)))
% 21.40/21.37 [7141]~P9(x71411)+P1(f789(f789(f342(x71411),f674(x71413,x71412,x71411)),x71412))+P1(f789(f789(f240(x71411),f51(x71411,x71412)),x71413))
% 21.40/21.37 [7171]~E(f789(f789(f8(x71711,a863),x71712),x71713),f789(a121,f2(a863)))+~P1(f789(f70(x71711),x71713))+P1(f789(f789(f342(x71711),f519(x71712,x71713,x71711)),x71713))
% 21.40/21.37 [7182]E(x71821,f2(a863))+P1(f789(x71822,f59(a863,x71823,x71821)))+P1(f789(f789(f241(a863),f824(x71821,x71823,x71822)),x71821))
% 21.40/21.37 [7306]~P1(f789(x73061,x73062))+P1(f789(x73061,f59(a863,x73062,x73063)))+P1(f789(f789(f241(a863),f824(x73063,x73062,x73061)),x73063))
% 21.40/21.37 [7433]E(x74331,f122(x74332))+~P1(f789(f789(f342(f864(x74332)),x74331),f156(x74332,x74333)))+P1(f789(f789(f342(x74332),f761(x74333,x74331,x74332)),x74333))
% 21.40/21.37 [7453]~P101(x74531)+E(f789(f789(f110(f870(x74531,a856)),f789(f789(f310(x74531),x74532),f184(f870(x74531,a856)))),f306(x74531,x74532,x74533)),f789(f302(x74531,x74532),x74533))+~P1(f789(f789(f241(x74531),x74532),x74533))
% 21.40/21.37 [7478]~P101(x74781)+E(f789(f789(f110(f870(x74781,a856)),f789(f789(f310(x74781),x74782),f184(f870(x74781,a856)))),f305(x74781,x74782,x74783)),f303(x74781,x74782,x74783))+~P1(f789(f789(f240(x74781),x74782),x74783))
% 21.40/21.37 [7590]~P101(x75901)+P1(f789(f789(f241(x75901),x75902),x75903))+~P1(f789(f789(f241(f870(x75901,a856)),f789(f265(x75901),x75902)),f789(f265(x75901),x75903)))
% 21.40/21.37 [7591]~P99(x75911)+P1(f789(f789(f240(x75911),x75912),x75913))+~P1(f789(f789(f240(f870(x75911,a856)),f789(f266(x75911),x75913)),f789(f266(x75911),x75912)))
% 21.40/21.37 [7592]~P101(x75921)+P1(f789(f789(f240(x75921),x75922),x75923))+~P1(f789(f789(f240(f870(x75921,a856)),f789(f304(x75921),x75923)),f789(f304(x75921),x75922)))
% 21.40/21.37 [7593]~P99(x75931)+P1(f789(f789(f240(x75931),x75932),x75933))+~P1(f789(f789(f240(f870(x75931,a856)),f789(f301(x75931),x75932)),f789(f301(x75931),x75933)))
% 21.40/21.37 [7594]~P101(x75941)+P1(f789(f789(f240(x75941),x75942),x75943))+~P1(f789(f789(f240(f870(x75941,a856)),f789(f265(x75941),x75942)),f789(f265(x75941),x75943)))
% 21.40/21.37 [7618]~P76(x76181)+~P1(f789(f789(f241(x76181),f789(f789(f3(x76181),x76182),x76183)),f2(x76181)))+P1(f789(f789(f241(x76181),x76182),x76183))
% 21.40/21.37 [7619]~P76(x76191)+~P1(f789(f789(f240(x76191),f789(f789(f3(x76191),x76192),x76193)),f2(x76191)))+P1(f789(f789(f240(x76191),x76192),x76193))
% 21.40/21.37 [7778]E(x77781,f2(a863))+~E(f789(f138(a863,a863,f89(a863),x77782),x77783),f2(a863))+~P1(f789(f789(f342(a863),x77781),f789(f163(a863),x77783)))
% 21.40/21.37 [7782]~P9(x77821)+~P1(f789(f789(f240(x77821),f674(x77823,x77822,x77821)),x77823))+P1(f789(f789(f240(x77821),f51(x77821,x77822)),x77823))
% 21.40/21.37 [7933]P1(f789(f789(f240(a1),f2(a1)),f818(x79331,x79332,x79333)))+P1(f789(f789(x79332,f789(f789(f50(a1),x79331),x79333)),f59(a1,x79331,x79333)))+~P1(f789(f789(f241(a1),f2(a1)),x79333))
% 21.40/21.37 [8024]E(x80241,x80242)+~E(f789(f185(f864(x80243)),x80241),f789(f185(f864(x80243)),x80242))+~P1(f789(f789(f259(x80243,x80243,a856),a338),f727(x80243,x80241,x80242)))
% 21.40/21.37 [8090]~P36(x80902,x80903)+E(x80901,f184(f870(x80902,a856)))+~P1(f789(f789(f240(f870(x80902,a856)),x80901),f789(f285(x80902,x80902,x80903),x80901)))
% 21.40/21.37 [8118]~P63(x81181)+~P1(f789(f789(f240(x81181),x81182),f789(f789(f89(x81181),x81183),f829(x81183,x81182,x81181))))+P1(f789(f789(f240(x81181),x81182),x81183))
% 21.40/21.37 [8154]P47(x81541,x81542,x81543)+P1(f789(f789(f342(x81541),f436(x81543,x81542,x81541)),x81542))+P1(f789(f789(f342(f869(x81541,x81541)),f437(x81543,x81542,x81541)),x81543))
% 21.40/21.37 [8176]P1(f789(f789(x81762,f789(f789(f50(a1),x81761),x81763)),f59(a1,x81761,x81763)))+~P1(f789(f789(f241(a1),f2(a1)),x81763))+P1(f789(f789(f241(a1),f818(x81761,x81762,x81763)),x81763))
% 21.40/21.37 [8200]E(f789(f311(a863,a863,f789(f789(f9(a863,a863,a863),f3(a863)),x82001)),f789(f302(a863,x82002),x82003)),f184(f870(a863,a856)))+P1(f789(f789(f241(a863),x82001),x82003))+P1(f789(f789(f241(a863),x82002),x82003))
% 21.40/21.37 [8303]E(f789(f311(a863,a863,f789(f789(f9(a863,a863,a863),f3(a863)),x83031)),f789(f302(a863,x83032),x83033)),f789(f789(f310(a863),f2(a863)),f184(f870(a863,a856))))+P1(f789(f789(f241(a863),x83031),x83033))+~P1(f789(f789(f241(a863),x83032),x83033))
% 21.40/21.37 [8318]~P101(x83181)+E(f145(x83181,x83181,f7(x83181),x83182,x83183),x83183)+~P1(f789(f789(f342(x83181),x83182),f789(f163(x83181),x83183)))
% 21.40/21.37 [8333]P29(x83331,x83331,x83332,x83333)+~P1(f789(f70(x83331),x83333))+~P1(f789(f789(f240(f870(x83331,a856)),x83333),f789(f311(x83331,x83331,x83332),x83333)))
% 21.40/21.37 [8360]E(f789(f789(f89(a1),f789(f789(f90(a1),x83601),f819(x83602,x83603,x83601))),f818(x83602,x83603,x83601)),x83602)+P1(f789(f789(x83603,f789(f789(f50(a1),x83602),x83601)),f59(a1,x83602,x83601)))+~P1(f789(f789(f241(a1),f2(a1)),x83601))
% 21.40/21.37 [8591]~P1(f789(f789(x85911,f819(x85912,x85911,x85913)),f818(x85912,x85911,x85913)))+P1(f789(f789(x85911,f789(f789(f50(a1),x85912),x85913)),f59(a1,x85912,x85913)))+~P1(f789(f789(f241(a1),f2(a1)),x85913))
% 21.40/21.37 [9383]~P1(f789(f70(x93831),x93832))+~P1(f789(f789(f342(x93831),x93833),x93832))+P1(f789(f789(f241(a863),f789(f49(x93831),f789(f789(f3(f870(x93831,a856)),x93832),f789(f789(f310(x93831),x93833),f184(f870(x93831,a856)))))),f789(f49(x93831),x93832)))
% 21.40/21.37 [9972]P47(x99721,x99722,x99723)+~P1(f789(f789(f259(x99721,x99721,a856),f789(f789(f9(x99721,f870(x99721,a856),f870(x99721,a856)),f789(f789(f10(f870(a856,a856),f870(f870(x99721,a856),f870(x99721,a856)),x99721),f10(a856,a856,x99721)),f789(f789(f10(a856,f870(a856,a856),x99721),a339),f789(f789(f9(x99721,f870(x99721,a856),a856),f342(x99721)),x99722)))),f789(f789(f9(x99721,f870(x99721,a856),a856),f342(x99721)),x99722))),f437(x99723,x99722,x99721)))+P1(f789(f789(f342(x99721),f436(x99723,x99722,x99721)),x99722))
% 21.40/21.37 [5401]~P113(x54012)+E(x54011,f2(x54012))+E(f789(f789(f291(x54012),x54013),f789(f88(x54012),x54011)),f789(f88(x54012),f789(f789(f291(x54012),x54013),x54011)))
% 21.40/21.37 [5532]~E(x55323,f184(f870(x55321,a856)))+~E(x55322,f184(f870(x55321,a856)))+E(f789(f789(f110(f870(x55321,a856)),x55322),x55323),f184(f870(x55321,a856)))
% 21.40/21.37 [5586]~E(x55863,f2(a863))+~P1(f789(x55861,f2(a863)))+P1(f789(x55861,f789(f789(f50(a863),x55862),x55863)))
% 21.40/21.37 [5587]~E(x55873,f2(a863))+~P1(f789(x55871,f2(a863)))+P1(f789(x55871,f789(f789(f50(a863),x55872),x55873)))
% 21.40/21.37 [5735]~P63(x57352)+E(x57351,f2(x57352))+E(f789(f789(f291(x57352),f789(f84(x57352),x57353)),f789(f84(x57352),x57351)),f789(f84(x57352),f789(f789(f291(x57352),x57353),x57351)))
% 21.40/21.37 [5829]~P70(x58291)+~E(x58292,f87(x58291))+P1(f789(f789(f287(x58291),x58292),f789(f789(f250(x58291),x58292),x58293)))
% 21.40/21.37 [5846]~P7(x58461)+E(f789(f789(f90(x58461),x58462),f789(f789(f50(x58461),x58463),x58462)),x58463)+~P1(f789(f789(f287(x58461),x58462),x58463))
% 21.40/21.37 [5899]~P1(f789(f70(x58991),x58993))+E(f789(f49(x58991),f789(f789(f310(x58991),x58992),x58993)),f789(a121,f789(f49(x58991),x58993)))+P1(f789(f789(f342(x58991),x58992),x58993))
% 21.40/21.37 [5900]~P1(f789(f70(x59001),x59003))+E(f789(f49(x59001),f789(f789(f310(x59001),x59002),x59003)),f789(a121,f789(f49(x59001),x59003)))+P1(f789(f789(f342(x59001),x59002),x59003))
% 21.40/21.37 [5976]~E(x59762,f2(a863))+P1(f789(x59761,f2(a863)))+~P1(f789(x59761,f789(f789(f50(a863),x59763),x59762)))
% 21.40/21.37 [5994]~P1(f789(f70(x59941),x59943))+E(f789(f49(x59941),f789(f789(f310(x59941),x59942),x59943)),f789(f49(x59941),x59943))+~P1(f789(f789(f342(x59941),x59942),x59943))
% 21.40/21.37 [6029]~P1(f789(f70(x60291),x60293))+E(f789(f49(x60291),f789(f789(f310(x60291),x60292),x60293)),f789(f789(f89(a863),f87(a863)),f789(f49(x60291),x60293)))+P1(f789(f789(f342(x60291),x60292),x60293))
% 21.40/21.37 [6036]~P8(x60361)+E(f789(f789(f50(x60361),x60362),f789(f88(x60361),x60363)),f789(f88(x60361),f789(f789(f50(x60361),x60362),x60363)))+~P1(f789(f789(f287(x60361),x60363),x60362))
% 21.40/21.37 [6149]E(f789(f789(f89(a863),x61491),f820(x61491,x61492,x61493)),x61492)+~P1(f789(x61493,f2(a863)))+P1(f789(x61493,f789(f789(f3(a863),x61492),x61491)))
% 21.40/21.37 [6150]E(f789(f789(f89(a863),x61501),f828(x61501,x61502,x61503)),x61502)+~P1(f789(x61503,f2(a863)))+P1(f789(x61503,f789(f789(f3(a863),x61502),x61501)))
% 21.40/21.37 [6174]~P8(x61741)+E(f789(f789(f50(x61741),f789(f88(x61741),x61742)),x61743),f789(f88(x61741),f789(f789(f50(x61741),x61742),x61743)))+~P1(f789(f789(f287(x61741),x61743),x61742))
% 21.40/21.37 [6197]~P9(x61971)+~P1(f789(f70(x61971),x61973))+E(f789(f789(f73(x61971,x61971,f110(x61971)),x61972),x61973),f789(f789(f110(x61971),x61972),f51(x61971,x61973)))
% 21.40/21.37 [6198]~P9(x61981)+~P1(f789(f70(x61981),x61983))+E(f789(f789(f73(x61981,x61981,f111(x61981)),x61982),x61983),f789(f789(f111(x61981),x61982),f52(x61981,x61983)))
% 21.40/21.37 [6204]~P88(x62041)+~E(f789(f113(x62041),x62042),f789(f113(x62041),x62043))+P33(x62041,f789(f113(x62041),f789(f789(f89(a1),x62042),f789(f88(a1),x62043))))
% 21.40/21.37 [6211]~P120(x62111)+E(f789(f789(f3(x62111),f789(f109(x62111),x62112)),f789(f109(x62111),x62113)),f789(f109(x62111),f789(f789(f3(a863),x62112),x62113)))+~P1(f789(f789(f240(a863),x62113),x62112))
% 21.40/21.37 [6217]~P104(x62171)+~P1(f789(f789(f287(x62171),x62172),x62173))+P1(f789(f789(f287(x62171),f789(f88(x62171),x62172)),x62173))
% 21.40/21.37 [6218]~P110(x62181)+~P1(f789(f789(f287(x62181),x62182),x62183))+P1(f789(f789(f287(x62181),f789(f84(x62181),x62182)),x62183))
% 21.40/21.37 [6301]E(f789(f789(f89(a863),x63011),f820(x63011,x63012,x63013)),x63012)+P1(f789(f789(f241(a863),x63012),x63011))+P1(f789(x63013,f789(f789(f3(a863),x63012),x63011)))
% 21.40/21.37 [6302]E(f789(f789(f89(a863),x63021),f828(x63021,x63022,x63023)),x63022)+P1(f789(f789(f241(a863),x63022),x63021))+P1(f789(x63023,f789(f789(f3(a863),x63022),x63021)))
% 21.40/21.37 [6320]~P110(x63201)+E(f789(f789(f90(x63201),f789(f84(x63201),x63202)),x63203),f789(f84(x63201),f789(f789(f90(x63201),x63202),x63203)))+~P1(f789(f789(f240(x63201),f2(x63201)),x63203))
% 21.40/21.37 [6321]~P62(x63211)+E(f789(f789(f291(x63211),f789(f84(x63211),x63212)),x63213),f789(f84(x63211),f789(f789(f291(x63211),x63212),x63213)))+~P1(f789(f789(f241(x63211),f2(x63211)),x63213))
% 21.40/21.37 [6330]~P95(x63301)+~P1(f789(f70(x63301),x63303))+E(f789(f789(f73(x63301,x63301,f111(x63301)),x63302),x63303),f12(x63301,f789(f789(f310(x63301),x63302),x63303)))
% 21.40/21.37 [6331]~P95(x63311)+~P1(f789(f70(x63311),x63313))+E(f789(f789(f73(x63311,x63311,f110(x63311)),x63312),x63313),f15(x63311,f789(f789(f310(x63311),x63312),x63313)))
% 21.40/21.37 [6332]~P101(x63321)+~P1(f789(f70(x63321),x63323))+E(f789(f789(f73(x63321,x63321,f239(x63321)),x63322),x63323),f16(x63321,f789(f789(f310(x63321),x63322),x63323)))
% 21.40/21.37 [6333]~P101(x63331)+~P1(f789(f70(x63331),x63333))+E(f789(f789(f73(x63331,x63331,f244(x63331)),x63332),x63333),f17(x63331,f789(f789(f310(x63331),x63332),x63333)))
% 21.40/21.37 [6377]E(x63771,f122(x63772))+~E(f168(x63772,x63773),f122(f864(x63772)))+~P1(f789(f789(f342(f864(x63772)),x63771),f789(f163(f864(x63772)),x63773)))
% 21.40/21.37 [6396]~P70(x63961)+~P1(f789(f789(f241(a863),f2(a863)),x63963))+P1(f789(f789(f287(x63961),x63962),f789(f789(f250(x63961),x63962),x63963)))
% 21.40/21.37 [6427]~P1(f789(f134(x64271),x64273))+P1(f789(f789(f342(x64271),x64272),f789(f163(x64271),x64273)))+P1(f789(f134(x64271),f789(f789(f146(x64271),x64272),x64273)))
% 21.40/21.37 [6438]~P91(x64381)+~P1(f789(f70(x64381),x64383))+E(f789(f72(x64381,f90(x64381)),f789(f789(f310(x64381),x64382),x64383)),f789(f789(f73(x64381,x64381,f90(x64381)),x64382),x64383))
% 21.40/21.37 [6459]~P101(x64591)+~P1(f789(f70(x64591),x64593))+E(f13(x64591,f239(x64591),f789(f789(f310(x64591),x64592),x64593)),f789(f789(f73(x64591,x64591,f239(x64591)),x64592),x64593))
% 21.40/21.37 [6460]~P101(x64601)+~P1(f789(f70(x64601),x64603))+E(f14(x64601,f244(x64601),f789(f789(f310(x64601),x64602),x64603)),f789(f789(f73(x64601,x64601,f244(x64601)),x64602),x64603))
% 21.40/21.37 [6461]P1(f789(x64611,f2(a863)))+~P1(f789(f789(f241(a863),x64612),x64613))+~P1(f789(x64611,f789(f789(f3(a863),x64612),x64613)))
% 21.40/21.37 [6462]P1(f789(x64621,f2(a863)))+~P1(f789(f789(f241(a863),x64622),x64623))+~P1(f789(x64621,f789(f789(f3(a863),x64622),x64623)))
% 21.40/21.37 [6481]~P110(x64811)+P1(f789(f789(f241(x64811),x64812),x64813))+~P1(f789(f789(f241(x64811),f789(f84(x64811),x64812)),x64813))
% 21.40/21.37 [6482]~P80(x64821)+P1(f789(f789(f240(x64821),x64822),x64823))+~P1(f789(f789(f240(x64821),f789(f84(x64821),x64822)),x64823))
% 21.40/21.37 [6483]~P80(x64831)+P1(f789(f789(f240(x64831),x64832),x64833))+~P1(f789(f789(f240(x64831),f789(f84(x64831),x64832)),x64833))
% 21.40/21.37 [6484]~P110(x64841)+P1(f789(f789(f287(x64841),x64842),x64843))+~P1(f789(f789(f287(x64841),f789(f84(x64841),x64842)),x64843))
% 21.40/21.37 [6485]~P104(x64851)+P1(f789(f789(f287(x64851),x64852),x64853))+~P1(f789(f789(f287(x64851),f789(f88(x64851),x64852)),x64853))
% 21.40/21.37 [6504]E(x65041,f122(x65042))+E(f789(f137(x65042),f789(f789(f135(x65042),x65043),x65041)),f789(f789(f159(x65042),x65041),x65043))+~P1(f789(f789(f241(a863),x65043),f789(f185(f864(x65042)),x65041)))
% 21.40/21.37 [6557]~P1(f789(x65571,x65573))+P1(f789(x65571,f508(x65571,x65572)))+~P1(f789(f789(f342(a863),x65573),f789(f302(a863,f2(a863)),x65572)))
% 21.40/21.37 [6580]P1(f789(x65801,x65802))+~P1(f789(f789(f241(a863),x65802),x65803))+P1(f789(f789(f342(a863),f471(x65801,x65803)),f789(f302(a863,f2(a863)),x65803)))
% 21.40/21.37 [6595]~P117(x65951)+~P1(f789(f789(f241(x65951),f2(x65951)),x65952))+P1(f789(f789(f241(x65951),f2(x65951)),f789(f789(f250(x65951),x65952),x65953)))
% 21.40/21.37 [6597]~P117(x65971)+~P1(f789(f789(f240(x65971),f2(x65971)),x65972))+P1(f789(f789(f240(x65971),f2(x65971)),f789(f789(f250(x65971),x65972),x65973)))
% 21.40/21.37 [6598]~P117(x65981)+~P1(f789(f789(f240(x65981),f87(x65981)),x65982))+P1(f789(f789(f240(x65981),f87(x65981)),f789(f789(f250(x65981),x65982),x65983)))
% 21.40/21.37 [6622]~P1(f789(x66221,x66223))+~P1(f789(f789(f241(a863),x66223),x66222))+P1(f789(f789(f342(a863),f466(x66221,x66222)),f789(f302(a863,f2(a863)),x66222)))
% 21.40/21.37 [6626]P1(f789(f70(x66261),x66262))+~P1(f789(f70(x66261),x66263))+~P1(f789(f789(f240(f870(x66261,a856)),x66262),x66263))
% 21.40/21.37 [6627]P1(f789(f70(x66271),x66272))+~P1(f789(f70(x66271),x66273))+~P1(f789(f789(f240(f870(x66271,a856)),x66272),x66273))
% 21.40/21.37 [6636]~P1(f789(f789(f287(a863),x66361),x66362))+~P1(f789(f789(f287(a863),x66361),x66363))+P1(f789(f789(f287(a863),x66361),f789(f789(f3(a863),x66362),x66363)))
% 21.40/21.37 [6637]P1(f789(x66371,x66372))+~P1(f789(x66371,f472(x66371,x66373)))+~P1(f789(f789(f342(a863),x66372),f789(f302(a863,f2(a863)),x66373)))
% 21.40/21.37 [6650]E(x66501,f2(a863))+P1(f789(x66502,f815(x66501,x66503,x66502)))+~P1(f789(x66502,f789(f789(f50(a863),x66503),x66501)))
% 21.40/21.37 [6659]~P118(x66592)+E(x66591,f2(x66592))+~E(f789(f789(f89(x66592),f789(f789(f90(x66592),x66593),x66593)),f789(f789(f90(x66592),x66591),x66591)),f2(x66592))
% 21.40/21.37 [6660]~P118(x66602)+E(x66601,f2(x66602))+~E(f789(f789(f89(x66602),f789(f789(f90(x66602),x66601),x66601)),f789(f789(f90(x66602),x66603),x66603)),f2(x66602))
% 21.40/21.37 [6707]E(x67071,f2(a863))+~P1(f789(x67072,f823(x67071,x67073,x67072)))+P1(f789(x67072,f789(f789(f50(a863),x67073),x67071)))
% 21.40/21.37 [6712]~P101(x67121)+~P18(x67121,x67123)+P18(x67121,f789(f789(f144(x67121,x67121,f7(x67121)),x67122),x67123))
% 21.40/21.37 [6756]P1(f789(x67561,f815(x67562,x67563,x67561)))+P1(f789(x67561,f2(a863)))+~P1(f789(x67561,f789(f789(f50(a863),x67563),x67562)))
% 21.40/21.37 [6762]~P88(x67621)+E(f789(f113(x67621),x67622),f789(f113(x67621),x67623))+~P33(x67621,f789(f113(x67621),f789(f789(f89(a1),x67622),f789(f88(a1),x67623))))
% 21.40/21.37 [6834]E(x68341,f2(a1))+E(x68342,f2(a1))+~P1(f789(f63(x68342,x68342),f789(f789(f249(a1,a1),x68343),x68341)))
% 21.40/21.37 [6835]E(x68351,f87(a1))+E(x68352,f2(a1))+~P1(f789(f63(x68352,x68352),f789(f789(f249(a1,a1),x68351),x68353)))
% 21.40/21.37 [6849]P1(f789(x68491,x68492))+P1(f789(f789(f241(a863),f472(x68491,x68493)),x68493))+~P1(f789(f789(f342(a863),x68492),f789(f302(a863,f2(a863)),x68493)))
% 21.40/21.37 [6874]~P1(f789(x68741,f823(x68743,x68742,x68741)))+~P1(f789(x68741,f2(a863)))+P1(f789(x68741,f789(f789(f50(a863),x68742),x68743)))
% 21.40/21.37 [6875]~P1(f789(x68751,f820(x68753,x68752,x68751)))+~P1(f789(x68751,f2(a863)))+P1(f789(x68751,f789(f789(f3(a863),x68752),x68753)))
% 21.40/21.37 [6876]~P1(f789(x68761,f828(x68763,x68762,x68761)))+~P1(f789(x68761,f2(a863)))+P1(f789(x68761,f789(f789(f3(a863),x68762),x68763)))
% 21.40/21.37 [6896]~P1(f789(x68961,x68963))+P1(f789(f789(f241(a863),f508(x68961,x68962)),x68962))+~P1(f789(f789(f342(a863),x68963),f789(f302(a863,f2(a863)),x68962)))
% 21.40/21.37 [6897]E(f789(f789(f3(a863),f789(f789(f3(a863),x68971),x68972)),f789(f789(f3(a863),x68973),x68972)),f789(f789(f3(a863),x68971),x68973))+~P1(f789(f789(f240(a863),x68972),x68971))+~P1(f789(f789(f240(a863),x68972),x68973))
% 21.40/21.37 [6929]~P76(x69291)+~P1(f789(f789(f241(x69291),f789(f88(x69291),x69293)),x69292))+P1(f789(f789(f241(x69291),f789(f88(x69291),x69292)),x69293))
% 21.40/21.37 [6930]~P76(x69301)+~P1(f789(f789(f241(x69301),f789(f88(x69301),x69303)),x69302))+P1(f789(f789(f241(x69301),f789(f88(x69301),x69302)),x69303))
% 21.40/21.37 [6931]~P110(x69311)+~P1(f789(f789(f241(x69311),f789(f84(x69311),x69312)),x69313))+P1(f789(f789(f241(x69311),f789(f88(x69311),x69312)),x69313))
% 21.40/21.37 [6932]~P76(x69321)+~P1(f789(f789(f240(x69321),f789(f88(x69321),x69323)),x69322))+P1(f789(f789(f240(x69321),f789(f88(x69321),x69322)),x69323))
% 21.40/21.37 [6933]~P76(x69331)+~P1(f789(f789(f240(x69331),f789(f88(x69331),x69333)),x69332))+P1(f789(f789(f240(x69331),f789(f88(x69331),x69332)),x69333))
% 21.40/21.37 [6934]~P80(x69341)+~P1(f789(f789(f240(x69341),f789(f84(x69341),x69342)),x69343))+P1(f789(f789(f240(x69341),f789(f88(x69341),x69342)),x69343))
% 21.40/21.37 [6935]~P80(x69351)+~P1(f789(f789(f240(x69351),f789(f84(x69351),x69352)),x69353))+P1(f789(f789(f240(x69351),f789(f88(x69351),x69352)),x69353))
% 21.40/21.37 [6938]~P1(f789(f789(f287(a1),x69381),x69383))+P1(f789(f789(f287(a1),x69381),x69382))+~P1(f789(f789(f287(a1),x69381),f789(f789(f3(a1),x69382),x69383)))
% 21.40/21.37 [6971]~P1(f789(x69713,f820(x69712,x69711,x69713)))+P1(f789(f789(f241(a863),x69711),x69712))+P1(f789(x69713,f789(f789(f3(a863),x69711),x69712)))
% 21.40/21.37 [6972]~P1(f789(x69723,f828(x69722,x69721,x69723)))+P1(f789(f789(f241(a863),x69721),x69722))+P1(f789(x69723,f789(f789(f3(a863),x69721),x69722)))
% 21.40/21.37 [7018]~E(f681(x70183,x70182,x70181),f682(x70183,x70182,x70181))+E(f789(f789(f111(f870(x70181,a856)),x70182),f51(f870(x70181,a856),x70183)),f184(f870(x70181,a856)))+P1(f789(f789(f342(f870(x70181,a856)),x70182),x70183))
% 21.40/21.37 [7027]~P1(f789(f70(x70271),x70273))+P1(f789(f70(x70271),f52(f870(x70271,a856),x70272)))+~P1(f789(f789(f342(f870(x70271,a856)),x70273),x70272))
% 21.40/21.37 [7089]~P101(x70891)+E(f789(f789(f110(f870(x70891,a856)),f789(f302(x70891,x70892),x70893)),f789(f789(f310(x70891),x70893),f184(f870(x70891,a856)))),f303(x70891,x70892,x70893))+~P1(f789(f789(f240(x70891),x70892),x70893))
% 21.40/21.37 [7092]E(x70921,f2(a863))+P1(f789(f789(f241(a863),f825(x70921,x70923,x70922)),x70921))+P1(f789(x70922,f789(f789(f50(a863),x70923),x70921)))
% 21.40/21.37 [7125]E(x71251,x71252)+~P1(f789(f789(f240(f870(x71253,a856)),x71251),x71252))+P1(f789(f789(f241(f870(x71253,a856)),x71251),x71252))
% 21.40/21.37 [7126]E(x71261,x71262)+~P1(f789(f789(f240(f870(x71263,a856)),x71261),x71262))+P1(f789(f789(f241(f870(x71263,a856)),x71261),x71262))
% 21.40/21.37 [7138]E(x71381,x71382)+~E(f789(f185(f864(x71383)),x71381),f789(f185(f864(x71383)),x71382))+P1(f789(f789(f241(a863),f737(x71383,x71381,x71382)),f789(f185(f864(x71383)),x71382)))
% 21.40/21.37 [7183]P12(x71831,x71832,x71833)+~E(f789(f269(x71831,x71831),x71833),x71832)+~E(f789(f789(f289(x71831,x71831,x71831),f789(f286(x71831,x71831),x71833)),x71833),x71833)
% 21.40/21.37 [7265]E(x72651,f2(a1))+~P1(f789(f789(f287(a1),x72652),x72653))+P1(f789(f789(f287(a1),f789(f789(f90(a1),x72651),x72652)),f789(f789(f90(a1),x72651),x72653)))
% 21.40/21.37 [7268]~P1(f789(x72681,f2(a863)))+P1(f789(f789(f241(a863),f825(x72683,x72682,x72681)),x72683))+P1(f789(x72681,f789(f789(f50(a863),x72682),x72683)))
% 21.40/21.37 [7281]~P101(x72811)+E(f789(f789(f110(f870(x72811,a856)),f306(x72811,x72812,x72813)),f789(f789(f310(x72811),x72813),f184(f870(x72811,a856)))),f305(x72811,x72812,x72813))+~P1(f789(f789(f241(x72811),x72812),x72813))
% 21.40/21.37 [7386]~P1(f789(f70(x73861),x73863))+P1(f789(f789(f241(a863),f789(f49(x73861),x73862)),f789(f49(x73861),x73863)))+~P1(f789(f789(f241(f870(x73861,a856)),x73862),x73863))
% 21.40/21.37 [7387]~P1(f789(f70(x73871),x73873))+P1(f789(f789(f240(a863),f789(f49(x73871),x73872)),f789(f49(x73871),x73873)))+~P1(f789(f789(f240(f870(x73871,a856)),x73872),x73873))
% 21.40/21.37 [7428]~P1(f789(x74283,x74282))+P1(f789(f789(f191(x74281),x74282),f434(x74282,x74281,x74283)))+~P1(f789(f789(f191(f37(x74283,x74281)),x74282),x74282))
% 21.40/21.37 [7525]E(x75251,x75252)+~P1(f789(f789(f240(f870(x75253,a856)),x75252),x75251))+~P1(f789(f789(f240(f870(x75253,a856)),x75251),x75252))
% 21.40/21.37 [7526]E(x75261,x75262)+~P1(f789(f789(f240(f870(x75263,a856)),x75262),x75261))+~P1(f789(f789(f240(f870(x75263,a856)),x75261),x75262))
% 21.40/21.37 [7529]~P101(x75291)+P18(x75291,x75292)+~P18(x75291,f789(f789(f144(x75291,x75291,f7(x75291)),x75293),x75292))
% 21.40/21.37 [7598]~P1(f789(f789(f241(a863),x75983),x75982))+~P1(f789(f789(f241(a863),x75983),x75981))+P1(f789(f789(f241(a863),f789(f789(f3(a863),x75981),x75982)),f789(f789(f3(a863),x75981),x75983)))
% 21.40/21.37 [7599]~P1(f789(f789(f241(a863),x75991),x75993))+~P1(f789(f789(f240(a863),x75992),x75991))+P1(f789(f789(f241(a863),f789(f789(f3(a863),x75991),x75992)),f789(f789(f3(a863),x75993),x75992)))
% 21.40/21.37 [7616]~P1(f789(f789(f241(a1),x76162),f2(a1)))+~P1(f789(f789(f240(a1),x76163),x76161))+P1(f789(f789(f240(a1),f789(f789(f50(a1),x76161),x76162)),f789(f789(f50(a1),x76163),x76162)))
% 21.40/21.37 [7633]~P1(f789(f789(f241(a863),f2(a863)),x76331))+~P1(f789(f789(f241(a863),x76332),x76333))+P1(f789(f789(f241(a863),f789(f789(f90(a863),x76331),x76332)),f789(f789(f90(a863),x76331),x76333)))
% 21.40/21.37 [7634]~P1(f789(f789(f241(a863),f2(a863)),x76341))+~P1(f789(f789(f241(a863),x76342),x76343))+P1(f789(f789(f241(a863),f789(f789(f90(a863),x76341),x76342)),f789(f789(f90(a863),x76341),x76343)))
% 21.40/21.37 [7635]~P1(f789(f789(f241(a863),f2(a863)),x76352))+~P1(f789(f789(f241(a863),x76351),x76353))+P1(f789(f789(f241(a863),f789(f789(f90(a863),x76351),x76352)),f789(f789(f90(a863),x76353),x76352)))
% 21.40/21.37 [7636]~P1(f789(f789(f241(a863),f2(a863)),x76362))+~P1(f789(f789(f241(a863),x76361),x76363))+P1(f789(f789(f241(a863),f789(f789(f90(a863),x76361),x76362)),f789(f789(f90(a863),x76363),x76362)))
% 21.40/21.37 [7637]~P1(f789(f789(f241(a863),f2(a863)),x76371))+~P1(f789(f789(f241(a863),x76372),x76373))+P1(f789(f789(f241(a863),f789(f789(f90(a863),x76371),x76372)),f789(f789(f90(a863),x76371),x76373)))
% 21.40/21.37 [7638]~P1(f789(f789(f241(a1),f2(a1)),x76381))+~P1(f789(f789(f241(a1),x76382),x76383))+P1(f789(f789(f241(a1),f789(f789(f90(a1),x76381),x76382)),f789(f789(f90(a1),x76381),x76383)))
% 21.40/21.37 [7639]~P1(f789(f789(f241(a863),f2(a863)),x76391))+~P1(f789(f789(f240(a863),x76392),x76393))+P1(f789(f789(f240(a863),f789(f789(f90(a863),x76391),x76392)),f789(f789(f90(a863),x76391),x76393)))
% 21.40/21.37 [7640]~P1(f789(f789(f241(a863),f2(a863)),x76403))+~P1(f789(f789(f240(a863),x76403),x76402))+P1(f789(f789(f240(a863),f789(f789(f50(a863),x76401),x76402)),f789(f789(f50(a863),x76401),x76403)))
% 21.40/21.37 [7641]~P1(f789(f789(f241(a1),f2(a1)),x76412))+~P1(f789(f789(f240(a1),x76411),x76413))+P1(f789(f789(f240(a1),f789(f789(f50(a1),x76411),x76412)),f789(f789(f50(a1),x76413),x76412)))
% 21.40/21.37 [7642]~P1(f789(f789(f241(a863),f2(a863)),x76421))+~P1(f789(f789(f287(a863),x76422),x76423))+P1(f789(f789(f287(a863),f789(f789(f90(a863),x76421),x76422)),f789(f789(f90(a863),x76421),x76423)))
% 21.40/21.37 [7690]E(x76901,f2(a863))+E(f789(f789(f89(a863),f789(f789(f90(a863),x76901),f823(x76901,x76902,x76903))),f825(x76901,x76902,x76903)),x76902)+P1(f789(x76903,f789(f789(f50(a863),x76902),x76901)))
% 21.40/21.37 [7747]E(f789(f789(f89(a863),f789(f789(f90(a863),x77471),f823(x77471,x77472,x77473))),f825(x77471,x77472,x77473)),x77472)+~P1(f789(x77473,f2(a863)))+P1(f789(x77473,f789(f789(f50(a863),x77472),x77471)))
% 21.40/21.37 [7763]~P1(f789(f70(x77631),x77633))+P1(f789(f789(f342(x77631),f412(x77632,x77633,x77631)),x77633))+P1(f789(f789(f241(a863),f2(a863)),f789(f789(f11(x77631,a863),x77632),x77633)))
% 21.40/21.37 [7764]~P1(f789(f70(x77641),x77643))+P1(f789(f789(f342(x77641),f566(x77642,x77643,x77641)),x77643))+P1(f789(f789(f241(a863),f2(a863)),f789(f789(f11(x77641,a863),x77642),x77643)))
% 21.40/21.37 [7869]E(x78691,f2(a863))+P1(f789(f789(f287(a863),x78692),x78693))+~P1(f789(f789(f287(a863),f789(f789(f90(a863),x78691),x78692)),f789(f789(f90(a863),x78691),x78693)))
% 21.40/21.37 [7870]E(x78701,f2(a1))+P1(f789(f789(f287(a1),x78702),x78703))+~P1(f789(f789(f287(a1),f789(f789(f90(a1),x78701),x78702)),f789(f789(f90(a1),x78701),x78703)))
% 21.40/21.37 [7871]E(x78711,f2(a1))+P1(f789(f789(f287(a1),x78712),x78713))+~P1(f789(f789(f287(a1),f789(f789(f90(a1),x78711),x78712)),f789(f789(f90(a1),x78711),x78713)))
% 21.40/21.37 [8055]E(x80551,f184(f870(x80552,a856)))+E(x80551,f789(f789(f310(x80552),x80553),f184(f870(x80552,a856))))+~P1(f789(f789(f240(f870(x80552,a856)),x80551),f789(f789(f310(x80552),x80553),f184(f870(x80552,a856)))))
% 21.40/21.37 [8091]~P1(f789(f789(f241(a863),f2(a863)),x80913))+P1(f789(f789(f241(a863),x80911),x80912))+~P1(f789(f789(f241(a863),f789(f789(f90(a863),x80913),x80911)),f789(f789(f90(a863),x80913),x80912)))
% 21.40/21.37 [8092]~P1(f789(f789(f241(a863),f2(a863)),x80923))+P1(f789(f789(f241(a863),x80921),x80922))+~P1(f789(f789(f241(a863),f789(f789(f250(a863),x80923),x80921)),f789(f789(f250(a863),x80923),x80922)))
% 21.40/21.37 [8093]~P1(f789(f789(f241(a863),f2(a863)),x80933))+P1(f789(f789(f240(a863),x80931),x80932))+~P1(f789(f789(f240(a863),f789(f789(f90(a863),x80933),x80931)),f789(f789(f90(a863),x80933),x80932)))
% 21.40/21.37 [8094]~P1(f789(f789(f241(a863),f2(a863)),x80943))+P1(f789(f789(f240(a863),x80941),x80942))+~P1(f789(f789(f240(a863),f789(f789(f90(a863),x80943),x80941)),f789(f789(f90(a863),x80943),x80942)))
% 21.40/21.37 [8095]~P1(f789(f789(f241(a863),f87(a863)),x80953))+P1(f789(f789(f240(a863),x80951),x80952))+~P1(f789(f789(f287(a863),f789(f789(f250(a863),x80953),x80951)),f789(f789(f250(a863),x80953),x80952)))
% 21.40/21.37 [8096]~P1(f789(f789(f241(a863),f2(a863)),x80963))+P1(f789(f789(f240(a863),x80961),x80962))+~P1(f789(f789(f240(a863),f789(f789(f90(a863),x80961),x80963)),f789(f789(f90(a863),x80962),x80963)))
% 21.40/21.37 [8097]~P1(f789(f789(f241(a863),f2(a863)),x80973))+P1(f789(f789(f287(a863),x80971),x80972))+~P1(f789(f789(f287(a863),f789(f789(f90(a863),x80973),x80971)),f789(f789(f90(a863),x80973),x80972)))
% 21.40/21.37 [8098]~P1(f789(f789(f241(a863),f2(a863)),x80983))+P1(f789(f789(f287(a863),x80981),x80982))+~P1(f789(f789(f287(a863),f789(f789(f90(a863),x80983),x80981)),f789(f789(f90(a863),x80983),x80982)))
% 21.40/21.37 [8126]~P1(f789(x81261,x81263))+P1(f789(f789(f191(f37(x81261,x81262)),f434(x81263,x81262,x81261)),x81263))+~P1(f789(f789(f191(f37(x81261,x81262)),x81263),x81263))
% 21.40/21.37 [8134]~E(f789(f789(f111(f870(x81341,a856)),f682(x81343,x81342,x81341)),f681(x81343,x81342,x81341)),f184(f870(x81341,a856)))+E(f789(f789(f111(f870(x81341,a856)),x81342),f51(f870(x81341,a856),x81343)),f184(f870(x81341,a856)))+P1(f789(f789(f342(f870(x81341,a856)),x81342),x81343))
% 21.40/21.37 [8148]E(x81481,f122(x81482))+~E(f789(f138(f864(x81482),f864(x81482),f132(x81482),f122(x81482)),x81483),f122(x81482))+~P1(f789(f789(f342(f864(x81482)),x81481),f789(f163(f864(x81482)),x81483)))
% 21.40/21.37 [8149]E(x81491,f122(x81492))+~E(f789(f138(f864(x81492),f864(x81492),f132(x81492),f122(x81492)),x81493),f122(x81492))+~P1(f789(f789(f342(f864(x81492)),x81491),f789(f163(f864(x81492)),x81493)))
% 21.40/21.37 [8205]E(x82051,f184(f870(f870(x82052,a856),a856)))+P1(f789(f789(f342(f870(x82052,a856)),f679(x82053,x82051,x82052)),x82051))+P1(f789(f789(f240(f870(x82052,a856)),f52(f870(x82052,a856),x82051)),x82053))
% 21.40/21.37 [8211]~P4(x82111)+~P69(x82111)+E(f789(f789(f11(a1,x82111),f789(f789(f10(a863,x82111,a1),x82112),a114)),f789(f311(a863,a1,f109(a1)),x82113)),f789(f789(f11(a863,x82111),x82112),x82113))
% 21.40/21.37 [8212]~P4(x82121)+~P69(x82121)+E(f789(f789(f8(a1,x82121),f789(f789(f10(a863,x82121,a1),x82122),a114)),f789(f311(a863,a1,f109(a1)),x82123)),f789(f789(f8(a863,x82121),x82122),x82123))
% 21.40/21.37 [8249]~P1(f789(f70(x82491),x82493))+~P1(f789(f789(f241(a863),f2(a863)),f789(x82492,f412(x82492,x82493,x82491))))+P1(f789(f789(f241(a863),f2(a863)),f789(f789(f11(x82491,a863),x82492),x82493)))
% 21.40/21.37 [8250]~P1(f789(f70(x82501),x82503))+~P1(f789(f789(f241(a863),f2(a863)),f789(x82502,f566(x82502,x82503,x82501))))+P1(f789(f789(f241(a863),f2(a863)),f789(f789(f11(x82501,a863),x82502),x82503)))
% 21.40/21.37 [8286]~P61(x82862)+E(x82861,f87(x82862))+E(f789(f789(f291(x82862),f789(f789(f3(x82862),f789(f789(f250(x82862),x82861),x82863)),f87(x82862))),f789(f789(f3(x82862),x82861),f87(x82862))),f789(f789(f8(a863,x82862),f789(f250(x82862),x82861)),f789(f302(a863,f2(a863)),x82863)))
% 21.40/21.37 [8345]E(x83451,f2(a863))+~P1(f789(x83453,f789(f789(f50(a863),x83452),x83451)))+P1(f789(f789(f241(a863),x83452),f789(f789(f90(a863),x83451),f789(a121,f815(x83451,x83452,x83453)))))
% 21.40/21.37 [8366]P1(f789(x83661,f2(a863)))+~P1(f789(x83661,f789(f789(f50(a863),x83662),x83663)))+P1(f789(f789(f241(a863),x83662),f789(f789(f90(a863),x83663),f789(a121,f815(x83663,x83662,x83661)))))
% 21.40/21.37 [8405]E(x84051,f2(a863))+~P1(f789(x84053,f789(f789(f50(a863),x84052),x84051)))+P1(f789(f789(f240(a863),f789(f789(f90(a863),x84051),f815(x84051,x84052,x84053))),x84052))
% 21.40/21.37 [8442]P1(f789(x84421,f2(a863)))+~P1(f789(x84421,f789(f789(f50(a863),x84423),x84422)))+P1(f789(f789(f240(a863),f789(f789(f90(a863),x84422),f815(x84422,x84423,x84421))),x84423))
% 21.40/21.37 [8445]~P101(x84451)+E(f789(f789(f144(x84451,x84451,f7(x84451)),x84452),x84453),f145(x84451,x84451,f7(x84451),x84452,x84453))+P1(f789(f789(f342(x84451),x84452),f789(f163(x84451),x84453)))
% 21.40/21.37 [8484]~E(f789(x84843,f618(x84842,x84843,x84841)),f789(x84843,f620(x84842,x84843,x84841)))+~P58(x84841,f789(x84843,f619(x84842,x84843,x84841)))+P58(x84841,f789(f789(f53(x84842,f870(x84841,f870(x84841,a856))),f247(f870(x84842,a856))),x84843))
% 21.40/21.37 [8492]E(x84921,f184(f870(f870(x84922,a856),a856)))+~P1(f789(f789(f240(f870(x84922,a856)),f679(x84923,x84921,x84922)),x84923))+P1(f789(f789(f240(f870(x84922,a856)),f52(f870(x84922,a856),x84921)),x84923))
% 21.40/21.37 [8551]~P63(x85511)+~P1(f789(f789(f241(x85511),x85512),x85513))+P1(f789(f789(f241(x85511),x85512),f789(f789(f291(x85511),f789(f789(f89(x85511),x85512),x85513)),f789(f789(f89(x85511),f87(x85511)),f87(x85511)))))
% 21.40/21.37 [8594]~P1(f789(f789(x85941,f844(x85941,x85943,x85942)),f845(x85941,x85943,x85942)))+P1(f789(f789(x85941,x85942),x85943))+~P1(f789(f329(f869(a1,a1),a66),f789(f789(f249(a1,a1),x85942),x85943)))
% 21.40/21.37 [8595]~P1(f789(f789(x85951,f846(x85951,x85953,x85952)),f847(x85951,x85953,x85952)))+P1(f789(f789(x85951,x85952),x85953))+~P1(f789(f329(f869(a1,a1),a69),f789(f789(f249(a1,a1),x85952),x85953)))
% 21.40/21.37 [8596]~P1(f789(f789(x85961,f848(x85961,x85963,x85962)),f851(x85961,x85963,x85962)))+P1(f789(f789(x85961,x85962),x85963))+~P1(f789(f329(f869(a1,a1),a223),f789(f789(f249(a1,a1),x85962),x85963)))
% 21.40/21.37 [8597]~P1(f789(f789(x85971,f852(x85971,x85973,x85972)),f348(x85971,x85973,x85972)))+P1(f789(f789(x85971,x85972),x85973))+~P1(f789(f329(f869(a863,a863),a221),f789(f789(f249(a863,a863),x85972),x85973)))
% 21.40/21.37 [8598]~P1(f789(f789(x85981,f744(x85981,x85983,x85982)),f747(x85981,x85983,x85982)))+P1(f789(f789(x85981,x85982),x85983))+~P1(f789(f329(f869(a1,a1),a172),f789(f789(f249(a1,a1),x85982),x85983)))
% 21.40/21.37 [8833]P1(f789(f789(x88331,x88332),x88333))+P1(f789(f329(f869(a863,a863),a221),f789(f789(f249(a863,a863),f852(x88331,x88333,x88332)),f348(x88331,x88333,x88332))))+~P1(f789(f329(f869(a863,a863),a221),f789(f789(f249(a863,a863),x88332),x88333)))
% 21.40/21.37 [8834]P1(f789(f789(x88341,x88342),x88343))+P1(f789(f329(f869(a1,a1),a66),f789(f789(f249(a1,a1),f844(x88341,x88343,x88342)),f845(x88341,x88343,x88342))))+~P1(f789(f329(f869(a1,a1),a66),f789(f789(f249(a1,a1),x88342),x88343)))
% 21.40/21.37 [8835]P1(f789(f789(x88351,x88352),x88353))+P1(f789(f329(f869(a1,a1),a69),f789(f789(f249(a1,a1),f846(x88351,x88353,x88352)),f847(x88351,x88353,x88352))))+~P1(f789(f329(f869(a1,a1),a69),f789(f789(f249(a1,a1),x88352),x88353)))
% 21.40/21.37 [8836]P1(f789(f789(x88361,x88362),x88363))+P1(f789(f329(f869(a1,a1),a223),f789(f789(f249(a1,a1),f848(x88361,x88363,x88362)),f851(x88361,x88363,x88362))))+~P1(f789(f329(f869(a1,a1),a223),f789(f789(f249(a1,a1),x88362),x88363)))
% 21.40/21.37 [8837]P1(f789(f789(x88371,x88372),x88373))+P1(f789(f329(f869(a1,a1),a172),f789(f789(f249(a1,a1),f744(x88371,x88373,x88372)),f747(x88371,x88373,x88372))))+~P1(f789(f329(f869(a1,a1),a172),f789(f789(f249(a1,a1),x88372),x88373)))
% 21.40/21.37 [9151]~P1(f789(f70(x91511),x91513))+P1(f789(f789(f342(f869(f870(x91511,a856),f870(x91511,a856))),f789(f789(f249(f870(x91511,a856),f870(x91511,a856)),x91512),x91513)),f307(x91511)))+~P1(f789(f789(f241(f870(x91511,a856)),x91512),x91513))
% 21.40/21.37 [9204]~P58(x92041,f789(x92043,f619(x92042,x92043,x92041)))+P58(x92041,f789(f789(f53(x92042,f870(x92041,f870(x92041,a856))),f247(f870(x92042,a856))),x92043))+~E(f789(f789(f111(f870(x92041,a856)),f254(x92041,x92041,f789(x92043,f618(x92042,x92043,x92041)))),f255(x92041,x92041,f789(x92043,f620(x92042,x92043,x92041)))),f184(f870(x92041,a856)))
% 21.40/21.37 [9395]P47(x93951,x93952,x93953)+P1(f789(f789(f342(f869(x93951,x93951)),f437(x93953,x93952,x93951)),x93953))+~P1(f789(f789(f342(f869(x93951,x93951)),f789(f789(f249(x93951,x93951),f436(x93953,x93952,x93951)),f436(x93953,x93952,x93951))),x93953))
% 21.40/21.37 [9974]P47(x99741,x99742,x99743)+~P1(f789(f789(f259(x99741,x99741,a856),f789(f789(f9(x99741,f870(x99741,a856),f870(x99741,a856)),f789(f789(f10(f870(a856,a856),f870(f870(x99741,a856),f870(x99741,a856)),x99741),f10(a856,a856,x99741)),f789(f789(f10(a856,f870(a856,a856),x99741),a339),f789(f789(f9(x99741,f870(x99741,a856),a856),f342(x99741)),x99742)))),f789(f789(f9(x99741,f870(x99741,a856),a856),f342(x99741)),x99742))),f437(x99743,x99742,x99741)))+~P1(f789(f789(f342(f869(x99741,x99741)),f789(f789(f249(x99741,x99741),f436(x99743,x99742,x99741)),f436(x99743,x99742,x99741))),x99743))
% 21.40/21.37 [5570]~P7(x55702)+E(x55701,f2(x55702))+E(f789(f789(f50(x55702),f789(f789(f90(x55702),x55703),x55701)),x55701),x55703)
% 21.40/21.37 [5571]~P7(x55712)+E(x55711,f2(x55712))+E(f789(f789(f50(x55712),f789(f789(f90(x55712),x55711),x55713)),x55711),x55713)
% 21.40/21.37 [6212]~P7(x62121)+E(f789(f789(f90(x62121),f789(f789(f50(x62121),x62122),x62123)),x62123),x62122)+~P1(f789(f789(f287(x62121),x62123),x62122))
% 21.40/21.37 [6376]~P4(x63761)+~E(f789(x63762,f2(a863)),f2(x63761))+E(f789(f789(f8(a863,x63761),x63762),f789(f302(a863,f789(a121,f2(a863))),x63763)),f789(f789(f8(a863,x63761),x63762),f789(f302(a863,f2(a863)),x63763)))
% 21.40/21.37 [6517]~P7(x65172)+E(x65171,f2(x65172))+E(f789(f789(f50(x65172),f789(f789(f89(x65172),x65173),x65171)),x65171),f789(f789(f89(x65172),f789(f789(f50(x65172),x65173),x65171)),f87(x65172)))
% 21.40/21.37 [6518]~P7(x65182)+E(x65181,f2(x65182))+E(f789(f789(f50(x65182),f789(f789(f89(x65182),x65181),x65183)),x65181),f789(f789(f89(x65182),f789(f789(f50(x65182),x65183),x65181)),f87(x65182)))
% 21.40/21.37 [6746]~P1(f789(x67463,f2(a1)))+P1(f789(f789(f240(a863),x67461),x67462))+P1(f789(x67463,f789(f109(a1),f789(f789(f3(a863),x67462),x67461))))
% 21.40/21.37 [6856]P1(f789(f789(f240(a863),x68562),x68561))+P1(f789(f789(f241(a863),x68561),x68562))+P1(f789(x68563,f789(f109(a1),f789(f789(f3(a863),x68561),x68562))))
% 21.40/21.37 [6928]E(f789(f789(f89(a863),f789(f113(a863),x69281)),f789(f789(f89(a863),f789(f113(a863),x69282)),x69283)),f789(f789(f89(a863),f789(f113(a863),x69281)),x69283))+P1(f789(a190,f789(f113(a1),x69281)))+~P1(f789(a190,f789(f113(a1),x69282)))
% 21.40/21.37 [7006]~E(x70062,f789(f789(f50(a863),x70063),x70061))+~P1(f789(f789(f241(a863),f2(a863)),x70061))+P1(f789(f789(f240(a863),f789(f789(f90(a863),x70061),x70062)),x70063))
% 21.40/21.37 [7122]~P1(f789(f70(x71221),x71223))+~P1(f789(f70(x71221),x71222))+P1(f789(f70(x71221),f789(f789(f3(f870(x71221,a856)),x71222),x71223)))
% 21.40/21.37 [7123]~P1(f789(f70(x71231),x71233))+~P1(f789(f70(x71231),x71232))+P1(f789(f70(x71231),f789(f789(f110(f870(x71231,a856)),x71232),x71233)))
% 21.40/21.37 [7124]~P1(f789(f70(x71241),x71243))+~P1(f789(f70(x71241),x71242))+P1(f789(f70(x71241),f789(f789(f110(f870(x71241,a856)),x71242),x71243)))
% 21.40/21.37 [7439]~P101(x74391)+~P1(f789(f70(x74391),x74392))+E(f136(x74391,f789(f789(f3(f870(x74391,a856)),x74392),f789(f789(f310(x74391),x74393),f184(f870(x74391,a856))))),f158(x74391,x74393,f136(x74391,x74392)))
% 21.40/21.37 [7505]P1(f789(x75051,f2(a1)))+~P1(f789(f789(f241(a863),x75052),x75053))+~P1(f789(x75051,f789(f109(a1),f789(f789(f3(a863),x75052),x75053))))
% 21.40/21.37 [7523]~P1(f789(f70(x75231),x75232))+E(f789(f49(x75231),f789(f789(f3(f870(x75231,a856)),x75232),f789(f789(f310(x75231),x75233),f184(f870(x75231,a856))))),f789(f49(x75231),x75232))+P1(f789(f789(f342(x75231),x75233),x75232))
% 21.40/21.37 [7657]~P117(x76571)+~P1(f789(f789(f241(x76571),f87(x76571)),x76572))+P1(f789(f789(f241(x76571),f87(x76571)),f789(f789(f90(x76571),x76572),f789(f789(f250(x76571),x76572),x76573))))
% 21.40/21.37 [7701]~P1(f789(f70(x77011),x77013))+E(f789(f789(f3(a863),f789(f49(x77011),x77012)),f789(f49(x77011),x77013)),f789(f49(x77011),f789(f789(f3(f870(x77011,a856)),x77012),x77013)))+~P1(f789(f789(f240(f870(x77011,a856)),x77013),x77012))
% 21.40/21.37 [7755]~P1(f789(f789(f240(a863),x77552),x77553))+~P1(f789(f789(f240(a863),x77551),f789(f789(f3(a863),x77553),x77552)))+P1(f789(f789(f240(a863),f789(f789(f89(a863),x77551),x77552)),x77553))
% 21.40/21.37 [7812]P1(f789(f70(x78121),x78122))+~P1(f789(f70(x78121),x78123))+~P1(f789(f70(x78121),f789(f789(f3(f870(x78121,a856)),x78122),x78123)))
% 21.40/21.37 [7818]~P1(f789(f70(x78181),x78182))+E(f789(f49(x78181),f789(f789(f3(f870(x78181,a856)),x78182),f789(f789(f310(x78181),x78183),f184(f870(x78181,a856))))),f789(f789(f3(a863),f789(f49(x78181),x78182)),f87(a863)))+~P1(f789(f789(f342(x78181),x78183),x78182))
% 21.40/21.37 [7819]~P1(f789(f70(x78191),x78192))+E(f789(f49(x78191),f789(f789(f3(f870(x78191,a856)),x78192),f789(f789(f310(x78191),x78193),f184(f870(x78191,a856))))),f789(f789(f3(a863),f789(f49(x78191),x78192)),f87(a863)))+~P1(f789(f789(f342(x78191),x78193),x78192))
% 21.40/21.37 [7894]P58(x78941,x78942)+~P58(x78941,x78943)+~P1(f789(f789(f240(f870(x78941,f870(x78941,a856))),x78942),x78943))
% 21.40/21.37 [7932]~P1(f789(f789(f240(a863),x79323),x79322))+P1(f789(f789(f240(a863),x79321),f789(f789(f3(a863),x79322),x79323)))+~P1(f789(f789(f240(a863),f789(f789(f89(a863),x79321),x79323)),x79322))
% 21.40/21.37 [7951]P36(x79511,x79512)+~P36(x79511,x79513)+~P1(f789(f789(f240(f870(f869(x79511,x79511),a856)),x79512),x79513))
% 21.40/21.37 [7952]P56(x79521,x79522)+~P56(x79521,x79523)+~P1(f789(f789(f240(f870(f869(x79521,x79521),a856)),x79522),x79523))
% 21.40/21.37 [8183]~P117(x81831)+~P1(f789(f789(f241(x81831),f87(x81831)),x81832))+P1(f789(f789(f241(x81831),f789(f789(f250(x81831),x81832),x81833)),f789(f789(f90(x81831),x81832),f789(f789(f250(x81831),x81832),x81833))))
% 21.40/21.37 [8269]~P1(f789(x82691,f2(a1)))+~P1(f789(x82691,f789(f789(f3(a1),f789(f109(a1),x82692)),f789(f109(a1),x82693))))+P1(f789(x82691,f789(f109(a1),f789(f789(f3(a863),x82692),x82693))))
% 21.40/21.37 [8282]~P1(f789(f789(f240(a863),x82823),x82822))+P1(f789(x82821,f789(f789(f3(a1),f789(f109(a1),x82822)),f789(f109(a1),x82823))))+~P1(f789(x82821,f789(f109(a1),f789(f789(f3(a863),x82822),x82823))))
% 21.40/21.37 [8300]P1(f789(f789(f241(a863),x83001),x83002))+~P1(f789(x83003,f789(f789(f3(a1),f789(f109(a1),x83001)),f789(f109(a1),x83002))))+P1(f789(x83003,f789(f109(a1),f789(f789(f3(a863),x83001),x83002))))
% 21.40/21.37 [8357]~P118(x83572)+E(x83571,f2(x83572))+P1(f789(f789(f241(x83572),f2(x83572)),f789(f789(f89(x83572),f789(f789(f90(x83572),x83573),x83573)),f789(f789(f90(x83572),x83571),x83571))))
% 21.40/21.37 [8358]~P118(x83582)+E(x83581,f2(x83582))+P1(f789(f789(f241(x83582),f2(x83582)),f789(f789(f89(x83582),f789(f789(f90(x83582),x83581),x83581)),f789(f789(f90(x83582),x83583),x83583))))
% 21.40/21.37 [8463]~P1(f789(f789(f241(a863),f2(a863)),x84631))+~P1(f789(f789(f241(a1),x84632),x84633))+P1(f789(f789(f241(a1),f789(f789(f90(a1),f789(f109(a1),x84631)),x84632)),f789(f789(f90(a1),f789(f109(a1),x84631)),x84633)))
% 21.40/21.37 [8523]E(f789(f789(f111(f870(x85231,a856)),x85232),f51(f870(x85231,a856),x85233)),f184(f870(x85231,a856)))+P1(f789(f789(f342(f870(x85231,a856)),x85232),x85233))+P1(f789(f789(f342(f870(x85231,a856)),f682(x85233,x85232,x85231)),f789(f789(f310(f870(x85231,a856)),x85232),x85233)))
% 21.40/21.37 [8524]E(f789(f789(f111(f870(x85241,a856)),x85242),f51(f870(x85241,a856),x85243)),f184(f870(x85241,a856)))+P1(f789(f789(f342(f870(x85241,a856)),x85242),x85243))+P1(f789(f789(f342(f870(x85241,a856)),f681(x85243,x85242,x85241)),f789(f789(f310(f870(x85241,a856)),x85242),x85243)))
% 21.40/21.37 [8550]E(x85501,x85502)+~E(f789(f185(f864(x85503)),x85501),f789(f185(f864(x85503)),x85502))+P1(f789(f789(f342(f869(x85503,x85503)),f727(x85503,x85501,x85502)),f789(f163(f869(x85503,x85503)),f789(f789(f171(x85503,x85503),x85502),x85501))))
% 21.40/21.37 [8761]E(f308(x87611,x87612),f308(x87611,x87613))+~P1(f789(f789(f240(f870(f869(x87611,x87611),a856)),x87613),f308(x87611,x87612)))+~P1(f789(f789(f240(f870(f869(x87611,x87611),a856)),x87612),x87613))
% 21.40/21.37 [8814]~P47(x88141,f247(f870(x88141,a856)),x88143)+P1(f789(f789(f240(f870(f869(f864(x88141),f864(x88141)),a856)),f153(x88141,x88142)),f154(x88141,x88143)))+~P1(f789(f789(f240(f870(f869(x88141,x88141),a856)),x88142),x88143))
% 21.40/21.37 [8993]P36(x89931,x89932)+~P1(f789(f789(f342(x89931),x89933),f700(x89932,x89931)))+P1(f789(f789(f342(f869(x89931,x89931)),f789(f789(f249(x89931,x89931),f708(x89932,x89931,x89933)),x89933)),x89932))
% 21.40/21.37 [9032]~P1(f789(f70(x90321),x90322))+P1(f789(f70(f870(x90321,a856)),f789(f789(f68(x90321),x90322),x90323)))+~P1(f789(f789(f240(f870(f869(x90321,x90321),a856)),x90323),f789(f789(f256(x90321,x90321),x90322),f789(f18(f870(x90321,a856),x90321),x90322))))
% 21.40/21.37 [9064]P47(x90641,x90642,x90643)+P1(f789(f789(f342(x90641),f554(x90643,x90642,x90641)),x90642))+~P1(f789(f789(f240(f870(f869(x90641,x90641),a856)),x90643),f789(f789(f256(x90641,x90641),x90642),f789(f18(f870(x90641,a856),x90641),x90642))))
% 21.40/21.37 [9065]P47(x90651,x90652,x90653)+P1(f789(f789(f342(x90651),f569(x90652,x90653,x90651)),x90652))+~P1(f789(f789(f240(f870(f869(x90651,x90651),a856)),x90653),f789(f789(f256(x90651,x90651),x90652),f789(f18(f870(x90651,a856),x90651),x90652))))
% 21.40/21.37 [9099]~P63(x90991)+~P1(f789(f789(f241(x90991),x90992),x90993))+P1(f789(f789(f241(x90991),f789(f789(f291(x90991),f789(f789(f89(x90991),x90992),x90993)),f789(f789(f89(x90991),f87(x90991)),f87(x90991)))),x90993))
% 21.40/21.37 [9127]~P62(x91271)+P1(f789(f789(f240(x91271),x91272),x91273))+~P1(f789(f789(f240(x91271),f789(f789(f90(x91271),f821(x91273,x91272,x91271)),x91272)),x91273))
% 21.40/21.37 [9232]E(f315(x92321,x92322,x92323),f187(f864(a854)))+~P1(f789(f789(f241(a1),x92322),x92323))+~P1(f789(f329(f869(f870(a1,f867(f864(a854))),f869(a1,a1)),a319),f789(f789(f249(f870(a1,f867(f864(a854))),f869(a1,a1)),x92321),f789(f789(f249(a1,a1),x92322),x92323))))
% 21.40/21.37 [9346]~P36(x93461,x93462)+P30(x93461,f789(f789(f249(f870(f869(x93461,x93461),a856),f870(f869(x93461,x93461),a856)),x93462),x93463))+~P1(f789(f789(f240(f870(f869(x93461,x93461),a856)),f789(f789(f289(x93461,x93461,x93461),x93462),x93463)),x93462))
% 21.40/21.37 [9348]E(f789(f236(f867(f864(a854)),f864(a854),f315(x93481,x93482,f789(f789(f89(a1),x93483),f87(a1))),f234(f864(a854))),f789(x93481,x93483)),f315(x93481,x93482,x93483))+P1(f789(f789(f241(a1),x93482),x93483))+~P1(f789(f329(f869(f870(a1,f867(f864(a854))),f869(a1,a1)),a319),f789(f789(f249(f870(a1,f867(f864(a854))),f869(a1,a1)),x93481),f789(f789(f249(a1,a1),x93482),x93483))))
% 21.40/21.37 [9353]E(f789(f789(f150(f864(x93531),x93531),f789(f789(f9(f864(x93531),a863,x93531),f159(x93531)),x93532)),f789(f133(f864(x93531),f789(f789(f10(a863,a856,f864(x93531)),f789(f241(a863),x93532)),f185(f864(x93531)))),f168(x93531,x93533))),f789(f789(f159(f864(x93531)),x93533),x93532))+~P18(a863,f789(f149(a863),f789(f789(f150(f864(x93531),a863),f185(f864(x93531))),x93533)))+~P1(f789(f789(f241(a863),x93532),f789(f185(f864(f864(x93531))),x93533)))
% 21.40/21.37 [9480]P47(x94801,x94802,x94803)+~P1(f789(f789(f342(f869(x94801,x94801)),f789(f789(f249(x94801,x94801),f554(x94803,x94802,x94801)),f554(x94803,x94802,x94801))),x94803))+~P1(f789(f789(f240(f870(f869(x94801,x94801),a856)),x94803),f789(f789(f256(x94801,x94801),x94802),f789(f18(f870(x94801,a856),x94801),x94802))))
% 21.40/21.37 [9481]P47(x94811,x94812,x94813)+~P1(f789(f789(f342(f869(x94811,x94811)),f789(f789(f249(x94811,x94811),f569(x94812,x94813,x94811)),f569(x94812,x94813,x94811))),x94813))+~P1(f789(f789(f240(f870(f869(x94811,x94811),a856)),x94813),f789(f789(f256(x94811,x94811),x94812),f789(f18(f870(x94811,a856),x94811),x94812))))
% 21.40/21.37 [9650]~P120(x96501)+~P116(x96501)+E(f789(f789(f291(x96501),f789(f112(x96501),f789(f789(f82(f869(a1,a1),a1,x96502,f248(a1,a1)),f214(x96502)),x96503))),f789(f112(x96501),f789(f789(f82(f869(a1,a1),a1,x96502,f258(a1,a1)),f214(x96502)),x96503))),f224(x96502,x96501,x96503))
% 21.40/21.37 [9845]~E(x98453,f2(a863))+~E(f789(f185(f864(x98451)),f789(f789(f159(f864(x98451)),x98452),f783(x98453,x98451,x98452))),x98453)+E(f789(f789(f150(a863,f864(x98451)),f789(f789(f9(a863,f864(a863),f864(x98451)),f789(f789(f10(f870(a863,x98451),f870(f864(a863),f864(x98451)),a863),f150(a863,x98451)),f789(f9(a863,a863,x98451),f789(f789(f10(f864(x98451),f870(a863,x98451),a863),f159(x98451)),f789(f159(f864(x98451)),x98452))))),f136(a863,f789(f302(a863,f2(a863)),f789(f185(f864(f864(x98451))),x98452))))),f136(a863,f789(f302(a863,f2(a863)),x98453))),f168(x98451,x98452))
% 21.40/21.37 [9846]E(x98461,f122(f864(x98462)))+~E(f789(f185(f864(x98462)),f789(f789(f159(f864(x98462)),x98461),f783(x98463,x98462,x98461))),x98463)+E(f789(f789(f150(a863,f864(x98462)),f789(f789(f9(a863,f864(a863),f864(x98462)),f789(f789(f10(f870(a863,x98462),f870(f864(a863),f864(x98462)),a863),f150(a863,x98462)),f789(f9(a863,a863,x98462),f789(f789(f10(f864(x98462),f870(a863,x98462),a863),f159(x98462)),f789(f159(f864(x98462)),x98461))))),f136(a863,f789(f302(a863,f2(a863)),f789(f185(f864(f864(x98462))),x98461))))),f136(a863,f789(f302(a863,f2(a863)),x98463))),f168(x98462,x98461))
% 21.40/21.37 [9847]~E(x98473,f2(a863))+E(f789(f789(f150(a863,f864(x98471)),f789(f789(f9(a863,f864(a863),f864(x98471)),f789(f789(f10(f870(a863,x98471),f870(f864(a863),f864(x98471)),a863),f150(a863,x98471)),f789(f9(a863,a863,x98471),f789(f789(f10(f864(x98471),f870(a863,x98471),a863),f159(x98471)),f789(f159(f864(x98471)),x98472))))),f136(a863,f789(f302(a863,f2(a863)),f789(f185(f864(f864(x98471))),x98472))))),f136(a863,f789(f302(a863,f2(a863)),x98473))),f168(x98471,x98472))+P1(f789(f789(f241(a863),f783(x98473,x98471,x98472)),f789(f185(f864(f864(x98471))),x98472)))
% 21.40/21.37 [9848]E(x98481,f122(f864(x98482)))+E(f789(f789(f150(a863,f864(x98482)),f789(f789(f9(a863,f864(a863),f864(x98482)),f789(f789(f10(f870(a863,x98482),f870(f864(a863),f864(x98482)),a863),f150(a863,x98482)),f789(f9(a863,a863,x98482),f789(f789(f10(f864(x98482),f870(a863,x98482),a863),f159(x98482)),f789(f159(f864(x98482)),x98481))))),f136(a863,f789(f302(a863,f2(a863)),f789(f185(f864(f864(x98482))),x98481))))),f136(a863,f789(f302(a863,f2(a863)),x98483))),f168(x98482,x98481))+P1(f789(f789(f241(a863),f783(x98483,x98482,x98481)),f789(f185(f864(f864(x98482))),x98481)))
% 21.40/21.37 [7698]E(f789(f789(f89(a863),f789(f113(a863),x76981)),f789(f789(f89(a863),f789(f113(a863),x76982)),x76983)),f789(f789(f89(a863),f789(f113(a863),f789(f789(f89(a1),x76981),x76982))),x76983))+P1(f789(a190,f789(f113(a1),x76981)))+P1(f789(a190,f789(f113(a1),x76982)))
% 21.40/21.37 [8454]~P1(f789(f70(x84541),x84542))+~P1(f789(f789(f342(x84541),x84543),x84542))+E(f789(a121,f789(f49(x84541),f789(f789(f3(f870(x84541,a856)),x84542),f789(f789(f310(x84541),x84543),f184(f870(x84541,a856)))))),f789(f49(x84541),x84542))
% 21.40/21.37 [8474]~P1(f789(f70(x84741),x84742))+~P1(f789(f789(f342(x84741),x84743),x84742))+E(f789(f789(f89(a863),f87(a863)),f789(f49(x84741),f789(f789(f3(f870(x84741,a856)),x84742),f789(f789(f310(x84741),x84743),f184(f870(x84741,a856)))))),f789(f49(x84741),x84742))
% 21.40/21.37 [8558]~P101(x85581)+~P1(f789(f70(x85581),x85583))+E(f789(f789(f144(x85581,x85581,f7(x85581)),x85582),f136(x85581,f789(f789(f3(f870(x85581,a856)),x85583),f789(f789(f310(x85581),x85582),f184(f870(x85581,a856)))))),f136(x85581,f789(f789(f310(x85581),x85582),x85583)))
% 21.40/21.37 [8696]~P1(f789(f70(x86961),x86963))+~P1(f789(f70(x86961),x86962))+E(f789(f789(f89(a863),f789(f49(x86961),f789(f789(f110(f870(x86961,a856)),x86962),x86963))),f789(f49(x86961),f789(f789(f111(f870(x86961,a856)),x86962),x86963))),f789(f789(f89(a863),f789(f49(x86961),x86962)),f789(f49(x86961),x86963)))
% 21.40/21.37 [8697]~P1(f789(f70(x86971),x86973))+~P1(f789(f70(x86971),x86972))+E(f789(f789(f89(a863),f789(f49(x86971),f789(f789(f110(f870(x86971,a856)),x86972),x86973))),f789(f49(x86971),f789(f789(f111(f870(x86971,a856)),x86972),x86973))),f789(f789(f89(a863),f789(f49(x86971),x86972)),f789(f49(x86971),x86973)))
% 21.40/21.37 [9794]~P29(x97941,f870(f870(x97941,a856),a856),f789(f789(f9(x97941,f870(f869(x97941,x97941),a856),f870(f870(x97941,a856),a856)),f789(f789(f10(f870(x97941,a856),f870(f870(f869(x97941,x97941),a856),f870(f870(x97941,a856),a856)),x97941),f68(x97941)),f789(f789(f9(x97941,f870(x97941,a856),f870(x97941,a856)),f310(x97941)),f184(f870(x97941,a856))))),x97943),x97942)+~P1(f789(f70(x97941),x97942))+E(f789(f49(f870(x97941,a856)),f789(f789(f68(x97941),x97942),x97943)),f789(f49(x97941),x97942))
% 21.40/21.37 [7967]~P88(x79671)+P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x79673)))+E(f789(f789(f250(x79671),x79672),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),x79673),x79673)),a106))),f87(x79671))
% 21.40/21.37 [8056]~P88(x80561)+P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x80563)))+E(f789(f789(f250(x80561),f789(f113(x80561),x80562)),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),x80563),x80563)),a106))),f87(x80561))
% 21.40/21.37 [9328]~P88(x93281)+~P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x93283)))+E(f789(f789(f250(x93281),x93282),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),x93283),x93283)),a106))),f789(f789(f95(x93281,x93281),f789(f789(f250(x93281),x93282),f789(f113(a863),x93283))),f789(f789(f20(x93281,x93281,x93281),f789(f789(f10(x93281,f870(x93281,x93281),x93281),f90(x93281)),f789(f90(x93281),x93282))),f7(x93281))))
% 21.40/21.37 [9394]~P88(x93941)+~P1(f789(f789(f240(a1),f2(a1)),f789(f113(a1),x93943)))+E(f789(f789(f250(x93941),f789(f113(x93941),x93942)),f789(f113(a863),f789(f789(f3(a1),f789(f789(f89(a1),x93943),x93943)),a106))),f789(f789(f95(x93941,x93941),f789(f789(f250(x93941),f789(f113(x93941),x93942)),f789(f113(a863),x93943))),f789(f789(f20(x93941,x93941,x93941),f789(f789(f10(x93941,f870(x93941,x93941),x93941),f90(x93941)),f789(f90(x93941),f789(f113(x93941),x93942)))),f7(x93941))))
% 21.40/21.37 [9759]P1(f789(f789(f240(f870(f869(x97591,x97591),a856)),f308(x97591,x97592)),x97593))+~P1(f789(f789(f240(f870(f869(x97591,x97591),a856)),f308(x97591,f184(f870(f869(x97591,x97591),a856)))),x97593))+~P1(f789(f789(f240(f870(f869(x97591,x97591),a856)),f789(f789(f289(x97591,x97591,x97591),f789(f789(f111(f870(f869(x97591,x97591),a856)),f308(x97591,x97592)),x97593)),x97592)),x97593))
% 21.40/21.37 [9624]~P1(f789(f70(x96241),f789(f264(x96241),x96243)))+~P1(f789(f70(x96241),f789(f264(x96241),x96242)))+P1(f789(f70(x96241),f789(f264(x96241),f789(f789(f20(x96241,a856,a856),f789(f789(f10(a856,f870(a856,a856),x96241),a340),x96242)),x96243))))
% 21.40/21.37 [9917]P1(f789(f789(f240(f870(f869(x99171,x99171),a856)),f789(f789(f289(x99171,x99171,x99171),x99172),f308(x99171,x99172))),x99173))+~P1(f789(f789(f240(f870(f869(x99171,x99171),a856)),x99172),x99173))+~P1(f789(f789(f240(f870(f869(x99171,x99171),a856)),f789(f789(f289(x99171,x99171,x99171),f789(f789(f111(f870(f869(x99171,x99171),a856)),f789(f789(f289(x99171,x99171,x99171),x99172),f308(x99171,x99172))),x99173)),x99172)),x99173))
% 21.40/21.37 [9862]~P110(x98622)+E(x98621,f2(x98622))+~E(f789(f789(f89(x98622),f789(f789(f250(x98622),x98623),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x98622),x98621),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f2(x98622))
% 21.40/21.37 [9863]~P110(x98632)+E(x98631,f2(x98632))+~E(f789(f789(f89(x98632),f789(f789(f250(x98632),x98631),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x98632),x98633),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f2(x98632))
% 21.40/21.37 [9959]~P110(x99592)+E(x99591,f2(x99592))+P1(f789(f789(f241(x99592),f2(x99592)),f789(f789(f89(x99592),f789(f789(f250(x99592),x99593),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x99592),x99591),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))))
% 21.40/21.37 [9960]~P110(x99602)+E(x99601,f2(x99602))+P1(f789(f789(f241(x99602),f2(x99602)),f789(f789(f89(x99602),f789(f789(f250(x99602),x99601),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x99602),x99603),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))))
% 21.40/21.37 [10010]~P110(x100101)+P1(f789(f789(f240(x100101),f2(x100101)),x100102))+~P1(f789(f789(f240(x100101),f2(x100101)),f789(f789(f250(x100101),x100102),f789(a121,f789(f789(f90(a863),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x100103)))))
% 21.40/21.37 [5415]~P28(x54151,x54154,x54153)+P28(x54151,x54152,x54153)+~P28(x54151,x54152,x54154)
% 21.40/21.37 [4892]~E(x48922,f99(x48923,x48921))+P1(f789(x48921,x48922))+~P1(f789(x48921,x48924))
% 21.40/21.37 [6651]~P36(x66512,x66514)+~P36(x66511,x66513)+P36(f869(x66511,x66512),f333(x66511,x66512,x66513,x66514))
% 21.40/21.37 [8038]~P39(f37(x80384,x80381),x80382,x80383,x80382)+P39(x80381,x80382,x80383,f378(x80383,x80382,x80381,x80384))+~P1(f789(x80384,x80382))
% 21.40/21.37 [8065]~P39(f37(x80651,x80652),x80654,x80653,x80654)+P39(f37(x80651,x80652),f378(x80653,x80654,x80652,x80651),x80653,x80654)+~P1(f789(x80651,x80654))
% 21.40/21.37 [5073]~P11(x50734,x50731)+~E(f789(x50731,x50732),f789(x50731,x50733))+P1(f789(f789(x50731,x50732),x50733))
% 21.40/21.37 [5234]~P11(x52344,x52341)+E(f789(x52341,x52342),f789(x52341,x52343))+~P1(f789(f789(x52341,x52342),x52343))
% 21.40/21.37 [5320]~P22(x53203,x53204,x53201)+E(f789(x53201,x53202),f789(f72(x53203,x53204),x53202))+~P1(f789(f70(x53203),x53202))
% 21.40/21.37 [5321]~P14(x53213,x53214,x53211)+E(f789(x53211,x53212),f789(f72(x53213,x53214),x53212))+~P1(f789(f70(x53213),x53212))
% 21.40/21.37 [5450]~P11(x54504,x54501)+~P1(f789(f789(x54501,x54503),x54502))+P1(f789(f789(x54501,x54502),x54503))
% 21.40/21.37 [5513]E(x55131,x55132)+~E(f789(f248(x55133,x55134),x55131),f789(f248(x55133,x55134),x55132))+~E(f789(f258(x55133,x55134),x55131),f789(f258(x55133,x55134),x55132))
% 21.40/21.37 [5514]E(x55141,x55142)+~E(f789(f248(x55143,x55144),x55141),f789(f248(x55143,x55144),x55142))+~E(f789(f258(x55143,x55144),x55141),f789(f258(x55143,x55144),x55142))
% 21.40/21.37 [5539]E(x55391,x55392)+~P1(f789(f62(x55393,x55394),x55392))+~P1(f789(f62(x55393,x55394),x55391))
% 21.40/21.37 [5734]~P4(x57342)+E(f232(x57341,x57342,x57343,x57344),f2(x57342))+P1(f789(f70(x57341),x57344))
% 21.40/21.37 [5868]~P1(f789(f329(x58681,x58682),x58684))+P1(f789(f329(x58681,x58682),x58683))+~P1(f789(f789(x58682,x58683),x58684))
% 21.40/21.37 [5869]~P1(f789(f329(x58691,x58692),x58694))+P1(f789(f329(x58691,x58692),x58693))+~P1(f789(f789(x58692,x58693),x58694))
% 21.40/21.37 [5870]~P1(f789(f329(x58701,x58702),x58704))+P1(f789(f329(x58701,x58702),x58703))+~P1(f789(f789(x58702,x58703),x58704))
% 21.40/21.37 [8108]~P1(f789(f70(x81082),x81084))+~P1(f789(f70(x81081),x81083))+P1(f789(f70(f871(x81081,x81082)),f322(x81081,x81082,x81083,x81084)))
% 21.40/21.37 [8109]~P1(f789(f70(x81092),x81094))+~P1(f789(f70(x81091),x81093))+P1(f789(f70(f871(x81091,x81092)),f322(x81091,x81092,x81093,x81094)))
% 21.40/21.37 [8112]P1(f789(f789(f342(f864(x81121)),f789(f789(f132(x81121),x81122),x81123)),f156(x81121,x81124)))+~P1(f789(f789(f342(f864(x81121)),x81123),f156(x81121,x81124)))+~P1(f789(f789(f342(f864(x81121)),x81122),f156(x81121,x81124)))
% 21.40/21.37 [8686]~P1(f789(f789(f342(f869(x86861,x86861)),f789(f789(f249(x86861,x86861),x86862),x86864)),f308(x86861,x86863)))+P1(f789(f789(f342(x86861),x86862),f330(x86861,x86863)))+~P1(f789(f789(f342(x86861),x86864),f330(x86861,x86863)))
% 21.40/21.37 [8687]~P1(f789(f789(f342(f869(x86871,x86871)),f789(f789(f249(x86871,x86871),x86872),x86874)),f308(x86871,x86873)))+P1(f789(f789(f342(x86871),x86872),f330(x86871,x86873)))+~P1(f789(f789(f342(x86871),x86874),f330(x86871,x86873)))
% 21.40/21.37 [5055]~P69(x50552)+E(f789(f789(f11(x50551,x50552),x50553),x50554),f87(x50552))+P1(f789(f70(x50551),x50554))
% 21.40/21.37 [5056]~P69(x50562)+E(f789(f789(f11(x50561,x50562),x50563),x50564),f87(x50562))+P1(f789(f70(x50561),x50564))
% 21.40/21.37 [5057]~P69(x50572)+E(f789(f789(f11(x50571,x50572),x50573),x50574),f87(x50572))+P1(f789(f70(x50571),x50574))
% 21.40/21.37 [5058]~P4(x50582)+E(f789(f789(f8(x50581,x50582),x50583),x50584),f2(x50582))+P1(f789(f70(x50581),x50584))
% 21.40/21.37 [5059]~P4(x50592)+E(f789(f789(f8(x50591,x50592),x50593),x50594),f2(x50592))+P1(f789(f70(x50591),x50594))
% 21.40/21.37 [5060]~P4(x50602)+E(f789(f789(f8(x50601,x50602),x50603),x50604),f2(x50602))+P1(f789(f70(x50601),x50604))
% 21.40/21.37 [5202]~P64(x52023)+E(x52021,x52022)+~E(f789(f789(f89(x52023),x52024),x52021),f789(f789(f89(x52023),x52024),x52022))
% 21.40/21.37 [5203]~P64(x52033)+E(x52031,x52032)+~E(f789(f789(f89(x52033),x52034),x52031),f789(f789(f89(x52033),x52034),x52032))
% 21.40/21.37 [5204]~P65(x52043)+E(x52041,x52042)+~E(f789(f789(f89(x52043),x52044),x52041),f789(f789(f89(x52043),x52044),x52042))
% 21.40/21.37 [5205]~P64(x52053)+E(x52051,x52052)+~E(f789(f789(f89(x52053),x52051),x52054),f789(f789(f89(x52053),x52052),x52054))
% 21.40/21.37 [5206]~P64(x52063)+E(x52061,x52062)+~E(f789(f789(f89(x52063),x52061),x52064),f789(f789(f89(x52063),x52062),x52064))
% 21.40/21.37 [5290]~P112(x52901)+~E(x52903,f789(f789(f90(x52901),x52902),x52904))+P1(f789(f789(f287(x52901),x52902),x52903))
% 21.40/21.37 [5315]~P9(x53153)+E(x53151,f184(f870(x53152,a856)))+E(f789(f789(f53(x53152,x53153),x53151),f789(f18(x53153,x53152),x53154)),x53154)
% 21.40/21.37 [5316]~P9(x53163)+E(x53161,f184(f870(x53162,a856)))+E(f789(f789(f54(x53162,x53163),x53161),f789(f18(x53163,x53162),x53164)),x53164)
% 21.40/21.37 [5527]~P99(x55273)+E(x55271,x55272)+~E(f303(x55273,x55274,x55271),f789(f789(f310(x55273),x55272),f184(f870(x55273,a856))))
% 21.40/21.37 [5528]~P99(x55283)+E(x55281,x55282)+~E(f303(x55283,x55281,x55282),f789(f789(f310(x55283),x55284),f184(f870(x55283,a856))))
% 21.40/21.37 [5832]P1(f789(x58321,x58322))+~P1(f789(f253(x58323,x58321),x58324))+~P1(f789(f789(f342(x58323),x58322),x58324))
% 21.40/21.37 [5861]E(x58611,x58612)+~P1(f789(f789(f191(x58613),x58614),x58612))+~P1(f789(f789(f191(x58613),x58614),x58611))
% 21.40/21.37 [5943]~P4(x59431)+E(f789(f789(f8(a863,x59431),x59432),f789(f302(a863,x59433),f789(a121,x59434))),f2(x59431))+~P1(f789(f789(f241(a863),x59434),x59433))
% 21.40/21.37 [5947]~P8(x59471)+~E(f59(x59471,x59472,x59473),f59(x59471,x59474,x59473))+E(f59(x59471,f789(f88(x59471),x59472),x59473),f59(x59471,f789(f88(x59471),x59474),x59473))
% 21.40/21.37 [6017]P1(f789(x60171,x60172))+~E(f789(f133(x60173,x60171),x60174),x60174)+~P1(f789(f789(f342(x60173),x60172),f789(f163(x60173),x60174)))
% 21.40/21.37 [6037]~E(f789(f789(f89(a863),x60373),x60372),f789(f789(f89(a863),x60371),x60374))+~P1(f789(f789(f241(a863),x60373),x60374))+P1(f789(f789(f241(a863),x60371),x60372))
% 21.40/21.37 [6044]~P7(x60441)+E(f59(x60441,f59(x60441,x60442,x60443),x60444),f59(x60441,x60442,x60444))+~P1(f789(f789(f287(x60441),x60444),x60443))
% 21.40/21.37 [6083]~E(f789(f133(x60831,x60832),x60833),f122(x60831))+~P1(f789(x60832,x60834))+~P1(f789(f789(f342(x60831),x60834),f789(f163(x60831),x60833)))
% 21.40/21.37 [6117]~E(x61174,f184(f870(x61172,a856)))+~E(x61173,f184(f870(x61171,a856)))+E(f322(x61171,x61172,x61173,x61174),f184(f870(f871(x61171,x61172),a856)))
% 21.40/21.37 [6546]~P4(x65461)+E(f789(f789(f8(a863,x65461),x65462),f303(a863,x65463,f789(a121,x65464))),f2(x65461))+~P1(f789(f789(f241(a863),f789(a121,x65464)),x65463))
% 21.40/21.37 [6694]~P101(x66941)+E(f789(f789(f3(f870(x66941,a856)),f789(f302(x66941,x66942),x66943)),f789(f302(x66941,x66942),x66944)),f789(f302(x66941,x66944),x66943))+~P1(f789(f789(f240(x66941),x66942),x66944))
% 21.40/21.37 [7054]~P1(f789(f789(f342(f864(x70541)),x70544),f156(x70541,x70543)))+P1(f789(f789(f342(x70541),x70542),x70543))+~P1(f789(f789(f342(x70541),x70542),f789(f163(x70541),x70544)))
% 21.40/21.37 [7062]~P36(x70621,x70622)+P1(f789(f789(f342(x70621),f701(x70622,x70621,x70623)),x70623))+~P1(f789(f789(f342(x70621),x70624),x70623))
% 21.40/21.37 [7093]~P29(x70932,x70931,x70933,x70934)+E(f789(f49(x70931),f789(f311(x70932,x70931,x70933),x70934)),f789(f49(x70932),x70934))+~P1(f789(f70(x70932),x70934))
% 21.40/21.37 [7117]~P69(x71171)+E(f789(f789(f789(f74(x71171,x71172,f90(x71171)),x71173),f87(x71171)),x71174),f789(f789(f11(x71172,x71171),x71173),x71174))+~P1(f789(f70(x71172),x71174))
% 21.40/21.37 [7118]~P69(x71181)+E(f789(f789(f789(f74(x71181,x71182,f90(x71181)),x71183),f87(x71181)),x71184),f789(f789(f11(x71182,x71181),x71183),x71184))+~P1(f789(f70(x71182),x71184))
% 21.40/21.37 [7119]~P4(x71191)+E(f789(f789(f789(f74(x71191,x71192,f89(x71191)),x71193),f2(x71191)),x71194),f789(f789(f8(x71192,x71191),x71193),x71194))+~P1(f789(f70(x71192),x71194))
% 21.40/21.37 [7120]~P4(x71201)+E(f789(f789(f789(f74(x71201,x71202,f89(x71201)),x71203),f2(x71201)),x71204),f789(f789(f8(x71202,x71201),x71203),x71204))+~P1(f789(f70(x71202),x71204))
% 21.40/21.37 [7146]P29(x71461,x71462,x71463,x71464)+~E(f789(f49(x71462),f789(f311(x71461,x71462,x71463),x71464)),f789(f49(x71461),x71464))+~P1(f789(f70(x71461),x71464))
% 21.40/21.37 [7147]P29(x71471,x71472,x71473,x71474)+~E(f789(f49(x71472),f789(f311(x71471,x71472,x71473),x71474)),f789(f49(x71471),x71474))+~P1(f789(f70(x71471),x71474))
% 21.40/21.37 [7351]~P4(x73511)+E(f789(f789(f89(x73511),f789(x73512,x73513)),f789(f789(f8(a863,x73511),x73512),f305(a863,x73513,x73514))),f789(f789(f8(a863,x73511),x73512),f303(a863,x73513,x73514)))+~P1(f789(f789(f240(a863),x73513),x73514))
% 21.40/21.37 [7361]~P69(x73611)+~P29(x73612,x73611,x73613,x73614)+E(f789(f789(f11(x73611,x73611),f41(x73611)),f789(f311(x73612,x73611,x73613),x73614)),f789(f789(f11(x73612,x73611),x73613),x73614))
% 21.40/21.37 [7362]~P4(x73621)+~P29(x73622,x73621,x73623,x73624)+E(f789(f789(f8(x73621,x73621),f41(x73621)),f789(f311(x73622,x73621,x73623),x73624)),f789(f789(f8(x73622,x73621),x73623),x73624))
% 21.40/21.37 [7420]E(f789(f49(f871(x74201,x74202)),f322(x74201,x74202,x74203,x74204)),f789(f789(f89(a863),f789(f49(x74201),x74203)),f789(f49(x74202),x74204)))+~P1(f789(f70(x74202),x74204))+~P1(f789(f70(x74201),x74203))
% 21.40/21.37 [7421]E(f789(f49(f871(x74211,x74212)),f322(x74211,x74212,x74213,x74214)),f789(f789(f89(a863),f789(f49(x74211),x74213)),f789(f49(x74212),x74214)))+~P1(f789(f70(x74212),x74214))+~P1(f789(f70(x74211),x74213))
% 21.40/21.37 [7506]E(x75061,x75062)+P1(f789(f789(f342(x75063),x75061),f789(f163(x75063),f158(x75063,x75062,x75064))))+~P1(f789(f789(f342(x75063),x75061),f789(f163(x75063),x75064)))
% 21.40/21.37 [7731]~P4(x77311)+E(f789(f789(f89(x77311),f789(f789(f8(a863,x77311),x77312),f789(f302(a863,x77313),x77314))),f789(x77312,x77314)),f789(f789(f8(a863,x77311),x77312),f789(f302(a863,x77313),f789(a121,x77314))))+P1(f789(f789(f241(a863),x77314),x77313))
% 21.40/21.37 [7788]~P29(x77881,x77882,x77883,f247(f870(x77881,a856)))+~P1(f789(f70(x77882),x77884))+P1(f789(f70(x77881),f789(f313(x77881,x77882,x77883),x77884)))
% 21.40/21.37 [7902]P1(f789(f789(f342(f864(x79021)),f789(f789(f146(x79021),x79022),x79023)),f156(x79021,x79024)))+~P1(f789(f789(f342(f864(x79021)),x79023),f156(x79021,x79024)))+~P1(f789(f789(f342(x79021),x79022),x79024))
% 21.40/21.37 [7950]E(x79501,x79502)+~P1(f789(f789(f342(x79503),x79501),f789(f163(x79503),f158(x79503,x79502,x79504))))+P1(f789(f789(f342(x79503),x79501),f789(f163(x79503),x79504)))
% 21.40/21.37 [7991]~E(f789(f311(x79913,x79911,x79914),f247(f870(x79913,a856))),f247(f870(x79911,a856)))+P1(f789(f70(x79911),x79912))+~P1(f789(f70(x79913),f789(f313(x79913,x79911,x79914),x79912)))
% 21.40/21.37 [8081]~P29(x80811,x80813,x80814,x80812)+P1(f789(f70(x80811),x80812))+~P1(f789(f70(x80813),f789(f311(x80811,x80813,x80814),x80812)))
% 21.40/21.37 [8103]~E(x81032,x81033)+P1(f789(f789(f342(f869(x81031,x81031)),f789(f789(f249(x81031,x81031),x81032),x81033)),f268(x81031,x81034)))+~P1(f789(f789(f342(x81031),x81032),x81034))
% 21.40/21.37 [8104]~E(x81042,x81043)+P1(f789(f789(f342(f869(x81041,x81041)),f789(f789(f249(x81041,x81041),x81042),x81043)),f268(x81041,x81044)))+~P1(f789(f789(f342(x81041),x81042),x81044))
% 21.40/21.37 [8135]~P4(x81351)+E(f789(f789(f89(x81351),f789(f789(f8(a863,x81351),x81352),f303(a863,x81353,x81354))),f789(x81352,f789(a121,x81354))),f789(f789(f8(a863,x81351),x81352),f303(a863,x81353,f789(a121,x81354))))+P1(f789(f789(f241(a863),f789(a121,x81354)),x81353))
% 21.40/21.37 [8195]~E(x81952,x81954)+P1(f789(f789(f342(f869(x81951,x81951)),f789(f789(f249(x81951,x81951),x81952),x81954)),f308(x81951,x81953)))+P1(f789(f789(f342(x81951),x81952),f789(f269(x81951,x81951),x81953)))
% 21.40/21.37 [8197]P1(f789(x81971,x81972))+~P1(f789(x81971,f789(f789(f159(x81973),x81974),f739(x81971,x81974,x81973))))+~P1(f789(f789(f342(x81973),x81972),f789(f163(x81973),x81974)))
% 21.40/21.37 [8332]~P1(f789(f789(f342(x83321),x83322),f330(x83321,x83324)))+P1(f789(f789(f342(f864(x83321)),f789(f789(f146(x83321),x83322),x83323)),f330(f864(x83321),f153(x83321,x83324))))+~P1(f789(f789(f342(f864(x83321)),x83323),f330(f864(x83321),f153(x83321,x83324))))
% 21.40/21.37 [8348]~P29(x83482,x83483,x83484,f676(x83484,x83483,x83482,x83481))+P29(x83482,x83483,x83484,f52(f870(x83482,a856),x83481))+E(x83481,f184(f870(f870(x83482,a856),a856)))
% 21.40/21.37 [8608]E(x86081,x86082)+~P1(f789(f789(f342(f869(x86083,x86083)),f789(f789(f249(x86083,x86083),x86081),x86082)),f308(x86083,x86084)))+P1(f789(f789(f342(x86083),x86081),f789(f269(x86083,x86083),x86084)))
% 21.40/21.37 [8859]P29(x88592,x88593,x88594,f52(f870(x88592,a856),x88591))+E(x88591,f184(f870(f870(x88592,a856),a856)))+P1(f789(f789(f342(f870(x88592,a856)),f676(x88594,x88593,x88592,x88591)),x88591))
% 21.40/21.37 [8984]P1(f789(f70(x89841),x89842))+~P1(f789(f70(x89844),f789(f311(x89841,x89844,x89843),x89842)))+P1(f789(f789(f342(x89841),f609(x89843,x89844,x89842,x89841)),x89842))
% 21.40/21.37 [9078]~P9(x90782)+E(f789(f789(f73(x90781,x90782,f789(f789(f10(x90782,f870(x90782,x90782),x90781),f110(x90782)),x90783)),f184(x90782)),x90784),f789(f789(f53(x90781,x90782),x90784),x90783))+~P1(f789(f70(x90781),x90784))
% 21.40/21.37 [9079]~P9(x90792)+E(f789(f789(f73(x90791,x90792,f789(f789(f10(x90792,f870(x90792,x90792),x90791),f111(x90792)),x90793)),f247(x90792)),x90794),f789(f789(f54(x90791,x90792),x90794),x90793))+~P1(f789(f70(x90791),x90794))
% 21.40/21.37 [9106]~P1(f789(f789(f287(a863),x91063),x91064))+P1(f789(f789(f287(a863),x91061),x91062))+P1(f789(f789(f241(f870(a863,a856)),f290(a863,f287(a863),x91061,x91062)),f290(a863,f287(a863),x91063,x91064)))
% 21.40/21.37 [9117]~P1(f789(f789(f287(a863),x91172),x91174))+~P1(f789(f789(f287(a863),x91173),x91171))+P1(f789(f789(f240(f870(a863,a856)),f290(a863,f287(a863),x91171,x91172)),f290(a863,f287(a863),x91173,x91174)))
% 21.40/21.37 [9173]E(x91731,x91732)+~P1(f789(f789(f342(f869(x91733,x91733)),f789(f789(f249(x91733,x91733),x91731),x91732)),f308(x91733,x91734)))+P1(f789(f789(f342(f869(x91733,x91733)),f789(f789(f249(x91733,x91733),x91731),x91732)),f789(f789(f289(x91733,x91733,x91733),x91734),f308(x91733,x91734))))
% 21.40/21.37 [9174]E(x91741,x91742)+~P1(f789(f789(f342(f869(x91743,x91743)),f789(f789(f249(x91743,x91743),x91741),x91742)),f308(x91743,x91744)))+P1(f789(f789(f342(f869(x91743,x91743)),f789(f789(f249(x91743,x91743),x91741),x91742)),f789(f789(f289(x91743,x91743,x91743),x91744),f308(x91743,x91744))))
% 21.40/21.37 [9205]~E(f789(f185(f864(x92051)),x92052),f789(f185(f864(x92051)),x92053))+~P1(f789(f789(f342(f869(f864(x92051),f864(x92051))),f789(f789(f249(f864(x92051),f864(x92051)),x92052),x92053)),f143(x92051,x92054)))+P1(f789(f789(f342(f869(f864(x92051),f864(x92051))),f789(f789(f249(f864(x92051),f864(x92051)),x92052),x92053)),f141(x92051,x92054)))
% 21.40/21.37 [9224]E(x92241,x92242)+P1(f789(f789(f342(f869(x92243,x92243)),f789(f789(f249(x92243,x92243),x92241),x92242)),f308(x92243,x92244)))+~P1(f789(f789(f342(f869(x92243,x92243)),f789(f789(f249(x92243,x92243),x92241),x92242)),f789(f789(f289(x92243,x92243,x92243),x92244),f308(x92243,x92244))))
% 21.40/21.37 [9315]P1(f789(f789(f287(a863),x93151),x93152))+~P1(f789(f789(f287(a863),x93153),x93151))+~P1(f789(f789(f241(f870(a863,a856)),f290(a863,f287(a863),x93153,x93151)),f290(a863,f287(a863),x93154,x93152)))
% 21.40/21.37 [9316]P1(f789(f789(f287(a863),x93161),x93162))+~P1(f789(f789(f287(a863),x93163),x93161))+~P1(f789(f789(f240(f870(a863,a856)),f290(a863,f287(a863),x93163,x93161)),f290(a863,f287(a863),x93164,x93162)))
% 21.40/21.37 [9317]P1(f789(f789(f287(a863),x93171),x93172))+~P1(f789(f789(f287(a863),x93172),x93173))+~P1(f789(f789(f241(f870(a863,a856)),f290(a863,f287(a863),x93172,x93173)),f290(a863,f287(a863),x93171,x93174)))
% 21.40/21.37 [9318]P1(f789(f789(f287(a863),x93181),x93182))+~P1(f789(f789(f287(a863),x93182),x93183))+~P1(f789(f789(f240(f870(a863,a856)),f290(a863,f287(a863),x93182,x93183)),f290(a863,f287(a863),x93181,x93184)))
% 21.40/21.37 [9627]~P6(x96271)+E(f789(f789(f8(a863,x96271),f789(f789(f20(a863,x96271,x96271),f789(f789(f10(x96271,f870(x96271,x96271),a863),f3(x96271)),x96272)),f789(f789(f10(a863,x96271,a863),x96272),f789(f789(f9(a863,a863,a863),f89(a863)),f87(a863))))),f303(a863,x96273,x96274)),f2(x96271))+P1(f789(f789(f240(a863),x96273),x96274))
% 21.40/21.37 [9860]~P36(x98602,x98604)+~P29(x98602,x98601,x98603,f247(f870(x98602,a856)))+P36(x98601,f789(f311(f869(x98602,x98602),f869(x98601,x98601),f260(x98602,x98601,x98602,x98601,x98603,x98603)),x98604))
% 21.40/21.37 [10038]~E(f789(f185(f864(x100381)),x100383),f789(f185(f864(x100381)),x100382))+P1(f789(f789(f342(f869(f864(x100381),f864(x100381))),f789(f789(f249(f864(x100381),f864(x100381)),x100382),x100383)),f154(x100381,x100384)))+~P1(f789(f789(f259(x100381,x100381,a856),f789(f789(f9(x100381,f870(f869(x100381,x100381),a856),f870(x100381,a856)),f789(f789(f10(f870(x100381,f870(f870(f869(x100381,x100381),a856),a856)),f870(f870(f869(x100381,x100381),a856),f870(x100381,a856)),x100381),f9(x100381,f870(f869(x100381,x100381),a856),a856)),f789(f789(f10(f870(x100381,f869(x100381,x100381)),f870(x100381,f870(f870(f869(x100381,x100381),a856),a856)),x100381),f789(f10(f869(x100381,x100381),f870(f870(f869(x100381,x100381),a856),a856),x100381),f342(f869(x100381,x100381)))),f249(x100381,x100381)))),x100384)),f730(x100384,x100383,x100382,x100381)))
% 21.40/21.37 [5907]~E(x59074,x59072)+P1(f789(x59071,x59072))+P1(f789(f789(f191(f37(x59071,x59073)),x59072),x59074))
% 21.40/21.37 [6001]~P7(x60011)+~E(x60012,f2(x60011))+E(f789(f789(f50(x60011),f789(f789(f90(x60011),x60012),x60013)),f789(f789(f90(x60011),x60012),x60014)),f2(x60011))
% 21.40/21.37 [6041]E(x60411,f122(x60412))+E(x60413,f789(f789(f3(a863),f789(f185(f864(x60412)),x60411)),f87(a863)))+E(f140(x60412,f789(f789(f155(x60412,x60411),x60413),x60414)),f140(x60412,x60411))
% 21.40/21.37 [6074]E(x60741,x60742)+P1(f789(x60743,x60742))+~P1(f789(f789(f789(f310(x60744),x60741),x60743),x60742))
% 21.40/21.37 [6087]~P4(x60871)+~P1(f789(f134(x60872),x60874))+E(f789(f161(x60871),f789(f789(f150(x60872,x60871),x60873),x60874)),f789(f789(f8(x60872,x60871),x60873),f789(f163(x60872),x60874)))
% 21.40/21.37 [6110]~P69(x61102)+~P1(f789(f70(x61101),x61104))+E(f789(f789(f11(x61101,x61102),f789(f18(x61102,x61101),x61103)),x61104),f789(f789(f250(x61102),x61103),f789(f49(x61101),x61104)))
% 21.40/21.37 [6163]~P7(x61632)+E(x61631,f2(x61632))+E(f789(f789(f50(x61632),f789(f789(f90(x61632),x61633),x61631)),f789(f789(f90(x61632),x61634),x61631)),f789(f789(f50(x61632),x61633),x61634))
% 21.40/21.37 [6164]~P7(x61642)+E(x61641,f2(x61642))+E(f789(f789(f50(x61642),f789(f789(f90(x61642),x61641),x61643)),f789(f789(f90(x61642),x61641),x61644)),f789(f789(f50(x61642),x61643),x61644))
% 21.40/21.37 [6165]~P60(x61652)+E(x61651,f2(x61652))+E(f789(f789(f291(x61652),f789(f789(f90(x61652),x61653),x61651)),f789(f789(f90(x61652),x61654),x61651)),f789(f789(f291(x61652),x61653),x61654))
% 21.40/21.37 [6166]~P60(x61662)+E(x61661,f2(x61662))+E(f789(f789(f291(x61662),f789(f789(f90(x61662),x61661),x61663)),f789(f789(f90(x61662),x61661),x61664)),f789(f789(f291(x61662),x61663),x61664))
% 21.40/21.37 [6167]~P7(x61672)+E(x61671,f2(x61672))+E(f789(f789(f50(x61672),f789(f789(f90(x61672),x61671),x61673)),f789(f789(f90(x61672),x61671),x61674)),f789(f789(f50(x61672),x61673),x61674))
% 21.40/21.37 [6232]P1(f789(x62321,x62322))+~E(x62323,f789(f789(f89(a863),x62324),x62322))+~P1(f789(x62321,f789(f789(f3(a863),x62323),x62324)))
% 21.40/21.37 [6233]P1(f789(x62331,x62332))+~E(x62333,f789(f789(f89(a863),x62334),x62332))+~P1(f789(x62331,f789(f789(f3(a863),x62333),x62334)))
% 21.40/21.37 [6314]P32(x63141,x63142,x63143)+P31(x63141,f822(x63143,x63142,x63141),x63144)+~P1(f789(f789(f342(f862(x63141)),x63144),x63142))
% 21.40/21.37 [6360]E(x63601,f122(x63602))+~E(x63603,f789(f789(f3(a863),f789(f185(f864(x63602)),x63601)),f87(a863)))+E(f140(x63602,f789(f789(f155(x63602,x63601),x63603),x63604)),x63604)
% 21.40/21.37 [6382]~P101(x63821)+~P1(f789(f789(f241(x63821),x63822),x63824))+P1(f789(f789(f241(x63821),x63822),f789(f789(f239(x63821),x63823),x63824)))
% 21.40/21.37 [6383]~P101(x63831)+~P1(f789(f789(f241(x63831),x63832),x63834))+P1(f789(f789(f241(x63831),x63832),f789(f789(f239(x63831),x63833),x63834)))
% 21.40/21.37 [6384]~P101(x63841)+~P1(f789(f789(f241(x63841),x63842),x63843))+P1(f789(f789(f241(x63841),x63842),f789(f789(f239(x63841),x63843),x63844)))
% 21.40/21.37 [6385]~P101(x63851)+~P1(f789(f789(f241(x63851),x63852),x63853))+P1(f789(f789(f241(x63851),x63852),f789(f789(f239(x63851),x63853),x63854)))
% 21.40/21.37 [6386]~P94(x63861)+~P1(f789(f789(f241(x63861),x63862),x63864))+P1(f789(f789(f241(x63861),x63862),f789(f789(f110(x63861),x63863),x63864)))
% 21.40/21.37 [6387]~P94(x63871)+~P1(f789(f789(f241(x63871),x63872),x63873))+P1(f789(f789(f241(x63871),x63872),f789(f789(f110(x63871),x63873),x63874)))
% 21.40/21.37 [6388]~P101(x63881)+~P1(f789(f789(f240(x63881),x63882),x63884))+P1(f789(f789(f240(x63881),x63882),f789(f789(f239(x63881),x63883),x63884)))
% 21.40/21.37 [6389]~P101(x63891)+~P1(f789(f789(f240(x63891),x63892),x63894))+P1(f789(f789(f240(x63891),x63892),f789(f789(f239(x63891),x63893),x63894)))
% 21.40/21.37 [6390]~P101(x63901)+~P1(f789(f789(f240(x63901),x63902),x63903))+P1(f789(f789(f240(x63901),x63902),f789(f789(f239(x63901),x63903),x63904)))
% 21.40/21.37 [6391]~P101(x63911)+~P1(f789(f789(f240(x63911),x63912),x63913))+P1(f789(f789(f240(x63911),x63912),f789(f789(f239(x63911),x63913),x63914)))
% 21.40/21.37 [6392]~P94(x63921)+~P1(f789(f789(f240(x63921),x63922),x63924))+P1(f789(f789(f240(x63921),x63922),f789(f789(f110(x63921),x63923),x63924)))
% 21.40/21.37 [6393]~P94(x63931)+~P1(f789(f789(f240(x63931),x63932),x63933))+P1(f789(f789(f240(x63931),x63932),f789(f789(f110(x63931),x63933),x63934)))
% 21.40/21.37 [6394]~P70(x63941)+~P1(f789(f789(f287(x63941),x63942),x63944))+P1(f789(f789(f287(x63941),x63942),f789(f789(f90(x63941),x63943),x63944)))
% 21.40/21.37 [6395]~P70(x63951)+~P1(f789(f789(f287(x63951),x63952),x63953))+P1(f789(f789(f287(x63951),x63952),f789(f789(f90(x63951),x63953),x63954)))
% 21.40/21.37 [6489]~E(f789(f789(f159(x64891),x64892),x64893),x64894)+E(f789(f789(f155(x64891,x64892),x64893),x64894),x64892)+~P1(f789(f789(f241(a863),x64893),f789(f185(f864(x64891)),x64892)))
% 21.40/21.37 [6508]E(x65081,x65082)+P1(f789(x65083,x65081))+~P1(f789(f789(f191(f37(x65083,x65084)),x65081),x65082))
% 21.40/21.37 [6509]E(x65091,x65092)+P1(f789(x65093,x65091))+~P1(f789(f789(f191(f37(x65093,x65094)),x65091),x65092))
% 21.40/21.37 [6528]P1(f789(x65281,x65282))+~P1(f789(x65283,x65282))+~P1(f789(f789(f240(f870(x65284,a856)),x65283),x65281))
% 21.40/21.37 [6529]P1(f789(x65291,x65292))+~P1(f789(x65293,x65292))+~P1(f789(f789(f240(f870(x65294,a856)),x65293),x65291))
% 21.40/21.37 [6565]~E(f789(f789(f155(x65651,x65652),x65653),x65654),x65652)+E(f789(f789(f159(x65651),x65652),x65653),x65654)+~P1(f789(f789(f241(a863),x65653),f789(f185(f864(x65651)),x65652)))
% 21.40/21.37 [6682]P31(x66821,x66822,x66823)+~P31(x66821,f789(a121,x66822),f842(x66822,x66824,x66821))+~P1(f789(f789(f342(f862(x66821)),x66823),x66824))
% 21.40/21.37 [6691]E(x66911,f184(f870(x66912,a856)))+E(x66913,f184(f870(x66914,a856)))+~E(f789(f789(f256(x66914,x66912),x66913),f789(f18(f870(x66912,a856),x66914),x66911)),f184(f870(f869(x66914,x66912),a856)))
% 21.40/21.37 [6708]E(x67081,x67082)+P1(f789(f789(f342(x67083),x67081),x67084))+~P1(f789(f789(f342(x67083),x67081),f789(f789(f310(x67083),x67082),x67084)))
% 21.40/21.37 [6709]E(x67091,x67092)+P1(f789(f789(f342(x67093),x67091),x67094))+~P1(f789(f789(f342(x67093),x67091),f789(f789(f310(x67093),x67092),x67094)))
% 21.40/21.37 [6726]~P101(x67261)+P1(f789(f789(f241(x67261),x67262),x67263))+~P1(f789(f789(f241(x67261),x67262),f789(f789(f244(x67261),x67264),x67263)))
% 21.40/21.37 [6727]~P101(x67271)+P1(f789(f789(f241(x67271),x67272),x67273))+~P1(f789(f789(f241(x67271),x67272),f789(f789(f244(x67271),x67273),x67274)))
% 21.40/21.37 [6728]~P101(x67281)+P1(f789(f789(f240(x67281),x67282),x67283))+~P1(f789(f789(f240(x67281),x67282),f789(f789(f244(x67281),x67284),x67283)))
% 21.40/21.37 [6729]~P101(x67291)+P1(f789(f789(f240(x67291),x67292),x67293))+~P1(f789(f789(f240(x67291),x67292),f789(f789(f244(x67291),x67294),x67293)))
% 21.40/21.37 [6730]~P101(x67301)+P1(f789(f789(f240(x67301),x67302),x67303))+~P1(f789(f789(f240(x67301),x67302),f789(f789(f244(x67301),x67303),x67304)))
% 21.40/21.37 [6731]~P101(x67311)+P1(f789(f789(f240(x67311),x67312),x67313))+~P1(f789(f789(f240(x67311),x67312),f789(f789(f244(x67311),x67313),x67314)))
% 21.40/21.37 [6732]~P98(x67321)+P1(f789(f789(f240(x67321),x67322),x67323))+~P1(f789(f789(f240(x67321),x67322),f789(f789(f111(x67321),x67324),x67323)))
% 21.40/21.37 [6733]~P98(x67331)+P1(f789(f789(f240(x67331),x67332),x67333))+~P1(f789(f789(f240(x67331),x67332),f789(f789(f111(x67331),x67334),x67333)))
% 21.40/21.37 [6734]~P98(x67341)+P1(f789(f789(f240(x67341),x67342),x67343))+~P1(f789(f789(f240(x67341),x67342),f789(f789(f111(x67341),x67343),x67344)))
% 21.40/21.37 [6735]~P98(x67351)+P1(f789(f789(f240(x67351),x67352),x67353))+~P1(f789(f789(f240(x67351),x67352),f789(f789(f111(x67351),x67353),x67354)))
% 21.40/21.37 [6757]~E(f789(f789(f159(x67571),x67573),x67574),x67572)+P1(f789(f789(f342(x67571),x67572),f789(f163(x67571),x67573)))+~P1(f789(f789(f241(a863),x67574),f789(f185(f864(x67571)),x67573)))
% 21.40/21.37 [6769]~P101(x67691)+~P18(x67691,f789(f789(f146(x67691),x67692),f789(f789(f146(x67691),x67693),x67694)))+P1(f789(f789(f240(x67691),x67692),x67693))
% 21.40/21.37 [6826]~P101(x68261)+P18(x68261,f789(f789(f146(x68261),x68262),x68263))+~P18(x68261,f789(f789(f146(x68261),x68264),f789(f789(f146(x68261),x68262),x68263)))
% 21.40/21.37 [6937]E(x69371,f2(a1))+E(f789(f789(f50(a1),x69372),x69371),x69373)+~P1(f789(f63(x69372,x69371),f789(f789(f249(a1,a1),x69373),x69374)))
% 21.40/21.37 [6960]E(f59(a1,x69602,x69601),x69603)+E(x69601,f2(a1))+~P1(f789(f63(x69602,x69601),f789(f789(f249(a1,a1),x69604),x69603)))
% 21.40/21.37 [7076]P1(f789(f789(f342(x70761),x70762),x70763))+~P1(f789(f789(f342(x70761),x70762),x70764))+~P1(f789(f789(f241(f870(x70761,a856)),x70764),x70763))
% 21.40/21.37 [7077]P1(f789(f789(f342(x70771),x70772),x70773))+~P1(f789(f789(f342(x70771),x70772),x70774))+~P1(f789(f789(f240(f870(x70771,a856)),x70774),x70773))
% 21.40/21.37 [7078]P1(f789(f789(f342(x70781),x70782),x70783))+~P1(f789(f789(f342(x70781),x70782),x70784))+~P1(f789(f789(f240(f870(x70781,a856)),x70784),x70783))
% 21.40/21.37 [7079]P1(f789(f789(f342(x70791),x70792),x70793))+~P1(f789(f789(f342(x70791),x70792),x70794))+~P1(f789(f789(f240(f870(x70791,a856)),x70794),x70793))
% 21.40/21.37 [7080]P1(f789(f789(f342(x70801),x70802),x70803))+~P1(f789(f789(f342(x70801),x70802),x70804))+~P1(f789(f789(f240(f870(x70801,a856)),x70804),x70803))
% 21.40/21.37 [7090]~P111(x70901)+~E(x70903,f2(x70901))+P1(f789(f789(f287(x70901),f789(f789(f90(x70901),x70902),x70903)),f789(f789(f90(x70901),x70904),x70903)))
% 21.40/21.37 [7091]~P111(x70911)+~E(x70912,f2(x70911))+P1(f789(f789(f287(x70911),f789(f789(f90(x70911),x70912),x70913)),f789(f789(f90(x70911),x70912),x70914)))
% 21.40/21.37 [7315]~P100(x73152)+~P1(f789(f789(f241(f870(x73151,x73152)),x73153),x73154))+P1(f789(f789(f240(f870(x73151,x73152)),x73153),x73154))
% 21.40/21.37 [7410]~P28(x74101,x74102,x74104)+P28(x74101,x74102,f789(f789(f310(f862(x74101)),x74103),x74104))+~P28(x74101,x74102,f789(f789(f310(f862(x74101)),x74103),f184(f870(f862(x74101),a856))))
% 21.40/21.37 [7449]~P1(f789(f789(f342(x74491),x74492),x74494))+P1(f789(f789(f342(x74491),x74492),f51(f870(x74491,a856),x74493)))+~P1(f789(f789(f342(f870(x74491,a856)),x74494),x74493))
% 21.40/21.37 [7451]~P70(x74511)+~P1(f789(f789(f240(a863),x74513),x74514))+P1(f789(f789(f287(x74511),f789(f789(f250(x74511),x74512),x74513)),f789(f789(f250(x74511),x74512),x74514)))
% 21.40/21.37 [7462]P31(x74621,x74622,x74623)+P1(f789(f789(f342(f862(x74621)),f842(x74622,x74624,x74621)),x74624))+~P1(f789(f789(f342(f862(x74621)),x74623),x74624))
% 21.40/21.37 [7481]~P75(x74811)+~P1(f789(f789(f241(x74811),x74813),x74814))+P1(f789(f789(f241(x74811),f789(f789(f89(x74811),x74812),x74813)),f789(f789(f89(x74811),x74812),x74814)))
% 21.40/21.37 [7482]~P81(x74821)+~P1(f789(f789(f241(x74821),x74823),x74824))+P1(f789(f789(f241(x74821),f789(f789(f89(x74821),x74822),x74823)),f789(f789(f89(x74821),x74822),x74824)))
% 21.40/21.37 [7483]~P75(x74831)+~P1(f789(f789(f241(x74831),x74832),x74834))+P1(f789(f789(f241(x74831),f789(f789(f89(x74831),x74832),x74833)),f789(f789(f89(x74831),x74834),x74833)))
% 21.40/21.37 [7484]~P81(x74841)+~P1(f789(f789(f241(x74841),x74842),x74844))+P1(f789(f789(f241(x74841),f789(f789(f89(x74841),x74842),x74843)),f789(f789(f89(x74841),x74844),x74843)))
% 21.40/21.37 [7485]~P75(x74851)+~P1(f789(f789(f240(x74851),x74853),x74854))+P1(f789(f789(f240(x74851),f789(f789(f89(x74851),x74852),x74853)),f789(f789(f89(x74851),x74852),x74854)))
% 21.40/21.37 [7486]~P79(x74861)+~P1(f789(f789(f240(x74861),x74863),x74864))+P1(f789(f789(f240(x74861),f789(f789(f89(x74861),x74862),x74863)),f789(f789(f89(x74861),x74862),x74864)))
% 21.40/21.37 [7487]~P75(x74871)+~P1(f789(f789(f240(x74871),x74872),x74874))+P1(f789(f789(f240(x74871),f789(f789(f89(x74871),x74872),x74873)),f789(f789(f89(x74871),x74874),x74873)))
% 21.40/21.37 [7488]~P79(x74881)+~P1(f789(f789(f240(x74881),x74882),x74884))+P1(f789(f789(f240(x74881),f789(f789(f89(x74881),x74882),x74883)),f789(f789(f89(x74881),x74884),x74883)))
% 21.40/21.37 [7489]~P111(x74891)+~P1(f789(f789(f287(x74891),x74893),x74894))+P1(f789(f789(f287(x74891),f789(f789(f90(x74891),x74892),x74893)),f789(f789(f90(x74891),x74892),x74894)))
% 21.40/21.37 [7490]~P111(x74901)+~P1(f789(f789(f287(x74901),x74902),x74904))+P1(f789(f789(f287(x74901),f789(f789(f90(x74901),x74902),x74903)),f789(f789(f90(x74901),x74904),x74903)))
% 21.40/21.37 [7491]~P70(x74911)+~P1(f789(f789(f287(x74911),x74912),x74914))+P1(f789(f789(f287(x74911),f789(f789(f250(x74911),x74912),x74913)),f789(f789(f250(x74911),x74914),x74913)))
% 21.40/21.37 [7500]~P135(x75001)+~P89(x75001)+E(f789(f789(f89(x75001),f789(f789(f90(x75001),x75002),f789(f113(x75001),x75003))),f789(f789(f90(x75001),x75004),f789(f113(x75001),x75003))),f789(f789(f90(x75001),f789(f789(f89(x75001),x75002),x75004)),f789(f113(x75001),x75003)))
% 21.40/21.37 [7501]~P121(x75011)+~P89(x75011)+E(f789(f789(f3(x75011),f789(f789(f90(x75011),x75012),f789(f113(x75011),x75013))),f789(f789(f90(x75011),x75014),f789(f113(x75011),x75013))),f789(f789(f90(x75011),f789(f789(f3(x75011),x75012),x75014)),f789(f113(x75011),x75013)))
% 21.40/21.37 [7537]~P4(x75371)+E(f789(f789(f89(x75371),f789(x75372,x75373)),f789(f789(f8(a863,x75371),x75372),f303(a863,f789(a121,x75373),x75374))),f789(f789(f8(a863,x75371),x75372),f303(a863,x75373,x75374)))+~P1(f789(f789(f240(a863),x75373),x75374))
% 21.40/21.37 [7548]~P29(x75482,x75481,x75483,f789(f163(x75482),x75484))+~P1(f789(f134(x75482),x75484))+P1(f789(f134(x75481),f789(f789(f150(x75482,x75481),x75483),x75484)))
% 21.40/21.37 [7597]~P1(f789(f789(f241(a863),x75972),x75974))+~P1(f789(f789(f241(a863),x75971),x75973))+P1(f789(f789(f241(a863),f789(f789(f89(a863),x75971),x75972)),f789(f789(f89(a863),x75973),x75974)))
% 21.40/21.37 [7600]~P1(f789(f789(f241(a1),x76001),x76003))+~P1(f789(f789(f240(a1),x76002),x76004))+P1(f789(f789(f241(a1),f789(f789(f89(a1),x76001),x76002)),f789(f789(f89(a1),x76003),x76004)))
% 21.40/21.37 [7601]~P1(f789(f789(f240(a863),x76012),x76014))+~P1(f789(f789(f240(a863),x76011),x76013))+P1(f789(f789(f240(a863),f789(f789(f89(a863),x76011),x76012)),f789(f789(f89(a863),x76013),x76014)))
% 21.40/21.37 [7602]~P1(f789(f789(f240(a863),x76022),x76024))+~P1(f789(f789(f240(a863),x76021),x76023))+P1(f789(f789(f240(a863),f789(f789(f90(a863),x76021),x76022)),f789(f789(f90(a863),x76023),x76024)))
% 21.40/21.37 [7651]P1(f789(f789(f342(x76511),x76512),x76513))+~P1(f789(f789(f342(x76511),x76512),f52(f870(x76511,a856),x76514)))+~P1(f789(f789(f342(f870(x76511,a856)),x76513),x76514))
% 21.40/21.38 [7652]P1(f789(f789(f342(x76521),x76522),x76523))+~P1(f789(f789(f342(x76521),x76522),f52(f870(x76521,a856),x76524)))+~P1(f789(f789(f342(f870(x76521,a856)),x76523),x76524))
% 21.40/21.38 [7668]~P1(f789(x76681,f738(x76681,x76683,x76682)))+P1(f789(x76681,f789(f789(f159(x76682),x76683),x76684)))+~P1(f789(f789(f241(a863),x76684),f789(f185(f864(x76682)),x76683)))
% 21.40/21.38 [7672]P1(f789(x76721,x76722))+~P1(f789(f789(f342(x76724),x76722),f789(f163(x76724),x76723)))+P1(f789(f789(f241(a863),f739(x76721,x76723,x76724)),f789(f185(f864(x76724)),x76723)))
% 21.40/21.38 [7691]~P1(f789(f789(f191(x76912),x76913),x76914))+~P1(f789(f789(f191(f37(x76911,x76912)),x76914),x76913))+P1(f789(f789(f191(f37(x76911,x76912)),x76913),x76913))
% 21.40/21.38 [7718]~P100(x77181)+~P1(f789(f789(f240(f870(x77182,x77181)),x77184),x77183))+~P1(f789(f789(f241(f870(x77182,x77181)),x77183),x77184))
% 21.40/21.38 [7761]~P1(f789(x77614,x77612))+~P1(f789(f789(f342(x77611),x77612),x77613))+P1(f789(f789(f342(x77611),x77612),f789(f789(f111(f870(x77611,a856)),x77613),f789(f264(x77611),x77614))))
% 21.40/21.38 [7780]P1(f789(f789(f342(x77801),x77802),x77803))+~P1(f789(f789(f240(f870(x77801,a856)),x77803),x77804))+P1(f789(f789(f240(f870(x77801,a856)),x77803),f789(f789(f310(x77801),x77802),x77804)))
% 21.40/21.38 [7781]P1(f789(f789(f342(x77811),x77812),x77813))+~P1(f789(f789(f240(f870(x77811,a856)),x77813),x77814))+P1(f789(f789(f240(f870(x77811,a856)),x77813),f789(f789(f310(x77811),x77812),x77814)))
% 21.40/21.38 [7910]~P1(f789(f789(f342(x79101),x79103),x79104))+~P1(f789(f789(f241(f870(x79101,a856)),x79102),x79104))+P1(f789(f789(f241(f870(x79101,a856)),x79102),f789(f789(f310(x79101),x79103),x79104)))
% 21.40/21.38 [7912]E(f789(f789(f111(f870(x79121,a856)),x79122),x79123),f184(f870(x79121,a856)))+~E(f789(f789(f111(f870(x79121,a856)),f51(f870(x79121,a856),x79124)),x79123),f184(f870(x79121,a856)))+~P1(f789(f789(f342(f870(x79121,a856)),x79122),x79124))
% 21.40/21.38 [7986]P1(f789(f789(f342(x79861),x79862),x79863))+~P1(f789(f789(f240(f870(x79861,a856)),x79863),f789(f789(f310(x79861),x79862),x79864)))+P1(f789(f789(f240(f870(x79861,a856)),x79863),x79864))
% 21.40/21.38 [7987]P1(f789(f789(f342(x79871),x79872),x79873))+~P1(f789(f789(f240(f870(x79871,a856)),x79873),f789(f789(f310(x79871),x79872),x79874)))+P1(f789(f789(f240(f870(x79871,a856)),x79873),x79874))
% 21.40/21.38 [8007]P1(f789(f789(f342(x80072),f738(x80071,x80073,x80072)),f789(f163(x80072),x80073)))+P1(f789(x80071,f789(f789(f159(x80072),x80073),x80074)))+~P1(f789(f789(f241(a863),x80074),f789(f185(f864(x80072)),x80073)))
% 21.40/21.38 [8015]~P1(f789(f789(f241(f870(x80151,a856)),x80152),x80154))+P1(f789(f789(f241(f870(x80151,a856)),x80152),x80153))+~P1(f789(f789(f241(f870(x80151,a856)),x80154),x80153))
% 21.40/21.38 [8016]~P1(f789(f789(f240(f870(x80161,a856)),x80162),x80164))+P1(f789(f789(f241(f870(x80161,a856)),x80162),x80163))+~P1(f789(f789(f241(f870(x80161,a856)),x80164),x80163))
% 21.40/21.38 [8017]~P1(f789(f789(f240(f870(x80171,a856)),x80174),x80173))+~P1(f789(f789(f241(f870(x80171,a856)),x80172),x80174))+P1(f789(f789(f241(f870(x80171,a856)),x80172),x80173))
% 21.40/21.38 [8018]~P1(f789(f789(f240(f870(x80181,a856)),x80182),x80184))+P1(f789(f789(f240(f870(x80181,a856)),x80182),x80183))+~P1(f789(f789(f240(f870(x80181,a856)),x80184),x80183))
% 21.40/21.38 [8054]~P1(f789(f789(f342(x80541),x80544),x80543))+~P1(f789(f789(f241(f870(x80541,a856)),x80542),f789(f789(f310(x80541),x80544),x80543)))+P1(f789(f789(f241(f870(x80541,a856)),x80542),x80543))
% 21.40/21.38 [8066]~P75(x80661)+P1(f789(f789(f241(x80661),x80662),x80663))+~P1(f789(f789(f241(x80661),f789(f789(f89(x80661),x80664),x80662)),f789(f789(f89(x80661),x80664),x80663)))
% 21.40/21.38 [8067]~P75(x80671)+P1(f789(f789(f241(x80671),x80672),x80673))+~P1(f789(f789(f241(x80671),f789(f789(f89(x80671),x80674),x80672)),f789(f789(f89(x80671),x80674),x80673)))
% 21.40/21.38 [8068]~P75(x80681)+P1(f789(f789(f241(x80681),x80682),x80683))+~P1(f789(f789(f241(x80681),f789(f789(f89(x80681),x80682),x80684)),f789(f789(f89(x80681),x80683),x80684)))
% 21.40/21.38 [8069]~P75(x80691)+P1(f789(f789(f241(x80691),x80692),x80693))+~P1(f789(f789(f241(x80691),f789(f789(f89(x80691),x80692),x80694)),f789(f789(f89(x80691),x80693),x80694)))
% 21.40/21.38 [8070]~P75(x80701)+P1(f789(f789(f240(x80701),x80702),x80703))+~P1(f789(f789(f240(x80701),f789(f789(f89(x80701),x80704),x80702)),f789(f789(f89(x80701),x80704),x80703)))
% 21.40/21.38 [8071]~P75(x80711)+P1(f789(f789(f240(x80711),x80712),x80713))+~P1(f789(f789(f240(x80711),f789(f789(f89(x80711),x80714),x80712)),f789(f789(f89(x80711),x80714),x80713)))
% 21.40/21.38 [8072]~P75(x80721)+P1(f789(f789(f240(x80721),x80722),x80723))+~P1(f789(f789(f240(x80721),f789(f789(f89(x80721),x80722),x80724)),f789(f789(f89(x80721),x80723),x80724)))
% 21.40/21.38 [8073]~P75(x80731)+P1(f789(f789(f240(x80731),x80732),x80733))+~P1(f789(f789(f240(x80731),f789(f789(f89(x80731),x80732),x80734)),f789(f789(f89(x80731),x80733),x80734)))
% 21.40/21.38 [8236]P1(f789(x82361,x82362))+~P1(f789(f789(f342(x82363),x82362),f789(f163(x82363),x82364)))+P1(f789(f789(f241(a863),f789(f185(f864(x82363)),f789(f133(x82363,x82361),x82364))),f789(f185(f864(x82363)),x82364)))
% 21.40/21.38 [8367]E(x83671,x83672)+P1(f789(f789(f191(x83673),x83671),f445(x83672,x83671,x83673,x83674)))+~P1(f789(f789(f191(f37(x83674,x83673)),x83671),x83672))
% 21.40/21.38 [8368]E(x83681,x83682)+P1(f789(f789(f191(x83683),x83681),f623(x83682,x83681,x83683,x83684)))+~P1(f789(f789(f191(f37(x83684,x83683)),x83681),x83682))
% 21.40/21.38 [8395]~P1(f789(x83954,x83952))+P1(f789(f789(f191(x83951),x83952),f445(x83953,x83952,x83951,x83954)))+~P1(f789(f789(f191(f37(x83954,x83951)),x83952),x83953))
% 21.40/21.38 [8396]~P1(f789(x83964,x83962))+P1(f789(f789(f191(x83961),x83962),f623(x83963,x83962,x83961,x83964)))+~P1(f789(f789(f191(f37(x83964,x83961)),x83962),x83963))
% 21.40/21.38 [8720]~P29(x87204,x87203,x87201,f247(f870(x87204,a856)))+E(f789(x87201,f537(x87202,x87201,x87203,x87204)),x87202)+~P1(f789(f789(f342(x87203),x87202),f789(f311(x87204,x87203,x87201),f247(f870(x87204,a856)))))
% 21.40/21.38 [8861]~P1(f789(f70(x88611),x88614))+P1(f789(f789(f342(x88611),f567(x88612,x88613,x88614,x88611)),x88614))+P1(f789(f70(f869(x88611,x88613)),f789(f789(f256(x88611,x88613),x88614),x88612)))
% 21.40/21.38 [8904]E(x89041,x89042)+P1(f789(f789(f191(f37(x89043,x89044)),f445(x89041,x89042,x89044,x89043)),x89041))+~P1(f789(f789(f191(f37(x89043,x89044)),x89042),x89041))
% 21.40/21.38 [8905]E(x89051,x89052)+P1(f789(f789(f191(f37(x89053,x89054)),f623(x89051,x89052,x89054,x89053)),x89051))+~P1(f789(f789(f191(f37(x89053,x89054)),x89052),x89051))
% 21.40/21.38 [8924]~P1(f789(x89241,x89244))+P1(f789(f789(f191(f37(x89241,x89242)),f445(x89243,x89244,x89242,x89241)),x89243))+~P1(f789(f789(f191(f37(x89241,x89242)),x89244),x89243))
% 21.40/21.38 [8925]~P1(f789(x89251,x89254))+P1(f789(f789(f191(f37(x89251,x89252)),f623(x89253,x89254,x89252,x89251)),x89253))+~P1(f789(f789(f191(f37(x89251,x89252)),x89254),x89253))
% 21.40/21.38 [9165]~P1(f789(f70(x91651),x91653))+~P1(f789(f70(x91652),f789(x91654,f567(x91654,x91652,x91653,x91651))))+P1(f789(f70(f869(x91651,x91652)),f789(f789(f256(x91651,x91652),x91653),x91654)))
% 21.40/21.38 [9180]~E(f789(f185(f864(x91804)),x91802),f789(f185(f864(x91804)),x91803))+P1(f789(f789(f342(f869(f864(x91804),f864(x91804))),f789(f789(f249(f864(x91804),f864(x91804)),x91803),x91802)),f154(x91804,x91801)))+P1(f789(f789(f241(a863),f745(x91801,x91802,x91803,x91804)),f789(f185(f864(x91804)),x91803)))
% 21.40/21.38 [9289]E(f789(f789(f164(x92891),f746(x92892,x92893,x92894,x92891)),x92893),f789(f789(f164(x92891),f746(x92892,x92893,x92894,x92891)),x92894))+~P1(f789(f789(f342(f869(f864(x92891),f864(x92891))),f789(f789(f249(f864(x92891),f864(x92891)),x92894),x92893)),f143(x92891,x92892)))+P1(f789(f789(f241(a863),f789(f185(f864(x92891)),x92894)),f789(f185(f864(x92891)),x92893)))
% 21.40/21.38 [9349]~P1(f789(f789(f241(a863),f2(a863)),x93493))+~P1(f789(f789(f241(a863),x93494),x93491))+P1(f789(f789(f241(a863),f789(f789(f89(a863),f789(f789(f90(a863),x93491),f59(a863,x93492,x93493))),x93494)),f789(f789(f90(a863),x93491),x93493)))
% 21.40/21.38 [9534]~P100(x95342)+~P1(f789(f789(f240(x95342),f789(x95343,f814(x95344,x95343,x95341,x95342))),f789(x95344,f814(x95344,x95343,x95341,x95342))))+P1(f789(f789(f240(f870(x95341,x95342)),x95343),x95344))
% 21.40/21.38 [9632]~P6(x96321)+E(f789(f789(f8(a863,x96321),f789(f789(f20(a863,x96321,x96321),f789(f789(f10(x96321,f870(x96321,x96321),a863),f3(x96321)),x96322)),f789(f789(f10(a863,x96321,a863),x96322),f789(f789(f9(a863,a863,a863),f89(a863)),f87(a863))))),f303(a863,x96323,x96324)),f789(f789(f3(x96321),f789(x96322,x96323)),f789(x96322,f789(f789(f89(a863),x96324),f87(a863)))))+~P1(f789(f789(f240(a863),x96323),x96324))
% 21.40/21.38 [6671]~P7(x66711)+E(f789(f789(f50(x66711),f789(f789(f90(x66711),x66712),x66713)),x66714),f789(f789(f90(x66711),x66712),f789(f789(f50(x66711),x66713),x66714)))+~P1(f789(f789(f287(x66711),x66714),x66713))
% 21.40/21.38 [6761]E(f789(f789(f132(x67611),x67612),x67613),x67614)+~E(x67613,f789(f789(f135(x67611),f789(f185(f864(x67611)),x67612)),x67614))+~E(f789(f789(f164(x67611),f789(f185(f864(x67611)),x67612)),x67614),x67612)
% 21.40/21.38 [6821]~P61(x68212)+E(x68211,f2(x68212))+E(f789(f789(f291(x68212),f789(f789(f250(x68212),x68213),x68214)),f789(f789(f250(x68212),x68211),x68214)),f789(f789(f250(x68212),f789(f789(f291(x68212),x68213),x68211)),x68214))
% 21.40/21.38 [6970]~P7(x69701)+E(f789(f789(f50(x69701),f789(f789(f90(x69701),x69702),x69703)),x69704),f789(f789(f90(x69701),f789(f789(f50(x69701),x69702),x69704)),x69703))+~P1(f789(f789(f287(x69701),x69704),x69702))
% 21.40/21.38 [6979]~P101(x69791)+~P1(f789(f789(f241(x69791),x69793),x69794))+P1(f789(f789(f241(x69791),f789(f789(f244(x69791),x69792),x69793)),x69794))
% 21.40/21.38 [6980]~P101(x69801)+~P1(f789(f789(f241(x69801),x69803),x69804))+P1(f789(f789(f241(x69801),f789(f789(f244(x69801),x69802),x69803)),x69804))
% 21.40/21.38 [6981]~P101(x69811)+~P1(f789(f789(f241(x69811),x69812),x69814))+P1(f789(f789(f241(x69811),f789(f789(f244(x69811),x69812),x69813)),x69814))
% 21.40/21.38 [6982]~P101(x69821)+~P1(f789(f789(f241(x69821),x69822),x69824))+P1(f789(f789(f241(x69821),f789(f789(f244(x69821),x69822),x69823)),x69824))
% 21.40/21.38 [6983]~P98(x69831)+~P1(f789(f789(f241(x69831),x69833),x69834))+P1(f789(f789(f241(x69831),f789(f789(f111(x69831),x69832),x69833)),x69834))
% 21.40/21.38 [6984]~P98(x69841)+~P1(f789(f789(f241(x69841),x69842),x69844))+P1(f789(f789(f241(x69841),f789(f789(f111(x69841),x69842),x69843)),x69844))
% 21.40/21.38 [6985]~P101(x69851)+~P1(f789(f789(f240(x69851),x69853),x69854))+P1(f789(f789(f240(x69851),f789(f789(f244(x69851),x69852),x69853)),x69854))
% 21.40/21.38 [6986]~P101(x69861)+~P1(f789(f789(f240(x69861),x69863),x69864))+P1(f789(f789(f240(x69861),f789(f789(f244(x69861),x69862),x69863)),x69864))
% 21.40/21.38 [6987]~P101(x69871)+~P1(f789(f789(f240(x69871),x69872),x69874))+P1(f789(f789(f240(x69871),f789(f789(f244(x69871),x69872),x69873)),x69874))
% 21.40/21.38 [6988]~P101(x69881)+~P1(f789(f789(f240(x69881),x69882),x69884))+P1(f789(f789(f240(x69881),f789(f789(f244(x69881),x69882),x69883)),x69884))
% 21.40/21.38 [6989]~P98(x69891)+~P1(f789(f789(f240(x69891),x69893),x69894))+P1(f789(f789(f240(x69891),f789(f789(f111(x69891),x69892),x69893)),x69894))
% 21.40/21.38 [6990]~P98(x69901)+~P1(f789(f789(f240(x69901),x69902),x69904))+P1(f789(f789(f240(x69901),f789(f789(f111(x69901),x69902),x69903)),x69904))
% 21.40/21.38 [7007]~P1(f789(x70073,x70074))+~P1(f789(x70072,x70074))+P1(f789(f789(f789(f111(f870(x70071,a856)),x70072),x70073),x70074))
% 21.40/21.38 [7039]~E(f789(f185(f864(x70391)),x70393),f789(f185(f864(x70392)),x70394))+~P1(f789(f134(x70391),x70393))+E(f173(x70391,x70392,f170(x70391,x70392,f789(f789(f171(x70391,x70392),x70393),x70394))),f789(f163(x70391),x70393))
% 21.40/21.38 [7133]P28(x71331,x71332,x71333)+~P28(x71331,x71334,x71333)+~P1(f789(f789(f240(f870(f862(x71331),a856)),x71334),x71332))
% 21.40/21.38 [7134]P28(x71341,x71342,x71343)+~P28(x71341,x71342,x71344)+~P1(f789(f789(f240(f870(f862(x71341),a856)),x71343),x71344))
% 21.40/21.38 [7272]~P7(x72721)+E(f789(f789(f50(x72721),f789(f789(f250(x72721),x72722),x72723)),f789(f789(f250(x72721),x72724),x72723)),f789(f789(f250(x72721),f789(f789(f50(x72721),x72722),x72724)),x72723))+~P1(f789(f789(f287(x72721),x72724),x72722))
% 21.40/21.38 [7527]~P4(x75271)+E(f789(f789(f89(x75271),f789(x75272,x75273)),f789(f789(f8(a863,x75271),x75272),f789(f302(a863,f789(a121,x75273)),x75274))),f789(f789(f8(a863,x75271),x75272),f789(f302(a863,x75273),x75274)))+~P1(f789(f789(f241(a863),x75273),x75274))
% 21.40/21.38 [7555]~P101(x75551)+P1(f789(f789(f241(x75551),x75552),x75553))+~P1(f789(f789(f241(x75551),f789(f789(f239(x75551),x75554),x75552)),x75553))
% 21.40/21.38 [7556]~P101(x75561)+P1(f789(f789(f241(x75561),x75562),x75563))+~P1(f789(f789(f241(x75561),f789(f789(f239(x75561),x75562),x75564)),x75563))
% 21.40/21.38 [7557]~P101(x75571)+P1(f789(f789(f240(x75571),x75572),x75573))+~P1(f789(f789(f240(x75571),f789(f789(f239(x75571),x75574),x75572)),x75573))
% 21.40/21.38 [7558]~P101(x75581)+P1(f789(f789(f240(x75581),x75582),x75583))+~P1(f789(f789(f240(x75581),f789(f789(f239(x75581),x75584),x75582)),x75583))
% 21.40/21.38 [7559]~P101(x75591)+P1(f789(f789(f240(x75591),x75592),x75593))+~P1(f789(f789(f240(x75591),f789(f789(f239(x75591),x75592),x75594)),x75593))
% 21.40/21.38 [7560]~P101(x75601)+P1(f789(f789(f240(x75601),x75602),x75603))+~P1(f789(f789(f240(x75601),f789(f789(f239(x75601),x75602),x75604)),x75603))
% 21.40/21.38 [7561]~P94(x75611)+P1(f789(f789(f240(x75611),x75612),x75613))+~P1(f789(f789(f240(x75611),f789(f789(f110(x75611),x75614),x75612)),x75613))
% 21.40/21.38 [7562]~P94(x75621)+P1(f789(f789(f240(x75621),x75622),x75623))+~P1(f789(f789(f240(x75621),f789(f789(f110(x75621),x75624),x75622)),x75623))
% 21.40/21.38 [7563]~P94(x75631)+P1(f789(f789(f240(x75631),x75632),x75633))+~P1(f789(f789(f240(x75631),f789(f789(f110(x75631),x75632),x75634)),x75633))
% 21.40/21.38 [7564]~P94(x75641)+P1(f789(f789(f240(x75641),x75642),x75643))+~P1(f789(f789(f240(x75641),f789(f789(f110(x75641),x75642),x75644)),x75643))
% 21.40/21.38 [7565]~P70(x75651)+P1(f789(f789(f287(x75651),x75652),x75653))+~P1(f789(f789(f287(x75651),f789(f789(f90(x75651),x75654),x75652)),x75653))
% 21.40/21.38 [7566]~P70(x75661)+P1(f789(f789(f287(x75661),x75662),x75663))+~P1(f789(f789(f287(x75661),f789(f789(f90(x75661),x75662),x75664)),x75663))
% 21.40/21.38 [7643]~P1(f789(f789(f342(x76431),x76432),x76434))+P1(f789(f789(f342(x76431),x76432),x76433))+P1(f789(f789(f342(x76431),x76432),f789(f789(f3(f870(x76431,a856)),x76434),x76433)))
% 21.40/21.38 [7644]~P1(f789(f789(f342(x76441),x76442),x76444))+P1(f789(f789(f342(x76441),x76442),x76443))+P1(f789(f789(f342(x76441),x76442),f789(f789(f3(f870(x76441,a856)),x76444),x76443)))
% 21.40/21.38 [7723]P1(f789(x77231,x77232))+P1(f789(x77233,x77232))+~P1(f789(f789(f789(f110(f870(x77234,a856)),x77233),x77231),x77232))
% 21.40/21.38 [7732]~P1(f789(f789(f342(x77321),x77322),x77324))+~P1(f789(f789(f342(x77321),x77322),x77323))+P1(f789(f789(f342(x77321),x77322),f789(f789(f111(f870(x77321,a856)),x77323),x77324)))
% 21.40/21.38 [7733]~P1(f789(f789(f342(x77331),x77332),x77334))+~P1(f789(f789(f342(x77331),x77332),x77333))+P1(f789(f789(f342(x77331),x77332),f789(f789(f111(f870(x77331,a856)),x77333),x77334)))
% 21.40/21.38 [7789]~P101(x77891)+~P1(f789(f70(x77891),x77894))+E(f789(f789(f73(x77891,x77891,f244(x77891)),x77892),f789(f789(f310(x77891),x77893),x77894)),f789(f789(f244(x77891),x77893),f789(f789(f73(x77891,x77891,f244(x77891)),x77892),x77894)))
% 21.40/21.38 [7790]~P101(x77901)+~P1(f789(f70(x77901),x77904))+E(f789(f789(f73(x77901,x77901,f239(x77901)),x77902),f789(f789(f310(x77901),x77903),x77904)),f789(f789(f239(x77901),x77903),f789(f789(f73(x77901,x77901,f239(x77901)),x77902),x77904)))
% 21.40/21.38 [7791]~P94(x77911)+~P1(f789(f70(x77911),x77914))+E(f789(f789(f73(x77911,x77911,f110(x77911)),x77912),f789(f789(f310(x77911),x77913),x77914)),f789(f789(f110(x77911),x77913),f789(f789(f73(x77911,x77911,f110(x77911)),x77912),x77914)))
% 21.40/21.38 [7792]~P98(x77921)+~P1(f789(f70(x77921),x77924))+E(f789(f789(f73(x77921,x77921,f111(x77921)),x77922),f789(f789(f310(x77921),x77923),x77924)),f789(f789(f111(x77921),x77923),f789(f789(f73(x77921,x77921,f111(x77921)),x77922),x77924)))
% 21.40/21.38 [7794]~P135(x77941)+~P89(x77941)+E(f789(f789(f89(x77941),f789(f789(f90(x77941),f789(f113(x77941),x77942)),x77943)),f789(f789(f90(x77941),f789(f113(x77941),x77942)),x77944)),f789(f789(f90(x77941),f789(f113(x77941),x77942)),f789(f789(f89(x77941),x77943),x77944)))
% 21.40/21.38 [7795]~P121(x77951)+~P89(x77951)+E(f789(f789(f3(x77951),f789(f789(f90(x77951),f789(f113(x77951),x77952)),x77953)),f789(f789(f90(x77951),f789(f113(x77951),x77952)),x77954)),f789(f789(f90(x77951),f789(f113(x77951),x77952)),f789(f789(f3(x77951),x77953),x77954)))
% 21.40/21.38 [7908]E(x79081,x79082)+P1(f789(f789(f342(x79083),x79081),f789(f163(x79083),x79084)))+~P1(f789(f789(f342(x79083),x79081),f789(f163(x79083),f789(f789(f146(x79083),x79082),x79084))))
% 21.40/21.38 [8077]P53(x80771,x80772,x80773)+~P53(x80771,x80772,x80774)+~P1(f789(f789(f240(f870(f869(x80771,x80772),a856)),x80773),x80774))
% 21.40/21.38 [8119]P1(f789(f789(f342(x81191),x81192),x81193))+P1(f789(f789(f342(x81191),x81192),x81194))+~P1(f789(f789(f342(x81191),x81192),f789(f789(f110(f870(x81191,a856)),x81194),x81193)))
% 21.40/21.38 [8120]P1(f789(f789(f342(x81201),x81202),x81203))+P1(f789(f789(f342(x81201),x81202),x81204))+~P1(f789(f789(f342(x81201),x81202),f789(f789(f110(f870(x81201,a856)),x81204),x81203)))
% 21.40/21.38 [8129]~P47(x81291,x81294,x81293)+~P1(f789(f789(f342(x81291),x81292),x81294))+P1(f789(f789(f342(f869(x81291,x81291)),f789(f789(f249(x81291,x81291),x81292),x81292)),x81293))
% 21.40/21.38 [8130]~P47(x81301,x81304,x81303)+~P1(f789(f789(f342(x81301),x81302),x81304))+P1(f789(f789(f342(f869(x81301,x81301)),f789(f789(f249(x81301,x81301),x81302),x81302)),x81303))
% 21.40/21.38 [8131]~P47(x81311,x81314,x81313)+~P1(f789(f789(f342(x81311),x81312),x81314))+P1(f789(f789(f342(f869(x81311,x81311)),f789(f789(f249(x81311,x81311),x81312),x81312)),x81313))
% 21.40/21.38 [8143]~P1(f789(f70(x81432),x81434))+~P1(f789(f70(x81431),x81433))+P1(f789(f70(f869(x81431,x81432)),f789(f789(f256(x81431,x81432),x81433),f789(f18(f870(x81432,a856),x81431),x81434))))
% 21.40/21.38 [8144]~P1(f789(f789(f342(x81441),x81442),x81444))+~P1(f789(f789(f240(f870(x81441,a856)),x81443),x81444))+P1(f789(f789(f240(f870(x81441,a856)),f789(f789(f310(x81441),x81442),x81443)),x81444))
% 21.40/21.38 [8152]~P2(x81522)+~P69(x81522)+E(f789(f789(f11(x81521,x81522),f789(f789(f10(a863,x81522,x81521),f109(x81522)),x81523)),x81524),f789(f109(x81522),f789(f789(f11(x81521,a863),x81523),x81524)))
% 21.40/21.38 [8153]~P120(x81532)+~P69(x81532)+E(f789(f789(f11(x81531,x81532),f789(f789(f10(a1,x81532,x81531),f112(x81532)),x81533)),x81534),f789(f112(x81532),f789(f789(f11(x81531,a1),x81533),x81534)))
% 21.40/21.38 [8178]E(f789(f789(f3(f870(x81781,a856)),x81782),f789(f789(f3(f870(x81781,a856)),x81783),x81784)),x81784)+~P1(f789(f789(f240(f870(x81781,a856)),x81782),x81783))+~P1(f789(f789(f240(f870(x81781,a856)),x81784),x81782))
% 21.40/21.38 [8270]~P1(f789(f70(x82701),x82704))+E(f789(f789(f3(a863),f789(f789(f8(x82701,a863),x82702),x82703)),f789(f789(f8(x82701,a863),x82702),x82704)),f789(f789(f8(x82701,a863),x82702),f789(f789(f3(f870(x82701,a856)),x82703),x82704)))+~P1(f789(f789(f240(f870(x82701,a856)),x82704),x82703))
% 21.40/21.38 [8428]~P12(x84281,x84284,x84283)+~P1(f789(f789(f342(x84281),x84282),x84284))+P1(f789(f789(f342(x84281),x84282),f789(f285(x84281,x84281,x84283),f789(f789(f310(x84281),x84282),f184(f870(x84281,a856))))))
% 21.40/21.38 [8490]~P1(f789(f789(f240(f870(x84901,a856)),x84902),x84903))+~P1(f789(f789(f240(f870(x84901,a856)),x84902),x84904))+P1(f789(f789(f240(f870(x84901,a856)),x84902),f789(f789(f111(f870(x84901,a856)),x84903),x84904)))
% 21.40/21.38 [8582]E(x85821,f184(f870(x85822,a856)))+P1(f789(f70(x85823),x85824))+~P1(f789(f70(f869(x85823,x85822)),f789(f789(f256(x85823,x85822),x85824),f789(f18(f870(x85822,a856),x85823),x85821))))
% 21.40/21.38 [8583]E(x85831,f184(f870(x85832,a856)))+P1(f789(f70(x85833),x85834))+~P1(f789(f70(f869(x85832,x85833)),f789(f789(f256(x85832,x85833),x85831),f789(f18(f870(x85833,a856),x85832),x85834))))
% 21.40/21.38 [8641]P1(f789(f789(f342(x86411),x86412),f330(x86411,x86413)))+~P1(f789(f789(f342(x86411),x86414),f330(x86411,x86413)))+~P1(f789(f789(f342(f869(x86411,x86411)),f789(f789(f249(x86411,x86411),x86412),x86414)),x86413))
% 21.40/21.38 [8642]P1(f789(f789(f342(x86421),x86422),f330(x86421,x86423)))+~P1(f789(f789(f342(x86421),x86424),f330(x86421,x86423)))+~P1(f789(f789(f342(f869(x86421,x86421)),f789(f789(f249(x86421,x86421),x86422),x86424)),x86423))
% 21.40/21.38 [8694]~P36(x86941,x86944)+P1(f789(f789(f342(f869(x86941,x86941)),f789(f789(f249(x86941,x86941),x86943),x86942)),f308(x86941,x86944)))+P36(x86941,f789(f789(f310(f869(x86941,x86941)),f789(f789(f249(x86941,x86941),x86942),x86943)),x86944))
% 21.40/21.38 [8695]~P56(x86951,x86954)+P1(f789(f789(f342(f869(x86951,x86951)),f789(f789(f249(x86951,x86951),x86953),x86952)),f308(x86951,x86954)))+P56(x86951,f789(f789(f310(f869(x86951,x86951)),f789(f789(f249(x86951,x86951),x86952),x86953)),x86954))
% 21.40/21.38 [8766]~E(x87662,x87663)+~P1(f789(f789(f342(x87661),x87662),f789(f163(x87661),x87664)))+P1(f789(f789(f342(f869(x87661,x87661)),f789(f789(f249(x87661,x87661),x87662),x87663)),f789(f163(f869(x87661,x87661)),f789(f789(f171(x87661,x87661),x87664),x87664))))
% 21.40/21.38 [8838]~E(x88383,x88384)+P1(f789(f789(f259(x88381,x88381,a856),a338),x88382))+~P1(f789(f789(f342(f869(x88381,x88381)),x88382),f789(f163(f869(x88381,x88381)),f789(f789(f171(x88381,x88381),x88383),x88384))))
% 21.40/21.38 [8876]P1(f789(f789(f342(f869(f864(x88761),f864(x88761))),f789(f789(f249(f864(x88761),f864(x88761)),x88762),x88763)),f143(x88761,x88764)))+~E(f789(f789(f164(x88761),f789(f185(f864(x88761)),x88762)),x88763),x88762)+~P1(f789(f789(f241(a863),f789(f185(f864(x88761)),x88762)),f789(f185(f864(x88761)),x88763)))
% 21.40/21.38 [8969]~P1(f789(f70(x89691),x89694))+P1(f789(f789(f342(x89691),f421(x89692,x89693,x89694,x89691)),x89694))+P1(f789(f70(x89693),f789(f789(f53(x89691,f870(x89693,a856)),x89694),x89692)))
% 21.40/21.38 [8970]~P1(f789(f70(x89701),x89704))+P1(f789(f789(f342(x89701),f617(x89702,x89703,x89704,x89701)),x89704))+P1(f789(f70(x89703),f789(f789(f53(x89701,f870(x89703,a856)),x89704),x89702)))
% 21.40/21.38 [9050]P1(f789(f789(f342(f869(x90501,x90501)),x90502),f789(f789(f289(x90501,x90501,x90501),x90503),f308(x90501,x90503))))+~P1(f789(f789(f241(a863),f2(a863)),x90504))+~P1(f789(f789(f342(f869(x90501,x90501)),x90502),f789(f789(f178(f869(x90501,x90501),a856),x90504),x90503)))
% 21.40/21.38 [9057]~P36(x90571,x90572)+~P1(f789(f789(f342(f869(x90571,x90571)),f789(f789(f249(x90571,x90571),x90574),x90573)),x90572))+~P1(f789(f789(f342(f869(x90571,x90571)),f789(f789(f249(x90571,x90571),x90573),x90574)),x90572))
% 21.40/21.38 [9058]~P36(x90581,x90582)+~P1(f789(f789(f342(f869(x90581,x90581)),f789(f789(f249(x90581,x90581),x90584),x90583)),x90582))+~P1(f789(f789(f342(f869(x90581,x90581)),f789(f789(f249(x90581,x90581),x90583),x90584)),x90582))
% 21.40/21.38 [9176]~P1(f789(f70(x91761),x91764))+E(f789(f789(f8(x91761,a863),f789(f789(f10(f870(x91762,a856),a863,x91761),f49(x91762)),x91763)),x91764),f789(f49(f869(x91761,x91762)),f789(f789(f256(x91761,x91762),x91764),x91763)))+P1(f789(f789(f342(x91761),f571(x91763,x91762,x91764,x91761)),x91764))
% 21.40/21.38 [9178]~P1(f789(f134(x91781),x91782))+P1(f789(f134(x91781),f789(f789(f155(x91781,x91782),x91783),x91784)))+P1(f789(f789(f342(x91781),x91784),f789(f789(f3(f870(x91781,a856)),f789(f163(x91781),x91782)),f789(f789(f310(x91781),f789(f789(f159(x91781),x91782),x91783)),f184(f870(x91781,a856))))))
% 21.40/21.38 [9187]~P1(f789(f70(x91872),x91873))+~P1(f789(f70(x91871),f789(x91874,f421(x91874,x91871,x91873,x91872))))+P1(f789(f70(x91871),f789(f789(f53(x91872,f870(x91871,a856)),x91873),x91874)))
% 21.40/21.38 [9188]~P1(f789(f70(x91882),x91883))+~P1(f789(f70(x91881),f789(x91884,f617(x91884,x91881,x91883,x91882))))+P1(f789(f70(x91881),f789(f789(f53(x91882,f870(x91881,a856)),x91883),x91884)))
% 21.40/21.38 [9250]~P1(f789(f789(f342(f869(x92501,x92501)),x92502),f789(f789(f289(x92501,x92501,x92501),x92504),f308(x92501,x92504))))+P1(f789(f789(f342(f869(x92501,x92501)),x92502),f789(f789(f289(x92501,x92501,x92501),x92503),f308(x92501,x92503))))+~P1(f789(f789(f240(f870(f869(x92501,x92501),a856)),x92504),x92503))
% 21.40/21.38 [9258]E(f789(f789(f164(x92581),f746(x92584,x92583,x92582,x92581)),x92583),f789(f789(f164(x92581),f746(x92584,x92583,x92582,x92581)),x92582))+~P1(f789(f789(f342(f869(f864(x92581),f864(x92581))),f789(f789(f249(f864(x92581),f864(x92581)),x92582),x92583)),f143(x92581,x92584)))+E(f789(f789(f164(x92581),f789(f185(f864(x92581)),x92582)),x92583),x92582)
% 21.40/21.38 [9274]~P1(f789(f70(x92741),x92744))+E(f789(f789(f8(x92741,a863),f789(f789(f10(f870(x92742,a856),a863,x92741),f49(x92742)),x92743)),x92744),f789(f49(f869(x92741,x92742)),f789(f789(f256(x92741,x92742),x92744),x92743)))+~P1(f789(f70(x92742),f789(x92743,f571(x92743,x92742,x92744,x92741))))
% 21.40/21.38 [9278]~E(f789(f185(f864(x92781)),x92783),f789(f185(f864(x92781)),x92782))+P1(f789(f789(f342(f869(f864(x92781),f864(x92781))),f789(f789(f249(f864(x92781),f864(x92781)),x92782),x92783)),f154(x92781,x92784)))+P1(f789(f789(f342(f869(x92781,x92781)),f730(x92784,x92783,x92782,x92781)),f789(f163(f869(x92781,x92781)),f789(f789(f171(x92781,x92781),x92782),x92783))))
% 21.40/21.38 [9361]~P1(f789(f789(f342(f869(f864(x93611),f864(x93611))),f789(f789(f249(f864(x93611),f864(x93611)),x93612),x93613)),f143(x93611,x93614)))+E(f789(f789(f164(x93611),f789(f185(f864(x93611)),x93612)),x93613),x93612)+P1(f789(f789(f241(a863),f746(x93614,x93613,x93612,x93611)),f789(f789(f244(a863),f789(f185(f864(x93611)),x93612)),f789(f185(f864(x93611)),x93613))))
% 21.40/21.38 [9381]~P1(f789(f789(f342(f869(f864(x93811),f864(x93811))),f789(f789(f249(f864(x93811),f864(x93811)),x93812),x93813)),f143(x93811,x93814)))+P1(f789(f789(f241(a863),f789(f185(f864(x93811)),x93812)),f789(f185(f864(x93811)),x93813)))+P1(f789(f789(f241(a863),f746(x93814,x93813,x93812,x93811)),f789(f789(f244(a863),f789(f185(f864(x93811)),x93812)),f789(f185(f864(x93811)),x93813))))
% 21.40/21.38 [9667]~P1(f789(f789(f789(x96671,f719(x96671,x96674,x96673,x96672)),f720(x96671,x96674,x96673,x96672)),f721(x96671,x96674,x96673,x96672)))+P1(f789(f789(f789(x96671,x96672),x96673),x96674))+~P1(f789(f329(f869(f870(a1,f867(f864(a854))),f869(a1,a1)),a319),f789(f789(f249(f870(a1,f867(f864(a854))),f869(a1,a1)),x96672),f789(f789(f249(a1,a1),x96673),x96674))))
% 21.40/21.38 [9726]P1(f789(f789(f789(x97261,x97262),x97263),x97264))+P1(f789(f329(f869(f870(a1,f867(f864(a854))),f869(a1,a1)),a319),f789(f789(f249(f870(a1,f867(f864(a854))),f869(a1,a1)),f719(x97261,x97264,x97263,x97262)),f789(f789(f249(a1,a1),f720(x97261,x97264,x97263,x97262)),f721(x97261,x97264,x97263,x97262)))))+~P1(f789(f329(f869(f870(a1,f867(f864(a854))),f869(a1,a1)),a319),f789(f789(f249(f870(a1,f867(f864(a854))),f869(a1,a1)),x97262),f789(f789(f249(a1,a1),x97263),x97264))))
% 21.40/21.38 [9765]~P1(f789(f789(f342(f869(f864(x97651),f864(x97651))),f789(f789(f249(f864(x97651),f864(x97651)),x97652),x97653)),f143(x97651,x97654)))+E(f789(f789(f164(x97651),f789(f185(f864(x97651)),x97652)),x97653),x97652)+P1(f789(f789(f342(f869(x97651,x97651)),f789(f789(f249(x97651,x97651),f789(f789(f159(x97651),x97652),f746(x97654,x97653,x97652,x97651))),f789(f789(f159(x97651),x97653),f746(x97654,x97653,x97652,x97651)))),x97654))
% 21.40/21.38 [9768]~P1(f789(f789(f342(f869(f864(x97681),f864(x97681))),f789(f789(f249(f864(x97681),f864(x97681)),x97682),x97683)),f143(x97681,x97684)))+P1(f789(f789(f241(a863),f789(f185(f864(x97681)),x97682)),f789(f185(f864(x97681)),x97683)))+P1(f789(f789(f342(f869(x97681,x97681)),f789(f789(f249(x97681,x97681),f789(f789(f159(x97681),x97682),f746(x97684,x97683,x97682,x97681))),f789(f789(f159(x97681),x97683),f746(x97684,x97683,x97682,x97681)))),x97684))
% 21.40/21.38 [9838]~E(f789(f185(f864(x98381)),x98382),f789(f185(f864(x98381)),x98383))+P1(f789(f789(f342(f869(f864(x98381),f864(x98381))),f789(f789(f249(f864(x98381),f864(x98381)),x98382),x98383)),f154(x98381,x98384)))+~P1(f789(f789(f342(f869(x98381,x98381)),f789(f789(f249(x98381,x98381),f789(f789(f159(x98381),x98382),f745(x98384,x98383,x98382,x98381))),f789(f789(f159(x98381),x98383),f745(x98384,x98383,x98382,x98381)))),x98384))
% 21.40/21.38 [9982]~P4(x99821)+~P1(f789(f70(x99822),x99824))+E(f789(f161(x99821),f789(f789(f150(x99822,x99821),x99823),f99(f864(x99822),f789(f789(f20(f864(x99822),a856,a856),f789(f789(f10(a856,f870(a856,a856),f864(x99822)),a339),f789(f789(f9(f864(x99822),f870(x99822,a856),a856),f789(f789(f10(f870(x99822,a856),f870(f870(x99822,a856),a856),f864(x99822)),a338),f163(x99822))),x99824))),f134(x99822))))),f232(x99822,x99821,x99823,x99824))
% 21.40/21.38 [7363]~P60(x73632)+E(x73631,f2(x73632))+E(f789(f789(f291(x73632),f789(f789(f89(x73632),x73633),f789(f789(f90(x73632),x73634),x73631))),x73631),f789(f789(f89(x73632),x73634),f789(f789(f291(x73632),x73633),x73631)))
% 21.40/21.38 [7364]~P7(x73642)+E(x73641,f2(x73642))+E(f789(f789(f50(x73642),f789(f789(f89(x73642),x73643),f789(f789(f90(x73642),x73644),x73641))),x73641),f789(f789(f89(x73642),x73644),f789(f789(f50(x73642),x73643),x73641)))
% 21.40/21.38 [7365]~P7(x73652)+E(x73651,f2(x73652))+E(f789(f789(f50(x73652),f789(f789(f89(x73652),x73653),f789(f789(f90(x73652),x73651),x73654))),x73651),f789(f789(f89(x73652),x73654),f789(f789(f50(x73652),x73653),x73651)))
% 21.40/21.38 [7606]~P60(x76062)+E(x76061,f2(x76062))+E(f789(f789(f291(x76062),f789(f789(f89(x76062),x76063),f789(f789(f90(x76062),x76064),x76061))),x76061),f789(f789(f89(x76062),f789(f789(f291(x76062),x76063),x76061)),x76064))
% 21.40/21.38 [7607]~P61(x76072)+E(x76071,f2(x76072))+E(f789(f789(f291(x76072),f789(f789(f89(x76072),x76073),f789(f789(f90(x76072),x76071),x76074))),x76071),f789(f789(f89(x76072),f789(f789(f291(x76072),x76073),x76071)),x76074))
% 21.40/21.38 [7608]~P61(x76082)+E(x76081,f2(x76082))+E(f789(f789(f291(x76082),f789(f789(f3(x76082),x76083),f789(f789(f90(x76082),x76081),x76084))),x76081),f789(f789(f3(x76082),f789(f789(f291(x76082),x76083),x76081)),x76084))
% 21.40/21.38 [8656]~E(f789(f789(f289(x86561,x86561,x86561),x86562),x86564),f184(f870(f869(x86561,x86561),a856)))+~E(f789(f789(f289(x86561,x86561,x86561),x86562),x86563),f184(f870(f869(x86561,x86561),a856)))+E(f789(f789(f289(x86561,x86561,x86561),x86562),f789(f789(f110(f870(f869(x86561,x86561),a856)),x86563),x86564)),f184(f870(f869(x86561,x86561),a856)))
% 21.40/21.38 [8767]~P1(f789(f789(f240(f870(x87671,a856)),x87673),x87674))+~P1(f789(f789(f240(f870(x87671,a856)),x87672),x87674))+P1(f789(f789(f240(f870(x87671,a856)),f789(f789(f110(f870(x87671,a856)),x87672),x87673)),x87674))
% 21.40/21.38 [9110]~P1(f789(f70(x91101),x91104))+~P1(f789(f70(x91101),x91103))+E(f789(f789(f3(a863),f789(f789(f89(a863),f789(f789(f8(x91101,a863),x91102),x91103)),f789(f789(f8(x91101,a863),x91102),x91104))),f789(f789(f8(x91101,a863),x91102),f789(f789(f111(f870(x91101,a856)),x91103),x91104))),f789(f789(f8(x91101,a863),x91102),f789(f789(f110(f870(x91101,a856)),x91103),x91104)))
% 21.40/21.38 [9185]~P1(f789(f789(f342(x91851),x91853),x91852))+~P1(f789(f789(f240(f870(x91851,a856)),x91852),f789(f789(f310(x91851),x91853),x91854)))+P1(f789(f789(f240(f870(x91851,a856)),f789(f789(f3(f870(x91851,a856)),x91852),f789(f789(f310(x91851),x91853),f184(f870(x91851,a856))))),x91854))
% 21.40/21.38 [9333]~P1(f789(f789(f342(x93331),x93333),x93332))+P1(f789(f789(f240(f870(x93331,a856)),x93332),f789(f789(f310(x93331),x93333),x93334)))+~P1(f789(f789(f240(f870(x93331,a856)),f789(f789(f3(f870(x93331,a856)),x93332),f789(f789(f310(x93331),x93333),f184(f870(x93331,a856))))),x93334))
% 21.40/21.38 [9334]~P1(f789(f789(f342(x93341),x93343),x93342))+P1(f789(f789(f240(f870(x93341,a856)),x93342),f789(f789(f310(x93341),x93343),x93344)))+~P1(f789(f789(f240(f870(x93341,a856)),f789(f789(f3(f870(x93341,a856)),x93342),f789(f789(f310(x93341),x93343),f184(f870(x93341,a856))))),x93344))
% 21.40/21.38 [9360]~P1(f789(f789(f240(f870(x93601,a856)),x93602),x93604))+P1(f789(f789(f240(f870(x93601,a856)),x93602),f789(f789(f310(x93601),x93603),x93604)))+~P1(f789(f789(f240(f870(x93601,a856)),f789(f789(f3(f870(x93601,a856)),x93602),f789(f789(f310(x93601),x93603),f184(f870(x93601,a856))))),x93604))
% 21.40/21.38 [9418]~P1(f789(f789(f241(a863),x94182),x94184))+~P1(f789(f789(f240(a863),x94181),x94183))+P1(f789(f789(f342(f869(f869(a863,a863),f869(a863,a863))),f789(f789(f249(f869(a863,a863),f869(a863,a863)),f789(f789(f249(a863,a863),x94181),x94182)),f789(f789(f249(a863,a863),x94183),x94184))),a47))
% 21.40/21.38 [9419]~P1(f789(f789(f240(a863),x94192),x94194))+~P1(f789(f789(f240(a863),x94191),x94193))+P1(f789(f789(f342(f869(f869(a863,a863),f869(a863,a863))),f789(f789(f249(f869(a863,a863),f869(a863,a863)),f789(f789(f249(a863,a863),x94191),x94192)),f789(f789(f249(a863,a863),x94193),x94194))),a79))
% 21.40/21.38 [9803]~P29(x98031,f870(f870(x98031,a856),a856),f789(f789(f9(x98031,f870(f869(x98031,x98031),a856),f870(f870(x98031,a856),a856)),f789(f789(f10(f870(x98031,a856),f870(f870(f869(x98031,x98031),a856),f870(f870(x98031,a856),a856)),x98031),f68(x98031)),f789(f789(f9(x98031,f870(x98031,a856),f870(x98031,a856)),f310(x98031)),f184(f870(x98031,a856))))),x98033),x98032)+~P1(f789(f789(f342(x98031),x98034),x98032))+E(f789(f789(f3(f870(f870(x98031,a856),a856)),f789(f789(f68(x98031),x98032),x98033)),f789(f789(f68(x98031),f789(f789(f310(x98031),x98034),f184(f870(x98031,a856)))),x98033)),f789(f789(f68(x98031),f789(f789(f3(f870(x98031,a856)),x98032),f789(f789(f310(x98031),x98034),f184(f870(x98031,a856))))),x98033))
% 21.40/21.38 [9946]~P47(x99461,x99462,x99464)+~P1(f789(f789(f342(f869(x99461,x99461)),x99463),x99464))+P1(f789(f789(f259(x99461,x99461,a856),f789(f789(f9(x99461,f870(x99461,a856),f870(x99461,a856)),f789(f789(f10(f870(a856,a856),f870(f870(x99461,a856),f870(x99461,a856)),x99461),f10(a856,a856,x99461)),f789(f789(f10(a856,f870(a856,a856),x99461),a339),f789(f789(f9(x99461,f870(x99461,a856),a856),f342(x99461)),x99462)))),f789(f789(f9(x99461,f870(x99461,a856),a856),f342(x99461)),x99462))),x99463))
% 21.40/21.38 [9956]P1(f789(f70(x99561),x99562))+~P1(f789(f70(x99563),f789(f311(x99561,x99563,x99564),x99562)))+~P1(f789(f70(x99561),f789(f264(x99561),f789(f789(f20(x99561,a856,a856),f789(f789(f10(a856,f870(a856,a856),x99561),a339),f789(f789(f9(x99561,f870(x99561,a856),a856),f342(x99561)),x99562))),f789(f789(f9(x99561,x99563,a856),f789(f789(f10(x99563,f870(x99563,a856),x99561),a338),x99564)),f789(x99564,f609(x99564,x99563,x99562,x99561)))))))
% 21.40/21.38 [8060]~P61(x80602)+E(x80601,f2(x80602))+E(f789(f789(f291(x80602),f789(f789(f89(x80602),f789(f789(f90(x80602),x80601),x80603)),x80604)),x80601),f789(f789(f89(x80602),x80603),f789(f789(f291(x80602),x80604),x80601)))
% 21.40/21.38 [8061]~P61(x80612)+E(x80611,f2(x80612))+E(f789(f789(f291(x80612),f789(f789(f3(x80612),f789(f789(f90(x80612),x80611),x80613)),x80614)),x80611),f789(f789(f3(x80612),x80613),f789(f789(f291(x80612),x80614),x80611)))
% 21.40/21.38 [8903]~E(f789(f789(f289(x89031,x89031,x89031),x89033),x89034),f184(f870(f869(x89031,x89031),a856)))+~E(f789(f789(f289(x89031,x89031,x89031),x89032),x89034),f184(f870(f869(x89031,x89031),a856)))+E(f789(f789(f289(x89031,x89031,x89031),f789(f789(f110(f870(f869(x89031,x89031),a856)),x89032),x89033)),x89034),f184(f870(f869(x89031,x89031),a856)))
% 21.40/21.38 [9890]~P139(x98901)+~P139(x98902)+E(f789(f789(f318(x98901),f789(f789(f9(x98901,a108,f867(f864(a854))),f789(f789(f10(f870(x98902,f867(f864(a854))),f870(a108,f867(f864(a854))),x98901),f318(x98902)),f789(f789(f10(f870(x98902,f869(x98901,x98902)),f870(x98902,f867(f864(a854))),x98901),f789(f10(f869(x98901,x98902),f867(f864(a854)),x98902),x98903)),f249(x98901,x98902)))),x98904)),x98904),f789(f789(f318(f869(x98901,x98902)),x98903),x98904))
% 21.40/21.38 [9882]P1(f789(x98821,f593(x98822,x98823,x98821,x98824)))+~P1(f789(f70(x98824),f789(f264(x98824),x98821)))+P1(f789(f70(x98823),f789(f264(x98823),f789(f789(f10(f870(x98824,a856),a856,x98823),f96(x98824)),f789(f789(f10(f870(x98824,a856),f870(x98824,a856),x98823),f789(f20(x98824,a856,a856),f789(f789(f10(a856,f870(a856,a856),x98824),a339),x98821))),x98822)))))
% 21.40/21.38 [9903]~P1(f789(f70(x99032),f789(f264(x99032),x99033)))+~P1(f789(f70(x99031),f789(f264(x99031),f789(f789(f9(x99031,x99032,a856),x99034),f593(x99034,x99031,x99033,x99032)))))+P1(f789(f70(x99031),f789(f264(x99031),f789(f789(f10(f870(x99032,a856),a856,x99031),f96(x99032)),f789(f789(f10(f870(x99032,a856),f870(x99032,a856),x99031),f789(f20(x99032,a856,a856),f789(f789(f10(a856,f870(a856,a856),x99032),a339),x99033))),x99034)))))
% 21.40/21.38 [5755]~E(x57555,x57552)+P39(f37(x57551,x57553),x57552,x57554,x57555)+P1(f789(x57551,x57552))
% 21.40/21.38 [6318]E(x63181,x63182)+~P39(f37(x63183,x63184),x63181,x63185,x63182)+P1(f789(x63183,x63181))
% 21.40/21.38 [6319]E(x63191,x63192)+~P39(f37(x63193,x63194),x63191,x63195,x63192)+P1(f789(x63193,x63191))
% 21.40/21.38 [7868]~P39(x78682,x78683,x78684,x78685)+~P39(f37(x78681,x78682),x78685,x78684,x78683)+P39(f37(x78681,x78682),x78683,x78684,x78683)
% 21.40/21.38 [9023]E(x90231,x90232)+~P39(f37(x90235,x90233),x90231,x90234,x90232)+P39(x90233,x90231,x90234,f370(x90232,x90234,x90231,x90233,x90235))
% 21.40/21.38 [9024]E(x90241,x90242)+~P39(f37(x90245,x90243),x90241,x90244,x90242)+P39(x90243,x90241,x90244,f392(x90242,x90244,x90241,x90243,x90245))
% 21.40/21.38 [9026]E(x90261,x90262)+P39(f37(x90263,x90264),f370(x90261,x90265,x90262,x90264,x90263),x90265,x90261)+~P39(f37(x90263,x90264),x90262,x90265,x90261)
% 21.40/21.38 [9027]E(x90271,x90272)+P39(f37(x90273,x90274),f392(x90271,x90275,x90272,x90274,x90273),x90275,x90271)+~P39(f37(x90273,x90274),x90272,x90275,x90271)
% 21.40/21.38 [9029]~P39(f37(x90295,x90291),x90292,x90293,x90294)+P39(x90291,x90292,x90293,f370(x90294,x90293,x90292,x90291,x90295))+~P1(f789(x90295,x90292))
% 21.40/21.38 [9030]~P39(f37(x90305,x90301),x90302,x90303,x90304)+P39(x90301,x90302,x90303,f392(x90304,x90303,x90302,x90301,x90305))+~P1(f789(x90305,x90302))
% 21.40/21.38 [9034]~P39(f37(x90341,x90342),x90345,x90344,x90343)+P39(f37(x90341,x90342),f370(x90343,x90344,x90345,x90342,x90341),x90344,x90343)+~P1(f789(x90341,x90345))
% 21.40/21.38 [9035]~P39(f37(x90351,x90352),x90355,x90354,x90353)+P39(f37(x90351,x90352),f392(x90353,x90354,x90355,x90352,x90351),x90354,x90353)+~P1(f789(x90351,x90355))
% 21.40/21.38 [6467]E(x64671,x64672)+~E(f789(x64673,x64671),f789(x64673,x64672))+~P29(x64674,x64675,x64673,f247(f870(x64674,a856)))
% 21.40/21.38 [6468]E(x64681,x64682)+~E(f789(x64683,x64681),f789(x64683,x64682))+~P29(x64684,x64685,x64683,f247(f870(x64684,a856)))
% 21.40/21.38 [6631]~E(f789(x66313,x66315),f187(x66312))+~E(f789(x66314,x66315),f187(x66312))+E(f789(f174(x66311,x66312,x66313,x66314),x66315),f187(x66312))
% 21.40/21.38 [7404]E(x74041,x74042)+~P29(x74043,x74044,x74045,f247(f870(x74043,a856)))+~E(f789(f311(x74043,x74044,x74045),x74041),f789(f311(x74043,x74044,x74045),x74042))
% 21.40/21.38 [7662]P29(x76622,x76623,f461(x76624,x76623,x76622,x76621),x76621)+~E(f789(f311(x76623,x76622,x76625),x76624),x76621)+E(x76621,f184(f870(x76622,a856)))
% 21.40/21.38 [8189]~P1(f789(f789(x81893,x81892),x81895))+~P1(f789(f789(x81893,x81894),x81892))+P1(f789(f789(f342(x81891),x81892),f299(x81891,x81893,x81894,x81895)))
% 21.40/21.38 [8190]~P1(f789(f789(x81903,x81902),x81905))+~P1(f789(f789(x81903,x81904),x81902))+P1(f789(f789(f342(x81901),x81902),f290(x81901,x81903,x81904,x81905)))
% 21.40/21.38 [8729]~P29(x87291,x87293,x87295,f247(f870(x87291,a856)))+~P29(x87293,x87292,x87294,f247(f870(x87293,a856)))+P29(x87291,x87292,f789(f82(x87293,x87292,x87291,x87294),x87295),f247(f870(x87291,a856)))
% 21.40/21.38 [9229]P1(f789(f789(f342(f869(x92291,x92291)),f789(f789(f249(x92291,x92291),x92292),x92293)),f308(x92291,x92294)))+~P1(f789(f789(f342(f869(x92291,x92291)),f789(f789(f249(x92291,x92291),x92292),x92295)),f308(x92291,x92294)))+~P1(f789(f789(f342(f869(x92291,x92291)),f789(f789(f249(x92291,x92291),x92295),x92293)),f308(x92291,x92294)))
% 21.40/21.38 [9265]~P101(x92652)+~P1(f789(f134(x92651),x92655))+P1(f789(f134(x92651),f145(x92651,x92652,x92653,x92654,x92655)))
% 21.40/21.38 [5285]~E(x52852,f122(x52851))+E(f789(f789(f132(x52851),x52852),x52853),f789(f789(f146(x52851),x52854),x52855))+~E(x52853,f789(f789(f146(x52851),x52854),x52855))
% 21.40/21.38 [5286]~E(x52862,f122(x52861))+E(f789(f789(f132(x52861),x52862),x52863),f789(f789(f146(x52861),x52864),x52865))+~E(f789(f789(f146(x52861),x52864),x52865),x52863)
% 21.40/21.38 [6425]~E(f789(f185(f864(x64251)),x64255),f789(f185(f864(x64252)),x64254))+E(f789(f789(f150(f869(x64251,x64252),x64252),f258(x64251,x64252)),x64253),x64254)+~E(f789(f789(f171(x64251,x64252),x64255),x64254),x64253)
% 21.40/21.38 [6426]~E(f789(f185(f864(x64261)),x64264),f789(f185(f864(x64262)),x64265))+E(f789(f789(f150(f869(x64261,x64262),x64261),f248(x64261,x64262)),x64263),x64264)+~E(f789(f789(f171(x64261,x64262),x64264),x64265),x64263)
% 21.40/21.38 [6919]~P101(x69191)+~P18(x69191,f789(f789(f150(x69192,x69191),x69193),x69195))+P18(x69191,f789(f789(f150(x69192,x69191),x69193),f789(f133(x69192,x69194),x69195)))
% 21.40/21.38 [6965]~P1(f789(x69653,x69655))+~P1(f789(f789(x69652,x69654),x69655))+P1(f789(f789(f101(x69651,x69652,x69653),x69654),x69655))
% 21.40/21.38 [7063]~P101(x70631)+P18(x70631,f789(f789(f150(x70632,x70631),x70633),f158(x70632,x70634,x70635)))+~P18(x70631,f789(f789(f150(x70632,x70631),x70633),x70635))
% 21.40/21.38 [7086]~P53(x70863,x70862,x70865)+~P53(x70861,x70863,x70864)+P53(x70861,x70862,f789(f789(f289(x70861,x70863,x70862),x70864),x70865))
% 21.40/21.38 [7175]E(x71751,x71752)+~P29(x71753,x71754,x71755,f247(f870(x71753,a856)))+~E(f789(f789(f150(x71753,x71754),x71755),x71751),f789(f789(f150(x71753,x71754),x71755),x71752))
% 21.40/21.38 [7176]E(x71761,x71762)+~P29(x71763,x71764,x71765,f247(f870(x71763,a856)))+~E(f789(f789(f150(x71763,x71764),x71765),x71761),f789(f789(f150(x71763,x71764),x71765),x71762))
% 21.40/21.38 [7259]P39(x72591,x72592,x72593,x72594)+~P39(x72591,x72592,x72595,x72594)+~P1(f789(f789(f240(a863),x72595),x72593))
% 21.40/21.38 [7349]~P1(f789(f789(f241(a863),x73491),f789(x73493,x73495)))+P1(f789(f789(f241(a863),x73491),f151(x73492,x73493,x73494)))+~P1(f789(f789(f342(x73492),x73495),f789(f163(x73492),x73494)))
% 21.40/21.38 [7350]~P1(f789(f789(f240(a863),x73501),f789(x73503,x73505)))+P1(f789(f789(f240(a863),x73501),f151(x73502,x73503,x73504)))+~P1(f789(f789(f342(x73502),x73505),f789(f163(x73502),x73504)))
% 21.40/21.38 [7760]~P99(x77601)+P1(f789(f789(f240(f870(x77601,a856)),f303(x77601,x77602,x77603)),f303(x77601,x77604,x77605)))+P1(f789(f789(f240(x77601),x77602),x77603))
% 21.40/21.38 [7787]~P9(x77871)+P1(f789(f789(f240(x77871),f789(f789(f54(x77872,x77871),x77873),x77874)),f789(x77874,x77875)))+~P1(f789(f789(f342(x77872),x77875),x77873))
% 21.40/21.38 [7855]~P29(x78551,x78552,x78554,x78553)+E(f789(f86(x78551,x78552,x78553,x78554),f789(x78554,x78555)),x78555)+~P1(f789(f789(f342(x78551),x78555),x78553))
% 21.40/21.38 [8049]~P1(f789(x80491,x80495))+P1(f789(x80491,f362(x80491,x80492,x80493,x80494)))+~P1(f789(f789(f342(x80494),x80495),x80493))
% 21.40/21.38 [8050]~P1(f789(x80501,x80505))+P1(f789(x80501,f362(x80501,x80502,x80503,x80504)))+~P1(f789(f789(f342(x80504),x80505),x80502))
% 21.40/21.38 [8141]P1(f789(f70(x81411),x81412))+~P1(f789(f70(x81413),x81414))+~P1(f789(f789(f240(f870(x81411,a856)),x81412),f789(f311(x81413,x81411,x81415),x81414)))
% 21.40/21.38 [8151]~P29(x81514,x81511,x81512,f247(f870(x81514,a856)))+~P1(f789(f789(f342(x81514),x81513),x81515))+P1(f789(f789(f342(x81511),f789(x81512,x81513)),f789(f311(x81514,x81511,x81512),x81515)))
% 21.40/21.38 [8301]E(x83011,x83012)+~P29(x83013,x83014,x83015,f789(f789(f110(f870(x83013,a856)),f789(f163(x83013),x83011)),f789(f163(x83013),x83012)))+~E(f789(f789(f150(x83013,x83014),x83015),x83011),f789(f789(f150(x83013,x83014),x83015),x83012))
% 21.40/21.38 [8302]E(x83021,x83022)+~P29(x83023,x83024,x83025,f789(f789(f110(f870(x83023,a856)),f789(f163(x83023),x83021)),f789(f163(x83023),x83022)))+~E(f789(f789(f150(x83023,x83024),x83025),x83021),f789(f789(f150(x83023,x83024),x83025),x83022))
% 21.40/21.38 [8359]~P99(x83591)+~P1(f789(f789(f241(f870(x83591,a856)),f303(x83591,x83594,x83595)),f303(x83591,x83592,x83593)))+P1(f789(f789(f240(x83591),x83592),x83593))
% 21.40/21.38 [8427]~P29(x84271,x84274,x84275,f247(f870(x84271,a856)))+~P1(f789(f789(f342(x84274),f789(x84275,x84272)),f789(f311(x84271,x84274,x84275),x84273)))+P1(f789(f789(f342(x84271),x84272),x84273))
% 21.40/21.38 [8506]P1(f789(x85061,x85062))+~P1(f789(x85061,f369(x85061,x85063,x85064,x85065)))+~P1(f789(f789(f342(x85065),x85062),x85064))
% 21.40/21.38 [8507]P1(f789(x85071,x85072))+~P1(f789(x85071,f369(x85071,x85073,x85074,x85075)))+~P1(f789(f789(f342(x85075),x85072),x85073))
% 21.40/21.38 [8764]~P29(x87642,x87643,x87641,x87644)+E(f789(x87641,f789(f86(x87642,x87643,x87644,x87641),x87645)),x87645)+~P1(f789(f789(f342(x87643),x87645),f789(f311(x87642,x87643,x87641),x87644)))
% 21.40/21.38 [8851]E(x88511,f122(x88512))+E(f789(f789(f146(x88512),x88513),f748(x88514,x88513,x88515,x88511,x88512)),x88511)+~E(f789(f789(f132(x88512),x88511),x88515),f789(f789(f146(x88512),x88513),x88514))
% 21.40/21.38 [8852]E(x88521,f122(x88522))+E(f789(f789(f146(x88522),x88523),f749(x88524,x88521,x88525,x88523,x88522)),x88521)+~E(f789(f789(f132(x88522),x88521),x88524),f789(f789(f146(x88522),x88523),x88525))
% 21.40/21.38 [8867]E(f789(f789(f146(x88672),x88673),f748(x88674,x88673,x88671,x88675,x88672)),x88675)+~E(f789(f789(f132(x88672),x88675),x88671),f789(f789(f146(x88672),x88673),x88674))+E(x88671,f789(f789(f146(x88672),x88673),x88674))
% 21.40/21.38 [8868]E(f789(f789(f146(x88681),x88682),f749(x88684,x88685,x88683,x88682,x88681)),x88685)+~E(f789(f789(f132(x88681),x88685),x88684),f789(f789(f146(x88681),x88682),x88683))+E(f789(f789(f146(x88681),x88682),x88683),x88684)
% 21.40/21.38 [8942]~E(f789(f311(x89423,x89422,x89424),f247(f870(x89423,a856))),f247(f870(x89422,a856)))+~E(f789(f311(x89421,x89423,x89425),f247(f870(x89421,a856))),f247(f870(x89423,a856)))+E(f789(f311(x89421,x89422,f789(f82(x89423,x89422,x89421,x89424),x89425)),f247(f870(x89421,a856))),f247(f870(x89422,a856)))
% 21.40/21.38 [9271]E(x92711,f122(x92712))+~E(f789(f789(f132(x92712),x92711),x92713),f789(f789(f146(x92712),x92715),x92714))+E(f789(f789(f132(x92712),f749(x92713,x92711,x92714,x92715,x92712)),x92713),x92714)
% 21.40/21.38 [9272]E(x92721,f122(x92722))+~E(f789(f789(f132(x92722),x92721),x92725),f789(f789(f146(x92722),x92724),x92723))+E(f789(f789(f132(x92722),f748(x92723,x92724,x92725,x92721,x92722)),x92725),x92723)
% 21.40/21.38 [9279]E(f789(f789(f132(x92792),f748(x92794,x92793,x92791,x92795,x92792)),x92791),x92794)+~E(f789(f789(f132(x92792),x92795),x92791),f789(f789(f146(x92792),x92793),x92794))+E(x92791,f789(f789(f146(x92792),x92793),x92794))
% 21.40/21.38 [9280]~E(f789(f789(f132(x92801),x92805),x92804),f789(f789(f146(x92801),x92802),x92803))+E(f789(f789(f132(x92801),f749(x92804,x92805,x92803,x92802,x92801)),x92804),x92803)+E(f789(f789(f146(x92801),x92802),x92803),x92804)
% 21.40/21.38 [9281]E(f789(f789(f132(x92811),x92815),f752(x92813,x92812,x92814,x92815,x92811)),x92812)+E(f789(f789(f132(x92811),x92812),f751(x92813,x92812,x92814,x92815,x92811)),x92815)+~E(f789(f789(f132(x92811),x92815),x92814),f789(f789(f132(x92811),x92812),x92813))
% 21.40/21.38 [9313]~P101(x93131)+P18(x93131,f789(f789(f150(x93132,x93131),x93133),f145(x93132,x93131,x93133,x93134,x93135)))+~P18(x93131,f789(f789(f150(x93132,x93131),x93133),x93135))
% 21.40/21.38 [9329]~P57(x93295,x93291,x93294,x93293)+P1(f789(f789(x93291,x93292),f553(x93293,x93294,x93291,x93295,x93292)))+~P1(f789(f789(f342(x93295),x93292),x93294))
% 21.40/21.38 [9427]~P1(f789(f789(f342(f869(x94271,x94271)),f789(f789(f249(x94271,x94271),x94275),x94273)),f308(x94271,x94274)))+P1(f789(f789(f342(f869(x94271,x94271)),f789(f789(f249(x94271,x94271),x94272),x94273)),f789(f789(f289(x94271,x94271,x94271),x94274),f308(x94271,x94274))))+~P1(f789(f789(f342(f869(x94271,x94271)),f789(f789(f249(x94271,x94271),x94272),x94275)),f789(f789(f289(x94271,x94271,x94271),x94274),f308(x94271,x94274))))
% 21.40/21.38 [9428]~P1(f789(f789(f342(f869(x94281,x94281)),f789(f789(f249(x94281,x94281),x94282),x94285)),f308(x94281,x94284)))+P1(f789(f789(f342(f869(x94281,x94281)),f789(f789(f249(x94281,x94281),x94282),x94283)),f789(f789(f289(x94281,x94281,x94281),x94284),f308(x94281,x94284))))+~P1(f789(f789(f342(f869(x94281,x94281)),f789(f789(f249(x94281,x94281),x94285),x94283)),f789(f789(f289(x94281,x94281,x94281),x94284),f308(x94281,x94284))))
% 21.40/21.38 [9430]P1(f789(f789(f342(f869(f864(x94301),f864(x94301))),f789(f789(f249(f864(x94301),f864(x94301)),x94302),x94303)),f154(x94301,f308(x94301,x94304))))+~P1(f789(f789(f342(f869(f864(x94301),f864(x94301))),f789(f789(f249(f864(x94301),f864(x94301)),x94302),x94305)),f154(x94301,f308(x94301,x94304))))+~P1(f789(f789(f342(f869(f864(x94301),f864(x94301))),f789(f789(f249(f864(x94301),f864(x94301)),x94305),x94303)),f154(x94301,f308(x94301,x94304))))
% 21.40/21.38 [9435]E(f789(f789(f132(x94351),x94352),f751(x94353,x94352,x94354,x94355,x94351)),x94355)+E(f789(f789(f132(x94351),f752(x94353,x94352,x94354,x94355,x94351)),x94353),x94354)+~E(f789(f789(f132(x94351),x94352),x94353),f789(f789(f132(x94351),x94355),x94354))
% 21.40/21.38 [9436]E(f789(f789(f132(x94361),x94362),f752(x94363,x94364,x94365,x94362,x94361)),x94364)+E(f789(f789(f132(x94361),f751(x94363,x94364,x94365,x94362,x94361)),x94365),x94363)+~E(f789(f789(f132(x94361),x94362),x94365),f789(f789(f132(x94361),x94364),x94363))
% 21.40/21.38 [9495]P1(f789(f789(f342(f869(x94951,x94951)),f789(f789(f249(x94951,x94951),x94952),x94953)),f789(f789(f289(x94951,x94951,x94951),x94954),f308(x94951,x94954))))+~P1(f789(f789(f342(f869(x94951,x94951)),f789(f789(f249(x94951,x94951),x94952),x94955)),f789(f789(f289(x94951,x94951,x94951),x94954),f308(x94951,x94954))))+~P1(f789(f789(f342(f869(x94951,x94951)),f789(f789(f249(x94951,x94951),x94955),x94953)),f789(f789(f289(x94951,x94951,x94951),x94954),f308(x94951,x94954))))
% 21.40/21.38 [9529]E(f789(f789(f132(x95291),f751(x95292,x95293,x95294,x95295,x95291)),x95294),x95292)+~E(f789(f789(f132(x95291),x95293),x95292),f789(f789(f132(x95291),x95295),x95294))+E(f789(f789(f132(x95291),f752(x95292,x95293,x95294,x95295,x95291)),x95292),x95294)
% 21.40/21.38 [9544]~P57(x95441,x95444,x95443,x95442)+~P1(f789(f789(f342(x95441),x95445),x95443))+P1(f789(f789(f342(x95441),f553(x95442,x95443,x95444,x95441,x95445)),x95442))
% 21.40/21.38 [9658]~P1(f789(f789(f342(f869(f870(x96581,a856),f870(x96581,a856))),f789(f789(f249(f870(x96581,a856),f870(x96581,a856)),x96584),x96583)),f332(x96581,x96582)))+~P1(f789(f789(f342(x96581),x96585),x96584))+P1(f789(f789(f342(x96581),f638(x96582,x96583,x96584,x96581,x96585)),x96583))
% 21.40/21.38 [6500]~P21(x65002,x65005,x65001)+~P1(f789(f70(x65002),x65004))+E(f789(x65001,f789(f789(f310(x65002),x65003),x65004)),f789(f789(f73(x65002,x65002,x65005),x65003),x65004))
% 21.40/21.38 [6501]~E(x65013,x65014)+~E(x65012,x65015)+E(f789(f789(f310(x65011),x65012),f789(f789(f310(x65011),x65013),f184(f870(x65011,a856)))),f789(f789(f310(x65011),x65014),f789(f789(f310(x65011),x65015),f184(f870(x65011,a856)))))
% 21.40/21.38 [6547]E(f789(x65471,x65472),f184(f870(x65473,a856)))+~E(f789(f789(f53(x65474,f870(x65473,a856)),x65475),x65471),f184(f870(x65473,a856)))+~P1(f789(f789(f342(x65474),x65472),x65475))
% 21.40/21.38 [6548]E(f789(x65481,x65482),f247(f870(x65483,a856)))+~E(f789(f789(f54(x65484,f870(x65483,a856)),x65485),x65481),f247(f870(x65483,a856)))+~P1(f789(f789(f342(x65484),x65482),x65485))
% 21.40/21.38 [6549]E(f789(x65491,x65492),f184(f870(x65493,a856)))+~E(f789(f789(f53(x65494,f870(x65493,a856)),x65495),x65491),f184(f870(x65493,a856)))+~P1(f789(f789(f342(x65494),x65492),x65495))
% 21.40/21.38 [6550]E(f789(x65501,x65502),f247(f870(x65503,a856)))+~E(f789(f789(f54(x65504,f870(x65503,a856)),x65505),x65501),f247(f870(x65503,a856)))+~P1(f789(f789(f342(x65504),x65502),x65505))
% 21.40/21.38 [6868]~P1(f789(f789(f191(x68681),x68683),x68685))+~P1(f789(f789(f191(x68682),x68685),x68684))+P1(f789(f789(f191(f38(x68681,x68682)),x68683),x68684))
% 21.40/21.38 [6869]~P1(f789(f789(f191(x68691),x68693),x68695))+~P1(f789(f789(f191(x68692),x68695),x68694))+P1(f789(f789(f191(f38(x68691,x68692)),x68693),x68694))
% 21.40/21.38 [7072]~E(x70722,x70724)+~P137(x70721)+E(f789(f789(f89(x70721),f789(f789(f90(x70721),x70722),x70723)),f789(f789(f90(x70721),x70724),x70725)),f789(f789(f89(x70721),f789(f789(f90(x70721),x70722),x70725)),f789(f789(f90(x70721),x70724),x70723)))
% 21.40/21.38 [7073]~E(x70732,x70734)+~P137(x70731)+E(f789(f789(f89(x70731),f789(f789(f90(x70731),x70732),x70733)),f789(f789(f90(x70731),x70734),x70735)),f789(f789(f89(x70731),f789(f789(f90(x70731),x70732),x70735)),f789(f789(f90(x70731),x70734),x70733)))
% 21.40/21.38 [7132]~P9(x71321)+~P1(f789(f789(f342(x71324),x71323),x71325))+P1(f789(f789(f240(x71321),f789(x71322,x71323)),f789(f789(f53(x71324,x71321),x71325),x71322)))
% 21.40/21.38 [7179]~P100(x71791)+P1(f789(f789(f240(x71791),f789(x71792,x71793)),f789(x71794,x71793)))+~P1(f789(f789(f240(f870(x71795,x71791)),x71792),x71794))
% 21.40/21.38 [7180]~P100(x71801)+P1(f789(f789(f240(x71801),f789(x71802,x71803)),f789(x71804,x71803)))+~P1(f789(f789(f240(f870(x71805,x71801)),x71802),x71804))
% 21.40/21.38 [7181]~P100(x71811)+P1(f789(f789(f240(x71811),f789(x71812,x71813)),f789(x71814,x71813)))+~P1(f789(f789(f240(f870(x71815,x71811)),x71812),x71814))
% 21.40/21.38 [7317]E(x73171,x73172)+E(x73173,x73171)+~E(f789(f789(f310(x73174),x73171),f789(f789(f310(x73174),x73175),f184(f870(x73174,a856)))),f789(f789(f310(x73174),x73172),f789(f789(f310(x73174),x73173),f184(f870(x73174,a856)))))
% 21.40/21.38 [7318]E(x73181,x73182)+E(x73183,x73181)+~E(f789(f789(f310(x73184),x73183),f789(f789(f310(x73184),x73182),f184(f870(x73184,a856)))),f789(f789(f310(x73184),x73185),f789(f789(f310(x73184),x73181),f184(f870(x73184,a856)))))
% 21.40/21.38 [7319]E(x73191,x73192)+E(x73191,x73193)+~E(f789(f789(f310(x73194),x73193),f789(f789(f310(x73194),x73192),f184(f870(x73194,a856)))),f789(f789(f310(x73194),x73195),f789(f789(f310(x73194),x73191),f184(f870(x73194,a856)))))
% 21.40/21.38 [7320]E(x73201,x73202)+E(x73201,x73203)+~E(f789(f789(f310(x73204),x73201),f789(f789(f310(x73204),x73205),f184(f870(x73204,a856)))),f789(f789(f310(x73204),x73202),f789(f789(f310(x73204),x73203),f184(f870(x73204,a856)))))
% 21.40/21.38 [7865]P29(x78651,x78652,x78653,x78654)+~P29(x78651,x78652,x78653,x78655)+~P1(f789(f789(f240(f870(x78651,a856)),x78654),x78655))
% 21.40/21.38 [7964]P1(f789(x79641,x79642))+~P1(f789(f789(f191(x79644),x79642),x79645))+P1(f789(f789(f191(f35(x79641,x79643,x79644)),x79642),x79645))
% 21.40/21.38 [7965]P1(f789(x79651,x79652))+~P1(f789(f789(f191(x79654),x79652),x79655))+P1(f789(f789(f191(f35(x79651,x79653,x79654)),x79652),x79655))
% 21.40/21.38 [7966]P1(f789(x79661,x79662))+~P1(f789(f789(f191(x79664),x79662),x79665))+P1(f789(f789(f191(f35(x79661,x79663,x79664)),x79662),x79665))
% 21.40/21.38 [7992]~P1(f789(x79921,x79924))+~P1(f789(f789(f191(x79922),x79924),x79925))+P1(f789(f789(f191(f35(x79921,x79922,x79923)),x79924),x79925))
% 21.40/21.38 [7993]~P1(f789(x79931,x79934))+~P1(f789(f789(f191(x79932),x79934),x79935))+P1(f789(f789(f191(f35(x79931,x79932,x79933)),x79934),x79935))
% 21.40/21.38 [7994]~P1(f789(x79941,x79944))+~P1(f789(f789(f191(x79942),x79944),x79945))+P1(f789(f789(f191(f35(x79941,x79942,x79943)),x79944),x79945))
% 21.40/21.38 [8039]E(x80391,x80392)+~E(f789(f311(x80393,x80394,x80395),x80391),f789(f311(x80393,x80394,x80395),x80392))+~P29(x80393,x80394,x80395,f789(f789(f110(f870(x80393,a856)),x80391),x80392))
% 21.40/21.38 [8139]~P29(x81391,x81392,x81393,x81395)+~P29(x81391,x81392,x81393,x81394)+P29(x81391,x81392,x81393,f789(f789(f111(f870(x81391,a856)),x81394),x81395))
% 21.40/21.38 [8243]~P4(x82431)+E(f789(f789(f89(x82431),f789(x82432,x82433)),f789(f161(x82431),f789(f789(f150(x82434,x82431),x82432),f158(x82434,x82433,x82435)))),f789(f161(x82431),f789(f789(f150(x82434,x82431),x82432),x82435)))+~P1(f789(f789(f342(x82434),x82433),f789(f163(x82434),x82435)))
% 21.40/21.38 [8331]~P101(x83311)+~P18(x83311,f789(f789(f150(x83312,x83311),x83313),x83315))+P18(x83311,f789(f789(f150(x83312,x83311),x83313),f789(f789(f144(x83312,x83311,x83313),x83314),x83315)))
% 21.40/21.38 [8410]P1(f789(x84101,x84102))+P1(f789(f789(f191(x84103),x84102),x84104))+~P1(f789(f789(f191(f35(x84101,x84105,x84103)),x84102),x84104))
% 21.40/21.38 [8411]P1(f789(x84111,x84112))+P1(f789(f789(f191(x84113),x84112),x84114))+~P1(f789(f789(f191(f35(x84111,x84115,x84113)),x84112),x84114))
% 21.40/21.38 [8412]P1(f789(x84121,x84122))+P1(f789(f789(f191(x84123),x84122),x84124))+~P1(f789(f789(f191(f35(x84121,x84125,x84123)),x84122),x84124))
% 21.40/21.38 [8423]~P9(x84231)+P1(f789(f789(f240(x84231),f789(f789(f53(x84232,x84231),x84233),x84234)),f789(f789(f53(x84232,x84231),x84235),x84234)))+~P1(f789(f789(f240(f870(x84232,a856)),x84233),x84235))
% 21.40/21.38 [8424]~P9(x84241)+P1(f789(f789(f240(x84241),f789(f789(f54(x84242,x84241),x84243),x84244)),f789(f789(f54(x84242,x84241),x84245),x84244)))+~P1(f789(f789(f240(f870(x84242,a856)),x84245),x84243))
% 21.40/21.38 [8431]~P1(f789(x84314,x84312))+P1(f789(f789(f191(x84311),x84312),x84313))+~P1(f789(f789(f191(f35(x84314,x84311,x84315)),x84312),x84313))
% 21.40/21.38 [8432]~P1(f789(x84324,x84322))+P1(f789(f789(f191(x84321),x84322),x84323))+~P1(f789(f789(f191(f35(x84324,x84321,x84325)),x84322),x84323))
% 21.40/21.38 [8433]~P1(f789(x84334,x84332))+P1(f789(f789(f191(x84331),x84332),x84333))+~P1(f789(f789(f191(f35(x84334,x84331,x84335)),x84332),x84333))
% 21.40/21.38 [8456]~P101(x84563)+P1(f789(f134(x84561),x84562))+~P1(f789(f134(x84561),f789(f789(f144(x84561,x84563,x84564),x84565),x84562)))
% 21.40/21.38 [8464]P1(f789(f789(f191(x84641),x84642),x84643))+P1(f789(f789(f191(x84644),x84642),x84643))+~P1(f789(f789(f191(f35(x84645,x84641,x84644)),x84642),x84643))
% 21.40/21.38 [8465]P1(f789(f789(f191(x84651),x84652),x84653))+P1(f789(f789(f191(x84654),x84652),x84653))+~P1(f789(f789(f191(f35(x84655,x84651,x84654)),x84652),x84653))
% 21.40/21.38 [8466]P1(f789(f789(f191(x84661),x84662),x84663))+P1(f789(f789(f191(x84664),x84662),x84663))+~P1(f789(f789(f191(f35(x84665,x84661,x84664)),x84662),x84663))
% 21.40/21.38 [8590]~P101(x85901)+~P1(f789(f789(f342(x85902),x85903),f789(f163(x85902),x85904)))+~P1(f789(f134(x85902),f789(f789(f144(x85902,x85901,x85905),x85903),x85904)))
% 21.40/21.38 [8666]~P101(x86661)+P18(x86661,f789(f789(f150(x86662,x86661),x86663),x86664))+~P18(x86661,f789(f789(f150(x86662,x86661),x86663),f789(f789(f144(x86662,x86661,x86663),x86665),x86664)))
% 21.40/21.38 [8751]~P101(x87512)+E(f789(f789(f144(x87511,x87512,x87513),x87514),x87515),f145(x87511,x87512,x87513,x87514,x87515))+P1(f789(f789(f342(x87512),f789(x87513,x87514)),f789(f311(x87511,x87512,x87513),f789(f163(x87511),x87515))))
% 21.40/21.38 [8818]~P101(x88182)+E(f145(x88181,x88182,x88183,x88184,x88185),x88185)+~P1(f789(f789(f342(x88182),f789(x88183,x88184)),f789(f311(x88181,x88182,x88183),f789(f163(x88181),x88185))))
% 21.40/21.38 [8832]~P29(x88322,x88321,x88323,x88325)+P1(f789(f789(f241(f870(x88321,a856)),f789(f311(x88322,x88321,x88323),x88324)),f789(f311(x88322,x88321,x88323),x88325)))+~P1(f789(f789(f241(f870(x88322,a856)),x88324),x88325))
% 21.40/21.38 [8858]~P29(x88582,x88581,x88583,f247(f870(x88582,a856)))+P1(f789(f789(f240(f870(x88581,a856)),f789(f311(x88582,x88581,x88583),x88584)),f789(f311(x88582,x88581,x88583),x88585)))+~P1(f789(f789(f240(f870(x88582,a856)),x88584),x88585))
% 21.40/21.38 [8980]~P29(x89801,x89802,x89803,f247(f870(x89801,a856)))+~P1(f789(f789(f240(f870(x89802,a856)),x89804),f789(f311(x89801,x89802,x89803),x89805)))+P1(f789(f789(f240(f870(x89801,a856)),f789(f313(x89801,x89802,x89803),x89804)),x89805))
% 21.40/21.38 [8998]~E(f789(f311(x89983,x89981,x89984),f247(f870(x89983,a856))),f247(f870(x89981,a856)))+P1(f789(f789(f240(f870(x89981,a856)),x89982),f789(f311(x89983,x89981,x89984),x89985)))+~P1(f789(f789(f240(f870(x89983,a856)),f789(f313(x89983,x89981,x89984),x89982)),x89985))
% 21.40/21.38 [9036]~E(f789(f234(x90362),x90364),f789(f170(x90361,x90362,x90365),x90363))+~P1(f789(f134(x90361),f789(f789(f150(f869(x90361,x90362),x90361),f248(x90361,x90362)),x90365)))+P1(f789(f789(f342(f869(x90361,x90362)),f789(f789(f249(x90361,x90362),x90363),x90364)),f789(f163(f869(x90361,x90362)),x90365)))
% 21.40/21.38 [9037]~E(f789(f170(x90371,x90372,x90375),x90373),f789(f234(x90372),x90374))+~P1(f789(f134(x90371),f789(f789(f150(f869(x90371,x90372),x90371),f248(x90371,x90372)),x90375)))+P1(f789(f789(f342(f869(x90371,x90372)),f789(f789(f249(x90371,x90372),x90373),x90374)),f789(f163(f869(x90371,x90372)),x90375)))
% 21.40/21.38 [9102]~P29(x91021,x91024,x91025,f247(f870(x91021,a856)))+~P1(f789(f789(f240(f870(x91024,a856)),f789(f311(x91021,x91024,x91025),x91022)),f789(f311(x91021,x91024,x91025),x91023)))+P1(f789(f789(f240(f870(x91021,a856)),x91022),x91023))
% 21.40/21.38 [9168]E(f789(f234(x91681),x91682),f789(f170(x91683,x91681,x91684),x91685))+~P1(f789(f134(x91683),f789(f789(f150(f869(x91683,x91681),x91683),f248(x91683,x91681)),x91684)))+~P1(f789(f789(f342(f869(x91683,x91681)),f789(f789(f249(x91683,x91681),x91685),x91682)),f789(f163(f869(x91683,x91681)),x91684)))
% 21.40/21.38 [9169]E(f789(f170(x91691,x91692,x91693),x91694),f789(f234(x91692),x91695))+~P1(f789(f134(x91691),f789(f789(f150(f869(x91691,x91692),x91691),f248(x91691,x91692)),x91693)))+~P1(f789(f789(f342(f869(x91691,x91692)),f789(f789(f249(x91691,x91692),x91694),x91695)),f789(f163(f869(x91691,x91692)),x91693)))
% 21.40/21.38 [9170]E(f789(f170(x91701,x91702,x91703),x91704),f789(f234(x91702),x91705))+~P1(f789(f134(x91701),f789(f789(f150(f869(x91701,x91702),x91701),f248(x91701,x91702)),x91703)))+~P1(f789(f789(f342(f869(x91701,x91702)),f789(f789(f249(x91701,x91702),x91704),x91705)),f789(f163(f869(x91701,x91702)),x91703)))
% 21.40/21.38 [9376]~P20(x93761,x93762,x93763)+~P1(f789(f70(x93761),x93765))+P1(f789(f75(x93761,x93762,x93763,x93764,x93765),f789(f789(f73(x93761,x93762,x93763),x93764),x93765)))
% 21.40/21.38 [9450]P1(f789(x94501,f713(x94502,x94501,x94503,x94504,x94505)))+~P1(f789(f789(f240(f870(x94505,a856)),x94504),x94503))+P1(f789(f789(f240(f870(x94505,a856)),f789(f789(f111(f870(x94505,a856)),x94504),f789(f264(x94505),x94501))),f789(f789(f111(f870(x94505,a856)),x94503),f789(f264(x94505),x94502))))
% 21.40/21.38 [9542]~P9(x95425)+P1(f789(f789(f342(x95421),f646(x95422,x95423,x95421,x95424,x95425)),x95423))+P1(f789(f789(f240(x95425),x95424),f789(f789(f54(x95421,x95425),x95423),x95422)))
% 21.40/21.38 [9554]~P1(f789(x95545,f713(x95545,x95543,x95544,x95542,x95541)))+~P1(f789(f789(f240(f870(x95541,a856)),x95542),x95544))+P1(f789(f789(f240(f870(x95541,a856)),f789(f789(f111(f870(x95541,a856)),x95542),f789(f264(x95541),x95543))),f789(f789(f111(f870(x95541,a856)),x95544),f789(f264(x95541),x95545))))
% 21.40/21.38 [9622]P1(f789(f789(f342(x96221),f713(x96222,x96223,x96224,x96225,x96221)),x96225))+~P1(f789(f789(f240(f870(x96221,a856)),x96225),x96224))+P1(f789(f789(f240(f870(x96221,a856)),f789(f789(f111(f870(x96221,a856)),x96225),f789(f264(x96221),x96223))),f789(f789(f111(f870(x96221,a856)),x96224),f789(f264(x96221),x96222))))
% 21.40/21.38 [9670]~P9(x96701)+~P1(f789(f789(f240(x96701),x96702),f789(x96705,f646(x96705,x96704,x96703,x96702,x96701))))+P1(f789(f789(f240(x96701),x96702),f789(f789(f54(x96703,x96701),x96704),x96705)))
% 21.40/21.38 [9700]~P69(x97001)+~P1(f789(f70(x97002),x97005))+E(f789(f789(f789(f74(x97001,x97002,f90(x97001)),f789(f789(f20(x97002,x97001,x97001),f789(f789(f10(x97001,f870(x97001,x97001),x97002),f90(x97001)),x97003)),x97004)),f87(x97001)),x97005),f789(f789(f90(x97001),f789(f789(f789(f74(x97001,x97002,f90(x97001)),x97003),f87(x97001)),x97005)),f789(f789(f789(f74(x97001,x97002,f90(x97001)),x97004),f87(x97001)),x97005)))
% 21.40/21.38 [9747]~P1(f789(f789(f342(f869(f870(x97471,a856),f870(x97471,a856))),f789(f789(f249(f870(x97471,a856),f870(x97471,a856)),x97475),x97474)),f332(x97471,x97473)))+~P1(f789(f789(f342(x97471),x97472),x97475))+P1(f789(f789(f342(f869(x97471,x97471)),f789(f789(f249(x97471,x97471),x97472),f638(x97473,x97474,x97475,x97471,x97472))),x97473))
% 21.40/21.38 [9900]~P1(f789(f789(f342(f869(f864(x99001),f864(x99001))),f789(f789(f249(f864(x99001),f864(x99001)),f789(f789(f132(x99001),x99005),x99002)),f789(f789(f132(x99001),x99005),x99003))),f143(x99001,x99004)))+P1(f789(f789(f342(f869(f864(x99001),f864(x99001))),f789(f789(f249(f864(x99001),f864(x99001)),x99002),x99003)),f143(x99001,x99004)))+P1(f789(f789(f342(f869(x99001,x99001)),f789(f789(f249(x99001,x99001),f753(x99004,x99003,x99002,x99005,x99001)),f753(x99004,x99003,x99002,x99005,x99001))),x99004))
% 21.40/21.38 [7184]~E(x71843,x71845)+E(f789(f789(f159(x71841),f789(f789(f155(x71841,x71842),x71843),x71844)),x71845),x71844)+~P1(f789(f789(f241(a863),x71843),f789(f185(f864(x71841)),x71842)))
% 21.40/21.38 [7193]~E(f789(f185(f864(x71931)),x71933),f789(f185(f864(x71932)),x71934))+E(f789(f170(x71931,x71932,f789(f789(f171(x71931,x71932),x71933),x71934)),x71935),f187(x71932))+P1(f789(f789(f342(x71931),x71935),f789(f163(x71931),x71933)))
% 21.40/21.38 [7313]~E(f789(f789(f132(x73131),x73132),x73134),f789(f789(f132(x73131),x73133),x73135))+E(f789(f789(f164(x73131),f789(f185(f864(x73131)),x73132)),x73133),x73132)+P1(f789(f789(f240(a863),f789(f185(f864(x73131)),x73133)),f789(f185(f864(x73131)),x73132)))
% 21.40/21.38 [7314]E(x73141,x73142)+E(f789(f789(f159(x73143),f789(f789(f155(x73143,x73144),x73141),x73145)),x73142),f789(f789(f159(x73143),x73144),x73142))+~P1(f789(f789(f241(a863),x73141),f789(f185(f864(x73143)),x73144)))
% 21.40/21.38 [7826]~E(f789(f789(f132(x78261),x78262),x78264),f789(f789(f132(x78261),x78263),x78265))+E(f789(f789(f164(x78261),f789(f185(f864(x78261)),x78262)),x78263),x78262)+~P1(f789(f789(f240(a863),f789(f185(f864(x78261)),x78262)),f789(f185(f864(x78261)),x78263)))
% 21.40/21.38 [7850]~P1(f789(f70(x78501),f789(x78504,x78505)))+~P1(f789(f789(f342(x78502),x78505),x78503))+P1(f789(f70(x78501),f789(f789(f54(x78502,f870(x78501,a856)),x78503),x78504)))
% 21.40/21.38 [7961]~E(f789(f185(f864(x79611)),x79612),f789(f185(f864(x79613)),x79614))+~E(f789(f170(x79611,x79613,f789(f789(f171(x79611,x79613),x79612),x79614)),x79615),f187(x79613))+~P1(f789(f789(f342(x79611),x79615),f789(f163(x79611),x79612)))
% 21.40/21.38 [8026]~P47(x80261,x80263,x80265)+~P47(x80261,x80262,x80264)+P47(x80261,f789(f789(f110(f870(x80261,a856)),x80262),x80263),f789(f789(f110(f870(f869(x80261,x80261),a856)),x80264),x80265))
% 21.40/21.38 [8027]~P47(x80271,x80273,x80275)+~P47(x80271,x80272,x80274)+P47(x80271,f789(f789(f111(f870(x80271,a856)),x80272),x80273),f789(f789(f111(f870(f869(x80271,x80271),a856)),x80274),x80275))
% 21.40/21.38 [8375]E(f789(f789(f249(x83751,x83752),f789(f789(f159(x83751),x83753),x83754)),f789(f789(f159(x83752),x83755),x83754)),f789(f789(f159(f869(x83751,x83752)),f789(f789(f171(x83751,x83752),x83753),x83755)),x83754))+~P1(f789(f789(f241(a863),x83754),f789(f185(f864(x83751)),x83753)))+~P1(f789(f789(f241(a863),x83754),f789(f185(f864(x83752)),x83755)))
% 21.40/21.38 [8534]~P47(x85341,x85343,x85344)+P1(f789(f789(f342(x85341),x85342),x85343))+~P1(f789(f789(f342(f869(x85341,x85341)),f789(f789(f249(x85341,x85341),x85345),x85342)),x85344))
% 21.40/21.38 [8535]~P47(x85351,x85353,x85354)+P1(f789(f789(f342(x85351),x85352),x85353))+~P1(f789(f789(f342(f869(x85351,x85351)),f789(f789(f249(x85351,x85351),x85352),x85355)),x85354))
% 21.40/21.38 [8536]~P12(x85361,x85363,x85364)+P1(f789(f789(f342(x85361),x85362),x85363))+~P1(f789(f789(f342(f869(x85361,x85361)),f789(f789(f249(x85361,x85361),x85365),x85362)),x85364))
% 21.40/21.38 [8537]~P12(x85371,x85373,x85374)+P1(f789(f789(f342(x85371),x85372),x85373))+~P1(f789(f789(f342(f869(x85371,x85371)),f789(f789(f249(x85371,x85371),x85372),x85375)),x85374))
% 21.40/21.38 [8773]~P12(x87731,x87735,x87732)+E(f789(f285(x87731,x87731,x87732),f789(f789(f310(x87731),x87733),f184(f870(x87731,a856)))),f789(f285(x87731,x87731,x87732),f789(f789(f310(x87731),x87734),f184(f870(x87731,a856)))))+~P1(f789(f789(f342(f869(x87731,x87731)),f789(f789(f249(x87731,x87731),x87733),x87734)),x87732))
% 21.40/21.38 [8774]~P12(x87741,x87745,x87742)+E(f789(f285(x87741,x87741,x87742),f789(f789(f310(x87741),x87743),f184(f870(x87741,a856)))),f789(f285(x87741,x87741,x87742),f789(f789(f310(x87741),x87744),f184(f870(x87741,a856)))))+~P1(f789(f789(f342(f869(x87741,x87741)),f789(f789(f249(x87741,x87741),x87743),x87744)),x87742))
% 21.40/21.38 [8939]P1(f789(x89391,x89392))+~P1(f789(f789(f342(x89393),x89392),x89395))+P1(f789(f789(f342(x89393),f369(x89391,x89394,x89395,x89393)),f789(f789(f110(f870(x89393,a856)),x89395),x89394)))
% 21.40/21.38 [8940]P1(f789(x89401,x89402))+~P1(f789(f789(f342(x89403),x89402),x89404))+P1(f789(f789(f342(x89403),f369(x89401,x89404,x89405,x89403)),f789(f789(f110(f870(x89403,a856)),x89405),x89404)))
% 21.40/21.38 [8948]~P1(f789(x89482,x89485))+~P1(f789(f789(f342(x89481),x89485),x89484))+P1(f789(f789(f342(x89481),f362(x89482,x89483,x89484,x89481)),f789(f789(f110(f870(x89481,a856)),x89484),x89483)))
% 21.40/21.38 [8949]~P1(f789(x89492,x89495))+~P1(f789(f789(f342(x89491),x89495),x89493))+P1(f789(f789(f342(x89491),f362(x89492,x89493,x89494,x89491)),f789(f789(f110(f870(x89491,a856)),x89494),x89493)))
% 21.40/21.38 [8962]~P1(f789(f789(f240(f870(x89621,a856)),x89625),x89623))+~P1(f789(f789(f240(f870(x89621,a856)),x89622),x89624))+P1(f789(f789(f240(f870(x89621,a856)),f789(f789(f3(f870(x89621,a856)),x89622),x89623)),f789(f789(f3(f870(x89621,a856)),x89624),x89625)))
% 21.40/21.38 [8963]~P1(f789(f789(f240(f870(x89631,a856)),x89633),x89635))+~P1(f789(f789(f240(f870(x89631,a856)),x89632),x89634))+P1(f789(f789(f240(f870(x89631,a856)),f789(f789(f110(f870(x89631,a856)),x89632),x89633)),f789(f789(f110(f870(x89631,a856)),x89634),x89635)))
% 21.40/21.38 [8964]~P1(f789(f789(f240(f870(x89641,a856)),x89643),x89645))+~P1(f789(f789(f240(f870(x89641,a856)),x89642),x89644))+P1(f789(f789(f240(f870(x89641,a856)),f789(f789(f111(f870(x89641,a856)),x89642),x89643)),f789(f789(f111(f870(x89641,a856)),x89644),x89645)))
% 21.40/21.38 [9053]P1(f789(f789(f342(f869(x90531,x90531)),f789(f789(f249(x90531,x90531),x90532),x90533)),f335(x90531,x90534,x90535)))+~P1(f789(f789(f240(a863),f789(x90534,x90532)),f789(x90534,x90533)))+~P1(f789(f789(f342(f869(x90531,x90531)),f789(f789(f249(x90531,x90531),x90532),x90533)),x90535))
% 21.40/21.38 [9060]~E(f789(f185(f864(x90601)),x90603),f789(f185(f864(x90602)),x90604))+E(f789(f170(x90601,x90602,f789(f789(f171(x90601,x90602),x90603),x90604)),x90605),f789(f234(x90602),f729(x90605,x90604,x90602,x90603,x90601)))+~P1(f789(f789(f342(x90601),x90605),f789(f163(x90601),x90603)))
% 21.40/21.38 [9210]P1(f789(f789(f342(f869(x92101,x92101)),f789(f789(f249(x92101,x92101),x92102),x92103)),f308(x92101,x92104)))+~P1(f789(f789(f342(f869(x92101,x92101)),f789(f789(f249(x92101,x92101),x92102),x92105)),f308(x92101,x92104)))+~P1(f789(f789(f342(f869(x92101,x92101)),f789(f789(f249(x92101,x92101),x92105),x92103)),x92104))
% 21.40/21.38 [9211]P1(f789(f789(f342(f869(x92111,x92111)),f789(f789(f249(x92111,x92111),x92112),x92113)),f308(x92111,x92114)))+~P1(f789(f789(f342(f869(x92111,x92111)),f789(f789(f249(x92111,x92111),x92115),x92113)),f308(x92111,x92114)))+~P1(f789(f789(f342(f869(x92111,x92111)),f789(f789(f249(x92111,x92111),x92112),x92115)),x92114))
% 21.40/21.38 [9303]E(x93031,x93032)+E(f789(a121,f670(x93033,x93034,x93031,x93032,x93035)),x93034)+~P1(f789(f789(f342(f869(x93035,x93035)),f789(f789(f249(x93035,x93035),x93032),x93031)),f789(f789(f178(f869(x93035,x93035),a856),x93034),x93033)))
% 21.40/21.38 [9304]E(x93041,x93042)+E(f789(a121,f672(x93043,x93044,x93041,x93042,x93045)),x93044)+~P1(f789(f789(f342(f869(x93045,x93045)),f789(f789(f249(x93045,x93045),x93042),x93041)),f789(f789(f178(f869(x93045,x93045),a856),x93044),x93043)))
% 21.40/21.38 [9305]E(x93051,f2(a863))+E(f789(a121,f670(x93052,x93051,x93053,x93054,x93055)),x93051)+~P1(f789(f789(f342(f869(x93055,x93055)),f789(f789(f249(x93055,x93055),x93054),x93053)),f789(f789(f178(f869(x93055,x93055),a856),x93051),x93052)))
% 21.40/21.38 [9306]E(x93061,f2(a863))+E(f789(a121,f672(x93062,x93061,x93063,x93064,x93065)),x93061)+~P1(f789(f789(f342(f869(x93065,x93065)),f789(f789(f249(x93065,x93065),x93064),x93063)),f789(f789(f178(f869(x93065,x93065),a856),x93061),x93062)))
% 21.40/21.38 [9325]P1(f789(f789(f342(f869(x93251,x93251)),f789(f789(f249(x93251,x93251),x93252),x93253)),f789(f789(f289(x93251,x93251,x93251),x93254),f308(x93251,x93254))))+~P1(f789(f789(f342(f869(x93251,x93251)),f789(f789(f249(x93251,x93251),x93252),x93255)),x93254))+~P1(f789(f789(f342(f869(x93251,x93251)),f789(f789(f249(x93251,x93251),x93255),x93253)),x93254))
% 21.40/21.38 [9335]~P1(f789(f789(f342(f869(x93351,x93351)),f789(f789(f249(x93351,x93351),x93352),x93355)),f308(x93351,x93354)))+P1(f789(f789(f342(f869(x93351,x93351)),f789(f789(f249(x93351,x93351),x93352),x93353)),f789(f789(f289(x93351,x93351,x93351),x93354),f308(x93351,x93354))))+~P1(f789(f789(f342(f869(x93351,x93351)),f789(f789(f249(x93351,x93351),x93355),x93353)),x93354))
% 21.40/21.38 [9336]~P1(f789(f789(f342(f869(x93361,x93361)),f789(f789(f249(x93361,x93361),x93365),x93363)),f308(x93361,x93364)))+P1(f789(f789(f342(f869(x93361,x93361)),f789(f789(f249(x93361,x93361),x93362),x93363)),f789(f789(f289(x93361,x93361,x93361),x93364),f308(x93361,x93364))))+~P1(f789(f789(f342(f869(x93361,x93361)),f789(f789(f249(x93361,x93361),x93362),x93365)),x93364))
% 21.40/21.38 [9372]~P12(x93721,x93725,x93722)+~P1(f789(f789(f342(f869(x93721,x93721)),f789(f789(f249(x93721,x93721),x93723),x93724)),x93722))+P1(f789(f789(f240(f870(x93721,a856)),f789(f285(x93721,x93721,x93722),f789(f789(f310(x93721),x93723),f184(f870(x93721,a856))))),f789(f285(x93721,x93721,x93722),f789(f789(f310(x93721),x93724),f184(f870(x93721,a856))))))
% 21.40/21.38 [9423]P1(f789(f789(f342(f869(x94231,x94231)),f789(f789(f249(x94231,x94231),x94232),x94233)),f789(f789(f289(x94231,x94231,x94231),x94234),f308(x94231,x94234))))+~P1(f789(f789(f342(f869(x94231,x94231)),f789(f789(f249(x94231,x94231),x94232),x94235)),f789(f789(f289(x94231,x94231,x94231),x94234),f308(x94231,x94234))))+~P1(f789(f789(f342(f869(x94231,x94231)),f789(f789(f249(x94231,x94231),x94235),x94233)),x94234))
% 21.40/21.38 [9424]P1(f789(f789(f342(f869(x94241,x94241)),f789(f789(f249(x94241,x94241),x94242),x94243)),f789(f789(f289(x94241,x94241,x94241),x94244),f308(x94241,x94244))))+~P1(f789(f789(f342(f869(x94241,x94241)),f789(f789(f249(x94241,x94241),x94245),x94243)),f789(f789(f289(x94241,x94241,x94241),x94244),f308(x94241,x94244))))+~P1(f789(f789(f342(f869(x94241,x94241)),f789(f789(f249(x94241,x94241),x94242),x94245)),x94244))
% 21.40/21.38 [9472]~P1(f789(f75(x94721,x94721,x94724,x94722,x94723),x94725))+P1(f789(f789(f342(x94721),x94722),x94723))+P1(f789(f71(x94721,x94724,f789(f789(f310(x94721),x94722),x94723)),x94725))
% 21.40/21.38 [9517]~E(f789(f311(x95173,x95172,x95175),x95174),x95171)+E(x95171,f184(f870(x95172,a856)))+P1(f789(f789(f240(f870(x95173,a856)),f789(f311(x95172,x95173,f461(x95174,x95173,x95172,x95171)),x95171)),x95174))
% 21.40/21.38 [9557]~P9(x95575)+P1(f789(f789(f342(x95571),f428(x95572,x95573,x95574,x95571,x95575)),x95574))+P1(f789(f789(f240(x95575),f789(f789(f53(x95571,x95575),x95574),x95573)),x95572))
% 21.40/21.38 [9724]E(x97241,x97242)+P1(f789(f789(f342(f869(x97243,x97243)),f789(f789(f249(x97243,x97243),x97241),f673(x97244,x97245,x97242,x97241,x97243))),x97244))+~P1(f789(f789(f342(f869(x97243,x97243)),f789(f789(f249(x97243,x97243),x97241),x97242)),f789(f789(f178(f869(x97243,x97243),a856),x97245),x97244)))
% 21.40/21.38 [9725]E(x97251,f2(a863))+P1(f789(f789(f342(f869(x97252,x97252)),f789(f789(f249(x97252,x97252),x97253),f673(x97254,x97251,x97255,x97253,x97252))),x97254))+~P1(f789(f789(f342(f869(x97252,x97252)),f789(f789(f249(x97252,x97252),x97253),x97255)),f789(f789(f178(f869(x97252,x97252),a856),x97251),x97254)))
% 21.40/21.38 [9770]~P9(x97701)+~P1(f789(f789(f240(x97701),f789(x97704,f428(x97705,x97704,x97703,x97702,x97701))),x97705))+P1(f789(f789(f240(x97701),f789(f789(f53(x97702,x97701),x97703),x97704)),x97705))
% 21.40/21.38 [9825]E(x98251,x98252)+P1(f789(f789(f342(f869(x98253,x98253)),f789(f789(f249(x98253,x98253),f671(x98254,x98255,x98251,x98252,x98253)),x98251)),x98254))+~P1(f789(f789(f342(f869(x98253,x98253)),f789(f789(f249(x98253,x98253),x98252),x98251)),f789(f789(f178(f869(x98253,x98253),a856),x98255),x98254)))
% 21.40/21.38 [9826]E(x98261,f2(a863))+P1(f789(f789(f342(f869(x98262,x98262)),f789(f789(f249(x98262,x98262),f671(x98263,x98261,x98264,x98265,x98262)),x98264)),x98263))+~P1(f789(f789(f342(f869(x98262,x98262)),f789(f789(f249(x98262,x98262),x98265),x98264)),f789(f789(f178(f869(x98262,x98262),a856),x98261),x98263)))
% 21.40/21.38 [9830]E(x98301,x98302)+P1(f789(f789(f342(f869(x98303,x98303)),f789(f789(f249(x98303,x98303),x98301),f671(x98304,x98305,x98302,x98301,x98303))),f789(f789(f178(f869(x98303,x98303),a856),f670(x98304,x98305,x98302,x98301,x98303)),x98304)))+~P1(f789(f789(f342(f869(x98303,x98303)),f789(f789(f249(x98303,x98303),x98301),x98302)),f789(f789(f178(f869(x98303,x98303),a856),x98305),x98304)))
% 21.40/21.38 [9831]E(x98311,f2(a863))+P1(f789(f789(f342(f869(x98312,x98312)),f789(f789(f249(x98312,x98312),x98313),f671(x98314,x98311,x98315,x98313,x98312))),f789(f789(f178(f869(x98312,x98312),a856),f670(x98314,x98311,x98315,x98313,x98312)),x98314)))+~P1(f789(f789(f342(f869(x98312,x98312)),f789(f789(f249(x98312,x98312),x98313),x98315)),f789(f789(f178(f869(x98312,x98312),a856),x98311),x98314)))
% 21.40/21.38 [9891]E(x98911,x98912)+P1(f789(f789(f342(f869(x98913,x98913)),f789(f789(f249(x98913,x98913),f673(x98914,x98915,x98911,x98912,x98913)),x98911)),f789(f789(f178(f869(x98913,x98913),a856),f672(x98914,x98915,x98911,x98912,x98913)),x98914)))+~P1(f789(f789(f342(f869(x98913,x98913)),f789(f789(f249(x98913,x98913),x98912),x98911)),f789(f789(f178(f869(x98913,x98913),a856),x98915),x98914)))
% 21.40/21.38 [9892]E(x98921,f2(a863))+P1(f789(f789(f342(f869(x98922,x98922)),f789(f789(f249(x98922,x98922),f673(x98923,x98921,x98924,x98925,x98922)),x98924)),f789(f789(f178(f869(x98922,x98922),a856),f672(x98923,x98921,x98924,x98925,x98922)),x98923)))+~P1(f789(f789(f342(f869(x98922,x98922)),f789(f789(f249(x98922,x98922),x98925),x98924)),f789(f789(f178(f869(x98922,x98922),a856),x98921),x98923)))
% 21.40/21.38 [9925]~P4(x99252)+~P1(f789(f70(x99251),x99255))+E(f789(f789(f8(x99251,x99252),f789(f789(f9(x99251,x99252,x99252),f789(f789(f20(x99251,x99252,f870(x99252,x99252)),f789(f789(f10(a856,f870(x99252,f870(x99252,x99252)),x99251),f105(x99252)),f789(f789(f9(x99251,f870(x99251,a856),a856),f342(x99251)),x99253))),x99254)),f2(x99252))),x99255),f789(f789(f8(x99251,x99252),x99254),f789(f789(f111(f870(x99251,a856)),x99255),x99253)))
% 21.40/21.38 [8588]~P69(x85881)+~P1(f789(f70(x85884),x85885))+E(f789(f789(f90(x85881),f789(x85882,x85883)),f789(f789(f11(x85884,x85881),x85882),f789(f789(f3(f870(x85884,a856)),x85885),f789(f789(f310(x85884),x85883),f184(f870(x85884,a856)))))),f789(f789(f11(x85884,x85881),x85882),f789(f789(f310(x85884),x85883),x85885)))
% 21.40/21.38 [8589]~P4(x85891)+~P1(f789(f70(x85894),x85895))+E(f789(f789(f89(x85891),f789(x85892,x85893)),f789(f789(f8(x85894,x85891),x85892),f789(f789(f3(f870(x85894,a856)),x85895),f789(f789(f310(x85894),x85893),f184(f870(x85894,a856)))))),f789(f789(f8(x85894,x85891),x85892),f789(f789(f310(x85894),x85893),x85895)))
% 21.40/21.38 [8893]~P4(x88931)+E(f789(f789(f89(x88931),f789(f789(f8(a863,x88931),x88932),f303(a863,x88933,x88934))),f789(f789(f8(a863,x88931),x88932),f303(a863,f789(f789(f89(a863),x88934),f87(a863)),f789(f789(f89(a863),x88934),x88935)))),f789(f789(f8(a863,x88931),x88932),f303(a863,x88933,f789(f789(f89(a863),x88934),x88935))))+~P1(f789(f789(f240(a863),x88933),f789(f789(f89(a863),x88934),f87(a863))))
% 21.40/21.38 [8894]~P1(f789(f789(f342(x88941),x88944),x88945))+~P1(f789(f789(f240(f870(x88941,a856)),f789(f163(x88941),x88942)),x88945))+P1(f789(f789(f240(f870(x88941,a856)),f789(f163(x88941),f789(f789(f155(x88941,x88942),x88943),x88944))),x88945))
% 21.40/21.38 [9112]~P9(x91122)+~P1(f789(f70(x91121),x91125))+E(f789(f789(f73(x91121,x91122,f789(f789(f10(x91122,f870(x91122,x91122),x91121),f110(x91122)),x91123)),x91124),x91125),f789(f789(f110(x91122),x91124),f789(f789(f53(x91121,x91122),x91125),x91123)))
% 21.40/21.38 [9113]~P9(x91132)+~P1(f789(f70(x91131),x91135))+E(f789(f789(f73(x91131,x91132,f789(f789(f10(x91132,f870(x91132,x91132),x91131),f111(x91132)),x91133)),x91134),x91135),f789(f789(f111(x91132),x91134),f789(f789(f54(x91131,x91132),x91135),x91133)))
% 21.40/21.38 [9197]~P29(x91971,x91972,x91973,x91975)+P29(x91971,x91972,x91973,f789(f789(f310(x91971),x91974),x91975))+P1(f789(f789(f342(x91972),f789(x91973,x91974)),f789(f311(x91971,x91972,x91973),f789(f789(f3(f870(x91971,a856)),x91975),f789(f789(f310(x91971),x91974),f184(f870(x91971,a856)))))))
% 21.40/21.38 [9397]~P1(f789(f789(f342(f869(f864(x93971),f864(x93971))),f789(f789(f249(f864(x93971),f864(x93971)),x93972),x93974)),f154(x93971,x93975)))+~P1(f789(f789(f241(a863),x93973),f789(f185(f864(x93971)),x93972)))+P1(f789(f789(f342(f869(x93971,x93971)),f789(f789(f249(x93971,x93971),f789(f789(f159(x93971),x93972),x93973)),f789(f789(f159(x93971),x93974),x93973))),x93975))
% 21.40/21.38 [9633]E(x96331,f2(a1))+~P1(f789(f63(x96333,x96331),f789(f789(f249(a1,a1),x96334),x96335)))+P1(f789(f63(f789(f789(f90(a1),x96332),x96333),x96331),f789(f789(f249(a1,a1),f789(f789(f89(a1),f789(f789(f90(a1),x96332),x96334)),f789(f789(f50(a1),f789(f789(f90(a1),x96332),x96335)),x96331))),f59(a1,f789(f789(f90(a1),x96332),x96335),x96331))))
% 21.40/21.38 [9636]~P1(f789(f789(f241(a863),f2(a863)),x96363))+~P1(f789(f62(x96362,x96363),f789(f789(f249(a863,a863),x96364),x96365)))+P1(f789(f62(f789(f789(f90(a863),x96361),x96362),x96363),f789(f789(f249(a863,a863),f789(f789(f89(a863),f789(f789(f90(a863),x96361),x96364)),f789(f789(f50(a863),f789(f789(f90(a863),x96361),x96365)),x96363))),f59(a863,f789(f789(f90(a863),x96361),x96365),x96363))))
% 21.40/21.38 [9947]~P4(x99472)+~P1(f789(f70(x99471),x99474))+E(f789(f789(f8(x99471,x99472),x99473),f789(f264(x99471),f789(f789(f20(x99471,a856,a856),f789(f789(f10(a856,f870(a856,a856),x99471),a339),f789(f789(f9(x99471,f870(x99471,a856),a856),f342(x99471)),x99474))),f789(f789(f9(x99471,f870(x99471,a856),a856),f342(x99471)),x99475)))),f789(f789(f8(x99471,x99472),f789(f789(f9(x99471,x99472,x99472),f789(f789(f20(x99471,x99472,f870(x99472,x99472)),f789(f789(f10(a856,f870(x99472,f870(x99472,x99472)),x99471),f105(x99472)),f789(f789(f9(x99471,f870(x99471,a856),a856),f342(x99471)),x99475))),x99473)),f2(x99472))),x99474))
% 21.40/21.38 [8226]~E(f789(f789(f132(x82261),x82262),x82265),f789(f789(f132(x82261),x82263),x82264))+E(f789(f789(f132(x82261),f789(f789(f135(x82261),f789(f185(f864(x82261)),x82262)),x82263)),x82264),x82265)+P1(f789(f789(f240(a863),f789(f185(f864(x82261)),x82263)),f789(f185(f864(x82261)),x82262)))
% 21.40/21.38 [8426]~E(f789(f789(f132(x84262),x84263),x84261),f789(f789(f132(x84262),x84264),x84265))+E(x84261,f789(f789(f132(x84262),f789(f789(f135(x84262),f789(f185(f864(x84262)),x84263)),x84264)),x84265))+~P1(f789(f789(f240(a863),f789(f185(f864(x84262)),x84263)),f789(f185(f864(x84262)),x84264)))
% 21.40/21.38 [8517]~E(f789(f789(f89(a863),f789(f789(f90(a863),x85173),x85174)),x85171),f789(f789(f89(a863),f789(f789(f90(a863),x85172),x85174)),x85175))+~P1(f789(f789(f240(a863),x85173),x85172))+E(x85171,f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f3(a863),x85172),x85173)),x85174)),x85175))
% 21.40/21.38 [8518]~E(f789(f789(f89(a863),f789(f789(f90(a863),x85181),x85183)),x85184),f789(f789(f89(a863),f789(f789(f90(a863),x85182),x85183)),x85185))+~P1(f789(f789(f240(a863),x85182),x85181))+E(f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f3(a863),x85181),x85182)),x85183)),x85184),x85185)
% 21.40/21.38 [8659]E(f789(f789(f89(a863),f789(f789(f90(a863),x86591),x86592)),x86593),f789(f789(f89(a863),f789(f789(f90(a863),x86594),x86592)),x86595))+~P1(f789(f789(f240(a863),x86594),x86591))+~E(x86595,f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f3(a863),x86591),x86594)),x86592)),x86593))
% 21.40/21.38 [8660]E(f789(f789(f89(a863),f789(f789(f90(a863),x86601),x86602)),x86603),f789(f789(f89(a863),f789(f789(f90(a863),x86604),x86602)),x86605))+~P1(f789(f789(f240(a863),x86604),x86601))+~E(f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f3(a863),x86601),x86604)),x86602)),x86603),x86605)
% 21.40/21.38 [8994]~P1(f789(f789(f287(a1),x89941),x89944))+~P1(f789(f789(f287(a1),x89941),f789(f789(f89(a1),x89942),x89945)))+P1(f789(f789(f287(a1),x89941),f789(f789(f89(a1),f789(f789(f89(a1),x89942),f789(f789(f90(a1),x89943),x89944))),x89945)))
% 21.40/21.38 [9198]~P1(f789(f789(f287(a1),x91981),x91984))+P1(f789(f789(f287(a1),x91981),f789(f789(f89(a1),x91982),x91983)))+~P1(f789(f789(f287(a1),x91981),f789(f789(f89(a1),f789(f789(f89(a1),x91982),f789(f789(f90(a1),x91985),x91984))),x91983)))
% 21.40/21.38 [9446]~P69(x94462)+~P1(f789(f70(x94461),x94465))+E(f789(f789(f11(x94461,x94462),f789(f789(f20(x94461,x94462,x94462),f789(f789(f10(x94462,f870(x94462,x94462),x94461),f90(x94462)),x94463)),x94464)),x94465),f789(f789(f90(x94462),f789(f789(f11(x94461,x94462),x94463),x94465)),f789(f789(f11(x94461,x94462),x94464),x94465)))
% 21.40/21.38 [9447]~P60(x94472)+~P1(f789(f70(x94471),x94475))+E(f789(f789(f11(x94471,x94472),f789(f789(f20(x94471,x94472,x94472),f789(f789(f10(x94472,f870(x94472,x94472),x94471),f291(x94472)),x94473)),x94474)),x94475),f789(f789(f291(x94472),f789(f789(f11(x94471,x94472),x94473),x94475)),f789(f789(f11(x94471,x94472),x94474),x94475)))
% 21.40/21.38 [9448]~P4(x94482)+~P1(f789(f70(x94481),x94485))+E(f789(f789(f8(x94481,x94482),f789(f789(f20(x94481,x94482,x94482),f789(f789(f10(x94482,f870(x94482,x94482),x94481),f89(x94482)),x94483)),x94484)),x94485),f789(f789(f89(x94482),f789(f789(f8(x94481,x94482),x94483),x94485)),f789(f789(f8(x94481,x94482),x94484),x94485)))
% 21.40/21.38 [9572]~E(f691(x95725,x95724,x95723,x95722,x95721),f692(x95725,x95724,x95723,x95722,x95721))+P1(f789(f789(f342(f869(x95721,x95721)),f789(f789(f249(x95721,x95721),x95722),x95723)),f308(x95721,x95724)))+~P1(f789(f789(f342(f869(x95721,x95721)),f789(f789(f249(x95721,x95721),x95722),x95723)),f308(x95721,f789(f789(f110(f870(f869(x95721,x95721),a856)),x95724),x95725))))
% 21.40/21.38 [9573]~E(f693(x95735,x95734,x95733,x95732,x95731),f694(x95735,x95734,x95733,x95732,x95731))+P1(f789(f789(f342(f869(x95731,x95731)),f789(f789(f249(x95731,x95731),x95732),x95733)),f308(x95731,x95734)))+~P1(f789(f789(f342(f869(x95731,x95731)),f789(f789(f249(x95731,x95731),x95732),x95733)),f308(x95731,f789(f789(f110(f870(f869(x95731,x95731),a856)),x95734),x95735))))
% 21.40/21.38 [9758]P1(f789(f789(f342(f869(x97581,x97581)),f789(f789(f249(x97581,x97581),x97582),f694(x97585,x97584,x97583,x97582,x97581))),f308(x97581,x97584)))+P1(f789(f789(f342(f869(x97581,x97581)),f789(f789(f249(x97581,x97581),x97582),x97583)),f308(x97581,x97584)))+~P1(f789(f789(f342(f869(x97581,x97581)),f789(f789(f249(x97581,x97581),x97582),x97583)),f308(x97581,f789(f789(f110(f870(f869(x97581,x97581),a856)),x97584),x97585))))
% 21.40/21.38 [9852]P1(f789(f789(f342(f869(x98521,x98521)),f789(f789(f249(x98521,x98521),f692(x98525,x98524,x98523,x98522,x98521)),x98523)),f308(x98521,x98524)))+P1(f789(f789(f342(f869(x98521,x98521)),f789(f789(f249(x98521,x98521),x98522),x98523)),f308(x98521,x98524)))+~P1(f789(f789(f342(f869(x98521,x98521)),f789(f789(f249(x98521,x98521),x98522),x98523)),f308(x98521,f789(f789(f110(f870(f869(x98521,x98521),a856)),x98524),x98525))))
% 21.40/21.38 [9898]P1(f789(f789(f342(f869(x98981,x98981)),f789(f789(f249(x98981,x98981),x98982),x98983)),f308(x98981,x98984)))+P1(f789(f789(f342(f869(x98981,x98981)),f789(f789(f249(x98981,x98981),f691(x98985,x98984,x98983,x98982,x98981)),f692(x98985,x98984,x98983,x98982,x98981))),x98985))+~P1(f789(f789(f342(f869(x98981,x98981)),f789(f789(f249(x98981,x98981),x98982),x98983)),f308(x98981,f789(f789(f110(f870(f869(x98981,x98981),a856)),x98984),x98985))))
% 21.40/21.38 [9899]P1(f789(f789(f342(f869(x98991,x98991)),f789(f789(f249(x98991,x98991),x98992),x98993)),f308(x98991,x98994)))+P1(f789(f789(f342(f869(x98991,x98991)),f789(f789(f249(x98991,x98991),f694(x98995,x98994,x98993,x98992,x98991)),f693(x98995,x98994,x98993,x98992,x98991))),x98995))+~P1(f789(f789(f342(f869(x98991,x98991)),f789(f789(f249(x98991,x98991),x98992),x98993)),f308(x98991,f789(f789(f110(f870(f869(x98991,x98991),a856)),x98994),x98995))))
% 21.40/21.38 [10026]~P1(f789(f789(f342(f869(f864(x100261),f864(x100261))),f789(f789(f249(f864(x100261),f864(x100261)),x100264),x100265)),f154(x100261,x100262)))+~P1(f789(f789(f342(f869(x100261,x100261)),x100263),f789(f163(f869(x100261,x100261)),f789(f789(f171(x100261,x100261),x100264),x100265))))+P1(f789(f789(f259(x100261,x100261,a856),f789(f789(f9(x100261,f870(f869(x100261,x100261),a856),f870(x100261,a856)),f789(f789(f10(f870(x100261,f870(f870(f869(x100261,x100261),a856),a856)),f870(f870(f869(x100261,x100261),a856),f870(x100261,a856)),x100261),f9(x100261,f870(f869(x100261,x100261),a856),a856)),f789(f789(f10(f870(x100261,f869(x100261,x100261)),f870(x100261,f870(f870(f869(x100261,x100261),a856),a856)),x100261),f789(f10(f869(x100261,x100261),f870(f870(f869(x100261,x100261),a856),a856),x100261),f342(f869(x100261,x100261)))),f249(x100261,x100261)))),x100262)),x100263))
% 21.40/21.38 [9476]~P1(f789(f789(f240(a863),x94763),x94762))+~P1(f789(f789(f241(a863),f789(f789(f89(a863),f789(f789(f90(a863),x94763),x94764)),x94761)),f789(f789(f89(a863),f789(f789(f90(a863),x94762),x94764)),x94765)))+P1(f789(f789(f241(a863),x94761),f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f3(a863),x94762),x94763)),x94764)),x94765)))
% 21.40/21.38 [9477]~P1(f789(f789(f240(a863),x94773),x94772))+~P1(f789(f789(f240(a863),f789(f789(f89(a863),f789(f789(f90(a863),x94773),x94774)),x94771)),f789(f789(f89(a863),f789(f789(f90(a863),x94772),x94774)),x94775)))+P1(f789(f789(f240(a863),x94771),f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f3(a863),x94772),x94773)),x94774)),x94775)))
% 21.40/21.38 [9499]~P1(f789(f789(f240(a863),x94991),x94994))+P1(f789(f789(f241(a863),f789(f789(f89(a863),f789(f789(f90(a863),x94991),x94992)),x94993)),f789(f789(f89(a863),f789(f789(f90(a863),x94994),x94992)),x94995)))+~P1(f789(f789(f241(a863),x94993),f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f3(a863),x94994),x94991)),x94992)),x94995)))
% 21.40/21.38 [9500]~P1(f789(f789(f240(a863),x95001),x95004))+P1(f789(f789(f240(a863),f789(f789(f89(a863),f789(f789(f90(a863),x95001),x95002)),x95003)),f789(f789(f89(a863),f789(f789(f90(a863),x95004),x95002)),x95005)))+~P1(f789(f789(f240(a863),x95003),f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f3(a863),x95004),x95001)),x95002)),x95005)))
% 21.40/21.38 [9610]~P1(f789(f789(f240(a863),x96102),x96101))+~P1(f789(f789(f241(a863),f789(f789(f89(a863),f789(f789(f90(a863),x96101),x96103)),x96104)),f789(f789(f89(a863),f789(f789(f90(a863),x96102),x96103)),x96105)))+P1(f789(f789(f241(a863),f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f3(a863),x96101),x96102)),x96103)),x96104)),x96105))
% 21.40/21.38 [9611]~P1(f789(f789(f240(a863),x96112),x96111))+~P1(f789(f789(f240(a863),f789(f789(f89(a863),f789(f789(f90(a863),x96111),x96113)),x96114)),f789(f789(f89(a863),f789(f789(f90(a863),x96112),x96113)),x96115)))+P1(f789(f789(f240(a863),f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f3(a863),x96111),x96112)),x96113)),x96114)),x96115))
% 21.40/21.38 [9655]~P1(f789(f789(f240(a863),x96554),x96551))+P1(f789(f789(f241(a863),f789(f789(f89(a863),f789(f789(f90(a863),x96551),x96552)),x96553)),f789(f789(f89(a863),f789(f789(f90(a863),x96554),x96552)),x96555)))+~P1(f789(f789(f241(a863),f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f3(a863),x96551),x96554)),x96552)),x96553)),x96555))
% 21.40/21.38 [9656]~P1(f789(f789(f240(a863),x96564),x96561))+P1(f789(f789(f240(a863),f789(f789(f89(a863),f789(f789(f90(a863),x96561),x96562)),x96563)),f789(f789(f89(a863),f789(f789(f90(a863),x96564),x96562)),x96565)))+~P1(f789(f789(f240(a863),f789(f789(f89(a863),f789(f789(f90(a863),f789(f789(f3(a863),x96561),x96564)),x96562)),x96563)),x96565))
% 21.40/21.38 [9883]~P16(x98831,x98832,x98835,x98833)+~P1(f789(f789(f342(f869(x98831,x98831)),x98834),x98835))+P1(f789(f789(f259(x98831,x98831,a856),f789(f789(f9(x98831,f870(x98831,x98832),f870(x98831,a856)),f789(f789(f10(f870(x98832,a856),f870(f870(x98831,x98832),f870(x98831,a856)),x98831),f10(x98832,a856,x98831)),f789(f789(f10(x98832,f870(x98832,a856),x98831),a338),x98833))),x98833)),x98834))
% 21.40/21.38 [7197]~P39(x71974,x71972,x71975,x71976)+P39(f35(x71971,x71973,x71974),x71972,x71975,x71976)+P1(f789(x71971,x71972))
% 21.40/21.38 [7198]~P39(x71984,x71982,x71985,x71986)+P39(f35(x71981,x71983,x71984),x71982,x71985,x71986)+P1(f789(x71981,x71982))
% 21.40/21.38 [7199]~P39(x71994,x71992,x71995,x71996)+P39(f35(x71991,x71993,x71994),x71992,x71995,x71996)+P1(f789(x71991,x71992))
% 21.40/21.38 [7277]~P39(x72772,x72774,x72775,x72776)+P39(f35(x72771,x72772,x72773),x72774,x72775,x72776)+~P1(f789(x72771,x72774))
% 21.40/21.38 [7278]~P39(x72782,x72784,x72785,x72786)+P39(f35(x72781,x72782,x72783),x72784,x72785,x72786)+~P1(f789(x72781,x72784))
% 21.40/21.38 [7279]~P39(x72792,x72794,x72795,x72796)+P39(f35(x72791,x72792,x72793),x72794,x72795,x72796)+~P1(f789(x72791,x72794))
% 21.40/21.38 [7368]P39(x73683,x73682,x73684,x73685)+~P39(f35(x73681,x73686,x73683),x73682,x73684,x73685)+P1(f789(x73681,x73682))
% 21.40/21.38 [7369]P39(x73693,x73692,x73694,x73695)+~P39(f35(x73691,x73696,x73693),x73692,x73694,x73695)+P1(f789(x73691,x73692))
% 21.40/21.38 [7370]P39(x73703,x73702,x73704,x73705)+~P39(f35(x73701,x73706,x73703),x73702,x73704,x73705)+P1(f789(x73701,x73702))
% 21.40/21.38 [7401]P39(x74011,x74012,x74013,x74014)+~P39(f35(x74015,x74011,x74016),x74012,x74013,x74014)+~P1(f789(x74015,x74012))
% 21.40/21.38 [7402]P39(x74021,x74022,x74023,x74024)+~P39(f35(x74025,x74021,x74026),x74022,x74023,x74024)+~P1(f789(x74025,x74022))
% 21.40/21.38 [7403]P39(x74031,x74032,x74033,x74034)+~P39(f35(x74035,x74031,x74036),x74032,x74033,x74034)+~P1(f789(x74035,x74032))
% 21.40/21.38 [7773]~P39(x77731,x77733,x77734,x77736)+~P39(x77732,x77736,x77734,x77735)+P39(f38(x77731,x77732),x77733,x77734,x77735)
% 21.40/21.38 [7774]~P39(x77741,x77743,x77744,x77746)+~P39(x77742,x77746,x77744,x77745)+P39(f38(x77741,x77742),x77743,x77744,x77745)
% 21.40/21.38 [7775]P39(x77751,x77752,x77753,x77754)+P39(x77755,x77752,x77753,x77754)+~P39(f35(x77756,x77751,x77755),x77752,x77753,x77754)
% 21.40/21.38 [7776]P39(x77761,x77762,x77763,x77764)+P39(x77765,x77762,x77763,x77764)+~P39(f35(x77766,x77761,x77765),x77762,x77763,x77764)
% 21.40/21.38 [7777]P39(x77771,x77772,x77773,x77774)+P39(x77775,x77772,x77773,x77774)+~P39(f35(x77776,x77771,x77775),x77772,x77773,x77774)
% 21.40/21.38 [6751]~E(f789(x67514,x67515),f187(x67512))+E(f789(f174(x67511,x67512,x67513,x67514),x67515),f789(f234(x67512),x67516))+~E(f789(x67513,x67515),f789(f234(x67512),x67516))
% 21.40/21.38 [6857]~E(f789(x68573,x68576),f187(x68571))+E(f789(f236(f867(x68571),x68572,f187(x68571),x68573),f789(x68574,x68575)),f187(x68571))+~E(f789(x68574,x68575),f789(f234(x68572),x68576))
% 21.40/21.38 [7460]E(f789(x74601,x74602),f187(x74603))+~E(f789(f174(x74605,x74603,x74606,x74601),x74602),f789(f234(x74603),x74604))+E(f789(x74601,x74602),f789(f234(x74603),x74604))
% 21.40/21.38 [7461]E(f789(x74611,x74612),f187(x74613))+~E(f789(f174(x74615,x74613,x74616,x74611),x74612),f789(f234(x74613),x74614))+E(f789(x74611,x74612),f789(f234(x74613),x74614))
% 21.40/21.38 [7498]~E(f789(f174(x74986,x74983,x74985,x74981),x74982),f789(f234(x74983),x74984))+E(f789(x74981,x74982),f789(f234(x74983),x74984))+E(f789(x74985,x74982),f789(f234(x74983),x74984))
% 21.40/21.38 [7499]~E(f789(f174(x74996,x74993,x74995,x74991),x74992),f789(f234(x74993),x74994))+E(f789(x74991,x74992),f789(f234(x74993),x74994))+E(f789(x74995,x74992),f789(f234(x74993),x74994))
% 21.40/21.38 [8387]~P23(x83876,x83871,x83872,x83874)+E(f789(f82(x83871,x83871,x83871,f789(x83872,x83873)),f789(x83874,x83875)),f789(f82(x83871,x83871,x83871,f789(x83874,x83875)),f789(x83872,x83873)))+~P1(f789(f70(x83876),x83875))
% 21.40/21.38 [8783]~P29(x87831,x87833,x87835,x87836)+~P29(x87833,x87832,x87834,f789(f311(x87831,x87833,x87835),x87836))+P29(x87831,x87832,f789(f82(x87833,x87832,x87831,x87834),x87835),x87836)
% 21.40/21.38 [8784]~P29(x87841,x87843,x87845,x87846)+~P29(x87843,x87842,x87844,f789(f311(x87841,x87843,x87845),x87846))+P29(x87841,x87842,f789(f82(x87843,x87842,x87841,x87844),x87845),x87846)
% 21.40/21.38 [8944]~P29(x89444,x89441,x89445,x89446)+~P29(x89444,x89442,f789(f82(x89441,x89442,x89444,x89443),x89445),x89446)+P29(x89441,x89442,x89443,f789(f311(x89444,x89441,x89445),x89446))
% 21.40/21.38 [9287]~P1(f789(f789(x92873,x92872),x92876))+~P1(f789(f789(x92874,x92875),x92872))+P1(f789(f789(f342(x92871),x92872),f300(x92871,x92873,x92874,x92875,x92876)))
% 21.40/21.38 [9288]~P1(f789(f789(x92884,x92882),x92886))+~P1(f789(f789(x92883,x92885),x92882))+P1(f789(f789(f342(x92881),x92882),f297(x92881,x92883,x92884,x92885,x92886)))
% 21.40/21.38 [9398]E(x93981,x93982)+E(x93983,x93984)+~P1(f789(f789(f342(f869(f864(x93985),f864(x93985))),f789(f789(f249(f864(x93985),f864(x93985)),f789(f789(f146(x93985),x93983),x93981)),f789(f789(f146(x93985),x93984),x93982))),f153(x93985,x93986)))
% 21.40/21.38 [9407]~E(x94072,x94074)+P1(f789(f789(f342(f869(f864(x94071),f864(x94071))),f789(f789(f249(f864(x94071),f864(x94071)),f789(f789(f146(x94071),x94072),x94073)),f789(f789(f146(x94071),x94074),x94075))),f141(x94071,x94076)))+~P1(f789(f789(f342(f869(f864(x94071),f864(x94071))),f789(f789(f249(f864(x94071),f864(x94071)),x94073),x94075)),f141(x94071,x94076)))
% 21.40/21.38 [9408]~E(x94082,x94084)+P1(f789(f789(f342(f869(f864(x94081),f864(x94081))),f789(f789(f249(f864(x94081),f864(x94081)),f789(f789(f146(x94081),x94082),x94083)),f789(f789(f146(x94081),x94084),x94085))),f143(x94081,x94086)))+~P1(f789(f789(f342(f869(f864(x94081),f864(x94081))),f789(f789(f249(f864(x94081),f864(x94081)),x94083),x94085)),f143(x94081,x94086)))
% 21.40/21.38 [9409]~E(x94092,x94094)+P1(f789(f789(f342(f869(f864(x94091),f864(x94091))),f789(f789(f249(f864(x94091),f864(x94091)),f789(f789(f146(x94091),x94092),x94093)),f789(f789(f146(x94091),x94094),x94095))),f153(x94091,x94096)))+~P1(f789(f789(f342(f869(f864(x94091),f864(x94091))),f789(f789(f249(f864(x94091),f864(x94091)),x94093),x94095)),f153(x94091,x94096)))
% 21.40/21.38 [9410]~E(x94102,x94104)+P1(f789(f789(f342(f869(f864(x94101),f864(x94101))),f789(f789(f249(f864(x94101),f864(x94101)),f789(f789(f132(x94101),x94102),x94103)),f789(f789(f132(x94101),x94104),x94105))),f153(x94101,x94106)))+~P1(f789(f789(f342(f869(f864(x94101),f864(x94101))),f789(f789(f249(f864(x94101),f864(x94101)),x94103),x94105)),f153(x94101,x94106)))
% 21.40/21.38 [9411]~E(x94113,x94115)+P1(f789(f789(f342(f869(f864(x94111),f864(x94111))),f789(f789(f249(f864(x94111),f864(x94111)),f789(f789(f132(x94111),x94112),x94113)),f789(f789(f132(x94111),x94114),x94115))),f153(x94111,x94116)))+~P1(f789(f789(f342(f869(f864(x94111),f864(x94111))),f789(f789(f249(f864(x94111),f864(x94111)),x94112),x94114)),f153(x94111,x94116)))
% 21.40/21.38 [9465]E(x94651,x94652)+P1(f789(f789(f342(f869(f864(x94653),f864(x94653))),f789(f789(f249(f864(x94653),f864(x94653)),x94651),x94652)),f153(x94653,x94654)))+~P1(f789(f789(f342(f869(f864(x94653),f864(x94653))),f789(f789(f249(f864(x94653),f864(x94653)),f789(f789(f146(x94653),x94655),x94651)),f789(f789(f146(x94653),x94656),x94652))),f153(x94653,x94654)))
% 21.40/21.38 [9612]~E(x96123,x96125)+P1(f789(f789(f342(f869(f864(x96121),f864(x96121))),f789(f789(f249(f864(x96121),f864(x96121)),f789(f789(f132(x96121),x96122),f789(f789(f146(x96121),x96123),f122(x96121)))),f789(f789(f132(x96121),x96124),f789(f789(f146(x96121),x96125),f122(x96121))))),f153(x96121,x96126)))+~P1(f789(f789(f342(f869(f864(x96121),f864(x96121))),f789(f789(f249(f864(x96121),f864(x96121)),x96122),x96124)),f153(x96121,x96126)))
% 21.40/21.38 [9625]E(f789(x96251,x96252),f187(x96253))+~E(f789(f236(f867(x96256),x96253,f187(x96256),x96254),f789(x96251,x96252)),f187(x96256))+E(f789(x96254,f725(x96252,x96251,x96254,x96255,x96256,x96253)),f187(x96256))
% 21.40/21.38 [9626]E(f789(x96261,x96262),f187(x96263))+~E(f789(f236(f867(x96266),x96263,f187(x96266),x96264),f789(x96261,x96262)),f187(x96266))+E(f789(f234(x96263),f725(x96262,x96261,x96264,x96265,x96266,x96263)),f789(x96261,x96262))
% 21.40/21.38 [9659]E(x96591,x96592)+E(x96593,x96594)+~P1(f789(f789(f342(f869(f864(x96595),f864(x96595))),f789(f789(f249(f864(x96595),f864(x96595)),f789(f789(f132(x96595),x96593),f789(f789(f146(x96595),x96591),f122(x96595)))),f789(f789(f132(x96595),x96594),f789(f789(f146(x96595),x96592),f122(x96595))))),f153(x96595,x96596)))
% 21.40/21.38 [9682]E(x96821,x96822)+~P1(f789(f789(f342(f869(f864(x96823),f864(x96823))),f789(f789(f249(f864(x96823),f864(x96823)),f789(f789(f132(x96823),x96821),f789(f789(f146(x96823),x96825),f122(x96823)))),f789(f789(f132(x96823),x96822),f789(f789(f146(x96823),x96826),f122(x96823))))),f153(x96823,x96824)))+P1(f789(f789(f342(f869(f864(x96823),f864(x96823))),f789(f789(f249(f864(x96823),f864(x96823)),x96821),x96822)),f153(x96823,x96824)))
% 21.40/21.38 [9710]~P1(f789(f789(f342(f869(f870(x97101,a856),f870(x97101,a856))),f789(f789(f249(f870(x97101,a856),f870(x97101,a856)),x97102),x97104)),f332(x97101,x97106)))+~P1(f789(f789(f342(f869(f870(x97101,a856),f870(x97101,a856))),f789(f789(f249(f870(x97101,a856),f870(x97101,a856)),x97103),x97105)),f332(x97101,x97106)))+P1(f789(f789(f342(f869(f870(x97101,a856),f870(x97101,a856))),f789(f789(f249(f870(x97101,a856),f870(x97101,a856)),f789(f789(f110(f870(x97101,a856)),x97102),x97103)),f789(f789(f110(f870(x97101,a856)),x97104),x97105))),f332(x97101,x97106)))
% 21.40/21.38 [5179]~E(f789(x51793,x51796),x51795)+~E(x51794,f789(f234(x51791),x51796))+E(f789(f789(f203(x51791,x51792),x51793),x51794),f789(f234(x51792),x51795))
% 21.40/21.38 [5578]~E(f789(f789(f132(x55781),x55786),x55783),x55785)+E(f789(f789(f132(x55781),x55782),x55783),f789(f789(f146(x55781),x55784),x55785))+~E(x55782,f789(f789(f146(x55781),x55784),x55786))
% 21.40/21.38 [5579]~E(f789(f789(f132(x55791),x55796),x55793),x55795)+E(f789(f789(f132(x55791),x55792),x55793),f789(f789(f132(x55791),x55794),x55795))+~E(x55792,f789(f789(f132(x55791),x55794),x55796))
% 21.40/21.38 [5580]E(f789(f789(f132(x55801),x55802),x55803),f789(f789(f146(x55801),x55804),x55805))+~E(f789(f789(f146(x55801),x55804),x55806),x55802)+~E(x55805,f789(f789(f132(x55801),x55806),x55803))
% 21.40/21.38 [5581]E(f789(f789(f132(x55811),x55812),x55813),f789(f789(f146(x55811),x55814),x55815))+~E(f789(f789(f146(x55811),x55814),x55816),x55812)+~E(x55815,f789(f789(f132(x55811),x55816),x55813))
% 21.40/21.38 [5582]~E(f789(f789(f132(x55821),x55822),x55826),x55824)+E(f789(f789(f132(x55821),x55822),x55823),f789(f789(f132(x55821),x55824),x55825))+~E(x55823,f789(f789(f132(x55821),x55826),x55825))
% 21.40/21.38 [5583]~E(f789(f789(f132(x55831),x55832),x55836),x55834)+E(f789(f789(f132(x55831),x55832),x55833),f789(f789(f132(x55831),x55834),x55835))+~E(x55833,f789(f789(f132(x55831),x55836),x55835))
% 21.40/21.38 [6744]E(f789(x67441,x67442),f789(x67443,x67442))+~E(f789(f789(f150(x67444,x67445),x67441),x67446),f789(f789(f150(x67444,x67445),x67443),x67446))+~P1(f789(f789(f342(x67444),x67442),f789(f163(x67444),x67446)))
% 21.40/21.38 [7135]~P23(x71354,x71355,x71356,x71351)+E(f789(f789(x71351,x71352),x71353),f789(f789(f73(x71354,x71355,x71356),x71353),x71352))+~P1(f789(f70(x71354),x71352))
% 21.40/21.38 [7202]~E(x72022,f789(x72024,x72026))+~P1(f789(f789(f342(x72023),x72026),x72025))+P1(f789(f789(f342(x72021),x72022),f789(f311(x72023,x72021,x72024),x72025)))
% 21.40/21.38 [7203]~E(x72032,f789(x72034,x72036))+~P1(f789(f789(f342(x72033),x72036),x72035))+P1(f789(f789(f342(x72031),x72032),f789(f311(x72033,x72031,x72034),x72035)))
% 21.40/21.38 [7204]~E(x72042,f789(x72044,x72046))+~P1(f789(f789(f342(x72043),x72046),x72045))+P1(f789(f789(f342(x72041),x72042),f789(f311(x72043,x72041,x72044),x72045)))
% 21.40/21.38 [7205]~E(f789(x72054,x72052),x72056)+~P1(f789(f789(f342(x72053),x72056),x72055))+P1(f789(f789(f342(x72051),x72052),f789(f313(x72051,x72053,x72054),x72055)))
% 21.40/21.38 [7680]~P34(x76801,x76802,x76804,x76806)+P34(x76801,x76802,f789(f789(f146(x76801),x76803),x76804),f789(f789(f146(x76801),x76805),x76806))+~P1(f789(f789(x76802,x76803),x76805))
% 21.40/21.38 [7681]~P34(x76811,x76812,x76814,x76816)+P34(x76811,x76812,f789(f789(f146(x76811),x76813),x76814),f789(f789(f146(x76811),x76815),x76816))+~P1(f789(f789(x76812,x76813),x76815))
% 21.40/21.38 [8667]~P55(x86674,x86675,x86671,x86672,x86676)+E(f789(x86671,f789(x86672,x86673)),x86673)+~P1(f789(f789(f342(x86675),x86673),x86676))
% 21.40/21.38 [9400]E(x94001,x94002)+E(f789(f185(f864(x94003)),x94004),f789(f185(f864(x94003)),x94005))+~P1(f789(f789(f342(f869(f864(x94003),f864(x94003))),f789(f789(f249(f864(x94003),f864(x94003)),f789(f789(f146(x94003),x94001),x94004)),f789(f789(f146(x94003),x94002),x94005))),f141(x94003,x94006)))
% 21.40/21.38 [9462]~P20(x94621,x94622,x94623)+E(f789(f789(f73(x94621,x94622,x94623),x94624),x94625),x94626)+~P1(f789(f75(x94621,x94622,x94623,x94624,x94625),x94626))
% 21.40/21.38 [9468]E(f789(f185(f864(x94681)),x94682),f789(f185(f864(x94681)),x94683))+P1(f789(f789(f342(f869(f864(x94681),f864(x94681))),f789(f789(f249(f864(x94681),f864(x94681)),x94682),x94683)),f141(x94681,x94684)))+~P1(f789(f789(f342(f869(f864(x94681),f864(x94681))),f789(f789(f249(f864(x94681),f864(x94681)),f789(f789(f146(x94681),x94685),x94682)),f789(f789(f146(x94681),x94686),x94683))),f141(x94681,x94684)))
% 21.40/21.38 [9490]~P1(f789(f789(f342(f869(x94901,x94901)),f789(f789(f249(x94901,x94901),x94902),x94904)),f308(x94901,x94906)))+P1(f789(f789(f342(f869(f864(x94901),f864(x94901))),f789(f789(f249(f864(x94901),f864(x94901)),f789(f789(f146(x94901),x94902),x94903)),f789(f789(f146(x94901),x94904),x94905))),f308(f864(x94901),f153(x94901,x94906))))+~P1(f789(f789(f342(f869(f864(x94901),f864(x94901))),f789(f789(f249(f864(x94901),f864(x94901)),x94903),x94905)),f308(f864(x94901),f153(x94901,x94906))))
% 21.40/21.38 [9975]~P4(x99752)+E(f789(f789(f8(x99751,x99752),f789(f789(f10(f870(x99753,a856),x99752,x99751),f789(f8(x99753,x99752),x99754)),f789(f789(f10(f870(x99753,a856),f870(x99753,a856),x99751),f264(x99753)),f789(f789(f10(f870(x99753,a856),f870(x99753,a856),x99751),f789(f20(x99753,a856,a856),f789(f789(f10(a856,f870(a856,a856),x99753),a339),f789(f789(f9(x99753,f870(x99753,a856),a856),f342(x99753)),x99755)))),f789(f9(x99753,x99751,a856),f789(f789(f10(x99751,f870(x99751,a856),x99753),a338),x99756)))))),f789(f311(x99753,x99751,x99756),x99755)),f789(f789(f8(x99753,x99752),x99754),x99755))+~P1(f789(f70(x99753),x99755))
% 21.40/21.38 [6804]~P101(x68043)+P1(f789(x68042,x68045))+E(f789(f133(x68041,x68042),f789(f789(f144(x68041,x68043,x68044),x68045),x68046)),f789(f133(x68041,x68042),x68046))
% 21.40/21.38 [6806]P1(f789(x68061,x68062))+~E(f162(x68063,x68061,x68064),f789(f789(f249(f864(x68063),f864(x68063)),x68065),x68066))+~P1(f789(f789(f342(x68063),x68062),f789(f163(x68063),x68065)))
% 21.40/21.38 [6854]~P1(f789(x68542,x68546))+~E(f162(x68541,x68542,x68543),f789(f789(f249(f864(x68541),f864(x68541)),x68544),x68545))+~P1(f789(f789(f342(x68541),x68546),f789(f163(x68541),x68545)))
% 21.40/21.38 [7544]~P19(x75441,x75442,x75443)+~P1(f789(f70(x75441),x75446))+E(f789(f789(f73(x75441,x75442,x75443),x75444),f789(f789(f310(x75441),x75445),x75446)),f789(f789(f73(x75441,x75442,x75443),f789(f789(x75443,x75445),x75444)),x75446))
% 21.40/21.38 [7596]~P101(x75962)+~P1(f789(f789(f240(x75962),f789(x75963,x75964)),f789(x75963,x75965)))+E(f789(f789(f144(x75961,x75962,x75963),x75964),f789(f789(f146(x75961),x75965),x75966)),f789(f789(f146(x75961),x75964),f789(f789(f146(x75961),x75965),x75966)))
% 21.40/21.38 [7711]E(x77111,x77112)+~E(f789(f789(f256(x77113,x77114),x77111),f789(f18(f870(x77114,a856),x77113),x77115)),f789(f789(f256(x77113,x77114),x77112),f789(f18(f870(x77114,a856),x77113),x77115)))+~P1(f789(f789(f342(x77114),x77116),x77115))
% 21.40/21.38 [7779]~P19(x77791,x77792,x77793)+~P1(f789(f70(x77791),x77796))+E(f789(f789(f73(x77791,x77792,x77793),x77794),f789(f789(f310(x77791),x77795),x77796)),f789(f789(x77793,x77795),f789(f789(f73(x77791,x77792,x77793),x77794),x77796)))
% 21.40/21.38 [7895]~P20(x78951,x78952,x78953)+~P1(f789(f70(x78951),x78956))+E(f789(f789(f73(x78951,x78952,x78953),f789(f789(x78953,x78954),x78955)),x78956),f789(f789(x78953,x78954),f789(f789(f73(x78951,x78952,x78953),x78955),x78956)))
% 21.40/21.38 [7962]~P24(x79622,x79625,x79626,x79621)+~P1(f789(f70(x79622),x79624))+E(f789(x79621,f789(f789(f310(x79622),x79623),x79624)),f789(f82(x79625,x79625,x79625,f789(x79621,x79624)),f789(x79626,x79623)))
% 21.40/21.38 [7999]~P101(x79992)+P1(f789(f789(f240(x79992),f789(x79993,x79994)),f789(x79993,x79995)))+E(f789(f789(f144(x79991,x79992,x79993),x79994),f789(f789(f146(x79991),x79995),x79996)),f789(f789(f146(x79991),x79995),f789(f789(f144(x79991,x79992,x79993),x79994),x79996)))
% 21.40/21.38 [8132]~E(f789(f185(f864(x81321)),x81325),f789(f185(f864(x81322)),x81326))+~E(f789(f185(f864(x81321)),x81323),f789(f185(f864(x81322)),x81324))+E(f789(f789(f132(f869(x81321,x81322)),f789(f789(f171(x81321,x81322),x81323),x81324)),f789(f789(f171(x81321,x81322),x81325),x81326)),f789(f789(f171(x81321,x81322),f789(f789(f132(x81321),x81323),x81325)),f789(f789(f132(x81322),x81324),x81326)))
% 21.40/21.38 [8240]~E(x82402,f789(f311(x82403,x82401,x82404),x82406))+P1(f789(f789(f240(f870(x82401,a856)),x82402),f789(f311(x82403,x82401,x82404),x82405)))+~P1(f789(f789(f240(f870(x82403,a856)),x82406),x82405))
% 21.40/21.38 [8343]~P101(x83435)+E(f789(x83431,x83432),f789(x83431,x83433))+E(f789(f789(f144(x83434,x83435,x83431),x83432),f789(f789(f144(x83434,x83435,x83431),x83433),x83436)),f789(f789(f144(x83434,x83435,x83431),x83433),f789(f789(f144(x83434,x83435,x83431),x83432),x83436)))
% 21.40/21.38 [8380]~P29(x83803,x83801,x83804,x83805)+P29(x83803,x83801,f789(f789(f789(f81(x83803,x83801),x83804),x83806),x83802),x83805)+P1(f789(f789(f342(x83801),x83802),f789(f311(x83803,x83801,x83804),x83805)))
% 21.40/21.38 [8525]~P1(f789(f789(f342(x85252),x85254),f789(x85256,x85253)))+~P1(f789(f789(f342(x85251),x85253),x85255))+P1(f789(f789(f342(f869(x85251,x85252)),f789(f789(f249(x85251,x85252),x85253),x85254)),f789(f789(f256(x85251,x85252),x85255),x85256)))
% 21.40/21.38 [8526]~P1(f789(f789(f342(x85262),x85264),f789(x85266,x85263)))+~P1(f789(f789(f342(x85261),x85263),x85265))+P1(f789(f789(f342(f869(x85261,x85262)),f789(f789(f249(x85261,x85262),x85263),x85264)),f789(f789(f256(x85261,x85262),x85265),x85266)))
% 21.40/21.38 [8937]~P69(x89372)+~P29(x89374,x89371,x89375,x89376)+E(f789(f789(f11(x89371,x89372),x89373),f789(f311(x89374,x89371,x89375),x89376)),f789(f789(f11(x89374,x89372),f789(f82(x89371,x89372,x89374,x89373),x89375)),x89376))
% 21.40/21.38 [8938]~P4(x89382)+~P29(x89384,x89381,x89385,x89386)+E(f789(f789(f8(x89381,x89382),x89383),f789(f311(x89384,x89381,x89385),x89386)),f789(f789(f8(x89384,x89382),f789(f82(x89381,x89382,x89384,x89383),x89385)),x89386))
% 21.40/21.38 [9175]~E(f789(f789(f789(a193,x91755),f42(x91751)),f789(f789(a194,x91754),x91751)),f789(f789(f789(a193,x91756),f42(x91751)),f789(f789(a194,x91754),x91751)))+~P1(f789(f789(f191(x91753),f789(f789(f789(a193,x91754),f42(x91751)),f789(x91752,x91754))),x91756))+P1(f789(f789(f191(f34(x91751,x91752,x91753)),x91754),f789(f789(f789(a193,x91755),f42(x91751)),f789(f789(a194,x91754),x91751))))
% 21.40/21.38 [9179]~P23(x91793,x91791,x91796,x91792)+~P1(f789(f70(x91793),x91794))+E(f789(f82(x91791,x91791,x91791,f789(x91792,f789(f789(f3(f870(x91793,a856)),x91794),f789(f789(f310(x91793),x91795),f184(f870(x91793,a856)))))),f789(x91796,x91795)),f789(x91792,f789(f789(f310(x91793),x91795),x91794)))
% 21.40/21.38 [9566]~E(f789(f789(f789(a193,f789(f789(a195,x95665),f789(a194,x95664))),x95661),f789(f789(a194,x95665),a27)),f789(f789(f789(a193,f789(f789(a195,x95666),f789(a194,x95664))),x95661),f789(f789(a194,x95666),a27)))+~P1(f789(f789(f191(f789(a29,x95662)),f789(f789(f789(a193,f789(f789(a195,x95664),a196)),f42(a28)),f789(x95663,x95664))),x95666))+P1(f789(f789(f191(f33(x95661,x95662,x95663)),x95664),f789(f789(f789(a193,f789(f789(a195,x95665),f789(a194,x95664))),x95661),f789(f789(a194,x95665),a27))))
% 21.40/21.38 [9738]~E(f789(f311(x97382,x97384,x97386),f247(f870(x97382,a856))),f247(f870(x97384,a856)))+~E(f789(f311(x97381,x97383,x97385),f247(f870(x97381,a856))),f247(f870(x97383,a856)))+E(f789(f311(f869(x97381,x97382),f869(x97383,x97384),f260(x97381,x97383,x97382,x97384,x97385,x97386)),f247(f870(f869(x97381,x97382),a856))),f247(f870(f869(x97383,x97384),a856)))
% 21.40/21.38 [9801]~P29(x98013,x98014,x98015,f789(x98016,f687(x98016,x98015,x98014,x98013,x98012,x98011)))+P29(x98013,x98014,x98015,f789(f789(f54(x98012,f870(x98013,a856)),x98011),x98016))+E(x98011,f184(f870(x98012,a856)))
% 21.40/21.38 [9859]P29(x98596,x98595,x98594,f789(f789(f54(x98592,f870(x98596,a856)),x98591),x98593))+E(x98591,f184(f870(x98592,a856)))+P1(f789(f789(f342(x98592),f687(x98593,x98594,x98595,x98596,x98592,x98591)),x98591))
% 21.40/21.38 [9867]P1(f789(f789(f342(x98671),f632(x98672,x98673,x98674,x98675,x98676,x98671)),x98676))+P1(f789(f789(f240(f870(f869(x98671,x98674),a856)),f789(f789(f256(x98671,x98674),x98676),x98673)),f789(f789(f256(x98671,x98674),x98675),x98672)))+~P1(f789(f789(f240(f870(x98671,a856)),x98676),x98675))
% 21.40/21.38 [9912]P28(x99126,x99125,f789(f789(f310(f862(x99126)),f789(f789(f789(f100(x99126),x99124),x99123),x99122)),f184(f870(f862(x99126),a856))))+~P28(x99126,x99125,f789(f789(f310(f862(x99126)),f789(f789(f789(f100(x99126),x99124),x99123),x99121)),f184(f870(f862(x99126),a856))))+P1(f789(f789(x99121,f356(x99122,x99121,x99123,x99124,x99125,x99126)),f357(x99122,x99121,x99123,x99124,x99125,x99126)))
% 21.40/21.38 [9913]P28(x99136,x99135,f789(f789(f310(f862(x99136)),f789(f789(f789(f100(x99136),x99131),x99133),x99132)),f184(f870(f862(x99136),a856))))+~P28(x99136,x99135,f789(f789(f310(f862(x99136)),f789(f789(f789(f100(x99136),x99134),x99133),x99132)),f184(f870(f862(x99136),a856))))+P1(f789(f789(x99131,f358(x99131,x99132,x99133,x99134,x99135,x99136)),f359(x99131,x99132,x99133,x99134,x99135,x99136)))
% 21.40/21.38 [9950]~P28(x99501,x99502,f789(f789(f310(f862(x99501)),f789(f789(f789(f100(x99501),x99503),x99504),x99506)),f184(f870(f862(x99501),a856))))+P28(x99501,x99502,f789(f789(f310(f862(x99501)),f789(f789(f789(f100(x99501),x99503),x99504),x99505)),f184(f870(f862(x99501),a856))))+~P1(f789(f789(x99505,f356(x99505,x99506,x99504,x99503,x99502,x99501)),f357(x99505,x99506,x99504,x99503,x99502,x99501)))
% 21.40/21.38 [9951]~P28(x99511,x99512,f789(f789(f310(f862(x99511)),f789(f789(f789(f100(x99511),x99516),x99514),x99515)),f184(f870(f862(x99511),a856))))+P28(x99511,x99512,f789(f789(f310(f862(x99511)),f789(f789(f789(f100(x99511),x99513),x99514),x99515)),f184(f870(f862(x99511),a856))))+~P1(f789(f789(x99516,f358(x99513,x99515,x99514,x99516,x99512,x99511)),f359(x99513,x99515,x99514,x99516,x99512,x99511)))
% 21.40/21.38 [9992]~P1(f789(f789(f240(f870(x99922,a856)),f789(x99924,f632(x99926,x99924,x99922,x99925,x99923,x99921))),f789(x99926,f632(x99926,x99924,x99922,x99925,x99923,x99921))))+~P1(f789(f789(f240(f870(x99921,a856)),x99923),x99925))+P1(f789(f789(f240(f870(f869(x99921,x99922),a856)),f789(f789(f256(x99921,x99922),x99923),x99924)),f789(f789(f256(x99921,x99922),x99925),x99926)))
% 21.40/21.38 [7728]~P1(f789(x77281,x77285))+~P1(f789(x77286,x77284))+P1(f789(x77281,f789(f258(x77282,x77283),f789(f789(f249(x77282,x77283),x77284),x77285))))
% 21.40/21.38 [7729]~P1(f789(x77291,x77294))+~P1(f789(x77296,x77295))+P1(f789(x77291,f789(f248(x77292,x77293),f789(f789(f249(x77292,x77293),x77294),x77295))))
% 21.40/21.38 [7783]~P1(f789(f789(x77834,x77836),x77835))+~P1(f789(f789(f342(x77831),x77836),x77833))+P1(f789(f789(f789(f53(x77831,f870(x77832,a856)),x77833),x77834),x77835))
% 21.40/21.38 [7784]~P1(f789(f789(x77844,x77846),x77845))+~P1(f789(f789(f342(x77841),x77846),x77843))+P1(f789(f789(f789(f53(x77841,f870(x77842,a856)),x77843),x77844),x77845))
% 21.40/21.38 [7817]~E(f789(f185(f864(x78171)),x78173),f789(f185(f864(x78174)),x78175))+~E(f789(f170(x78171,x78174,f789(f789(f171(x78171,x78174),x78173),x78175)),x78172),f789(f234(x78174),x78176))+P1(f789(f789(f342(x78171),x78172),f789(f163(x78171),x78173)))
% 21.40/21.38 [8084]~P1(f789(f789(f342(x80841),x80842),f789(x80845,x80846)))+~P1(f789(f789(f342(x80843),x80846),x80844))+P1(f789(f789(f342(x80841),x80842),f789(f789(f53(x80843,f870(x80841,a856)),x80844),x80845)))
% 21.40/21.38 [8085]~P1(f789(f789(f342(x80851),x80852),f789(x80855,x80856)))+~P1(f789(f789(f342(x80853),x80856),x80854))+P1(f789(f789(f342(x80851),x80852),f789(f789(f53(x80853,f870(x80851,a856)),x80854),x80855)))
% 21.40/21.38 [8124]P1(f789(f789(x81241,x81242),x81243))+~P1(f789(f789(x81244,x81242),x81243))+~P1(f789(f789(f240(f870(x81245,f870(x81246,a856))),x81244),x81241))
% 21.40/21.38 [8125]P1(f789(f789(x81251,x81252),x81253))+~P1(f789(f789(x81254,x81252),x81253))+~P1(f789(f789(f240(f870(x81255,f870(x81256,a856))),x81254),x81251))
% 21.40/21.38 [8262]P1(f789(f789(x82621,x82622),x82623))+~P1(f789(f789(f342(x82624),x82622),x82625))+~P1(f789(f789(f789(f54(x82624,f870(x82626,a856)),x82625),x82621),x82623))
% 21.40/21.38 [8263]P1(f789(f789(x82631,x82632),x82633))+~P1(f789(f789(f342(x82634),x82632),x82635))+~P1(f789(f789(f789(f54(x82634,f870(x82636,a856)),x82635),x82631),x82633))
% 21.40/21.38 [8264]P1(f789(f789(x82641,x82642),x82643))+~P1(f789(f789(f342(x82644),x82642),x82645))+~P1(f789(f789(f789(f54(x82644,f870(x82646,a856)),x82645),x82641),x82643))
% 21.40/21.38 [8401]P1(f789(f789(f342(x84011),x84012),f789(x84013,x84014)))+~P1(f789(f789(f342(x84015),x84014),x84016))+~P1(f789(f789(f342(x84011),x84012),f789(f789(f54(x84015,f870(x84011,a856)),x84016),x84013)))
% 21.40/21.38 [8402]P1(f789(f789(f342(x84021),x84022),f789(x84023,x84024)))+~P1(f789(f789(f342(x84025),x84024),x84026))+~P1(f789(f789(f342(x84021),x84022),f789(f789(f54(x84025,f870(x84021,a856)),x84026),x84023)))
% 21.40/21.38 [8403]P1(f789(f789(f342(x84031),x84032),f789(x84033,x84034)))+~P1(f789(f789(f342(x84035),x84034),x84036))+~P1(f789(f789(f342(x84031),x84032),f789(f789(f54(x84035,f870(x84031,a856)),x84036),x84033)))
% 21.40/21.38 [8649]~P16(x86494,x86495,x86496,x86491)+E(f789(x86491,x86492),f789(x86491,x86493))+~P1(f789(f789(f342(f869(x86494,x86494)),f789(f789(f249(x86494,x86494),x86492),x86493)),x86496))
% 21.40/21.38 [8680]P1(f789(f789(f240(f870(x86801,a856)),x86802),f789(x86803,x86804)))+~P1(f789(f789(f342(x86805),x86804),x86806))+~P1(f789(f789(f240(f870(x86801,a856)),x86802),f789(f789(f54(x86805,f870(x86801,a856)),x86806),x86803)))
% 21.40/21.38 [8705]~P53(x87053,x87054,f789(f286(x87054,x87053),x87055))+E(x87051,f184(f870(x87052,a856)))+E(f789(f789(f54(x87052,f870(x87053,a856)),x87051),f789(f789(f10(f870(x87054,a856),f870(x87053,a856),x87052),f285(x87054,x87053,x87055)),x87056)),f789(f285(x87054,x87053,x87055),f789(f789(f54(x87052,f870(x87054,a856)),x87051),x87056)))
% 21.40/21.38 [8776]P1(f789(f789(f342(x87761),x87762),f789(f285(x87763,x87761,x87764),x87765)))+~P1(f789(f789(f342(x87763),x87766),x87765))+~P1(f789(f789(f342(f869(x87763,x87761)),f789(f789(f249(x87763,x87761),x87766),x87762)),x87764))
% 21.40/21.38 [8777]P1(f789(f789(f342(x87771),x87772),f789(f285(x87773,x87771,x87774),x87775)))+~P1(f789(f789(f342(x87773),x87776),x87775))+~P1(f789(f789(f342(f869(x87773,x87771)),f789(f789(f249(x87773,x87771),x87776),x87772)),x87774))
% 21.40/21.38 [9055]P1(f789(f789(f240(f870(x90551,a856)),f789(f285(x90552,x90551,x90553),x90554)),f789(f285(x90552,x90551,x90555),x90556)))+~P1(f789(f789(f240(f870(x90552,a856)),x90554),x90556))+~P1(f789(f789(f240(f870(f869(x90552,x90551),a856)),x90553),x90555))
% 21.40/21.38 [9212]~P1(f789(f789(f342(x92122),x92126),x92124))+~P1(f789(f789(f240(f870(x92121,a856)),x92123),x92125))+P1(f789(f789(f240(f870(f869(x92121,x92122),a856)),f789(f789(f256(x92121,x92122),x92123),f789(f18(f870(x92122,a856),x92121),x92124))),f789(f789(f256(x92121,x92122),x92125),f789(f18(f870(x92122,a856),x92121),x92124))))
% 21.40/21.38 [9359]~E(x93593,x93595)+P1(f789(f789(f342(f869(f864(x93591),f864(x93591))),f789(f789(f249(f864(x93591),f864(x93591)),f789(f789(f146(x93591),x93592),x93593)),f789(f789(f146(x93591),x93594),x93595))),f153(x93591,x93596)))+~P1(f789(f789(f342(f869(x93591,x93591)),f789(f789(f249(x93591,x93591),x93592),x93594)),x93596))
% 21.40/21.38 [9364]~E(f789(f185(f864(x93641)),x93645),f789(f185(f864(x93642)),x93646))+E(f176(x93641,x93642,f177(x93641,x93642,x93643,f789(f789(f3(f870(x93641,a856)),x93644),f789(f163(x93641),x93645))),x93645,x93646),f177(x93641,x93642,f176(x93641,x93642,x93643,x93645,x93646),x93644))+~P1(f789(f789(f240(f870(x93641,a856)),f789(f163(x93641),x93645)),x93644))
% 21.40/21.38 [9365]~E(f789(f185(f864(x93651)),x93653),f789(f185(f864(x93651)),x93655))+P1(f789(f789(f342(f869(f864(x93651),f864(x93651))),f789(f789(f249(f864(x93651),f864(x93651)),f789(f789(f146(x93651),x93652),x93653)),f789(f789(f146(x93651),x93654),x93655))),f141(x93651,x93656)))+~P1(f789(f789(f342(f869(x93651,x93651)),f789(f789(f249(x93651,x93651),x93652),x93654)),x93656))
% 21.40/21.38 [9392]P1(f789(f789(f342(f869(x93921,x93921)),f789(f789(f249(x93921,x93921),x93922),x93923)),f789(f789(f178(f869(x93921,x93921),a856),f789(a121,x93924)),x93925)))+~P1(f789(f789(f342(f869(x93921,x93921)),f789(f789(f249(x93921,x93921),x93926),x93923)),x93925))+~P1(f789(f789(f342(f869(x93921,x93921)),f789(f789(f249(x93921,x93921),x93922),x93926)),f789(f789(f178(f869(x93921,x93921),a856),x93924),x93925)))
% 21.40/21.38 [9393]P1(f789(f789(f342(f869(x93931,x93931)),f789(f789(f249(x93931,x93931),x93932),x93933)),f789(f789(f178(f869(x93931,x93931),a856),f789(a121,x93934)),x93935)))+~P1(f789(f789(f342(f869(x93931,x93931)),f789(f789(f249(x93931,x93931),x93932),x93936)),x93935))+~P1(f789(f789(f342(f869(x93931,x93931)),f789(f789(f249(x93931,x93931),x93936),x93933)),f789(f789(f178(f869(x93931,x93931),a856),x93934),x93935)))
% 21.40/21.38 [9396]~P1(f789(f789(f342(x93964),x93965),x93966))+P1(f789(f789(f240(f870(x93961,a856)),x93962),x93963))+~P1(f789(f789(f240(f870(f869(x93961,x93964),a856)),f789(f789(f256(x93961,x93964),x93962),f789(f18(f870(x93964,a856),x93961),x93966))),f789(f789(f256(x93961,x93964),x93963),f789(f18(f870(x93964,a856),x93961),x93966))))
% 21.40/21.38 [9437]E(x94371,x94372)+~P1(f789(f789(f342(f869(f864(x94373),f864(x94373))),f789(f789(f249(f864(x94373),f864(x94373)),f789(f789(f146(x94373),x94371),x94375)),f789(f789(f146(x94373),x94372),x94376))),f141(x94373,x94374)))+P1(f789(f789(f342(f869(x94373,x94373)),f789(f789(f249(x94373,x94373),x94371),x94372)),x94374))
% 21.40/21.38 [9438]E(x94381,x94382)+~P1(f789(f789(f342(f869(f864(x94383),f864(x94383))),f789(f789(f249(f864(x94383),f864(x94383)),f789(f789(f146(x94383),x94381),x94385)),f789(f789(f146(x94383),x94382),x94386))),f143(x94383,x94384)))+P1(f789(f789(f342(f869(x94383,x94383)),f789(f789(f249(x94383,x94383),x94381),x94382)),x94384))
% 21.40/21.38 [9439]E(x94391,x94392)+~P1(f789(f789(f342(f869(f864(x94393),f864(x94393))),f789(f789(f249(f864(x94393),f864(x94393)),f789(f789(f146(x94393),x94391),x94395)),f789(f789(f146(x94393),x94392),x94396))),f153(x94393,x94394)))+P1(f789(f789(f342(f869(x94393,x94393)),f789(f789(f249(x94393,x94393),x94391),x94392)),x94394))
% 21.40/21.38 [9475]P1(f789(f789(f342(f869(f864(x94751),f864(x94751))),f789(f789(f249(f864(x94751),f864(x94751)),f789(f789(f146(x94751),x94752),x94753)),f789(f789(f146(x94751),x94754),x94755))),f154(x94751,x94756)))+~P1(f789(f789(f342(f869(f864(x94751),f864(x94751))),f789(f789(f249(f864(x94751),f864(x94751)),x94753),x94755)),f154(x94751,x94756)))+~P1(f789(f789(f342(f869(x94751,x94751)),f789(f789(f249(x94751,x94751),x94752),x94754)),x94756))
% 21.40/21.38 [9497]P1(f789(x94971,x94972))+~P1(f789(x94971,f425(x94971,x94973,x94974,x94975,x94976)))+~P1(f789(f789(f342(x94976),x94972),f789(f789(f53(x94975,f870(x94976,a856)),x94974),x94973)))
% 21.40/21.38 [9502]~P1(f789(f789(f342(f869(f864(x95021),f864(x95021))),f789(f789(f249(f864(x95021),f864(x95021)),f789(f789(f146(x95021),x95022),x95025)),f789(f789(f146(x95021),x95023),x95026))),f141(x95021,x95024)))+P1(f789(f789(f342(f869(f864(x95021),f864(x95021))),f789(f789(f249(f864(x95021),f864(x95021)),x95025),x95026)),f141(x95021,x95024)))+P1(f789(f789(f342(f869(x95021,x95021)),f789(f789(f249(x95021,x95021),x95022),x95023)),x95024))
% 21.40/21.38 [9503]~P1(f789(f789(f342(f869(f864(x95031),f864(x95031))),f789(f789(f249(f864(x95031),f864(x95031)),f789(f789(f146(x95031),x95032),x95035)),f789(f789(f146(x95031),x95033),x95036))),f143(x95031,x95034)))+P1(f789(f789(f342(f869(f864(x95031),f864(x95031))),f789(f789(f249(f864(x95031),f864(x95031)),x95035),x95036)),f143(x95031,x95034)))+P1(f789(f789(f342(f869(x95031,x95031)),f789(f789(f249(x95031,x95031),x95032),x95033)),x95034))
% 21.40/21.38 [9504]~P1(f789(f789(f342(f869(f864(x95041),f864(x95041))),f789(f789(f249(f864(x95041),f864(x95041)),f789(f789(f146(x95041),x95042),x95045)),f789(f789(f146(x95041),x95043),x95046))),f153(x95041,x95044)))+P1(f789(f789(f342(f869(f864(x95041),f864(x95041))),f789(f789(f249(f864(x95041),f864(x95041)),x95045),x95046)),f153(x95041,x95044)))+P1(f789(f789(f342(f869(x95041,x95041)),f789(f789(f249(x95041,x95041),x95042),x95043)),x95044))
% 21.40/21.38 [9582]P1(f789(x95821,x95822))+P1(f789(f789(f342(x95823),f426(x95821,x95824,x95825,x95823,x95826)),x95825))+~P1(f789(f789(f342(x95826),x95822),f789(f789(f53(x95823,f870(x95826,a856)),x95825),x95824)))
% 21.40/21.38 [9588]~E(x95882,x95884)+P1(f789(f789(f342(f869(f864(x95881),f864(x95881))),f789(f789(f249(f864(x95881),f864(x95881)),f789(f789(f132(x95881),x95882),f789(f789(f146(x95881),x95883),f122(x95881)))),f789(f789(f132(x95881),x95884),f789(f789(f146(x95881),x95885),f122(x95881))))),f153(x95881,x95886)))+~P1(f789(f789(f342(f869(x95881,x95881)),f789(f789(f249(x95881,x95881),x95883),x95885)),x95886))
% 21.40/21.38 [9674]E(x96741,x96742)+~P1(f789(f789(f342(f869(f864(x96743),f864(x96743))),f789(f789(f249(f864(x96743),f864(x96743)),f789(f789(f132(x96743),x96745),f789(f789(f146(x96743),x96741),f122(x96743)))),f789(f789(f132(x96743),x96746),f789(f789(f146(x96743),x96742),f122(x96743))))),f153(x96743,x96744)))+P1(f789(f789(f342(f869(x96743,x96743)),f789(f789(f249(x96743,x96743),x96741),x96742)),x96744))
% 21.40/21.38 [9699]~P1(f789(f789(f342(f869(f864(x96991),f864(x96991))),f789(f789(f249(f864(x96991),f864(x96991)),f789(f789(f132(x96991),x96995),f789(f789(f146(x96991),x96992),f122(x96991)))),f789(f789(f132(x96991),x96996),f789(f789(f146(x96991),x96993),f122(x96991))))),f153(x96991,x96994)))+P1(f789(f789(f342(f869(f864(x96991),f864(x96991))),f789(f789(f249(f864(x96991),f864(x96991)),x96995),x96996)),f153(x96991,x96994)))+P1(f789(f789(f342(f869(x96991,x96991)),f789(f789(f249(x96991,x96991),x96992),x96993)),x96994))
% 21.40/21.38 [9711]P1(f789(x97111,x97112))+P1(f789(f789(f342(x97113),f425(x97111,x97114,x97115,x97116,x97113)),f789(x97114,f426(x97111,x97114,x97115,x97116,x97113))))+~P1(f789(f789(f342(x97113),x97112),f789(f789(f53(x97116,f870(x97113,a856)),x97115),x97114)))
% 21.40/21.38 [8790]~P20(x87903,x87904,x87901)+~P1(f789(f70(x87903),x87906))+E(f789(f789(x87901,x87902),f789(f789(f73(x87903,x87904,x87901),x87905),f789(f789(f3(f870(x87903,a856)),x87906),f789(f789(f310(x87903),x87902),f184(f870(x87903,a856)))))),f789(f789(f73(x87903,x87904,x87901),x87905),f789(f789(f310(x87903),x87902),x87906)))
% 21.40/21.38 [8889]~E(f789(f170(x88891,x88892,x88894),x88895),f789(f234(x88892),x88896))+~P1(f789(f789(x88893,x88895),x88896))+E(f789(f170(x88891,x88892,f789(f133(f869(x88891,x88892),f789(f259(x88891,x88892,a856),x88893)),x88894)),x88895),f789(f234(x88892),x88896))
% 21.40/21.38 [9061]~P1(f789(f789(f342(x90615),x90613),x90616))+P1(f789(f789(f240(f870(x90611,a856)),f789(x90612,x90613)),x90614))+~P1(f789(f789(f240(f870(x90611,a856)),f789(f789(f53(x90615,f870(x90611,a856)),x90616),x90612)),x90614))
% 21.40/21.38 [9649]~P12(x96491,x96495,x96494)+P1(f789(f789(f342(f869(x96491,x96491)),f789(f789(f249(x96491,x96491),x96492),x96493)),x96494))+~P1(f789(f789(f342(x96491),x96496),f789(f789(f111(f870(x96491,a856)),f789(f285(x96491,x96491,x96494),f789(f789(f310(x96491),x96492),f184(f870(x96491,a856))))),f789(f285(x96491,x96491,x96494),f789(f789(f310(x96491),x96493),f184(f870(x96491,a856)))))))
% 21.40/21.38 [8559]~P121(x85592)+~E(f789(f789(f89(x85592),f789(f789(f90(x85592),x85594),x85595)),x85591),f789(f789(f89(x85592),f789(f789(f90(x85592),x85593),x85595)),x85596))+E(x85591,f789(f789(f89(x85592),f789(f789(f90(x85592),f789(f789(f3(x85592),x85593),x85594)),x85595)),x85596))
% 21.40/21.38 [8560]~P121(x85601)+~E(f789(f789(f89(x85601),f789(f789(f90(x85601),x85602),x85604)),x85605),f789(f789(f89(x85601),f789(f789(f90(x85601),x85603),x85604)),x85606))+E(f789(f789(f89(x85601),f789(f789(f90(x85601),f789(f789(f3(x85601),x85602),x85603)),x85604)),x85605),x85606)
% 21.40/21.38 [8708]~P121(x87081)+E(f789(f789(f89(x87081),f789(f789(f90(x87081),x87082),x87083)),x87084),f789(f789(f89(x87081),f789(f789(f90(x87081),x87085),x87083)),x87086))+~E(x87086,f789(f789(f89(x87081),f789(f789(f90(x87081),f789(f789(f3(x87081),x87082),x87085)),x87083)),x87084))
% 21.40/21.38 [8709]~P121(x87091)+E(f789(f789(f89(x87091),f789(f789(f90(x87091),x87092),x87093)),x87094),f789(f789(f89(x87091),f789(f789(f90(x87091),x87095),x87093)),x87096))+~E(f789(f789(f89(x87091),f789(f789(f90(x87091),f789(f789(f3(x87091),x87092),x87095)),x87093)),x87094),x87096)
% 21.40/21.38 [9000]~P1(f789(f789(x90004,x90005),x90006))+~P1(f789(f789(x90003,x90005),x90006))+P1(f789(f789(f789(f789(f111(f870(x90001,f870(x90002,a856))),x90003),x90004),x90005),x90006))
% 21.40/21.38 [9230]P1(f789(f789(x92301,x92302),x92303))+P1(f789(f789(x92304,x92302),x92303))+~P1(f789(f789(f789(f789(f110(f870(x92305,f870(x92306,a856))),x92304),x92301),x92302),x92303))
% 21.40/21.38 [9519]~P129(x95191)+~P1(f789(f789(f241(x95191),f789(f789(f89(x95191),f789(f789(f90(x95191),x95194),x95195)),x95192)),f789(f789(f89(x95191),f789(f789(f90(x95191),x95193),x95195)),x95196)))+P1(f789(f789(f241(x95191),x95192),f789(f789(f89(x95191),f789(f789(f90(x95191),f789(f789(f3(x95191),x95193),x95194)),x95195)),x95196)))
% 21.40/21.38 [9520]~P129(x95201)+~P1(f789(f789(f240(x95201),f789(f789(f89(x95201),f789(f789(f90(x95201),x95204),x95205)),x95202)),f789(f789(f89(x95201),f789(f789(f90(x95201),x95203),x95205)),x95206)))+P1(f789(f789(f240(x95201),x95202),f789(f789(f89(x95201),f789(f789(f90(x95201),f789(f789(f3(x95201),x95203),x95204)),x95205)),x95206)))
% 21.40/21.38 [9538]~P129(x95381)+P1(f789(f789(f241(x95381),f789(f789(f89(x95381),f789(f789(f90(x95381),x95382),x95383)),x95384)),f789(f789(f89(x95381),f789(f789(f90(x95381),x95385),x95383)),x95386)))+~P1(f789(f789(f241(x95381),x95384),f789(f789(f89(x95381),f789(f789(f90(x95381),f789(f789(f3(x95381),x95385),x95382)),x95383)),x95386)))
% 21.40/21.38 [9539]~P129(x95391)+P1(f789(f789(f240(x95391),f789(f789(f89(x95391),f789(f789(f90(x95391),x95392),x95393)),x95394)),f789(f789(f89(x95391),f789(f789(f90(x95391),x95395),x95393)),x95396)))+~P1(f789(f789(f240(x95391),x95394),f789(f789(f89(x95391),f789(f789(f90(x95391),f789(f789(f3(x95391),x95395),x95392)),x95393)),x95396)))
% 21.40/21.38 [9642]~P129(x96421)+~P1(f789(f789(f241(x96421),f789(f789(f89(x96421),f789(f789(f90(x96421),x96422),x96424)),x96425)),f789(f789(f89(x96421),f789(f789(f90(x96421),x96423),x96424)),x96426)))+P1(f789(f789(f241(x96421),f789(f789(f89(x96421),f789(f789(f90(x96421),f789(f789(f3(x96421),x96422),x96423)),x96424)),x96425)),x96426))
% 21.40/21.38 [9643]~P129(x96431)+~P1(f789(f789(f240(x96431),f789(f789(f89(x96431),f789(f789(f90(x96431),x96432),x96434)),x96435)),f789(f789(f89(x96431),f789(f789(f90(x96431),x96433),x96434)),x96436)))+P1(f789(f789(f240(x96431),f789(f789(f89(x96431),f789(f789(f90(x96431),f789(f789(f3(x96431),x96432),x96433)),x96434)),x96435)),x96436))
% 21.40/21.38 [9684]~P129(x96841)+P1(f789(f789(f241(x96841),f789(f789(f89(x96841),f789(f789(f90(x96841),x96842),x96843)),x96844)),f789(f789(f89(x96841),f789(f789(f90(x96841),x96845),x96843)),x96846)))+~P1(f789(f789(f241(x96841),f789(f789(f89(x96841),f789(f789(f90(x96841),f789(f789(f3(x96841),x96842),x96845)),x96843)),x96844)),x96846))
% 21.40/21.38 [9685]~P129(x96851)+P1(f789(f789(f240(x96851),f789(f789(f89(x96851),f789(f789(f90(x96851),x96852),x96853)),x96854)),f789(f789(f89(x96851),f789(f789(f90(x96851),x96855),x96853)),x96856)))+~P1(f789(f789(f240(x96851),f789(f789(f89(x96851),f789(f789(f90(x96851),f789(f789(f3(x96851),x96852),x96855)),x96853)),x96854)),x96856))
% 21.40/21.38 [9853]~P4(x98532)+~P1(f789(f70(x98531),x98536))+E(f789(f789(f8(x98531,x98532),f789(f789(f20(x98531,x98532,x98532),f789(f789(f20(x98531,x98532,f870(x98532,x98532)),f789(f789(f10(a856,f870(x98532,f870(x98532,x98532)),x98531),f105(x98532)),x98533)),x98534)),x98535)),x98536),f789(f789(f89(x98532),f789(f789(f8(x98531,x98532),x98534),f789(f789(f111(f870(x98531,a856)),x98536),f789(f264(x98531),x98533)))),f789(f789(f8(x98531,x98532),x98535),f789(f789(f111(f870(x98531,a856)),x98536),f789(f88(f870(x98531,a856)),f789(f264(x98531),x98533))))))
% 21.40/21.38 [9921]P1(f789(f789(f342(x99212),x99214),x99216))+P1(f789(f789(f342(x99212),x99215),x99216))+E(f789(f313(x99211,x99212,f789(f789(f9(x99211,x99212,x99212),f789(f789(f9(x99211,x99212,f870(x99212,x99212)),f789(f789(f10(a856,f870(x99212,f870(x99212,x99212)),x99211),f105(x99212)),f789(f789(f9(x99211,f870(x99211,a856),a856),f342(x99211)),x99213))),x99214)),x99215)),x99216),f184(f870(x99211,a856)))
% 21.40/21.38 [9922]P1(f789(f789(f342(x99222),x99225),x99226))+~P1(f789(f789(f342(x99222),x99224),x99226))+E(f789(f313(x99221,x99222,f789(f789(f9(x99221,x99222,x99222),f789(f789(f9(x99221,x99222,f870(x99222,x99222)),f789(f789(f10(a856,f870(x99222,f870(x99222,x99222)),x99221),f105(x99222)),f789(f789(f9(x99221,f870(x99221,a856),a856),f342(x99221)),x99223))),x99224)),x99225)),x99226),x99223)
% 21.40/21.38 [9923]P1(f789(f789(f342(x99232),x99234),x99236))+~P1(f789(f789(f342(x99232),x99235),x99236))+E(f789(f313(x99231,x99232,f789(f789(f9(x99231,x99232,x99232),f789(f789(f9(x99231,x99232,f870(x99232,x99232)),f789(f789(f10(a856,f870(x99232,f870(x99232,x99232)),x99231),f105(x99232)),f789(f789(f9(x99231,f870(x99231,a856),a856),f342(x99231)),x99233))),x99234)),x99235)),x99236),f789(f88(f870(x99231,a856)),x99233))
% 21.40/21.38 [9924]~P1(f789(f789(f342(x99242),x99244),x99246))+~P1(f789(f789(f342(x99242),x99245),x99246))+E(f789(f313(x99241,x99242,f789(f789(f9(x99241,x99242,x99242),f789(f789(f9(x99241,x99242,f870(x99242,x99242)),f789(f789(f10(a856,f870(x99242,f870(x99242,x99242)),x99241),f105(x99242)),f789(f789(f9(x99241,f870(x99241,a856),a856),f342(x99241)),x99243))),x99244)),x99245)),x99246),f247(f870(x99241,a856)))
% 21.40/21.38 [10059]P28(x100591,x100592,f789(f789(f310(f862(x100591)),f789(f789(f789(f100(x100591),f789(x100593,x100594)),f789(a29,x100594)),f789(x100595,x100594))),f184(f870(f862(x100591),a856))))+~P1(f789(f789(f342(a859),x100594),x100596))+~P28(x100591,f789(f789(f110(f870(f862(x100591),a856)),x100592),f789(f311(a859,f862(x100591),f789(f789(f20(a859,f870(x100591,f870(a861,a856)),f862(x100591)),f789(f789(f20(a859,a857,f870(f870(x100591,f870(a861,a856)),f862(x100591))),f789(f789(f10(f870(x100591,f870(a861,a856)),f870(a857,f870(f870(x100591,f870(a861,a856)),f862(x100591))),a859),f100(x100591)),x100593)),a29)),x100595)),x100596)),f789(f311(a859,f862(x100591),f789(f789(f20(a859,f870(x100591,f870(a861,a856)),f862(x100591)),f789(f789(f20(a859,a857,f870(f870(x100591,f870(a861,a856)),f862(x100591))),f789(f789(f10(f870(x100591,f870(a861,a856)),f870(a857,f870(f870(x100591,f870(a861,a856)),f862(x100591))),a859),f100(x100591)),x100593)),f789(f789(f10(f867(a857),a857,a859),f238(a857)),a32))),x100595)),x100596))
% 21.40/21.38 [8584]E(x85841,x85842)+~P55(x85844,x85845,x85843,x85846,x85847)+~E(f789(x85843,x85841),f789(x85843,x85842))
% 21.40/21.38 [6963]E(f789(f236(f867(x69631),x69632,f187(x69631),x69633),f789(x69634,x69635)),f789(f234(x69631),x69636))+~E(f789(x69634,x69635),f789(f234(x69632),x69637))+~E(f789(x69633,x69637),f789(f234(x69631),x69636))
% 21.40/21.38 [8605]~P15(x86056,x86055,x86057,x86054,x86051)+E(f789(f789(x86051,x86052),x86053),x86054)+P1(f789(f70(x86055),x86053))
% 21.40/21.38 [8606]~P15(x86066,x86065,x86067,x86064,x86061)+E(f789(f789(x86061,x86062),x86063),x86064)+P1(f789(f70(x86065),x86063))
% 21.40/21.38 [9384]P41(x93841,x93842,x93843,x93844,x93845,f789(f789(x93843,x93846),x93847))+~E(f789(f789(x93843,x93846),x93847),x93844)+~E(x93845,f184(f870(x93841,a856)))
% 21.40/21.38 [9558]~P1(f789(x95586,x95583))+~P1(f789(f789(f342(f869(x95582,x95582)),f789(f789(f249(x95582,x95582),x95584),x95585)),f789(x95587,x95583)))+P1(f789(f789(f342(f869(f869(x95581,x95582),f869(x95581,x95582))),f789(f789(f249(f869(x95581,x95582),f869(x95581,x95582)),f789(f789(f249(x95581,x95582),x95583),x95584)),f789(f789(f249(x95581,x95582),x95583),x95585))),f283(x95581,x95582,x95586,x95587)))
% 21.40/21.38 [9736]~P29(x97363,x97361,x97364,f247(f870(x97363,a856)))+E(f789(f170(x97361,x97362,f789(f789(f150(f869(x97363,x97362),f869(x97361,x97362)),f789(f259(x97363,x97362,f869(x97361,x97362)),f789(f789(f10(x97361,f870(x97362,f869(x97361,x97362)),x97363),f249(x97361,x97362)),x97364))),x97365)),f789(x97364,x97366)),f789(f234(x97362),x97367))+~E(f789(f170(x97363,x97362,x97365),x97366),f789(f234(x97362),x97367))
% 21.40/21.38 [9977]~P41(x99772,x99777,x99773,x99776,x99771,f789(f789(x99773,x99775),x99774))+E(f789(f789(x99773,f365(x99774,x99775,x99771,x99776,x99773,x99777,x99772)),f366(x99774,x99775,x99771,x99776,x99773,x99777,x99772)),f789(f789(x99773,x99775),x99774))+E(x99771,f184(f870(x99772,a856)))
% 21.40/21.38 [9978]~P41(x99787,x99786,x99781,x99784,x99785,f789(f789(x99781,x99782),x99783))+E(f789(f789(x99781,f365(x99783,x99782,x99785,x99784,x99781,x99786,x99787)),f366(x99783,x99782,x99785,x99784,x99781,x99786,x99787)),f789(f789(x99781,x99782),x99783))+E(f789(f789(x99781,x99782),x99783),x99784)
% 21.40/21.38 [8612]~P39(x86123,f789(f789(f789(a193,x86124),f42(x86121)),f789(x86122,x86124)),x86125,x86127)+P39(f34(x86121,x86122,x86123),x86124,x86125,f789(f789(f789(a193,x86126),f42(x86121)),f789(f789(a194,x86124),x86121)))+~E(f789(f789(f789(a193,x86126),f42(x86121)),f789(f789(a194,x86124),x86121)),f789(f789(f789(a193,x86127),f42(x86121)),f789(f789(a194,x86124),x86121)))
% 21.40/21.38 [9299]~P39(f789(a29,x92992),f789(f789(f789(a193,f789(f789(a195,x92994),a196)),f42(a28)),f789(x92993,x92994)),x92995,x92997)+P39(f33(x92991,x92992,x92993),x92994,x92995,f789(f789(f789(a193,f789(f789(a195,x92996),f789(a194,x92994))),x92991),f789(f789(a194,x92996),a27)))+~E(f789(f789(f789(a193,f789(f789(a195,x92996),f789(a194,x92994))),x92991),f789(f789(a194,x92996),a27)),f789(f789(f789(a193,f789(f789(a195,x92997),f789(a194,x92994))),x92991),f789(f789(a194,x92997),a27)))
% 21.40/21.38 [9629]~P1(f789(f75(x96291,x96294,x96295,x96296,x96293),x96297))+P1(f789(f75(x96291,x96294,x96295,x96296,f789(f789(f310(x96291),x96292),x96293)),f789(f789(x96295,x96292),x96297)))+P1(f789(f789(f342(x96291),x96292),x96293))
% 21.40/21.38 [10004]~P41(x100042,x100047,x100046,x100045,x100041,f789(f789(x100046,x100044),x100043))+E(x100041,f184(f870(x100042,a856)))+P1(f789(f789(f342(x100042),f365(x100043,x100044,x100041,x100045,x100046,x100047,x100042)),x100041))
% 21.40/21.38 [10005]~P41(x100055,x100057,x100051,x100054,x100056,f789(f789(x100051,x100052),x100053))+E(f789(f789(x100051,x100052),x100053),x100054)+P1(f789(f789(f342(x100055),f365(x100053,x100052,x100056,x100054,x100051,x100057,x100055)),x100056))
% 21.40/21.38 [6743]~E(x67435,x67437)+~E(x67436,x67434)+E(f789(f789(f789(f789(f81(x67431,f867(x67432)),x67433),x67434),f789(f234(x67432),x67435)),x67436),f789(f234(x67432),x67437))
% 21.40/21.38 [6878]E(x68781,x68782)+~E(f789(x68785,x68781),f789(f234(x68784),x68787))+E(f789(f789(f789(f789(f81(x68783,f867(x68784)),x68785),x68782),f789(f234(x68784),x68786)),x68781),f789(f234(x68784),x68787))
% 21.40/21.38 [7622]E(x76221,x76222)+~E(x76223,x76224)+~E(f789(f789(f789(f789(f81(x76225,f867(x76226)),x76227),x76224),f789(f234(x76226),x76221)),x76223),f789(f234(x76226),x76222))
% 21.40/21.38 [7687]E(x76871,x76872)+E(f789(x76873,x76874),f789(f234(x76875),x76871))+~E(f789(f789(f789(f789(f81(x76876,f867(x76875)),x76873),x76877),f789(f234(x76875),x76872)),x76874),f789(f234(x76875),x76871))
% 21.40/21.38 [7688]E(x76881,x76882)+E(f789(x76883,x76881),f789(f234(x76884),x76885))+~E(f789(f789(f789(f789(f81(x76886,f867(x76884)),x76883),x76882),f789(f234(x76884),x76887)),x76881),f789(f234(x76884),x76885))
% 21.40/21.38 [8811]~P25(x88114,x88115,x88116,x88117,x88111)+~P1(f789(f70(x88115),x88113))+E(f789(f789(x88111,x88112),x88113),f789(f789(f789(f74(x88114,x88115,x88116),x88112),x88117),x88113))
% 21.40/21.38 [8812]~P15(x88124,x88125,x88126,x88127,x88121)+~P1(f789(f70(x88125),x88123))+E(f789(f789(x88121,x88122),x88123),f789(f789(f789(f74(x88124,x88125,x88126),x88122),x88127),x88123))
% 21.40/21.38 [9352]~P28(x93521,x93522,f789(f789(f310(f862(x93521)),f789(f789(f789(f100(x93521),x93523),x93524),x93527)),f184(f870(f862(x93521),a856))))+P28(x93521,x93522,f789(f789(f310(f862(x93521)),f789(f789(f789(f100(x93521),x93523),f38(x93524,x93525)),x93526)),f184(f870(f862(x93521),a856))))+~P28(x93521,x93522,f789(f789(f310(f862(x93521)),f789(f789(f789(f100(x93521),x93527),x93525),x93526)),f184(f870(f862(x93521),a856))))
% 21.40/21.38 [9533]~P27(x95333,x95334,x95335,x95337,x95336,x95331)+~P1(f789(f70(x95334),x95332))+E(f789(x95331,x95332),f789(f789(f789(f74(x95333,x95334,x95335),x95336),x95337),x95332))
% 21.40/21.38 [9679]P41(x96791,x96792,x96793,x96794,x96795,f789(f789(x96793,x96796),x96797))+~P41(x96791,x96792,x96793,x96794,f789(f789(f3(f870(x96791,a856)),x96795),f789(f789(f310(x96791),x96796),f184(f870(x96791,a856)))),x96797)+~P1(f789(f789(f342(x96791),x96796),x96795))
% 21.40/21.38 [9952]~P28(x99521,x99522,f789(f789(f310(f862(x99521)),f789(f789(f789(f100(x99521),f101(x99521,x99523,x99524)),x99525),x99527)),f184(f870(f862(x99521),a856))))+P28(x99521,x99522,f789(f789(f310(f862(x99521)),f789(f789(f789(f100(x99521),x99523),f35(x99524,x99525,x99526)),x99527)),f184(f870(f862(x99521),a856))))+~P28(x99521,x99522,f789(f789(f310(f862(x99521)),f789(f789(f789(f100(x99521),f101(x99521,x99523,f789(f82(a856,a856,a861,a336),x99524))),x99526),x99527)),f184(f870(f862(x99521),a856))))
% 21.40/21.38 [10022]P1(f789(f789(x100227,f349(x100224,x100225,x100221,x100226,x100223,x100222,x100227)),f350(x100224,x100225,x100221,x100226,x100223,x100222,x100227)))+~P1(f789(f789(x100227,f789(f258(x100222,x100223),x100226)),f789(f248(x100222,x100223),x100226)))+P1(f789(x100221,f789(f789(f259(x100222,x100223,x100224),x100225),x100226)))
% 21.40/21.38 [10031]~P41(x100312,x100313,x100314,x100315,x100311,f789(f789(x100314,x100317),x100316))+P41(x100312,x100313,x100314,x100315,f789(f789(f3(f870(x100312,a856)),x100311),f789(f789(f310(x100312),f365(x100316,x100317,x100311,x100315,x100314,x100313,x100312)),f184(f870(x100312,a856)))),f366(x100316,x100317,x100311,x100315,x100314,x100313,x100312))+E(x100311,f184(f870(x100312,a856)))
% 21.40/21.38 [10032]~P41(x100325,x100326,x100321,x100324,x100327,f789(f789(x100321,x100322),x100323))+P41(x100325,x100326,x100321,x100324,f789(f789(f3(f870(x100325,a856)),x100327),f789(f789(f310(x100325),f365(x100323,x100322,x100327,x100324,x100321,x100326,x100325)),f184(f870(x100325,a856)))),f366(x100323,x100322,x100327,x100324,x100321,x100326,x100325))+E(f789(f789(x100321,x100322),x100323),x100324)
% 21.40/21.38 [10052]~P1(f789(x100521,f789(f789(x100525,f350(x100524,x100525,x100521,x100526,x100523,x100522,x100527)),f349(x100524,x100525,x100521,x100526,x100523,x100522,x100527))))+~P1(f789(f789(x100527,f789(f258(x100522,x100523),x100526)),f789(f248(x100522,x100523),x100526)))+P1(f789(x100521,f789(f789(f259(x100522,x100523,x100524),x100525),x100526)))
% 21.40/21.38 [9103]E(f176(x91031,x91032,x91033,x91034,f789(f789(f155(x91032,x91035),x91036),x91037)),f176(x91031,x91032,x91033,x91034,x91035))+~P1(f789(f789(f241(a863),x91036),f789(f185(f864(x91032)),x91035)))+~P1(f789(f789(f240(a863),f789(f185(f864(x91031)),x91034)),x91036))
% 21.40/21.38 [9373]P1(f789(f789(f240(f870(f869(x93731,x93732),a856)),f789(f789(f289(x93731,x93733,x93732),x93734),x93735)),f789(f789(f289(x93731,x93733,x93732),x93736),x93737)))+~P1(f789(f789(f240(f870(f869(x93733,x93732),a856)),x93735),x93737))+~P1(f789(f789(f240(f870(f869(x93731,x93733),a856)),x93734),x93736))
% 21.40/21.38 [9690]~P1(f789(f789(f342(x96901),x96906),x96905))+P1(f789(f75(x96901,x96902,x96903,x96904,x96905),f789(f789(x96903,x96906),x96907)))+~P1(f789(f75(x96901,x96902,x96903,x96904,f789(f789(f3(f870(x96901,a856)),x96905),f789(f789(f310(x96901),x96906),f184(f870(x96901,a856))))),x96907))
% 21.40/21.38 [10085]~P136(x100851)+~P29(f869(x100852,x100853),x100851,f789(f259(x100852,x100853,x100851),f789(f789(f9(x100852,f870(x100853,x100851),f870(x100853,x100851)),f789(f789(f10(f870(x100851,x100851),f870(f870(x100853,x100851),f870(x100853,x100851)),x100852),f10(x100851,x100851,x100853)),f789(f789(f10(x100851,f870(x100851,x100851),x100852),f90(x100851)),x100854))),x100855)),f789(f789(f256(x100852,x100853),x100856),f789(f18(f870(x100853,a856),x100852),x100857)))+E(f789(f789(f8(x100851,x100851),f41(x100851)),f789(f264(x100851),f789(f789(f10(f870(x100852,a856),a856,x100851),f96(x100852)),f789(f789(f10(f870(x100852,f870(x100853,a856)),f870(x100852,a856),x100851),f789(f10(f870(x100853,a856),a856,x100852),f96(x100853))),f789(f789(f9(x100851,f870(x100852,f870(x100853,a856)),f870(x100852,f870(x100853,a856))),f789(f789(f10(f870(x100852,f870(f870(x100853,a856),f870(x100853,a856))),f870(f870(x100852,f870(x100853,a856)),f870(x100852,f870(x100853,a856))),x100851),f20(x100852,f870(x100853,a856),f870(x100853,a856))),f789(f789(f10(f870(x100852,f870(x100853,f870(a856,a856))),f870(x100852,f870(f870(x100853,a856),f870(x100853,a856))),x100851),f789(f10(f870(x100853,f870(a856,a856)),f870(f870(x100853,a856),f870(x100853,a856)),x100852),f20(x100853,a856,a856))),f789(f789(f10(f870(x100852,f870(x100853,a856)),f870(x100852,f870(x100853,f870(a856,a856))),x100851),f789(f10(f870(x100853,a856),f870(x100853,f870(a856,a856)),x100852),f789(f10(a856,f870(a856,a856),x100853),a339))),f789(f789(f9(x100851,f870(x100852,f870(x100853,x100851)),f870(x100852,f870(x100853,a856))),f789(f789(f10(f870(f870(x100853,x100851),f870(x100853,a856)),f870(f870(x100852,f870(x100853,x100851)),f870(x100852,f870(x100853,a856))),x100851),f10(f870(x100853,x100851),f870(x100853,a856),x100852)),f789(f789(f10(f870(x100851,a856),f870(f870(x100853,x100851),f870(x100853,a856)),x100851),f10(x100851,a856,x100853)),a338))),f789(f789(f9(x100852,f870(x100853,x100851),f870(x100853,x100851)),f789(f789(f10(f870(x100851,x100851),f870(f870(x100853,x100851),f870(x100853,x100851)),x100852),f10(x100851,x100851,x100853)),f789(f789(f10(x100851,f870(x100851,x100851),x100852),f90(x100851)),x100854))),x100855)))))),f789(f789(f9(x100852,f870(x100853,a856),f870(x100853,a856)),f789(f789(f10(f870(a856,a856),f870(f870(x100853,a856),f870(x100853,a856)),x100852),f10(a856,a856,x100853)),f789(f789(f10(a856,f870(a856,a856),x100852),a339),f789(f789(f9(x100852,f870(x100852,a856),a856),f342(x100852)),x100856)))),f789(f789(f9(x100853,f870(x100853,a856),a856),f342(x100853)),x100857))))))),f789(f789(f90(x100851),f789(f789(f8(x100852,x100851),x100854),x100856)),f789(f789(f8(x100853,x100851),x100855),x100857)))
% 21.40/21.38 [9766]P51(x97661,x97662,x97663,x97664,x97665,x97666,x97667)+~P1(f789(f789(x97664,x97666),x97668))+~P1(f789(f789(x97665,x97668),x97667))
% 21.40/21.38 [9767]P51(x97671,x97672,x97673,x97674,x97675,x97676,x97677)+~P1(f789(f789(x97674,x97676),x97678))+~P1(f789(f789(x97675,x97678),x97677))
% 21.40/21.38 [9160]~P23(x91608,x91601,x91603,x91605)+~P1(f789(f70(x91608),x91606))+E(f789(f82(x91601,x91601,x91602,f789(x91603,x91604)),f789(f82(x91601,x91601,x91602,f789(x91605,x91606)),x91607)),f789(f82(x91601,x91601,x91602,f789(x91605,x91606)),f789(f82(x91601,x91601,x91602,f789(x91603,x91604)),x91607)))
% 21.40/21.38 [9524]~P26(x95247,x95242,x95245,x95248,x95246,x95241)+~P1(f789(f70(x95242),x95244))+E(f789(x95241,f789(f789(f310(x95242),x95243),x95244)),f789(f789(x95245,f789(x95246,x95243)),f789(x95241,x95244)))
% 21.40/21.38 [9638]~P29(x96382,x96384,x96386,x96388)+~P29(x96381,x96383,x96385,x96387)+P29(f869(x96381,x96382),f869(x96383,x96384),f260(x96381,x96383,x96382,x96384,x96385,x96386),f789(f789(f256(x96381,x96382),x96387),f789(f18(f870(x96382,a856),x96381),x96388)))
% 21.40/21.38 [9314]P1(f789(f789(f342(f869(x93141,x93142)),f789(f789(f249(x93141,x93142),x93143),x93144)),f789(f789(f289(x93141,x93145,x93142),x93146),x93147)))+~P1(f789(f789(f342(f869(x93141,x93145)),f789(f789(f249(x93141,x93145),x93143),x93148)),x93146))+~P1(f789(f789(f342(f869(x93145,x93142)),f789(f789(f249(x93145,x93142),x93148),x93144)),x93147))
% 21.40/21.38 [9507]~P1(f789(f789(f240(f870(f869(x95073,x95072),a856)),x95075),f789(f789(f256(x95073,x95072),x95078),f789(f18(f870(x95072,a856),x95073),x95077))))+~P1(f789(f789(f240(f870(f869(x95071,x95073),a856)),x95074),f789(f789(f256(x95071,x95073),x95076),f789(f18(f870(x95073,a856),x95071),x95078))))+P1(f789(f789(f240(f870(f869(x95071,x95072),a856)),f789(f789(f289(x95071,x95073,x95072),x95074),x95075)),f789(f789(f256(x95071,x95072),x95076),f789(f18(f870(x95072,a856),x95071),x95077))))
% 21.40/21.38 [9553]~E(x95533,x95535)+P1(f789(f789(f342(f869(f869(x95531,x95532),f869(x95531,x95532))),f789(f789(f249(f869(x95531,x95532),f869(x95531,x95532)),f789(f789(f249(x95531,x95532),x95533),x95534)),f789(f789(f249(x95531,x95532),x95535),x95536))),f333(x95531,x95532,x95537,x95538)))+~P1(f789(f789(f342(f869(x95532,x95532)),f789(f789(f249(x95532,x95532),x95534),x95536)),x95538))
% 21.40/21.38 [9657]E(x96571,x96572)+~P1(f789(f789(f342(f869(f869(x96573,x96575),f869(x96573,x96575))),f789(f789(f249(f869(x96573,x96575),f869(x96573,x96575)),f789(f789(f249(x96573,x96575),x96571),x96576)),f789(f789(f249(x96573,x96575),x96572),x96577))),f333(x96573,x96575,x96574,x96578)))+P1(f789(f789(f342(f869(x96573,x96573)),f789(f789(f249(x96573,x96573),x96571),x96572)),x96574))
% 21.40/21.38 [9673]~P1(f789(f789(f342(f869(f869(x96731,x96735),f869(x96731,x96735))),f789(f789(f249(f869(x96731,x96735),f869(x96731,x96735)),f789(f789(f249(x96731,x96735),x96732),x96736)),f789(f789(f249(x96731,x96735),x96733),x96737))),f333(x96731,x96735,x96734,x96738)))+P1(f789(f789(f342(f869(x96731,x96731)),f789(f789(f249(x96731,x96731),x96732),x96733)),x96734))+P1(f789(f789(f342(f869(x96735,x96735)),f789(f789(f249(x96735,x96735),x96736),x96737)),x96738))
% 21.40/21.38 [9583]~P27(x95837,x95835,x95831,x95838,x95832,x95834)+~P1(f789(f70(x95835),x95836))+E(f789(f789(x95831,f789(x95832,x95833)),f789(x95834,f789(f789(f3(f870(x95835,a856)),x95836),f789(f789(f310(x95835),x95833),f184(f870(x95835,a856)))))),f789(x95834,f789(f789(f310(x95835),x95833),x95836)))
% 21.40/21.38 [9119]~P1(f789(f789(f789(x91195,x91198),x91196),x91197))+~P1(f789(f789(f342(x91191),x91198),x91194))+P1(f789(f789(f789(f789(f53(x91191,f870(x91192,f870(x91193,a856))),x91194),x91195),x91196),x91197))
% 21.40/21.38 [9120]~P1(f789(f789(f789(x91205,x91208),x91206),x91207))+~P1(f789(f789(f342(x91201),x91208),x91204))+P1(f789(f789(f789(f789(f53(x91201,f870(x91202,f870(x91203,a856))),x91204),x91205),x91206),x91207))
% 21.40/21.38 [9300]P1(f789(f789(f789(x93001,x93002),x93003),x93004))+~P1(f789(f789(f342(x93005),x93002),x93006))+~P1(f789(f789(f789(f789(f54(x93005,f870(x93007,f870(x93008,a856))),x93006),x93001),x93003),x93004))
% 21.40/21.38 [9301]P1(f789(f789(f789(x93011,x93012),x93013),x93014))+~P1(f789(f789(f342(x93015),x93012),x93016))+~P1(f789(f789(f789(f789(f54(x93015,f870(x93017,f870(x93018,a856))),x93016),x93011),x93013),x93014))
% 21.40/21.38 [9302]P1(f789(f789(f789(x93021,x93022),x93023),x93024))+~P1(f789(f789(f342(x93025),x93022),x93026))+~P1(f789(f789(f789(f789(f54(x93025,f870(x93027,f870(x93028,a856))),x93026),x93021),x93023),x93024))
% 21.40/21.38 [9498]~P25(x94983,x94982,x94984,x94988,x94981)+~P1(f789(f70(x94982),x94987))+E(f789(f789(x94981,f789(f789(f20(x94982,x94983,x94983),f789(f789(f10(x94983,f870(x94983,x94983),x94982),x94984),x94985)),x94986)),x94987),f789(f789(x94984,f789(f789(x94981,x94985),x94987)),f789(f789(x94981,x94986),x94987)))
% 21.40/21.38 [9744]~E(f789(f311(x97442,x97444,x97446),x97448),x974410)+~E(f789(f311(x97441,x97443,x97445),x97447),x97449)+E(f789(f311(f869(x97441,x97442),f869(x97443,x97444),f260(x97441,x97443,x97442,x97444,x97445,x97446)),f789(f789(f256(x97441,x97442),x97447),f789(f18(f870(x97442,a856),x97441),x97448))),f789(f789(f256(x97443,x97444),x97449),f789(f18(f870(x97444,a856),x97443),x974410)))
% 21.40/21.38 [4780]~P101(x47802)+~P18(x47802,x47801)+P18(x47802,f123(x47802,x47801))+E(x47801,f122(x47802))
% 21.40/21.38 [5012]~P9(x50122)+E(f12(x50122,x50121),f52(x50122,x50121))+E(x50121,f184(f870(x50122,a856)))+~P1(f789(f70(x50122),x50121))
% 21.40/21.38 [5013]~P9(x50132)+E(f15(x50132,x50131),f51(x50132,x50131))+E(x50131,f184(f870(x50132,a856)))+~P1(f789(f70(x50132),x50131))
% 21.40/21.38 [5951]~P95(x59512)+E(x59511,f184(f870(x59512,a856)))+P1(f789(f789(f240(x59512),f12(x59512,x59511)),f15(x59512,x59511)))+~P1(f789(f70(x59512),x59511))
% 21.40/21.38 [5965]~P38(x59652)+~P38(x59651)+E(x59651,x59652)+~E(f789(f311(a1,a863,a114),x59651),f789(f311(a1,a863,a114),x59652))
% 21.40/21.38 [8981]~P110(x89811)+~P1(f789(f789(f342(x89811),x89812),f119(x89811)))+P1(f789(f789(f241(x89811),f789(f789(f89(x89811),f789(f789(f89(x89811),f87(x89811)),x89812)),x89812)),f2(x89811)))+~P1(f789(f789(f241(x89811),x89812),f2(x89811)))
% 21.40/21.38 [9201]~P110(x92011)+~P1(f789(f789(f342(x92011),x92012),f119(x92011)))+~P1(f789(f789(f241(x92011),f789(f789(f89(x92011),f789(f789(f89(x92011),f87(x92011)),x92012)),x92012)),f2(x92011)))+P1(f789(f789(f241(x92011),x92012),f2(x92011)))
% 21.40/21.38 [4832]~P106(x48322)+~P136(x48322)+E(x48321,f2(a863))+E(f789(f789(f250(x48322),f2(x48322)),x48321),f2(x48322))
% 21.40/21.38 [4836]~P106(x48361)+~P136(x48361)+~E(x48362,f2(a863))+E(f789(f789(f250(x48361),f2(x48361)),x48362),f87(x48361))
% 21.40/21.38 [4999]~P134(x49992)+E(x49991,f87(x49992))+E(x49991,f789(f88(x49992),f87(x49992)))+~E(f789(f789(f90(x49992),x49991),x49991),f87(x49992))
% 21.40/21.38 [5243]~P84(x52432)+E(x52431,f2(x52432))+E(f91(x52432,x52431),f789(f88(x52432),f87(x52432)))+P1(f789(f789(f241(x52432),f2(x52432)),x52431))
% 21.40/21.38 [5435]~E(x54352,f87(a1))+~E(x54351,f87(a1))+E(f789(f789(f90(a1),x54351),x54352),f87(a1))+~P1(f789(f789(f241(a1),f2(a1)),x54351))
% 21.40/21.38 [5475]~P84(x54752)+E(f91(x54752,x54751),f87(x54752))+E(x54751,f2(x54752))+~P1(f789(f789(f241(x54752),f2(x54752)),x54751))
% 21.40/21.38 [5484]E(x54841,x54842)+~E(f789(f113(a863),x54841),f789(f113(a863),x54842))+P1(f789(a190,f789(f113(a1),x54842)))+P1(f789(a190,f789(f113(a1),x54841)))
% 21.40/21.38 [5530]~P87(x55301)+~E(x55302,f2(x55301))+E(f789(f789(f89(x55301),x55302),x55302),f2(x55301))+~P1(f789(f789(f342(x55301),x55302),f119(x55301)))
% 21.40/21.38 [5567]E(x55671,f2(a1))+~E(f789(f789(f50(a1),x55672),x55671),f2(a1))+P1(f789(f789(f241(a1),x55671),x55672))+P1(f789(f789(f241(a1),x55672),x55671))
% 21.40/21.38 [5596]E(x55961,f2(a1))+~E(f789(f789(f50(a1),x55962),x55961),f2(a1))+P1(f789(f789(f240(a1),x55962),f2(a1)))+P1(f789(f789(f241(a1),x55962),x55961))
% 21.40/21.38 [5628]E(x56281,f2(a1))+~E(f789(f789(f50(a1),x56282),x56281),f2(a1))+P1(f789(f789(f240(a1),f2(a1)),x56282))+P1(f789(f789(f241(a1),x56281),x56282))
% 21.40/21.38 [5664]E(x56641,f2(a1))+~E(f789(f789(f50(a1),x56642),x56641),f2(a1))+P1(f789(f789(f240(a1),x56642),f2(a1)))+P1(f789(f789(f240(a1),f2(a1)),x56642))
% 21.40/21.38 [5665]~P87(x56652)+E(x56651,f2(x56652))+~E(f789(f789(f89(x56652),x56651),x56651),f2(x56652))+~P1(f789(f789(f342(x56652),x56651),f119(x56652)))
% 21.40/21.38 [5732]E(f789(f113(a863),x57321),f789(f113(a863),x57322))+~E(f789(f113(a1),x57322),f2(a1))+P1(f789(a190,f789(f113(a1),x57322)))+~P1(f789(a190,f789(f113(a1),x57321)))
% 21.40/21.38 [5761]~E(f789(f113(a863),x57612),f789(f113(a863),x57611))+E(f789(f113(a1),x57611),f2(a1))+P1(f789(a190,f789(f113(a1),x57611)))+~P1(f789(a190,f789(f113(a1),x57612)))
% 21.40/21.38 [5770]~P101(x57702)+E(x57701,f184(f870(x57702,a856)))+~P1(f789(f70(x57702),x57701))+P1(f789(f789(f342(x57702),f16(x57702,x57701)),x57701))
% 21.40/21.38 [5771]~P101(x57712)+E(x57711,f184(f870(x57712,a856)))+~P1(f789(f70(x57712),x57711))+P1(f789(f789(f342(x57712),f17(x57712,x57711)),x57711))
% 21.40/21.38 [5932]~P110(x59321)+~P88(x59321)+P1(f789(f789(f241(x59321),f2(x59321)),f789(f113(x59321),x59322)))+~P1(f789(f789(f241(a1),a92),x59322))
% 21.40/21.38 [5933]~P110(x59331)+~P88(x59331)+P1(f789(f789(f240(x59331),f2(x59331)),f789(f113(x59331),x59332)))+~P1(f789(f789(f240(a1),a92),x59332))
% 21.40/21.38 [5950]~P110(x59501)+~P88(x59501)+E(f789(f84(x59501),f789(f113(x59501),x59502)),f789(f113(x59501),x59502))+P1(f789(f789(f241(x59501),f789(f113(x59501),x59502)),f2(x59501)))
% 21.40/21.38 [5992]E(x59921,x59922)+~E(f789(a114,x59921),f789(a114,x59922))+~P1(f789(f789(f240(a1),f2(a1)),x59922))+~P1(f789(f789(f240(a1),f2(a1)),x59921))
% 21.40/21.38 [5993]E(x59931,x59932)+~E(f789(a114,x59931),f789(a114,x59932))+~P1(f789(f789(f240(a1),f2(a1)),x59932))+~P1(f789(f789(f240(a1),f2(a1)),x59931))
% 21.40/21.38 [6020]~E(x60201,f2(a1))+E(f60(x60201,x60202),f789(f789(f249(a1,a1),f2(a1)),f2(a1)))+P1(f789(f789(f240(a1),f2(a1)),x60202))+~P1(f789(f789(f240(a1),f2(a1)),x60201))
% 21.40/21.38 [6189]~P88(x61892)+~P110(x61892)+~P1(f789(f789(f241(x61892),f2(x61892)),f789(f113(x61892),x61891)))+P1(f789(f789(f241(a1),a92),x61891))
% 21.40/21.38 [6190]~P88(x61902)+~P110(x61902)+~P1(f789(f789(f240(x61902),f2(x61902)),f789(f113(x61902),x61901)))+P1(f789(f789(f240(a1),a92),x61901))
% 21.40/21.38 [6195]~P110(x61951)+~P88(x61951)+P1(f789(f789(f241(x61951),f789(f113(x61951),x61952)),f2(x61951)))+~P1(f789(f789(f241(a1),x61952),a92))
% 21.40/21.38 [6196]~P110(x61961)+~P88(x61961)+P1(f789(f789(f240(x61961),f789(f113(x61961),x61962)),f2(x61961)))+~P1(f789(f789(f240(a1),x61962),a92))
% 21.40/21.38 [6523]~P88(x65232)+~P110(x65232)+~P1(f789(f789(f241(x65232),f789(f113(x65232),x65231)),f2(x65232)))+P1(f789(f789(f241(a1),x65231),a92))
% 21.40/21.38 [6524]~P88(x65242)+~P110(x65242)+~P1(f789(f789(f240(x65242),f789(f113(x65242),x65241)),f2(x65242)))+P1(f789(f789(f240(a1),x65241),a92))
% 21.40/21.38 [6615]~P110(x66151)+~P88(x66151)+E(f789(f84(x66151),f789(f113(x66151),x66152)),f789(f88(x66151),f789(f113(x66151),x66152)))+~P1(f789(f789(f241(x66151),f789(f113(x66151),x66152)),f2(x66151)))
% 21.40/21.38 [6632]E(f789(f113(a863),x66321),f789(f113(a863),x66322))+~E(f789(f113(a1),x66322),f2(a1))+~P1(f789(f789(f240(a1),f789(f113(a1),x66321)),f2(a1)))+~P1(f789(a190,f789(f113(a1),x66321)))
% 21.40/21.38 [6813]E(x68131,x68132)+~E(f789(a5,x68131),f789(a5,x68132))+~P1(f789(f789(f342(a863),x68132),f247(f870(a863,a856))))+~P1(f789(f789(f342(a863),x68131),f247(f870(a863,a856))))
% 21.40/21.38 [7041]P1(f789(f789(f241(a863),f789(a114,x70411)),f789(a114,x70412)))+~P1(f789(f789(f240(a1),f2(a1)),x70412))+~P1(f789(f789(f240(a1),f2(a1)),x70411))+~P1(f789(f789(f241(a1),x70411),x70412))
% 21.40/21.38 [7042]P1(f789(f789(f240(a863),f789(a114,x70421)),f789(a114,x70422)))+~P1(f789(f789(f240(a1),f2(a1)),x70422))+~P1(f789(f789(f240(a1),f2(a1)),x70421))+~P1(f789(f789(f240(a1),x70421),x70422))
% 21.40/21.38 [7043]P1(f789(f789(f287(a863),f789(a114,x70431)),f789(a114,x70432)))+~P1(f789(f789(f240(a1),f2(a1)),x70432))+~P1(f789(f789(f240(a1),f2(a1)),x70431))+~P1(f789(f789(f287(a1),x70431),x70432))
% 21.40/21.38 [7276]~P10(x72761)+~P38(x72762)+~P1(f789(f789(f342(a1),x72761),x72762))+P1(f789(f789(f342(a863),f789(a114,x72761)),f789(f311(a1,a863,a114),x72762)))
% 21.40/21.38 [7284]~P1(f789(f789(f241(a863),f789(a114,x72841)),f789(a114,x72842)))+~P1(f789(f789(f240(a1),f2(a1)),x72842))+~P1(f789(f789(f240(a1),f2(a1)),x72841))+P1(f789(f789(f241(a1),x72841),x72842))
% 21.40/21.38 [7285]~P1(f789(f789(f240(a863),f789(a114,x72851)),f789(a114,x72852)))+~P1(f789(f789(f240(a1),f2(a1)),x72852))+~P1(f789(f789(f240(a1),f2(a1)),x72851))+P1(f789(f789(f240(a1),x72851),x72852))
% 21.40/21.38 [7286]~P1(f789(f789(f287(a863),f789(a114,x72861)),f789(a114,x72862)))+~P1(f789(f789(f240(a1),f2(a1)),x72862))+~P1(f789(f789(f240(a1),f2(a1)),x72861))+P1(f789(f789(f287(a1),x72861),x72862))
% 21.40/21.38 [7550]~P101(x75502)+E(x75501,f184(f870(x75502,a856)))+~P1(f789(f70(x75502),x75501))+P1(f789(f789(f240(x75502),f14(x75502,f244(x75502),x75501)),f13(x75502,f239(x75502),x75501)))
% 21.40/21.38 [7874]~P10(x78741)+~P38(x78742)+P1(f789(f789(f342(a1),x78741),x78742))+~P1(f789(f789(f342(a863),f789(a114,x78741)),f789(f311(a1,a863,a114),x78742)))
% 21.40/21.38 [5767]~P120(x57672)+E(x57671,f2(a1))+E(f789(f88(x57672),f789(f112(x57672),f789(f88(a1),x57671))),f789(f112(x57672),x57671))+~P1(f789(f789(f241(a1),x57671),f2(a1)))
% 21.40/21.38 [5842]~P87(x58421)+~P88(x58421)+~P33(x58421,f789(f113(x58421),x58422))+P33(x58421,f789(f113(x58421),f789(f789(f89(a1),x58422),x58422)))
% 21.40/21.38 [6179]~P3(x61792)+E(x61791,f184(f870(x61792,a856)))+E(f17(x61792,f789(f311(x61792,x61792,f88(x61792)),x61791)),f789(f88(x61792),f16(x61792,x61791)))+~P1(f789(f70(x61792),x61791))
% 21.40/21.38 [6180]~P3(x61802)+E(x61801,f184(f870(x61802,a856)))+E(f16(x61802,f789(f311(x61802,x61802,f88(x61802)),x61801)),f789(f88(x61802),f17(x61802,x61801)))+~P1(f789(f70(x61802),x61801))
% 21.40/21.38 [6210]~P87(x62101)+~P88(x62101)+P33(x62101,f789(f113(x62101),x62102))+~P33(x62101,f789(f113(x62101),f789(f789(f89(a1),x62102),x62102)))
% 21.40/21.38 [6303]E(x63031,f2(a1))+E(f789(a65,f64(f789(f88(a1),x63031),f789(f88(a1),x63032))),f60(x63031,x63032))+P1(f789(f789(f240(a1),f2(a1)),x63032))+~P1(f789(f789(f240(a1),f2(a1)),x63031))
% 21.40/21.38 [7186]~P1(f789(f789(f241(a1),f2(a1)),x71862))+~P1(f789(f789(f240(a1),f2(a1)),x71861))+~P1(f789(f789(f240(a1),x71862),x71861))+P1(f789(f789(f241(a1),f2(a1)),f789(f789(f50(a1),x71861),x71862)))
% 21.40/21.38 [7627]~E(x76272,f2(a1))+E(f217(x76271,x76272),f789(f789(f249(a1,a1),f2(a1)),f87(a1)))+P1(f789(f789(f241(a1),x76272),f2(a1)))+~P1(f789(f329(f869(a1,a1),a223),f789(f789(f249(a1,a1),x76271),x76272)))
% 21.40/21.38 [7628]~E(x76281,f2(a1))+E(f217(x76281,x76282),f789(f789(f249(a1,a1),f2(a1)),f87(a1)))+P1(f789(f789(f241(a1),x76282),f2(a1)))+~P1(f789(f329(f869(a1,a1),a223),f789(f789(f249(a1,a1),x76281),x76282)))
% 21.40/21.38 [8629]~P38(x86292)+~P38(x86291)+P1(f789(f789(f241(f870(a863,a856)),f789(f311(a1,a863,a114),x86291)),f789(f311(a1,a863,a114),x86292)))+~P1(f789(f789(f241(f870(a1,a856)),x86291),x86292))
% 21.40/21.38 [8630]~P38(x86302)+~P38(x86301)+P1(f789(f789(f240(f870(a863,a856)),f789(f311(a1,a863,a114),x86301)),f789(f311(a1,a863,a114),x86302)))+~P1(f789(f789(f240(f870(a1,a856)),x86301),x86302))
% 21.40/21.38 [8906]~P38(x89062)+~P38(x89061)+~P1(f789(f789(f241(f870(a863,a856)),f789(f311(a1,a863,a114),x89061)),f789(f311(a1,a863,a114),x89062)))+P1(f789(f789(f241(f870(a1,a856)),x89061),x89062))
% 21.40/21.38 [8907]~P38(x89072)+~P38(x89071)+~P1(f789(f789(f240(f870(a863,a856)),f789(f311(a1,a863,a114),x89071)),f789(f311(a1,a863,a114),x89072)))+P1(f789(f789(f240(f870(a1,a856)),x89071),x89072))
% 21.40/21.38 [9344]E(x93441,f2(a1))+E(x93442,f2(a1))+E(f789(f789(f95(a1,f869(a1,a1)),f789(f789(a219,x93442),x93441)),f789(f789(f20(a1,a1,f869(a1,a1)),f789(f789(f10(a1,f870(a1,f869(a1,a1)),a1),f249(a1,a1)),f789(f50(a1),x93442))),f789(f50(a1),x93441))),f217(x93442,x93441))+P1(f789(f789(f241(a1),x93441),f2(a1)))
% 21.40/21.38 [8193]~P88(x81932)+~P110(x81932)+~P1(f789(f789(f241(x81932),f789(f113(x81932),x81931)),f87(x81932)))+P1(f789(f789(f241(a1),x81931),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))
% 21.40/21.38 [8194]~P88(x81942)+~P110(x81942)+~P1(f789(f789(f240(x81942),f789(f113(x81942),x81941)),f87(x81942)))+P1(f789(f789(f240(a1),x81941),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))
% 21.40/21.38 [8468]~P110(x84681)+~P88(x84681)+P1(f789(f789(f241(x84681),f789(f113(x84681),x84682)),f87(x84681)))+~P1(f789(f789(f241(a1),x84682),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))
% 21.40/21.38 [8469]~P110(x84691)+~P88(x84691)+P1(f789(f789(f240(x84691),f789(f113(x84691),x84692)),f87(x84691)))+~P1(f789(f789(f240(a1),x84692),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))
% 21.40/21.38 [8654]~P88(x86542)+~P110(x86542)+~P1(f789(f789(f241(x86542),f87(x86542)),f789(f113(x86542),x86541)))+P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),x86541))
% 21.40/21.38 [8655]~P88(x86552)+~P110(x86552)+~P1(f789(f789(f240(x86552),f87(x86552)),f789(f113(x86552),x86551)))+P1(f789(f789(f240(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),x86551))
% 21.40/21.38 [8987]~P110(x89871)+~P88(x89871)+P1(f789(f789(f241(x89871),f87(x89871)),f789(f113(x89871),x89872)))+~P1(f789(f789(f241(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),x89872))
% 21.40/21.38 [8988]~P110(x89881)+~P88(x89881)+P1(f789(f789(f240(x89881),f87(x89881)),f789(f113(x89881),x89882)))+~P1(f789(f789(f240(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),x89882))
% 21.40/21.38 [9467]~P134(x94672)+E(x94671,f87(x94672))+E(x94671,f789(f88(x94672),f87(x94672)))+~E(f789(f789(f250(x94672),x94671),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f87(x94672))
% 21.40/21.38 [9720]~P62(x97201)+~P88(x97201)+~P1(f789(f789(f241(x97201),f2(x97201)),x97202))+P1(f789(f789(f241(x97201),f2(x97201)),f789(f789(f291(x97201),x97202),f789(f113(x97201),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))
% 21.40/21.38 [9721]~P62(x97211)+~P88(x97211)+~P1(f789(f789(f241(x97211),f2(x97211)),x97212))+P1(f789(f789(f241(x97211),f2(x97211)),f789(f789(f291(x97211),x97212),f789(f113(x97211),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))
% 21.40/21.38 [9776]~P62(x97761)+~P88(x97761)+P1(f789(f789(f241(x97761),f2(x97761)),x97762))+~P1(f789(f789(f241(x97761),f2(x97761)),f789(f789(f291(x97761),x97762),f789(f113(x97761),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))
% 21.40/21.38 [10057]~P120(x100572)+E(x100571,f2(a1))+P1(f789(f789(f241(a1),x100571),f2(a1)))+E(f789(f789(f259(a1,a1,x100572),f789(f789(f9(a1,f870(a1,f870(x100572,x100572)),f870(a1,x100572)),f789(f789(f10(f870(f870(x100572,x100572),x100572),f870(f870(a1,f870(x100572,x100572)),f870(a1,x100572)),a1),f10(f870(x100572,x100572),x100572,a1)),f789(f789(f10(x100572,f870(f870(x100572,x100572),x100572),a1),f95(x100572,x100572)),f112(x100572)))),f789(f789(f9(a1,f870(x100572,x100572),f870(x100572,x100572)),f789(f789(f10(f870(x100572,f870(x100572,x100572)),f870(f870(x100572,x100572),f870(x100572,x100572)),a1),f20(x100572,x100572,x100572)),f789(f789(f9(a1,f870(x100572,x100572),f870(x100572,f870(x100572,x100572))),f789(f789(f10(f870(x100572,f870(x100572,x100572)),f870(f870(x100572,x100572),f870(x100572,f870(x100572,x100572))),a1),f10(x100572,f870(x100572,x100572),x100572)),f789(f789(f10(a856,f870(x100572,f870(x100572,x100572)),a1),f105(x100572)),f789(f789(f9(a1,a1,a856),a338),f2(a1))))),f789(f789(f20(x100572,x100572,x100572),f89(x100572)),f7(x100572))))),f789(f789(f9(x100572,x100572,x100572),f789(f789(f10(x100572,f870(x100572,x100572),x100572),f89(x100572)),f789(f789(f20(x100572,x100572,x100572),f89(x100572)),f7(x100572)))),f87(x100572))))),f60(x100571,f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f112(x100572),x100571))
% 21.40/21.38 [9823]P1(f789(f789(f240(a1),x98231),f2(a1)))+P1(f789(f789(f241(a1),x98232),x98231))+~P1(f789(f329(f869(a1,a1),a69),f789(f789(f249(a1,a1),x98232),x98231)))+E(f789(f57(x98231),f61(x98232,f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x98231))),f61(x98232,x98231))
% 21.40/21.38 [9827]P1(f789(f789(f240(a1),x98271),f2(a1)))+~P1(f789(f329(f869(a1,a1),a66),f789(f789(f249(a1,a1),x98272),x98271)))+P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),x98272),x98271)))+E(f789(f57(x98271),f64(x98272,f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),x98271))),f64(x98272,x98271))
% 21.40/21.38 [4806]~P87(x48063)+~P88(x48063)+E(x48061,x48062)+~E(f789(f113(x48063),x48061),f789(f113(x48063),x48062))
% 21.40/21.38 [5941]~P1(f789(x59411,x59412))+~P1(f789(x59411,x59413))+~P1(f789(f789(f240(a863),x59413),f813(x59412,x59411)))+P1(f789(x59411,f2(a863)))
% 21.40/21.38 [6370]P140(x63702,x63703,x63701)+E(x63701,f2(a1))+P1(f789(f789(f240(a1),f2(a1)),f796(x63701,x63703,x63702)))+P1(f789(f789(f241(a1),x63701),f2(a1)))
% 21.40/21.38 [6371]P141(x63712,x63713,x63711)+E(x63711,f2(a1))+P1(f789(f789(f240(a1),f2(a1)),f799(x63711,x63713,x63712)))+P1(f789(f789(f241(a1),x63711),f2(a1)))
% 21.40/21.38 [6502]P140(x65021,x65022,x65023)+~P1(f789(x65021,x65022))+P1(f789(f789(f240(a1),f2(a1)),f796(x65023,x65022,x65021)))+P1(f789(f789(f241(a1),x65023),f2(a1)))
% 21.40/21.38 [6526]P141(x65261,x65262,x65263)+P1(f789(f789(f240(a1),f2(a1)),f799(x65263,x65262,x65261)))+~P1(f789(x65261,f2(a1)))+P1(f789(f789(f241(a1),x65263),f2(a1)))
% 21.40/21.38 [6558]P140(x65582,x65583,x65581)+E(x65581,f2(a1))+~P1(f789(x65582,f796(x65581,x65583,x65582)))+P1(f789(f789(f241(a1),x65581),f2(a1)))
% 21.40/21.38 [6559]P141(x65592,x65593,x65591)+E(x65591,f2(a1))+~P1(f789(x65592,f800(x65591,x65593,x65592)))+P1(f789(f789(f241(a1),x65591),f2(a1)))
% 21.40/21.38 [6662]~P101(x66621)+~P9(x66621)+~P1(f789(f789(f241(x66621),x66622),f51(x66621,x66623)))+P1(f789(f789(f241(x66621),x66622),f667(x66623,x66622,x66621)))
% 21.40/21.38 [6672]P140(x66721,x66722,x66723)+~P1(f789(x66721,x66722))+~P1(f789(x66721,f796(x66723,x66722,x66721)))+P1(f789(f789(f241(a1),x66723),f2(a1)))
% 21.40/21.38 [6705]P141(x67051,x67052,x67053)+~P1(f789(x67051,f800(x67053,x67052,x67051)))+~P1(f789(x67051,f2(a1)))+P1(f789(f789(f241(a1),x67053),f2(a1)))
% 21.40/21.38 [6966]P140(x69662,x69663,x69661)+E(x69661,f2(a1))+P1(f789(f789(f240(a1),f2(a1)),f796(x69661,x69663,x69662)))+P1(f789(f789(f241(a1),x69661),f795(x69661,x69663,x69662)))
% 21.40/21.38 [6967]P141(x69672,x69673,x69671)+E(x69671,f2(a1))+P1(f789(f789(f240(a1),f2(a1)),f799(x69671,x69673,x69672)))+P1(f789(f789(f241(a1),x69671),f801(x69671,x69673,x69672)))
% 21.40/21.38 [7085]P140(x70851,x70852,x70853)+~P1(f789(x70851,x70852))+P1(f789(f789(f240(a1),f2(a1)),f796(x70853,x70852,x70851)))+P1(f789(f789(f241(a1),x70853),f795(x70853,x70852,x70851)))
% 21.40/21.38 [7105]P141(x71051,x71052,x71053)+P1(f789(f789(f240(a1),f2(a1)),f799(x71053,x71052,x71051)))+P1(f789(f789(f241(a1),x71053),f801(x71053,x71052,x71051)))+~P1(f789(x71051,f2(a1)))
% 21.40/21.38 [7136]P140(x71362,x71363,x71361)+E(x71361,f2(a1))+~P1(f789(x71362,f796(x71361,x71363,x71362)))+P1(f789(f789(f241(a1),x71361),f795(x71361,x71363,x71362)))
% 21.40/21.38 [7137]P141(x71372,x71373,x71371)+E(x71371,f2(a1))+~P1(f789(x71372,f800(x71371,x71373,x71372)))+P1(f789(f789(f241(a1),x71371),f801(x71371,x71373,x71372)))
% 21.40/21.38 [7177]P140(x71772,x71773,x71771)+E(x71771,f2(a1))+P1(f789(f789(f240(a1),f2(a1)),f796(x71771,x71773,x71772)))+~P1(f789(x71772,f795(x71771,x71773,x71772)))
% 21.40/21.38 [7178]P141(x71782,x71783,x71781)+E(x71781,f2(a1))+P1(f789(f789(f240(a1),f2(a1)),f799(x71781,x71783,x71782)))+~P1(f789(x71782,f802(x71781,x71783,x71782)))
% 21.40/21.38 [7283]P140(x72831,x72832,x72833)+~P1(f789(x72831,x72832))+~P1(f789(x72831,f796(x72833,x72832,x72831)))+P1(f789(f789(f241(a1),x72833),f795(x72833,x72832,x72831)))
% 21.40/21.38 [7299]P141(x72991,x72992,x72993)+~P1(f789(x72991,f800(x72993,x72992,x72991)))+P1(f789(f789(f241(a1),x72993),f801(x72993,x72992,x72991)))+~P1(f789(x72991,f2(a1)))
% 21.40/21.38 [7305]P140(x73051,x73052,x73053)+~P1(f789(x73051,x73052))+P1(f789(f789(f240(a1),f2(a1)),f796(x73053,x73052,x73051)))+~P1(f789(x73051,f795(x73053,x73052,x73051)))
% 21.40/21.38 [7323]P141(x73231,x73232,x73233)+P1(f789(f789(f240(a1),f2(a1)),f799(x73233,x73232,x73231)))+~P1(f789(x73231,f802(x73233,x73232,x73231)))+~P1(f789(x73231,f2(a1)))
% 21.40/21.38 [7347]P140(x73472,x73473,x73471)+E(x73471,f2(a1))+~P1(f789(x73472,f796(x73471,x73473,x73472)))+~P1(f789(x73472,f795(x73471,x73473,x73472)))
% 21.40/21.38 [7348]P141(x73482,x73483,x73481)+E(x73481,f2(a1))+~P1(f789(x73482,f800(x73481,x73483,x73482)))+~P1(f789(x73482,f802(x73481,x73483,x73482)))
% 21.40/21.38 [7444]P140(x74441,x74442,x74443)+~P1(f789(x74441,x74442))+~P1(f789(x74441,f796(x74443,x74442,x74441)))+~P1(f789(x74441,f795(x74443,x74442,x74441)))
% 21.40/21.38 [7459]P141(x74591,x74592,x74593)+~P1(f789(x74591,f800(x74593,x74592,x74591)))+~P1(f789(x74591,f802(x74593,x74592,x74591)))+~P1(f789(x74591,f2(a1)))
% 21.40/21.38 [7510]P140(x75102,x75103,x75101)+E(x75101,f2(a1))+P1(f789(f789(f240(a1),f2(a1)),f796(x75101,x75103,x75102)))+P1(f789(f789(f240(a1),f795(x75101,x75103,x75102)),f2(a1)))
% 21.40/21.38 [7511]P141(x75112,x75113,x75111)+E(x75111,f2(a1))+P1(f789(f789(f240(a1),f2(a1)),f799(x75111,x75113,x75112)))+P1(f789(f789(f240(a1),f801(x75111,x75113,x75112)),f2(a1)))
% 21.40/21.38 [7512]~P2(x75121)+~P1(f789(f789(f342(x75121),x75123),f181(x75121)))+~P1(f789(f789(f342(x75121),x75122),f181(x75121)))+P1(f789(f789(f342(x75121),f789(f789(f89(x75121),x75122),x75123)),f181(x75121)))
% 21.40/21.38 [7513]~P120(x75131)+~P1(f789(f789(f342(x75131),x75133),f119(x75131)))+~P1(f789(f789(f342(x75131),x75132),f119(x75131)))+P1(f789(f789(f342(x75131),f789(f789(f89(x75131),x75132),x75133)),f119(x75131)))
% 21.40/21.38 [7514]~P2(x75141)+~P1(f789(f789(f342(x75141),x75143),f181(x75141)))+~P1(f789(f789(f342(x75141),x75142),f181(x75141)))+P1(f789(f789(f342(x75141),f789(f789(f90(x75141),x75142),x75143)),f181(x75141)))
% 21.40/21.38 [7515]~P120(x75151)+~P1(f789(f789(f342(x75151),x75153),f119(x75151)))+~P1(f789(f789(f342(x75151),x75152),f119(x75151)))+P1(f789(f789(f342(x75151),f789(f789(f90(x75151),x75152),x75153)),f119(x75151)))
% 21.40/21.38 [7516]~P120(x75161)+~P1(f789(f789(f342(x75161),x75163),f119(x75161)))+~P1(f789(f789(f342(x75161),x75162),f119(x75161)))+P1(f789(f789(f342(x75161),f789(f789(f3(x75161),x75162),x75163)),f119(x75161)))
% 21.40/21.38 [7517]~P82(x75171)+~P1(f789(f789(f241(x75171),x75173),f2(x75171)))+~P1(f789(f789(f241(x75171),x75172),f2(x75171)))+P1(f789(f789(f241(x75171),f789(f789(f89(x75171),x75172),x75173)),f2(x75171)))
% 21.40/21.38 [7518]~P82(x75181)+~P1(f789(f789(f240(x75181),x75182),f2(x75181)))+~P1(f789(f789(f241(x75181),x75183),f2(x75181)))+P1(f789(f789(f241(x75181),f789(f789(f89(x75181),x75182),x75183)),f2(x75181)))
% 21.40/21.38 [7519]~P82(x75191)+~P1(f789(f789(f240(x75191),x75193),f2(x75191)))+~P1(f789(f789(f241(x75191),x75192),f2(x75191)))+P1(f789(f789(f241(x75191),f789(f789(f89(x75191),x75192),x75193)),f2(x75191)))
% 21.40/21.38 [7520]~P82(x75201)+~P1(f789(f789(f240(x75201),x75203),f2(x75201)))+~P1(f789(f789(f240(x75201),x75202),f2(x75201)))+P1(f789(f789(f240(x75201),f789(f789(f89(x75201),x75202),x75203)),f2(x75201)))
% 21.40/21.38 [7546]P140(x75463,x75462,x75461)+E(x75461,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x75461),f797(x75461,x75462,x75463))),f796(x75461,x75462,x75463)),x75462)+P1(f789(f789(f241(a1),x75461),f2(a1)))
% 21.40/21.38 [7547]P141(x75473,x75472,x75471)+E(x75471,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x75471),f800(x75471,x75472,x75473))),f799(x75471,x75472,x75473)),x75472)+P1(f789(f789(f241(a1),x75471),f2(a1)))
% 21.40/21.38 [7632]P140(x76321,x76322,x76323)+~P1(f789(x76321,x76322))+P1(f789(f789(f240(a1),f2(a1)),f796(x76323,x76322,x76321)))+P1(f789(f789(f240(a1),f795(x76323,x76322,x76321)),f2(a1)))
% 21.40/21.38 [7663]P141(x76631,x76632,x76633)+P1(f789(f789(f240(a1),f2(a1)),f799(x76633,x76632,x76631)))+~P1(f789(x76631,f2(a1)))+P1(f789(f789(f240(a1),f801(x76633,x76632,x76631)),f2(a1)))
% 21.40/21.38 [7671]P140(x76713,x76712,x76711)+~P1(f789(x76713,x76712))+E(f789(f789(f89(a1),f789(f789(f90(a1),x76711),f797(x76711,x76712,x76713))),f796(x76711,x76712,x76713)),x76712)+P1(f789(f789(f241(a1),x76711),f2(a1)))
% 21.40/21.38 [7676]P140(x76762,x76763,x76761)+E(x76761,f2(a1))+~P1(f789(x76762,f796(x76761,x76763,x76762)))+P1(f789(f789(f240(a1),f795(x76761,x76763,x76762)),f2(a1)))
% 21.40/21.38 [7677]P141(x76772,x76773,x76771)+E(x76771,f2(a1))+~P1(f789(x76772,f800(x76771,x76773,x76772)))+P1(f789(f789(f240(a1),f801(x76771,x76773,x76772)),f2(a1)))
% 21.40/21.38 [7682]P141(x76823,x76822,x76821)+E(f789(f789(f89(a1),f789(f789(f90(a1),x76821),f800(x76821,x76822,x76823))),f799(x76821,x76822,x76823)),x76822)+~P1(f789(x76823,f2(a1)))+P1(f789(f789(f241(a1),x76821),f2(a1)))
% 21.40/21.38 [7734]P140(x77341,x77342,x77343)+~P1(f789(x77341,x77342))+~P1(f789(x77341,f796(x77343,x77342,x77341)))+P1(f789(f789(f240(a1),f795(x77343,x77342,x77341)),f2(a1)))
% 21.40/21.38 [7739]P141(x77391,x77392,x77393)+~P1(f789(x77391,f800(x77393,x77392,x77391)))+~P1(f789(x77391,f2(a1)))+P1(f789(f789(f240(a1),f801(x77393,x77392,x77391)),f2(a1)))
% 21.40/21.38 [7813]~P62(x78131)+~P1(f789(f789(f241(x78131),f789(f789(f291(x78131),x78133),x78132)),f2(x78131)))+P1(f789(f789(f241(x78131),x78132),f2(x78131)))+P1(f789(f789(f241(x78131),x78133),f2(x78131)))
% 21.40/21.38 [7814]~P118(x78141)+~P1(f789(f789(f240(x78141),f789(f789(f90(x78141),x78143),x78142)),f2(x78141)))+P1(f789(f789(f240(x78141),x78142),f2(x78141)))+P1(f789(f789(f240(x78141),x78143),f2(x78141)))
% 21.40/21.38 [7815]~P62(x78151)+~P1(f789(f789(f240(x78151),f789(f789(f291(x78151),x78153),x78152)),f2(x78151)))+P1(f789(f789(f240(x78151),x78152),f2(x78151)))+P1(f789(f789(f240(x78151),x78153),f2(x78151)))
% 21.40/21.38 [7927]P140(x79273,x79272,x79271)+E(x79271,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x79271),f797(x79271,x79272,x79273))),f796(x79271,x79272,x79273)),x79272)+P1(f789(f789(f241(a1),x79271),f795(x79271,x79272,x79273)))
% 21.40/21.38 [7928]P141(x79283,x79282,x79281)+E(x79281,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x79281),f800(x79281,x79282,x79283))),f799(x79281,x79282,x79283)),x79282)+P1(f789(f789(f241(a1),x79281),f801(x79281,x79282,x79283)))
% 21.40/21.38 [7939]P140(x79393,x79392,x79391)+E(x79391,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x79391),f798(x79391,x79392,x79393))),f795(x79391,x79392,x79393)),x79392)+P1(f789(f789(f240(a1),f2(a1)),f796(x79391,x79392,x79393)))
% 21.40/21.38 [7940]P141(x79403,x79402,x79401)+E(x79401,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x79401),f802(x79401,x79402,x79403))),f801(x79401,x79402,x79403)),x79402)+P1(f789(f789(f240(a1),f2(a1)),f799(x79401,x79402,x79403)))
% 21.40/21.38 [7985]P140(x79853,x79852,x79851)+~P1(f789(x79853,x79852))+E(f789(f789(f89(a1),f789(f789(f90(a1),x79851),f797(x79851,x79852,x79853))),f796(x79851,x79852,x79853)),x79852)+P1(f789(f789(f241(a1),x79851),f795(x79851,x79852,x79853)))
% 21.40/21.38 [7996]P141(x79963,x79962,x79961)+E(f789(f789(f89(a1),f789(f789(f90(a1),x79961),f800(x79961,x79962,x79963))),f799(x79961,x79962,x79963)),x79962)+P1(f789(f789(f241(a1),x79961),f801(x79961,x79962,x79963)))+~P1(f789(x79963,f2(a1)))
% 21.40/21.38 [8002]P140(x80023,x80022,x80021)+~P1(f789(x80023,x80022))+E(f789(f789(f89(a1),f789(f789(f90(a1),x80021),f798(x80021,x80022,x80023))),f795(x80021,x80022,x80023)),x80022)+P1(f789(f789(f240(a1),f2(a1)),f796(x80021,x80022,x80023)))
% 21.40/21.38 [8009]P141(x80093,x80092,x80091)+E(f789(f789(f89(a1),f789(f789(f90(a1),x80091),f802(x80091,x80092,x80093))),f801(x80091,x80092,x80093)),x80092)+P1(f789(f789(f240(a1),f2(a1)),f799(x80091,x80092,x80093)))+~P1(f789(x80093,f2(a1)))
% 21.40/21.38 [8019]P140(x80193,x80192,x80191)+E(x80191,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x80191),f797(x80191,x80192,x80193))),f796(x80191,x80192,x80193)),x80192)+~P1(f789(x80193,f795(x80191,x80192,x80193)))
% 21.40/21.38 [8020]P141(x80203,x80202,x80201)+E(x80201,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x80201),f800(x80201,x80202,x80203))),f799(x80201,x80202,x80203)),x80202)+~P1(f789(x80203,f802(x80201,x80202,x80203)))
% 21.40/21.38 [8021]P140(x80213,x80212,x80211)+E(x80211,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x80211),f798(x80211,x80212,x80213))),f795(x80211,x80212,x80213)),x80212)+~P1(f789(x80213,f796(x80211,x80212,x80213)))
% 21.40/21.38 [8022]P141(x80223,x80222,x80221)+E(x80221,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x80221),f802(x80221,x80222,x80223))),f801(x80221,x80222,x80223)),x80222)+~P1(f789(x80223,f800(x80221,x80222,x80223)))
% 21.40/21.38 [8075]P140(x80753,x80752,x80751)+~P1(f789(x80753,x80752))+E(f789(f789(f89(a1),f789(f789(f90(a1),x80751),f797(x80751,x80752,x80753))),f796(x80751,x80752,x80753)),x80752)+~P1(f789(x80753,f795(x80751,x80752,x80753)))
% 21.40/21.38 [8076]P140(x80763,x80762,x80761)+~P1(f789(x80763,x80762))+E(f789(f789(f89(a1),f789(f789(f90(a1),x80761),f798(x80761,x80762,x80763))),f795(x80761,x80762,x80763)),x80762)+~P1(f789(x80763,f796(x80761,x80762,x80763)))
% 21.40/21.38 [8088]P141(x80883,x80882,x80881)+E(f789(f789(f89(a1),f789(f789(f90(a1),x80881),f800(x80881,x80882,x80883))),f799(x80881,x80882,x80883)),x80882)+~P1(f789(x80883,f802(x80881,x80882,x80883)))+~P1(f789(x80883,f2(a1)))
% 21.40/21.38 [8089]P141(x80893,x80892,x80891)+E(f789(f789(f89(a1),f789(f789(f90(a1),x80891),f802(x80891,x80892,x80893))),f801(x80891,x80892,x80893)),x80892)+~P1(f789(x80893,f800(x80891,x80892,x80893)))+~P1(f789(x80893,f2(a1)))
% 21.40/21.38 [8186]P140(x81863,x81862,x81861)+E(x81861,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x81861),f797(x81861,x81862,x81863))),f796(x81861,x81862,x81863)),x81862)+P1(f789(f789(f240(a1),f795(x81861,x81862,x81863)),f2(a1)))
% 21.40/21.38 [8187]P141(x81873,x81872,x81871)+E(x81871,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x81871),f800(x81871,x81872,x81873))),f799(x81871,x81872,x81873)),x81872)+P1(f789(f789(f240(a1),f801(x81871,x81872,x81873)),f2(a1)))
% 21.40/21.38 [8225]P140(x82253,x82252,x82251)+~P1(f789(x82253,x82252))+E(f789(f789(f89(a1),f789(f789(f90(a1),x82251),f797(x82251,x82252,x82253))),f796(x82251,x82252,x82253)),x82252)+P1(f789(f789(f240(a1),f795(x82251,x82252,x82253)),f2(a1)))
% 21.40/21.38 [8230]P141(x82303,x82302,x82301)+E(f789(f789(f89(a1),f789(f789(f90(a1),x82301),f800(x82301,x82302,x82303))),f799(x82301,x82302,x82303)),x82302)+~P1(f789(x82303,f2(a1)))+P1(f789(f789(f240(a1),f801(x82301,x82302,x82303)),f2(a1)))
% 21.40/21.38 [8362]P140(x83623,x83622,x83621)+E(x83621,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x83621),f798(x83621,x83622,x83623))),f795(x83621,x83622,x83623)),x83622)+E(f789(f789(f89(a1),f789(f789(f90(a1),x83621),f797(x83621,x83622,x83623))),f796(x83621,x83622,x83623)),x83622)
% 21.40/21.38 [8363]P141(x83633,x83632,x83631)+E(x83631,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x83631),f802(x83631,x83632,x83633))),f801(x83631,x83632,x83633)),x83632)+E(f789(f789(f89(a1),f789(f789(f90(a1),x83631),f800(x83631,x83632,x83633))),f799(x83631,x83632,x83633)),x83632)
% 21.40/21.38 [8386]P140(x83863,x83862,x83861)+~P1(f789(x83863,x83862))+E(f789(f789(f89(a1),f789(f789(f90(a1),x83861),f798(x83861,x83862,x83863))),f795(x83861,x83862,x83863)),x83862)+E(f789(f789(f89(a1),f789(f789(f90(a1),x83861),f797(x83861,x83862,x83863))),f796(x83861,x83862,x83863)),x83862)
% 21.40/21.38 [8398]P141(x83983,x83982,x83981)+E(f789(f789(f89(a1),f789(f789(f90(a1),x83981),f802(x83981,x83982,x83983))),f801(x83981,x83982,x83983)),x83982)+E(f789(f789(f89(a1),f789(f789(f90(a1),x83981),f800(x83981,x83982,x83983))),f799(x83981,x83982,x83983)),x83982)+~P1(f789(x83983,f2(a1)))
% 21.40/21.38 [8992]~P118(x89921)+~E(x89923,f2(x89921))+~E(x89922,f2(x89921))+P1(f789(f789(f240(x89921),f789(f789(f89(x89921),f789(f789(f90(x89921),x89922),x89922)),f789(f789(f90(x89921),x89923),x89923))),f2(x89921)))
% 21.40/21.38 [10007]~P110(x100071)+~E(x100073,f2(x100071))+~E(x100072,f2(x100071))+P1(f789(f789(f240(x100071),f789(f789(f89(x100071),f789(f789(f250(x100071),x100072),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x100071),x100073),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))),f2(x100071)))
% 21.40/21.38 [4756]~E(x47563,x47561)+~P113(x47562)+E(x47561,f2(x47562))+E(f789(f789(f291(x47562),x47563),x47561),f87(x47562))
% 21.40/21.38 [4807]~P92(x48071)+~E(x48073,f184(x48071))+~E(x48072,f184(x48071))+E(f789(f789(f110(x48071),x48072),x48073),f184(x48071))
% 21.40/21.38 [4808]~P97(x48081)+~E(x48083,f247(x48081))+~E(x48082,f247(x48081))+E(f789(f789(f111(x48081),x48082),x48083),f247(x48081))
% 21.40/21.38 [4893]~P113(x48933)+E(x48931,x48932)+E(x48932,f2(x48933))+~E(f789(f789(f291(x48933),x48931),x48932),f87(x48933))
% 21.40/21.38 [4909]~P122(x49092)+E(x49091,f2(x49092))+E(x49093,f2(x49092))+~E(f789(f789(f90(x49092),x49093),x49091),f2(x49092))
% 21.40/21.38 [4910]~P122(x49102)+E(x49101,f2(x49102))+E(x49103,f2(x49102))+~E(f789(f789(f90(x49102),x49103),x49101),f2(x49102))
% 21.40/21.38 [4911]~P133(x49112)+E(x49111,f2(x49112))+E(x49113,f2(x49112))+~E(f789(f789(f90(x49112),x49113),x49111),f2(x49112))
% 21.40/21.38 [5278]~P111(x52783)+E(x52781,x52782)+E(x52781,f789(f88(x52783),x52782))+~E(f789(f789(f90(x52783),x52781),x52781),f789(f789(f90(x52783),x52782),x52782))
% 21.40/21.38 [5314]~P90(x53141)+E(f789(f88(x53141),x53142),x53143)+~E(f789(f789(f110(x53141),x53142),x53143),f247(x53141))+~E(f789(f789(f111(x53141),x53142),x53143),f184(x53141))
% 21.40/21.38 [5390]~P110(x53903)+E(x53901,x53902)+P1(f789(f789(f241(x53903),x53902),x53901))+P1(f789(f789(f241(x53903),x53901),x53902))
% 21.40/21.38 [5391]~P101(x53913)+E(x53911,x53912)+P1(f789(f789(f241(x53913),x53912),x53911))+P1(f789(f789(f241(x53913),x53911),x53912))
% 21.40/21.38 [5392]~P101(x53923)+E(x53921,x53922)+P1(f789(f789(f241(x53923),x53922),x53921))+P1(f789(f789(f241(x53923),x53921),x53922))
% 21.40/21.38 [5393]~P101(x53933)+E(x53931,x53932)+P1(f789(f789(f241(x53933),x53932),x53931))+P1(f789(f789(f241(x53933),x53931),x53932))
% 21.40/21.38 [5394]~P101(x53943)+E(x53941,x53942)+P1(f789(f789(f241(x53943),x53942),x53941))+P1(f789(f789(f241(x53943),x53941),x53942))
% 21.40/21.38 [5395]~P101(x53953)+E(x53951,x53952)+P1(f789(f789(f241(x53953),x53952),x53951))+P1(f789(f789(f241(x53953),x53951),x53952))
% 21.40/21.38 [5396]~P101(x53963)+E(x53961,x53962)+P1(f789(f789(f241(x53963),x53962),x53961))+P1(f789(f789(f241(x53963),x53961),x53962))
% 21.40/21.38 [5397]~E(x53972,x53973)+~P101(x53971)+P1(f789(f789(f240(x53971),x53972),x53973))+P1(f789(f789(f241(x53971),x53972),x53973))
% 21.40/21.38 [5559]P140(x55592,x55593,x55591)+E(x55591,f2(a1))+P1(f789(f789(f241(a1),x55591),f2(a1)))+P1(f789(f789(f241(a1),f2(a1)),x55591))
% 21.40/21.38 [5560]P141(x55602,x55603,x55601)+E(x55601,f2(a1))+P1(f789(f789(f241(a1),x55601),f2(a1)))+P1(f789(f789(f241(a1),f2(a1)),x55601))
% 21.40/21.38 [5585]E(x55851,x55852)+P1(f789(f789(x55853,x55851),x55852))+P1(f789(f789(f241(a863),x55852),x55851))+P1(f789(f789(f241(a863),x55851),x55852))
% 21.40/21.38 [5644]~P99(x56443)+E(x56441,x56442)+~P1(f789(f789(f240(x56443),x56442),x56441))+P1(f789(f789(f241(x56443),x56442),x56441))
% 21.40/21.38 [5645]~P99(x56453)+E(x56451,x56452)+~P1(f789(f789(f240(x56453),x56451),x56452))+P1(f789(f789(f241(x56453),x56451),x56452))
% 21.40/21.38 [5646]~P99(x56463)+E(x56461,x56462)+~P1(f789(f789(f240(x56463),x56461),x56462))+P1(f789(f789(f241(x56463),x56461),x56462))
% 21.40/21.38 [5647]~P99(x56473)+E(x56471,x56472)+~P1(f789(f789(f240(x56473),x56471),x56472))+P1(f789(f789(f241(x56473),x56471),x56472))
% 21.40/21.38 [5648]~P99(x56483)+E(x56481,x56482)+~P1(f789(f789(f240(x56483),x56481),x56482))+P1(f789(f789(f241(x56483),x56481),x56482))
% 21.40/21.38 [5649]~P99(x56493)+E(x56491,x56492)+~P1(f789(f789(f240(x56493),x56491),x56492))+P1(f789(f789(f241(x56493),x56491),x56492))
% 21.40/21.38 [5650]~P99(x56503)+E(x56501,x56502)+~P1(f789(f789(f240(x56503),x56501),x56502))+P1(f789(f789(f241(x56503),x56501),x56502))
% 21.40/21.38 [5651]~P101(x56513)+E(x56511,x56512)+~P1(f789(f789(f240(x56513),x56511),x56512))+P1(f789(f789(f241(x56513),x56511),x56512))
% 21.40/21.38 [5652]~P101(x56523)+E(x56521,x56522)+~P1(f789(f789(f240(x56523),x56521),x56522))+P1(f789(f789(f241(x56523),x56521),x56522))
% 21.40/21.38 [5764]P140(x57641,x57642,x57643)+~P1(f789(x57641,x57642))+P1(f789(f789(f241(a1),x57643),f2(a1)))+P1(f789(f789(f241(a1),f2(a1)),x57643))
% 21.40/21.38 [5815]P141(x58151,x58152,x58153)+~P1(f789(x58151,f2(a1)))+P1(f789(f789(f241(a1),x58153),f2(a1)))+P1(f789(f789(f241(a1),f2(a1)),x58153))
% 21.40/21.38 [5819]~P95(x58191)+E(f789(f789(f110(x58191),x58192),f12(x58191,x58193)),x58192)+~P1(f789(f70(x58191),x58193))+~P1(f789(f789(f342(x58191),x58192),x58193))
% 21.40/21.38 [5820]~P95(x58201)+E(f789(f789(f111(x58201),x58202),f15(x58201,x58203)),x58202)+~P1(f789(f70(x58201),x58203))+~P1(f789(f789(f342(x58201),x58202),x58203))
% 21.40/21.38 [5852]~P101(x58521)+E(f789(f789(f244(x58521),x58522),f17(x58521,x58523)),f17(x58521,x58523))+~P1(f789(f70(x58521),x58523))+~P1(f789(f789(f342(x58521),x58522),x58523))
% 21.40/21.38 [5853]~P101(x58531)+E(f789(f789(f239(x58531),x58532),f16(x58531,x58533)),f16(x58531,x58533))+~P1(f789(f70(x58531),x58533))+~P1(f789(f789(f342(x58531),x58532),x58533))
% 21.40/21.38 [5854]~P95(x58541)+E(f789(f789(f110(x58541),x58542),f15(x58541,x58543)),f15(x58541,x58543))+~P1(f789(f70(x58541),x58543))+~P1(f789(f789(f342(x58541),x58542),x58543))
% 21.40/21.38 [5855]~P95(x58551)+E(f789(f789(f111(x58551),x58552),f12(x58551,x58553)),f12(x58551,x58553))+~P1(f789(f70(x58551),x58553))+~P1(f789(f789(f342(x58551),x58552),x58553))
% 21.40/21.38 [5892]E(x58921,x58922)+~P99(x58923)+~P1(f789(f789(f240(x58923),x58922),x58921))+~P1(f789(f789(f240(x58923),x58921),x58922))
% 21.40/21.38 [5893]E(x58931,x58932)+~P99(x58933)+~P1(f789(f789(f240(x58933),x58932),x58931))+~P1(f789(f789(f240(x58933),x58931),x58932))
% 21.40/21.38 [5894]E(x58941,x58942)+~P99(x58943)+~P1(f789(f789(f240(x58943),x58942),x58941))+~P1(f789(f789(f240(x58943),x58941),x58942))
% 21.40/21.38 [5895]E(x58951,x58952)+~P99(x58953)+~P1(f789(f789(f240(x58953),x58952),x58951))+~P1(f789(f789(f240(x58953),x58951),x58952))
% 21.40/21.38 [5897]~E(x58971,x58972)+~P101(x58973)+~P1(f789(f789(f241(x58973),x58971),x58972))+~P1(f789(f789(f240(x58973),x58971),x58972))
% 21.40/21.38 [6038]~P105(x60381)+P1(f789(f789(f240(x60381),x60383),x60382))+~P1(f789(f789(f240(x60381),x60382),x60383))+P1(f789(f789(f241(x60381),x60382),x60383))
% 21.40/21.38 [6063]~P101(x60631)+~P1(f789(f70(x60631),x60633))+P1(f789(f789(f240(x60631),x60632),f16(x60631,x60633)))+~P1(f789(f789(f342(x60631),x60632),x60633))
% 21.40/21.38 [6115]~P101(x61151)+E(f789(f789(f244(x61151),x61152),f13(x61151,f239(x61151),x61153)),x61152)+~P1(f789(f70(x61151),x61153))+~P1(f789(f789(f342(x61151),x61152),x61153))
% 21.40/21.38 [6116]~P101(x61161)+E(f789(f789(f239(x61161),x61162),f14(x61161,f244(x61161),x61163)),x61162)+~P1(f789(f70(x61161),x61163))+~P1(f789(f789(f342(x61161),x61162),x61163))
% 21.40/21.38 [6255]E(x62551,x62552)+~E(f789(f789(f3(a863),x62551),x62553),f789(f789(f3(a863),x62552),x62553))+~P1(f789(f789(f240(a863),x62553),x62551))+~P1(f789(f789(f240(a863),x62553),x62552))
% 21.40/21.38 [6282]~P101(x62821)+~P1(f789(f70(x62821),x62822))+~P1(f789(f789(f342(x62821),x62823),x62822))+P1(f789(f789(f240(x62821),f17(x62821,x62822)),x62823))
% 21.40/21.38 [6326]E(x63261,f2(a863))+~P1(f789(f62(x63263,x63261),x63262))+P1(f789(f789(f241(a863),f2(a863)),x63261))+P1(f789(f789(f241(a863),x63261),f789(f258(a863,a863),x63262)))
% 21.40/21.38 [6349]P140(x63492,x63493,x63491)+E(x63491,f2(a1))+P1(f789(f789(f241(a1),x63491),f795(x63491,x63493,x63492)))+P1(f789(f789(f241(a1),f2(a1)),x63491))
% 21.40/21.38 [6350]P141(x63502,x63503,x63501)+E(x63501,f2(a1))+P1(f789(f789(f241(a1),x63501),f801(x63501,x63503,x63502)))+P1(f789(f789(f241(a1),f2(a1)),x63501))
% 21.40/21.38 [6351]~P101(x63511)+E(f789(f789(f244(x63511),x63512),f14(x63511,f244(x63511),x63513)),f14(x63511,f244(x63511),x63513))+~P1(f789(f70(x63511),x63513))+~P1(f789(f789(f342(x63511),x63512),x63513))
% 21.40/21.38 [6352]~P101(x63521)+E(f789(f789(f239(x63521),x63522),f13(x63521,f239(x63521),x63523)),f13(x63521,f239(x63521),x63523))+~P1(f789(f70(x63521),x63523))+~P1(f789(f789(f342(x63521),x63522),x63523))
% 21.40/21.38 [6359]~P1(f789(x63591,x63592))+P1(f789(x63591,f833(x63592,x63591,x63593)))+P1(f789(x63591,f2(a863)))+~P1(f789(f789(f241(a863),x63592),x63593))
% 21.40/21.38 [6397]~P1(f789(f789(f287(a863),x63972),x63971))+~P1(f789(f789(f287(a863),x63971),x63973))+P1(f789(f789(f287(a863),x63971),x63972))+P1(f789(f789(f287(a863),x63972),x63973))
% 21.40/21.38 [6398]~P1(f789(f789(f287(a863),x63983),x63982))+~P1(f789(f789(f287(a863),x63982),x63981))+P1(f789(f789(f287(a863),x63981),x63982))+P1(f789(f789(f287(a863),x63983),x63981))
% 21.40/21.38 [6418]~P1(f789(x64181,x64182))+~P1(f789(f70(x64183),x64182))+P1(f789(x64181,f458(x64181,x64182,x64183)))+P1(f789(x64181,f184(f870(x64183,a856))))
% 21.40/21.38 [6433]~P110(x64331)+~P88(x64331)+P1(f789(f789(f241(x64331),f789(f113(x64331),x64332)),f789(f113(x64331),x64333)))+~P1(f789(f789(f241(a1),x64332),x64333))
% 21.40/21.38 [6434]~P110(x64341)+~P88(x64341)+P1(f789(f789(f240(x64341),f789(f113(x64341),x64342)),f789(f113(x64341),x64343)))+~P1(f789(f789(f240(a1),x64342),x64343))
% 21.40/21.38 [6437]~P1(f789(x64371,x64373))+~P1(f789(f70(x64372),x64373))+P1(f789(f70(x64372),f458(x64371,x64373,x64372)))+P1(f789(x64371,f184(f870(x64372,a856))))
% 21.40/21.38 [6470]P140(x64701,x64702,x64703)+~P1(f789(x64701,x64702))+P1(f789(f789(f241(a1),x64703),f795(x64703,x64702,x64701)))+P1(f789(f789(f241(a1),f2(a1)),x64703))
% 21.40/21.38 [6510]P141(x65101,x65102,x65103)+P1(f789(f789(f241(a1),x65103),f801(x65103,x65102,x65101)))+~P1(f789(x65101,f2(a1)))+P1(f789(f789(f241(a1),f2(a1)),x65103))
% 21.40/21.38 [6537]~P100(x65371)+~P89(x65371)+E(f789(f789(f244(x65371),f789(f113(x65371),x65372)),f789(f113(x65371),x65373)),f789(f113(x65371),x65373))+P1(f789(f789(f240(x65371),f789(f113(x65371),x65372)),f789(f113(x65371),x65373)))
% 21.40/21.38 [6538]~P100(x65381)+~P89(x65381)+E(f789(f789(f239(x65381),f789(f113(x65381),x65382)),f789(f113(x65381),x65383)),f789(f113(x65381),x65382))+P1(f789(f789(f240(x65381),f789(f113(x65381),x65382)),f789(f113(x65381),x65383)))
% 21.40/21.38 [6545]E(x65451,f2(a863))+~P1(f789(f62(x65453,x65451),x65452))+~P1(f789(f789(f241(a863),f2(a863)),x65451))+P1(f789(f789(f240(a863),f2(a863)),f789(f258(a863,a863),x65452)))
% 21.40/21.38 [6551]~P1(f789(f789(f287(a863),x65511),x65513))+~P1(f789(f789(f287(a863),x65512),x65511))+~P1(f789(f789(f287(a863),x65513),x65512))+P1(f789(f789(f287(a863),x65511),x65512))
% 21.40/21.38 [6552]~P1(f789(f789(f287(a863),x65521),x65523))+~P1(f789(f789(f287(a863),x65522),x65521))+P1(f789(f789(f287(a863),x65521),x65522))+~P1(f789(f789(f287(a863),x65523),x65522))
% 21.40/21.38 [6600]P140(x66002,x66003,x66001)+E(x66001,f2(a1))+~P1(f789(x66002,f795(x66001,x66003,x66002)))+P1(f789(f789(f241(a1),f2(a1)),x66001))
% 21.40/21.38 [6601]P141(x66012,x66013,x66011)+E(x66011,f2(a1))+~P1(f789(x66012,f802(x66011,x66013,x66012)))+P1(f789(f789(f241(a1),f2(a1)),x66011))
% 21.40/21.38 [6621]~P7(x66211)+~P89(x66211)+~E(f59(x66211,f789(f113(x66211),x66213),f789(f113(x66211),x66212)),f2(x66211))+P1(f789(f789(f287(x66211),f789(f113(x66211),x66212)),f789(f113(x66211),x66213)))
% 21.40/21.38 [6695]P140(x66951,x66952,x66953)+~P1(f789(x66951,x66952))+~P1(f789(x66951,f795(x66953,x66952,x66951)))+P1(f789(f789(f241(a1),f2(a1)),x66953))
% 21.40/21.38 [6725]P141(x67251,x67252,x67253)+~P1(f789(x67251,f802(x67253,x67252,x67251)))+~P1(f789(x67251,f2(a1)))+P1(f789(f789(f241(a1),f2(a1)),x67253))
% 21.40/21.38 [6736]E(x67361,f2(a863))+~P1(f789(f62(x67363,x67361),x67362))+P1(f789(f789(f240(a863),f789(f258(a863,a863),x67362)),f2(a863)))+P1(f789(f789(f241(a863),f2(a863)),x67361))
% 21.40/21.38 [6841]~P88(x68413)+~P110(x68413)+~P1(f789(f789(f241(x68413),f789(f113(x68413),x68411)),f789(f113(x68413),x68412)))+P1(f789(f789(f241(a1),x68411),x68412))
% 21.40/21.38 [6842]~P88(x68423)+~P110(x68423)+~P1(f789(f789(f240(x68423),f789(f113(x68423),x68421)),f789(f113(x68423),x68422)))+P1(f789(f789(f240(a1),x68421),x68422))
% 21.40/21.38 [6871]~P101(x68711)+~P18(x68711,x68713)+P18(x68711,f789(f789(f146(x68711),x68712),x68713))+~P1(f789(f789(f240(x68711),x68712),f778(x68713,x68712,x68711)))
% 21.40/21.38 [6872]~P101(x68721)+~P18(x68721,x68723)+P18(x68721,f789(f789(f146(x68721),x68722),x68723))+~P1(f789(f789(f240(x68721),x68722),f779(x68723,x68722,x68721)))
% 21.40/21.38 [6944]~P7(x69441)+~P89(x69441)+E(f59(x69441,f789(f113(x69441),x69442),f789(f113(x69441),x69443)),f2(x69441))+~P1(f789(f789(f287(x69441),f789(f113(x69441),x69443)),f789(f113(x69441),x69442)))
% 21.40/21.38 [6958]P140(x69582,x69583,x69581)+E(x69581,f2(a1))+P1(f789(f789(f241(a1),x69581),f2(a1)))+P1(f789(f789(f241(a1),f796(x69581,x69583,x69582)),x69581))
% 21.40/21.38 [6959]P141(x69592,x69593,x69591)+E(x69591,f2(a1))+P1(f789(f789(f241(a1),x69591),f2(a1)))+P1(f789(f789(f241(a1),f799(x69591,x69593,x69592)),x69591))
% 21.40/21.38 [6964]~P101(x69641)+~P89(x69641)+P1(f789(f789(f241(x69641),f789(f113(x69641),x69642)),f789(f113(x69641),x69643)))+P1(f789(f789(f240(x69641),f789(f113(x69641),x69643)),f789(f113(x69641),x69642)))
% 21.40/21.38 [6998]P140(x69982,x69983,x69981)+E(x69981,f2(a1))+P1(f789(f789(f240(a1),f795(x69981,x69983,x69982)),f2(a1)))+P1(f789(f789(f241(a1),f2(a1)),x69981))
% 21.40/21.38 [6999]P141(x69992,x69993,x69991)+E(x69991,f2(a1))+P1(f789(f789(f240(a1),f801(x69991,x69993,x69992)),f2(a1)))+P1(f789(f789(f241(a1),f2(a1)),x69991))
% 21.40/21.38 [7017]~P101(x70171)+~P18(x70171,x70173)+E(f789(f789(f144(x70171,x70171,f7(x70171)),x70172),f158(x70171,x70172,x70173)),x70173)+~P1(f789(f789(f342(x70171),x70172),f789(f163(x70171),x70173)))
% 21.40/21.38 [7068]P140(x70681,x70682,x70683)+~P1(f789(x70681,x70682))+P1(f789(f789(f241(a1),x70683),f2(a1)))+P1(f789(f789(f241(a1),f796(x70683,x70682,x70681)),x70683))
% 21.40/21.38 [7074]~P100(x70741)+~P89(x70741)+E(f789(f789(f244(x70741),f789(f113(x70741),x70742)),f789(f113(x70741),x70743)),f789(f113(x70741),x70742))+~P1(f789(f789(f240(x70741),f789(f113(x70741),x70742)),f789(f113(x70741),x70743)))
% 21.40/21.38 [7075]~P100(x70751)+~P89(x70751)+E(f789(f789(f239(x70751),f789(f113(x70751),x70752)),f789(f113(x70751),x70753)),f789(f113(x70751),x70753))+~P1(f789(f789(f240(x70751),f789(f113(x70751),x70752)),f789(f113(x70751),x70753)))
% 21.40/21.38 [7088]P141(x70881,x70882,x70883)+~P1(f789(x70881,f2(a1)))+P1(f789(f789(f241(a1),x70883),f2(a1)))+P1(f789(f789(f241(a1),f799(x70883,x70882,x70881)),x70883))
% 21.40/21.38 [7097]P140(x70971,x70972,x70973)+~P1(f789(x70971,x70972))+P1(f789(f789(f240(a1),f795(x70973,x70972,x70971)),f2(a1)))+P1(f789(f789(f241(a1),f2(a1)),x70973))
% 21.40/21.38 [7121]P141(x71211,x71212,x71213)+~P1(f789(x71211,f2(a1)))+P1(f789(f789(f240(a1),f801(x71213,x71212,x71211)),f2(a1)))+P1(f789(f789(f241(a1),f2(a1)),x71213))
% 21.40/21.38 [7148]~P1(f789(x71481,x71482))+P1(f789(x71481,f2(a863)))+~P1(f789(f789(f241(a863),x71482),x71483))+P1(f789(f789(f241(a863),f833(x71482,x71481,x71483)),x71483))
% 21.40/21.38 [7165]~P101(x71651)+~P18(x71651,x71653)+P18(x71651,f789(f789(f146(x71651),x71652),x71653))+P1(f789(f789(f342(x71651),f778(x71653,x71652,x71651)),f789(f163(x71651),x71653)))
% 21.40/21.38 [7166]~P101(x71661)+~P18(x71661,x71663)+P18(x71661,f789(f789(f146(x71661),x71662),x71663))+P1(f789(f789(f342(x71661),f779(x71663,x71662,x71661)),f789(f163(x71661),x71663)))
% 21.40/21.38 [7288]~P101(x72881)+~P9(x72881)+~P1(f789(f789(f241(x72881),x72883),f51(x72881,x72882)))+P1(f789(f789(f342(x72881),f667(x72882,x72883,x72881)),x72882))
% 21.40/21.38 [7457]~P101(x74571)+~P9(x74571)+~P1(f789(f789(f241(x74571),f52(x74571,x74573)),x74572))+P1(f789(f789(f342(x74571),f669(x74572,x74573,x74571)),x74573))
% 21.40/21.38 [7458]~P101(x74581)+~P9(x74581)+~P1(f789(f789(f241(x74581),f52(x74581,x74583)),x74582))+P1(f789(f789(f241(x74581),f669(x74582,x74583,x74581)),x74582))
% 21.40/21.38 [7472]P140(x74722,x74723,x74721)+E(x74721,f2(a1))+P1(f789(f789(f241(a1),x74721),f795(x74721,x74723,x74722)))+P1(f789(f789(f241(a1),f796(x74721,x74723,x74722)),x74721))
% 21.40/21.38 [7473]P141(x74732,x74733,x74731)+E(x74731,f2(a1))+P1(f789(f789(f241(a1),x74731),f801(x74731,x74733,x74732)))+P1(f789(f789(f241(a1),f799(x74731,x74733,x74732)),x74731))
% 21.40/21.38 [7569]P140(x75693,x75692,x75691)+E(x75691,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x75691),f798(x75691,x75692,x75693))),f795(x75691,x75692,x75693)),x75692)+P1(f789(f789(f241(a1),f2(a1)),x75691))
% 21.40/21.38 [7570]P141(x75703,x75702,x75701)+E(x75701,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x75701),f802(x75701,x75702,x75703))),f801(x75701,x75702,x75703)),x75702)+P1(f789(f789(f241(a1),f2(a1)),x75701))
% 21.40/21.38 [7571]~P124(x75711)+~P1(f789(f789(f241(x75711),x75712),f2(x75711)))+P1(f789(f789(f241(x75711),f789(f789(f90(x75711),x75712),x75713)),f2(x75711)))+~P1(f789(f789(f241(x75711),f2(x75711)),x75713))
% 21.40/21.38 [7572]~P124(x75721)+~P1(f789(f789(f241(x75721),x75723),f2(x75721)))+P1(f789(f789(f241(x75721),f789(f789(f90(x75721),x75722),x75723)),f2(x75721)))+~P1(f789(f789(f241(x75721),f2(x75721)),x75722))
% 21.40/21.38 [7573]~P124(x75731)+~P1(f789(f789(f241(x75731),x75732),f2(x75731)))+P1(f789(f789(f241(x75731),f789(f789(f90(x75731),x75732),x75733)),f2(x75731)))+~P1(f789(f789(f241(x75731),f2(x75731)),x75733))
% 21.40/21.38 [7574]~P62(x75741)+~P1(f789(f789(f241(x75741),x75743),f2(x75741)))+P1(f789(f789(f241(x75741),f789(f789(f291(x75741),x75742),x75743)),f2(x75741)))+~P1(f789(f789(f241(x75741),f2(x75741)),x75742))
% 21.40/21.38 [7575]~P62(x75751)+~P1(f789(f789(f241(x75751),x75752),f2(x75751)))+P1(f789(f789(f241(x75751),f789(f789(f291(x75751),x75752),x75753)),f2(x75751)))+~P1(f789(f789(f241(x75751),f2(x75751)),x75753))
% 21.40/21.38 [7576]~P63(x75761)+~P1(f789(f789(f241(x75761),x75763),f2(x75761)))+P1(f789(f789(f241(x75761),f789(f789(f291(x75761),x75762),x75763)),f2(x75761)))+~P1(f789(f789(f241(x75761),f2(x75761)),x75762))
% 21.40/21.38 [7577]~P63(x75771)+~P1(f789(f789(f241(x75771),x75772),f2(x75771)))+P1(f789(f789(f241(x75771),f789(f789(f291(x75771),x75772),x75773)),f2(x75771)))+~P1(f789(f789(f241(x75771),f2(x75771)),x75773))
% 21.40/21.38 [7578]~P128(x75781)+~P1(f789(f789(f240(x75781),x75782),f2(x75781)))+P1(f789(f789(f240(x75781),f789(f789(f90(x75781),x75782),x75783)),f2(x75781)))+~P1(f789(f789(f240(x75781),f2(x75781)),x75783))
% 21.40/21.38 [7579]~P118(x75791)+~P1(f789(f789(f240(x75791),x75793),f2(x75791)))+P1(f789(f789(f240(x75791),f789(f789(f90(x75791),x75792),x75793)),f2(x75791)))+~P1(f789(f789(f240(x75791),f2(x75791)),x75792))
% 21.40/21.38 [7580]~P118(x75801)+~P1(f789(f789(f240(x75801),x75802),f2(x75801)))+P1(f789(f789(f240(x75801),f789(f789(f90(x75801),x75802),x75803)),f2(x75801)))+~P1(f789(f789(f240(x75801),f2(x75801)),x75803))
% 21.40/21.38 [7581]~P128(x75811)+~P1(f789(f789(f240(x75811),x75813),f2(x75811)))+P1(f789(f789(f240(x75811),f789(f789(f90(x75811),x75812),x75813)),f2(x75811)))+~P1(f789(f789(f240(x75811),f2(x75811)),x75812))
% 21.40/21.38 [7582]~P128(x75821)+~P1(f789(f789(f240(x75821),x75823),f2(x75821)))+P1(f789(f789(f240(x75821),f789(f789(f90(x75821),x75822),x75823)),f2(x75821)))+~P1(f789(f789(f240(x75821),f2(x75821)),x75822))
% 21.40/21.38 [7583]~P128(x75831)+~P1(f789(f789(f240(x75831),x75832),f2(x75831)))+P1(f789(f789(f240(x75831),f789(f789(f90(x75831),x75832),x75833)),f2(x75831)))+~P1(f789(f789(f240(x75831),f2(x75831)),x75833))
% 21.40/21.38 [7584]~P128(x75841)+~P1(f789(f789(f240(x75841),x75842),f2(x75841)))+P1(f789(f789(f240(x75841),f789(f789(f90(x75841),x75842),x75843)),f2(x75841)))+~P1(f789(f789(f240(x75841),f2(x75841)),x75843))
% 21.40/21.38 [7585]~P62(x75851)+~P1(f789(f789(f240(x75851),x75853),f2(x75851)))+P1(f789(f789(f240(x75851),f789(f789(f291(x75851),x75852),x75853)),f2(x75851)))+~P1(f789(f789(f240(x75851),f2(x75851)),x75852))
% 21.40/21.38 [7586]~P62(x75861)+~P1(f789(f789(f240(x75861),x75862),f2(x75861)))+P1(f789(f789(f240(x75861),f789(f789(f291(x75861),x75862),x75863)),f2(x75861)))+~P1(f789(f789(f240(x75861),f2(x75861)),x75863))
% 21.40/21.38 [7587]~P63(x75871)+~P1(f789(f789(f241(x75871),x75873),f2(x75871)))+P1(f789(f789(f240(x75871),f789(f789(f291(x75871),x75872),x75873)),f2(x75871)))+~P1(f789(f789(f240(x75871),f2(x75871)),x75872))
% 21.40/21.38 [7588]~P63(x75881)+~P1(f789(f789(f240(x75881),x75882),f2(x75881)))+P1(f789(f789(f240(x75881),f789(f789(f291(x75881),x75882),x75883)),f2(x75881)))+~P1(f789(f789(f241(x75881),f2(x75881)),x75883))
% 21.40/21.38 [7604]P140(x76041,x76042,x76043)+~P1(f789(x76041,x76042))+P1(f789(f789(f241(a1),x76043),f795(x76043,x76042,x76041)))+P1(f789(f789(f241(a1),f796(x76043,x76042,x76041)),x76043))
% 21.40/21.38 [7617]P141(x76171,x76172,x76173)+P1(f789(f789(f241(a1),x76173),f801(x76173,x76172,x76171)))+~P1(f789(x76171,f2(a1)))+P1(f789(f789(f241(a1),f799(x76173,x76172,x76171)),x76173))
% 21.40/21.38 [7669]P140(x76692,x76693,x76691)+E(x76691,f2(a1))+~P1(f789(x76692,f795(x76691,x76693,x76692)))+P1(f789(f789(f241(a1),f796(x76691,x76693,x76692)),x76691))
% 21.40/21.38 [7670]P141(x76702,x76703,x76701)+E(x76701,f2(a1))+~P1(f789(x76702,f802(x76701,x76703,x76702)))+P1(f789(f789(f241(a1),f799(x76701,x76703,x76702)),x76701))
% 21.40/21.38 [7679]P140(x76793,x76792,x76791)+~P1(f789(x76793,x76792))+E(f789(f789(f89(a1),f789(f789(f90(a1),x76791),f798(x76791,x76792,x76793))),f795(x76791,x76792,x76793)),x76792)+P1(f789(f789(f241(a1),f2(a1)),x76791))
% 21.40/21.38 [7697]P141(x76973,x76972,x76971)+E(f789(f789(f89(a1),f789(f789(f90(a1),x76971),f802(x76971,x76972,x76973))),f801(x76971,x76972,x76973)),x76972)+~P1(f789(x76973,f2(a1)))+P1(f789(f789(f241(a1),f2(a1)),x76971))
% 21.40/21.38 [7720]~P1(f789(x77201,x77203))+~P1(f789(f70(x77202),x77203))+P1(f789(f789(f342(x77202),f459(x77201,x77203,x77202)),f458(x77201,x77203,x77202)))+P1(f789(x77201,f184(f870(x77202,a856))))
% 21.40/21.38 [7730]P140(x77301,x77302,x77303)+~P1(f789(x77301,x77302))+~P1(f789(x77301,f795(x77303,x77302,x77301)))+P1(f789(f789(f241(a1),f796(x77303,x77302,x77301)),x77303))
% 21.40/21.38 [7736]P141(x77361,x77362,x77363)+~P1(f789(x77361,f802(x77363,x77362,x77361)))+~P1(f789(x77361,f2(a1)))+P1(f789(f789(f241(a1),f799(x77363,x77362,x77361)),x77363))
% 21.40/21.38 [7808]~P89(x78081)+~P101(x78081)+~P1(f789(f789(f241(x78081),f789(f113(x78081),x78082)),f789(f113(x78081),x78083)))+~P1(f789(f789(f240(x78081),f789(f113(x78081),x78083)),f789(f113(x78081),x78082)))
% 21.40/21.38 [7844]~P62(x78441)+~P1(f789(f789(f241(x78441),f789(f789(f291(x78441),x78443),x78442)),f2(x78441)))+P1(f789(f789(f241(x78441),x78442),f2(x78441)))+P1(f789(f789(f241(x78441),f2(x78441)),x78442))
% 21.40/21.38 [7845]~P62(x78451)+~P1(f789(f789(f241(x78451),f789(f789(f291(x78451),x78452),x78453)),f2(x78451)))+P1(f789(f789(f241(x78451),x78452),f2(x78451)))+P1(f789(f789(f241(x78451),f2(x78451)),x78452))
% 21.40/21.38 [7846]~P118(x78461)+~P1(f789(f789(f240(x78461),f789(f789(f90(x78461),x78463),x78462)),f2(x78461)))+P1(f789(f789(f240(x78461),x78462),f2(x78461)))+P1(f789(f789(f240(x78461),f2(x78461)),x78462))
% 21.40/21.38 [7847]~P118(x78471)+~P1(f789(f789(f240(x78471),f789(f789(f90(x78471),x78472),x78473)),f2(x78471)))+P1(f789(f789(f240(x78471),x78472),f2(x78471)))+P1(f789(f789(f240(x78471),f2(x78471)),x78472))
% 21.40/21.38 [7848]~P62(x78481)+~P1(f789(f789(f240(x78481),f789(f789(f291(x78481),x78483),x78482)),f2(x78481)))+P1(f789(f789(f240(x78481),x78482),f2(x78481)))+P1(f789(f789(f240(x78481),f2(x78481)),x78482))
% 21.40/21.38 [7849]~P62(x78491)+~P1(f789(f789(f240(x78491),f789(f789(f291(x78491),x78492),x78493)),f2(x78491)))+P1(f789(f789(f240(x78491),x78492),f2(x78491)))+P1(f789(f789(f240(x78491),f2(x78491)),x78492))
% 21.40/21.38 [7875]~P62(x78751)+~P1(f789(f789(f241(x78751),f789(f789(f291(x78751),x78752),x78753)),f2(x78751)))+P1(f789(f789(f241(x78751),f2(x78751)),x78752))+P1(f789(f789(f241(x78751),f2(x78751)),x78753))
% 21.40/21.38 [7876]~P118(x78761)+~P1(f789(f789(f240(x78761),f789(f789(f90(x78761),x78762),x78763)),f2(x78761)))+P1(f789(f789(f240(x78761),f2(x78761)),x78762))+P1(f789(f789(f240(x78761),f2(x78761)),x78763))
% 21.40/21.38 [7877]~P62(x78771)+~P1(f789(f789(f240(x78771),f789(f789(f291(x78771),x78772),x78773)),f2(x78771)))+P1(f789(f789(f240(x78771),f2(x78771)),x78772))+P1(f789(f789(f240(x78771),f2(x78771)),x78773))
% 21.40/21.38 [7896]P140(x78962,x78963,x78961)+E(x78961,f2(a1))+P1(f789(f789(f240(a1),f795(x78961,x78963,x78962)),f2(a1)))+P1(f789(f789(f241(a1),f796(x78961,x78963,x78962)),x78961))
% 21.40/21.38 [7897]P141(x78972,x78973,x78971)+E(x78971,f2(a1))+P1(f789(f789(f240(a1),f801(x78971,x78973,x78972)),f2(a1)))+P1(f789(f789(f241(a1),f799(x78971,x78973,x78972)),x78971))
% 21.40/21.38 [7903]~P117(x79031)+~P1(f789(f789(f241(x79031),x79032),f87(x79031)))+P1(f789(f789(f241(x79031),f789(f789(f250(x79031),x79032),f789(a121,x79033))),f87(x79031)))+~P1(f789(f789(f241(x79031),f2(x79031)),x79032))
% 21.40/21.38 [7956]~P101(x79561)+~E(x79563,f122(x79561))+~P18(x79561,f789(f149(x79561),x79563))+E(f789(f138(x79561,x79561,f789(f9(x79561,x79561,x79561),f239(x79561)),x79562),f789(f149(x79561),x79563)),x79562)
% 21.40/21.38 [7958]P140(x79581,x79582,x79583)+~P1(f789(x79581,x79582))+P1(f789(f789(f240(a1),f795(x79583,x79582,x79581)),f2(a1)))+P1(f789(f789(f241(a1),f796(x79583,x79582,x79581)),x79583))
% 21.40/21.38 [7969]P141(x79691,x79692,x79693)+~P1(f789(x79691,f2(a1)))+P1(f789(f789(f240(a1),f801(x79693,x79692,x79691)),f2(a1)))+P1(f789(f789(f241(a1),f799(x79693,x79692,x79691)),x79693))
% 21.40/21.38 [8181]P140(x81813,x81812,x81811)+E(x81811,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x81811),f798(x81811,x81812,x81813))),f795(x81811,x81812,x81813)),x81812)+P1(f789(f789(f241(a1),f796(x81811,x81812,x81813)),x81811))
% 21.40/21.38 [8182]P141(x81823,x81822,x81821)+E(x81821,f2(a1))+E(f789(f789(f89(a1),f789(f789(f90(a1),x81821),f802(x81821,x81822,x81823))),f801(x81821,x81822,x81823)),x81822)+P1(f789(f789(f241(a1),f799(x81821,x81822,x81823)),x81821))
% 21.40/21.38 [8217]P140(x82173,x82172,x82171)+~P1(f789(x82173,x82172))+E(f789(f789(f89(a1),f789(f789(f90(a1),x82171),f798(x82171,x82172,x82173))),f795(x82171,x82172,x82173)),x82172)+P1(f789(f789(f241(a1),f796(x82171,x82172,x82173)),x82171))
% 21.40/21.38 [8218]~P4(x82181)+~P69(x82181)+~P38(x82183)+E(f789(f789(f11(a863,x82181),f789(f789(f10(a1,x82181,a863),x82182),f109(a1))),f789(f311(a1,a863,a114),x82183)),f789(f789(f11(a1,x82181),x82182),x82183))
% 21.40/21.38 [8219]~P4(x82191)+~P69(x82191)+~P38(x82193)+E(f789(f789(f8(a863,x82191),f789(f789(f10(a1,x82191,a863),x82192),f109(a1))),f789(f311(a1,a863,a114),x82193)),f789(f789(f8(a1,x82191),x82192),x82193))
% 21.40/21.38 [8227]P141(x82273,x82272,x82271)+E(f789(f789(f89(a1),f789(f789(f90(a1),x82271),f802(x82271,x82272,x82273))),f801(x82271,x82272,x82273)),x82272)+~P1(f789(x82273,f2(a1)))+P1(f789(f789(f241(a1),f799(x82271,x82272,x82273)),x82271))
% 21.40/21.38 [8245]~E(x82452,f2(a863))+~E(f789(f248(a863,a863),x82453),f2(a863))+~E(x82451,f789(f789(f89(a863),f789(f789(f90(a863),f789(f248(a863,a863),x82453)),x82452)),f789(f258(a863,a863),x82453)))+P1(f789(f62(x82451,x82452),x82453))
% 21.40/21.38 [9096]P1(f789(f789(f240(a1),x90961),f2(a1)))+~P1(f789(f789(f241(a1),f789(f789(f89(a1),f789(f789(f90(a1),x90962),x90961)),x90963)),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x90962))+~P1(f789(f789(f240(a1),f2(a1)),x90963))
% 21.40/21.38 [5713]~P95(x57132)+E(x57131,f184(f870(x57132,a856)))+~P1(f789(f70(x57132),x57131))+E(f12(x57132,f789(f789(f310(x57132),x57133),x57131)),f789(f789(f111(x57132),x57133),f12(x57132,x57131)))
% 21.40/21.38 [5714]~P95(x57142)+E(x57141,f184(f870(x57142,a856)))+~P1(f789(f70(x57142),x57141))+E(f15(x57142,f789(f789(f310(x57142),x57143),x57141)),f789(f789(f110(x57142),x57143),f15(x57142,x57141)))
% 21.40/21.38 [5715]~P101(x57152)+E(x57151,f184(f870(x57152,a856)))+~P1(f789(f70(x57152),x57151))+E(f16(x57152,f789(f789(f310(x57152),x57153),x57151)),f789(f789(f239(x57152),x57153),f16(x57152,x57151)))
% 21.40/21.38 [5716]~P101(x57162)+E(x57161,f184(f870(x57162,a856)))+~P1(f789(f70(x57162),x57161))+E(f17(x57162,f789(f789(f310(x57162),x57163),x57161)),f789(f789(f244(x57162),x57163),f17(x57162,x57161)))
% 21.40/21.38 [6035]~P118(x60351)+~E(x60353,f2(x60351))+~E(x60352,f2(x60351))+E(f789(f789(f89(x60351),f789(f789(f90(x60351),x60352),x60352)),f789(f789(f90(x60351),x60353),x60353)),f2(x60351))
% 21.40/21.38 [6109]~P91(x61092)+E(x61091,f184(f870(x61092,a856)))+~P1(f789(f70(x61092),x61091))+E(f789(f72(x61092,f90(x61092)),f789(f789(f310(x61092),x61093),x61091)),f789(f789(f90(x61092),x61093),f789(f72(x61092,f90(x61092)),x61091)))
% 21.40/21.38 [6234]~P101(x62342)+E(x62341,f184(f870(x62342,a856)))+~P1(f789(f70(x62342),x62341))+E(f13(x62342,f239(x62342),f789(f789(f310(x62342),x62343),x62341)),f789(f789(f239(x62342),x62343),f13(x62342,f239(x62342),x62341)))
% 21.40/21.38 [6235]~P101(x62352)+E(x62351,f184(f870(x62352,a856)))+~P1(f789(f70(x62352),x62351))+E(f14(x62352,f244(x62352),f789(f789(f310(x62352),x62353),x62351)),f789(f789(f244(x62352),x62353),f14(x62352,f244(x62352),x62351)))
% 21.40/21.38 [6642]~P95(x66421)+~P1(f789(f70(x66421),x66423))+E(f789(f789(f73(x66421,x66421,f111(x66421)),x66422),x66423),f12(x66421,f789(f789(f310(x66421),x66422),x66423)))+P1(f789(f789(f342(x66421),x66422),x66423))
% 21.40/21.38 [6643]~P95(x66431)+~P1(f789(f70(x66431),x66433))+E(f789(f789(f73(x66431,x66431,f110(x66431)),x66432),x66433),f15(x66431,f789(f789(f310(x66431),x66432),x66433)))+P1(f789(f789(f342(x66431),x66432),x66433))
% 21.40/21.38 [6644]~P101(x66441)+~P1(f789(f70(x66441),x66443))+E(f789(f789(f73(x66441,x66441,f239(x66441)),x66442),x66443),f16(x66441,f789(f789(f310(x66441),x66442),x66443)))+P1(f789(f789(f342(x66441),x66442),x66443))
% 21.40/21.38 [6645]~P101(x66451)+~P1(f789(f70(x66451),x66453))+E(f789(f789(f73(x66451,x66451,f244(x66451)),x66452),x66453),f17(x66451,f789(f789(f310(x66451),x66452),x66453)))+P1(f789(f789(f342(x66451),x66452),x66453))
% 21.40/21.38 [6760]~P66(x67601)+~P1(f789(f70(x67601),x67603))+E(f789(f72(x67601,f90(x67601)),f789(f789(f310(x67601),x67602),x67603)),f789(f789(f73(x67601,x67601,f90(x67601)),x67602),x67603))+P1(f789(f789(f342(x67601),x67602),x67603))
% 21.40/21.38 [6778]~P101(x67781)+~P1(f789(f70(x67781),x67783))+E(f13(x67781,f239(x67781),f789(f789(f310(x67781),x67782),x67783)),f789(f789(f73(x67781,x67781,f239(x67781)),x67782),x67783))+P1(f789(f789(f342(x67781),x67782),x67783))
% 21.40/21.38 [6779]~P101(x67791)+~P1(f789(f70(x67791),x67793))+E(f14(x67791,f244(x67791),f789(f789(f310(x67791),x67792),x67793)),f789(f789(f73(x67791,x67791,f244(x67791)),x67792),x67793))+P1(f789(f789(f342(x67791),x67792),x67793))
% 21.40/21.38 [6846]~E(f789(f789(f89(a1),x68462),f789(f789(f90(a1),x68463),x68461)),x68463)+~P1(f789(f789(f241(a1),f2(a1)),x68463))+P1(f789(f789(f240(a1),f87(a1)),x68461))+~P1(f789(f789(f241(a1),x68462),x68463))
% 21.40/21.38 [6877]~E(f789(f789(f89(a1),x68772),f789(f789(f90(a1),x68773),x68771)),x68773)+P1(f789(f789(f240(a1),x68771),f87(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x68773))+~P1(f789(f789(f240(a1),f2(a1)),x68772))
% 21.40/21.38 [6895]E(x68951,f2(a863))+~P1(f789(f62(x68953,x68951),x68952))+~P1(f789(f789(f241(a863),f2(a863)),x68951))+P1(f789(f789(f241(a863),f789(f258(a863,a863),x68952)),x68951))
% 21.40/21.38 [6923]~P132(x69231)+~P1(f789(f789(f240(x69231),x69232),f2(x69231)))+~P1(f789(f789(f240(x69231),x69233),f2(x69231)))+E(f789(f789(f90(x69231),f789(f84(x69231),x69232)),f789(f84(x69231),x69233)),f789(f84(x69231),f789(f789(f90(x69231),x69232),x69233)))
% 21.40/21.38 [6975]~P132(x69751)+~P1(f789(f789(f240(x69751),x69752),f2(x69751)))+E(f789(f789(f90(x69751),f789(f84(x69751),x69752)),f789(f84(x69751),x69753)),f789(f84(x69751),f789(f789(f90(x69751),x69752),x69753)))+~P1(f789(f789(f240(x69751),f2(x69751)),x69753))
% 21.40/21.38 [6976]~P132(x69761)+~P1(f789(f789(f240(x69761),x69763),f2(x69761)))+E(f789(f789(f90(x69761),f789(f84(x69761),x69762)),f789(f84(x69761),x69763)),f789(f84(x69761),f789(f789(f90(x69761),x69762),x69763)))+~P1(f789(f789(f240(x69761),f2(x69761)),x69762))
% 21.40/21.38 [7026]~P132(x70261)+E(f789(f789(f90(x70261),f789(f84(x70261),x70262)),f789(f84(x70261),x70263)),f789(f84(x70261),f789(f789(f90(x70261),x70262),x70263)))+~P1(f789(f789(f240(x70261),f2(x70261)),x70262))+~P1(f789(f789(f240(x70261),f2(x70261)),x70263))
% 21.40/21.38 [7044]~P118(x70441)+~P1(f789(f789(f241(x70441),x70443),f2(x70441)))+~P1(f789(f789(f241(x70441),x70442),f2(x70441)))+P1(f789(f789(f241(x70441),f2(x70441)),f789(f789(f90(x70441),x70442),x70443)))
% 21.40/21.38 [7045]~P62(x70451)+~P1(f789(f789(f241(x70451),x70453),f2(x70451)))+~P1(f789(f789(f241(x70451),x70452),f2(x70451)))+P1(f789(f789(f241(x70451),f2(x70451)),f789(f789(f291(x70451),x70452),x70453)))
% 21.40/21.38 [7046]~P63(x70461)+~P1(f789(f789(f241(x70461),x70463),f2(x70461)))+~P1(f789(f789(f241(x70461),x70462),f2(x70461)))+P1(f789(f789(f241(x70461),f2(x70461)),f789(f789(f291(x70461),x70462),x70463)))
% 21.40/21.38 [7047]~P118(x70471)+~P1(f789(f789(f240(x70471),x70473),f2(x70471)))+~P1(f789(f789(f240(x70471),x70472),f2(x70471)))+P1(f789(f789(f240(x70471),f2(x70471)),f789(f789(f90(x70471),x70472),x70473)))
% 21.40/21.38 [7048]~P129(x70481)+~P1(f789(f789(f240(x70481),x70483),f2(x70481)))+~P1(f789(f789(f240(x70481),x70482),f2(x70481)))+P1(f789(f789(f240(x70481),f2(x70481)),f789(f789(f90(x70481),x70482),x70483)))
% 21.40/21.38 [7049]~P129(x70491)+~P1(f789(f789(f240(x70491),x70493),f2(x70491)))+~P1(f789(f789(f240(x70491),x70492),f2(x70491)))+P1(f789(f789(f240(x70491),f2(x70491)),f789(f789(f90(x70491),x70492),x70493)))
% 21.40/21.38 [7050]~P62(x70501)+~P1(f789(f789(f240(x70501),x70503),f2(x70501)))+~P1(f789(f789(f240(x70501),x70502),f2(x70501)))+P1(f789(f789(f240(x70501),f2(x70501)),f789(f789(f291(x70501),x70502),x70503)))
% 21.40/21.38 [7051]~P63(x70511)+~P1(f789(f789(f241(x70511),x70513),f2(x70511)))+~P1(f789(f789(f240(x70511),x70512),f2(x70511)))+P1(f789(f789(f240(x70511),f2(x70511)),f789(f789(f291(x70511),x70512),x70513)))
% 21.40/21.38 [7052]~P117(x70521)+~P1(f789(f789(f241(a863),f2(a863)),x70523))+~P1(f789(f789(f241(x70521),f87(x70521)),x70522))+P1(f789(f789(f241(x70521),f87(x70521)),f789(f789(f250(x70521),x70522),x70523)))
% 21.40/21.38 [7149]~P82(x71491)+~P1(f789(f789(f241(x71491),f2(x71491)),x71493))+~P1(f789(f789(f241(x71491),f2(x71491)),x71492))+P1(f789(f789(f241(x71491),f2(x71491)),f789(f789(f89(x71491),x71492),x71493)))
% 21.40/21.38 [7150]~P82(x71501)+~P1(f789(f789(f240(x71501),f2(x71501)),x71502))+~P1(f789(f789(f241(x71501),f2(x71501)),x71503))+P1(f789(f789(f241(x71501),f2(x71501)),f789(f789(f89(x71501),x71502),x71503)))
% 21.40/21.38 [7151]~P82(x71511)+~P1(f789(f789(f240(x71511),f2(x71511)),x71513))+~P1(f789(f789(f241(x71511),f2(x71511)),x71512))+P1(f789(f789(f241(x71511),f2(x71511)),f789(f789(f89(x71511),x71512),x71513)))
% 21.40/21.38 [7152]~P124(x71521)+~P1(f789(f789(f241(x71521),f2(x71521)),x71523))+~P1(f789(f789(f241(x71521),f2(x71521)),x71522))+P1(f789(f789(f241(x71521),f2(x71521)),f789(f789(f90(x71521),x71522),x71523)))
% 21.40/21.38 [7153]~P62(x71531)+~P1(f789(f789(f241(x71531),f2(x71531)),x71533))+~P1(f789(f789(f241(x71531),f2(x71531)),x71532))+P1(f789(f789(f241(x71531),f2(x71531)),f789(f789(f291(x71531),x71532),x71533)))
% 21.40/21.38 [7154]~P63(x71541)+~P1(f789(f789(f241(x71541),f2(x71541)),x71543))+~P1(f789(f789(f241(x71541),f2(x71541)),x71542))+P1(f789(f789(f241(x71541),f2(x71541)),f789(f789(f291(x71541),x71542),x71543)))
% 21.40/21.38 [7155]~P117(x71551)+~P1(f789(f789(f241(x71551),f87(x71551)),x71553))+~P1(f789(f789(f241(x71551),f87(x71551)),x71552))+P1(f789(f789(f241(x71551),f87(x71551)),f789(f789(f90(x71551),x71552),x71553)))
% 21.40/21.38 [7156]~P82(x71561)+~P1(f789(f789(f240(x71561),f2(x71561)),x71563))+~P1(f789(f789(f240(x71561),f2(x71561)),x71562))+P1(f789(f789(f240(x71561),f2(x71561)),f789(f789(f89(x71561),x71562),x71563)))
% 21.40/21.38 [7157]~P118(x71571)+~P1(f789(f789(f240(x71571),f2(x71571)),x71573))+~P1(f789(f789(f240(x71571),f2(x71571)),x71572))+P1(f789(f789(f240(x71571),f2(x71571)),f789(f789(f90(x71571),x71572),x71573)))
% 21.40/21.38 [7158]~P128(x71581)+~P1(f789(f789(f240(x71581),f2(x71581)),x71583))+~P1(f789(f789(f240(x71581),f2(x71581)),x71582))+P1(f789(f789(f240(x71581),f2(x71581)),f789(f789(f90(x71581),x71582),x71583)))
% 21.40/21.38 [7159]~P129(x71591)+~P1(f789(f789(f240(x71591),f2(x71591)),x71593))+~P1(f789(f789(f240(x71591),f2(x71591)),x71592))+P1(f789(f789(f240(x71591),f2(x71591)),f789(f789(f90(x71591),x71592),x71593)))
% 21.40/21.38 [7160]~P62(x71601)+~P1(f789(f789(f240(x71601),f2(x71601)),x71603))+~P1(f789(f789(f240(x71601),f2(x71601)),x71602))+P1(f789(f789(f240(x71601),f2(x71601)),f789(f789(f291(x71601),x71602),x71603)))
% 21.40/21.38 [7161]~P63(x71611)+~P1(f789(f789(f241(x71611),f2(x71611)),x71613))+~P1(f789(f789(f240(x71611),f2(x71611)),x71612))+P1(f789(f789(f240(x71611),f2(x71611)),f789(f789(f291(x71611),x71612),x71613)))
% 21.40/21.38 [7239]~P95(x72391)+~P1(f789(f70(x72391),x72393))+E(f12(x72391,f789(f789(f310(x72391),x72392),x72393)),x72392)+~E(f789(f789(f3(f870(x72391,a856)),x72393),f789(f789(f310(x72391),x72392),f184(f870(x72391,a856)))),f184(f870(x72391,a856)))
% 21.40/21.38 [7240]~P95(x72401)+~P1(f789(f70(x72401),x72403))+E(f15(x72401,f789(f789(f310(x72401),x72402),x72403)),x72402)+~E(f789(f789(f3(f870(x72401,a856)),x72403),f789(f789(f310(x72401),x72402),f184(f870(x72401,a856)))),f184(f870(x72401,a856)))
% 21.40/21.38 [7241]~P101(x72411)+~P1(f789(f70(x72411),x72413))+E(f16(x72411,f789(f789(f310(x72411),x72412),x72413)),x72412)+~E(f789(f789(f3(f870(x72411,a856)),x72413),f789(f789(f310(x72411),x72412),f184(f870(x72411,a856)))),f184(f870(x72411,a856)))
% 21.40/21.38 [7242]~P101(x72421)+~P1(f789(f70(x72421),x72423))+E(f17(x72421,f789(f789(f310(x72421),x72422),x72423)),x72422)+~E(f789(f789(f3(f870(x72421,a856)),x72423),f789(f789(f310(x72421),x72422),f184(f870(x72421,a856)))),f184(f870(x72421,a856)))
% 21.40/21.38 [7243]~P62(x72431)+P1(f789(f789(f241(x72431),x72432),f2(x72431)))+P1(f789(f789(f241(x72431),f2(x72431)),x72433))+~P1(f789(f789(f241(x72431),f2(x72431)),f789(f789(f291(x72431),x72433),x72432)))
% 21.40/21.38 [7244]~P62(x72441)+P1(f789(f789(f241(x72441),x72442),f2(x72441)))+P1(f789(f789(f241(x72441),f2(x72441)),x72443))+~P1(f789(f789(f241(x72441),f2(x72441)),f789(f789(f291(x72441),x72442),x72443)))
% 21.40/21.38 [7245]~P62(x72451)+P1(f789(f789(f241(x72451),x72452),f2(x72451)))+P1(f789(f789(f241(x72451),f2(x72451)),x72452))+~P1(f789(f789(f241(x72451),f2(x72451)),f789(f789(f291(x72451),x72453),x72452)))
% 21.40/21.38 [7246]~P62(x72461)+P1(f789(f789(f241(x72461),x72462),f2(x72461)))+P1(f789(f789(f241(x72461),f2(x72461)),x72462))+~P1(f789(f789(f241(x72461),f2(x72461)),f789(f789(f291(x72461),x72462),x72463)))
% 21.40/21.38 [7247]~P118(x72471)+P1(f789(f789(f240(x72471),x72472),f2(x72471)))+P1(f789(f789(f240(x72471),f2(x72471)),x72473))+~P1(f789(f789(f240(x72471),f2(x72471)),f789(f789(f90(x72471),x72473),x72472)))
% 21.40/21.38 [7248]~P118(x72481)+P1(f789(f789(f240(x72481),x72482),f2(x72481)))+P1(f789(f789(f240(x72481),f2(x72481)),x72483))+~P1(f789(f789(f240(x72481),f2(x72481)),f789(f789(f90(x72481),x72482),x72483)))
% 21.40/21.38 [7249]~P62(x72491)+P1(f789(f789(f240(x72491),x72492),f2(x72491)))+P1(f789(f789(f240(x72491),f2(x72491)),x72493))+~P1(f789(f789(f240(x72491),f2(x72491)),f789(f789(f291(x72491),x72493),x72492)))
% 21.40/21.38 [7250]~P62(x72501)+P1(f789(f789(f240(x72501),x72502),f2(x72501)))+P1(f789(f789(f240(x72501),f2(x72501)),x72503))+~P1(f789(f789(f240(x72501),f2(x72501)),f789(f789(f291(x72501),x72502),x72503)))
% 21.40/21.38 [7251]~P118(x72511)+P1(f789(f789(f240(x72511),x72512),f2(x72511)))+P1(f789(f789(f240(x72511),f2(x72511)),x72512))+~P1(f789(f789(f240(x72511),f2(x72511)),f789(f789(f90(x72511),x72513),x72512)))
% 21.40/21.38 [7252]~P118(x72521)+P1(f789(f789(f240(x72521),x72522),f2(x72521)))+P1(f789(f789(f240(x72521),f2(x72521)),x72522))+~P1(f789(f789(f240(x72521),f2(x72521)),f789(f789(f90(x72521),x72522),x72523)))
% 21.40/21.38 [7253]~P62(x72531)+P1(f789(f789(f240(x72531),x72532),f2(x72531)))+P1(f789(f789(f240(x72531),f2(x72531)),x72532))+~P1(f789(f789(f240(x72531),f2(x72531)),f789(f789(f291(x72531),x72533),x72532)))
% 21.40/21.38 [7254]~P62(x72541)+P1(f789(f789(f240(x72541),x72542),f2(x72541)))+P1(f789(f789(f240(x72541),f2(x72541)),x72542))+~P1(f789(f789(f240(x72541),f2(x72541)),f789(f789(f291(x72541),x72542),x72543)))
% 21.40/21.38 [7339]~P1(f789(f789(f287(a863),x73391),x73393))+P1(f789(f789(f287(a863),x73391),x73392))+~P1(f789(f789(f240(a863),x73392),x73393))+~P1(f789(f789(f287(a863),x73391),f789(f789(f3(a863),x73393),x73392)))
% 21.40/21.38 [7340]~P1(f789(f789(f287(a863),x73401),x73403))+P1(f789(f789(f287(a863),x73401),x73402))+~P1(f789(f789(f240(a863),x73403),x73402))+~P1(f789(f789(f287(a863),x73401),f789(f789(f3(a863),x73402),x73403)))
% 21.40/21.38 [7355]~E(f789(f789(f111(f870(x73551,a856)),f789(f163(x73551),x73552)),f789(f163(x73551),x73553)),f184(f870(x73551,a856)))+~P1(f789(f134(x73551),x73553))+~P1(f789(f134(x73551),x73552))+P1(f789(f134(x73551),f789(f789(f132(x73551),x73552),x73553)))
% 21.40/21.38 [7356]~P101(x73561)+~P1(f789(f70(x73561),x73563))+E(f13(x73561,f239(x73561),f789(f789(f310(x73561),x73562),x73563)),x73562)+~E(f789(f789(f3(f870(x73561,a856)),x73563),f789(f789(f310(x73561),x73562),f184(f870(x73561,a856)))),f184(f870(x73561,a856)))
% 21.40/21.38 [7357]~P101(x73571)+~P1(f789(f70(x73571),x73573))+E(f14(x73571,f244(x73571),f789(f789(f310(x73571),x73572),x73573)),x73572)+~E(f789(f789(f3(f870(x73571,a856)),x73573),f789(f789(f310(x73571),x73572),f184(f870(x73571,a856)))),f184(f870(x73571,a856)))
% 21.40/21.38 [7375]~P110(x73751)+~P1(f789(f789(f241(x73751),x73752),x73753))+~P1(f789(f789(f241(x73751),f789(f88(x73751),x73752)),x73753))+P1(f789(f789(f241(x73751),f789(f84(x73751),x73752)),x73753))
% 21.40/21.38 [7376]~P80(x73761)+~P1(f789(f789(f240(x73761),x73762),x73763))+~P1(f789(f789(f240(x73761),f789(f88(x73761),x73762)),x73763))+P1(f789(f789(f240(x73761),f789(f84(x73761),x73762)),x73763))
% 21.40/21.38 [7377]~P80(x73771)+~P1(f789(f789(f240(x73771),x73772),x73773))+~P1(f789(f789(f240(x73771),f789(f88(x73771),x73772)),x73773))+P1(f789(f789(f240(x73771),f789(f84(x73771),x73772)),x73773))
% 21.40/21.38 [7446]~P124(x74461)+P1(f789(f789(f241(x74461),f2(x74461)),x74462))+~P1(f789(f789(f241(x74461),f2(x74461)),x74463))+~P1(f789(f789(f241(x74461),f2(x74461)),f789(f789(f90(x74461),x74463),x74462)))
% 21.40/21.38 [7447]~P124(x74471)+P1(f789(f789(f241(x74471),f2(x74471)),x74472))+~P1(f789(f789(f241(x74471),f2(x74471)),x74473))+~P1(f789(f789(f241(x74471),f2(x74471)),f789(f789(f90(x74471),x74472),x74473)))
% 21.40/21.38 [7753]E(x77531,x77532)+~P1(f789(f70(x77533),x77531))+~P1(f789(f789(f240(a863),f789(f49(x77533),x77531)),f789(f49(x77533),x77532)))+~P1(f789(f789(f240(f870(x77533,a856)),x77532),x77531))
% 21.40/21.38 [7824]~P1(f789(f789(f240(a863),x78242),x78241))+~P1(f789(f789(f241(a863),x78241),x78243))+~P1(f789(f789(f240(a863),x78242),x78243))+P1(f789(f789(f241(a863),f789(f789(f3(a863),x78241),x78242)),f789(f789(f3(a863),x78243),x78242)))
% 21.40/21.38 [7825]~P1(f789(f789(f240(a863),x78252),x78251))+~P1(f789(f789(f240(a863),x78252),x78253))+~P1(f789(f789(f240(a863),x78251),x78253))+P1(f789(f789(f240(a863),f789(f789(f3(a863),x78251),x78252)),f789(f789(f3(a863),x78253),x78252)))
% 21.40/21.38 [7900]~P1(f789(f789(f241(a1),x79001),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x79002))+~P1(f789(f789(f240(a1),x79002),x79003))+P1(f789(f789(f240(a1),f789(f789(f50(a1),x79001),x79002)),f789(f789(f50(a1),x79001),x79003)))
% 21.40/21.38 [7911]~P1(f789(f789(f241(a1),f2(a1)),x79113))+~P1(f789(f789(f240(a1),f2(a1)),x79111))+~P1(f789(f789(f240(a1),x79113),x79112))+P1(f789(f789(f240(a1),f789(f789(f50(a1),x79111),x79112)),f789(f789(f50(a1),x79111),x79113)))
% 21.40/21.38 [8044]E(f789(x80441,f834(x80442,x80441,x80443)),x80442)+~P1(f789(f789(f240(a1),x80442),f789(x80441,x80443)))+P1(f789(f789(f241(a863),f835(x80442,x80441,x80443)),x80443))+~P1(f789(f789(f240(a1),f789(x80441,f2(a863))),x80442))
% 21.40/21.38 [8045]E(f789(x80451,f836(x80452,x80451,x80453)),x80452)+~P1(f789(f789(f240(a1),x80452),f789(x80451,x80453)))+P1(f789(f789(f241(a863),f837(x80452,x80451,x80453)),x80453))+~P1(f789(f789(f240(a1),f789(x80451,f2(a863))),x80452))
% 21.40/21.38 [8142]~P1(f789(f70(x81421),x81423))+~P1(f789(f789(f241(a863),f789(f49(x81421),x81422)),f789(f49(x81421),x81423)))+~P1(f789(f789(f240(f870(x81421,a856)),x81422),x81423))+P1(f789(f789(f241(f870(x81421,a856)),x81422),x81423))
% 21.40/21.38 [8170]E(f789(f789(f3(a1),f482(x81703,x81701,x81702)),f483(x81703,x81701,x81702)),x81701)+E(f789(f789(f89(a1),x81701),x81702),x81701)+~P1(f789(f789(f241(a1),f2(a1)),x81702))+~P1(f789(f789(f342(a1),f789(f789(f89(a1),x81701),f87(a1))),x81703))
% 21.40/21.38 [8171]E(f789(f789(f89(a1),f474(x81713,x81711,x81712)),f475(x81713,x81711,x81712)),x81711)+E(f789(f789(f3(a1),x81711),x81712),x81711)+~P1(f789(f789(f241(a1),f2(a1)),x81712))+~P1(f789(f789(f342(a1),f789(f789(f3(a1),x81711),f87(a1))),x81713))
% 21.40/21.38 [8223]~P1(f789(f789(f240(a863),x82233),x82231))+P1(f789(f789(f241(a863),x82231),x82232))+~P1(f789(f789(f240(a863),x82233),x82232))+~P1(f789(f789(f241(a863),f789(f789(f3(a863),x82231),x82233)),f789(f789(f3(a863),x82232),x82233)))
% 21.40/21.38 [8224]~P1(f789(f789(f240(a863),x82243),x82241))+P1(f789(f789(f240(a863),x82241),x82242))+~P1(f789(f789(f240(a863),x82243),x82242))+~P1(f789(f789(f240(a863),f789(f789(f3(a863),x82241),x82243)),f789(f789(f3(a863),x82242),x82243)))
% 21.40/21.38 [8238]~P101(x82382)+E(x82381,f122(x82382))+~P18(x82382,f789(f149(x82382),x82381))+E(f789(f138(x82382,x82382,f789(f9(x82382,x82382,x82382),f239(x82382)),x82383),f789(f149(x82382),x82381)),f789(f789(f239(x82382),f789(f789(f159(x82382),x82381),f2(a863))),x82383))
% 21.40/21.38 [8304]E(f789(f789(f89(a1),x83041),x83042),x83041)+~P1(f789(f789(f241(a1),f2(a1)),x83042))+P1(f789(f789(f342(a1),f482(x83043,x83041,x83042)),x83043))+~P1(f789(f789(f342(a1),f789(f789(f89(a1),x83041),f87(a1))),x83043))
% 21.40/21.38 [8305]E(f789(f789(f3(a1),x83051),x83052),x83051)+~P1(f789(f789(f241(a1),f2(a1)),x83052))+P1(f789(f789(f342(a1),f474(x83053,x83051,x83052)),x83053))+~P1(f789(f789(f342(a1),f789(f789(f3(a1),x83051),f87(a1))),x83053))
% 21.40/21.38 [8384]~P1(f789(f789(f240(a1),x83841),f789(x83842,x83843)))+P1(f789(f789(f240(a863),f834(x83841,x83842,x83843)),x83843))+P1(f789(f789(f241(a863),f835(x83841,x83842,x83843)),x83843))+~P1(f789(f789(f240(a1),f789(x83842,f2(a863))),x83841))
% 21.40/21.38 [8385]~P1(f789(f789(f240(a1),x83851),f789(x83852,x83853)))+P1(f789(f789(f240(a863),f836(x83851,x83852,x83853)),x83853))+P1(f789(f789(f241(a863),f837(x83851,x83852,x83853)),x83853))+~P1(f789(f789(f240(a1),f789(x83852,f2(a863))),x83851))
% 21.40/21.38 [8459]E(f789(f789(f89(a1),x84591),x84592),x84591)+~P1(f789(f789(f241(a1),f2(a1)),x84592))+P1(f789(f789(f342(a1),f483(x84593,x84591,x84592)),f303(a1,f87(a1),x84592)))+~P1(f789(f789(f342(a1),f789(f789(f89(a1),x84591),f87(a1))),x84593))
% 21.40/21.38 [8460]E(f789(f789(f3(a1),x84601),x84602),x84601)+~P1(f789(f789(f241(a1),f2(a1)),x84602))+P1(f789(f789(f342(a1),f475(x84603,x84601,x84602)),f303(a1,f87(a1),x84602)))+~P1(f789(f789(f342(a1),f789(f789(f3(a1),x84601),f87(a1))),x84603))
% 21.40/21.38 [8585]~P117(x85851)+~P1(f789(f789(f241(x85851),x85852),f87(x85851)))+~P1(f789(f789(f241(x85851),f2(x85851)),x85852))+P1(f789(f789(f241(x85851),f789(f789(f90(x85851),x85852),f789(f789(f250(x85851),x85852),x85853))),f789(f789(f250(x85851),x85852),x85853)))
% 21.40/21.38 [8661]~P1(f789(x86611,x86612))+P1(f789(x86611,f2(a863)))+~P1(f789(f789(f241(a863),x86612),x86613))+~P1(f789(x86611,f59(a863,f789(a121,f833(x86612,x86611,x86613)),x86613)))
% 21.40/21.38 [8791]E(f348(x87911,x87912,x87913),f2(a863))+P1(f789(f789(x87911,x87913),x87912))+P1(f789(f789(x87911,f348(x87911,x87912,x87913)),f59(a863,f852(x87911,x87912,x87913),f348(x87911,x87912,x87913))))+~P1(f789(f329(f869(a863,a863),a221),f789(f789(f249(a863,a863),x87913),x87912)))
% 21.40/21.38 [8823]~P29(x88231,x88231,x88232,x88233)+E(f789(f311(x88231,x88231,x88232),x88233),x88233)+~P1(f789(f70(x88231),x88233))+~P1(f789(f789(f240(f870(x88231,a856)),f789(f311(x88231,x88231,x88232),x88233)),x88233))
% 21.40/21.38 [9043]P1(f789(f789(x90431,x90432),x90433))+~P1(f789(f789(f241(a1),f851(x90431,x90433,x90432)),f2(a1)))+P1(f789(f789(x90431,f789(f88(a1),f848(x90431,x90433,x90432))),f789(f88(a1),f851(x90431,x90433,x90432))))+~P1(f789(f329(f869(a1,a1),a223),f789(f789(f249(a1,a1),x90432),x90433)))
% 21.40/21.38 [9203]P1(f789(f789(x92031,x92032),x92033))+P1(f789(f789(x92031,f789(f789(f89(a1),f744(x92031,x92033,x92032)),f87(a1))),f747(x92031,x92033,x92032)))+~P1(f789(f789(f240(a1),f744(x92031,x92033,x92032)),f747(x92031,x92033,x92032)))+~P1(f789(f329(f869(a1,a1),a172),f789(f789(f249(a1,a1),x92032),x92033)))
% 21.40/21.38 [9888]E(f789(x98881,f834(x98882,x98881,x98883)),x98882)+~P1(f789(f789(f240(a1),x98882),f789(x98881,x98883)))+~P1(f789(f789(f240(a1),f789(f84(a1),f789(f789(f3(a1),f789(x98881,f789(f789(f89(a863),f835(x98882,x98881,x98883)),f87(a863)))),f789(x98881,f835(x98882,x98881,x98883))))),f87(a1)))+~P1(f789(f789(f240(a1),f789(x98881,f2(a863))),x98882))
% 21.40/21.38 [9889]E(f789(x98891,f836(x98892,x98891,x98893)),x98892)+~P1(f789(f789(f240(a1),x98892),f789(x98891,x98893)))+~P1(f789(f789(f240(a1),f789(f84(a1),f789(f789(f3(a1),f789(x98891,f789(f789(f89(a863),f837(x98892,x98891,x98893)),f87(a863)))),f789(x98891,f837(x98892,x98891,x98893))))),f87(a1)))+~P1(f789(f789(f240(a1),f789(x98891,f2(a863))),x98892))
% 21.40/21.38 [9893]~P1(f789(f789(f240(a1),x98931),f789(x98932,x98933)))+~P1(f789(f789(f240(a1),f789(f84(a1),f789(f789(f3(a1),f789(x98932,f789(f789(f89(a863),f835(x98931,x98932,x98933)),f87(a863)))),f789(x98932,f835(x98931,x98932,x98933))))),f87(a1)))+P1(f789(f789(f240(a863),f834(x98931,x98932,x98933)),x98933))+~P1(f789(f789(f240(a1),f789(x98932,f2(a863))),x98931))
% 21.40/21.38 [9894]~P1(f789(f789(f240(a1),x98941),f789(x98942,x98943)))+~P1(f789(f789(f240(a1),f789(f84(a1),f789(f789(f3(a1),f789(x98942,f789(f789(f89(a863),f837(x98941,x98942,x98943)),f87(a863)))),f789(x98942,f837(x98941,x98942,x98943))))),f87(a1)))+P1(f789(f789(f240(a863),f836(x98941,x98942,x98943)),x98943))+~P1(f789(f789(f240(a1),f789(x98942,f2(a863))),x98941))
% 21.40/21.38 [9948]E(x99481,x99482)+~E(f789(f138(f864(x99483),f864(x99483),f132(x99483),f122(x99483)),x99481),f789(f138(f864(x99483),f864(x99483),f132(x99483),f122(x99483)),x99482))+~E(f789(f185(f864(f864(x99483))),x99481),f789(f185(f864(f864(x99483))),x99482))+~P1(f789(f789(f259(f864(x99483),f864(x99483),a856),f789(f789(f9(f864(x99483),f870(f864(x99483),a863),f870(f864(x99483),a856)),f789(f789(f10(f870(a863,a856),f870(f870(f864(x99483),a863),f870(f864(x99483),a856)),f864(x99483)),f10(a863,a856,f864(x99483))),f789(f789(f10(a863,f870(a863,a856),f864(x99483)),a338),f185(f864(x99483))))),f185(f864(x99483)))),f785(x99481,x99482,x99483)))
% 21.40/21.38 [9949]E(x99491,x99492)+~E(f789(f138(f864(x99493),f864(x99493),f132(x99493),f122(x99493)),x99491),f789(f138(f864(x99493),f864(x99493),f132(x99493),f122(x99493)),x99492))+~E(f789(f185(f864(f864(x99493))),x99491),f789(f185(f864(f864(x99493))),x99492))+~P1(f789(f789(f259(f864(x99493),f864(x99493),a856),f789(f789(f9(f864(x99493),f870(f864(x99493),a863),f870(f864(x99493),a856)),f789(f789(f10(f870(a863,a856),f870(f870(f864(x99493),a863),f870(f864(x99493),a856)),f864(x99493)),f10(a863,a856,f864(x99493))),f789(f789(f10(a863,f870(a863,a856),f864(x99493)),a338),f185(f864(x99493))))),f185(f864(x99493)))),f787(x99492,x99491,x99493)))
% 21.40/21.38 [6749]~E(f87(a863),f2(a863))+~P1(f789(f70(x67491),x67493))+~P1(f789(f70(x67491),x67492))+E(f789(f789(f89(a863),f789(f49(x67491),x67492)),f789(f49(x67491),x67493)),f789(f49(x67491),f789(f789(f110(f870(x67491,a856)),x67492),x67493)))
% 21.40/21.38 [7167]~P101(x71671)+~P1(f789(f70(x71671),x71672))+~P1(f789(f789(f342(x71671),x71673),x71672))+P1(f789(f789(f240(x71671),f789(f72(x71671,f244(x71671)),x71672)),x71673))
% 21.40/21.38 [7168]~P98(x71681)+~P1(f789(f70(x71681),x71682))+~P1(f789(f789(f342(x71681),x71683),x71682))+P1(f789(f789(f240(x71681),f789(f72(x71681,f111(x71681)),x71682)),x71683))
% 21.40/21.38 [7443]~P1(f789(f70(x74431),x74433))+~P1(f789(f70(x74431),x74432))+~E(f789(f789(f111(f870(x74431,a856)),x74432),x74433),f184(f870(x74431,a856)))+E(f789(f789(f89(a863),f789(f49(x74431),x74432)),f789(f49(x74431),x74433)),f789(f49(x74431),f789(f789(f110(f870(x74431,a856)),x74432),x74433)))
% 21.40/21.38 [8228]~P36(x82281,x82283)+~P36(x82281,x82282)+~E(f789(f789(f111(f870(x82281,a856)),f789(f269(x82281,x82281),x82282)),f789(f267(x82281,x82281),x82283)),f184(f870(x82281,a856)))+P36(x82281,f789(f789(f110(f870(f869(x82281,x82281),a856)),x82282),x82283))
% 21.40/21.38 [8317]E(x83171,f789(f789(f50(a863),x83172),x83173))+~P1(f789(f789(f241(a863),f2(a863)),x83173))+~P1(f789(f789(f241(a863),x83172),f789(f789(f90(a863),x83173),f789(a121,x83171))))+~P1(f789(f789(f240(a863),f789(f789(f90(a863),x83173),x83171)),x83172))
% 21.40/21.38 [8457]~P1(f789(f70(x84571),x84572))+~P1(f789(f70(x84571),x84573))+E(f789(f789(f89(a863),f789(f49(x84571),x84572)),f789(f49(x84571),x84573)),f789(f49(x84571),f789(f789(f110(f870(x84571,a856)),x84572),x84573)))+P1(f789(f789(f342(x84571),f390(x84573,x84572,x84571)),f789(f789(f111(f870(x84571,a856)),x84572),x84573)))
% 21.40/21.38 [8802]~P118(x88022)+~E(x88021,f2(x88022))+~E(x88023,f2(x88022))+~P1(f789(f789(f241(x88022),f2(x88022)),f789(f789(f89(x88022),f789(f789(f90(x88022),x88023),x88023)),f789(f789(f90(x88022),x88021),x88021))))
% 21.40/21.38 [9273]~P36(x92731,x92733)+~P36(x92731,x92732)+P36(x92731,f789(f789(f110(f870(f869(x92731,x92731),a856)),x92732),x92733))+~P1(f789(f789(f240(f870(f869(x92731,x92731),a856)),f789(f789(f289(x92731,x92731,x92731),x92732),x92733)),x92732))
% 21.40/21.38 [9399]~P1(f789(x93991,x93993))+~P1(f789(f70(x93992),x93993))+P1(f789(x93991,f184(f870(x93992,a856))))+~P1(f789(x93991,f789(f789(f3(f870(x93992,a856)),f458(x93991,x93993,x93992)),f789(f789(f310(x93992),f459(x93991,x93993,x93992)),f184(f870(x93992,a856))))))
% 21.40/21.38 [8615]~P1(f789(f789(f241(a1),f2(a1)),x86153))+P1(f789(f789(f240(a1),f2(a1)),x86151))+~P1(f789(f789(f241(a1),x86152),x86153))+~P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),f789(f789(f90(a1),x86153),x86151)),x86152)))
% 21.40/21.38 [8635]~P95(x86351)+~P1(f789(f70(x86351),x86352))+E(f789(f789(f3(f870(x86351,a856)),x86352),f789(f789(f310(x86351),x86353),f184(f870(x86351,a856)))),f184(f870(x86351,a856)))+E(f789(f789(f111(x86351),x86353),f12(x86351,f789(f789(f3(f870(x86351,a856)),x86352),f789(f789(f310(x86351),x86353),f184(f870(x86351,a856)))))),f12(x86351,f789(f789(f310(x86351),x86353),x86352)))
% 21.40/21.38 [8636]~P95(x86361)+~P1(f789(f70(x86361),x86362))+E(f789(f789(f3(f870(x86361,a856)),x86362),f789(f789(f310(x86361),x86363),f184(f870(x86361,a856)))),f184(f870(x86361,a856)))+E(f789(f789(f110(x86361),x86363),f15(x86361,f789(f789(f3(f870(x86361,a856)),x86362),f789(f789(f310(x86361),x86363),f184(f870(x86361,a856)))))),f15(x86361,f789(f789(f310(x86361),x86363),x86362)))
% 21.40/21.38 [8637]~P101(x86371)+~P1(f789(f70(x86371),x86372))+E(f789(f789(f3(f870(x86371,a856)),x86372),f789(f789(f310(x86371),x86373),f184(f870(x86371,a856)))),f184(f870(x86371,a856)))+E(f789(f789(f239(x86371),x86373),f16(x86371,f789(f789(f3(f870(x86371,a856)),x86372),f789(f789(f310(x86371),x86373),f184(f870(x86371,a856)))))),f16(x86371,f789(f789(f310(x86371),x86373),x86372)))
% 21.40/21.38 [8638]~P101(x86381)+~P1(f789(f70(x86381),x86382))+E(f789(f789(f3(f870(x86381,a856)),x86382),f789(f789(f310(x86381),x86383),f184(f870(x86381,a856)))),f184(f870(x86381,a856)))+E(f789(f789(f244(x86381),x86383),f17(x86381,f789(f789(f3(f870(x86381,a856)),x86382),f789(f789(f310(x86381),x86383),f184(f870(x86381,a856)))))),f17(x86381,f789(f789(f310(x86381),x86383),x86382)))
% 21.40/21.38 [8700]~P101(x87001)+~P1(f789(f70(x87001),x87002))+E(f789(f789(f3(f870(x87001,a856)),x87002),f789(f789(f310(x87001),x87003),f184(f870(x87001,a856)))),f184(f870(x87001,a856)))+E(f789(f789(f239(x87001),x87003),f13(x87001,f239(x87001),f789(f789(f3(f870(x87001,a856)),x87002),f789(f789(f310(x87001),x87003),f184(f870(x87001,a856)))))),f13(x87001,f239(x87001),f789(f789(f310(x87001),x87003),x87002)))
% 21.40/21.38 [8701]~P101(x87011)+~P1(f789(f70(x87011),x87012))+E(f789(f789(f3(f870(x87011,a856)),x87012),f789(f789(f310(x87011),x87013),f184(f870(x87011,a856)))),f184(f870(x87011,a856)))+E(f789(f789(f244(x87011),x87013),f14(x87011,f244(x87011),f789(f789(f3(f870(x87011,a856)),x87012),f789(f789(f310(x87011),x87013),f184(f870(x87011,a856)))))),f14(x87011,f244(x87011),f789(f789(f310(x87011),x87013),x87012)))
% 21.40/21.38 [9217]E(x92171,x92172)+~E(f789(f138(f864(x92173),f864(x92173),f132(x92173),f122(x92173)),x92171),f789(f138(f864(x92173),f864(x92173),f132(x92173),f122(x92173)),x92172))+~E(f789(f185(f864(f864(x92173))),x92171),f789(f185(f864(f864(x92173))),x92172))+P1(f789(f789(f342(f869(f864(x92173),f864(x92173))),f785(x92171,x92172,x92173)),f789(f163(f869(f864(x92173),f864(x92173))),f789(f789(f171(f864(x92173),f864(x92173)),x92172),x92171))))
% 21.40/21.38 [9218]E(x92181,x92182)+~E(f789(f138(f864(x92183),f864(x92183),f132(x92183),f122(x92183)),x92181),f789(f138(f864(x92183),f864(x92183),f132(x92183),f122(x92183)),x92182))+~E(f789(f185(f864(f864(x92183))),x92181),f789(f185(f864(f864(x92183))),x92182))+P1(f789(f789(f342(f869(f864(x92183),f864(x92183))),f787(x92182,x92181,x92183)),f789(f163(f869(f864(x92183),f864(x92183))),f789(f789(f171(f864(x92183),f864(x92183)),x92181),x92182))))
% 21.40/21.38 [10041]~P73(x100412)+E(x100411,f184(f870(x100412,a856)))+~P1(f789(f70(x100412),x100411))+E(f16(x100412,f789(f264(x100412),f789(f789(f10(f870(x100412,a856),a856,x100412),f96(x100412)),f789(f789(f9(x100412,f870(x100412,a856),f870(x100412,a856)),f789(f789(f10(f870(x100412,f870(a856,a856)),f870(f870(x100412,a856),f870(x100412,a856)),x100412),f20(x100412,a856,a856)),f789(f789(f10(f870(x100412,a856),f870(x100412,f870(a856,a856)),x100412),f789(f10(a856,f870(a856,a856),x100412),a339)),f789(f789(f9(x100412,f870(x100412,x100412),f870(x100412,a856)),f789(f789(f10(f870(x100412,a856),f870(f870(x100412,x100412),f870(x100412,a856)),x100412),f10(x100412,a856,x100412)),a338)),f789(f89(x100412),x100413))))),f789(f789(f9(x100412,f870(x100412,a856),a856),f342(x100412)),x100411))))),f789(f789(f89(x100412),x100413),f16(x100412,x100411)))
% 21.40/21.38 [10042]~P73(x100422)+E(x100421,f184(f870(x100422,a856)))+~P1(f789(f70(x100422),x100421))+E(f17(x100422,f789(f264(x100422),f789(f789(f10(f870(x100422,a856),a856,x100422),f96(x100422)),f789(f789(f9(x100422,f870(x100422,a856),f870(x100422,a856)),f789(f789(f10(f870(x100422,f870(a856,a856)),f870(f870(x100422,a856),f870(x100422,a856)),x100422),f20(x100422,a856,a856)),f789(f789(f10(f870(x100422,a856),f870(x100422,f870(a856,a856)),x100422),f789(f10(a856,f870(a856,a856),x100422),a339)),f789(f789(f9(x100422,f870(x100422,x100422),f870(x100422,a856)),f789(f789(f10(f870(x100422,a856),f870(f870(x100422,x100422),f870(x100422,a856)),x100422),f10(x100422,a856,x100422)),a338)),f789(f89(x100422),x100423))))),f789(f789(f9(x100422,f870(x100422,a856),a856),f342(x100422)),x100421))))),f789(f789(f89(x100422),x100423),f17(x100422,x100421)))
% 21.40/21.38 [10043]~P96(x100432)+E(x100431,f184(f870(x100432,a856)))+~P1(f789(f70(x100432),x100431))+E(f12(x100432,f789(f264(x100432),f789(f789(f10(f870(x100432,a856),a856,x100432),f96(x100432)),f789(f789(f9(x100432,f870(x100432,a856),f870(x100432,a856)),f789(f789(f10(f870(x100432,f870(a856,a856)),f870(f870(x100432,a856),f870(x100432,a856)),x100432),f20(x100432,a856,a856)),f789(f789(f10(f870(x100432,a856),f870(x100432,f870(a856,a856)),x100432),f789(f10(a856,f870(a856,a856),x100432),a339)),f789(f789(f9(x100432,f870(x100432,x100432),f870(x100432,a856)),f789(f789(f10(f870(x100432,a856),f870(f870(x100432,x100432),f870(x100432,a856)),x100432),f10(x100432,a856,x100432)),a338)),f789(f110(x100432),x100433))))),f789(f789(f9(x100432,f870(x100432,a856),a856),f342(x100432)),x100431))))),f789(f789(f110(x100432),x100433),f12(x100432,x100431)))
% 21.40/21.38 [10044]~P96(x100442)+E(x100441,f184(f870(x100442,a856)))+~P1(f789(f70(x100442),x100441))+E(f15(x100442,f789(f264(x100442),f789(f789(f10(f870(x100442,a856),a856,x100442),f96(x100442)),f789(f789(f9(x100442,f870(x100442,a856),f870(x100442,a856)),f789(f789(f10(f870(x100442,f870(a856,a856)),f870(f870(x100442,a856),f870(x100442,a856)),x100442),f20(x100442,a856,a856)),f789(f789(f10(f870(x100442,a856),f870(x100442,f870(a856,a856)),x100442),f789(f10(a856,f870(a856,a856),x100442),a339)),f789(f789(f9(x100442,f870(x100442,x100442),f870(x100442,a856)),f789(f789(f10(f870(x100442,a856),f870(f870(x100442,x100442),f870(x100442,a856)),x100442),f10(x100442,a856,x100442)),a338)),f789(f111(x100442),x100443))))),f789(f789(f9(x100442,f870(x100442,a856),a856),f342(x100442)),x100441))))),f789(f789(f111(x100442),x100443),f15(x100442,x100441)))
% 21.40/21.38 [10045]~P101(x100452)+E(x100451,f184(f870(x100452,a856)))+~P1(f789(f70(x100452),x100451))+E(f13(x100452,f239(x100452),f789(f264(x100452),f789(f789(f10(f870(x100452,a856),a856,x100452),f96(x100452)),f789(f789(f9(x100452,f870(x100452,a856),f870(x100452,a856)),f789(f789(f10(f870(x100452,f870(a856,a856)),f870(f870(x100452,a856),f870(x100452,a856)),x100452),f20(x100452,a856,a856)),f789(f789(f10(f870(x100452,a856),f870(x100452,f870(a856,a856)),x100452),f789(f10(a856,f870(a856,a856),x100452),a339)),f789(f789(f9(x100452,f870(x100452,x100452),f870(x100452,a856)),f789(f789(f10(f870(x100452,a856),f870(f870(x100452,x100452),f870(x100452,a856)),x100452),f10(x100452,a856,x100452)),a338)),f789(f244(x100452),x100453))))),f789(f789(f9(x100452,f870(x100452,a856),a856),f342(x100452)),x100451))))),f789(f789(f244(x100452),x100453),f13(x100452,f239(x100452),x100451)))
% 21.40/21.38 [10046]~P101(x100462)+E(x100461,f184(f870(x100462,a856)))+~P1(f789(f70(x100462),x100461))+E(f14(x100462,f244(x100462),f789(f264(x100462),f789(f789(f10(f870(x100462,a856),a856,x100462),f96(x100462)),f789(f789(f9(x100462,f870(x100462,a856),f870(x100462,a856)),f789(f789(f10(f870(x100462,f870(a856,a856)),f870(f870(x100462,a856),f870(x100462,a856)),x100462),f20(x100462,a856,a856)),f789(f789(f10(f870(x100462,a856),f870(x100462,f870(a856,a856)),x100462),f789(f10(a856,f870(a856,a856),x100462),a339)),f789(f789(f9(x100462,f870(x100462,x100462),f870(x100462,a856)),f789(f789(f10(f870(x100462,a856),f870(f870(x100462,x100462),f870(x100462,a856)),x100462),f10(x100462,a856,x100462)),a338)),f789(f239(x100462),x100463))))),f789(f789(f9(x100462,f870(x100462,a856),a856),f342(x100462)),x100461))))),f789(f789(f239(x100462),x100463),f14(x100462,f244(x100462),x100461)))
% 21.40/21.38 [9769]~P110(x97691)+~E(x97693,f2(x97691))+~E(x97692,f2(x97691))+E(f789(f789(f89(x97691),f789(f789(f250(x97691),x97692),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x97691),x97693),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f2(x97691))
% 21.40/21.38 [9932]~P117(x99321)+~P1(f789(f789(f240(x99321),f2(x99321)),x99323))+P1(f789(f789(f241(x99321),x99322),x99323))+~P1(f789(f789(f241(x99321),f789(f789(f250(x99321),x99322),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x99321),x99323),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))
% 21.40/21.38 [9933]~P117(x99331)+~P1(f789(f789(f240(x99331),f2(x99331)),x99333))+P1(f789(f789(f240(x99331),x99332),x99333))+~P1(f789(f789(f240(x99331),f789(f789(f250(x99331),x99332),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x99331),x99333),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))))
% 21.40/21.38 [9979]~P110(x99792)+~E(x99791,f2(x99792))+~E(x99793,f2(x99792))+~P1(f789(f789(f241(x99792),f2(x99792)),f789(f789(f89(x99792),f789(f789(f250(x99792),x99793),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106))))),f789(f789(f250(x99792),x99791),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))))
% 21.40/21.38 [9192]E(x91921,x91922)+~E(f765(x91921,x91922,x91924,x91923),f769(x91921,x91922,x91924,x91923))+P1(f789(f789(f342(f869(f864(x91923),f864(x91923))),f789(f789(f249(f864(x91923),f864(x91923)),x91922),x91921)),f143(x91923,x91924)))+P1(f789(f789(f342(f869(f864(x91923),f864(x91923))),f789(f789(f249(f864(x91923),f864(x91923)),x91921),x91922)),f143(x91923,x91924)))
% 21.40/21.38 [4793]~P60(x47932)+~E(x47934,f2(x47932))+~E(x47931,f2(x47932))+E(x47931,f789(f789(f291(x47932),x47933),x47934))
% 21.40/21.38 [4794]~P60(x47941)+~E(x47943,f2(x47941))+~E(x47944,f2(x47941))+E(f789(f789(f291(x47941),x47942),x47943),x47944)
% 21.40/21.38 [4900]~P60(x49002)+E(x49001,f2(x49002))+~E(x49003,f2(x49002))+~E(x49001,f789(f789(f291(x49002),x49004),x49003))
% 21.40/21.38 [4901]~P60(x49012)+E(x49011,f2(x49012))+~E(x49013,f2(x49012))+~E(f789(f789(f291(x49012),x49014),x49013),x49011)
% 21.40/21.38 [5080]~P113(x50802)+E(x50801,f2(x50802))+~E(f789(f789(f291(x50802),x50803),x50801),x50804)+E(x50803,f789(f789(f90(x50802),x50804),x50801))
% 21.40/21.38 [5081]~P113(x50812)+E(x50811,f2(x50812))+~E(f789(f789(f90(x50812),x50813),x50811),x50814)+E(x50813,f789(f789(f291(x50812),x50814),x50811))
% 21.40/21.38 [5082]~P113(x50822)+E(x50821,f2(x50822))+~E(f789(f789(f90(x50822),x50823),x50821),x50824)+E(x50823,f789(f789(f291(x50822),x50824),x50821))
% 21.40/21.38 [5083]~P60(x50832)+E(x50831,f2(x50832))+~E(f789(f789(f291(x50832),x50833),x50831),x50834)+E(x50833,f789(f789(f90(x50832),x50834),x50831))
% 21.40/21.38 [5084]~P60(x50842)+E(x50841,f2(x50842))+~E(f789(f789(f90(x50842),x50843),x50841),x50844)+E(x50843,f789(f789(f291(x50842),x50844),x50841))
% 21.40/21.38 [5085]~P113(x50852)+E(x50851,f2(x50852))+~E(x50853,f789(f789(f291(x50852),x50854),x50851))+E(f789(f789(f90(x50852),x50853),x50851),x50854)
% 21.40/21.38 [5086]~P113(x50862)+E(x50861,f2(x50862))+~E(x50863,f789(f789(f90(x50862),x50864),x50861))+E(f789(f789(f291(x50862),x50863),x50861),x50864)
% 21.40/21.38 [5087]~P113(x50872)+E(x50871,f2(x50872))+~E(x50873,f789(f789(f90(x50872),x50874),x50871))+E(f789(f789(f291(x50872),x50873),x50871),x50874)
% 21.40/21.38 [5088]~P60(x50882)+E(x50881,f2(x50882))+~E(x50883,f789(f789(f291(x50882),x50884),x50881))+E(f789(f789(f90(x50882),x50883),x50881),x50884)
% 21.40/21.38 [5089]~P60(x50892)+E(x50891,f2(x50892))+~E(x50893,f789(f789(f90(x50892),x50894),x50891))+E(f789(f789(f291(x50892),x50893),x50891),x50894)
% 21.40/21.38 [5121]~P60(x51212)+~E(x51211,f2(x51212))+~E(f789(f789(f90(x51212),x51211),x51214),x51213)+E(x51211,f789(f789(f291(x51212),x51213),x51214))
% 21.40/21.38 [5122]~P60(x51221)+~E(x51224,f2(x51221))+~E(x51222,f789(f789(f90(x51221),x51224),x51223))+E(f789(f789(f291(x51221),x51222),x51223),x51224)
% 21.40/21.38 [5190]~E(x51903,x51904)+~E(x51902,x51903)+~P99(x51901)+E(f303(x51901,x51902,x51903),f789(f789(f310(x51901),x51904),f184(f870(x51901,a856))))
% 21.40/21.38 [5384]~E(f140(x53842,x53841),x53844)+~E(f123(x53842,x53841),x53843)+E(x53841,f122(x53842))+E(f789(f789(f132(x53842),x53843),f789(f789(f146(x53842),x53844),f122(x53842))),x53841)
% 21.40/21.38 [6002]~P117(x60023)+E(x60021,x60022)+~E(f789(f789(f250(x60023),x60024),x60021),f789(f789(f250(x60023),x60024),x60022))+~P1(f789(f789(f241(x60023),f87(x60023)),x60024))
% 21.40/21.38 [6003]E(x60031,x60032)+~E(f789(f789(f310(x60033),x60034),x60031),f789(f789(f310(x60033),x60034),x60032))+P1(f789(f789(f342(x60033),x60034),x60032))+P1(f789(f789(f342(x60033),x60034),x60031))
% 21.40/21.38 [6042]E(f789(x60421,x60422),f2(a863))+~E(f789(f789(f8(x60423,a863),x60421),x60424),f2(a863))+~P1(f789(f70(x60423),x60424))+~P1(f789(f789(f342(x60423),x60422),x60424))
% 21.40/21.38 [6043]E(f789(x60431,x60432),f87(a863))+~E(f789(f789(f11(x60433,a863),x60431),x60434),f87(a863))+~P1(f789(f70(x60433),x60434))+~P1(f789(f789(f342(x60433),x60432),x60434))
% 21.40/21.38 [6264]~P99(x62641)+~P1(f789(f789(f241(x62641),x62644),x62643))+P1(f789(f789(f241(x62641),x62642),x62643))+~P1(f789(f789(f241(x62641),x62642),x62644))
% 21.40/21.38 [6265]~P99(x62651)+~P1(f789(f789(f240(x62651),x62654),x62653))+P1(f789(f789(f241(x62651),x62652),x62653))+~P1(f789(f789(f241(x62651),x62652),x62654))
% 21.40/21.38 [6266]~P99(x62661)+~P1(f789(f789(f240(x62661),x62662),x62664))+P1(f789(f789(f241(x62661),x62662),x62663))+~P1(f789(f789(f241(x62661),x62664),x62663))
% 21.40/21.38 [6267]~P105(x62671)+~P1(f789(f789(f241(x62671),x62672),x62674))+P1(f789(f789(f241(x62671),x62672),x62673))+~P1(f789(f789(f241(x62671),x62674),x62673))
% 21.40/21.38 [6268]~P105(x62681)+~P1(f789(f789(f240(x62681),x62682),x62684))+P1(f789(f789(f241(x62681),x62682),x62683))+~P1(f789(f789(f241(x62681),x62684),x62683))
% 21.40/21.38 [6269]~P105(x62691)+~P1(f789(f789(f240(x62691),x62694),x62693))+P1(f789(f789(f241(x62691),x62692),x62693))+~P1(f789(f789(f241(x62691),x62692),x62694))
% 21.40/21.38 [6270]~P99(x62701)+~P1(f789(f789(f240(x62701),x62704),x62703))+P1(f789(f789(f240(x62701),x62702),x62703))+~P1(f789(f789(f240(x62701),x62702),x62704))
% 21.40/21.38 [6271]~P105(x62711)+~P1(f789(f789(f240(x62711),x62712),x62714))+P1(f789(f789(f240(x62711),x62712),x62713))+~P1(f789(f789(f240(x62711),x62714),x62713))
% 21.40/21.38 [6272]~P70(x62721)+~P1(f789(f789(f287(x62721),x62722),x62724))+P1(f789(f789(f287(x62721),x62722),x62723))+~P1(f789(f789(f287(x62721),x62724),x62723))
% 21.40/21.38 [6515]~P9(x65151)+~P1(f789(f789(f240(x65151),x65152),f52(x65151,x65154)))+P1(f789(f789(f240(x65151),x65152),x65153))+~P1(f789(f789(f342(x65151),x65153),x65154))
% 21.40/21.38 [6664]~P101(x66641)+~P18(x66641,f789(f789(f146(x66641),x66642),x66644))+~P1(f789(f789(f342(x66641),x66643),f789(f163(x66641),x66644)))+P1(f789(f789(f240(x66641),x66642),x66643))
% 21.40/21.38 [6665]~P101(x66651)+~P18(x66651,f789(f789(f146(x66651),x66652),x66654))+~P1(f789(f789(f342(x66651),x66653),f789(f163(x66651),x66654)))+P1(f789(f789(f240(x66651),x66652),x66653))
% 21.40/21.38 [6758]~P9(x67581)+~P1(f789(f789(f240(x67581),f51(x67581,x67584)),x67583))+P1(f789(f789(f240(x67581),x67582),x67583))+~P1(f789(f789(f342(x67581),x67582),x67584))
% 21.40/21.38 [6909]~P7(x69091)+P1(f789(f789(f287(x69091),x69092),f59(x69091,x69093,x69094)))+~P1(f789(f789(f287(x69091),x69092),x69094))+~P1(f789(f789(f287(x69091),x69092),x69093))
% 21.40/21.38 [6910]~P7(x69101)+P1(f789(f789(f287(x69101),x69102),f59(x69101,x69103,x69104)))+~P1(f789(f789(f287(x69101),x69102),x69104))+~P1(f789(f789(f287(x69101),x69102),x69103))
% 21.40/21.38 [7170]~P101(x71701)+E(f789(f789(f110(f870(x71701,a856)),f789(f302(x71701,x71702),x71703)),f789(f302(x71701,x71703),x71704)),f789(f302(x71701,x71702),x71704))+~P1(f789(f789(f240(x71701),x71703),x71704))+~P1(f789(f789(f240(x71701),x71702),x71703))
% 21.40/21.38 [7256]~P7(x72561)+~P1(f789(f789(f287(x72561),x72562),f59(x72561,x72563,x72564)))+P1(f789(f789(f287(x72561),x72562),x72563))+~P1(f789(f789(f287(x72561),x72562),x72564))
% 21.40/21.38 [7257]~P7(x72571)+~P1(f789(f789(f287(x72571),x72572),f59(x72571,x72573,x72574)))+P1(f789(f789(f287(x72571),x72572),x72573))+~P1(f789(f789(f287(x72571),x72572),x72574))
% 21.40/21.38 [7298]~P101(x72981)+E(f789(f789(f110(f870(x72981,a856)),f789(f302(x72981,x72982),x72983)),f303(x72981,x72983,x72984)),f303(x72981,x72982,x72984))+~P1(f789(f789(f240(x72981),x72983),x72984))+~P1(f789(f789(f240(x72981),x72982),x72983))
% 21.40/21.38 [7312]~P99(x73121)+~P50(a863,x73121,f287(a863),x73122)+P1(f789(f789(f240(x73121),f789(x73122,x73123)),f789(x73122,x73124)))+~P1(f789(f789(f287(a863),x73123),x73124))
% 21.40/21.38 [7366]~P101(x73661)+E(f789(f789(f110(f870(x73661,a856)),f306(x73661,x73662,x73663)),f789(f302(x73661,x73663),x73664)),f306(x73661,x73662,x73664))+~P1(f789(f789(f241(x73661),x73662),x73663))+~P1(f789(f789(f240(x73661),x73663),x73664))
% 21.40/21.38 [7389]~P101(x73891)+E(f789(f789(f110(f870(x73891,a856)),f303(x73891,x73892,x73893)),f306(x73891,x73893,x73894)),f789(f302(x73891,x73892),x73894))+~P1(f789(f789(f241(x73891),x73893),x73894))+~P1(f789(f789(f240(x73891),x73892),x73893))
% 21.40/21.38 [7424]~P101(x74241)+E(f789(f789(f110(f870(x74241,a856)),f306(x74241,x74242,x74243)),f303(x74241,x74243,x74244)),f305(x74241,x74242,x74244))+~P1(f789(f789(f241(x74241),x74242),x74243))+~P1(f789(f789(f240(x74241),x74243),x74244))
% 21.40/21.38 [7425]~P101(x74251)+E(f789(f789(f110(f870(x74251,a856)),f305(x74251,x74252,x74253)),f306(x74251,x74253,x74254)),f306(x74251,x74252,x74254))+~P1(f789(f789(f241(x74251),x74253),x74254))+~P1(f789(f789(f240(x74251),x74252),x74253))
% 21.40/21.38 [7426]~P101(x74261)+E(f789(f789(f110(f870(x74261,a856)),f305(x74261,x74262,x74263)),f305(x74261,x74263,x74264)),f305(x74261,x74262,x74264))+~P1(f789(f789(f240(x74261),x74263),x74264))+~P1(f789(f789(f240(x74261),x74262),x74263))
% 21.40/21.38 [7427]~P101(x74271)+E(f789(f789(f110(f870(x74271,a856)),f303(x74271,x74272,x74273)),f305(x74271,x74273,x74274)),f303(x74271,x74272,x74274))+~P1(f789(f789(f240(x74271),x74273),x74274))+~P1(f789(f789(f240(x74271),x74272),x74273))
% 21.40/21.38 [8213]P29(x82131,x82132,f463(x82133,x82132,x82134,x82131),x82134)+~P1(f789(f70(x82132),x82133))+~P1(f789(f70(x82131),x82134))+~P1(f789(f789(f240(a863),f789(f49(x82131),x82134)),f789(f49(x82132),x82133)))
% 21.40/21.38 [8283]~P69(x82831)+~E(f789(x82833,f634(x82833,x82834,x82832,x82831)),f87(x82831))+E(f789(f789(f789(f74(x82831,x82832,f90(x82831)),x82833),f87(x82831)),x82834),f87(x82831))+~P1(f789(f70(x82832),x82834))
% 21.40/21.38 [8557]~P117(x85571)+~P1(f789(f789(f240(x85571),f2(x85571)),x85573))+P1(f789(f789(f240(x85571),x85572),x85573))+~P1(f789(f789(f240(x85571),f789(f789(f250(x85571),x85572),f789(a121,x85574))),f789(f789(f250(x85571),x85573),f789(a121,x85574))))
% 21.40/21.38 [8890]~P69(x88901)+E(f789(f789(f789(f74(x88901,x88902,f90(x88901)),x88903),f87(x88901)),x88904),f87(x88901))+~P1(f789(f70(x88902),x88904))+P1(f789(f789(f342(x88902),f634(x88903,x88904,x88902,x88901)),x88904))
% 21.40/21.38 [9142]~P12(x91422,x91423,x91424)+~P1(f789(f70(x91422),x91423))+~P1(f789(f789(f287(a863),x91421),f789(f49(x91422),f410(x91421,x91424,x91423,x91422))))+P1(f789(f789(f287(a863),x91421),f789(f49(x91422),x91423)))
% 21.40/21.38 [9326]~P1(f789(f789(f287(a863),x93262),x93263))+P1(f789(f789(f287(a863),x93261),x93262))+P1(f789(f789(f287(a863),x93263),x93264))+~P1(f789(f789(f241(f870(a863,a856)),f290(a863,f287(a863),x93262,x93263)),f290(a863,f287(a863),x93261,x93264)))
% 21.40/21.38 [9331]P1(f789(f789(f287(a863),x93311),x93312))+~P1(f789(f789(f287(a863),x93312),x93313))+~P1(f789(f789(f287(a863),x93314),x93313))+~P1(f789(f789(f241(f870(a863,a856)),f290(a863,f287(a863),x93312,x93313)),f290(a863,f287(a863),x93311,x93314)))
% 21.40/21.38 [9332]~P1(f789(f789(f287(a863),x93323),x93321))+P1(f789(f789(f287(a863),x93321),x93322))+~P1(f789(f789(f287(a863),x93323),x93324))+~P1(f789(f789(f241(f870(a863,a856)),f290(a863,f287(a863),x93323,x93321)),f290(a863,f287(a863),x93324,x93322)))
% 21.40/21.38 [9339]~P1(f789(f789(f287(a863),x93391),x93393))+~P1(f789(f789(f287(a863),x93391),x93392))+~P1(f789(f789(f287(a863),x93394),x93393))+~P1(f789(f789(f241(f870(a863,a856)),f290(a863,f287(a863),x93391,x93393)),f290(a863,f287(a863),x93392,x93394)))
% 21.40/21.38 [9345]~P1(f789(f789(f240(a1),x93454),f2(a1)))+P1(f789(f789(f240(a1),f789(f789(f89(a1),f789(f789(f90(a1),x93451),f59(a1,x93452,x93453))),x93454)),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x93453))+~P1(f789(f789(f241(a1),x93451),x93454))
% 21.40/21.38 [9760]~P1(f789(f70(x97601),x97602))+~P1(f789(f789(f342(x97601),x97604),x97602))+~P1(f789(f789(f342(x97601),x97603),x97602))+P1(f789(f789(f241(a863),f789(f49(x97601),f789(f789(f3(f870(x97601,a856)),f789(f789(f3(f870(x97601,a856)),x97602),f789(f789(f310(x97601),x97603),f184(f870(x97601,a856))))),f789(f789(f310(x97601),x97604),f184(f870(x97601,a856)))))),f789(f49(x97601),x97602)))
% 21.40/21.38 [6820]~P136(x68203)+~P112(x68203)+P1(f789(x68201,f351(x68202,x68201,x68203)))+~P1(f789(x68201,f789(f789(f90(x68203),x68202),x68204)))
% 21.40/21.38 [6880]~P101(x68801)+~P1(f789(f789(f241(x68801),x68802),x68804))+~P1(f789(f789(f241(x68801),x68802),x68803))+P1(f789(f789(f241(x68801),x68802),f789(f789(f244(x68801),x68803),x68804)))
% 21.40/21.38 [6881]~P101(x68811)+~P1(f789(f789(f240(x68811),x68812),x68814))+~P1(f789(f789(f240(x68811),x68812),x68813))+P1(f789(f789(f240(x68811),x68812),f789(f789(f244(x68811),x68813),x68814)))
% 21.40/21.38 [6882]~P101(x68821)+~P1(f789(f789(f240(x68821),x68822),x68824))+~P1(f789(f789(f240(x68821),x68822),x68823))+P1(f789(f789(f240(x68821),x68822),f789(f789(f244(x68821),x68823),x68824)))
% 21.40/21.38 [6883]~P101(x68831)+~P1(f789(f789(f240(x68831),x68832),x68834))+~P1(f789(f789(f240(x68831),x68832),x68833))+P1(f789(f789(f240(x68831),x68832),f789(f789(f244(x68831),x68833),x68834)))
% 21.40/21.38 [6884]~P98(x68841)+~P1(f789(f789(f240(x68841),x68842),x68844))+~P1(f789(f789(f240(x68841),x68842),x68843))+P1(f789(f789(f240(x68841),x68842),f789(f789(f111(x68841),x68843),x68844)))
% 21.40/21.38 [6885]~P98(x68851)+~P1(f789(f789(f240(x68851),x68852),x68854))+~P1(f789(f789(f240(x68851),x68852),x68853))+P1(f789(f789(f240(x68851),x68852),f789(f789(f111(x68851),x68853),x68854)))
% 21.40/21.38 [6886]~P98(x68861)+~P1(f789(f789(f240(x68861),x68862),x68864))+~P1(f789(f789(f240(x68861),x68862),x68863))+P1(f789(f789(f240(x68861),x68862),f789(f789(f111(x68861),x68863),x68864)))
% 21.40/21.38 [6887]~P70(x68871)+~P1(f789(f789(f287(x68871),x68872),x68874))+~P1(f789(f789(f287(x68871),x68872),x68873))+P1(f789(f789(f287(x68871),x68872),f789(f789(f89(x68871),x68873),x68874)))
% 21.40/21.38 [6888]~P104(x68881)+~P1(f789(f789(f287(x68881),x68882),x68884))+~P1(f789(f789(f287(x68881),x68882),x68883))+P1(f789(f789(f287(x68881),x68882),f789(f789(f3(x68881),x68883),x68884)))
% 21.40/21.38 [6908]~P61(x69082)+E(x69081,f2(x69082))+E(f789(f789(f291(x69082),f789(f789(f250(x69082),x69081),x69083)),f789(f789(f250(x69082),x69081),x69084)),f789(f789(f250(x69082),x69081),f789(f789(f3(a863),x69083),x69084)))+~P1(f789(f789(f240(a863),x69084),x69083))
% 21.40/21.38 [6951]~P101(x69511)+~P18(x69511,f789(f789(f146(x69511),x69513),x69514))+P18(x69511,f789(f789(f146(x69511),x69512),f789(f789(f146(x69511),x69513),x69514)))+~P1(f789(f789(f240(x69511),x69512),x69513))
% 21.40/21.38 [6952]~P101(x69521)+~P18(x69521,f789(f789(f146(x69521),x69523),x69524))+P18(x69521,f789(f789(f146(x69521),x69522),f789(f789(f146(x69521),x69523),x69524)))+~P1(f789(f789(f240(x69521),x69522),x69523))
% 21.40/21.38 [6992]~P82(x69921)+~P1(f789(f789(f240(x69921),f2(x69921)),x69923))+~P1(f789(f789(f241(x69921),x69922),x69924))+P1(f789(f789(f241(x69921),x69922),f789(f789(f89(x69921),x69923),x69924)))
% 21.40/21.38 [6993]~P82(x69931)+~P1(f789(f789(f240(x69931),x69932),x69934))+~P1(f789(f789(f241(x69931),f2(x69931)),x69933))+P1(f789(f789(f241(x69931),x69932),f789(f789(f89(x69931),x69933),x69934)))
% 21.40/21.38 [6994]~P117(x69941)+~P1(f789(f789(f241(x69941),f2(x69941)),x69943))+~P1(f789(f789(f241(x69941),x69942),x69944))+P1(f789(f789(f241(x69941),x69942),f789(f789(f89(x69941),x69943),x69944)))
% 21.40/21.38 [6995]~P82(x69951)+~P1(f789(f789(f240(x69951),f2(x69951)),x69954))+~P1(f789(f789(f240(x69951),x69952),x69953))+P1(f789(f789(f240(x69951),x69952),f789(f789(f89(x69951),x69953),x69954)))
% 21.40/21.38 [6996]~P82(x69961)+~P1(f789(f789(f240(x69961),f2(x69961)),x69963))+~P1(f789(f789(f240(x69961),x69962),x69964))+P1(f789(f789(f240(x69961),x69962),f789(f789(f89(x69961),x69963),x69964)))
% 21.40/21.38 [7030]~P101(x70301)+P1(f789(f789(f241(x70301),x70302),x70303))+P1(f789(f789(f241(x70301),x70302),x70304))+~P1(f789(f789(f241(x70301),x70302),f789(f789(f239(x70301),x70304),x70303)))
% 21.40/21.38 [7031]~P101(x70311)+P1(f789(f789(f240(x70311),x70312),x70313))+P1(f789(f789(f240(x70311),x70312),x70314))+~P1(f789(f789(f240(x70311),x70312),f789(f789(f239(x70311),x70314),x70313)))
% 21.40/21.38 [7714]~P63(x77141)+~P1(f789(f789(f241(x77141),x77144),f2(x77141)))+~P1(f789(f789(f241(x77141),x77143),f789(f789(f291(x77141),x77142),x77144)))+P1(f789(f789(f241(x77141),x77142),f789(f789(f90(x77141),x77143),x77144)))
% 21.40/21.38 [7715]~P63(x77151)+~P1(f789(f789(f241(x77151),x77154),f2(x77151)))+~P1(f789(f789(f241(x77151),x77153),f789(f789(f90(x77151),x77152),x77154)))+P1(f789(f789(f241(x77151),x77152),f789(f789(f291(x77151),x77153),x77154)))
% 21.40/21.38 [7716]~P63(x77161)+~P1(f789(f789(f241(x77161),x77164),f2(x77161)))+~P1(f789(f789(f240(x77161),x77163),f789(f789(f291(x77161),x77162),x77164)))+P1(f789(f789(f240(x77161),x77162),f789(f789(f90(x77161),x77163),x77164)))
% 21.40/21.38 [7717]~P63(x77171)+~P1(f789(f789(f241(x77171),x77174),f2(x77171)))+~P1(f789(f789(f240(x77171),x77173),f789(f789(f90(x77171),x77172),x77174)))+P1(f789(f789(f240(x77171),x77172),f789(f789(f291(x77171),x77173),x77174)))
% 21.40/21.38 [7827]~P118(x78271)+~P1(f789(f789(f241(x78271),x78272),f2(x78271)))+~P1(f789(f789(f241(x78271),x78274),x78273))+P1(f789(f789(f241(x78271),f789(f789(f90(x78271),x78272),x78273)),f789(f789(f90(x78271),x78272),x78274)))
% 21.40/21.38 [7828]~P118(x78281)+~P1(f789(f789(f241(x78281),x78282),f2(x78281)))+~P1(f789(f789(f241(x78281),x78284),x78283))+P1(f789(f789(f241(x78281),f789(f789(f90(x78281),x78282),x78283)),f789(f789(f90(x78281),x78282),x78284)))
% 21.40/21.38 [7829]~P118(x78291)+~P1(f789(f789(f241(x78291),x78293),f2(x78291)))+~P1(f789(f789(f241(x78291),x78294),x78292))+P1(f789(f789(f241(x78291),f789(f789(f90(x78291),x78292),x78293)),f789(f789(f90(x78291),x78294),x78293)))
% 21.40/21.38 [7830]~P118(x78301)+~P1(f789(f789(f241(x78301),x78303),f2(x78301)))+~P1(f789(f789(f241(x78301),x78304),x78302))+P1(f789(f789(f241(x78301),f789(f789(f90(x78301),x78302),x78303)),f789(f789(f90(x78301),x78304),x78303)))
% 21.40/21.38 [7831]~P118(x78311)+~P1(f789(f789(f241(x78311),x78312),f2(x78311)))+~P1(f789(f789(f241(x78311),x78314),x78313))+P1(f789(f789(f241(x78311),f789(f789(f90(x78311),x78312),x78313)),f789(f789(f90(x78311),x78312),x78314)))
% 21.40/21.38 [7832]~P63(x78321)+~P1(f789(f789(f241(x78321),x78323),f2(x78321)))+~P1(f789(f789(f241(x78321),x78324),x78322))+P1(f789(f789(f241(x78321),f789(f789(f291(x78321),x78322),x78323)),f789(f789(f291(x78321),x78324),x78323)))
% 21.40/21.38 [7833]~P118(x78331)+~P1(f789(f789(f241(x78331),x78332),f2(x78331)))+~P1(f789(f789(f240(x78331),x78334),x78333))+P1(f789(f789(f240(x78331),f789(f789(f90(x78331),x78332),x78333)),f789(f789(f90(x78331),x78332),x78334)))
% 21.40/21.38 [7834]~P129(x78341)+~P1(f789(f789(f240(x78341),x78342),f2(x78341)))+~P1(f789(f789(f240(x78341),x78344),x78343))+P1(f789(f789(f240(x78341),f789(f789(f90(x78341),x78342),x78343)),f789(f789(f90(x78341),x78342),x78344)))
% 21.40/21.38 [7835]~P129(x78351)+~P1(f789(f789(f240(x78351),x78353),f2(x78351)))+~P1(f789(f789(f240(x78351),x78354),x78352))+P1(f789(f789(f240(x78351),f789(f789(f90(x78351),x78352),x78353)),f789(f789(f90(x78351),x78354),x78353)))
% 21.40/21.38 [7836]~P62(x78361)+~P1(f789(f789(f240(x78361),x78363),f2(x78361)))+~P1(f789(f789(f240(x78361),x78364),x78362))+P1(f789(f789(f240(x78361),f789(f789(f291(x78361),x78362),x78363)),f789(f789(f291(x78361),x78364),x78363)))
% 21.40/21.38 [7837]~P117(x78371)+~P1(f789(f789(f241(x78371),f87(x78371)),x78372))+~P1(f789(f789(f241(a863),x78373),x78374))+P1(f789(f789(f241(x78371),f789(f789(f250(x78371),x78372),x78373)),f789(f789(f250(x78371),x78372),x78374)))
% 21.40/21.38 [7838]~P117(x78381)+~P1(f789(f789(f241(x78381),f87(x78381)),x78382))+~P1(f789(f789(f241(a863),x78383),x78384))+P1(f789(f789(f241(x78381),f789(f789(f250(x78381),x78382),x78383)),f789(f789(f250(x78381),x78382),x78384)))
% 21.40/21.38 [7839]~P117(x78391)+~P1(f789(f789(f241(x78391),f87(x78391)),x78392))+~P1(f789(f789(f240(a863),x78393),x78394))+P1(f789(f789(f240(x78391),f789(f789(f250(x78391),x78392),x78393)),f789(f789(f250(x78391),x78392),x78394)))
% 21.40/21.38 [7840]~P117(x78401)+~P1(f789(f789(f240(x78401),f87(x78401)),x78402))+~P1(f789(f789(f240(a863),x78403),x78404))+P1(f789(f789(f240(x78401),f789(f789(f250(x78401),x78402),x78403)),f789(f789(f250(x78401),x78402),x78404)))
% 21.40/21.38 [7867]P1(f789(f789(f241(a863),f2(a863)),f789(x78671,x78672)))+~P1(f789(f70(x78673),x78674))+~P1(f789(f789(f342(x78673),x78672),x78674))+~P1(f789(f789(f241(a863),f2(a863)),f789(f789(f11(x78673,a863),x78671),x78674)))
% 21.40/21.38 [7878]~P118(x78781)+~P1(f789(f789(f241(x78781),x78783),x78784))+~P1(f789(f789(f241(x78781),f2(x78781)),x78782))+P1(f789(f789(f241(x78781),f789(f789(f90(x78781),x78782),x78783)),f789(f789(f90(x78781),x78782),x78784)))
% 21.40/21.38 [7879]~P115(x78791)+~P1(f789(f789(f241(x78791),x78793),x78794))+~P1(f789(f789(f241(x78791),f2(x78791)),x78792))+P1(f789(f789(f241(x78791),f789(f789(f90(x78791),x78792),x78793)),f789(f789(f90(x78791),x78792),x78794)))
% 21.40/21.38 [7880]~P124(x78801)+~P1(f789(f789(f241(x78801),x78803),x78804))+~P1(f789(f789(f241(x78801),f2(x78801)),x78802))+P1(f789(f789(f241(x78801),f789(f789(f90(x78801),x78802),x78803)),f789(f789(f90(x78801),x78802),x78804)))
% 21.40/21.38 [7881]~P118(x78811)+~P1(f789(f789(f241(x78811),x78812),x78814))+~P1(f789(f789(f241(x78811),f2(x78811)),x78813))+P1(f789(f789(f241(x78811),f789(f789(f90(x78811),x78812),x78813)),f789(f789(f90(x78811),x78814),x78813)))
% 21.40/21.38 [7882]~P124(x78821)+~P1(f789(f789(f241(x78821),x78822),x78824))+~P1(f789(f789(f241(x78821),f2(x78821)),x78823))+P1(f789(f789(f241(x78821),f789(f789(f90(x78821),x78822),x78823)),f789(f789(f90(x78821),x78824),x78823)))
% 21.40/21.38 [7883]~P118(x78831)+~P1(f789(f789(f241(x78831),x78833),x78834))+~P1(f789(f789(f241(x78831),f2(x78831)),x78832))+P1(f789(f789(f241(x78831),f789(f789(f90(x78831),x78832),x78833)),f789(f789(f90(x78831),x78832),x78834)))
% 21.40/21.38 [7884]~P63(x78841)+~P1(f789(f789(f241(x78841),x78842),x78844))+~P1(f789(f789(f241(x78841),f2(x78841)),x78843))+P1(f789(f789(f241(x78841),f789(f789(f291(x78841),x78842),x78843)),f789(f789(f291(x78841),x78844),x78843)))
% 21.40/21.38 [7885]~P118(x78851)+~P1(f789(f789(f241(x78851),f2(x78851)),x78852))+~P1(f789(f789(f240(x78851),x78853),x78854))+P1(f789(f789(f240(x78851),f789(f789(f90(x78851),x78852),x78853)),f789(f789(f90(x78851),x78852),x78854)))
% 21.40/21.38 [7886]~P131(x78861)+~P1(f789(f789(f240(x78861),x78863),x78864))+~P1(f789(f789(f240(x78861),f2(x78861)),x78862))+P1(f789(f789(f240(x78861),f789(f789(f90(x78861),x78862),x78863)),f789(f789(f90(x78861),x78862),x78864)))
% 21.40/21.38 [7887]~P130(x78871)+~P1(f789(f789(f240(x78871),x78873),x78874))+~P1(f789(f789(f240(x78871),f2(x78871)),x78872))+P1(f789(f789(f240(x78871),f789(f789(f90(x78871),x78872),x78873)),f789(f789(f90(x78871),x78872),x78874)))
% 21.40/21.38 [7888]~P131(x78881)+~P1(f789(f789(f240(x78881),x78882),x78884))+~P1(f789(f789(f240(x78881),f2(x78881)),x78883))+P1(f789(f789(f240(x78881),f789(f789(f90(x78881),x78882),x78883)),f789(f789(f90(x78881),x78884),x78883)))
% 21.40/21.38 [7889]~P117(x78891)+~P1(f789(f789(f240(x78891),x78892),x78894))+~P1(f789(f789(f240(x78891),f2(x78891)),x78892))+P1(f789(f789(f240(x78891),f789(f789(f250(x78891),x78892),x78893)),f789(f789(f250(x78891),x78894),x78893)))
% 21.40/21.38 [7890]~P62(x78901)+~P1(f789(f789(f240(x78901),x78902),x78904))+~P1(f789(f789(f240(x78901),f2(x78901)),x78903))+P1(f789(f789(f240(x78901),f789(f789(f291(x78901),x78902),x78903)),f789(f789(f291(x78901),x78904),x78903)))
% 21.40/21.38 [7929]~P100(x79292)+P1(f789(f789(f240(f870(x79291,x79292)),x79294),x79293))+~P1(f789(f789(f240(f870(x79291,x79292)),x79293),x79294))+P1(f789(f789(f241(f870(x79291,x79292)),x79293),x79294))
% 21.40/21.38 [7971]P1(f789(f789(f342(x79711),x79712),x79713))+P1(f789(f789(f342(x79711),x79712),x79714))+~P1(f789(f789(f240(f870(x79711,a856)),x79714),x79713))+P1(f789(f789(f241(f870(x79711,a856)),x79714),f789(f789(f310(x79711),x79712),x79713)))
% 21.40/21.38 [8078]~P111(x80782)+E(x80781,f2(x80782))+P1(f789(f789(f287(x80782),x80783),x80784))+~P1(f789(f789(f287(x80782),f789(f789(f90(x80782),x80783),x80781)),f789(f789(f90(x80782),x80784),x80781)))
% 21.40/21.38 [8079]~P111(x80792)+E(x80791,f2(x80792))+P1(f789(f789(f287(x80792),x80793),x80794))+~P1(f789(f789(f287(x80792),f789(f789(f90(x80792),x80791),x80793)),f789(f789(f90(x80792),x80791),x80794)))
% 21.40/21.38 [8123]P1(f789(f789(f342(x81231),x81232),x81233))+P1(f789(f789(f342(x81231),x81232),x81234))+~P1(f789(f789(f241(f870(x81231,a856)),x81234),f789(f789(f310(x81231),x81232),x81233)))+P1(f789(f789(f240(f870(x81231,a856)),x81234),x81233))
% 21.40/21.38 [8191]~P118(x81911)+P1(f789(f789(f241(x81911),x81913),x81912))+P1(f789(f789(f241(x81911),x81912),x81913))+~P1(f789(f789(f241(x81911),f789(f789(f90(x81911),x81914),x81912)),f789(f789(f90(x81911),x81914),x81913)))
% 21.40/21.38 [8192]~P118(x81921)+P1(f789(f789(f241(x81921),x81923),x81922))+P1(f789(f789(f241(x81921),x81922),x81923))+~P1(f789(f789(f241(x81921),f789(f789(f90(x81921),x81922),x81924)),f789(f789(f90(x81921),x81923),x81924)))
% 21.40/21.38 [8203]~P118(x82031)+P1(f789(f789(f241(x82031),x82034),f2(x82031)))+P1(f789(f789(f241(x82031),x82032),x82033))+~P1(f789(f789(f241(x82031),f789(f789(f90(x82031),x82032),x82034)),f789(f789(f90(x82031),x82033),x82034)))
% 21.40/21.38 [8204]~P118(x82041)+P1(f789(f789(f241(x82041),x82044),f2(x82041)))+P1(f789(f789(f241(x82041),x82042),x82043))+~P1(f789(f789(f241(x82041),f789(f789(f90(x82041),x82044),x82042)),f789(f789(f90(x82041),x82044),x82043)))
% 21.40/21.38 [8207]~P118(x82071)+P1(f789(f789(f241(x82071),x82072),x82073))+P1(f789(f789(f241(x82071),f2(x82071)),x82074))+~P1(f789(f789(f241(x82071),f789(f789(f90(x82071),x82074),x82073)),f789(f789(f90(x82071),x82074),x82072)))
% 21.40/21.38 [8208]~P118(x82081)+P1(f789(f789(f241(x82081),x82082),x82083))+P1(f789(f789(f241(x82081),f2(x82081)),x82084))+~P1(f789(f789(f241(x82081),f789(f789(f90(x82081),x82083),x82084)),f789(f789(f90(x82081),x82082),x82084)))
% 21.40/21.38 [8221]~P118(x82211)+P1(f789(f789(f241(x82211),x82212),f2(x82211)))+P1(f789(f789(f241(x82211),f2(x82211)),x82212))+~P1(f789(f789(f241(x82211),f789(f789(f90(x82211),x82213),x82212)),f789(f789(f90(x82211),x82214),x82212)))
% 21.40/21.38 [8222]~P118(x82221)+P1(f789(f789(f241(x82221),x82222),f2(x82221)))+P1(f789(f789(f241(x82221),f2(x82221)),x82222))+~P1(f789(f789(f241(x82221),f789(f789(f90(x82221),x82222),x82223)),f789(f789(f90(x82221),x82222),x82224)))
% 21.40/21.38 [8246]~P118(x82461)+~P1(f789(f789(f241(x82461),x82464),f2(x82461)))+P1(f789(f789(f241(x82461),x82462),x82463))+~P1(f789(f789(f241(x82461),f789(f789(f90(x82461),x82464),x82463)),f789(f789(f90(x82461),x82464),x82462)))
% 21.40/21.38 [8247]~P118(x82471)+~P1(f789(f789(f241(x82471),x82474),f2(x82471)))+P1(f789(f789(f240(x82471),x82472),x82473))+~P1(f789(f789(f240(x82471),f789(f789(f90(x82471),x82474),x82473)),f789(f789(f90(x82471),x82474),x82472)))
% 21.40/21.38 [8258]~P117(x82583)+~P1(f789(f789(f241(x82583),f87(x82583)),x82584))+P1(f789(f789(f241(a863),x82581),x82582))+~P1(f789(f789(f241(x82583),f789(f789(f250(x82583),x82584),x82581)),f789(f789(f250(x82583),x82584),x82582)))
% 21.40/21.38 [8259]~P117(x82593)+~P1(f789(f789(f241(x82593),f87(x82593)),x82594))+P1(f789(f789(f241(a863),x82591),x82592))+~P1(f789(f789(f241(x82593),f789(f789(f250(x82593),x82594),x82591)),f789(f789(f250(x82593),x82594),x82592)))
% 21.40/21.38 [8260]~P117(x82603)+~P1(f789(f789(f241(x82603),f87(x82603)),x82604))+P1(f789(f789(f240(a863),x82601),x82602))+~P1(f789(f789(f240(x82603),f789(f789(f250(x82603),x82604),x82601)),f789(f789(f250(x82603),x82604),x82602)))
% 21.40/21.38 [8261]~P117(x82613)+~P1(f789(f789(f241(x82613),f87(x82613)),x82614))+P1(f789(f789(f240(a863),x82611),x82612))+~P1(f789(f789(f240(x82613),f789(f789(f250(x82613),x82614),x82611)),f789(f789(f250(x82613),x82614),x82612)))
% 21.40/21.38 [8271]~P118(x82711)+P1(f789(f789(f241(x82711),x82712),x82713))+~P1(f789(f789(f241(x82711),f2(x82711)),x82714))+~P1(f789(f789(f241(x82711),f789(f789(f90(x82711),x82714),x82712)),f789(f789(f90(x82711),x82714),x82713)))
% 21.40/21.38 [8272]~P124(x82721)+P1(f789(f789(f241(x82721),x82722),x82723))+~P1(f789(f789(f240(x82721),f2(x82721)),x82724))+~P1(f789(f789(f241(x82721),f789(f789(f90(x82721),x82724),x82722)),f789(f789(f90(x82721),x82724),x82723)))
% 21.40/21.38 [8273]~P126(x82731)+P1(f789(f789(f241(x82731),x82732),x82733))+~P1(f789(f789(f240(x82731),f2(x82731)),x82734))+~P1(f789(f789(f241(x82731),f789(f789(f90(x82731),x82734),x82732)),f789(f789(f90(x82731),x82734),x82733)))
% 21.40/21.38 [8274]~P117(x82741)+~P1(f789(f789(f240(x82741),f2(x82741)),x82743))+P1(f789(f789(f241(x82741),x82742),x82743))+~P1(f789(f789(f241(x82741),f789(f789(f250(x82741),x82742),x82744)),f789(f789(f250(x82741),x82743),x82744)))
% 21.40/21.38 [8275]~P124(x82751)+P1(f789(f789(f241(x82751),x82752),x82753))+~P1(f789(f789(f240(x82751),f2(x82751)),x82754))+~P1(f789(f789(f241(x82751),f789(f789(f90(x82751),x82752),x82754)),f789(f789(f90(x82751),x82753),x82754)))
% 21.40/21.38 [8276]~P126(x82761)+P1(f789(f789(f241(x82761),x82762),x82763))+~P1(f789(f789(f240(x82761),f2(x82761)),x82764))+~P1(f789(f789(f241(x82761),f789(f789(f90(x82761),x82762),x82764)),f789(f789(f90(x82761),x82763),x82764)))
% 21.40/21.38 [8277]~P118(x82771)+P1(f789(f789(f240(x82771),x82772),x82773))+~P1(f789(f789(f241(x82771),f2(x82771)),x82774))+~P1(f789(f789(f240(x82771),f789(f789(f90(x82771),x82774),x82772)),f789(f789(f90(x82771),x82774),x82773)))
% 21.40/21.38 [8278]~P124(x82781)+P1(f789(f789(f240(x82781),x82782),x82783))+~P1(f789(f789(f241(x82781),f2(x82781)),x82784))+~P1(f789(f789(f240(x82781),f789(f789(f90(x82781),x82784),x82782)),f789(f789(f90(x82781),x82784),x82783)))
% 21.40/21.38 [8279]~P124(x82791)+P1(f789(f789(f240(x82791),x82792),x82793))+~P1(f789(f789(f241(x82791),f2(x82791)),x82794))+~P1(f789(f789(f240(x82791),f789(f789(f90(x82791),x82792),x82794)),f789(f789(f90(x82791),x82793),x82794)))
% 21.40/21.38 [8320]P1(f789(f789(f342(x83201),x83202),x83203))+~P1(f789(f789(f240(f870(x83201,a856)),x83203),x83204))+~P1(f789(f789(f241(f870(x83201,a856)),x83203),x83204))+P1(f789(f789(f241(f870(x83201,a856)),x83203),f789(f789(f310(x83201),x83202),x83204)))
% 21.40/21.38 [8355]~P136(x83551)+~P112(x83551)+P1(f789(f789(f287(x83551),x83552),f789(f789(f89(x83551),f351(x83552,x83553,x83551)),f2(x83551))))+~P1(f789(x83553,f789(f789(f90(x83551),x83552),x83554)))
% 21.40/21.38 [8681]E(f789(f789(f3(a1),f489(x86811,x86812,x86813,x86814)),f490(x86811,x86812,x86813,x86814)),x86814)+~P1(f789(f789(f241(a1),f2(a1)),x86813))+~P1(f789(f789(f240(a1),x86811),x86814))+P1(f789(f789(f240(a1),x86811),f789(f789(f89(a1),x86814),x86813)))
% 21.40/21.38 [8682]E(f789(f789(f3(a1),f499(x86821,x86822,x86823,x86824)),f500(x86821,x86822,x86823,x86824)),x86824)+~P1(f789(f789(f241(a1),f2(a1)),x86823))+~P1(f789(f789(f241(a1),x86821),x86824))+P1(f789(f789(f241(a1),x86821),f789(f789(f89(a1),x86824),x86823)))
% 21.40/21.38 [8808]~E(f789(f789(f159(x88081),x88083),f771(x88084,x88083,x88081,x88082)),f789(f789(f159(x88081),x88084),f771(x88084,x88083,x88081,x88082)))+E(f789(f789(f164(x88081),x88082),x88083),f789(f789(f164(x88081),x88082),x88084))+~P1(f789(f789(f240(a863),x88082),f789(f185(f864(x88081)),x88083)))+~P1(f789(f789(f240(a863),x88082),f789(f185(f864(x88081)),x88084)))
% 21.40/21.38 [8862]~P1(f789(f789(f241(a1),f2(a1)),x88623))+~P1(f789(f789(f240(a1),x88621),x88624))+P1(f789(f789(f342(a1),f489(x88621,x88622,x88623,x88624)),x88622))+P1(f789(f789(f240(a1),x88621),f789(f789(f89(a1),x88624),x88623)))
% 21.40/21.38 [8863]~P1(f789(f789(f241(a1),f2(a1)),x88633))+~P1(f789(f789(f241(a1),x88631),x88634))+P1(f789(f789(f342(a1),f499(x88631,x88632,x88633,x88634)),x88632))+P1(f789(f789(f241(a1),x88631),f789(f789(f89(a1),x88634),x88633)))
% 21.40/21.38 [8899]~P101(x88991)+~P1(f789(f70(x88991),x88993))+~P1(f789(f789(f342(x88991),x88994),x88993))+P1(f789(f789(f240(x88991),f789(f789(f73(x88991,x88991,f244(x88991)),x88992),x88993)),f789(f789(f244(x88991),x88994),x88992)))
% 21.40/21.38 [8900]~P98(x89001)+~P1(f789(f70(x89001),x89003))+~P1(f789(f789(f342(x89001),x89004),x89003))+P1(f789(f789(f240(x89001),f789(f789(f73(x89001,x89001,f111(x89001)),x89002),x89003)),f789(f789(f111(x89001),x89004),x89002)))
% 21.40/21.38 [8909]~P12(x89092,x89093,x89094)+~P1(f789(f70(x89092),x89093))+P1(f789(f789(f287(a863),x89091),f789(f49(x89092),x89093)))+P1(f789(f789(f342(f870(x89092,a856)),f410(x89091,x89094,x89093,x89092)),f789(f789(f68(x89092),x89093),x89094)))
% 21.40/21.38 [8947]E(f789(f789(f164(x89471),x89472),x89473),f789(f789(f164(x89471),x89472),x89474))+P1(f789(f789(f241(a863),f771(x89473,x89474,x89471,x89472)),x89472))+~P1(f789(f789(f240(a863),x89472),f789(f185(f864(x89471)),x89473)))+~P1(f789(f789(f240(a863),x89472),f789(f185(f864(x89471)),x89474)))
% 21.40/21.38 [8952]~P1(f789(f789(f241(a1),f2(a1)),x89523))+~P1(f789(f789(f241(a1),x89521),x89522))+P1(f789(f789(f342(a1),f500(x89521,x89524,x89523,x89522)),f303(a1,f87(a1),x89523)))+P1(f789(f789(f241(a1),x89521),f789(f789(f89(a1),x89522),x89523)))
% 21.40/21.38 [8953]~P1(f789(f789(f241(a1),f2(a1)),x89533))+~P1(f789(f789(f240(a1),x89531),x89532))+P1(f789(f789(f342(a1),f490(x89531,x89534,x89533,x89532)),f303(a1,f87(a1),x89533)))+P1(f789(f789(f240(a1),x89531),f789(f789(f89(a1),x89532),x89533)))
% 21.40/21.38 [9118]~E(f170(x91181,x91182,x91183),f170(x91181,x91182,x91184))+E(f789(f163(f869(x91181,x91182)),x91183),f789(f163(f869(x91181,x91182)),x91184))+~P1(f789(f134(x91181),f789(f789(f150(f869(x91181,x91182),x91181),f248(x91181,x91182)),x91184)))+~P1(f789(f134(x91181),f789(f789(f150(f869(x91181,x91182),x91181),f248(x91181,x91182)),x91183)))
% 21.40/21.38 [9121]E(f170(x91211,x91212,x91213),f170(x91211,x91212,x91214))+~E(f789(f163(f869(x91211,x91212)),x91213),f789(f163(f869(x91211,x91212)),x91214))+~P1(f789(f134(x91211),f789(f789(f150(f869(x91211,x91212),x91211),f248(x91211,x91212)),x91214)))+~P1(f789(f134(x91211),f789(f789(f150(f869(x91211,x91212),x91211),f248(x91211,x91212)),x91213)))
% 21.40/21.38 [9235]~P101(x92351)+~P1(f789(f70(x92351),x92354))+P1(f789(f789(f342(x92351),f689(x92352,x92353,x92354,x92351)),x92354))+P1(f789(f789(f240(x92351),f789(f789(f73(x92351,x92351,f239(x92351)),x92352),x92354)),f789(f789(f239(x92351),x92353),x92352)))
% 21.40/21.38 [9236]~P94(x92361)+~P1(f789(f70(x92361),x92364))+P1(f789(f789(f342(x92361),f706(x92362,x92363,x92364,x92361)),x92364))+P1(f789(f789(f240(x92361),f789(f789(f73(x92361,x92361,f110(x92361)),x92362),x92364)),f789(f789(f110(x92361),x92363),x92362)))
% 21.40/21.38 [9362]~P101(x93621)+~P1(f789(f70(x93621),x93623))+~P1(f789(f789(f240(x93621),f689(x93622,x93624,x93623,x93621)),x93624))+P1(f789(f789(f240(x93621),f789(f789(f73(x93621,x93621,f239(x93621)),x93622),x93623)),f789(f789(f239(x93621),x93624),x93622)))
% 21.40/21.38 [9363]~P94(x93631)+~P1(f789(f70(x93631),x93633))+~P1(f789(f789(f240(x93631),f706(x93632,x93634,x93633,x93631)),x93634))+P1(f789(f789(f240(x93631),f789(f789(f73(x93631,x93631,f110(x93631)),x93632),x93633)),f789(f789(f110(x93631),x93634),x93632)))
% 21.40/21.38 [9366]~P1(f789(f789(f241(a1),f2(a1)),x93663))+~P1(f789(f789(f240(a1),f2(a1)),x93664))+~P1(f789(f789(f241(a1),x93664),x93661))+P1(f789(f789(f241(a1),f789(f789(f89(a1),f789(f789(f90(a1),x93661),f59(a1,x93662,x93663))),x93664)),f789(f789(f90(a1),x93661),x93663)))
% 21.40/21.38 [9635]~P99(x96351)+P1(f789(f789(f241(x96351),f789(x96352,x96353)),f789(x96352,x96354)))+~P1(f789(f789(f241(a863),x96353),x96354))+~P1(f789(f789(f241(x96351),f789(x96352,f768(x96354,x96353,x96352,x96351))),f789(x96352,f789(a121,f768(x96354,x96353,x96352,x96351)))))
% 21.40/21.38 [9729]E(x97291,x97292)+P1(f789(f789(f342(f869(f864(x97293),f864(x97293))),f789(f789(f249(f864(x97293),f864(x97293)),x97292),x97291)),f143(x97293,x97294)))+P1(f789(f789(f342(f869(f864(x97293),f864(x97293))),f789(f789(f249(f864(x97293),f864(x97293)),x97291),x97292)),f143(x97293,x97294)))+~P1(f789(f789(f342(f869(x97293,x97293)),f789(f789(f249(x97293,x97293),f765(x97291,x97292,x97294,x97293)),f769(x97291,x97292,x97294,x97293))),x97294))
% 21.40/21.38 [9730]E(x97301,x97302)+P1(f789(f789(f342(f869(f864(x97303),f864(x97303))),f789(f789(f249(f864(x97303),f864(x97303)),x97302),x97301)),f143(x97303,x97304)))+P1(f789(f789(f342(f869(f864(x97303),f864(x97303))),f789(f789(f249(f864(x97303),f864(x97303)),x97301),x97302)),f143(x97303,x97304)))+~P1(f789(f789(f342(f869(x97303,x97303)),f789(f789(f249(x97303,x97303),f769(x97301,x97302,x97304,x97303)),f765(x97301,x97302,x97304,x97303))),x97304))
% 21.40/21.38 [7413]~P101(x74131)+~P1(f789(f789(f241(x74131),x74133),x74134))+~P1(f789(f789(f241(x74131),x74132),x74134))+P1(f789(f789(f241(x74131),f789(f789(f239(x74131),x74132),x74133)),x74134))
% 21.40/21.38 [7414]~P101(x74141)+~P1(f789(f789(f240(x74141),x74143),x74144))+~P1(f789(f789(f240(x74141),x74142),x74144))+P1(f789(f789(f240(x74141),f789(f789(f239(x74141),x74142),x74143)),x74144))
% 21.40/21.38 [7415]~P101(x74151)+~P1(f789(f789(f240(x74151),x74153),x74154))+~P1(f789(f789(f240(x74151),x74152),x74154))+P1(f789(f789(f240(x74151),f789(f789(f239(x74151),x74152),x74153)),x74154))
% 21.40/21.38 [7416]~P101(x74161)+~P1(f789(f789(f240(x74161),x74163),x74164))+~P1(f789(f789(f240(x74161),x74162),x74164))+P1(f789(f789(f240(x74161),f789(f789(f239(x74161),x74162),x74163)),x74164))
% 21.40/21.38 [7417]~P94(x74171)+~P1(f789(f789(f240(x74171),x74173),x74174))+~P1(f789(f789(f240(x74171),x74172),x74174))+P1(f789(f789(f240(x74171),f789(f789(f110(x74171),x74172),x74173)),x74174))
% 21.40/21.38 [7418]~P94(x74181)+~P1(f789(f789(f240(x74181),x74183),x74184))+~P1(f789(f789(f240(x74181),x74182),x74184))+P1(f789(f789(f240(x74181),f789(f789(f110(x74181),x74182),x74183)),x74184))
% 21.40/21.38 [7419]~P94(x74191)+~P1(f789(f789(f240(x74191),x74193),x74194))+~P1(f789(f789(f240(x74191),x74192),x74194))+P1(f789(f789(f240(x74191),f789(f789(f110(x74191),x74192),x74193)),x74194))
% 21.40/21.38 [7660]~P7(x76601)+E(f789(f789(f89(x76601),f789(f789(f50(x76601),x76602),x76603)),f789(f789(f50(x76601),x76604),x76603)),f789(f789(f50(x76601),f789(f789(f89(x76601),x76602),x76604)),x76603))+~P1(f789(f789(f287(x76601),x76603),x76604))+~P1(f789(f789(f287(x76601),x76603),x76602))
% 21.40/21.38 [7737]~E(x77371,x77373)+E(f136(a863,f789(f302(a863,x77371),x77372)),f789(f789(f146(a863),x77373),x77374))+~E(f136(a863,f789(f302(a863,f789(f789(f89(a863),x77371),f87(a863))),x77372)),x77374)+~P1(f789(f789(f241(a863),x77371),x77372))
% 21.40/21.38 [7748]~P101(x77481)+P1(f789(f789(f241(x77481),x77482),x77483))+P1(f789(f789(f241(x77481),x77484),x77483))+~P1(f789(f789(f241(x77481),f789(f789(f244(x77481),x77484),x77482)),x77483))
% 21.40/21.38 [7749]~P101(x77491)+P1(f789(f789(f240(x77491),x77492),x77493))+P1(f789(f789(f240(x77491),x77494),x77493))+~P1(f789(f789(f240(x77491),f789(f789(f244(x77491),x77494),x77492)),x77493))
% 21.40/21.38 [8028]~P62(x80281)+~P1(f789(f789(f241(x80281),f2(x80281)),x80283))+~P1(f789(f789(f241(x80281),x80282),f789(f789(f291(x80281),x80284),x80283)))+P1(f789(f789(f241(x80281),f789(f789(f90(x80281),x80282),x80283)),x80284))
% 21.40/21.38 [8029]~P63(x80291)+~P1(f789(f789(f241(x80291),f2(x80291)),x80293))+~P1(f789(f789(f241(x80291),x80292),f789(f789(f291(x80291),x80294),x80293)))+P1(f789(f789(f241(x80291),f789(f789(f90(x80291),x80292),x80293)),x80294))
% 21.40/21.38 [8030]~P62(x80301)+~P1(f789(f789(f241(x80301),f2(x80301)),x80303))+~P1(f789(f789(f241(x80301),x80302),f789(f789(f90(x80301),x80304),x80303)))+P1(f789(f789(f241(x80301),f789(f789(f291(x80301),x80302),x80303)),x80304))
% 21.40/21.38 [8031]~P63(x80311)+~P1(f789(f789(f241(x80311),f2(x80311)),x80313))+~P1(f789(f789(f241(x80311),x80312),f789(f789(f90(x80311),x80314),x80313)))+P1(f789(f789(f241(x80311),f789(f789(f291(x80311),x80312),x80313)),x80314))
% 21.40/21.38 [8032]~P63(x80321)+~P1(f789(f789(f241(x80321),f2(x80321)),x80323))+~P1(f789(f789(f241(x80321),x80322),f789(f789(f90(x80321),x80324),x80323)))+P1(f789(f789(f241(x80321),f789(f789(f291(x80321),x80322),x80323)),x80324))
% 21.40/21.38 [8033]~P62(x80331)+~P1(f789(f789(f241(x80331),f2(x80331)),x80333))+~P1(f789(f789(f240(x80331),x80332),f789(f789(f291(x80331),x80334),x80333)))+P1(f789(f789(f240(x80331),f789(f789(f90(x80331),x80332),x80333)),x80334))
% 21.40/21.38 [8034]~P63(x80341)+~P1(f789(f789(f241(x80341),f2(x80341)),x80343))+~P1(f789(f789(f240(x80341),x80342),f789(f789(f291(x80341),x80344),x80343)))+P1(f789(f789(f240(x80341),f789(f789(f90(x80341),x80342),x80343)),x80344))
% 21.40/21.38 [8035]~P62(x80351)+~P1(f789(f789(f241(x80351),f2(x80351)),x80353))+~P1(f789(f789(f240(x80351),x80352),f789(f789(f90(x80351),x80354),x80353)))+P1(f789(f789(f240(x80351),f789(f789(f291(x80351),x80352),x80353)),x80354))
% 21.40/21.38 [8036]~P63(x80361)+~P1(f789(f789(f241(x80361),f2(x80361)),x80363))+~P1(f789(f789(f240(x80361),x80362),f789(f789(f90(x80361),x80364),x80363)))+P1(f789(f789(f240(x80361),f789(f789(f291(x80361),x80362),x80363)),x80364))
% 21.40/21.38 [8037]~P63(x80371)+~P1(f789(f789(f241(x80371),f2(x80371)),x80373))+~P1(f789(f789(f240(x80371),x80372),f789(f789(f90(x80371),x80374),x80373)))+P1(f789(f789(f240(x80371),f789(f789(f291(x80371),x80372),x80373)),x80374))
% 21.40/21.38 [8160]~P62(x81601)+~P1(f789(f789(f241(x81601),f2(x81601)),x81604))+P1(f789(f789(f241(x81601),x81602),f789(f789(f90(x81601),x81603),x81604)))+~P1(f789(f789(f241(x81601),f789(f789(f291(x81601),x81602),x81604)),x81603))
% 21.40/21.38 [8161]~P62(x81611)+~P1(f789(f789(f241(x81611),f2(x81611)),x81614))+P1(f789(f789(f241(x81611),x81612),f789(f789(f291(x81611),x81613),x81614)))+~P1(f789(f789(f241(x81611),f789(f789(f90(x81611),x81612),x81614)),x81613))
% 21.40/21.38 [8162]~P63(x81621)+~P1(f789(f789(f241(x81621),f2(x81621)),x81624))+P1(f789(f789(f241(x81621),x81622),f789(f789(f291(x81621),x81623),x81624)))+~P1(f789(f789(f241(x81621),f789(f789(f90(x81621),x81622),x81624)),x81623))
% 21.40/21.38 [8163]~P63(x81631)+~P1(f789(f789(f241(x81631),f2(x81631)),x81634))+P1(f789(f789(f241(x81631),x81632),f789(f789(f90(x81631),x81633),x81634)))+~P1(f789(f789(f241(x81631),f789(f789(f291(x81631),x81632),x81634)),x81633))
% 21.40/21.38 [8164]~P63(x81641)+~P1(f789(f789(f241(x81641),f2(x81641)),x81644))+P1(f789(f789(f241(x81641),x81642),f789(f789(f291(x81641),x81643),x81644)))+~P1(f789(f789(f241(x81641),f789(f789(f90(x81641),x81642),x81644)),x81643))
% 21.40/21.38 [8165]~P62(x81651)+~P1(f789(f789(f241(x81651),f2(x81651)),x81654))+P1(f789(f789(f240(x81651),x81652),f789(f789(f90(x81651),x81653),x81654)))+~P1(f789(f789(f240(x81651),f789(f789(f291(x81651),x81652),x81654)),x81653))
% 21.40/21.38 [8166]~P62(x81661)+~P1(f789(f789(f241(x81661),f2(x81661)),x81664))+P1(f789(f789(f240(x81661),x81662),f789(f789(f291(x81661),x81663),x81664)))+~P1(f789(f789(f240(x81661),f789(f789(f90(x81661),x81662),x81664)),x81663))
% 21.40/21.38 [8167]~P63(x81671)+~P1(f789(f789(f241(x81671),f2(x81671)),x81674))+P1(f789(f789(f240(x81671),x81672),f789(f789(f291(x81671),x81673),x81674)))+~P1(f789(f789(f240(x81671),f789(f789(f90(x81671),x81672),x81674)),x81673))
% 21.40/21.38 [8168]~P63(x81681)+~P1(f789(f789(f241(x81681),f2(x81681)),x81684))+P1(f789(f789(f240(x81681),x81682),f789(f789(f90(x81681),x81683),x81684)))+~P1(f789(f789(f240(x81681),f789(f789(f291(x81681),x81682),x81684)),x81683))
% 21.40/21.38 [8169]~P63(x81691)+~P1(f789(f789(f241(x81691),f2(x81691)),x81694))+P1(f789(f789(f240(x81691),x81692),f789(f789(f291(x81691),x81693),x81694)))+~P1(f789(f789(f240(x81691),f789(f789(f90(x81691),x81692),x81694)),x81693))
% 21.40/21.38 [8325]~P63(x83251)+~P1(f789(f789(f241(x83251),x83253),f2(x83251)))+~P1(f789(f789(f241(x83251),f789(f789(f291(x83251),x83254),x83253)),x83252))+P1(f789(f789(f241(x83251),f789(f789(f90(x83251),x83252),x83253)),x83254))
% 21.40/21.38 [8326]~P63(x83261)+~P1(f789(f789(f241(x83261),x83263),f2(x83261)))+~P1(f789(f789(f241(x83261),f789(f789(f90(x83261),x83264),x83263)),x83262))+P1(f789(f789(f241(x83261),f789(f789(f291(x83261),x83262),x83263)),x83264))
% 21.40/21.38 [8327]~P63(x83271)+~P1(f789(f789(f241(x83271),x83273),f2(x83271)))+~P1(f789(f789(f240(x83271),f789(f789(f291(x83271),x83274),x83273)),x83272))+P1(f789(f789(f240(x83271),f789(f789(f90(x83271),x83272),x83273)),x83274))
% 21.40/21.38 [8328]~P63(x83281)+~P1(f789(f789(f241(x83281),x83283),f2(x83281)))+~P1(f789(f789(f240(x83281),f789(f789(f90(x83281),x83284),x83283)),x83282))+P1(f789(f789(f240(x83281),f789(f789(f291(x83281),x83282),x83283)),x83284))
% 21.40/21.38 [8341]~P1(f789(x83411,x83414))+~P1(f789(f789(f241(a863),x83412),f789(f789(f90(a863),x83413),f789(a121,x83414))))+P1(f789(x83411,f789(f789(f50(a863),x83412),x83413)))+~P1(f789(f789(f240(a863),f789(f789(f90(a863),x83413),x83414)),x83412))
% 21.40/21.38 [8555]~P101(x85551)+~P1(f789(f70(x85551),x85554))+~P1(f789(f789(f342(x85551),x85552),x85554))+P1(f789(f789(f240(x85551),f789(f789(f239(x85551),x85552),x85553)),f789(f789(f73(x85551,x85551,f239(x85551)),x85553),x85554)))
% 21.40/21.38 [8556]~P94(x85561)+~P1(f789(f70(x85561),x85564))+~P1(f789(f789(f342(x85561),x85562),x85564))+P1(f789(f789(f240(x85561),f789(f789(f110(x85561),x85562),x85563)),f789(f789(f73(x85561,x85561,f110(x85561)),x85563),x85564)))
% 21.40/21.38 [8683]~P1(f789(f70(x86831),x86832))+E(f789(f49(x86831),f789(f789(f3(f870(x86831,a856)),x86832),f789(f789(f310(x86831),x86833),x86834))),f789(f789(f3(a863),f789(f49(x86831),f789(f789(f3(f870(x86831,a856)),x86832),x86834))),f87(a863)))+P1(f789(f789(f342(x86831),x86833),x86834))+~P1(f789(f789(f342(x86831),x86833),x86832))
% 21.40/21.38 [8747]E(f789(f789(f89(a1),f493(x87471,x87472,x87473,x87474)),f494(x87471,x87472,x87473,x87474)),x87474)+~P1(f789(f789(f241(a1),f2(a1)),x87473))+~P1(f789(f789(f240(a1),x87474),x87471))+P1(f789(f789(f240(a1),f789(f789(f3(a1),x87474),x87473)),x87471))
% 21.40/21.38 [8748]E(f789(f789(f89(a1),f501(x87481,x87482,x87483,x87484)),f502(x87481,x87482,x87483,x87484)),x87484)+~P1(f789(f789(f241(a1),f2(a1)),x87483))+~P1(f789(f789(f241(a1),x87484),x87481))+P1(f789(f789(f241(a1),f789(f789(f3(a1),x87484),x87483)),x87481))
% 21.40/21.38 [8932]~P1(f789(f789(f241(a1),f2(a1)),x89323))+~P1(f789(f789(f240(a1),x89324),x89321))+P1(f789(f789(f342(a1),f493(x89321,x89322,x89323,x89324)),x89322))+P1(f789(f789(f240(a1),f789(f789(f3(a1),x89324),x89323)),x89321))
% 21.40/21.38 [8933]~P1(f789(f789(f241(a1),f2(a1)),x89333))+~P1(f789(f789(f241(a1),x89334),x89331))+P1(f789(f789(f342(a1),f501(x89331,x89332,x89333,x89334)),x89332))+P1(f789(f789(f241(a1),f789(f789(f3(a1),x89334),x89333)),x89331))
% 21.40/21.38 [9011]~P1(f789(f789(f241(a1),f2(a1)),x90112))+~P1(f789(f789(f241(a1),x90111),x90113))+P1(f789(f789(f342(a1),f502(x90113,x90114,x90112,x90111)),f303(a1,f87(a1),x90112)))+P1(f789(f789(f241(a1),f789(f789(f3(a1),x90111),x90112)),x90113))
% 21.40/21.38 [9012]~P1(f789(f789(f241(a1),f2(a1)),x90122))+~P1(f789(f789(f240(a1),x90121),x90123))+P1(f789(f789(f342(a1),f494(x90123,x90124,x90122,x90121)),f303(a1,f87(a1),x90122)))+P1(f789(f789(f240(a1),f789(f789(f3(a1),x90121),x90122)),x90123))
% 21.40/21.38 [9033]~P1(f789(f789(f241(a1),f2(a1)),x90333))+~P1(f789(f789(f240(a1),f2(a1)),x90334))+~P1(f789(f789(f241(a1),x90334),x90331))+P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),f789(f789(f90(a1),x90331),f59(a1,x90332,x90333))),x90334)))
% 21.40/21.38 [9093]~P101(x90931)+~P1(f789(f70(x90931),x90934))+~P1(f789(f789(f240(x90931),x90932),f703(x90933,x90932,x90934,x90931)))+P1(f789(f789(f240(x90931),f789(f789(f244(x90931),x90932),x90933)),f789(f789(f73(x90931,x90931,f244(x90931)),x90933),x90934)))
% 21.40/21.38 [9094]~P98(x90941)+~P1(f789(f70(x90941),x90944))+~P1(f789(f789(f240(x90941),x90942),f705(x90943,x90942,x90944,x90941)))+P1(f789(f789(f240(x90941),f789(f789(f111(x90941),x90942),x90943)),f789(f789(f73(x90941,x90941,f111(x90941)),x90943),x90944)))
% 21.40/21.38 [9108]~P1(f789(f789(f240(a1),x91084),f2(a1)))+~P1(f789(f789(f241(a1),f2(a1)),x91082))+~P1(f789(f789(f241(a1),x91081),x91084))+P1(f789(f789(f241(a1),f789(f789(f90(a1),x91081),x91082)),f789(f789(f89(a1),f789(f789(f90(a1),x91081),f59(a1,x91083,x91082))),x91084)))
% 21.40/21.38 [9130]P1(f789(f70(x91301),x91302))+~P1(f789(f70(x91301),x91303))+~P1(f789(f789(f342(f870(x91301,a856)),x91302),f789(f789(f68(x91301),x91303),x91304)))+~P1(f789(f789(f240(f870(f869(x91301,x91301),a856)),x91304),f789(f789(f256(x91301,x91301),x91303),f789(f18(f870(x91301,a856),x91301),x91303))))
% 21.40/21.38 [9152]~P101(x91521)+~P1(f789(f70(x91521),x91524))+P1(f789(f789(f342(x91521),f703(x91522,x91523,x91524,x91521)),x91524))+P1(f789(f789(f240(x91521),f789(f789(f244(x91521),x91523),x91522)),f789(f789(f73(x91521,x91521,f244(x91521)),x91522),x91524)))
% 21.40/21.38 [9153]~P98(x91531)+~P1(f789(f70(x91531),x91534))+P1(f789(f789(f342(x91531),f705(x91532,x91533,x91534,x91531)),x91534))+P1(f789(f789(f240(x91531),f789(f789(f111(x91531),x91533),x91532)),f789(f789(f73(x91531,x91531,f111(x91531)),x91532),x91534)))
% 21.40/21.38 [9527]~P1(f789(f70(x95272),x95274))+~P1(f789(f70(x95271),x95273))+~P1(f789(f789(f240(a863),f789(f49(x95272),x95274)),f789(f49(x95271),x95273)))+P1(f789(f789(f240(f870(x95271,a856)),f789(f311(x95272,x95271,f463(x95273,x95271,x95274,x95272)),x95274)),x95273))
% 21.40/21.38 [9191]~P1(f789(f789(f342(x91911),x91912),x91914))+P1(f789(f789(f342(x91911),x91912),x91913))+~P1(f789(f789(f241(f870(x91911,a856)),x91914),f789(f789(f310(x91911),x91912),x91913)))+P1(f789(f789(f241(f870(x91911,a856)),f789(f789(f3(f870(x91911,a856)),x91914),f789(f789(f310(x91911),x91912),f184(f870(x91911,a856))))),x91913))
% 21.40/21.38 [9341]~P1(f789(f789(f342(x93411),x93412),x93414))+P1(f789(f789(f342(x93411),x93412),x93413))+P1(f789(f789(f241(f870(x93411,a856)),x93414),f789(f789(f310(x93411),x93412),x93413)))+~P1(f789(f789(f241(f870(x93411,a856)),f789(f789(f3(f870(x93411,a856)),x93414),f789(f789(f310(x93411),x93412),f184(f870(x93411,a856))))),x93413))
% 21.40/21.38 [9369]P1(f789(f789(f342(x93691),x93692),x93693))+~P1(f789(f789(f240(f870(x93691,a856)),x93694),x93693))+P1(f789(f789(f241(f870(x93691,a856)),x93694),f789(f789(f310(x93691),x93692),x93693)))+~P1(f789(f789(f241(f870(x93691,a856)),f789(f789(f3(f870(x93691,a856)),x93694),f789(f789(f310(x93691),x93692),f184(f870(x93691,a856))))),x93693))
% 21.40/21.38 [9374]~P1(f789(f789(f342(x93741),x93743),x93742))+~P1(f789(f789(f241(f870(x93741,a856)),x93742),x93744))+P1(f789(f789(f241(f870(x93741,a856)),x93742),f789(f789(f310(x93741),x93743),x93744)))+~P1(f789(f789(f241(f870(x93741,a856)),f789(f789(f3(f870(x93741,a856)),x93742),f789(f789(f310(x93741),x93743),f184(f870(x93741,a856))))),x93744))
% 21.40/21.38 [9386]~P1(f789(f789(f240(f870(x93861,a856)),x93862),x93864))+~P1(f789(f789(f241(f870(x93861,a856)),x93862),x93864))+P1(f789(f789(f241(f870(x93861,a856)),x93862),f789(f789(f310(x93861),x93863),x93864)))+~P1(f789(f789(f241(f870(x93861,a856)),f789(f789(f3(f870(x93861,a856)),x93862),f789(f789(f310(x93861),x93863),f184(f870(x93861,a856))))),x93864))
% 21.40/21.38 [9742]~P1(f789(f789(f342(f869(a863,a863)),x97424),x97421))+~P1(f789(f789(f342(f869(f869(a863,a863),f869(a863,a863))),f789(f789(f249(f869(a863,a863),f869(a863,a863)),x97424),x97422)),a47))+~P1(f789(f789(f342(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f249(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),x97421),x97423)),a77))+P1(f789(f789(f342(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f249(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),x97421),f789(f789(f310(f869(a863,a863)),x97422),x97423))),a77))
% 21.40/21.38 [9743]~P1(f789(f789(f342(f869(a863,a863)),x97434),x97431))+~P1(f789(f789(f342(f869(f869(a863,a863),f869(a863,a863))),f789(f789(f249(f869(a863,a863),f869(a863,a863)),x97434),x97432)),a79))+~P1(f789(f789(f342(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f249(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),x97431),x97433)),a80))+P1(f789(f789(f342(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f249(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),x97431),f789(f789(f310(f869(a863,a863)),x97432),x97433))),a80))
% 21.40/21.38 [9756]~P1(f789(f789(f342(f869(a863,a863)),x97564),x97563))+~P1(f789(f789(f342(f869(f869(a863,a863),f869(a863,a863))),f789(f789(f249(f869(a863,a863),f869(a863,a863)),x97561),x97564)),a47))+~P1(f789(f789(f342(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f249(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),x97562),x97563)),a48))+P1(f789(f789(f342(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f249(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),f789(f789(f310(f869(a863,a863)),x97561),x97562)),x97563)),a48))
% 21.40/21.38 [9757]~P1(f789(f789(f342(f869(a863,a863)),x97574),x97573))+~P1(f789(f789(f342(f869(f869(a863,a863),f869(a863,a863))),f789(f789(f249(f869(a863,a863),f869(a863,a863)),x97571),x97574)),a79))+~P1(f789(f789(f342(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f249(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),x97572),x97573)),a78))+P1(f789(f789(f342(f869(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856))),f789(f789(f249(f870(f869(a863,a863),a856),f870(f869(a863,a863),a856)),f789(f789(f310(f869(a863,a863)),x97571),x97572)),x97573)),a78))
% 21.40/21.38 [5949]~P11(x59494,x59491)+~P1(f789(f789(x59491,x59492),x59495))+P1(f789(f789(x59491,x59492),x59493))+~P1(f789(f789(x59491,x59495),x59493))
% 21.40/21.38 [5217]~P6(x52175)+E(x52171,x52172)+~E(x52173,x52174)+~E(f789(f789(f3(x52175),x52173),x52174),f789(f789(f3(x52175),x52171),x52172))
% 21.40/21.38 [5218]~P6(x52185)+E(x52181,x52182)+~E(x52183,x52184)+~E(f789(f789(f3(x52185),x52183),x52184),f789(f789(f3(x52185),x52181),x52182))
% 21.40/21.38 [6064]~P21(x60645,x60641,x60643)+E(f789(f789(x60641,x60642),f789(x60643,x60644)),f789(x60643,x60644))+~P1(f789(f70(x60645),x60644))+~P1(f789(f789(f342(x60645),x60642),x60644))
% 21.40/21.38 [6256]~P76(x62561)+~E(f789(f789(f3(x62561),x62564),x62565),f789(f789(f3(x62561),x62562),x62563))+~P1(f789(f789(f241(x62561),x62564),x62565))+P1(f789(f789(f241(x62561),x62562),x62563))
% 21.40/21.38 [6257]~P76(x62571)+~E(f789(f789(f3(x62571),x62574),x62575),f789(f789(f3(x62571),x62572),x62573))+~P1(f789(f789(f241(x62571),x62574),x62575))+P1(f789(f789(f241(x62571),x62572),x62573))
% 21.40/21.38 [6258]~P76(x62581)+~E(f789(f789(f3(x62581),x62584),x62585),f789(f789(f3(x62581),x62582),x62583))+~P1(f789(f789(f240(x62581),x62584),x62585))+P1(f789(f789(f240(x62581),x62582),x62583))
% 21.40/21.38 [6259]~P76(x62591)+~E(f789(f789(f3(x62591),x62594),x62595),f789(f789(f3(x62591),x62592),x62593))+~P1(f789(f789(f240(x62591),x62594),x62595))+P1(f789(f789(f240(x62591),x62592),x62593))
% 21.40/21.38 [7258]~E(x72582,f789(f789(f146(x72581),x72584),x72585))+P1(f789(f789(f342(f864(x72581)),x72582),f156(x72581,x72583)))+~P1(f789(f789(f342(f864(x72581)),x72585),f156(x72581,x72583)))+~P1(f789(f789(f342(x72581),x72584),x72583))
% 21.40/21.38 [7692]~E(f789(f185(f864(x76921)),x76923),f789(f185(f864(x76922)),x76924))+~E(f789(f789(f150(f869(x76921,x76922),x76922),f258(x76921,x76922)),x76925),x76924)+~E(f789(f789(f150(f869(x76921,x76922),x76921),f248(x76921,x76922)),x76925),x76923)+E(f789(f789(f171(x76921,x76922),x76923),x76924),x76925)
% 21.40/21.38 [8025]~P99(x80251)+P1(f789(f789(f241(f870(x80251,a856)),f303(x80251,x80252,x80253)),f303(x80251,x80254,x80255)))+~P1(f789(f789(f240(x80251),x80254),x80255))+P1(f789(f789(f240(x80251),x80252),x80253))
% 21.40/21.38 [8117]~P99(x81171)+P1(f789(f789(f240(f870(x81171,a856)),f303(x81171,x81172,x81173)),f303(x81171,x81174,x81175)))+~P1(f789(f789(f240(x81171),x81173),x81175))+~P1(f789(f789(f240(x81171),x81174),x81172))
% 21.40/21.38 [8234]~P101(x82341)+P1(f789(f789(f240(x82341),x82342),x82343))+P1(f789(f789(f240(x82341),x82344),x82343))+~P1(f789(f789(f240(f870(x82341,a856)),f789(f302(x82341,x82343),x82342)),f789(f302(x82341,x82344),x82345)))
% 21.40/21.38 [8235]~P101(x82351)+P1(f789(f789(f240(x82351),x82352),x82353))+P1(f789(f789(f240(x82351),x82352),x82354))+~P1(f789(f789(f240(f870(x82351,a856)),f789(f302(x82351,x82353),x82352)),f789(f302(x82351,x82355),x82354)))
% 21.40/21.38 [8475]~P99(x84751)+~P1(f789(f789(f241(f870(x84751,a856)),f303(x84751,x84754,x84752)),f303(x84751,x84755,x84753)))+P1(f789(f789(f240(x84751),x84752),x84753))+~P1(f789(f789(f240(x84751),x84754),x84752))
% 21.40/21.38 [8476]~P99(x84761)+~P1(f789(f789(f240(f870(x84761,a856)),f303(x84761,x84764,x84762)),f303(x84761,x84765,x84763)))+P1(f789(f789(f240(x84761),x84762),x84763))+~P1(f789(f789(f240(x84761),x84764),x84762))
% 21.40/21.38 [8477]~P99(x84771)+~P1(f789(f789(f241(f870(x84771,a856)),f303(x84771,x84773,x84774)),f303(x84771,x84772,x84775)))+P1(f789(f789(f240(x84771),x84772),x84773))+~P1(f789(f789(f240(x84771),x84773),x84774))
% 21.40/21.38 [8478]~P99(x84781)+~P1(f789(f789(f240(f870(x84781,a856)),f303(x84781,x84783,x84784)),f303(x84781,x84782,x84785)))+P1(f789(f789(f240(x84781),x84782),x84783))+~P1(f789(f789(f240(x84781),x84783),x84784))
% 21.40/21.38 [5948]~P21(x59482,x59485,x59483)+E(x59481,f184(f870(x59482,a856)))+~P1(f789(f70(x59482),x59481))+E(f789(x59483,f789(f789(f310(x59482),x59484),x59481)),f789(f789(x59485,x59484),f789(x59483,x59481)))
% 21.40/21.38 [6747]~E(x67471,x67472)+~E(f789(f789(f111(f870(x67473,a856)),x67474),x67475),f184(f870(x67473,a856)))+~P1(f789(f789(f342(x67473),x67472),x67475))+~P1(f789(f789(f342(x67473),x67471),x67474))
% 21.40/21.38 [6833]~P22(x68332,x68335,x68331)+~P1(f789(f70(x68332),x68334))+E(f789(x68331,f789(f789(f310(x68332),x68333),x68334)),f789(f789(f73(x68332,x68332,x68335),x68333),x68334))+P1(f789(f789(f342(x68332),x68333),x68334))
% 21.40/21.38 [6903]~P69(x69032)+~P1(f789(f70(x69031),x69035))+E(f789(f789(f11(x69031,x69032),x69033),f789(f789(f310(x69031),x69034),x69035)),f789(f789(f90(x69032),f789(x69033,x69034)),f789(f789(f11(x69031,x69032),x69033),x69035)))+P1(f789(f789(f342(x69031),x69034),x69035))
% 21.40/21.38 [6904]~P69(x69042)+~P1(f789(f70(x69041),x69045))+E(f789(f789(f11(x69041,x69042),x69043),f789(f789(f310(x69041),x69044),x69045)),f789(f789(f90(x69042),f789(x69043,x69044)),f789(f789(f11(x69041,x69042),x69043),x69045)))+P1(f789(f789(f342(x69041),x69044),x69045))
% 21.40/21.38 [6905]~P4(x69052)+~P1(f789(f70(x69051),x69055))+E(f789(f789(f8(x69051,x69052),x69053),f789(f789(f310(x69051),x69054),x69055)),f789(f789(f89(x69052),f789(x69053,x69054)),f789(f789(f8(x69051,x69052),x69053),x69055)))+P1(f789(f789(f342(x69051),x69054),x69055))
% 21.40/21.38 [6906]~P4(x69062)+~P1(f789(f70(x69061),x69065))+E(f789(f789(f8(x69061,x69062),x69063),f789(f789(f310(x69061),x69064),x69065)),f789(f789(f89(x69062),f789(x69063,x69064)),f789(f789(f8(x69061,x69062),x69063),x69065)))+P1(f789(f789(f342(x69061),x69064),x69065))
% 21.40/21.38 [7316]~P70(x73161)+~P1(f789(f70(x73164),x73165))+~P1(f789(f789(f342(x73164),x73163),x73165))+P1(f789(f789(f287(x73161),f789(x73162,x73163)),f789(f789(f11(x73164,x73161),x73162),x73165)))
% 21.40/21.38 [7429]~P22(x74292,x74295,x74291)+~P1(f789(f70(x74292),x74294))+E(f789(x74291,f789(f789(f310(x74292),x74293),x74294)),x74293)+~E(f789(f789(f3(f870(x74292,a856)),x74294),f789(f789(f310(x74292),x74293),f184(f870(x74292,a856)))),f184(f870(x74292,a856)))
% 21.40/21.38 [7740]~P1(f789(x77401,x77403))+~P1(f789(f789(f191(x77402),x77403),x77405))+~P1(f789(f789(f191(f37(x77401,x77402)),x77405),x77404))+P1(f789(f789(f191(f37(x77401,x77402)),x77403),x77404))
% 21.40/21.38 [7741]~P1(f789(x77411,x77413))+~P1(f789(f789(f191(x77412),x77413),x77415))+~P1(f789(f789(f191(f37(x77411,x77412)),x77415),x77414))+P1(f789(f789(f191(f37(x77411,x77412)),x77413),x77414))
% 21.40/21.38 [7759]~P70(x77591)+~P1(f789(f789(f287(x77591),x77592),x77594))+~P1(f789(f789(f240(a863),x77593),x77595))+P1(f789(f789(f287(x77591),f789(f789(f250(x77591),x77592),x77593)),f789(f789(f250(x77591),x77594),x77595)))
% 21.40/21.38 [7793]~P7(x77931)+E(f789(f789(f50(x77931),f789(f789(f90(x77931),x77932),x77933)),f789(f789(f90(x77931),x77934),x77935)),f789(f789(f90(x77931),f789(f789(f50(x77931),x77932),x77934)),f789(f789(f50(x77931),x77933),x77935)))+~P1(f789(f789(f287(x77931),x77935),x77933))+~P1(f789(f789(f287(x77931),x77934),x77932))
% 21.40/21.38 [7797]~P81(x77971)+~P1(f789(f789(f241(x77971),x77973),x77975))+~P1(f789(f789(f241(x77971),x77972),x77974))+P1(f789(f789(f241(x77971),f789(f789(f89(x77971),x77972),x77973)),f789(f789(f89(x77971),x77974),x77975)))
% 21.40/21.38 [7798]~P81(x77981)+~P1(f789(f789(f240(x77981),x77982),x77984))+~P1(f789(f789(f241(x77981),x77983),x77985))+P1(f789(f789(f241(x77981),f789(f789(f89(x77981),x77982),x77983)),f789(f789(f89(x77981),x77984),x77985)))
% 21.40/21.38 [7799]~P81(x77991)+~P1(f789(f789(f240(x77991),x77993),x77995))+~P1(f789(f789(f241(x77991),x77992),x77994))+P1(f789(f789(f241(x77991),f789(f789(f89(x77991),x77992),x77993)),f789(f789(f89(x77991),x77994),x77995)))
% 21.40/21.38 [7800]~P79(x78001)+~P1(f789(f789(f240(x78001),x78003),x78005))+~P1(f789(f789(f240(x78001),x78002),x78004))+P1(f789(f789(f240(x78001),f789(f789(f89(x78001),x78002),x78003)),f789(f789(f89(x78001),x78004),x78005)))
% 21.40/21.38 [7801]~P101(x78011)+~P1(f789(f789(f240(x78011),x78013),x78015))+~P1(f789(f789(f240(x78011),x78012),x78014))+P1(f789(f789(f240(x78011),f789(f789(f244(x78011),x78012),x78013)),f789(f789(f244(x78011),x78014),x78015)))
% 21.40/21.38 [7802]~P101(x78021)+~P1(f789(f789(f240(x78021),x78023),x78025))+~P1(f789(f789(f240(x78021),x78022),x78024))+P1(f789(f789(f240(x78021),f789(f789(f239(x78021),x78022),x78023)),f789(f789(f239(x78021),x78024),x78025)))
% 21.40/21.38 [7803]~P94(x78031)+~P1(f789(f789(f240(x78031),x78033),x78035))+~P1(f789(f789(f240(x78031),x78032),x78034))+P1(f789(f789(f240(x78031),f789(f789(f110(x78031),x78032),x78033)),f789(f789(f110(x78031),x78034),x78035)))
% 21.40/21.38 [7804]~P98(x78041)+~P1(f789(f789(f240(x78041),x78043),x78045))+~P1(f789(f789(f240(x78041),x78042),x78044))+P1(f789(f789(f240(x78041),f789(f789(f111(x78041),x78042),x78043)),f789(f789(f111(x78041),x78044),x78045)))
% 21.40/21.38 [7805]~P70(x78051)+~P1(f789(f789(f287(x78051),x78053),x78055))+~P1(f789(f789(f287(x78051),x78052),x78054))+P1(f789(f789(f287(x78051),f789(f789(f90(x78051),x78052),x78053)),f789(f789(f90(x78051),x78054),x78055)))
% 21.40/21.38 [7937]~P137(x79375)+E(x79371,x79372)+E(x79373,x79374)+~E(f789(f789(f89(x79375),f789(f789(f90(x79375),x79373),x79371)),f789(f789(f90(x79375),x79374),x79372)),f789(f789(f89(x79375),f789(f789(f90(x79375),x79373),x79372)),f789(f789(f90(x79375),x79374),x79371)))
% 21.40/21.38 [7938]~P137(x79385)+E(x79381,x79382)+E(x79383,x79384)+~E(f789(f789(f89(x79385),f789(f789(f90(x79385),x79383),x79381)),f789(f789(f90(x79385),x79384),x79382)),f789(f789(f89(x79385),f789(f789(f90(x79385),x79383),x79382)),f789(f789(f90(x79385),x79384),x79381)))
% 21.40/21.38 [8074]P31(x80741,x80742,x80743)+~P32(x80741,x80744,x80745)+~P31(x80741,x80742,f812(x80745,x80744,x80741,x80742))+~P1(f789(f789(f342(f862(x80741)),x80743),x80745))
% 21.40/21.38 [8137]~P101(x81374)+~P1(f789(f134(x81371),x81373))+P1(f789(f789(f342(x81371),x81372),f789(f163(x81371),x81373)))+P1(f789(f134(x81371),f789(f789(f144(x81371,x81374,x81375),x81372),x81373)))
% 21.40/21.38 [8280]~P4(x82801)+E(f789(f789(f89(x82801),f789(f789(f8(a863,x82801),x82802),f789(f302(a863,x82803),x82804))),f789(f789(f8(a863,x82801),x82802),f789(f302(a863,x82804),x82805))),f789(f789(f8(a863,x82801),x82802),f789(f302(a863,x82803),x82805)))+~P1(f789(f789(f240(a863),x82804),x82805))+~P1(f789(f789(f240(a863),x82803),x82804))
% 21.40/21.38 [8281]~P6(x82811)+E(f789(f789(f3(x82811),f789(f789(f8(a863,x82811),x82812),f789(f302(a863,x82813),x82814))),f789(f789(f8(a863,x82811),x82812),f789(f302(a863,x82813),x82815))),f789(f789(f8(a863,x82811),x82812),f789(f302(a863,x82815),x82814)))+~P1(f789(f789(f240(a863),x82815),x82814))+~P1(f789(f789(f240(a863),x82813),x82815))
% 21.40/21.38 [8600]~P61(x86002)+E(x86001,f2(x86002))+E(x86003,f2(x86002))+E(f789(f789(f291(x86002),f789(f789(f89(x86002),f789(f789(f90(x86002),x86004),x86001)),f789(f789(f90(x86002),x86005),x86003))),f789(f789(f90(x86002),x86003),x86001)),f789(f789(f89(x86002),f789(f789(f291(x86002),x86004),x86003)),f789(f789(f291(x86002),x86005),x86001)))
% 21.40/21.38 [8601]~P61(x86012)+E(x86011,f2(x86012))+E(x86013,f2(x86012))+E(f789(f789(f291(x86012),f789(f789(f3(x86012),f789(f789(f90(x86012),x86014),x86011)),f789(f789(f90(x86012),x86015),x86013))),f789(f789(f90(x86012),x86013),x86011)),f789(f789(f3(x86012),f789(f789(f291(x86012),x86014),x86013)),f789(f789(f291(x86012),x86015),x86011)))
% 21.40/21.38 [8610]~E(x86102,f789(x86103,x86101))+E(x86101,f537(x86102,x86103,x86104,x86105))+~P29(x86105,x86104,x86103,f247(f870(x86105,a856)))+~P1(f789(f789(f342(x86104),x86102),f789(f311(x86105,x86104,x86103),f247(f870(x86105,a856)))))
% 21.40/21.38 [8795]~P110(x87951)+~P1(f789(f789(f241(x87951),f789(f84(x87951),x87952)),x87954))+P1(f789(f789(f241(x87951),f789(f789(f90(x87951),f789(f84(x87951),x87952)),f789(f84(x87951),x87953))),f789(f789(f90(x87951),x87954),x87955)))+~P1(f789(f789(f241(x87951),f789(f84(x87951),x87953)),x87955))
% 21.40/21.38 [8809]~P32(x88091,x88095,x88094)+P31(x88091,x88092,x88093)+P1(f789(f789(f342(f862(x88091)),f812(x88094,x88095,x88091,x88092)),x88095))+~P1(f789(f789(f342(f862(x88091)),x88093),x88094))
% 21.40/21.38 [8891]~P29(x88911,x88913,x88915,x88912)+~P1(f789(f70(x88913),x88914))+P1(f789(f789(f240(a863),f789(f49(x88911),x88912)),f789(f49(x88913),x88914)))+~P1(f789(f789(f240(f870(x88913,a856)),f789(f311(x88911,x88913,x88915),x88912)),x88914))
% 21.40/21.38 [8959]~P69(x89592)+~P29(x89591,x89591,x89594,x89595)+~P1(f789(f70(x89591),x89595))+E(f789(f789(f11(x89591,x89592),f789(f82(x89591,x89592,x89591,x89593),x89594)),x89595),f789(f789(f11(x89591,x89592),x89593),f789(f311(x89591,x89591,x89594),x89595)))
% 21.40/21.38 [8960]~P4(x89602)+~P29(x89601,x89601,x89604,x89605)+~P1(f789(f70(x89601),x89605))+E(f789(f789(f8(x89601,x89602),f789(f82(x89601,x89602,x89601,x89603),x89604)),x89605),f789(f789(f8(x89601,x89602),x89603),f789(f311(x89601,x89601,x89604),x89605)))
% 21.40/21.38 [9040]~E(f543(x90402,x90404,x90401,x90403,x90405),x90405)+~E(x90402,f789(x90404,x90405))+~P29(x90403,x90401,x90404,f247(f870(x90403,a856)))+P1(f789(f789(f342(x90401),x90402),f789(f311(x90403,x90401,x90404),f247(f870(x90403,a856)))))
% 21.40/21.38 [9072]~P36(x90721,x90722)+~P1(f789(f789(f342(x90721),x90723),x90724))+~P1(f789(f789(f342(x90721),x90725),x90724))+~P1(f789(f789(f342(f869(x90721,x90721)),f789(f789(f249(x90721,x90721),x90725),f701(x90722,x90721,x90724))),x90722))
% 21.40/21.38 [9107]~P29(x91072,x91073,x91075,x91071)+E(x91071,f184(f870(x91072,a856)))+E(f789(f311(x91073,x91072,f465(x91074,x91073,x91072,x91071)),x91074),x91071)+~P1(f789(f789(f240(f870(x91073,a856)),f789(f311(x91072,x91073,x91075),x91071)),x91074))
% 21.40/21.38 [9145]~E(x91452,f789(x91451,x91455))+~P29(x91454,x91453,x91451,f247(f870(x91454,a856)))+E(f789(x91451,f543(x91452,x91451,x91453,x91454,x91455)),x91452)+P1(f789(f789(f342(x91453),x91452),f789(f311(x91454,x91453,x91451),f247(f870(x91454,a856)))))
% 21.40/21.38 [9550]~P101(x95505)+~P9(x95505)+P1(f789(f789(f342(x95501),f427(x95502,x95503,x95501,x95504,x95505)),x95503))+~P1(f789(f789(f241(x95505),x95504),f789(f789(f53(x95501,x95505),x95503),x95502)))
% 21.40/21.38 [9555]~P101(x95551)+~P9(x95551)+P1(f789(f789(f241(x95551),x95552),f789(x95553,f427(x95553,x95554,x95555,x95552,x95551))))+~P1(f789(f789(f241(x95551),x95552),f789(f789(f53(x95555,x95551),x95554),x95553)))
% 21.40/21.38 [9630]~P66(x96301)+~P1(f789(f75(x96301,x96301,f90(x96301),x96302,x96303),x96305))+P1(f789(f789(f342(x96301),x96302),x96303))+P1(f789(f75(x96301,x96301,f90(x96301),x96304,f789(f789(f310(x96301),x96302),x96303)),f789(f789(f90(x96301),x96304),x96305)))
% 21.40/21.38 [9839]~P69(x98392)+~P1(f789(f70(x98391),x98395))+E(f789(f789(f11(x98391,x98392),f789(f789(f9(x98391,x98392,x98392),f789(f789(f20(x98391,x98392,f870(x98392,x98392)),f789(f789(f10(a856,f870(x98392,f870(x98392,x98392)),x98391),f105(x98392)),f789(a338,x98393))),x98394)),f87(x98392))),x98395),f87(x98392))+P1(f789(f789(f342(x98391),x98393),x98395))
% 21.40/21.38 [9840]~P4(x98402)+~P1(f789(f70(x98401),x98405))+E(f789(f789(f8(x98401,x98402),f789(f789(f9(x98401,x98402,x98402),f789(f789(f20(x98401,x98402,f870(x98402,x98402)),f789(f789(f10(a856,f870(x98402,f870(x98402,x98402)),x98401),f105(x98402)),f789(a338,x98403))),x98404)),f2(x98402))),x98405),f2(x98402))+P1(f789(f789(f342(x98401),x98403),x98405))
% 21.40/21.38 [9841]~P69(x98412)+~P1(f789(f70(x98411),x98415))+E(f789(f789(f11(x98411,x98412),f789(f789(f9(x98411,x98412,x98412),f789(f789(f20(x98411,x98412,f870(x98412,x98412)),f789(f789(f10(a856,f870(x98412,f870(x98412,x98412)),x98411),f105(x98412)),f789(a338,x98413))),x98414)),f87(x98412))),x98415),f789(x98414,x98413))+~P1(f789(f789(f342(x98411),x98413),x98415))
% 21.40/21.38 [9842]~P4(x98422)+~P1(f789(f70(x98421),x98425))+E(f789(f789(f8(x98421,x98422),f789(f789(f9(x98421,x98422,x98422),f789(f789(f20(x98421,x98422,f870(x98422,x98422)),f789(f789(f10(a856,f870(x98422,f870(x98422,x98422)),x98421),f105(x98422)),f789(a338,x98423))),x98424)),f2(x98422))),x98425),f789(x98424,x98423))+~P1(f789(f789(f342(x98421),x98423),x98425))
% 21.40/21.38 [9907]~P69(x99072)+~P1(f789(f70(x99071),x99075))+E(f789(f789(f11(x99071,x99072),f789(f789(f9(x99071,x99072,x99072),f789(f789(f20(x99071,x99072,f870(x99072,x99072)),f789(f789(f10(a856,f870(x99072,f870(x99072,x99072)),x99071),f105(x99072)),f789(f789(f9(x99071,x99071,a856),a338),x99073))),x99074)),f87(x99072))),x99075),f87(x99072))+P1(f789(f789(f342(x99071),x99073),x99075))
% 21.40/21.38 [9908]~P4(x99082)+~P1(f789(f70(x99081),x99085))+E(f789(f789(f8(x99081,x99082),f789(f789(f9(x99081,x99082,x99082),f789(f789(f20(x99081,x99082,f870(x99082,x99082)),f789(f789(f10(a856,f870(x99082,f870(x99082,x99082)),x99081),f105(x99082)),f789(f789(f9(x99081,x99081,a856),a338),x99083))),x99084)),f2(x99082))),x99085),f2(x99082))+P1(f789(f789(f342(x99081),x99083),x99085))
% 21.40/21.38 [9910]~P69(x99102)+~P1(f789(f70(x99101),x99105))+E(f789(f789(f11(x99101,x99102),f789(f789(f9(x99101,x99102,x99102),f789(f789(f20(x99101,x99102,f870(x99102,x99102)),f789(f789(f10(a856,f870(x99102,f870(x99102,x99102)),x99101),f105(x99102)),f789(f789(f9(x99101,x99101,a856),a338),x99103))),x99104)),f87(x99102))),x99105),f789(x99104,x99103))+~P1(f789(f789(f342(x99101),x99103),x99105))
% 21.40/21.38 [9911]~P4(x99112)+~P1(f789(f70(x99111),x99115))+E(f789(f789(f8(x99111,x99112),f789(f789(f9(x99111,x99112,x99112),f789(f789(f20(x99111,x99112,f870(x99112,x99112)),f789(f789(f10(a856,f870(x99112,f870(x99112,x99112)),x99111),f105(x99112)),f789(f789(f9(x99111,x99111,a856),a338),x99113))),x99114)),f2(x99112))),x99115),f789(x99114,x99113))+~P1(f789(f789(f342(x99111),x99113),x99115))
% 21.40/21.38 [7796]~P6(x77962)+~P1(f789(f70(x77961),x77964))+E(f789(f789(f8(x77961,x77962),x77963),f789(f789(f3(f870(x77961,a856)),x77964),f789(f789(f310(x77961),x77965),f184(f870(x77961,a856))))),f789(f789(f8(x77961,x77962),x77963),x77964))+P1(f789(f789(f342(x77961),x77965),x77964))
% 21.40/21.38 [8287]~P121(x82872)+~P1(f789(f70(x82871),x82874))+E(f789(f789(f8(x82871,x82872),x82873),f789(f789(f3(f870(x82871,a856)),x82874),f789(f789(f310(x82871),x82875),f184(f870(x82871,a856))))),f789(f789(f3(x82872),f789(f789(f8(x82871,x82872),x82873),x82874)),f789(x82873,x82875)))+~P1(f789(f789(f342(x82871),x82875),x82874))
% 21.40/21.38 [8288]~P6(x82882)+~P1(f789(f70(x82881),x82884))+E(f789(f789(f8(x82881,x82882),x82883),f789(f789(f3(f870(x82881,a856)),x82884),f789(f789(f310(x82881),x82885),f184(f870(x82881,a856))))),f789(f789(f3(x82882),f789(f789(f8(x82881,x82882),x82883),x82884)),f789(x82883,x82885)))+~P1(f789(f789(f342(x82881),x82885),x82884))
% 21.40/21.38 [8299]~P70(x82991)+~P1(f789(f789(f240(a863),x82993),x82995))+~P1(f789(f789(f287(x82991),f789(f789(f250(x82991),x82992),x82995)),x82994))+P1(f789(f789(f287(x82991),f789(f789(f250(x82991),x82992),x82993)),x82994))
% 21.40/21.38 [8316]~P6(x83161)+~P1(f789(f70(x83162),x83164))+E(f789(f789(f3(x83161),f789(f789(f8(x83162,x83161),x83163),x83164)),f789(f789(f8(x83162,x83161),x83163),x83165)),f789(f789(f8(x83162,x83161),x83163),f789(f789(f3(f870(x83162,a856)),x83164),x83165)))+~P1(f789(f789(f240(f870(x83162,a856)),x83165),x83164))
% 21.40/21.38 [8337]P1(f789(f70(x83371),f789(x83372,x83373)))+~P1(f789(f70(x83374),x83375))+~P1(f789(f789(f342(x83374),x83373),x83375))+~P1(f789(f70(x83371),f789(f789(f53(x83374,f870(x83371,a856)),x83375),x83372)))
% 21.40/21.38 [8760]~P12(x87601,x87605,x87604)+~E(f789(f285(x87601,x87601,x87604),f789(f789(f310(x87601),x87602),f184(f870(x87601,a856)))),f789(f285(x87601,x87601,x87604),f789(f789(f310(x87601),x87603),f184(f870(x87601,a856)))))+~P1(f789(f789(f342(x87601),x87603),x87605))+P1(f789(f789(f342(f869(x87601,x87601)),f789(f789(f249(x87601,x87601),x87602),x87603)),x87604))
% 21.40/21.38 [9031]~P1(f789(x90311,x90315))+P1(f789(x90311,f367(x90311,x90312,x90313,x90314)))+P1(f789(x90311,f364(x90311,x90312,x90313,x90314)))+~P1(f789(f789(f342(x90314),x90315),f789(f789(f110(f870(x90314,a856)),x90313),x90312)))
% 21.40/21.38 [9194]~P1(f789(x91941,x91945))+P1(f789(x91941,f364(x91941,x91942,x91943,x91944)))+P1(f789(f789(f342(x91944),f367(x91941,x91942,x91943,x91944)),x91942))+~P1(f789(f789(f342(x91944),x91945),f789(f789(f110(f870(x91944,a856)),x91943),x91942)))
% 21.40/21.38 [9195]~P1(f789(x91951,x91955))+P1(f789(x91951,f367(x91951,x91952,x91953,x91954)))+P1(f789(f789(f342(x91954),f364(x91951,x91952,x91953,x91954)),x91953))+~P1(f789(f789(f342(x91954),x91955),f789(f789(f110(f870(x91954,a856)),x91953),x91952)))
% 21.40/21.38 [9199]P1(f789(x91991,x91992))+~P1(f789(x91991,f373(x91991,x91993,x91994,x91995)))+~P1(f789(x91991,f372(x91991,x91993,x91994,x91995)))+~P1(f789(f789(f342(x91995),x91992),f789(f789(f110(f870(x91995,a856)),x91994),x91993)))
% 21.40/21.38 [9231]E(x92311,x92312)+~P1(f789(f789(f342(f869(x92313,x92313)),f789(f789(f249(x92313,x92313),x92311),x92312)),f308(x92313,x92315)))+P1(f789(f789(f342(x92313),x92311),x92314))+~P1(f789(f789(f240(f870(f869(x92313,x92313),a856)),x92315),f789(f789(f256(x92313,x92313),x92314),f789(f18(f870(x92313,a856),x92313),x92314))))
% 21.40/21.38 [9247]P1(f789(x92471,x92472))+~P1(f789(x92471,f372(x92471,x92474,x92475,x92473)))+P1(f789(f789(f342(x92473),f373(x92471,x92474,x92475,x92473)),x92474))+~P1(f789(f789(f342(x92473),x92472),f789(f789(f110(f870(x92473,a856)),x92475),x92474)))
% 21.40/21.38 [9248]P1(f789(x92481,x92482))+~P1(f789(x92481,f373(x92481,x92484,x92485,x92483)))+P1(f789(f789(f342(x92483),f372(x92481,x92484,x92485,x92483)),x92485))+~P1(f789(f789(f342(x92483),x92482),f789(f789(f110(f870(x92483,a856)),x92485),x92484)))
% 21.40/21.38 [9310]P1(f789(x93101,x93102))+P1(f789(f789(f342(x93103),f373(x93101,x93104,x93105,x93103)),x93104))+P1(f789(f789(f342(x93103),f372(x93101,x93104,x93105,x93103)),x93105))+~P1(f789(f789(f342(x93103),x93102),f789(f789(f110(f870(x93103,a856)),x93105),x93104)))
% 21.40/21.38 [9312]~P1(f789(x93122,x93125))+P1(f789(f789(f342(x93121),f367(x93122,x93123,x93124,x93121)),x93123))+P1(f789(f789(f342(x93121),f364(x93122,x93123,x93124,x93121)),x93124))+~P1(f789(f789(f342(x93121),x93125),f789(f789(f110(f870(x93121,a856)),x93124),x93123)))
% 21.40/21.38 [9460]~P12(x94601,x94605,x94604)+~P1(f789(f789(f342(x94601),x94603),x94605))+P1(f789(f789(f342(f869(x94601,x94601)),f789(f789(f249(x94601,x94601),x94602),x94603)),x94604))+~P1(f789(f789(f240(f870(x94601,a856)),f789(f285(x94601,x94601,x94604),f789(f789(f310(x94601),x94603),f184(f870(x94601,a856))))),f789(f285(x94601,x94601,x94604),f789(f789(f310(x94601),x94602),f184(f870(x94601,a856))))))
% 21.40/21.38 [9580]~P101(x95805)+~P9(x95805)+P1(f789(f789(f342(x95801),f651(x95802,x95803,x95804,x95801,x95805)),x95804))+~P1(f789(f789(f241(x95805),f789(f789(f54(x95801,x95805),x95804),x95803)),x95802))
% 21.40/21.38 [9614]~P71(x96145)+~P79(x96145)+P1(f789(f789(f342(x96141),f767(x96142,x96143,x96144,x96141,x96145)),f789(f163(x96141),x96144)))+P1(f789(f789(f240(x96145),f789(f161(x96145),f789(f789(f150(x96141,x96145),x96143),x96144))),f789(f161(x96145),f789(f789(f150(x96141,x96145),x96142),x96144))))
% 21.40/21.38 [9712]~P101(x97121)+~P9(x97121)+P1(f789(f789(f241(x97121),f789(x97122,f651(x97123,x97122,x97124,x97125,x97121))),x97123))+~P1(f789(f789(f241(x97121),f789(f789(f54(x97125,x97121),x97124),x97122)),x97123))
% 21.40/21.38 [9856]~P71(x98561)+~P79(x98561)+~P1(f789(f789(f240(x98561),f789(x98563,f767(x98565,x98563,x98564,x98562,x98561))),f789(x98565,f767(x98565,x98563,x98564,x98562,x98561))))+P1(f789(f789(f240(x98561),f789(f161(x98561),f789(f789(f150(x98562,x98561),x98563),x98564))),f789(f161(x98561),f789(f789(f150(x98562,x98561),x98565),x98564))))
% 21.40/21.38 [8618]~P69(x86181)+~P1(f789(f70(x86184),x86185))+~P1(f789(f789(f342(x86184),x86183),x86185))+E(f789(f789(f90(x86181),f789(x86182,x86183)),f789(f789(f11(x86184,x86181),x86182),f789(f789(f3(f870(x86184,a856)),x86185),f789(f789(f310(x86184),x86183),f184(f870(x86184,a856)))))),f789(f789(f11(x86184,x86181),x86182),x86185))
% 21.40/21.38 [8619]~P4(x86191)+~P1(f789(f70(x86194),x86195))+~P1(f789(f789(f342(x86194),x86193),x86195))+E(f789(f789(f89(x86191),f789(x86192,x86193)),f789(f789(f8(x86194,x86191),x86192),f789(f789(f3(f870(x86194,a856)),x86195),f789(f789(f310(x86194),x86193),f184(f870(x86194,a856)))))),f789(f789(f8(x86194,x86191),x86192),x86195))
% 21.40/21.38 [8620]~P4(x86201)+~P1(f789(f70(x86204),x86205))+~P1(f789(f789(f342(x86204),x86203),x86205))+E(f789(f789(f89(x86201),f789(x86202,x86203)),f789(f789(f8(x86204,x86201),x86202),f789(f789(f3(f870(x86204,a856)),x86205),f789(f789(f310(x86204),x86203),f184(f870(x86204,a856)))))),f789(f789(f8(x86204,x86201),x86202),x86205))
% 21.40/21.38 [8673]~P22(x86731,x86734,x86735)+~P1(f789(f70(x86731),x86732))+E(f789(f789(f3(f870(x86731,a856)),x86732),f789(f789(f310(x86731),x86733),f184(f870(x86731,a856)))),f184(f870(x86731,a856)))+E(f789(f789(x86734,x86733),f789(x86735,f789(f789(f3(f870(x86731,a856)),x86732),f789(f789(f310(x86731),x86733),f184(f870(x86731,a856)))))),f789(x86735,f789(f789(f310(x86731),x86733),x86732)))
% 21.40/21.38 [9006]~P4(x90061)+~P1(f789(f70(x90062),x90065))+~P1(f789(f70(x90062),x90064))+E(f789(f789(f89(x90061),f789(f789(f8(x90062,x90061),x90063),f789(f789(f110(f870(x90062,a856)),x90064),x90065))),f789(f789(f8(x90062,x90061),x90063),f789(f789(f111(f870(x90062,a856)),x90064),x90065))),f789(f789(f89(x90061),f789(f789(f8(x90062,x90061),x90063),x90064)),f789(f789(f8(x90062,x90061),x90063),x90065)))
% 21.40/21.38 [9007]~P69(x90071)+~P1(f789(f70(x90072),x90075))+~P1(f789(f70(x90072),x90074))+E(f789(f789(f90(x90071),f789(f789(f11(x90072,x90071),x90073),f789(f789(f110(f870(x90072,a856)),x90074),x90075))),f789(f789(f11(x90072,x90071),x90073),f789(f789(f111(f870(x90072,a856)),x90074),x90075))),f789(f789(f90(x90071),f789(f789(f11(x90072,x90071),x90073),x90074)),f789(f789(f11(x90072,x90071),x90073),x90075)))
% 21.40/21.38 [9008]~P69(x90081)+~P1(f789(f70(x90082),x90085))+~P1(f789(f70(x90082),x90084))+E(f789(f789(f90(x90081),f789(f789(f11(x90082,x90081),x90083),f789(f789(f110(f870(x90082,a856)),x90084),x90085))),f789(f789(f11(x90082,x90081),x90083),f789(f789(f111(f870(x90082,a856)),x90084),x90085))),f789(f789(f90(x90081),f789(f789(f11(x90082,x90081),x90083),x90084)),f789(f789(f11(x90082,x90081),x90083),x90085)))
% 21.40/21.38 [9144]~P6(x91441)+~P1(f789(f70(x91442),x91445))+~P1(f789(f70(x91442),x91444))+E(f789(f789(f3(x91441),f789(f789(f89(x91441),f789(f789(f8(x91442,x91441),x91443),x91444)),f789(f789(f8(x91442,x91441),x91443),x91445))),f789(f789(f8(x91442,x91441),x91443),f789(f789(f111(f870(x91442,a856)),x91444),x91445))),f789(f789(f8(x91442,x91441),x91443),f789(f789(f110(f870(x91442,a856)),x91444),x91445)))
% 21.40/21.38 [9324]~P29(x93241,x93242,x93243,x93245)+~P29(x93241,x93242,x93243,x93244)+P29(x93241,x93242,x93243,f789(f789(f110(f870(x93241,a856)),x93244),x93245))+~E(f789(f789(f111(f870(x93242,a856)),f789(f311(x93241,x93242,x93243),f789(f789(f3(f870(x93241,a856)),x93244),x93245))),f789(f311(x93241,x93242,x93243),f789(f789(f3(f870(x93241,a856)),x93245),x93244))),f184(f870(x93242,a856)))
% 21.40/21.38 [9431]E(x94311,f2(a1))+~P1(f789(f789(f241(a1),f2(a1)),x94313))+~P1(f789(f63(x94312,x94311),f789(f789(f249(a1,a1),x94314),x94315)))+P1(f789(f63(x94312,f789(f789(f90(a1),x94311),x94313)),f789(f789(f249(a1,a1),f789(f789(f50(a1),x94314),x94313)),f789(f789(f89(a1),f789(f789(f90(a1),x94311),f59(a1,x94314,x94313))),x94315))))
% 21.40/21.38 [9440]~P1(f789(f789(f241(a863),f2(a863)),x94403))+~P1(f789(f789(f241(a863),f2(a863)),x94402))+~P1(f789(f62(x94401,x94402),f789(f789(f249(a863,a863),x94404),x94405)))+P1(f789(f62(x94401,f789(f789(f90(a863),x94402),x94403)),f789(f789(f249(a863,a863),f789(f789(f50(a863),x94404),x94403)),f789(f789(f89(a863),f789(f789(f90(a863),x94402),f59(a863,x94404,x94403))),x94405))))
% 21.40/21.38 [9492]E(f789(f789(f89(a1),f503(x94921,x94922,x94923,x94924,x94925)),f504(x94921,x94922,x94923,x94924,x94925)),x94925)+~P1(f789(f789(f287(a1),x94924),x94923))+~P1(f789(f789(f287(a1),x94924),f789(f789(f89(a1),x94925),x94921)))+P1(f789(f789(f287(a1),x94924),f789(f789(f89(a1),f789(f789(f3(a1),x94925),x94923)),x94921)))
% 21.40/21.38 [9493]E(f789(f789(f3(a1),f515(x94931,x94932,x94933,x94934,x94935)),f516(x94931,x94932,x94933,x94934,x94935)),x94935)+~P1(f789(f789(f287(a1),x94934),x94933))+~P1(f789(f789(f287(a1),x94934),f789(f789(f89(a1),x94935),x94931)))+P1(f789(f789(f287(a1),x94934),f789(f789(f89(a1),f789(f789(f89(a1),x94935),x94933)),x94931)))
% 21.40/21.38 [9494]~P69(x94941)+~P1(f789(f70(x94942),x94945))+~P1(f789(f70(x94942),x94944))+E(f789(f789(f90(x94941),f789(f789(f789(f74(x94941,x94942,f90(x94941)),x94943),f87(x94941)),f789(f789(f110(f870(x94942,a856)),x94944),x94945))),f789(f789(f789(f74(x94941,x94942,f90(x94941)),x94943),f87(x94941)),f789(f789(f111(f870(x94942,a856)),x94944),x94945))),f789(f789(f90(x94941),f789(f789(f789(f74(x94941,x94942,f90(x94941)),x94943),f87(x94941)),x94944)),f789(f789(f789(f74(x94941,x94942,f90(x94941)),x94943),f87(x94941)),x94945)))
% 21.40/21.38 [9496]~E(f789(f789(f164(x94961),x94965),x94962),f789(f789(f164(x94961),x94965),x94963))+P1(f789(f789(f342(f869(f864(x94961),f864(x94961))),f789(f789(f249(f864(x94961),f864(x94961)),x94962),x94963)),f143(x94961,x94964)))+~P1(f789(f789(f241(a863),x94965),f789(f789(f244(a863),f789(f185(f864(x94961)),x94962)),f789(f185(f864(x94961)),x94963))))+~P1(f789(f789(f342(f869(x94961,x94961)),f789(f789(f249(x94961,x94961),f789(f789(f159(x94961),x94962),x94965)),f789(f789(f159(x94961),x94963),x94965))),x94964))
% 21.40/21.38 [9505]E(f789(f789(f89(a1),f510(x95051,x95052,x95053,x95054,x95055)),f511(x95051,x95052,x95053,x95054,x95055)),x95055)+~P1(f789(f789(f287(a1),x95054),x95053))+P1(f789(f789(f287(a1),x95054),f789(f789(f89(a1),x95055),x95051)))+~P1(f789(f789(f287(a1),x95054),f789(f789(f89(a1),f789(f789(f3(a1),x95055),x95053)),x95051)))
% 21.40/21.38 [9506]E(f789(f789(f3(a1),f512(x95061,x95062,x95063,x95064,x95065)),f513(x95061,x95062,x95063,x95064,x95065)),x95065)+~P1(f789(f789(f287(a1),x95064),x95063))+P1(f789(f789(f287(a1),x95064),f789(f789(f89(a1),x95065),x95061)))+~P1(f789(f789(f287(a1),x95064),f789(f789(f89(a1),f789(f789(f89(a1),x95065),x95063)),x95061)))
% 21.40/21.38 [9589]~P1(f789(f789(f287(a1),x95894),x95893))+P1(f789(f789(f342(a1),f503(x95891,x95892,x95893,x95894,x95895)),x95892))+~P1(f789(f789(f287(a1),x95894),f789(f789(f89(a1),x95895),x95891)))+P1(f789(f789(f287(a1),x95894),f789(f789(f89(a1),f789(f789(f3(a1),x95895),x95893)),x95891)))
% 21.40/21.38 [9590]~P1(f789(f789(f287(a1),x95904),x95903))+P1(f789(f789(f342(a1),f515(x95901,x95902,x95903,x95904,x95905)),x95902))+~P1(f789(f789(f287(a1),x95904),f789(f789(f89(a1),x95905),x95901)))+P1(f789(f789(f287(a1),x95904),f789(f789(f89(a1),f789(f789(f89(a1),x95905),x95903)),x95901)))
% 21.40/21.38 [9598]~P1(f789(f789(f287(a1),x95984),x95983))+P1(f789(f789(f342(a1),f504(x95981,x95982,x95983,x95984,x95985)),f303(a1,f87(a1),x95983)))+~P1(f789(f789(f287(a1),x95984),f789(f789(f89(a1),x95985),x95981)))+P1(f789(f789(f287(a1),x95984),f789(f789(f89(a1),f789(f789(f3(a1),x95985),x95983)),x95981)))
% 21.40/21.38 [9599]~P1(f789(f789(f287(a1),x95994),x95993))+P1(f789(f789(f342(a1),f516(x95991,x95992,x95993,x95994,x95995)),f303(a1,f87(a1),x95993)))+~P1(f789(f789(f287(a1),x95994),f789(f789(f89(a1),x95995),x95991)))+P1(f789(f789(f287(a1),x95994),f789(f789(f89(a1),f789(f789(f89(a1),x95995),x95993)),x95991)))
% 21.40/21.38 [9600]~P2(x96005)+~P79(x96005)+P1(f789(f789(f342(x96001),f517(x96002,x96003,x96004,x96001,x96005)),x96004))+P1(f789(f789(f240(x96005),f789(f789(f8(x96001,x96005),x96003),x96004)),f789(f789(f90(x96005),f789(f109(x96005),f789(f49(x96001),x96004))),x96002)))
% 21.40/21.38 [9601]~P1(f789(f789(f287(a1),x96014),x96013))+P1(f789(f789(f342(a1),f512(x96011,x96012,x96013,x96014,x96015)),x96012))+P1(f789(f789(f287(a1),x96014),f789(f789(f89(a1),x96015),x96011)))+~P1(f789(f789(f287(a1),x96014),f789(f789(f89(a1),f789(f789(f89(a1),x96015),x96013)),x96011)))
% 21.40/21.38 [9602]~P1(f789(f789(f287(a1),x96024),x96023))+P1(f789(f789(f342(a1),f510(x96021,x96022,x96023,x96024,x96025)),x96022))+P1(f789(f789(f287(a1),x96024),f789(f789(f89(a1),x96025),x96021)))+~P1(f789(f789(f287(a1),x96024),f789(f789(f89(a1),f789(f789(f3(a1),x96025),x96023)),x96021)))
% 21.40/21.38 [9604]~P1(f789(f789(f287(a1),x96041),x96045))+P1(f789(f789(f342(a1),f513(x96043,x96044,x96045,x96041,x96042)),f303(a1,f87(a1),x96045)))+P1(f789(f789(f287(a1),x96041),f789(f789(f89(a1),x96042),x96043)))+~P1(f789(f789(f287(a1),x96041),f789(f789(f89(a1),f789(f789(f89(a1),x96042),x96045)),x96043)))
% 21.40/21.38 [9605]~P1(f789(f789(f287(a1),x96051),x96055))+P1(f789(f789(f342(a1),f511(x96053,x96054,x96055,x96051,x96052)),f303(a1,f87(a1),x96055)))+P1(f789(f789(f287(a1),x96051),f789(f789(f89(a1),x96052),x96053)))+~P1(f789(f789(f287(a1),x96051),f789(f789(f89(a1),f789(f789(f3(a1),x96052),x96055)),x96053)))
% 21.40/21.38 [9772]~P2(x97721)+~P79(x97721)+~P1(f789(f789(f240(x97721),f789(x97723,f517(x97725,x97723,x97724,x97722,x97721))),x97725))+P1(f789(f789(f240(x97721),f789(f789(f8(x97722,x97721),x97723),x97724)),f789(f789(f90(x97721),f789(f109(x97721),f789(f49(x97722),x97724))),x97725)))
% 21.40/21.38 [8645]E(f789(f789(f132(x86451),x86452),x86453),f789(f789(f132(x86451),x86454),x86455))+~E(f789(f789(f164(x86451),f789(f185(f864(x86451)),x86452)),x86454),x86452)+~E(f789(f789(f132(x86451),f789(f789(f135(x86451),f789(f185(f864(x86451)),x86452)),x86454)),x86455),x86453)+P1(f789(f789(f240(a863),f789(f185(f864(x86451)),x86454)),f789(f185(f864(x86451)),x86452)))
% 21.40/21.38 [8758]E(f789(f789(f132(x87581),x87582),x87583),f789(f789(f132(x87581),x87584),x87585))+~E(f789(f789(f164(x87581),f789(f185(f864(x87581)),x87582)),x87584),x87582)+~E(x87583,f789(f789(f132(x87581),f789(f789(f135(x87581),f789(f185(f864(x87581)),x87582)),x87584)),x87585))+~P1(f789(f789(f240(a863),f789(f185(f864(x87581)),x87582)),f789(f185(f864(x87581)),x87584)))
% 21.40/21.38 [9928]~P1(f789(x99285,x99284))+~P1(f789(f70(x99282),f789(f264(x99282),x99285)))+P1(f789(f70(x99281),f789(f264(x99281),f789(f789(f9(x99281,x99282,a856),x99283),x99284))))+~P1(f789(f70(x99281),f789(f264(x99281),f789(f789(f10(f870(x99282,a856),a856,x99281),f96(x99282)),f789(f789(f10(f870(x99282,a856),f870(x99282,a856),x99281),f789(f20(x99282,a856,a856),f789(f789(f10(a856,f870(a856,a856),x99282),a339),x99285))),x99283)))))
% 21.40/21.38 [7941]~P39(x79412,x79413,x79414,x79416)+~P39(f37(x79411,x79412),x79416,x79414,x79415)+P39(f37(x79411,x79412),x79413,x79414,x79415)+~P1(f789(x79411,x79413))
% 21.40/21.38 [7942]~P39(x79422,x79423,x79424,x79426)+~P39(f37(x79421,x79422),x79426,x79424,x79425)+P39(f37(x79421,x79422),x79423,x79424,x79425)+~P1(f789(x79421,x79423))
% 21.40/21.38 [8451]~P23(x84515,x84511,x84516,x84512)+E(f789(f82(x84511,x84511,x84511,f789(x84512,x84513)),f789(x84512,x84514)),f789(f82(x84511,x84511,x84511,f789(x84512,x84514)),f789(x84512,x84513)))+~P1(f789(f70(x84515),x84514))+~P1(f789(f70(x84515),x84513))
% 21.40/21.38 [7852]~P29(x78521,x78522,x78524,x78523)+~E(f789(x78524,x78526),x78525)+E(f789(f86(x78521,x78522,x78523,x78524),x78525),x78526)+~P1(f789(f789(f342(x78521),x78526),x78523))
% 21.40/21.38 [8043]~P24(x80436,x80431,x80434,x80432)+E(f789(f82(x80431,x80431,x80431,f789(x80432,x80433)),f789(x80434,x80435)),f789(x80432,x80433))+~P1(f789(f70(x80436),x80433))+~P1(f789(f789(f342(x80436),x80435),x80433))
% 21.40/21.38 [9183]~P23(x91833,x91831,x91836,x91832)+E(f789(f82(x91831,x91831,x91831,f789(x91832,f789(f789(f3(f870(x91833,a856)),x91834),f789(f789(f310(x91833),x91835),f184(f870(x91833,a856)))))),f789(x91836,x91835)),f789(x91832,x91834))+~P1(f789(f70(x91833),x91834))+~P1(f789(f789(f342(x91833),x91835),x91834))
% 21.40/21.38 [6911]~P7(x69111)+~E(f59(x69111,x69113,x69114),f59(x69111,x69116,x69114))+~E(f59(x69111,x69112,x69114),f59(x69111,x69115,x69114))+E(f59(x69111,f789(f789(f89(x69111),x69112),x69113),x69114),f59(x69111,f789(f789(f89(x69111),x69115),x69116),x69114))
% 21.40/21.38 [6912]~P7(x69121)+~E(f59(x69121,x69123,x69124),f59(x69121,x69126,x69124))+~E(f59(x69121,x69122,x69124),f59(x69121,x69125,x69124))+E(f59(x69121,f789(f789(f90(x69121),x69122),x69123),x69124),f59(x69121,f789(f789(f90(x69121),x69125),x69126),x69124))
% 21.40/21.38 [6913]~P8(x69131)+~E(f59(x69131,x69133,x69134),f59(x69131,x69136,x69134))+~E(f59(x69131,x69132,x69134),f59(x69131,x69135,x69134))+E(f59(x69131,f789(f789(f3(x69131),x69132),x69133),x69134),f59(x69131,f789(f789(f3(x69131),x69135),x69136),x69134))
% 21.40/21.38 [7743]~P20(x77431,x77432,x77433)+~P1(f789(f70(x77431),x77436))+E(f789(f789(f73(x77431,x77432,x77433),x77434),f789(f789(f310(x77431),x77435),x77436)),f789(f789(f73(x77431,x77432,x77433),f789(f789(x77433,x77435),x77434)),x77436))+P1(f789(f789(f342(x77431),x77435),x77436))
% 21.40/21.38 [7810]~P9(x78101)+P1(f789(f789(f240(x78101),x78102),f789(x78103,x78104)))+~P1(f789(f789(f342(x78105),x78104),x78106))+~P1(f789(f789(f240(x78101),x78102),f789(f789(f54(x78105,x78101),x78106),x78103)))
% 21.40/21.38 [7968]~P20(x79681,x79682,x79683)+~P1(f789(f70(x79681),x79686))+E(f789(f789(f73(x79681,x79682,x79683),x79684),f789(f789(f310(x79681),x79685),x79686)),f789(f789(x79683,x79685),f789(f789(f73(x79681,x79682,x79683),x79684),x79686)))+P1(f789(f789(f342(x79681),x79685),x79686))
% 21.40/21.38 [8059]~P101(x80593)+~P1(f789(x80592,x80595))+~P18(x80593,f789(f789(f150(x80591,x80593),x80594),x80596))+E(f789(f133(x80591,x80592),f789(f789(f144(x80591,x80593,x80594),x80595),x80596)),f789(f789(f144(x80591,x80593,x80594),x80595),f789(f133(x80591,x80592),x80596)))
% 21.40/21.38 [8082]E(x80821,x80822)+E(x80823,f2(a1))+~P1(f789(f63(x80824,x80823),f789(f789(f249(a1,a1),x80825),x80822)))+~P1(f789(f63(x80824,x80823),f789(f789(f249(a1,a1),x80826),x80821)))
% 21.40/21.38 [8083]E(x80831,x80832)+E(x80833,f2(a1))+~P1(f789(f63(x80834,x80833),f789(f789(f249(a1,a1),x80832),x80835)))+~P1(f789(f63(x80834,x80833),f789(f789(f249(a1,a1),x80831),x80836)))
% 21.40/21.38 [8105]~P23(x81052,x81055,x81056,x81051)+~P1(f789(f70(x81052),x81054))+E(f789(x81051,f789(f789(f310(x81052),x81053),x81054)),f789(f82(x81055,x81055,x81055,f789(x81051,x81054)),f789(x81056,x81053)))+P1(f789(f789(f342(x81052),x81053),x81054))
% 21.40/21.38 [8319]~P24(x83195,x83191,x83196,x83192)+E(f789(f82(x83191,x83191,x83191,f789(x83192,x83193)),f789(x83192,x83194)),f789(x83192,x83193))+~P1(f789(f70(x83195),x83193))+~P1(f789(f789(f240(f870(x83195,a856)),x83194),x83193))
% 21.40/21.38 [9371]~P29(x93711,x93712,x93714,x93713)+~P1(f789(f789(f342(x93712),x93715),f789(f311(x93711,x93712,x93714),x93713)))+P1(f789(f789(f342(x93711),f789(f86(x93711,x93712,x93713,x93714),x93715)),x93716))+~P1(f789(f789(f240(f870(x93711,a856)),x93713),x93716))
% 21.40/21.38 [9722]~P4(x97222)+~E(f540(x97221,x97223,x97225,x97226,x97224,x97222),f541(x97221,x97223,x97225,x97226,x97224,x97222))+~P1(f789(f70(x97224),x97226))+E(f789(f789(f8(x97221,x97222),x97223),f789(f311(x97224,x97221,x97225),x97226)),f789(f789(f8(x97224,x97222),f789(f82(x97221,x97222,x97224,x97223),x97225)),x97226))
% 21.40/21.38 [9752]~P4(x97526)+E(f789(x97521,f540(x97522,x97523,x97521,x97524,x97525,x97526)),f789(x97521,f541(x97522,x97523,x97521,x97524,x97525,x97526)))+E(f789(f789(f8(x97522,x97526),x97523),f789(f311(x97525,x97522,x97521),x97524)),f789(f789(f8(x97525,x97526),f789(f82(x97522,x97526,x97525,x97523),x97521)),x97524))+~P1(f789(f70(x97525),x97524))
% 21.40/21.38 [9806]~P4(x98062)+~E(f789(x98063,f789(x98065,f541(x98061,x98063,x98065,x98066,x98064,x98062))),f2(x98062))+~P1(f789(f70(x98064),x98066))+E(f789(f789(f8(x98061,x98062),x98063),f789(f311(x98064,x98061,x98065),x98066)),f789(f789(f8(x98064,x98062),f789(f82(x98061,x98062,x98064,x98063),x98065)),x98066))
% 21.40/21.38 [9869]~P4(x98692)+~P1(f789(f70(x98694),x98696))+E(f789(f789(f8(x98691,x98692),x98693),f789(f311(x98694,x98691,x98695),x98696)),f789(f789(f8(x98694,x98692),f789(f82(x98691,x98692,x98694,x98693),x98695)),x98696))+P1(f789(f789(f342(x98694),f541(x98691,x98693,x98695,x98696,x98694,x98692)),x98696))
% 21.40/21.38 [9870]~P4(x98702)+~P1(f789(f70(x98704),x98706))+E(f789(f789(f8(x98701,x98702),x98703),f789(f311(x98704,x98701,x98705),x98706)),f789(f789(f8(x98704,x98702),f789(f82(x98701,x98702,x98704,x98703),x98705)),x98706))+P1(f789(f789(f342(x98704),f540(x98701,x98703,x98705,x98706,x98704,x98702)),x98706))
% 21.40/21.38 [9993]~P69(x99931)+~P1(f789(f70(x99932),x99936))+E(f789(f789(f789(f74(x99931,x99932,f90(x99931)),f789(f789(f20(x99932,f870(x99933,a856),x99931),f789(f789(f9(x99932,x99931,f870(f870(x99933,a856),x99931)),f789(f789(f10(f870(x99933,x99931),f870(x99931,f870(f870(x99933,a856),x99931)),x99932),f74(x99931,x99933,f90(x99931))),x99934)),f87(x99931))),x99935)),f87(x99931)),x99936),f789(f789(f789(f74(x99931,f869(x99932,x99933),f90(x99931)),f789(f259(x99932,x99933,x99931),x99934)),f87(x99931)),f789(f789(f256(x99932,x99933),x99936),x99935)))+P1(f789(f789(f342(x99932),f574(x99934,x99935,x99933,x99936,x99932,x99931)),x99936))
% 21.40/21.38 [10011]~P69(x100111)+~P1(f789(f70(x100112),x100116))+E(f789(f789(f789(f74(x100111,x100112,f90(x100111)),f789(f789(f20(x100112,f870(x100113,a856),x100111),f789(f789(f9(x100112,x100111,f870(f870(x100113,a856),x100111)),f789(f789(f10(f870(x100113,x100111),f870(x100111,f870(f870(x100113,a856),x100111)),x100112),f74(x100111,x100113,f90(x100111))),x100114)),f87(x100111))),x100115)),f87(x100111)),x100116),f789(f789(f789(f74(x100111,f869(x100112,x100113),f90(x100111)),f789(f259(x100112,x100113,x100111),x100114)),f87(x100111)),f789(f789(f256(x100112,x100113),x100116),x100115)))+~P1(f789(f70(x100113),f789(x100115,f574(x100114,x100115,x100113,x100116,x100112,x100111))))
% 21.40/21.38 [8233]~P24(x82332,x82335,x82336,x82331)+~P1(f789(f70(x82332),x82334))+~P1(f789(f70(x82332),x82333))+E(f789(x82331,f789(f789(f110(f870(x82332,a856)),x82333),x82334)),f789(f82(x82335,x82335,x82335,f789(x82331,x82333)),f789(x82331,x82334)))
% 21.40/21.38 [8453]~P9(x84531)+P1(f789(f789(f240(x84531),f789(x84532,x84533)),x84534))+~P1(f789(f789(f342(x84535),x84533),x84536))+~P1(f789(f789(f240(x84531),f789(f789(f53(x84535,x84531),x84536),x84532)),x84534))
% 21.40/21.38 [8828]~P29(x88282,x88281,x88283,x88286)+E(f789(f789(f3(f870(x88281,a856)),f789(f311(x88282,x88281,x88283),x88284)),f789(f311(x88282,x88281,x88283),x88285)),f789(f311(x88282,x88281,x88283),f789(f789(f3(f870(x88282,a856)),x88284),x88285)))+~P1(f789(f789(f240(f870(x88282,a856)),x88285),x88286))+~P1(f789(f789(f240(f870(x88282,a856)),x88284),x88286))
% 21.40/21.38 [8829]~P29(x88292,x88291,x88293,x88296)+E(f789(f789(f111(f870(x88291,a856)),f789(f311(x88292,x88291,x88293),x88294)),f789(f311(x88292,x88291,x88293),x88295)),f789(f311(x88292,x88291,x88293),f789(f789(f111(f870(x88292,a856)),x88294),x88295)))+~P1(f789(f789(f240(f870(x88292,a856)),x88295),x88296))+~P1(f789(f789(f240(f870(x88292,a856)),x88294),x88296))
% 21.40/21.38 [9074]E(x90741,x90742)+~P53(x90743,x90744,x90745)+~P1(f789(f789(f342(f869(x90743,x90744)),f789(f789(f249(x90743,x90744),x90746),x90742)),x90745))+~P1(f789(f789(f342(f869(x90743,x90744)),f789(f789(f249(x90743,x90744),x90746),x90741)),x90745))
% 21.40/21.38 [9075]E(x90751,x90752)+~P53(x90753,x90754,x90755)+~P1(f789(f789(f342(f869(x90753,x90754)),f789(f789(f249(x90753,x90754),x90756),x90752)),x90755))+~P1(f789(f789(f342(f869(x90753,x90754)),f789(f789(f249(x90753,x90754),x90756),x90751)),x90755))
% 21.40/21.38 [9663]~P4(x96631)+~P1(f789(f70(x96633),x96636))+~P1(f789(f70(x96632),x96635))+E(f789(f789(f89(x96631),f789(f789(f8(x96632,x96631),f789(f82(f871(x96632,x96633),x96631,x96632,x96634),f312(x96632,x96633))),x96635)),f789(f789(f8(x96633,x96631),f789(f82(f871(x96632,x96633),x96631,x96633,x96634),f321(x96633,x96632))),x96636)),f789(f789(f8(f871(x96632,x96633),x96631),x96634),f322(x96632,x96633,x96635,x96636)))
% 21.40/21.38 [9802]~P66(x98021)+~E(f789(x98023,f639(x98024,x98026,x98023,x98025,x98022,x98021)),f789(x98026,f639(x98024,x98026,x98023,x98025,x98022,x98021)))+~P1(f789(f70(x98022),x98025))+E(f789(f789(f789(f74(x98021,x98022,f90(x98021)),x98023),x98024),x98025),f789(f789(f789(f74(x98021,x98022,f90(x98021)),x98026),x98024),x98025))
% 21.40/21.38 [9864]~P66(x98641)+~P1(f789(f70(x98642),x98645))+E(f789(f789(f789(f74(x98641,x98642,f90(x98641)),x98643),x98644),x98645),f789(f789(f789(f74(x98641,x98642,f90(x98641)),x98646),x98644),x98645))+P1(f789(f789(f342(x98642),f639(x98644,x98643,x98646,x98645,x98642,x98641)),x98645))
% 21.40/21.38 [8658]~P66(x86581)+~P1(f789(f70(x86582),x86586))+P1(f789(f789(f342(x86582),x86585),x86586))+E(f789(f789(f789(f74(x86581,x86582,f90(x86581)),x86583),x86584),f789(f789(f310(x86582),x86585),x86586)),f789(f789(f90(x86581),f789(x86583,x86585)),f789(f789(f789(f74(x86581,x86582,f90(x86581)),x86583),x86584),x86586)))
% 21.40/21.38 [8702]~P12(x87021,x87026,x87023)+~P16(x87021,f870(x87022,a856),x87023,x87025)+~P1(f789(f789(f342(x87021),x87024),x87026))+E(f789(f789(f53(x87021,f870(x87022,a856)),f789(f285(x87021,x87021,x87023),f789(f789(f310(x87021),x87024),f184(f870(x87021,a856))))),x87025),f789(x87025,x87024))
% 21.40/21.38 [8810]~P20(x88103,x88104,x88101)+~P1(f789(f70(x88103),x88106))+~P1(f789(f789(f342(x88103),x88102),x88106))+E(f789(f789(x88101,x88102),f789(f789(f73(x88103,x88104,x88101),x88105),f789(f789(f3(f870(x88103,a856)),x88106),f789(f789(f310(x88103),x88102),f184(f870(x88103,a856)))))),f789(f789(f73(x88103,x88104,x88101),x88105),x88106))
% 21.40/21.38 [9085]~P23(x90853,x90851,x90856,x90852)+~P1(f789(f70(x90853),x90855))+~P1(f789(f70(x90853),x90854))+E(f789(f82(x90851,x90851,x90851,f789(x90852,f789(f789(f110(f870(x90853,a856)),x90854),x90855))),f789(x90852,f789(f789(f111(f870(x90853,a856)),x90854),x90855))),f789(f82(x90851,x90851,x90851,f789(x90852,x90854)),f789(x90852,x90855)))
% 21.40/21.38 [9390]~E(x93903,f789(f789(f155(x93901,x93902),x93905),x93906))+P1(f789(f789(f342(f869(f864(x93901),f864(x93901))),f789(f789(f249(f864(x93901),f864(x93901)),x93902),x93903)),f153(x93901,x93904)))+~P1(f789(f789(f241(a863),x93905),f789(f185(f864(x93901)),x93902)))+~P1(f789(f789(f342(f869(x93901,x93901)),f789(f789(f249(x93901,x93901),f789(f789(f159(x93901),x93902),x93905)),x93906)),x93904))
% 21.40/21.38 [9886]~P69(x98862)+~P1(f789(f70(x98861),x98866))+P1(f789(f789(f342(x98861),f572(x98864,x98865,x98863,x98866,x98861,x98862)),x98866))+E(f789(f789(f11(x98861,x98862),f789(f789(f20(x98861,f870(x98863,a856),x98862),f789(f789(f10(f870(x98863,x98862),f870(f870(x98863,a856),x98862),x98861),f11(x98863,x98862)),x98864)),x98865)),x98866),f789(f789(f11(f869(x98861,x98863),x98862),f789(f259(x98861,x98863,x98862),x98864)),f789(f789(f256(x98861,x98863),x98866),x98865)))
% 21.40/21.38 [9887]~P4(x98872)+~P1(f789(f70(x98871),x98876))+P1(f789(f789(f342(x98871),f573(x98874,x98875,x98873,x98876,x98871,x98872)),x98876))+E(f789(f789(f8(x98871,x98872),f789(f789(f20(x98871,f870(x98873,a856),x98872),f789(f789(f10(f870(x98873,x98872),f870(f870(x98873,a856),x98872),x98871),f8(x98873,x98872)),x98874)),x98875)),x98876),f789(f789(f8(f869(x98871,x98873),x98872),f789(f259(x98871,x98873,x98872),x98874)),f789(f789(f256(x98871,x98873),x98876),x98875)))
% 21.40/21.38 [9926]~P69(x99262)+~P1(f789(f70(x99261),x99266))+~P1(f789(f70(x99263),f789(x99265,f572(x99264,x99265,x99263,x99266,x99261,x99262))))+E(f789(f789(f11(x99261,x99262),f789(f789(f20(x99261,f870(x99263,a856),x99262),f789(f789(f10(f870(x99263,x99262),f870(f870(x99263,a856),x99262),x99261),f11(x99263,x99262)),x99264)),x99265)),x99266),f789(f789(f11(f869(x99261,x99263),x99262),f789(f259(x99261,x99263,x99262),x99264)),f789(f789(f256(x99261,x99263),x99266),x99265)))
% 21.40/21.38 [9927]~P4(x99272)+~P1(f789(f70(x99271),x99276))+~P1(f789(f70(x99273),f789(x99275,f573(x99274,x99275,x99273,x99276,x99271,x99272))))+E(f789(f789(f8(x99271,x99272),f789(f789(f20(x99271,f870(x99273,a856),x99272),f789(f789(f10(f870(x99273,x99272),f870(f870(x99273,a856),x99272),x99271),f8(x99273,x99272)),x99274)),x99275)),x99276),f789(f789(f8(f869(x99271,x99273),x99272),f789(f259(x99271,x99273,x99272),x99274)),f789(f789(f256(x99271,x99273),x99276),x99275)))
% 21.40/21.38 [9909]~P69(x99092)+~P1(f789(f70(x99091),x99096))+P1(f789(f789(f342(x99091),x99093),x99096))+E(f789(f789(f11(x99091,x99092),f789(f789(f9(x99091,x99092,x99092),f789(f789(f20(x99091,x99092,f870(x99092,x99092)),f789(f789(f10(a856,f870(x99092,f870(x99092,x99092)),x99091),f105(x99092)),f789(f789(f9(x99091,x99091,a856),a338),x99093))),x99094)),x99095)),x99096),f789(f789(f250(x99092),x99095),f789(f49(x99091),x99096)))
% 21.40/21.38 [9914]~P69(x99142)+~P1(f789(f70(x99141),x99146))+~P1(f789(f789(f342(x99141),x99143),x99146))+E(f789(f789(f11(x99141,x99142),f789(f789(f9(x99141,x99142,x99142),f789(f789(f20(x99141,x99142,f870(x99142,x99142)),f789(f789(f10(a856,f870(x99142,f870(x99142,x99142)),x99141),f105(x99142)),f789(f789(f9(x99141,x99141,a856),a338),x99143))),x99144)),x99145)),x99146),f789(f789(f90(x99142),f789(x99144,x99143)),f789(f789(f250(x99142),x99145),f789(f789(f3(a863),f789(f49(x99141),x99146)),f87(a863)))))
% 21.40/21.38 [9980]~P1(f789(f70(x99801),x99805))+~P1(f789(f70(x99802),x99803))+P1(f789(f789(f342(x99802),f594(x99806,x99804,x99803,x99802,x99805,x99801)),x99803))+E(f789(f789(f8(x99801,a863),f789(f789(f10(f870(x99802,a856),a863,x99801),f49(x99802)),f789(f789(f10(f870(x99802,a856),f870(x99802,a856),x99801),f264(x99802)),f789(f789(f10(f870(x99802,a856),f870(x99802,a856),x99801),f789(f20(x99802,a856,a856),f789(f789(f10(a856,f870(a856,a856),x99802),a339),f789(f789(f9(x99802,f870(x99802,a856),a856),f342(x99802)),x99803)))),x99804)))),x99805),f789(f789(f90(a863),x99806),f789(f49(x99802),x99803)))
% 21.40/21.38 [9981]~P1(f789(f70(x99811),x99815))+~P1(f789(f70(x99812),x99813))+P1(f789(f789(f342(x99812),f595(x99816,x99814,x99813,x99812,x99815,x99811)),x99813))+E(f789(f789(f8(x99811,a863),f789(f789(f10(f870(x99812,a856),a863,x99811),f49(x99812)),f789(f789(f10(f870(x99812,a856),f870(x99812,a856),x99811),f264(x99812)),f789(f789(f10(f870(x99812,a856),f870(x99812,a856),x99811),f789(f20(x99812,a856,a856),f789(f789(f10(a856,f870(a856,a856),x99812),a339),f789(f789(f9(x99812,f870(x99812,a856),a856),f342(x99812)),x99813)))),x99814)))),x99815),f789(f789(f8(x99812,a863),x99816),x99813))
% 21.40/21.38 [10017]~P1(f789(f70(x100172),x100173))+~P1(f789(f70(x100171),x100175))+~E(f789(f49(x100171),f789(f264(x100171),f789(f789(f20(x100171,a856,a856),f789(f789(f10(a856,f870(a856,a856),x100171),a339),f789(f789(f9(x100171,f870(x100171,a856),a856),f342(x100171)),x100175))),f789(f789(f9(x100171,x100172,a856),x100174),f594(x100176,x100174,x100173,x100172,x100175,x100171))))),x100176)+E(f789(f789(f8(x100171,a863),f789(f789(f10(f870(x100172,a856),a863,x100171),f49(x100172)),f789(f789(f10(f870(x100172,a856),f870(x100172,a856),x100171),f264(x100172)),f789(f789(f10(f870(x100172,a856),f870(x100172,a856),x100171),f789(f20(x100172,a856,a856),f789(f789(f10(a856,f870(a856,a856),x100172),a339),f789(f789(f9(x100172,f870(x100172,a856),a856),f342(x100172)),x100173)))),x100174)))),x100175),f789(f789(f90(a863),x100176),f789(f49(x100172),x100173)))
% 21.40/21.38 [10019]~P1(f789(f70(x100192),x100193))+~P1(f789(f70(x100191),x100195))+~E(f789(f49(x100191),f789(f264(x100191),f789(f789(f20(x100191,a856,a856),f789(f789(f10(a856,f870(a856,a856),x100191),a339),f789(f789(f9(x100191,f870(x100191,a856),a856),f342(x100191)),x100195))),f789(f789(f9(x100191,x100192,a856),x100194),f595(x100196,x100194,x100193,x100192,x100195,x100191))))),f789(x100196,f595(x100196,x100194,x100193,x100192,x100195,x100191)))+E(f789(f789(f8(x100191,a863),f789(f789(f10(f870(x100192,a856),a863,x100191),f49(x100192)),f789(f789(f10(f870(x100192,a856),f870(x100192,a856),x100191),f264(x100192)),f789(f789(f10(f870(x100192,a856),f870(x100192,a856),x100191),f789(f20(x100192,a856,a856),f789(f789(f10(a856,f870(a856,a856),x100192),a339),f789(f789(f9(x100192,f870(x100192,a856),a856),f342(x100192)),x100193)))),x100194)))),x100195),f789(f789(f8(x100192,a863),x100196),x100193))
% 21.40/21.38 [9662]E(x96621,x96622)+~P20(x96623,x96624,x96625)+~P1(f789(f75(x96623,x96624,x96625,x96626,x96627),x96622))+~P1(f789(f75(x96623,x96624,x96625,x96626,x96627),x96621))
% 21.40/21.38 [9463]P1(f789(x94631,x94632))+~P1(f789(f789(f342(x94637),x94632),f789(x94636,x94634)))+~P1(f789(x94631,f422(x94631,x94636,x94635,x94633,x94637)))+~P1(f789(f789(f342(x94633),x94634),x94635))
% 21.40/21.38 [9901]~P20(x99017,x99016,x99011)+E(f789(f789(x99011,x99012),f648(x99012,x99013,x99014,x99015,x99011,x99016,x99017)),x99013)+~P1(f789(f75(x99017,x99016,x99011,x99015,x99014),x99013))+~P1(f789(f789(f342(x99017),x99012),x99014))
% 21.40/21.38 [9965]~P20(x99651,x99652,x99653)+~P1(f789(f75(x99651,x99652,x99653,x99654,x99655),x99657))+P1(f789(f75(x99651,x99652,x99653,x99654,f789(f789(f3(f870(x99651,a856)),x99655),f789(f789(f310(x99651),x99656),f184(f870(x99651,a856))))),f648(x99656,x99657,x99655,x99654,x99653,x99652,x99651)))+~P1(f789(f789(f342(x99651),x99656),x99655))
% 21.40/21.38 [9367]~P66(x93671)+~P29(x93675,x93672,x93676,x93677)+~P1(f789(f70(x93675),x93677))+E(f789(f789(f789(f74(x93671,x93672,f90(x93671)),x93673),x93674),f789(f311(x93675,x93672,x93676),x93677)),f789(f789(f789(f74(x93671,x93675,f90(x93671)),f789(f82(x93672,x93671,x93675,x93673),x93676)),x93674),x93677))
% 21.40/21.38 [9486]~E(f789(f789(f310(x94861),x94865),x94866),f789(f789(f310(x94861),x94862),x94863))+~P1(f789(f75(x94861,x94861,x94864,x94862,x94863),x94867))+P1(f789(f789(f342(x94861),x94862),x94863))+P1(f789(f71(x94861,x94864,f789(f789(f310(x94861),x94865),x94866)),x94867))
% 21.40/21.38 [9568]P1(f789(x95681,x95682))+~P1(f789(f789(f342(x95683),x95682),f789(x95684,x95687)))+~P1(f789(f789(f342(x95686),x95687),x95685))+P1(f789(f789(f342(x95683),f422(x95681,x95684,x95685,x95686,x95683)),f789(f789(f53(x95686,f870(x95683,a856)),x95685),x95684)))
% 21.40/21.38 [9581]~P29(x95812,x95811,x95815,x95814)+~P29(x95811,x95813,x95816,f789(f311(x95812,x95811,x95815),x95814))+E(f789(f789(f82(x95811,x95812,x95813,f86(x95812,x95811,x95814,x95815)),f86(x95811,x95813,f789(f311(x95812,x95811,x95815),x95814),x95816)),x95817),f789(f86(x95812,x95813,x95814,f789(f82(x95811,x95813,x95812,x95816),x95815)),x95817))+~P1(f789(f789(f342(x95813),x95817),f789(f311(x95811,x95813,x95816),f789(f311(x95812,x95811,x95815),x95814))))
% 21.40/21.38 [9902]~P20(x99027,x99026,x99021)+E(f789(f789(x99021,x99022),f688(x99023,x99024,x99022,x99025,x99021,x99026,x99027)),x99023)+P1(f789(f789(f342(x99027),x99022),x99024))+~P1(f789(f75(x99027,x99026,x99021,x99025,f789(f789(f310(x99027),x99022),x99024)),x99023))
% 21.40/21.38 [9964]~P20(x99641,x99644,x99645)+P1(f789(f75(x99641,x99644,x99645,x99646,x99643),f688(x99647,x99643,x99642,x99646,x99645,x99644,x99641)))+P1(f789(f789(f342(x99641),x99642),x99643))+~P1(f789(f75(x99641,x99644,x99645,x99646,f789(f789(f310(x99641),x99642),x99643)),x99647))
% 21.40/21.38 [9646]E(x96461,f2(a1))+~P1(f789(f63(x96463,x96461),f789(f789(f249(a1,a1),x96465),x96467)))+~P1(f789(f63(x96462,x96461),f789(f789(f249(a1,a1),x96464),x96466)))+P1(f789(f63(f789(f789(f89(a1),x96462),x96463),x96461),f789(f789(f249(a1,a1),f789(f789(f89(a1),f789(f789(f89(a1),x96464),x96465)),f789(f789(f50(a1),f789(f789(f89(a1),x96466),x96467)),x96461))),f59(a1,f789(f789(f89(a1),x96466),x96467),x96461))))
% 21.40/21.38 [9648]~P1(f789(f789(f241(a863),f2(a863)),x96483))+~P1(f789(f62(x96482,x96483),f789(f789(f249(a863,a863),x96485),x96487)))+~P1(f789(f62(x96481,x96483),f789(f789(f249(a863,a863),x96484),x96486)))+P1(f789(f62(f789(f789(f89(a863),x96481),x96482),x96483),f789(f789(f249(a863,a863),f789(f789(f89(a863),f789(f789(f89(a863),x96484),x96485)),f789(f789(f50(a863),f789(f789(f89(a863),x96486),x96487)),x96483))),f59(a863,f789(f789(f89(a863),x96486),x96487),x96483))))
% 21.40/21.38 [10016]~P4(x100162)+~P1(f789(f70(x100163),x100165))+~P1(f789(f70(x100161),x100167))+E(f789(f789(f8(x100161,x100162),f789(f789(f20(x100161,f870(x100163,a856),x100162),f789(f789(f10(f870(x100163,x100162),f870(f870(x100163,a856),x100162),x100161),f8(x100163,x100162)),x100164)),f789(f789(f10(f870(x100163,a856),f870(x100163,a856),x100161),f264(x100163)),f789(f789(f10(f870(x100163,a856),f870(x100163,a856),x100161),f789(f20(x100163,a856,a856),f789(f789(f10(a856,f870(a856,a856),x100163),a339),f789(f789(f9(x100163,f870(x100163,a856),a856),f342(x100163)),x100165)))),x100166)))),x100167),f789(f789(f8(x100163,x100162),f789(f789(f20(x100163,f870(x100161,a856),x100162),f789(f789(f10(f870(x100161,x100162),f870(f870(x100161,a856),x100162),x100163),f8(x100161,x100162)),f789(f9(x100161,x100163,x100162),x100164))),f789(f789(f10(f870(x100161,a856),f870(x100161,a856),x100163),f264(x100161)),f789(f789(f10(f870(x100161,a856),f870(x100161,a856),x100163),f789(f20(x100161,a856,a856),f789(f789(f10(a856,f870(a856,a856),x100161),a339),f789(f789(f9(x100161,f870(x100161,a856),a856),f342(x100161)),x100167)))),f789(f9(x100161,x100163,a856),x100166))))),x100165))
% 21.40/21.38 [9526]~P26(x95267,x95266,x95261,x95268,x95262,x95264)+E(f789(f789(x95261,f789(x95262,x95263)),f789(x95264,x95265)),f789(x95264,x95265))+~P1(f789(f70(x95266),x95265))+~P1(f789(f789(f342(x95266),x95263),x95265))
% 21.40/21.38 [9530]~P17(x95306,x95301,x95302,x95308,x95303,x95304)+~P12(x95306,x95307,x95308)+P16(x95301,x95302,x95303,f789(x95304,x95305))+~P1(f789(f789(f342(x95306),x95305),x95307))
% 21.40/21.38 [7770]~P39(x77704,x77705,x77706,x77703)+~P31(x77708,x77706,f789(f789(f789(f100(x77708),x77707),x77704),x77701))+P1(f789(f789(x77701,x77702),x77703))+~P1(f789(f789(x77707,x77702),x77705))
% 21.40/21.38 [9172]~P23(x91727,x91721,x91728,x91723)+~P1(f789(f70(x91727),x91725))+~P1(f789(f70(x91727),x91724))+E(f789(f82(x91721,x91721,x91722,f789(x91723,x91724)),f789(f82(x91721,x91721,x91722,f789(x91723,x91725)),x91726)),f789(f82(x91721,x91721,x91722,f789(x91723,x91725)),f789(f82(x91721,x91721,x91722,f789(x91723,x91724)),x91726)))
% 21.40/21.38 [9237]~P29(x92372,x92372,x92375,x92376)+~P25(x92373,x92372,x92377,x92378,x92371)+~P1(f789(f70(x92372),x92376))+E(f789(f789(x92371,f789(f82(x92372,x92373,x92372,x92374),x92375)),x92376),f789(f789(x92371,x92374),f789(f311(x92372,x92372,x92375),x92376)))
% 21.40/21.38 [9528]~P27(x95287,x95282,x95285,x95288,x95286,x95281)+~P1(f789(f70(x95282),x95284))+E(f789(x95281,f789(f789(f310(x95282),x95283),x95284)),f789(f789(x95285,f789(x95286,x95283)),f789(x95281,x95284)))+P1(f789(f789(f342(x95282),x95283),x95284))
% 21.40/21.38 [9535]~P26(x95356,x95355,x95351,x95357,x95358,x95352)+E(f789(f789(x95351,f789(x95352,x95353)),f789(x95352,x95354)),f789(x95352,x95354))+~P1(f789(f70(x95355),x95354))+~P1(f789(f789(f240(f870(x95355,a856)),x95353),x95354))
% 21.40/21.38 [9159]P1(f789(f789(f342(f869(f864(x91591),f864(x91591))),f789(f789(f249(f864(x91591),f864(x91591)),x91592),x91593)),f153(x91591,x91594)))+~E(x91593,f789(f789(f132(x91591),x91595),f789(f789(f146(x91591),x91596),x91597)))+~E(x91592,f789(f789(f132(x91591),x91595),f789(f789(f146(x91591),x91598),x91597)))+~P1(f789(f789(f342(f869(x91591,x91591)),f789(f789(f249(x91591,x91591),x91598),x91596)),x91594))
% 21.40/21.38 [9531]~P26(x95316,x95312,x95315,x95317,x95318,x95311)+~P1(f789(f70(x95312),x95314))+~P1(f789(f70(x95312),x95313))+E(f789(x95311,f789(f789(f110(f870(x95312,a856)),x95313),x95314)),f789(f789(x95315,f789(x95311,x95313)),f789(x95311,x95314)))
% 21.40/21.38 [10056]~P29(x100564,x100562,x100565,x100568)+E(f789(f789(f54(x100561,f870(x100562,a856)),x100563),f789(f789(f10(f870(x100564,a856),f870(x100562,a856),x100561),f311(x100564,x100562,x100565)),x100566)),f789(f311(x100564,x100562,x100565),f789(f789(f54(x100561,f870(x100564,a856)),x100563),x100566)))+~P1(f789(f789(f342(x100561),x100567),x100563))+P1(f789(f789(f342(x100561),f660(x100567,x100566,x100563,x100561,x100568,x100565,x100562,x100564)),x100563))
% 21.40/21.38 [10076]~P29(x100764,x100762,x100765,x100767)+E(f789(f789(f54(x100761,f870(x100762,a856)),x100763),f789(f789(f10(f870(x100764,a856),f870(x100762,a856),x100761),f311(x100764,x100762,x100765)),x100766)),f789(f311(x100764,x100762,x100765),f789(f789(f54(x100761,f870(x100764,a856)),x100763),x100766)))+~P1(f789(f789(f342(x100761),x100768),x100763))+~P1(f789(f789(f240(f870(x100764,a856)),f789(x100766,f660(x100768,x100766,x100763,x100761,x100767,x100765,x100762,x100764))),x100767))
% 21.40/21.38 [9586]~P27(x95867,x95865,x95861,x95868,x95862,x95864)+~P1(f789(f70(x95865),x95866))+~P1(f789(f789(f342(x95865),x95863),x95866))+E(f789(f789(x95861,f789(x95862,x95863)),f789(x95864,f789(f789(f3(f870(x95865,a856)),x95866),f789(f789(f310(x95865),x95863),f184(f870(x95865,a856)))))),f789(x95864,x95866))
% 21.40/21.38 [9596]~P27(x95966,x95963,x95961,x95967,x95968,x95962)+~P1(f789(f70(x95963),x95965))+~P1(f789(f70(x95963),x95964))+E(f789(f789(x95961,f789(x95962,f789(f789(f110(f870(x95963,a856)),x95964),x95965))),f789(x95962,f789(f789(f111(f870(x95963,a856)),x95964),x95965))),f789(f789(x95961,f789(x95962,x95964)),f789(x95962,x95965)))
% 21.40/21.38 [9683]P41(x96831,x96832,x96833,x96834,x96835,f789(f789(x96833,x96836),x96837))+~P41(x96831,x96832,x96833,x96834,f789(f789(f3(f870(x96831,a856)),x96835),f789(f789(f310(x96831),x96838),f184(f870(x96831,a856)))),x96839)+~E(f789(f789(x96833,x96836),x96837),f789(f789(x96833,x96838),x96839))+~P1(f789(f789(f342(x96831),x96838),x96835))
% 21.40/21.38 [10088]P28(x100881,x100882,f789(f789(f310(f862(x100881)),f789(f789(f789(f100(x100881),f789(x100883,f384(x100884,x100885,x100886,x100887,x100883,x100882,x100881,x100888,x100889))),f789(x100887,f384(x100884,x100885,x100886,x100887,x100883,x100882,x100881,x100888,x100889))),f789(x100886,f384(x100884,x100885,x100886,x100887,x100883,x100882,x100881,x100888,x100889)))),f184(f870(f862(x100881),a856))))+~P1(f789(f70(x100889),x100888))+~P28(x100881,x100882,f789(f311(x100889,f862(x100881),f789(f789(f20(x100889,f870(x100881,f870(a861,a856)),f862(x100881)),f789(f789(f20(x100889,a857,f870(f870(x100881,f870(a861,a856)),f862(x100881))),f789(f789(f10(f870(x100881,f870(a861,a856)),f870(a857,f870(f870(x100881,f870(a861,a856)),f862(x100881))),x100889),f100(x100881)),x100883)),x100887)),x100886)),x100888))+P28(x100881,x100882,f789(f311(x100889,f862(x100881),f789(f789(f20(x100889,f870(x100881,f870(a861,a856)),f862(x100881)),f789(f789(f20(x100889,a857,f870(f870(x100881,f870(a861,a856)),f862(x100881))),f789(f789(f10(f870(x100881,f870(a861,a856)),f870(a857,f870(f870(x100881,f870(a861,a856)),f862(x100881))),x100889),f100(x100881)),x100885)),x100887)),x100884)),x100888))
% 21.40/21.38 [10089]~P28(x100891,x100892,f789(f789(f310(f862(x100891)),f789(f789(f789(f100(x100891),f789(x100894,f384(x100896,x100894,x100898,x100895,x100899,x100892,x100891,x100897,x100893))),f789(x100895,f384(x100896,x100894,x100898,x100895,x100899,x100892,x100891,x100897,x100893))),f789(x100896,f384(x100896,x100894,x100898,x100895,x100899,x100892,x100891,x100897,x100893)))),f184(f870(f862(x100891),a856))))+~P1(f789(f70(x100893),x100897))+~P28(x100891,x100892,f789(f311(x100893,f862(x100891),f789(f789(f20(x100893,f870(x100891,f870(a861,a856)),f862(x100891)),f789(f789(f20(x100893,a857,f870(f870(x100891,f870(a861,a856)),f862(x100891))),f789(f789(f10(f870(x100891,f870(a861,a856)),f870(a857,f870(f870(x100891,f870(a861,a856)),f862(x100891))),x100893),f100(x100891)),x100899)),x100895)),x100898)),x100897))+P28(x100891,x100892,f789(f311(x100893,f862(x100891),f789(f789(f20(x100893,f870(x100891,f870(a861,a856)),f862(x100891)),f789(f789(f20(x100893,a857,f870(f870(x100891,f870(a861,a856)),f862(x100891))),f789(f789(f10(f870(x100891,f870(a861,a856)),f870(a857,f870(f870(x100891,f870(a861,a856)),f862(x100891))),x100893),f100(x100891)),x100894)),x100895)),x100896)),x100897))
% 21.40/21.38 [9623]~P17(x96236,x96237,x96238,x96239,x962310,x96231)+E(f789(f789(x96231,x96232),x96233),f789(f789(x96231,x96234),x96235))+~P1(f789(f789(f342(f869(x96237,x96237)),f789(f789(f249(x96237,x96237),x96233),x96235)),x962310))+~P1(f789(f789(f342(f869(x96236,x96236)),f789(f789(f249(x96236,x96236),x96232),x96234)),x96239))
% 21.40/21.38 [6840]E(x68401,x68402)+~P1(f789(f789(f240(a1),f2(a1)),x68402))+~P1(f789(f789(f240(a1),f2(a1)),x68401))+~P1(f789(f789(f287(a1),x68402),x68401))+~P1(f789(f789(f287(a1),x68401),x68402))
% 21.40/21.38 [9389]E(x93891,f2(a1))+E(x93892,f2(a1))+E(f789(f789(f95(a1,f869(a1,a1)),f789(f789(a219,x93892),x93891)),f789(f789(f20(a1,a1,f869(a1,a1)),f789(f789(f10(a1,f870(a1,f869(a1,a1)),a1),f249(a1,a1)),f789(f50(a1),x93892))),f789(f50(a1),x93891))),f217(x93892,x93891))+P1(f789(f789(f241(a1),x93891),f2(a1)))+~P1(f789(f329(f869(a1,a1),a223),f789(f789(f249(a1,a1),x93892),x93891)))
% 21.40/21.38 [9239]~P95(x92392)+E(x92391,f184(f870(x92392,a856)))+~P1(f789(f70(x92392),x92391))+P1(f789(f789(f342(x92392),f12(x92392,x92391)),x92391))+~P1(f789(f789(f342(x92392),f789(f789(f111(x92392),f393(x92391,x92392)),f397(x92391,x92392))),f789(f789(f310(x92392),f393(x92391,x92392)),f789(f789(f310(x92392),f397(x92391,x92392)),f184(f870(x92392,a856))))))
% 21.40/21.38 [9240]~P95(x92402)+E(x92401,f184(f870(x92402,a856)))+~P1(f789(f70(x92402),x92401))+P1(f789(f789(f342(x92402),f15(x92402,x92401)),x92401))+~P1(f789(f789(f342(x92402),f789(f789(f110(x92402),f398(x92401,x92402)),f399(x92401,x92402))),f789(f789(f310(x92402),f398(x92401,x92402)),f789(f789(f310(x92402),f399(x92401,x92402)),f184(f870(x92402,a856))))))
% 21.40/21.38 [9241]~P101(x92412)+E(x92411,f184(f870(x92412,a856)))+~P1(f789(f70(x92412),x92411))+P1(f789(f789(f342(x92412),f16(x92412,x92411)),x92411))+~P1(f789(f789(f342(x92412),f789(f789(f239(x92412),f394(x92411,x92412)),f396(x92411,x92412))),f789(f789(f310(x92412),f394(x92411,x92412)),f789(f789(f310(x92412),f396(x92411,x92412)),f184(f870(x92412,a856))))))
% 21.40/21.38 [9242]~P101(x92422)+E(x92421,f184(f870(x92422,a856)))+~P1(f789(f70(x92422),x92421))+P1(f789(f789(f342(x92422),f17(x92422,x92421)),x92421))+~P1(f789(f789(f342(x92422),f789(f789(f244(x92422),f400(x92421,x92422)),f401(x92421,x92422))),f789(f789(f310(x92422),f400(x92421,x92422)),f789(f789(f310(x92422),f401(x92421,x92422)),f184(f870(x92422,a856))))))
% 21.40/21.38 [9270]~P66(x92702)+E(x92701,f184(f870(x92702,a856)))+~P1(f789(f70(x92702),x92701))+P1(f789(f789(f342(x92702),f789(f72(x92702,f90(x92702)),x92701)),x92701))+~P1(f789(f789(f342(x92702),f789(f789(f90(x92702),f575(x92701,x92702)),f576(x92701,x92702))),f789(f789(f310(x92702),f575(x92701,x92702)),f789(f789(f310(x92702),f576(x92701,x92702)),f184(f870(x92702,a856))))))
% 21.40/21.38 [9276]~P101(x92762)+E(x92761,f184(f870(x92762,a856)))+~P1(f789(f70(x92762),x92761))+P1(f789(f789(f342(x92762),f13(x92762,f239(x92762),x92761)),x92761))+~P1(f789(f789(f342(x92762),f789(f789(f239(x92762),f402(x92761,x92762)),f403(x92761,x92762))),f789(f789(f310(x92762),f402(x92761,x92762)),f789(f789(f310(x92762),f403(x92761,x92762)),f184(f870(x92762,a856))))))
% 21.40/21.38 [9277]~P101(x92772)+E(x92771,f184(f870(x92772,a856)))+~P1(f789(f70(x92772),x92771))+P1(f789(f789(f342(x92772),f14(x92772,f244(x92772),x92771)),x92771))+~P1(f789(f789(f342(x92772),f789(f789(f244(x92772),f404(x92771,x92772)),f405(x92771,x92772))),f789(f789(f310(x92772),f404(x92771,x92772)),f789(f789(f310(x92772),f405(x92771,x92772)),f184(f870(x92772,a856))))))
% 21.40/21.38 [6455]~P82(x64552)+E(x64551,f2(x64552))+~E(f789(f789(f89(x64552),x64553),x64551),f2(x64552))+~P1(f789(f789(f240(x64552),f2(x64552)),x64553))+~P1(f789(f789(f240(x64552),f2(x64552)),x64551))
% 21.40/21.38 [6456]~P82(x64562)+E(x64561,f2(x64562))+~E(f789(f789(f89(x64562),x64561),x64563),f2(x64562))+~P1(f789(f789(f240(x64562),f2(x64562)),x64563))+~P1(f789(f789(f240(x64562),f2(x64562)),x64561))
% 21.40/21.38 [6657]~P1(f789(f789(f287(a863),x66572),x66571))+~P1(f789(f789(f287(a863),x66571),x66573))+P1(f789(f789(f287(a863),x66572),x66573))+P1(f789(f789(f287(a863),x66571),x66572))+P1(f789(f789(f287(a863),x66573),x66571))
% 21.40/21.38 [6839]~P1(f789(f789(f287(a863),x68391),x68393))+~P1(f789(f789(f287(a863),x68393),x68392))+~P1(f789(f789(f287(a863),x68392),x68391))+P1(f789(f789(f287(a863),x68391),x68392))+P1(f789(f789(f287(a863),x68393),x68391))
% 21.40/21.38 [7172]~P101(x71721)+E(f17(x71721,x71722),x71723)+~P1(f789(f70(x71721),x71722))+~P1(f789(f789(f240(x71721),x71723),f635(x71723,x71722,x71721)))+~P1(f789(f789(f342(x71721),x71723),x71722))
% 21.40/21.38 [7207]~P101(x72071)+~P18(x72071,x72072)+~P18(x72071,x72073)+P18(x72071,f789(f789(f132(x72071),x72072),x72073))+P1(f789(f789(f342(x72071),f780(x72073,x72072,x72071)),f789(f163(x72071),x72072)))
% 21.40/21.38 [7208]~P101(x72081)+~P18(x72081,x72082)+~P18(x72081,x72083)+P18(x72081,f789(f789(f132(x72081),x72082),x72083))+P1(f789(f789(f342(x72081),f781(x72083,x72082,x72081)),f789(f163(x72081),x72083)))
% 21.40/21.38 [7274]~P101(x72741)+E(f16(x72741,x72742),x72743)+~P1(f789(f70(x72741),x72742))+P1(f789(f789(f342(x72741),f636(x72743,x72742,x72741)),x72742))+~P1(f789(f789(f342(x72741),x72743),x72742))
% 21.40/21.38 [7275]~P101(x72751)+E(f17(x72751,x72752),x72753)+~P1(f789(f70(x72751),x72752))+P1(f789(f789(f342(x72751),f635(x72753,x72752,x72751)),x72752))+~P1(f789(f789(f342(x72751),x72753),x72752))
% 21.40/21.38 [7873]~P101(x78731)+E(f16(x78731,x78732),x78733)+~P1(f789(f70(x78731),x78732))+~P1(f789(f789(f342(x78731),x78733),x78732))+~P1(f789(f789(f240(x78731),f636(x78733,x78732,x78731)),x78733))
% 21.40/21.38 [8184]~P101(x81841)+~P18(x81841,x81842)+~P18(x81841,x81843)+P18(x81841,f789(f789(f132(x81841),x81842),x81843))+~P1(f789(f789(f240(x81841),f780(x81843,x81842,x81841)),f781(x81843,x81842,x81841)))
% 21.40/21.38 [8916]~P95(x89162)+E(x89161,f184(f870(x89162,a856)))+~E(f789(f789(f111(x89162),f789(x89163,f446(x89161,x89163,x89162))),f789(x89163,f452(x89161,x89163,x89162))),f789(x89163,f789(f789(f111(x89162),f446(x89161,x89163,x89162)),f452(x89161,x89163,x89162))))+E(f12(x89162,f789(f311(x89162,x89162,x89163),x89161)),f789(x89163,f12(x89162,x89161)))+~P1(f789(f70(x89162),x89161))
% 21.40/21.38 [8917]~P95(x89172)+E(x89171,f184(f870(x89172,a856)))+~E(f789(f789(f110(x89172),f789(x89173,f453(x89171,x89173,x89172))),f789(x89173,f454(x89171,x89173,x89172))),f789(x89173,f789(f789(f110(x89172),f453(x89171,x89173,x89172)),f454(x89171,x89173,x89172))))+E(f15(x89172,f789(f311(x89172,x89172,x89173),x89171)),f789(x89173,f15(x89172,x89171)))+~P1(f789(f70(x89172),x89171))
% 21.40/21.38 [8918]~P101(x89182)+E(x89181,f184(f870(x89182,a856)))+~E(f789(f789(f239(x89182),f789(x89183,f447(x89181,x89183,x89182))),f789(x89183,f449(x89181,x89183,x89182))),f789(x89183,f789(f789(f239(x89182),f447(x89181,x89183,x89182)),f449(x89181,x89183,x89182))))+E(f16(x89182,f789(f311(x89182,x89182,x89183),x89181)),f789(x89183,f16(x89182,x89181)))+~P1(f789(f70(x89182),x89181))
% 21.40/21.38 [8919]~P101(x89192)+E(x89191,f184(f870(x89192,a856)))+~E(f789(f789(f244(x89192),f789(x89193,f450(x89191,x89193,x89192))),f789(x89193,f451(x89191,x89193,x89192))),f789(x89193,f789(f789(f244(x89192),f450(x89191,x89193,x89192)),f451(x89191,x89193,x89192))))+E(f17(x89192,f789(f311(x89192,x89192,x89193),x89191)),f789(x89193,f17(x89192,x89191)))+~P1(f789(f70(x89192),x89191))
% 21.40/21.38 [8982]~P101(x89822)+E(x89821,f184(f870(x89822,a856)))+~E(f789(f789(f239(x89822),f789(x89823,f442(x89821,x89823,x89822))),f789(x89823,f443(x89821,x89823,x89822))),f789(x89823,f789(f789(f239(x89822),f442(x89821,x89823,x89822)),f443(x89821,x89823,x89822))))+E(f13(x89822,f239(x89822),f789(f311(x89822,x89822,x89823),x89821)),f789(x89823,f13(x89822,f239(x89822),x89821)))+~P1(f789(f70(x89822),x89821))
% 21.40/21.38 [8983]~P101(x89832)+E(x89831,f184(f870(x89832,a856)))+~E(f789(f789(f244(x89832),f789(x89833,f444(x89831,x89833,x89832))),f789(x89833,f448(x89831,x89833,x89832))),f789(x89833,f789(f789(f244(x89832),f444(x89831,x89833,x89832)),f448(x89831,x89833,x89832))))+E(f14(x89832,f244(x89832),f789(f311(x89832,x89832,x89833),x89831)),f789(x89833,f14(x89832,f244(x89832),x89831)))+~P1(f789(f70(x89832),x89831))
% 21.40/21.38 [6078]~P95(x60782)+E(x60781,f184(f870(x60782,a856)))+~P1(f789(f70(x60782),x60781))+E(f12(x60782,f789(f789(f310(x60782),x60783),x60781)),f789(f789(f111(x60782),x60783),f12(x60782,x60781)))+P1(f789(f789(f342(x60782),x60783),x60781))
% 21.40/21.38 [6079]~P95(x60792)+E(x60791,f184(f870(x60792,a856)))+~P1(f789(f70(x60792),x60791))+E(f15(x60792,f789(f789(f310(x60792),x60793),x60791)),f789(f789(f110(x60792),x60793),f15(x60792,x60791)))+P1(f789(f789(f342(x60792),x60793),x60791))
% 21.40/21.38 [6080]~P101(x60802)+E(x60801,f184(f870(x60802,a856)))+~P1(f789(f70(x60802),x60801))+E(f16(x60802,f789(f789(f310(x60802),x60803),x60801)),f789(f789(f239(x60802),x60803),f16(x60802,x60801)))+P1(f789(f789(f342(x60802),x60803),x60801))
% 21.40/21.38 [6081]~P101(x60812)+E(x60811,f184(f870(x60812,a856)))+~P1(f789(f70(x60812),x60811))+E(f17(x60812,f789(f789(f310(x60812),x60813),x60811)),f789(f789(f244(x60812),x60813),f17(x60812,x60811)))+P1(f789(f789(f342(x60812),x60813),x60811))
% 21.40/21.38 [6472]~P66(x64722)+E(x64721,f184(f870(x64722,a856)))+~P1(f789(f70(x64722),x64721))+E(f789(f72(x64722,f90(x64722)),f789(f789(f310(x64722),x64723),x64721)),f789(f789(f90(x64722),x64723),f789(f72(x64722,f90(x64722)),x64721)))+P1(f789(f789(f342(x64722),x64723),x64721))
% 21.40/21.38 [6561]~P101(x65612)+E(x65611,f184(f870(x65612,a856)))+~P1(f789(f70(x65612),x65611))+E(f13(x65612,f239(x65612),f789(f789(f310(x65612),x65613),x65611)),f789(f789(f239(x65612),x65613),f13(x65612,f239(x65612),x65611)))+P1(f789(f789(f342(x65612),x65613),x65611))
% 21.40/21.38 [6562]~P101(x65622)+E(x65621,f184(f870(x65622,a856)))+~P1(f789(f70(x65622),x65621))+E(f14(x65622,f244(x65622),f789(f789(f310(x65622),x65623),x65621)),f789(f789(f244(x65622),x65623),f14(x65622,f244(x65622),x65621)))+P1(f789(f789(f342(x65622),x65623),x65621))
% 21.40/21.38 [7010]~P101(x70102)+E(f789(f789(f244(x70102),f17(x70102,x70101)),f17(x70102,x70103)),f17(x70102,x70103))+E(x70101,f184(f870(x70102,a856)))+~P1(f789(f70(x70102),x70103))+~P1(f789(f789(f240(f870(x70102,a856)),x70101),x70103))
% 21.40/21.38 [7011]~P101(x70112)+E(f789(f789(f239(x70112),f16(x70112,x70111)),f16(x70112,x70113)),f16(x70112,x70113))+E(x70111,f184(f870(x70112,a856)))+~P1(f789(f70(x70112),x70113))+~P1(f789(f789(f240(f870(x70112,a856)),x70111),x70113))
% 21.40/21.38 [7012]~P95(x70122)+E(f789(f789(f110(x70122),f15(x70122,x70121)),f15(x70122,x70123)),f15(x70122,x70123))+E(x70121,f184(f870(x70122,a856)))+~P1(f789(f70(x70122),x70123))+~P1(f789(f789(f240(f870(x70122,a856)),x70121),x70123))
% 21.40/21.38 [7013]~P95(x70132)+E(f789(f789(f111(x70132),f12(x70132,x70131)),f12(x70132,x70133)),f12(x70132,x70133))+E(x70131,f184(f870(x70132,a856)))+~P1(f789(f70(x70132),x70133))+~P1(f789(f789(f240(f870(x70132,a856)),x70131),x70133))
% 21.40/21.38 [7330]~P101(x73302)+E(x73301,f184(f870(x73302,a856)))+~P1(f789(f70(x73302),x73303))+P1(f789(f789(f240(x73302),f16(x73302,x73301)),f16(x73302,x73303)))+~P1(f789(f789(f240(f870(x73302,a856)),x73301),x73303))
% 21.40/21.38 [7331]~P101(x73312)+E(x73311,f184(f870(x73312,a856)))+~P1(f789(f70(x73312),x73313))+P1(f789(f789(f240(x73312),f17(x73312,x73313)),f17(x73312,x73311)))+~P1(f789(f789(f240(f870(x73312,a856)),x73311),x73313))
% 21.40/21.38 [7393]~P95(x73931)+E(f12(x73931,x73932),x73933)+~P1(f789(f70(x73931),x73932))+~E(f789(f789(f3(f870(x73931,a856)),x73932),f789(f789(f310(x73931),x73933),f184(f870(x73931,a856)))),f184(f870(x73931,a856)))+~P1(f789(f789(f342(x73931),x73933),x73932))
% 21.40/21.38 [7394]~P95(x73941)+E(f15(x73941,x73942),x73943)+~P1(f789(f70(x73941),x73942))+~E(f789(f789(f3(f870(x73941,a856)),x73942),f789(f789(f310(x73941),x73943),f184(f870(x73941,a856)))),f184(f870(x73941,a856)))+~P1(f789(f789(f342(x73941),x73943),x73942))
% 21.40/21.38 [7395]~P101(x73951)+E(f16(x73951,x73952),x73953)+~P1(f789(f70(x73951),x73952))+~E(f789(f789(f3(f870(x73951,a856)),x73952),f789(f789(f310(x73951),x73953),f184(f870(x73951,a856)))),f184(f870(x73951,a856)))+~P1(f789(f789(f342(x73951),x73953),x73952))
% 21.40/21.38 [7396]~P101(x73961)+E(f17(x73961,x73962),x73963)+~P1(f789(f70(x73961),x73962))+~E(f789(f789(f3(f870(x73961,a856)),x73962),f789(f789(f310(x73961),x73963),f184(f870(x73961,a856)))),f184(f870(x73961,a856)))+~P1(f789(f789(f342(x73961),x73963),x73962))
% 21.40/21.38 [7496]~P101(x74961)+E(f13(x74961,f239(x74961),x74962),x74963)+~P1(f789(f70(x74961),x74962))+~E(f789(f789(f3(f870(x74961,a856)),x74962),f789(f789(f310(x74961),x74963),f184(f870(x74961,a856)))),f184(f870(x74961,a856)))+~P1(f789(f789(f342(x74961),x74963),x74962))
% 21.40/21.38 [7497]~P101(x74971)+E(f14(x74971,f244(x74971),x74972),x74973)+~P1(f789(f70(x74971),x74972))+~E(f789(f789(f3(f870(x74971,a856)),x74972),f789(f789(f310(x74971),x74973),f184(f870(x74971,a856)))),f184(f870(x74971,a856)))+~P1(f789(f789(f342(x74971),x74973),x74972))
% 21.40/21.38 [7534]~P101(x75342)+E(x75341,f184(f870(x75342,a856)))+~P1(f789(f70(x75342),x75341))+~P1(f789(f789(f241(x75342),x75343),f549(x75343,x75341,x75342)))+P1(f789(f789(f241(x75342),x75343),f789(f72(x75342,f244(x75342)),x75341)))
% 21.40/21.38 [7535]~P101(x75352)+E(x75351,f184(f870(x75352,a856)))+~P1(f789(f70(x75352),x75351))+~P1(f789(f789(f240(x75352),x75353),f550(x75353,x75351,x75352)))+P1(f789(f789(f240(x75352),x75353),f789(f72(x75352,f244(x75352)),x75351)))
% 21.40/21.38 [7536]~P98(x75362)+E(x75361,f184(f870(x75362,a856)))+~P1(f789(f70(x75362),x75361))+~P1(f789(f789(f240(x75362),x75363),f551(x75363,x75361,x75362)))+P1(f789(f789(f240(x75362),x75363),f789(f72(x75362,f111(x75362)),x75361)))
% 21.40/21.38 [7624]~P98(x76242)+E(x76241,f184(f870(x76242,a856)))+~P1(f789(f70(x76242),x76241))+P1(f789(f789(f342(x76242),f551(x76243,x76241,x76242)),x76241))+P1(f789(f789(f240(x76242),x76243),f789(f72(x76242,f111(x76242)),x76241)))
% 21.40/21.38 [7625]~P101(x76252)+E(x76251,f184(f870(x76252,a856)))+~P1(f789(f70(x76252),x76251))+P1(f789(f789(f342(x76252),f550(x76253,x76251,x76252)),x76251))+P1(f789(f789(f240(x76252),x76253),f789(f72(x76252,f244(x76252)),x76251)))
% 21.40/21.38 [7626]~P101(x76262)+E(x76261,f184(f870(x76262,a856)))+~P1(f789(f70(x76262),x76261))+P1(f789(f789(f342(x76262),f549(x76263,x76261,x76262)),x76261))+P1(f789(f789(f241(x76262),x76263),f789(f72(x76262,f244(x76262)),x76261)))
% 21.40/21.38 [7745]~P101(x77452)+E(x77451,f184(f870(x77452,a856)))+E(f789(f789(f244(x77452),f14(x77452,f244(x77452),x77451)),f14(x77452,f244(x77452),x77453)),f14(x77452,f244(x77452),x77453))+~P1(f789(f70(x77452),x77453))+~P1(f789(f789(f240(f870(x77452,a856)),x77451),x77453))
% 21.40/21.38 [7746]~P101(x77462)+E(x77461,f184(f870(x77462,a856)))+E(f789(f789(f239(x77462),f13(x77462,f239(x77462),x77461)),f13(x77462,f239(x77462),x77463)),f13(x77462,f239(x77462),x77463))+~P1(f789(f70(x77462),x77463))+~P1(f789(f789(f240(f870(x77462,a856)),x77461),x77463))
% 21.40/21.38 [7947]~E(f683(x79471,x79473,x79472),f684(x79471,x79473,x79472))+~E(f789(f49(x79472),f685(x79471,x79473,x79472)),x79471)+E(f789(f789(f90(a863),x79471),f789(f49(f870(x79472,a856)),x79473)),f789(f49(x79472),f51(f870(x79472,a856),x79473)))+~P1(f789(f70(x79472),f51(f870(x79472,a856),x79473)))+~P1(f789(f70(f870(x79472,a856)),x79473))
% 21.40/21.38 [8121]~P101(x81212)+E(x81211,f184(f870(x81212,a856)))+~P1(f789(f70(x81212),x81213))+P1(f789(f789(f240(x81212),f789(f72(x81212,f244(x81212)),x81213)),f789(f72(x81212,f244(x81212)),x81211)))+~P1(f789(f789(f240(f870(x81212,a856)),x81211),x81213))
% 21.40/21.38 [8425]~E(f683(x84251,x84253,x84252),f684(x84251,x84253,x84252))+E(f789(f789(f90(a863),x84251),f789(f49(f870(x84252,a856)),x84253)),f789(f49(x84252),f51(f870(x84252,a856),x84253)))+P1(f789(f789(f342(f870(x84252,a856)),f685(x84251,x84253,x84252)),x84253))+~P1(f789(f70(x84252),f51(f870(x84252,a856),x84253)))+~P1(f789(f70(f870(x84252,a856)),x84253))
% 21.40/21.38 [8449]~E(f789(f49(x84492),f685(x84491,x84493,x84492)),x84491)+E(f789(f789(f90(a863),x84491),f789(f49(f870(x84492,a856)),x84493)),f789(f49(x84492),f51(f870(x84492,a856),x84493)))+P1(f789(f789(f342(f870(x84492,a856)),f684(x84491,x84493,x84492)),x84493))+~P1(f789(f70(x84492),f51(f870(x84492,a856),x84493)))+~P1(f789(f70(f870(x84492,a856)),x84493))
% 21.40/21.38 [8450]~E(f789(f49(x84502),f685(x84501,x84503,x84502)),x84501)+E(f789(f789(f90(a863),x84501),f789(f49(f870(x84502,a856)),x84503)),f789(f49(x84502),f51(f870(x84502,a856),x84503)))+P1(f789(f789(f342(f870(x84502,a856)),f683(x84501,x84503,x84502)),x84503))+~P1(f789(f70(x84502),f51(f870(x84502,a856),x84503)))+~P1(f789(f70(f870(x84502,a856)),x84503))
% 21.40/21.38 [8479]~E(f789(f49(x84792),f685(x84791,x84793,x84792)),x84791)+~E(f789(f789(f111(f870(x84792,a856)),f684(x84791,x84793,x84792)),f683(x84791,x84793,x84792)),f184(f870(x84792,a856)))+E(f789(f789(f90(a863),x84791),f789(f49(f870(x84792,a856)),x84793)),f789(f49(x84792),f51(f870(x84792,a856),x84793)))+~P1(f789(f70(f870(x84792,a856)),x84793))+~P1(f789(f70(x84792),f51(f870(x84792,a856),x84793)))
% 21.40/21.38 [8706]E(f789(f789(f90(a863),x87061),f789(f49(f870(x87062,a856)),x87063)),f789(f49(x87062),f51(f870(x87062,a856),x87063)))+P1(f789(f789(f342(f870(x87062,a856)),f685(x87061,x87063,x87062)),x87063))+P1(f789(f789(f342(f870(x87062,a856)),f684(x87061,x87063,x87062)),x87063))+~P1(f789(f70(f870(x87062,a856)),x87063))+~P1(f789(f70(x87062),f51(f870(x87062,a856),x87063)))
% 21.40/21.38 [8707]E(f789(f789(f90(a863),x87071),f789(f49(f870(x87072,a856)),x87073)),f789(f49(x87072),f51(f870(x87072,a856),x87073)))+P1(f789(f789(f342(f870(x87072,a856)),f685(x87071,x87073,x87072)),x87073))+P1(f789(f789(f342(f870(x87072,a856)),f683(x87071,x87073,x87072)),x87073))+~P1(f789(f70(f870(x87072,a856)),x87073))+~P1(f789(f70(x87072),f51(f870(x87072,a856),x87073)))
% 21.40/21.38 [8732]~E(f789(f789(f111(f870(x87322,a856)),f684(x87321,x87323,x87322)),f683(x87321,x87323,x87322)),f184(f870(x87322,a856)))+E(f789(f789(f90(a863),x87321),f789(f49(f870(x87322,a856)),x87323)),f789(f49(x87322),f51(f870(x87322,a856),x87323)))+~P1(f789(f70(f870(x87322,a856)),x87323))+P1(f789(f789(f342(f870(x87322,a856)),f685(x87321,x87323,x87322)),x87323))+~P1(f789(f70(x87322),f51(f870(x87322,a856),x87323)))
% 21.40/21.38 [8961]~P91(x89612)+E(x89611,f184(f870(x89612,a856)))+~E(f789(f789(f90(x89612),f789(x89613,f577(x89611,x89613,x89612))),f789(x89613,f578(x89611,x89613,x89612))),f789(x89613,f789(f789(f90(x89612),f577(x89611,x89613,x89612)),f578(x89611,x89613,x89612))))+~P1(f789(f70(x89612),x89611))+E(f789(f72(x89612,f90(x89612)),f789(f311(x89612,x89612,x89613),x89611)),f789(x89613,f789(f72(x89612,f90(x89612)),x89611)))
% 21.40/21.38 [9837]P1(f789(f789(x98371,x98372),x98373))+P1(f789(f789(f241(a1),f846(x98371,x98373,x98372)),f847(x98371,x98373,x98372)))+P1(f789(f789(f240(a1),f847(x98371,x98373,x98372)),f2(a1)))+P1(f789(f789(x98371,f846(x98371,x98373,x98372)),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f847(x98371,x98373,x98372))))+~P1(f789(f329(f869(a1,a1),a69),f789(f789(f249(a1,a1),x98372),x98373)))
% 21.40/21.38 [9843]P1(f789(f789(x98431,x98432),x98433))+P1(f789(f789(f240(a1),f845(x98431,x98433,x98432)),f2(a1)))+P1(f789(f789(x98431,f844(x98431,x98433,x98432)),f789(f789(f90(a1),f789(f113(a1),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f845(x98431,x98433,x98432))))+P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),f844(x98431,x98433,x98432)),f845(x98431,x98433,x98432))))+~P1(f789(f329(f869(a1,a1),a66),f789(f789(f249(a1,a1),x98432),x98433)))
% 21.40/21.38 [7918]~P110(x79181)+~P1(f789(f789(f240(x79181),x79182),f87(x79181)))+~P1(f789(f789(f240(x79181),f2(x79181)),x79182))+~P1(f789(f789(f240(x79181),f2(x79181)),x79183))+P1(f789(f789(f240(x79181),f789(f789(f90(x79181),x79182),x79183)),x79183))
% 21.40/21.38 [7919]~P110(x79191)+~P1(f789(f789(f240(x79191),x79193),f87(x79191)))+~P1(f789(f789(f240(x79191),f2(x79191)),x79193))+~P1(f789(f789(f240(x79191),f2(x79191)),x79192))+P1(f789(f789(f240(x79191),f789(f789(f90(x79191),x79192),x79193)),x79192))
% 21.40/21.38 [8265]~P101(x82652)+E(x82651,f184(f870(x82652,a856)))+~P1(f789(f70(x82652),x82651))+P1(f789(f789(f342(x82652),f561(x82653,x82651,x82652)),x82651))+~P1(f789(f789(f240(x82652),f789(f72(x82652,f244(x82652)),x82651)),x82653))
% 21.40/21.38 [8266]~P101(x82662)+E(x82661,f184(f870(x82662,a856)))+~P1(f789(f70(x82662),x82661))+P1(f789(f789(f342(x82662),f562(x82663,x82661,x82662)),x82661))+~P1(f789(f789(f241(x82662),f789(f72(x82662,f244(x82662)),x82661)),x82663))
% 21.40/21.38 [8267]~P101(x82672)+E(x82671,f184(f870(x82672,a856)))+~P1(f789(f70(x82672),x82671))+P1(f789(f789(f241(x82672),f562(x82673,x82671,x82672)),x82673))+~P1(f789(f789(f241(x82672),f789(f72(x82672,f244(x82672)),x82671)),x82673))
% 21.40/21.38 [8268]~P101(x82682)+E(x82681,f184(f870(x82682,a856)))+~P1(f789(f70(x82682),x82681))+P1(f789(f789(f240(x82682),f561(x82683,x82681,x82682)),x82683))+~P1(f789(f789(f240(x82682),f789(f72(x82682,f244(x82682)),x82681)),x82683))
% 21.40/21.38 [8354]~P1(f789(x83541,x83543))+P1(f789(x83541,f496(x83541,x83542)))+P1(f789(x83541,f484(x83541,x83542)))+~P1(f789(f789(f241(a1),f2(a1)),x83542))+P1(f789(x83541,f789(f789(f3(a1),f484(x83541,x83542)),f789(f789(f90(a1),f497(x83541,x83542)),x83542))))
% 21.40/21.38 [8571]~P1(f789(x85711,x85713))+P1(f789(x85711,f484(x85711,x85712)))+~P1(f789(f789(f241(a1),f2(a1)),x85712))+P1(f789(f789(f342(a1),f496(x85711,x85712)),f303(a1,f87(a1),x85712)))+P1(f789(x85711,f789(f789(f3(a1),f484(x85711,x85712)),f789(f789(f90(a1),f497(x85711,x85712)),x85712))))
% 21.40/21.38 [8750]~P1(f789(x87501,x87503))+~P1(f789(x87501,f484(x87501,x87502)))+P1(f789(x87501,f496(x87501,x87502)))+~P1(f789(f789(f241(a1),f2(a1)),x87502))+~P1(f789(x87501,f789(f789(f3(a1),f484(x87501,x87502)),f789(f789(f90(a1),f497(x87501,x87502)),x87502))))
% 21.40/21.38 [8856]~P1(f789(x88561,x88563))+~P1(f789(x88561,f484(x88561,x88562)))+~P1(f789(f789(f241(a1),f2(a1)),x88562))+P1(f789(f789(f342(a1),f496(x88561,x88562)),f303(a1,f87(a1),x88562)))+~P1(f789(x88561,f789(f789(f3(a1),f484(x88561,x88562)),f789(f789(f90(a1),f497(x88561,x88562)),x88562))))
% 21.40/21.38 [8669]~P95(x86691)+~P1(f789(f70(x86691),x86692))+E(f789(f789(f3(f870(x86691,a856)),x86692),f789(f789(f310(x86691),x86693),f184(f870(x86691,a856)))),f184(f870(x86691,a856)))+~P1(f789(f789(f342(x86691),x86693),x86692))+E(f789(f789(f111(x86691),x86693),f12(x86691,f789(f789(f3(f870(x86691,a856)),x86692),f789(f789(f310(x86691),x86693),f184(f870(x86691,a856)))))),f12(x86691,x86692))
% 21.40/21.38 [8670]~P95(x86701)+~P1(f789(f70(x86701),x86702))+E(f789(f789(f3(f870(x86701,a856)),x86702),f789(f789(f310(x86701),x86703),f184(f870(x86701,a856)))),f184(f870(x86701,a856)))+~P1(f789(f789(f342(x86701),x86703),x86702))+E(f789(f789(f110(x86701),x86703),f15(x86701,f789(f789(f3(f870(x86701,a856)),x86702),f789(f789(f310(x86701),x86703),f184(f870(x86701,a856)))))),f15(x86701,x86702))
% 21.40/21.38 [8671]~P101(x86711)+~P1(f789(f70(x86711),x86712))+E(f789(f789(f3(f870(x86711,a856)),x86712),f789(f789(f310(x86711),x86713),f184(f870(x86711,a856)))),f184(f870(x86711,a856)))+~P1(f789(f789(f342(x86711),x86713),x86712))+E(f789(f789(f239(x86711),x86713),f16(x86711,f789(f789(f3(f870(x86711,a856)),x86712),f789(f789(f310(x86711),x86713),f184(f870(x86711,a856)))))),f16(x86711,x86712))
% 21.40/21.38 [8672]~P101(x86721)+~P1(f789(f70(x86721),x86722))+E(f789(f789(f3(f870(x86721,a856)),x86722),f789(f789(f310(x86721),x86723),f184(f870(x86721,a856)))),f184(f870(x86721,a856)))+~P1(f789(f789(f342(x86721),x86723),x86722))+E(f789(f789(f244(x86721),x86723),f17(x86721,f789(f789(f3(f870(x86721,a856)),x86722),f789(f789(f310(x86721),x86723),f184(f870(x86721,a856)))))),f17(x86721,x86722))
% 21.40/21.38 [8727]~P101(x87271)+~P1(f789(f70(x87271),x87272))+E(f789(f789(f3(f870(x87271,a856)),x87272),f789(f789(f310(x87271),x87273),f184(f870(x87271,a856)))),f184(f870(x87271,a856)))+~P1(f789(f789(f342(x87271),x87273),x87272))+E(f789(f789(f239(x87271),x87273),f13(x87271,f239(x87271),f789(f789(f3(f870(x87271,a856)),x87272),f789(f789(f310(x87271),x87273),f184(f870(x87271,a856)))))),f13(x87271,f239(x87271),x87272))
% 21.40/21.38 [8728]~P101(x87281)+~P1(f789(f70(x87281),x87282))+E(f789(f789(f3(f870(x87281,a856)),x87282),f789(f789(f310(x87281),x87283),f184(f870(x87281,a856)))),f184(f870(x87281,a856)))+~P1(f789(f789(f342(x87281),x87283),x87282))+E(f789(f789(f244(x87281),x87283),f14(x87281,f244(x87281),f789(f789(f3(f870(x87281,a856)),x87282),f789(f789(f310(x87281),x87283),f184(f870(x87281,a856)))))),f14(x87281,f244(x87281),x87282))
% 21.40/21.38 [8738]~P101(x87381)+~P1(f789(f70(x87381),x87383))+~P1(f789(f70(x87381),x87382))+E(f789(f789(f111(f870(x87381,a856)),x87382),x87383),f184(f870(x87381,a856)))+E(f789(f789(f244(x87381),f17(x87381,f789(f789(f110(f870(x87381,a856)),x87382),x87383))),f17(x87381,f789(f789(f111(f870(x87381,a856)),x87382),x87383))),f789(f789(f244(x87381),f17(x87381,x87382)),f17(x87381,x87383)))
% 21.40/21.38 [8739]~P101(x87391)+~P1(f789(f70(x87391),x87393))+~P1(f789(f70(x87391),x87392))+E(f789(f789(f111(f870(x87391,a856)),x87392),x87393),f184(f870(x87391,a856)))+E(f789(f789(f239(x87391),f16(x87391,f789(f789(f110(f870(x87391,a856)),x87392),x87393))),f16(x87391,f789(f789(f111(f870(x87391,a856)),x87392),x87393))),f789(f789(f239(x87391),f16(x87391,x87392)),f16(x87391,x87393)))
% 21.40/21.38 [8740]~P95(x87401)+~P1(f789(f70(x87401),x87403))+~P1(f789(f70(x87401),x87402))+E(f789(f789(f111(f870(x87401,a856)),x87402),x87403),f184(f870(x87401,a856)))+E(f789(f789(f110(x87401),f15(x87401,f789(f789(f110(f870(x87401,a856)),x87402),x87403))),f15(x87401,f789(f789(f111(f870(x87401,a856)),x87402),x87403))),f789(f789(f110(x87401),f15(x87401,x87402)),f15(x87401,x87403)))
% 21.40/21.38 [8741]~P95(x87411)+~P1(f789(f70(x87411),x87413))+~P1(f789(f70(x87411),x87412))+E(f789(f789(f111(f870(x87411,a856)),x87412),x87413),f184(f870(x87411,a856)))+E(f789(f789(f111(x87411),f12(x87411,f789(f789(f110(f870(x87411,a856)),x87412),x87413))),f12(x87411,f789(f789(f111(f870(x87411,a856)),x87412),x87413))),f789(f789(f111(x87411),f12(x87411,x87412)),f12(x87411,x87413)))
% 21.40/21.38 [8935]~P101(x89351)+~P1(f789(f70(x89351),x89353))+~P1(f789(f70(x89351),x89352))+E(f789(f789(f111(f870(x89351,a856)),x89352),x89353),f184(f870(x89351,a856)))+E(f789(f789(f244(x89351),f14(x89351,f244(x89351),f789(f789(f110(f870(x89351,a856)),x89352),x89353))),f14(x89351,f244(x89351),f789(f789(f111(f870(x89351,a856)),x89352),x89353))),f789(f789(f244(x89351),f14(x89351,f244(x89351),x89352)),f14(x89351,f244(x89351),x89353)))
% 21.40/21.38 [8936]~P101(x89361)+~P1(f789(f70(x89361),x89363))+~P1(f789(f70(x89361),x89362))+E(f789(f789(f111(f870(x89361,a856)),x89362),x89363),f184(f870(x89361,a856)))+E(f789(f789(f239(x89361),f13(x89361,f239(x89361),f789(f789(f110(f870(x89361,a856)),x89362),x89363))),f13(x89361,f239(x89361),f789(f789(f111(f870(x89361,a856)),x89362),x89363))),f789(f789(f239(x89361),f13(x89361,f239(x89361),x89362)),f13(x89361,f239(x89361),x89363)))
% 21.40/21.38 [9680]~P117(x96803)+E(x96801,x96802)+~P1(f789(f789(f240(x96803),f2(x96803)),x96802))+~P1(f789(f789(f240(x96803),f2(x96803)),x96801))+~E(f789(f789(f250(x96803),x96801),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))),f789(f789(f250(x96803),x96802),f789(f113(a863),f789(f789(f89(a1),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)),f789(f789(f3(a1),f789(f789(f89(a1),a92),a92)),a106)))))
% 21.40/21.38 [5023]~P89(x50231)+~P60(x50231)+~E(x50234,f2(x50231))+~E(f789(f113(x50231),x50232),f2(x50231))+E(f789(f113(x50231),x50232),f789(f789(f291(x50231),x50233),x50234))
% 21.40/21.38 [5024]~P89(x50241)+~P60(x50241)+~E(x50243,f2(x50241))+~E(f789(f113(x50241),x50244),f2(x50241))+E(f789(f789(f291(x50241),x50242),x50243),f789(f113(x50241),x50244))
% 21.40/21.38 [5118]~P89(x51182)+~P60(x51182)+~E(x51181,f2(x51182))+~E(f789(f113(x51182),x51184),f2(x51182))+E(x51181,f789(f789(f291(x51182),x51183),f789(f113(x51182),x51184)))
% 21.40/21.38 [5119]~P89(x51191)+~P60(x51191)+~E(x51194,f2(x51191))+~E(f789(f113(x51191),x51193),f2(x51191))+E(f789(f789(f291(x51191),x51192),f789(f113(x51191),x51193)),x51194)
% 21.40/21.38 [5143]~P89(x51431)+~P60(x51431)+~E(x51433,f2(x51431))+E(f789(f113(x51431),x51432),f2(x51431))+~E(f789(f113(x51431),x51432),f789(f789(f291(x51431),x51434),x51433))
% 21.40/21.38 [5144]~P89(x51441)+~P60(x51441)+~E(x51443,f2(x51441))+E(f789(f113(x51441),x51442),f2(x51441))+~E(f789(f789(f291(x51441),x51444),x51443),f789(f113(x51441),x51442))
% 21.40/21.38 [5303]~P89(x53032)+~P60(x53032)+E(x53031,f2(x53032))+~E(f789(f113(x53032),x53033),f2(x53032))+~E(x53031,f789(f789(f291(x53032),x53034),f789(f113(x53032),x53033)))
% 21.40/21.38 [5304]~P89(x53042)+~P60(x53042)+E(x53041,f2(x53042))+~E(f789(f113(x53042),x53043),f2(x53042))+~E(f789(f789(f291(x53042),x53044),f789(f113(x53042),x53043)),x53041)
% 21.40/21.38 [5525]~P89(x55252)+~P60(x55252)+~E(x55251,f2(x55252))+E(x55251,f789(f789(f291(x55252),x55253),f789(f113(x55252),x55254)))+~E(f789(f789(f90(x55252),x55251),f789(f113(x55252),x55254)),x55253)
% 21.40/21.38 [5526]~P89(x55261)+~P60(x55261)+~E(x55264,f2(x55261))+~E(x55262,f789(f789(f90(x55261),x55264),f789(f113(x55261),x55263)))+E(f789(f789(f291(x55261),x55262),f789(f113(x55261),x55263)),x55264)
% 21.40/21.38 [5588]~P89(x55881)+~P60(x55881)+E(f789(f113(x55881),x55882),f2(x55881))+~E(f789(f789(f291(x55881),x55883),f789(f113(x55881),x55882)),x55884)+E(x55883,f789(f789(f90(x55881),x55884),f789(f113(x55881),x55882)))
% 21.40/21.38 [5589]~P89(x55891)+~P60(x55891)+E(f789(f113(x55891),x55892),f2(x55891))+~E(f789(f789(f90(x55891),x55893),f789(f113(x55891),x55892)),x55894)+E(x55893,f789(f789(f291(x55891),x55894),f789(f113(x55891),x55892)))
% 21.40/21.38 [5590]~P89(x55901)+~P60(x55901)+E(f789(f113(x55901),x55902),f2(x55901))+~E(x55903,f789(f789(f291(x55901),x55904),f789(f113(x55901),x55902)))+E(f789(f789(f90(x55901),x55903),f789(f113(x55901),x55902)),x55904)
% 21.40/21.38 [5591]~P89(x55911)+~P60(x55911)+E(f789(f113(x55911),x55912),f2(x55911))+~E(x55913,f789(f789(f90(x55911),x55914),f789(f113(x55911),x55912)))+E(f789(f789(f291(x55911),x55913),f789(f113(x55911),x55912)),x55914)
% 21.40/21.38 [5799]~P7(x57992)+E(x57991,f2(x57992))+~E(f789(f789(f50(x57992),x57993),x57991),x57994)+E(x57993,f789(f789(f90(x57992),x57994),x57991))+~P1(f789(f789(f287(x57992),x57991),x57993))
% 21.40/21.38 [5800]~P7(x58002)+E(x58001,f2(x58002))+~E(x58003,f789(f789(f90(x58002),x58004),x58001))+E(f789(f789(f50(x58002),x58003),x58001),x58004)+~P1(f789(f789(f287(x58002),x58001),x58003))
% 21.40/21.38 [6260]E(f506(x62601,x62602,x62603),x62604)+E(f789(x62601,x62604),f2(a863))+~E(f789(f789(f8(x62603,a863),x62601),x62602),f87(a863))+~P1(f789(f70(x62603),x62602))+~P1(f789(f789(f342(x62603),x62604),x62602))
% 21.40/21.38 [6328]E(f519(x63281,x63282,x63283),x63284)+E(f789(x63281,x63284),f2(a863))+~E(f789(f789(f8(x63283,a863),x63281),x63282),f789(a121,f2(a863)))+~P1(f789(f70(x63283),x63282))+~P1(f789(f789(f342(x63283),x63284),x63282))
% 21.40/21.38 [6441]~P101(x64411)+~P9(x64411)+P1(f789(f789(f241(x64411),x64412),f51(x64411,x64413)))+~P1(f789(f789(f241(x64411),x64412),x64414))+~P1(f789(f789(f342(x64411),x64414),x64413))
% 21.40/21.38 [6618]~P101(x66181)+~P9(x66181)+~P1(f789(f789(f241(x66181),x66184),x66183))+P1(f789(f789(f241(x66181),f52(x66181,x66182)),x66183))+~P1(f789(f789(f342(x66181),x66184),x66182))
% 21.40/21.38 [6894]~P117(x68943)+E(x68941,x68942)+~E(f789(f789(f250(x68943),x68941),f789(a121,x68944)),f789(f789(f250(x68943),x68942),f789(a121,x68944)))+~P1(f789(f789(f240(x68943),f2(x68943)),x68942))+~P1(f789(f789(f240(x68943),f2(x68943)),x68941))
% 21.40/21.38 [7104]~E(f521(x71042,x71043,x71041,x71044),x71044)+~E(f789(x71042,x71044),f87(a863))+E(f789(f789(f8(x71041,a863),x71042),x71043),f87(a863))+~P1(f789(f70(x71041),x71043))+~P1(f789(f789(f342(x71041),x71044),x71043))
% 21.40/21.38 [7111]~P70(x71114)+~P122(x71114)+E(f789(x71111,f409(x71111,x71112,x71113,x71114)),f2(x71114))+~E(f789(f789(f11(x71113,x71114),x71111),x71112),f2(x71114))+~P1(f789(f70(x71113),x71112))
% 21.40/21.38 [7194]~E(f520(x71942,x71943,x71941,x71944),x71944)+~E(f789(x71942,x71944),f789(a121,f2(a863)))+E(f789(f789(f8(x71941,a863),x71942),x71943),f789(a121,f2(a863)))+~P1(f789(f70(x71941),x71943))+~P1(f789(f789(f342(x71941),x71944),x71943))
% 21.40/21.38 [7957]~E(f789(x79572,x79574),f87(a863))+~E(f789(x79572,f521(x79572,x79573,x79571,x79574)),f2(a863))+E(f789(f789(f8(x79571,a863),x79572),x79573),f87(a863))+~P1(f789(f70(x79571),x79573))+~P1(f789(f789(f342(x79571),x79574),x79573))
% 21.40/21.38 [8001]~E(f789(x80012,x80014),f789(a121,f2(a863)))+~E(f789(x80012,f520(x80012,x80013,x80011,x80014)),f2(a863))+E(f789(f789(f8(x80011,a863),x80012),x80013),f789(a121,f2(a863)))+~P1(f789(f70(x80011),x80013))+~P1(f789(f789(f342(x80011),x80014),x80013))
% 21.40/21.38 [8080]~P136(x80802)+~P112(x80802)+~P1(f789(x80801,x80804))+~P1(f789(f789(f287(x80802),x80803),f789(f789(f89(x80802),x80804),f2(x80802))))+P1(f789(x80801,f789(f789(f90(x80802),x80803),f352(x80803,x80801,x80802))))
% 21.40/21.38 [8574]E(x85741,x85742)+E(f789(f789(f89(a1),f485(x85743,x85742,x85744,x85741)),f486(x85743,x85742,x85744,x85741)),x85741)+~E(f789(f789(f3(a1),x85741),x85744),x85742)+~P1(f789(f789(f241(a1),f2(a1)),x85744))+~P1(f789(f789(f342(a1),x85742),x85743))
% 21.40/21.38 [8575]E(x85751,x85752)+E(f789(f789(f3(a1),f476(x85753,x85752,x85754,x85751)),f477(x85753,x85752,x85754,x85751)),x85751)+~E(f789(f789(f89(a1),x85751),x85754),x85752)+~P1(f789(f789(f241(a1),f2(a1)),x85754))+~P1(f789(f789(f342(a1),x85752),x85753))
% 21.40/21.38 [8737]E(f789(x87371,f838(x87372,x87371,x87373,x87374)),x87372)+P1(f789(f789(f240(a863),x87374),f839(x87372,x87371,x87373,x87374)))+~P1(f789(f789(f240(a1),x87372),f789(x87371,x87373)))+~P1(f789(f789(f241(a863),x87374),x87373))+~P1(f789(f789(f240(a1),f789(x87371,x87374)),x87372))
% 21.40/21.38 [8754]~P70(x87544)+~P122(x87544)+~E(f789(f789(f11(x87541,x87544),x87542),x87543),f2(x87544))+~P1(f789(f70(x87541),x87543))+P1(f789(f789(f342(x87541),f409(x87542,x87543,x87541,x87544)),x87543))
% 21.40/21.38 [8787]~E(f789(x87872,x87874),f87(a863))+E(f789(f789(f8(x87871,a863),x87872),x87873),f87(a863))+~P1(f789(f70(x87871),x87873))+~P1(f789(f789(f342(x87871),x87874),x87873))+P1(f789(f789(f342(x87871),f521(x87872,x87873,x87871,x87874)),x87873))
% 21.40/21.38 [8796]E(x87961,x87962)+~E(f789(f789(f89(a1),x87962),x87964),x87961)+~P1(f789(f789(f241(a1),f2(a1)),x87964))+~P1(f789(f789(f342(a1),x87961),x87963))+P1(f789(f789(f342(a1),f476(x87963,x87961,x87964,x87962)),x87963))
% 21.40/21.38 [8797]E(x87971,x87972)+~E(f789(f789(f3(a1),x87972),x87974),x87971)+~P1(f789(f789(f241(a1),f2(a1)),x87974))+~P1(f789(f789(f342(a1),x87971),x87973))+P1(f789(f789(f342(a1),f485(x87973,x87971,x87974,x87972)),x87973))
% 21.40/21.38 [8799]~E(f789(x87992,x87994),f789(a121,f2(a863)))+E(f789(f789(f8(x87991,a863),x87992),x87993),f789(a121,f2(a863)))+~P1(f789(f70(x87991),x87993))+~P1(f789(f789(f342(x87991),x87994),x87993))+P1(f789(f789(f342(x87991),f520(x87992,x87993,x87991,x87994)),x87993))
% 21.40/21.38 [8803]P57(x88032,x88033,x88034,x88031)+E(x88031,f184(f870(x88032,a856)))+~P1(f789(f70(x88032),x88034))+~P1(f789(f70(x88032),x88031))+P1(f789(f789(f342(x88032),f552(x88031,x88034,x88033,x88032)),x88034))
% 21.40/21.38 [8869]E(x88691,x88692)+~E(f789(f789(f89(a1),x88692),x88694),x88691)+~P1(f789(f789(f241(a1),f2(a1)),x88694))+~P1(f789(f789(f342(a1),x88691),x88693))+P1(f789(f789(f342(a1),f477(x88693,x88691,x88694,x88692)),f303(a1,f87(a1),x88694)))
% 21.40/21.38 [8870]E(x88701,x88702)+~E(f789(f789(f3(a1),x88702),x88704),x88701)+~P1(f789(f789(f241(a1),f2(a1)),x88704))+~P1(f789(f789(f342(a1),x88701),x88703))+P1(f789(f789(f342(a1),f486(x88703,x88701,x88704,x88702)),f303(a1,f87(a1),x88704)))
% 21.40/21.38 [8941]P1(f789(f789(f240(a863),x89411),f838(x89412,x89413,x89414,x89411)))+~P1(f789(f789(f240(a1),x89412),f789(x89413,x89414)))+P1(f789(f789(f240(a863),x89411),f839(x89412,x89413,x89414,x89411)))+~P1(f789(f789(f241(a863),x89411),x89414))+~P1(f789(f789(f240(a1),f789(x89413,x89411)),x89412))
% 21.40/21.38 [9048]E(f789(x90481,f838(x90482,x90481,x90483,x90484)),x90482)+~P1(f789(f789(f240(a1),x90482),f789(x90481,x90483)))+P1(f789(f789(f241(a863),f839(x90482,x90481,x90483,x90484)),x90483))+~P1(f789(f789(f241(a863),x90484),x90483))+~P1(f789(f789(f240(a1),f789(x90481,x90484)),x90482))
% 21.40/21.38 [9154]~P1(f789(f789(f287(a863),x91544),x91541))+~P1(f789(f789(f287(a863),x91544),x91543))+~P1(f789(f789(f287(a863),x91542),x91541))+P1(f789(f789(f287(a863),x91541),x91542))+P1(f789(f789(f241(f870(a863,a856)),f290(a863,f287(a863),x91543,x91542)),f290(a863,f287(a863),x91544,x91541)))
% 21.40/21.38 [9155]~P1(f789(f789(f287(a863),x91552),x91551))+~P1(f789(f789(f287(a863),x91553),x91554))+~P1(f789(f789(f287(a863),x91552),x91554))+P1(f789(f789(f287(a863),x91551),x91552))+P1(f789(f789(f241(f870(a863,a856)),f290(a863,f287(a863),x91551,x91553)),f290(a863,f287(a863),x91552,x91554)))
% 21.40/21.38 [9166]~P1(f789(f789(f240(a1),x91662),f789(x91663,x91664)))+P1(f789(f789(f240(a863),x91661),f839(x91662,x91663,x91664,x91661)))+P1(f789(f789(f240(a863),f838(x91662,x91663,x91664,x91661)),x91664))+~P1(f789(f789(f241(a863),x91661),x91664))+~P1(f789(f789(f240(a1),f789(x91663,x91661)),x91662))
% 21.40/21.38 [9167]~P1(f789(f789(f240(a1),x91672),f789(x91673,x91674)))+P1(f789(f789(f240(a863),x91671),f838(x91672,x91673,x91674,x91671)))+P1(f789(f789(f241(a863),f839(x91672,x91673,x91674,x91671)),x91674))+~P1(f789(f789(f241(a863),x91671),x91674))+~P1(f789(f789(f240(a1),f789(x91673,x91671)),x91672))
% 21.40/21.38 [9252]~P1(f789(f789(f240(a1),x92521),f789(x92522,x92523)))+P1(f789(f789(f240(a863),f838(x92521,x92522,x92523,x92524)),x92523))+~P1(f789(f789(f241(a863),x92524),x92523))+~P1(f789(f789(f240(a1),f789(x92522,x92524)),x92521))+P1(f789(f789(f241(a863),f839(x92521,x92522,x92523,x92524)),x92523))
% 21.40/21.38 [9337]E(x93371,f184(f870(x93372,a856)))+~P1(f789(f70(x93372),x93374))+~P1(f789(f70(x93372),x93371))+P1(f789(f789(f342(f869(f870(x93372,a856),f870(x93372,a856))),f789(f789(f249(f870(x93372,a856),f870(x93372,a856)),x93374),x93371)),f332(x93372,x93373)))+P1(f789(f789(f342(x93372),f555(x93373,x93371,x93374,x93372)),x93374))
% 21.40/21.38 [9338]E(x93381,f184(f870(x93382,a856)))+~P1(f789(f70(x93382),x93384))+~P1(f789(f70(x93382),x93381))+P1(f789(f789(f342(f869(f870(x93382,a856),f870(x93382,a856))),f789(f789(f249(f870(x93382,a856),f870(x93382,a856)),x93384),x93381)),f332(x93382,x93383)))+P1(f789(f789(f342(x93382),f637(x93383,x93381,x93384,x93382)),x93384))
% 21.40/21.38 [9994]E(f789(x99941,f838(x99942,x99941,x99943,x99944)),x99942)+~P1(f789(f789(f240(a1),x99942),f789(x99941,x99943)))+~P1(f789(f789(f240(a1),f789(f84(a1),f789(f789(f3(a1),f789(x99941,f789(f789(f89(a863),f839(x99942,x99941,x99943,x99944)),f87(a863)))),f789(x99941,f839(x99942,x99941,x99943,x99944))))),f87(a1)))+~P1(f789(f789(f241(a863),x99944),x99943))+~P1(f789(f789(f240(a1),f789(x99941,x99944)),x99942))
% 21.40/21.38 [9995]~P1(f789(f789(f240(a1),x99952),f789(x99953,x99954)))+P1(f789(f789(f240(a863),x99951),f838(x99952,x99953,x99954,x99951)))+~P1(f789(f789(f240(a1),f789(f84(a1),f789(f789(f3(a1),f789(x99953,f789(f789(f89(a863),f839(x99952,x99953,x99954,x99951)),f87(a863)))),f789(x99953,f839(x99952,x99953,x99954,x99951))))),f87(a1)))+~P1(f789(f789(f241(a863),x99951),x99954))+~P1(f789(f789(f240(a1),f789(x99953,x99951)),x99952))
% 21.40/21.38 [9996]~P1(f789(f789(f240(a1),x99961),f789(x99962,x99963)))+~P1(f789(f789(f240(a1),f789(f84(a1),f789(f789(f3(a1),f789(x99962,f789(f789(f89(a863),f839(x99961,x99962,x99963,x99964)),f87(a863)))),f789(x99962,f839(x99961,x99962,x99963,x99964))))),f87(a1)))+~P1(f789(f789(f241(a863),x99964),x99963))+~P1(f789(f789(f240(a1),f789(x99962,x99964)),x99961))+P1(f789(f789(f240(a863),f838(x99961,x99962,x99963,x99964)),x99963))
% 21.40/21.38 [5547]~P89(x55472)+~P60(x55472)+E(x55471,f2(x55472))+~E(f789(f789(f291(x55472),x55473),x55471),f789(f113(x55472),x55474))+E(x55473,f789(f789(f90(x55472),f789(f113(x55472),x55474)),x55471))
% 21.40/21.38 [5548]~P89(x55482)+~P60(x55482)+E(x55481,f2(x55482))+~E(f789(f113(x55482),x55483),f789(f789(f291(x55482),x55484),x55481))+E(f789(f789(f90(x55482),f789(f113(x55482),x55483)),x55481),x55484)
% 21.40/21.38 [5699]~P89(x56992)+~P60(x56992)+E(x56991,f2(x56992))+E(f789(f113(x56992),x56993),f789(f789(f291(x56992),x56994),x56991))+~E(f789(f789(f90(x56992),f789(f113(x56992),x56993)),x56991),x56994)
% 21.40/21.38 [5700]~P89(x57002)+~P60(x57002)+E(x57001,f2(x57002))+E(f789(f789(f291(x57002),x57003),x57001),f789(f113(x57002),x57004))+~E(x57003,f789(f789(f90(x57002),f789(f113(x57002),x57004)),x57001))
% 21.40/21.38 [5836]~P89(x58361)+~P60(x58361)+~E(f789(f113(x58361),x58362),f2(x58361))+E(f789(f113(x58361),x58362),f789(f789(f291(x58361),x58363),x58364))+~E(f789(f789(f90(x58361),f789(f113(x58361),x58362)),x58364),x58363)
% 21.40/21.38 [5837]~P89(x58371)+~P60(x58371)+~E(f789(f113(x58371),x58374),f2(x58371))+E(f789(f789(f291(x58371),x58372),x58373),f789(f113(x58371),x58374))+~E(x58372,f789(f789(f90(x58371),f789(f113(x58371),x58374)),x58373))
% 21.40/21.38 [7162]~P62(x71621)+P1(f789(f789(f241(x71621),x71622),f2(x71621)))+~P1(f789(f789(f241(x71621),x71623),f2(x71621)))+P1(f789(f789(f241(x71621),f2(x71621)),x71622))+P1(f789(f789(f241(x71621),x71623),f789(f789(f291(x71621),x71624),x71622)))
% 21.40/21.38 [7163]~P62(x71631)+P1(f789(f789(f241(x71631),x71632),f2(x71631)))+~P1(f789(f789(f240(x71631),x71633),f2(x71631)))+P1(f789(f789(f241(x71631),f2(x71631)),x71632))+P1(f789(f789(f240(x71631),x71633),f789(f789(f291(x71631),x71634),x71632)))
% 21.40/21.38 [7434]~P62(x74341)+P1(f789(f789(f241(x74341),x74342),f2(x74341)))+P1(f789(f789(f241(x74341),x74343),f2(x74341)))+P1(f789(f789(f241(x74341),f2(x74341)),x74343))+~P1(f789(f789(f241(x74341),x74342),f789(f789(f291(x74341),x74344),x74343)))
% 21.40/21.38 [7435]~P62(x74351)+P1(f789(f789(f241(x74351),x74352),f2(x74351)))+P1(f789(f789(f240(x74351),x74353),f2(x74351)))+P1(f789(f789(f241(x74351),f2(x74351)),x74352))+~P1(f789(f789(f240(x74351),x74353),f789(f789(f291(x74351),x74354),x74352)))
% 21.40/21.38 [7553]E(x75531,x75532)+~E(f789(f789(f159(x75533),x75534),x75531),f789(f789(f159(x75533),x75534),x75532))+~P1(f789(f134(x75533),x75534))+~P1(f789(f789(f241(a863),x75532),f789(f185(f864(x75533)),x75534)))+~P1(f789(f789(f241(a863),x75531),f789(f185(f864(x75533)),x75534)))
% 21.40/21.38 [7554]E(x75541,x75542)+~E(f789(f789(f159(x75543),x75544),x75541),f789(f789(f159(x75543),x75544),x75542))+~P1(f789(f134(x75543),x75544))+~P1(f789(f789(f241(a863),x75542),f789(f185(f864(x75543)),x75544)))+~P1(f789(f789(f241(a863),x75541),f789(f185(f864(x75543)),x75544)))
% 21.40/21.38 [7920]~P62(x79201)+~P1(f789(f789(f241(x79201),x79203),f2(x79201)))+P1(f789(f789(f241(x79201),f2(x79201)),x79202))+~P1(f789(f789(f241(x79201),x79204),f789(f789(f90(x79201),x79203),x79202)))+P1(f789(f789(f241(x79201),x79203),f789(f789(f291(x79201),x79204),x79202)))
% 21.40/21.38 [7921]~P62(x79211)+~P1(f789(f789(f240(x79211),x79213),f2(x79211)))+P1(f789(f789(f241(x79211),f2(x79211)),x79212))+~P1(f789(f789(f240(x79211),x79214),f789(f789(f90(x79211),x79213),x79212)))+P1(f789(f789(f240(x79211),x79213),f789(f789(f291(x79211),x79214),x79212)))
% 21.40/21.38 [7922]~P62(x79221)+~P1(f789(f789(f241(x79221),x79222),f2(x79221)))+P1(f789(f789(f241(x79221),f2(x79221)),x79222))+~P1(f789(f789(f241(x79221),x79224),f789(f789(f90(x79221),x79223),x79222)))+P1(f789(f789(f241(x79221),x79223),f789(f789(f291(x79221),x79224),x79222)))
% 21.40/21.38 [7923]~P62(x79231)+~P1(f789(f789(f241(x79231),x79232),f2(x79231)))+P1(f789(f789(f241(x79231),f2(x79231)),x79232))+~P1(f789(f789(f241(x79231),x79234),f789(f789(f291(x79231),x79233),x79232)))+P1(f789(f789(f241(x79231),x79233),f789(f789(f90(x79231),x79234),x79232)))
% 21.40/21.38 [7924]~P62(x79241)+~P1(f789(f789(f241(x79241),x79242),f2(x79241)))+P1(f789(f789(f241(x79241),f2(x79241)),x79242))+~P1(f789(f789(f240(x79241),x79244),f789(f789(f90(x79241),x79243),x79242)))+P1(f789(f789(f240(x79241),x79243),f789(f789(f291(x79241),x79244),x79242)))
% 21.40/21.38 [7925]~P62(x79251)+~P1(f789(f789(f241(x79251),x79252),f2(x79251)))+P1(f789(f789(f241(x79251),f2(x79251)),x79252))+~P1(f789(f789(f240(x79251),x79254),f789(f789(f291(x79251),x79253),x79252)))+P1(f789(f789(f240(x79251),x79253),f789(f789(f90(x79251),x79254),x79252)))
% 21.40/21.38 [8048]~P7(x80481)+~P1(f789(f789(f287(x80481),x80483),x80484))+~P1(f789(f789(f287(x80481),x80483),x80482))+~P1(f789(f789(f287(x80481),x80482),x80484))+P1(f789(f789(f287(x80481),f789(f789(f50(x80481),x80482),x80483)),f789(f789(f50(x80481),x80484),x80483)))
% 21.40/21.38 [8062]~P101(x80621)+~P18(x80621,x80622)+~P1(f789(f789(f240(a863),x80623),x80624))+P1(f789(f789(f240(x80621),f789(f789(f159(x80621),x80622),x80623)),f789(f789(f159(x80621),x80622),x80624)))+~P1(f789(f789(f241(a863),x80624),f789(f185(f864(x80621)),x80622)))
% 21.40/21.38 [8063]~P101(x80631)+~P18(x80631,x80632)+~P1(f789(f789(f240(a863),x80633),x80634))+P1(f789(f789(f240(x80631),f789(f789(f159(x80631),x80632),x80633)),f789(f789(f159(x80631),x80632),x80634)))+~P1(f789(f789(f241(a863),x80634),f789(f185(f864(x80631)),x80632)))
% 21.40/21.38 [8113]~P117(x81131)+~P1(f789(f789(f241(x81131),x81132),f87(x81131)))+~P1(f789(f789(f241(x81131),f2(x81131)),x81132))+~P1(f789(f789(f241(a863),x81134),x81133))+P1(f789(f789(f241(x81131),f789(f789(f250(x81131),x81132),x81133)),f789(f789(f250(x81131),x81132),x81134)))
% 21.40/21.38 [8114]~P117(x81141)+~P1(f789(f789(f240(x81141),x81142),f87(x81141)))+~P1(f789(f789(f240(x81141),f2(x81141)),x81142))+~P1(f789(f789(f240(a863),x81144),x81143))+P1(f789(f789(f240(x81141),f789(f789(f250(x81141),x81142),x81143)),f789(f789(f250(x81141),x81142),x81144)))
% 21.40/21.38 [8115]~P117(x81151)+~P1(f789(f789(f240(x81151),f2(x81151)),x81152))+~P1(f789(f789(f241(a863),f2(a863)),x81153))+~P1(f789(f789(f241(x81151),x81152),x81154))+P1(f789(f789(f241(x81151),f789(f789(f250(x81151),x81152),x81153)),f789(f789(f250(x81151),x81154),x81153)))
% 21.40/21.38 [8133]~P101(x81331)+~P18(x81331,f789(f149(x81331),x81332))+~P1(f789(f789(f240(a863),x81334),x81333))+P1(f789(f789(f240(x81331),f789(f789(f159(x81331),x81332),x81333)),f789(f789(f159(x81331),x81332),x81334)))+~P1(f789(f789(f241(a863),x81333),f789(f185(f864(x81331)),x81332)))
% 21.40/21.38 [8361]~P7(x83611)+P1(f789(f789(f287(x83611),x83612),x83613))+~P1(f789(f789(f287(x83611),x83614),x83613))+~P1(f789(f789(f287(x83611),x83614),x83612))+~P1(f789(f789(f287(x83611),f789(f789(f50(x83611),x83612),x83614)),f789(f789(f50(x83611),x83613),x83614)))
% 21.40/21.38 [8378]~P63(x83781)+~P1(f789(f789(f241(x83781),x83782),f2(x83781)))+~P1(f789(f789(f241(x83781),x83783),x83784))+~P1(f789(f789(f241(x83781),f2(x83781)),f789(f789(f90(x83781),x83783),x83784)))+P1(f789(f789(f241(x83781),f789(f789(f291(x83781),x83782),x83783)),f789(f789(f291(x83781),x83782),x83784)))
% 21.40/21.38 [8379]~P62(x83791)+~P1(f789(f789(f240(x83791),x83792),f2(x83791)))+~P1(f789(f789(f240(x83791),x83793),x83794))+~P1(f789(f789(f241(x83791),f2(x83791)),f789(f789(f90(x83791),x83793),x83794)))+P1(f789(f789(f240(x83791),f789(f789(f291(x83791),x83792),x83793)),f789(f789(f291(x83791),x83792),x83794)))
% 21.40/21.38 [8389]~P63(x83891)+~P1(f789(f789(f241(x83891),x83894),x83893))+~P1(f789(f789(f241(x83891),f2(x83891)),x83892))+~P1(f789(f789(f241(x83891),f2(x83891)),f789(f789(f90(x83891),x83893),x83894)))+P1(f789(f789(f241(x83891),f789(f789(f291(x83891),x83892),x83893)),f789(f789(f291(x83891),x83892),x83894)))
% 21.40/21.38 [8390]~P63(x83901)+~P1(f789(f789(f240(x83901),x83904),x83903))+~P1(f789(f789(f240(x83901),f2(x83901)),x83902))+~P1(f789(f789(f241(x83901),f2(x83901)),f789(f789(f90(x83901),x83903),x83904)))+P1(f789(f789(f240(x83901),f789(f789(f291(x83901),x83902),x83903)),f789(f789(f291(x83901),x83902),x83904)))
% 21.40/21.38 [8497]P1(f789(x84971,x84972))+~P1(f789(f70(x84974),x84972))+P1(f789(x84971,f524(x84971,x84973,x84972,x84974)))+~P1(f789(x84971,f184(f870(x84974,a856))))+~P1(f789(f789(f240(f870(x84974,a856)),x84972),x84973))
% 21.40/21.38 [8505]P1(f789(x85051,x85052))+P1(f789(f70(x85053),f524(x85051,x85054,x85052,x85053)))+~P1(f789(f70(x85053),x85052))+~P1(f789(x85051,f184(f870(x85053,a856))))+~P1(f789(f789(f240(f870(x85053,a856)),x85052),x85054))
% 21.40/21.38 [8734]E(f789(f789(f89(a1),f491(x87341,x87342,x87343,x87344)),f492(x87341,x87342,x87343,x87344)),x87344)+~P1(f789(f789(f241(a1),f2(a1)),x87343))+~P1(f789(f789(f241(a1),x87342),x87344))+~P1(f789(f789(f342(a1),x87342),x87341))+P1(f789(f789(f241(a1),x87342),f789(f789(f3(a1),x87344),x87343)))
% 21.40/21.38 [8921]~P1(f789(f789(f241(a1),f2(a1)),x89213))+~P1(f789(f789(f241(a1),x89212),x89214))+~P1(f789(f789(f342(a1),x89212),x89211))+P1(f789(f789(f342(a1),f491(x89211,x89212,x89213,x89214)),x89211))+P1(f789(f789(f241(a1),x89212),f789(f789(f3(a1),x89214),x89213)))
% 21.40/21.38 [8934]P1(f789(x89341,x89342))+~P1(f789(f70(x89343),x89342))+P1(f789(f789(f342(x89343),f526(x89341,x89344,x89342,x89343)),x89344))+~P1(f789(x89341,f184(f870(x89343,a856))))+~P1(f789(f789(f240(f870(x89343,a856)),x89342),x89344))
% 21.40/21.38 [8951]E(f789(f789(f89(a1),f478(x89511,x89512,x89513,x89514)),f479(x89511,x89512,x89513,x89514)),x89514)+~P1(f789(f789(f241(a1),f2(a1)),x89513))+~P1(f789(f789(f240(a1),x89512),x89514))+P1(f789(f789(f240(a1),x89512),f789(f789(f3(a1),x89514),x89513)))+~P1(f789(f789(f342(a1),f789(f789(f3(a1),x89512),f87(a1))),x89511))
% 21.40/21.38 [8997]~P1(f789(f789(f241(a1),f2(a1)),x89973))+~P1(f789(f789(f241(a1),x89971),x89972))+~P1(f789(f789(f342(a1),x89971),x89974))+P1(f789(f789(f342(a1),f492(x89974,x89971,x89973,x89972)),f303(a1,f87(a1),x89973)))+P1(f789(f789(f241(a1),x89971),f789(f789(f3(a1),x89972),x89973)))
% 21.40/21.38 [9092]~P1(f789(f789(f241(a1),f2(a1)),x90923))+~P1(f789(f789(f240(a1),x90922),x90924))+P1(f789(f789(f342(a1),f478(x90921,x90922,x90923,x90924)),x90921))+P1(f789(f789(f240(a1),x90922),f789(f789(f3(a1),x90924),x90923)))+~P1(f789(f789(f342(a1),f789(f789(f3(a1),x90922),f87(a1))),x90921))
% 21.40/21.38 [9131]~P1(f789(f789(f241(a1),f2(a1)),x91313))+~P1(f789(f789(f240(a1),x91311),x91312))+P1(f789(f789(f342(a1),f479(x91314,x91311,x91313,x91312)),f303(a1,f87(a1),x91313)))+P1(f789(f789(f240(a1),x91311),f789(f789(f3(a1),x91312),x91313)))+~P1(f789(f789(f342(a1),f789(f789(f3(a1),x91311),f87(a1))),x91314))
% 21.40/21.38 [9340]P1(f789(x93401,x93402))+~P1(f789(f789(f342(x93403),f526(x93401,x93404,x93402,x93403)),f524(x93401,x93404,x93402,x93403)))+~P1(f789(f70(x93403),x93402))+~P1(f789(x93401,f184(f870(x93403,a856))))+~P1(f789(f789(f240(f870(x93403,a856)),x93402),x93404))
% 21.40/21.38 [9547]P1(f789(x95471,x95472))+~P1(f789(f70(x95473),x95472))+~P1(f789(x95471,f789(f789(f310(x95473),f526(x95471,x95474,x95472,x95473)),f524(x95471,x95474,x95472,x95473))))+~P1(f789(x95471,f184(f870(x95473,a856))))+~P1(f789(f789(f240(f870(x95473,a856)),x95472),x95474))
% 21.40/21.38 [9875]~P99(x98753)+~P52(a863,x98753,f789(f789(f20(a863,f870(a863,a856),f870(a863,a856)),f789(f789(f10(f870(a863,f870(a856,a856)),f870(f870(a863,a856),f870(a863,a856)),a863),f20(a863,a856,a856)),f789(f789(f10(f870(a863,a856),f870(a863,f870(a856,a856)),a863),f789(f10(a856,f870(a856,a856),a863),a339)),f287(a863)))),f789(f789(f10(f870(a863,a856),f870(a863,a856),a863),f789(f10(a856,a856,a863),a336)),f789(f9(a863,a863,a856),f287(a863)))),x98754)+P1(f789(f789(f241(x98753),f789(x98754,x98752)),f789(x98754,x98751)))+~P1(f789(f789(f287(a863),x98752),x98751))+P1(f789(f789(f287(a863),x98751),x98752))
% 21.40/21.38 [7693]~P62(x76931)+P1(f789(f789(f241(x76931),x76932),f2(x76931)))+P1(f789(f789(f241(x76931),f2(x76931)),x76932))+~P1(f789(f789(f241(x76931),f2(x76931)),x76934))+P1(f789(f789(f241(x76931),f789(f789(f291(x76931),x76933),x76932)),x76934))
% 21.40/21.38 [7694]~P62(x76941)+P1(f789(f789(f241(x76941),x76942),f2(x76941)))+~P1(f789(f789(f240(x76941),f2(x76941)),x76944))+P1(f789(f789(f241(x76941),f2(x76941)),x76942))+P1(f789(f789(f240(x76941),f789(f789(f291(x76941),x76943),x76942)),x76944))
% 21.40/21.38 [7974]~P1(f789(f789(f240(a1),x79744),f2(a1)))+~E(x79742,f789(f789(f89(a1),f789(f789(f90(a1),x79741),x79743)),x79744))+P1(f789(f789(f241(a1),f2(a1)),x79741))+~P1(f789(f789(f241(a1),x79741),x79744))+P1(f789(f63(x79742,x79741),f789(f789(f249(a1,a1),x79743),x79744)))
% 21.40/21.38 [8011]~P1(f789(x80111,x80114))+P1(f789(x80111,f827(x80112,x80111,x80113)))+~P1(f789(f789(f241(a1),f2(a1)),x80113))+~P1(f789(f789(f240(a1),f2(a1)),x80112))+P1(f789(x80111,f789(f789(f89(a1),x80114),f789(f789(f90(a1),x80112),x80113))))
% 21.40/21.38 [8012]~P1(f789(x80121,x80124))+P1(f789(x80121,f832(x80122,x80121,x80123)))+~P1(f789(f789(f241(a1),f2(a1)),x80123))+~P1(f789(f789(f240(a1),f2(a1)),x80122))+P1(f789(x80121,f789(f789(f3(a1),x80124),f789(f789(f90(a1),x80122),x80123))))
% 21.40/21.38 [8013]~P62(x80131)+P1(f789(f789(f241(x80131),x80132),f2(x80131)))+P1(f789(f789(f241(x80131),f2(x80131)),x80132))+P1(f789(f789(f241(x80131),f2(x80131)),x80133))+~P1(f789(f789(f241(x80131),f789(f789(f291(x80131),x80134),x80132)),x80133))
% 21.40/21.38 [8014]~P62(x80141)+P1(f789(f789(f241(x80141),x80142),f2(x80141)))+P1(f789(f789(f241(x80141),f2(x80141)),x80142))+P1(f789(f789(f240(x80141),f2(x80141)),x80143))+~P1(f789(f789(f240(x80141),f789(f789(f291(x80141),x80144),x80142)),x80143))
% 21.40/21.38 [8058]~E(x80581,f789(f789(f89(a1),f789(f789(f90(a1),x80582),x80583)),x80584))+~P1(f789(f789(f241(a1),f2(a1)),x80582))+~P1(f789(f789(f240(a1),f2(a1)),x80584))+~P1(f789(f789(f241(a1),x80584),x80582))+P1(f789(f63(x80581,x80582),f789(f789(f249(a1,a1),x80583),x80584)))
% 21.40/21.38 [8174]~P62(x81741)+P1(f789(f789(f241(x81741),x81742),f2(x81741)))+~P1(f789(f789(f241(x81741),f2(x81741)),x81744))+~P1(f789(f789(f241(x81741),x81743),f789(f789(f90(x81741),x81744),x81742)))+P1(f789(f789(f241(x81741),f789(f789(f291(x81741),x81743),x81742)),x81744))
% 21.40/21.38 [8175]~P62(x81751)+P1(f789(f789(f241(x81751),x81752),f2(x81751)))+~P1(f789(f789(f240(x81751),f2(x81751)),x81754))+~P1(f789(f789(f240(x81751),x81753),f789(f789(f90(x81751),x81754),x81752)))+P1(f789(f789(f240(x81751),f789(f789(f291(x81751),x81753),x81752)),x81754))
% 21.40/21.38 [8253]~P62(x82531)+P1(f789(f789(f241(x82531),x82532),f2(x82531)))+~P1(f789(f789(f241(x82531),x82533),f2(x82531)))+P1(f789(f789(f241(x82531),x82533),f789(f789(f291(x82531),x82534),x82532)))+~P1(f789(f789(f241(x82531),f789(f789(f90(x82531),x82533),x82532)),x82534))
% 21.40/21.38 [8254]~P62(x82541)+P1(f789(f789(f241(x82541),x82542),f2(x82541)))+~P1(f789(f789(f240(x82541),x82543),f2(x82541)))+P1(f789(f789(f240(x82541),x82543),f789(f789(f291(x82541),x82544),x82542)))+~P1(f789(f789(f240(x82541),f789(f789(f90(x82541),x82543),x82542)),x82544))
% 21.40/21.38 [8414]~P62(x84141)+~P1(f789(f789(f241(x84141),x84142),f2(x84141)))+P1(f789(f789(f241(x84141),f2(x84141)),x84142))+~P1(f789(f789(f241(x84141),f789(f789(f291(x84141),x84144),x84142)),x84143))+P1(f789(f789(f241(x84141),f789(f789(f90(x84141),x84143),x84142)),x84144))
% 21.40/21.38 [8415]~P62(x84151)+~P1(f789(f789(f241(x84151),x84152),f2(x84151)))+P1(f789(f789(f241(x84151),f2(x84151)),x84152))+~P1(f789(f789(f241(x84151),f789(f789(f90(x84151),x84154),x84152)),x84153))+P1(f789(f789(f241(x84151),f789(f789(f291(x84151),x84153),x84152)),x84154))
% 21.40/21.38 [8416]~P62(x84161)+~P1(f789(f789(f241(x84161),x84162),f2(x84161)))+P1(f789(f789(f241(x84161),f2(x84161)),x84162))+~P1(f789(f789(f240(x84161),f789(f789(f291(x84161),x84164),x84162)),x84163))+P1(f789(f789(f240(x84161),f789(f789(f90(x84161),x84163),x84162)),x84164))
% 21.40/21.38 [8417]~P62(x84171)+~P1(f789(f789(f241(x84171),x84172),f2(x84171)))+P1(f789(f789(f241(x84171),f2(x84171)),x84172))+~P1(f789(f789(f240(x84171),f789(f789(f90(x84171),x84174),x84172)),x84173))+P1(f789(f789(f240(x84171),f789(f789(f291(x84171),x84173),x84172)),x84174))
% 21.40/21.38 [8436]~P62(x84361)+~P1(f789(f789(f241(x84361),f2(x84361)),x84364))+P1(f789(f789(f241(x84361),f2(x84361)),x84362))+~P1(f789(f789(f241(x84361),f789(f789(f90(x84361),x84364),x84362)),x84363))+P1(f789(f789(f241(x84361),f789(f789(f291(x84361),x84363),x84362)),x84364))
% 21.40/21.38 [8437]~P62(x84371)+~P1(f789(f789(f240(x84371),f2(x84371)),x84374))+P1(f789(f789(f241(x84371),f2(x84371)),x84372))+~P1(f789(f789(f240(x84371),f789(f789(f90(x84371),x84374),x84372)),x84373))+P1(f789(f789(f240(x84371),f789(f789(f291(x84371),x84373),x84372)),x84374))
% 21.40/21.38 [8488]~P62(x84881)+~P89(x84881)+~P1(f789(f789(f241(x84881),f2(x84881)),x84884))+~P1(f789(f789(f241(x84881),f789(f789(f291(x84881),x84882),x84884)),f789(f113(x84881),x84883)))+P1(f789(f789(f241(x84881),x84882),f789(f789(f90(x84881),f789(f113(x84881),x84883)),x84884)))
% 21.40/21.38 [8489]~P62(x84891)+~P89(x84891)+~P1(f789(f789(f241(x84891),f2(x84891)),x84894))+~P1(f789(f789(f240(x84891),f789(f789(f291(x84891),x84892),x84894)),f789(f113(x84891),x84893)))+P1(f789(f789(f240(x84891),x84892),f789(f789(f90(x84891),f789(f113(x84891),x84893)),x84894)))
% 21.40/21.38 [8498]~P62(x84981)+~P89(x84981)+~P1(f789(f789(f241(x84981),f2(x84981)),x84983))+P1(f789(f789(f241(x84981),f789(f789(f291(x84981),x84982),x84983)),f789(f113(x84981),x84984)))+~P1(f789(f789(f241(x84981),x84982),f789(f789(f90(x84981),f789(f113(x84981),x84984)),x84983)))
% 21.40/21.38 [8499]~P62(x84991)+~P89(x84991)+~P1(f789(f789(f241(x84991),f2(x84991)),x84993))+P1(f789(f789(f240(x84991),f789(f789(f291(x84991),x84992),x84993)),f789(f113(x84991),x84994)))+~P1(f789(f789(f240(x84991),x84992),f789(f789(f90(x84991),f789(f113(x84991),x84994)),x84993)))
% 21.40/21.38 [8513]~P62(x85131)+~P1(f789(f789(f241(x85131),x85134),f2(x85131)))+~P1(f789(f789(f241(x85131),x85133),f789(f789(f90(x85131),x85132),x85134)))+P1(f789(f789(f241(x85131),x85132),f789(f789(f291(x85131),x85133),x85134)))+~P1(f789(f789(f241(x85131),f789(f789(f90(x85131),x85132),x85134)),x85133))
% 21.40/21.38 [8514]~P62(x85141)+~P1(f789(f789(f241(x85141),x85142),f2(x85141)))+~P1(f789(f789(f241(x85141),x85143),f789(f789(f90(x85141),x85142),x85144)))+P1(f789(f789(f241(x85141),x85142),f789(f789(f291(x85141),x85143),x85144)))+~P1(f789(f789(f241(x85141),f789(f789(f90(x85141),x85142),x85144)),x85143))
% 21.40/21.38 [8515]~P62(x85151)+~P1(f789(f789(f241(x85151),x85154),f2(x85151)))+~P1(f789(f789(f240(x85151),x85153),f789(f789(f90(x85151),x85152),x85154)))+P1(f789(f789(f240(x85151),x85152),f789(f789(f291(x85151),x85153),x85154)))+~P1(f789(f789(f240(x85151),f789(f789(f90(x85151),x85152),x85154)),x85153))
% 21.40/21.38 [8516]~P62(x85161)+~P1(f789(f789(f240(x85161),x85162),f2(x85161)))+~P1(f789(f789(f240(x85161),x85163),f789(f789(f90(x85161),x85162),x85164)))+P1(f789(f789(f240(x85161),x85162),f789(f789(f291(x85161),x85163),x85164)))+~P1(f789(f789(f240(x85161),f789(f789(f90(x85161),x85162),x85164)),x85163))
% 21.40/21.38 [8561]~P62(x85611)+~P89(x85611)+~P1(f789(f789(f241(x85611),f2(x85611)),f789(f113(x85611),x85613)))+~P1(f789(f789(f241(x85611),x85612),f789(f789(f291(x85611),x85614),f789(f113(x85611),x85613))))+P1(f789(f789(f241(x85611),f789(f789(f90(x85611),x85612),f789(f113(x85611),x85613))),x85614))
% 21.40/21.38 [8562]~P62(x85621)+~P89(x85621)+~P1(f789(f789(f241(x85621),f2(x85621)),f789(f113(x85621),x85623)))+~P1(f789(f789(f241(x85621),x85622),f789(f789(f90(x85621),x85624),f789(f113(x85621),x85623))))+P1(f789(f789(f241(x85621),f789(f789(f291(x85621),x85622),f789(f113(x85621),x85623))),x85624))
% 21.40/21.38 [8563]~P62(x85631)+~P89(x85631)+~P1(f789(f789(f241(x85631),f2(x85631)),f789(f113(x85631),x85633)))+~P1(f789(f789(f240(x85631),x85632),f789(f789(f291(x85631),x85634),f789(f113(x85631),x85633))))+P1(f789(f789(f240(x85631),f789(f789(f90(x85631),x85632),f789(f113(x85631),x85633))),x85634))
% 21.40/21.38 [8564]~P62(x85641)+~P89(x85641)+~P1(f789(f789(f241(x85641),f2(x85641)),f789(f113(x85641),x85643)))+~P1(f789(f789(f240(x85641),x85642),f789(f789(f90(x85641),x85644),f789(f113(x85641),x85643))))+P1(f789(f789(f240(x85641),f789(f789(f291(x85641),x85642),f789(f113(x85641),x85643))),x85644))
% 21.40/21.38 [8616]~P62(x86161)+~P1(f789(f789(f241(x86161),x86163),f2(x86161)))+~P1(f789(f789(f241(x86161),x86162),f789(f789(f90(x86161),x86164),x86163)))+~P1(f789(f789(f241(x86161),f789(f789(f90(x86161),x86164),x86163)),x86162))+P1(f789(f789(f241(x86161),f789(f789(f291(x86161),x86162),x86163)),x86164))
% 21.40/21.38 [8617]~P62(x86171)+~P1(f789(f789(f241(x86171),x86173),f2(x86171)))+~P1(f789(f789(f240(x86171),x86172),f789(f789(f90(x86171),x86174),x86173)))+~P1(f789(f789(f240(x86171),f789(f789(f90(x86171),x86174),x86173)),x86172))+P1(f789(f789(f240(x86171),f789(f789(f291(x86171),x86172),x86173)),x86174))
% 21.40/21.38 [8631]~P62(x86311)+~P1(f789(f789(f241(x86311),f2(x86311)),x86314))+~P1(f789(f789(f241(x86311),x86312),f789(f789(f90(x86311),x86314),x86313)))+~P1(f789(f789(f241(x86311),f789(f789(f90(x86311),x86314),x86313)),x86312))+P1(f789(f789(f241(x86311),f789(f789(f291(x86311),x86312),x86313)),x86314))
% 21.40/21.38 [8632]~P62(x86321)+~P1(f789(f789(f240(x86321),f2(x86321)),x86324))+~P1(f789(f789(f240(x86321),x86322),f789(f789(f90(x86321),x86324),x86323)))+~P1(f789(f789(f240(x86321),f789(f789(f90(x86321),x86324),x86323)),x86322))+P1(f789(f789(f240(x86321),f789(f789(f291(x86321),x86322),x86323)),x86324))
% 21.40/21.38 [8662]~P62(x86621)+~P89(x86621)+~P1(f789(f789(f241(x86621),f2(x86621)),f789(f113(x86621),x86624)))+P1(f789(f789(f241(x86621),x86622),f789(f789(f90(x86621),x86623),f789(f113(x86621),x86624))))+~P1(f789(f789(f241(x86621),f789(f789(f291(x86621),x86622),f789(f113(x86621),x86624))),x86623))
% 21.40/21.38 [8663]~P62(x86631)+~P89(x86631)+~P1(f789(f789(f241(x86631),f2(x86631)),f789(f113(x86631),x86634)))+P1(f789(f789(f241(x86631),x86632),f789(f789(f291(x86631),x86633),f789(f113(x86631),x86634))))+~P1(f789(f789(f241(x86631),f789(f789(f90(x86631),x86632),f789(f113(x86631),x86634))),x86633))
% 21.40/21.38 [8664]~P62(x86641)+~P89(x86641)+~P1(f789(f789(f241(x86641),f2(x86641)),f789(f113(x86641),x86644)))+P1(f789(f789(f240(x86641),x86642),f789(f789(f90(x86641),x86643),f789(f113(x86641),x86644))))+~P1(f789(f789(f240(x86641),f789(f789(f291(x86641),x86642),f789(f113(x86641),x86644))),x86643))
% 21.40/21.38 [8665]~P62(x86651)+~P89(x86651)+~P1(f789(f789(f241(x86651),f2(x86651)),f789(f113(x86651),x86654)))+P1(f789(f789(f240(x86651),x86652),f789(f789(f291(x86651),x86653),f789(f113(x86651),x86654))))+~P1(f789(f789(f240(x86651),f789(f789(f90(x86651),x86652),f789(f113(x86651),x86654))),x86653))
% 21.40/21.38 [8789]E(f789(f789(f3(a1),f487(x87891,x87892,x87893,x87894)),f488(x87891,x87892,x87893,x87894)),x87894)+~P1(f789(f789(f241(a1),f2(a1)),x87893))+~P1(f789(f789(f342(a1),x87892),x87891))+~P1(f789(f789(f241(a1),x87894),x87892))+P1(f789(f789(f241(a1),f789(f789(f89(a1),x87894),x87893)),x87892))
% 21.40/21.38 [8853]~P1(f789(x88531,x88532))+~P1(f789(f789(f241(a1),f2(a1)),x88534))+~P1(f789(f789(f240(a1),f2(a1)),x88533))+~P1(f789(x88531,f789(f789(f89(a1),f827(x88533,x88531,x88534)),x88534)))+P1(f789(x88531,f789(f789(f89(a1),x88532),f789(f789(f90(a1),x88533),x88534))))
% 21.40/21.38 [8854]~P1(f789(x88541,x88542))+~P1(f789(f789(f241(a1),f2(a1)),x88544))+~P1(f789(f789(f240(a1),f2(a1)),x88543))+~P1(f789(x88541,f789(f789(f3(a1),f832(x88543,x88541,x88544)),x88544)))+P1(f789(x88541,f789(f789(f3(a1),x88542),f789(f789(f90(a1),x88543),x88544))))
% 21.40/21.38 [8990]~P1(f789(f789(f241(a1),f2(a1)),x89903))+~P1(f789(f789(f342(a1),x89902),x89901))+~P1(f789(f789(f241(a1),x89904),x89902))+P1(f789(f789(f342(a1),f487(x89901,x89902,x89903,x89904)),x89901))+P1(f789(f789(f241(a1),f789(f789(f89(a1),x89904),x89903)),x89902))
% 21.40/21.38 [9010]E(f789(f789(f3(a1),f480(x90101,x90102,x90103,x90104)),f481(x90101,x90102,x90103,x90104)),x90104)+~P1(f789(f789(f241(a1),f2(a1)),x90103))+~P1(f789(f789(f240(a1),x90104),x90102))+~P1(f789(f789(f342(a1),f789(f789(f89(a1),x90102),f87(a1))),x90101))+P1(f789(f789(f240(a1),f789(f789(f89(a1),x90104),x90103)),x90102))
% 21.40/21.38 [9042]~P1(f789(f789(f241(a1),f2(a1)),x90422))+~P1(f789(f789(f342(a1),x90423),x90424))+~P1(f789(f789(f241(a1),x90421),x90423))+P1(f789(f789(f342(a1),f488(x90424,x90423,x90422,x90421)),f303(a1,f87(a1),x90422)))+P1(f789(f789(f241(a1),f789(f789(f89(a1),x90421),x90422)),x90423))
% 21.40/21.38 [9124]~P1(f789(f789(f241(a1),f2(a1)),x91243))+~P1(f789(f789(f240(a1),x91244),x91242))+P1(f789(f789(f342(a1),f480(x91241,x91242,x91243,x91244)),x91241))+~P1(f789(f789(f342(a1),f789(f789(f89(a1),x91242),f87(a1))),x91241))+P1(f789(f789(f240(a1),f789(f789(f89(a1),x91244),x91243)),x91242))
% 21.40/21.38 [9162]~P1(f789(f789(f241(a1),f2(a1)),x91622))+~P1(f789(f789(f240(a1),x91621),x91623))+P1(f789(f789(f342(a1),f481(x91624,x91623,x91622,x91621)),f303(a1,f87(a1),x91622)))+~P1(f789(f789(f342(a1),f789(f789(f89(a1),x91623),f87(a1))),x91624))+P1(f789(f789(f240(a1),f789(f789(f89(a1),x91621),x91622)),x91623))
% 21.40/21.38 [9426]~P36(x94261,x94263)+~P30(x94261,x94264)+P36(x94261,f789(f789(f110(f870(f869(x94261,x94261),a856)),x94262),x94263))+~P1(f789(f789(f240(f870(f869(x94261,x94261),a856)),x94262),f789(f248(f870(f869(x94261,x94261),a856),f870(f869(x94261,x94261),a856)),x94264)))+~P1(f789(f789(f240(f870(f869(x94261,x94261),a856)),x94263),f789(f258(f870(f869(x94261,x94261),a856),f870(f869(x94261,x94261),a856)),x94264)))
% 21.40/21.38 [9704]~E(f789(f719(x97041,x97044,x97043,x97042),f721(x97041,x97044,x97043,x97042)),f187(f864(a854)))+P1(f789(f789(f241(a1),f720(x97041,x97044,x97043,x97042)),f721(x97041,x97044,x97043,x97042)))+P1(f789(f789(f789(x97041,x97042),x97043),x97044))+P1(f789(f789(f789(x97041,f719(x97041,x97044,x97043,x97042)),f720(x97041,x97044,x97043,x97042)),f789(f789(f89(a1),f721(x97041,x97044,x97043,x97042)),f87(a1))))+~P1(f789(f329(f869(f870(a1,f867(f864(a854))),f869(a1,a1)),a319),f789(f789(f249(f870(a1,f867(f864(a854))),f869(a1,a1)),x97042),f789(f789(f249(a1,a1),x97043),x97044))))
% 21.40/21.38 [9805]~P22(x98052,x98054,x98053)+E(x98051,f184(f870(x98052,a856)))+~P1(f789(f70(x98052),x98051))+P1(f789(f789(f342(x98052),f789(x98053,x98051)),x98051))+~P1(f789(f789(f342(x98052),f789(f789(x98054,f406(x98051,x98053,x98054,x98052)),f407(x98051,x98053,x98054,x98052))),f789(f789(f310(x98052),f406(x98051,x98053,x98054,x98052)),f789(f789(f310(x98052),f407(x98051,x98053,x98054,x98052)),f184(f870(x98052,a856))))))
% 21.40/21.38 [8652]~P62(x86521)+~P89(x86521)+~P1(f789(f789(f241(x86521),f2(x86521)),x86523))+~P1(f789(f789(f241(x86521),f789(f113(x86521),x86522)),f789(f789(f291(x86521),x86524),x86523)))+P1(f789(f789(f241(x86521),f789(f789(f90(x86521),f789(f113(x86521),x86522)),x86523)),x86524))
% 21.40/21.38 [8653]~P62(x86531)+~P89(x86531)+~P1(f789(f789(f241(x86531),f2(x86531)),x86533))+~P1(f789(f789(f240(x86531),f789(f113(x86531),x86532)),f789(f789(f291(x86531),x86534),x86533)))+P1(f789(f789(f240(x86531),f789(f789(f90(x86531),f789(f113(x86531),x86532)),x86533)),x86534))
% 21.40/21.38 [8792]~P62(x87921)+~P89(x87921)+~P1(f789(f789(f241(x87921),f2(x87921)),x87924))+P1(f789(f789(f241(x87921),f789(f113(x87921),x87922)),f789(f789(f291(x87921),x87923),x87924)))+~P1(f789(f789(f241(x87921),f789(f789(f90(x87921),f789(f113(x87921),x87922)),x87924)),x87923))
% 21.40/21.38 [8793]~P62(x87931)+~P89(x87931)+~P1(f789(f789(f241(x87931),f2(x87931)),x87934))+P1(f789(f789(f240(x87931),f789(f113(x87931),x87932)),f789(f789(f291(x87931),x87933),x87934)))+~P1(f789(f789(f240(x87931),f789(f789(f90(x87931),f789(f113(x87931),x87932)),x87934)),x87933))
% 21.40/21.38 [9347]~P53(x93471,x93471,x93474)+P1(f789(f789(f342(f869(x93471,x93471)),f789(f789(f249(x93471,x93471),x93472),x93473)),f308(x93471,x93474)))+P1(f789(f789(f342(f869(x93471,x93471)),f789(f789(f249(x93471,x93471),x93473),x93472)),f308(x93471,x93474)))+~P1(f789(f789(f342(f869(x93471,x93471)),f789(f789(f249(x93471,x93471),x93475),x93472)),f308(x93471,x93474)))+~P1(f789(f789(f342(f869(x93471,x93471)),f789(f789(f249(x93471,x93471),x93475),x93473)),f308(x93471,x93474)))
% 21.40/21.38 [5537]E(x55371,f2(a863))+~E(f789(f49(x55372),x55375),x55371)+E(f789(f49(x55372),x55373),f789(a121,x55371))+~E(x55373,f789(f789(f310(x55372),x55374),x55375))+P1(f789(f789(f342(x55372),x55374),x55375))
% 21.40/21.38 [5659]~P61(x56592)+E(x56591,f2(x56592))+E(x56593,f2(x56592))+~E(f789(f789(f291(x56592),x56594),x56593),f789(f789(f291(x56592),x56595),x56591))+E(f789(f789(f90(x56592),x56594),x56591),f789(f789(f90(x56592),x56595),x56593))
% 21.40/21.38 [5660]~P61(x56602)+E(x56601,f2(x56602))+E(x56603,f2(x56602))+~E(f789(f789(f90(x56602),x56604),x56603),f789(f789(f90(x56602),x56605),x56601))+E(f789(f789(f291(x56602),x56604),x56601),f789(f789(f291(x56602),x56605),x56603))
% 21.40/21.38 [5733]~E(f789(f49(x57331),x57335),x57333)+~E(x57335,f184(f870(x57331,a856)))+E(f789(f49(x57331),x57332),f789(a121,x57333))+~E(x57332,f789(f789(f310(x57331),x57334),x57335))+P1(f789(f789(f342(x57331),x57334),x57335))
% 21.40/21.38 [5958]~P70(x59582)+~E(f789(x59583,x59585),f2(x59582))+E(f789(f789(f11(x59581,x59582),x59583),x59584),f2(x59582))+~P1(f789(f70(x59581),x59584))+~P1(f789(f789(f342(x59581),x59585),x59584))
% 21.40/21.38 [6339]~P101(x63393)+E(x63391,x63392)+~E(f789(f302(x63393,x63394),x63391),f789(f302(x63393,x63395),x63392))+~P1(f789(f789(f241(x63393),x63395),x63392))+~P1(f789(f789(f241(x63393),x63394),x63391))
% 21.40/21.38 [6340]~P101(x63403)+E(x63401,x63402)+~E(f789(f302(x63403,x63401),x63404),f789(f302(x63403,x63402),x63405))+~P1(f789(f789(f241(x63403),x63402),x63405))+~P1(f789(f789(f241(x63403),x63401),x63404))
% 21.40/21.38 [6341]~P101(x63413)+E(x63411,x63412)+~E(f789(f302(x63413,x63414),x63411),f789(f302(x63413,x63415),x63412))+~P1(f789(f789(f241(x63413),x63415),x63412))+~P1(f789(f789(f241(x63413),x63414),x63411))
% 21.40/21.38 [6342]~P101(x63423)+E(x63421,x63422)+~E(f789(f302(x63423,x63421),x63424),f789(f302(x63423,x63422),x63425))+~P1(f789(f789(f241(x63423),x63422),x63425))+~P1(f789(f789(f241(x63423),x63421),x63424))
% 21.40/21.38 [7448]~P101(x74481)+~P18(x74481,f789(f789(f132(x74481),x74484),x74485))+~P1(f789(f789(f342(x74481),x74483),f789(f163(x74481),x74485)))+~P1(f789(f789(f342(x74481),x74482),f789(f163(x74481),x74484)))+P1(f789(f789(f240(x74481),x74482),x74483))
% 21.40/21.38 [8547]~P99(x85471)+~P1(f789(f789(f241(f870(x85471,a856)),f303(x85471,x85475,x85472)),f303(x85471,x85474,x85473)))+~P1(f789(f789(f240(x85471),x85475),x85472))+P1(f789(f789(f241(x85471),x85472),x85473))+P1(f789(f789(f241(x85471),x85474),x85475))
% 21.40/21.38 [9849]~P21(x98492,x98495,x98493)+E(x98491,f184(f870(x98492,a856)))+~E(f789(f789(x98495,f789(x98494,f585(x98491,x98494,x98493,x98495,x98492))),f789(x98494,f586(x98491,x98494,x98493,x98495,x98492))),f789(x98494,f789(f789(x98495,f585(x98491,x98494,x98493,x98495,x98492)),f586(x98491,x98494,x98493,x98495,x98492))))+E(f789(x98493,f789(f311(x98492,x98492,x98494),x98491)),f789(x98494,f789(x98493,x98491)))+~P1(f789(f70(x98492),x98491))
% 21.40/21.38 [6338]~P22(x63382,x63385,x63383)+E(x63381,f184(f870(x63382,a856)))+~P1(f789(f70(x63382),x63381))+E(f789(x63383,f789(f789(f310(x63382),x63384),x63381)),f789(f789(x63385,x63384),f789(x63383,x63381)))+P1(f789(f789(f342(x63382),x63384),x63381))
% 21.40/21.38 [7185]~P21(x71852,x71853,x71854)+E(f789(f789(x71853,f789(x71854,x71851)),f789(x71854,x71855)),f789(x71854,x71855))+E(x71851,f184(f870(x71852,a856)))+~P1(f789(f70(x71852),x71855))+~P1(f789(f789(f240(f870(x71852,a856)),x71851),x71855))
% 21.40/21.38 [7589]~P22(x75894,x75895,x75891)+E(f789(x75891,x75892),x75893)+~P1(f789(f70(x75894),x75892))+~E(f789(f789(f3(f870(x75894,a856)),x75892),f789(f789(f310(x75894),x75893),f184(f870(x75894,a856)))),f184(f870(x75894,a856)))+~P1(f789(f789(f342(x75894),x75893),x75892))
% 21.40/21.38 [7735]E(x77351,x77352)+~E(f789(f185(f864(x77353)),x77352),f789(f185(f864(x77354)),x77355))+~E(f789(f185(f864(x77353)),x77351),f789(f185(f864(x77354)),x77355))+~E(f170(x77354,x77353,f789(f789(f171(x77354,x77353),x77355),x77351)),f170(x77354,x77353,f789(f789(f171(x77354,x77353),x77355),x77352)))+~P1(f789(f134(x77354),x77355))
% 21.40/21.38 [8470]~P69(x84701)+~P112(x84701)+~P1(f789(f70(x84702),x84705))+P1(f789(f789(f287(x84701),f789(f789(f11(x84702,x84701),x84703),x84704)),f789(f789(f11(x84702,x84701),x84703),x84705)))+~P1(f789(f789(f240(f870(x84702,a856)),x84704),x84705))
% 21.40/21.38 [8520]E(x85201,x85202)+~P12(x85203,x85204,x85205)+E(f789(f789(f111(f870(x85203,a856)),x85201),x85202),f184(f870(x85203,a856)))+~P1(f789(f789(f342(f870(x85203,a856)),x85202),f789(f789(f68(x85203),x85204),x85205)))+~P1(f789(f789(f342(f870(x85203,a856)),x85201),f789(f789(f68(x85203),x85204),x85205)))
% 21.40/21.38 [8923]~P29(x89231,x89233,x89235,x89232)+~P1(f789(f70(x89233),x89234))+~P1(f789(f70(x89231),x89232))+P1(f789(f789(f240(a863),f789(f49(x89231),x89232)),f789(f49(x89233),x89234)))+~P1(f789(f789(f240(f870(x89233,a856)),f789(f311(x89231,x89233,x89235),x89232)),x89234))
% 21.40/21.38 [9225]~P69(x92252)+~E(f789(x92253,f455(x92253,x92254,x92255,x92251,x92252)),f87(x92252))+E(f789(f789(f11(x92251,x92252),x92253),x92254),f789(f789(f11(x92251,x92252),x92253),x92255))+~P1(f789(f70(x92251),x92255))+~P1(f789(f789(f240(f870(x92251,a856)),x92254),x92255))
% 21.40/21.38 [9226]~P69(x92262)+~E(f789(x92263,f460(x92263,x92264,x92265,x92261,x92262)),f87(x92262))+E(f789(f789(f11(x92261,x92262),x92263),x92264),f789(f789(f11(x92261,x92262),x92263),x92265))+~P1(f789(f70(x92261),x92265))+~P1(f789(f789(f240(f870(x92261,a856)),x92264),x92265))
% 21.40/21.38 [9227]~P4(x92272)+~E(f789(x92273,f527(x92273,x92274,x92275,x92271,x92272)),f2(x92272))+E(f789(f789(f8(x92271,x92272),x92273),x92274),f789(f789(f8(x92271,x92272),x92273),x92275))+~P1(f789(f70(x92271),x92275))+~P1(f789(f789(f240(f870(x92271,a856)),x92274),x92275))
% 21.40/21.38 [9228]~P4(x92282)+~E(f789(x92283,f533(x92283,x92284,x92285,x92281,x92282)),f2(x92282))+E(f789(f789(f8(x92281,x92282),x92283),x92284),f789(f789(f8(x92281,x92282),x92283),x92285))+~P1(f789(f70(x92281),x92285))+~P1(f789(f789(f240(f870(x92281,a856)),x92284),x92285))
% 21.40/21.38 [9688]~P82(x96881)+~P1(f789(f70(x96882),x96885))+~P1(f789(f789(f240(x96881),f2(x96881)),f789(x96883,f518(x96883,x96884,x96885,x96882,x96881))))+P1(f789(f789(f240(x96881),f789(f789(f8(x96882,x96881),x96883),x96884)),f789(f789(f8(x96882,x96881),x96883),x96885)))+~P1(f789(f789(f240(f870(x96882,a856)),x96884),x96885))
% 21.40/21.38 [7445]E(x74451,f2(a863))+P1(f789(x74452,x74453))+~E(x74454,f789(f789(f89(a863),f789(f789(f90(a863),x74451),x74453)),x74455))+~P1(f789(f789(f241(a863),x74455),x74451))+~P1(f789(x74452,f789(f789(f50(a863),x74454),x74451)))
% 21.40/21.38 [7528]E(x75281,f2(a863))+P1(f789(x75282,x75283))+~P1(f789(x75282,f59(a863,x75284,x75281)))+~E(x75284,f789(f789(f89(a863),f789(f789(f90(a863),x75281),x75285)),x75283))+~P1(f789(f789(f241(a863),x75283),x75281))
% 21.40/21.38 [7823]~P61(x78233)+E(f789(x78231,x78232),f2(x78233))+~P1(f789(f70(x78234),x78235))+E(f789(f789(f11(x78234,x78233),x78231),f789(f789(f3(f870(x78234,a856)),x78235),f789(f789(f310(x78234),x78232),f184(f870(x78234,a856))))),f789(f789(f11(x78234,x78233),x78231),x78235))+P1(f789(f789(f342(x78234),x78232),x78235))
% 21.40/21.38 [8214]~P69(x82141)+~P1(f789(f70(x82142),x82145))+~P1(f789(f70(x82142),x82144))+~E(f789(f789(f111(f870(x82142,a856)),x82144),x82145),f184(f870(x82142,a856)))+E(f789(f789(f90(x82141),f789(f789(f11(x82142,x82141),x82143),x82144)),f789(f789(f11(x82142,x82141),x82143),x82145)),f789(f789(f11(x82142,x82141),x82143),f789(f789(f110(f870(x82142,a856)),x82144),x82145)))
% 21.40/21.38 [8215]~P69(x82151)+~P1(f789(f70(x82152),x82155))+~P1(f789(f70(x82152),x82154))+~E(f789(f789(f111(f870(x82152,a856)),x82154),x82155),f184(f870(x82152,a856)))+E(f789(f789(f90(x82151),f789(f789(f11(x82152,x82151),x82153),x82154)),f789(f789(f11(x82152,x82151),x82153),x82155)),f789(f789(f11(x82152,x82151),x82153),f789(f789(f110(f870(x82152,a856)),x82154),x82155)))
% 21.40/21.38 [8216]~P4(x82161)+~P1(f789(f70(x82162),x82165))+~P1(f789(f70(x82162),x82164))+~E(f789(f789(f111(f870(x82162,a856)),x82164),x82165),f184(f870(x82162,a856)))+E(f789(f789(f89(x82161),f789(f789(f8(x82162,x82161),x82163),x82164)),f789(f789(f8(x82162,x82161),x82163),x82165)),f789(f789(f8(x82162,x82161),x82163),f789(f789(f110(f870(x82162,a856)),x82164),x82165)))
% 21.40/21.38 [8307]~P61(x83073)+E(f789(x83071,x83072),f2(x83073))+~P1(f789(f70(x83074),x83075))+E(f789(f789(f11(x83074,x83073),x83071),f789(f789(f3(f870(x83074,a856)),x83075),f789(f789(f310(x83074),x83072),f184(f870(x83074,a856))))),f789(f789(f291(x83073),f789(f789(f11(x83074,x83073),x83071),x83075)),f789(x83071,x83072)))+~P1(f789(f789(f342(x83074),x83072),x83075))
% 21.40/21.38 [8804]~P12(x88041,x88045,x88044)+~E(f789(f285(x88041,x88041,x88044),f789(f789(f310(x88041),x88042),f184(f870(x88041,a856)))),f789(f285(x88041,x88041,x88044),f789(f789(f310(x88041),x88043),f184(f870(x88041,a856)))))+~P1(f789(f789(f342(x88041),x88043),x88045))+~P1(f789(f789(f342(x88041),x88042),x88045))+P1(f789(f789(f342(f869(x88041,x88041)),f789(f789(f249(x88041,x88041),x88042),x88043)),x88044))
% 21.40/21.38 [8805]~P12(x88051,x88055,x88054)+~E(f789(f285(x88051,x88051,x88054),f789(f789(f310(x88051),x88052),f184(f870(x88051,a856)))),f789(f285(x88051,x88051,x88054),f789(f789(f310(x88051),x88053),f184(f870(x88051,a856)))))+~P1(f789(f789(f342(x88051),x88053),x88055))+~P1(f789(f789(f342(x88051),x88052),x88055))+P1(f789(f789(f342(f869(x88051,x88051)),f789(f789(f249(x88051,x88051),x88052),x88053)),x88054))
% 21.40/21.38 [8885]~P12(x88851,x88855,x88852)+E(f789(f285(x88851,x88851,x88852),f789(f789(f310(x88851),x88853),f184(f870(x88851,a856)))),f789(f285(x88851,x88851,x88852),f789(f789(f310(x88851),x88854),f184(f870(x88851,a856)))))+~P1(f789(f789(f342(x88851),x88854),x88855))+~P1(f789(f789(f342(x88851),x88853),x88855))+~P1(f789(f789(f342(f869(x88851,x88851)),f789(f789(f249(x88851,x88851),x88853),x88854)),x88852))
% 21.40/21.38 [8973]~P12(x89731,x89735,x89734)+~E(f789(f789(f68(x89731),f789(f789(f310(x89731),x89732),f184(f870(x89731,a856)))),x89734),f789(f789(f68(x89731),f789(f789(f310(x89731),x89733),f184(f870(x89731,a856)))),x89734))+~P1(f789(f789(f342(x89731),x89733),x89735))+~P1(f789(f789(f342(x89731),x89732),x89735))+P1(f789(f789(f342(f869(x89731,x89731)),f789(f789(f249(x89731,x89731),x89732),x89733)),x89734))
% 21.40/21.38 [8989]~P12(x89891,x89895,x89893)+E(f789(f789(f68(x89891),f789(f789(f310(x89891),x89892),f184(f870(x89891,a856)))),x89893),f789(f789(f68(x89891),f789(f789(f310(x89891),x89894),f184(f870(x89891,a856)))),x89893))+~P1(f789(f789(f342(x89891),x89894),x89895))+~P1(f789(f789(f342(x89891),x89892),x89895))+~P1(f789(f789(f342(f869(x89891,x89891)),f789(f789(f249(x89891,x89891),x89892),x89894)),x89893))
% 21.40/21.38 [9251]~P69(x92511)+~P1(f789(f70(x92512),x92515))+~P1(f789(f70(x92512),x92514))+~E(f789(f789(f111(f870(x92512,a856)),x92514),x92515),f184(f870(x92512,a856)))+E(f789(f789(f90(x92511),f789(f789(f789(f74(x92511,x92512,f90(x92511)),x92513),f87(x92511)),x92514)),f789(f789(f789(f74(x92511,x92512,f90(x92511)),x92513),f87(x92511)),x92515)),f789(f789(f789(f74(x92511,x92512,f90(x92511)),x92513),f87(x92511)),f789(f789(f110(f870(x92512,a856)),x92514),x92515)))
% 21.40/21.38 [9261]~P69(x92611)+~E(f789(x92613,f418(x92613,x92615,x92614,x92612,x92611)),f87(x92611))+~P1(f789(f70(x92612),x92614))+~P1(f789(f70(x92612),x92615))+E(f789(f789(f90(x92611),f789(f789(f11(x92612,x92611),x92613),x92614)),f789(f789(f11(x92612,x92611),x92613),x92615)),f789(f789(f11(x92612,x92611),x92613),f789(f789(f110(f870(x92612,a856)),x92614),x92615)))
% 21.40/21.38 [9262]~P69(x92621)+~E(f789(x92623,f420(x92623,x92625,x92624,x92622,x92621)),f87(x92621))+~P1(f789(f70(x92622),x92624))+~P1(f789(f70(x92622),x92625))+E(f789(f789(f90(x92621),f789(f789(f11(x92622,x92621),x92623),x92624)),f789(f789(f11(x92622,x92621),x92623),x92625)),f789(f789(f11(x92622,x92621),x92623),f789(f789(f110(f870(x92622,a856)),x92624),x92625)))
% 21.40/21.38 [9263]~P4(x92631)+~E(f789(x92633,f514(x92633,x92635,x92634,x92632,x92631)),f2(x92631))+~P1(f789(f70(x92632),x92634))+~P1(f789(f70(x92632),x92635))+E(f789(f789(f89(x92631),f789(f789(f8(x92632,x92631),x92633),x92634)),f789(f789(f8(x92632,x92631),x92633),x92635)),f789(f789(f8(x92632,x92631),x92633),f789(f789(f110(f870(x92632,a856)),x92634),x92635)))
% 21.40/21.38 [9264]~P4(x92641)+~E(f789(x92643,f528(x92643,x92645,x92644,x92642,x92641)),f2(x92641))+~P1(f789(f70(x92642),x92644))+~P1(f789(f70(x92642),x92645))+E(f789(f789(f89(x92641),f789(f789(f8(x92642,x92641),x92643),x92644)),f789(f789(f8(x92642,x92641),x92643),x92645)),f789(f789(f8(x92642,x92641),x92643),f789(f789(f110(f870(x92642,a856)),x92644),x92645)))
% 21.40/21.38 [9469]~P69(x94691)+~E(f789(x94693,f441(x94693,x94695,x94694,x94692,x94691)),f87(x94691))+~P1(f789(f70(x94692),x94694))+~P1(f789(f70(x94692),x94695))+E(f789(f789(f90(x94691),f789(f789(f789(f74(x94691,x94692,f90(x94691)),x94693),f87(x94691)),x94694)),f789(f789(f789(f74(x94691,x94692,f90(x94691)),x94693),f87(x94691)),x94695)),f789(f789(f789(f74(x94691,x94692,f90(x94691)),x94693),f87(x94691)),f789(f789(f110(f870(x94692,a856)),x94694),x94695)))
% 21.40/21.38 [9574]~P69(x95742)+E(f789(f789(f11(x95741,x95742),x95743),x95744),f789(f789(f11(x95741,x95742),x95743),x95745))+~P1(f789(f70(x95741),x95745))+~P1(f789(f789(f240(f870(x95741,a856)),x95744),x95745))+P1(f789(f789(f342(x95741),f455(x95743,x95744,x95745,x95741,x95742)),f789(f789(f3(f870(x95741,a856)),x95745),x95744)))
% 21.40/21.38 [9575]~P69(x95752)+E(f789(f789(f11(x95751,x95752),x95753),x95754),f789(f789(f11(x95751,x95752),x95753),x95755))+~P1(f789(f70(x95751),x95755))+~P1(f789(f789(f240(f870(x95751,a856)),x95754),x95755))+P1(f789(f789(f342(x95751),f460(x95753,x95754,x95755,x95751,x95752)),f789(f789(f3(f870(x95751,a856)),x95755),x95754)))
% 21.40/21.38 [9576]~P4(x95762)+E(f789(f789(f8(x95761,x95762),x95763),x95764),f789(f789(f8(x95761,x95762),x95763),x95765))+~P1(f789(f70(x95761),x95765))+~P1(f789(f789(f240(f870(x95761,a856)),x95764),x95765))+P1(f789(f789(f342(x95761),f527(x95763,x95764,x95765,x95761,x95762)),f789(f789(f3(f870(x95761,a856)),x95765),x95764)))
% 21.40/21.38 [9577]~P4(x95772)+E(f789(f789(f8(x95771,x95772),x95773),x95774),f789(f789(f8(x95771,x95772),x95773),x95775))+~P1(f789(f70(x95771),x95775))+~P1(f789(f789(f240(f870(x95771,a856)),x95774),x95775))+P1(f789(f789(f342(x95771),f533(x95773,x95774,x95775,x95771,x95772)),f789(f789(f3(f870(x95771,a856)),x95775),x95774)))
% 21.40/21.38 [9592]~P69(x95921)+~P1(f789(f70(x95922),x95924))+~P1(f789(f70(x95922),x95925))+E(f789(f789(f90(x95921),f789(f789(f11(x95922,x95921),x95923),x95924)),f789(f789(f11(x95922,x95921),x95923),x95925)),f789(f789(f11(x95922,x95921),x95923),f789(f789(f110(f870(x95922,a856)),x95924),x95925)))+P1(f789(f789(f342(x95922),f418(x95923,x95925,x95924,x95922,x95921)),f789(f789(f111(f870(x95922,a856)),x95924),x95925)))
% 21.40/21.38 [9593]~P69(x95931)+~P1(f789(f70(x95932),x95934))+~P1(f789(f70(x95932),x95935))+E(f789(f789(f90(x95931),f789(f789(f11(x95932,x95931),x95933),x95934)),f789(f789(f11(x95932,x95931),x95933),x95935)),f789(f789(f11(x95932,x95931),x95933),f789(f789(f110(f870(x95932,a856)),x95934),x95935)))+P1(f789(f789(f342(x95932),f420(x95933,x95935,x95934,x95932,x95931)),f789(f789(f111(f870(x95932,a856)),x95934),x95935)))
% 21.40/21.38 [9594]~P4(x95941)+~P1(f789(f70(x95942),x95944))+~P1(f789(f70(x95942),x95945))+E(f789(f789(f89(x95941),f789(f789(f8(x95942,x95941),x95943),x95944)),f789(f789(f8(x95942,x95941),x95943),x95945)),f789(f789(f8(x95942,x95941),x95943),f789(f789(f110(f870(x95942,a856)),x95944),x95945)))+P1(f789(f789(f342(x95942),f514(x95943,x95945,x95944,x95942,x95941)),f789(f789(f111(f870(x95942,a856)),x95944),x95945)))
% 21.40/21.38 [9595]~P4(x95951)+~P1(f789(f70(x95952),x95954))+~P1(f789(f70(x95952),x95955))+E(f789(f789(f89(x95951),f789(f789(f8(x95952,x95951),x95953),x95954)),f789(f789(f8(x95952,x95951),x95953),x95955)),f789(f789(f8(x95952,x95951),x95953),f789(f789(f110(f870(x95952,a856)),x95954),x95955)))+P1(f789(f789(f342(x95952),f528(x95953,x95955,x95954,x95952,x95951)),f789(f789(f111(f870(x95952,a856)),x95954),x95955)))
% 21.40/21.38 [9608]~P82(x96085)+~P1(f789(f70(x96081),x96084))+P1(f789(f789(f240(x96085),f789(f789(f8(x96081,x96085),x96082),x96083)),f789(f789(f8(x96081,x96085),x96082),x96084)))+~P1(f789(f789(f240(f870(x96081,a856)),x96083),x96084))+P1(f789(f789(f342(x96081),f518(x96082,x96083,x96084,x96081,x96085)),f789(f789(f3(f870(x96081,a856)),x96084),x96083)))
% 21.40/21.38 [9653]~P69(x96531)+~P1(f789(f70(x96532),x96534))+~P1(f789(f70(x96532),x96535))+E(f789(f789(f90(x96531),f789(f789(f789(f74(x96531,x96532,f90(x96531)),x96533),f87(x96531)),x96534)),f789(f789(f789(f74(x96531,x96532,f90(x96531)),x96533),f87(x96531)),x96535)),f789(f789(f789(f74(x96531,x96532,f90(x96531)),x96533),f87(x96531)),f789(f789(f110(f870(x96532,a856)),x96534),x96535)))+P1(f789(f789(f342(x96532),f441(x96533,x96535,x96534,x96532,x96531)),f789(f789(f111(f870(x96532,a856)),x96534),x96535)))
% 21.40/21.38 [8698]~P22(x86981,x86984,x86985)+~P1(f789(f70(x86981),x86982))+E(f789(f789(f3(f870(x86981,a856)),x86982),f789(f789(f310(x86981),x86983),f184(f870(x86981,a856)))),f184(f870(x86981,a856)))+~P1(f789(f789(f342(x86981),x86983),x86982))+E(f789(f789(x86984,x86983),f789(x86985,f789(f789(f3(f870(x86981,a856)),x86982),f789(f789(f310(x86981),x86983),f184(f870(x86981,a856)))))),f789(x86985,x86982))
% 21.40/21.38 [8765]~P22(x87651,x87654,x87655)+~P1(f789(f70(x87651),x87653))+~P1(f789(f70(x87651),x87652))+E(f789(f789(f111(f870(x87651,a856)),x87652),x87653),f184(f870(x87651,a856)))+E(f789(f789(x87654,f789(x87655,f789(f789(f110(f870(x87651,a856)),x87652),x87653))),f789(x87655,f789(f789(f111(f870(x87651,a856)),x87652),x87653))),f789(f789(x87654,f789(x87655,x87652)),f789(x87655,x87653)))
% 21.40/21.38 [9266]~P1(f789(f789(f240(a1),x92664),f2(a1)))+~P1(f789(f789(f241(a1),x92663),x92665))+P1(f789(f789(f240(a1),x92661),x92662))+~P1(f789(f789(f241(a1),x92663),x92664))+~P1(f789(f789(f240(a1),f789(f789(f89(a1),f789(f789(f90(a1),x92663),x92662)),x92665)),f789(f789(f89(a1),f789(f789(f90(a1),x92663),x92661)),x92664)))
% 21.40/21.38 [9268]~P1(f789(f789(f240(a1),f2(a1)),x92685))+P1(f789(f789(f240(a1),x92681),x92682))+~P1(f789(f789(f241(a1),x92683),x92684))+~P1(f789(f789(f241(a1),x92685),x92684))+~P1(f789(f789(f240(a1),f789(f789(f89(a1),f789(f789(f90(a1),x92684),x92681)),x92685)),f789(f789(f89(a1),f789(f789(f90(a1),x92684),x92682)),x92683)))
% 21.40/21.38 [9382]~P61(x93825)+E(f789(x93821,f419(x93821,x93822,x93823,x93824,x93825)),f2(x93825))+~P1(f789(f70(x93824),x93823))+~P1(f789(f70(x93824),x93822))+E(f789(f789(f291(x93825),f789(f789(f90(x93825),f789(f789(f11(x93824,x93825),x93821),x93823)),f789(f789(f11(x93824,x93825),x93821),x93822))),f789(f789(f11(x93824,x93825),x93821),f789(f789(f111(f870(x93824,a856)),x93823),x93822))),f789(f789(f11(x93824,x93825),x93821),f789(f789(f110(f870(x93824,a856)),x93823),x93822)))
% 21.40/21.38 [9647]~P61(x96471)+~P1(f789(f70(x96472),x96474))+~P1(f789(f70(x96472),x96475))+E(f789(f789(f291(x96471),f789(f789(f90(x96471),f789(f789(f11(x96472,x96471),x96473),x96474)),f789(f789(f11(x96472,x96471),x96473),x96475))),f789(f789(f11(x96472,x96471),x96473),f789(f789(f111(f870(x96472,a856)),x96474),x96475))),f789(f789(f11(x96472,x96471),x96473),f789(f789(f110(f870(x96472,a856)),x96474),x96475)))+P1(f789(f789(f342(x96472),f419(x96473,x96475,x96474,x96472,x96471)),f789(f789(f111(f870(x96472,a856)),x96474),x96475)))
% 21.40/21.38 [9009]E(f789(f789(f132(x90091),x90092),x90093),f789(f789(f132(x90091),x90094),x90095))+~E(f789(f789(f164(x90091),f789(f185(f864(x90091)),x90094)),x90092),x90094)+~E(f789(f789(f164(x90091),f789(f185(f864(x90091)),x90092)),x90094),x90092)+~E(x90095,f789(f789(f132(x90091),f789(f789(f135(x90091),f789(f185(f864(x90091)),x90094)),x90092)),x90093))+~E(f789(f789(f132(x90091),f789(f789(f135(x90091),f789(f185(f864(x90091)),x90092)),x90094)),x90095),x90093)
% 21.40/21.38 [9380]~P101(x93802)+E(f789(f789(f144(x93801,x93802,x93803),x93804),f158(x93801,x93804,x93805)),x93805)+~P18(x93802,f789(f789(f150(x93801,x93802),x93803),x93805))+~P1(f789(f789(f342(x93801),x93804),f789(f163(x93801),x93805)))+~E(f789(f137(x93801),f789(f133(x93801,f789(f789(f10(x93802,a856,x93801),f789(a338,f789(x93803,x93804))),x93803)),x93805)),x93804)
% 21.40/21.38 [9702]~P66(x97021)+~P1(f789(f75(x97021,x97021,f90(x97021),x97022,x97023),x97025))+~P1(f789(f789(f342(x97021),x97024),x97023))+P1(f789(f789(f342(x97021),x97022),x97023))+P1(f789(f75(x97021,x97021,f90(x97021),x97024,f789(f789(f310(x97021),x97022),f789(f789(f3(f870(x97021,a856)),x97023),f789(f789(f310(x97021),x97024),f184(f870(x97021,a856)))))),x97025))
% 21.40/21.38 [7189]E(x71891,x71892)+~P29(x71894,x71895,x71893,x71896)+~E(f789(x71893,x71891),f789(x71893,x71892))+~P1(f789(f789(f342(x71894),x71892),x71896))+~P1(f789(f789(f342(x71894),x71891),x71896))
% 21.40/21.38 [7190]E(x71901,x71902)+~P29(x71904,x71905,x71903,x71906)+~E(f789(x71903,x71901),f789(x71903,x71902))+~P1(f789(f789(f342(x71904),x71902),x71906))+~P1(f789(f789(f342(x71904),x71901),x71906))
% 21.40/21.38 [7191]E(x71911,x71912)+~P29(x71914,x71915,x71913,x71916)+~E(f789(x71913,x71911),f789(x71913,x71912))+~P1(f789(f789(f342(x71914),x71912),x71916))+~P1(f789(f789(f342(x71914),x71911),x71916))
% 21.40/21.38 [7192]E(x71921,x71922)+~P29(x71924,x71925,x71923,x71926)+~E(f789(x71923,x71921),f789(x71923,x71922))+~P1(f789(f789(f342(x71924),x71922),x71926))+~P1(f789(f789(f342(x71924),x71921),x71926))
% 21.40/21.38 [6436]~P137(x64364)+E(x64361,x64362)+~E(x64365,x64366)+E(x64363,f2(x64364))+~E(f789(f789(f89(x64364),x64365),f789(f789(f90(x64364),x64363),x64361)),f789(f789(f89(x64364),x64366),f789(f789(f90(x64364),x64363),x64362)))
% 21.40/21.38 [7508]~P101(x75081)+~P9(x75081)+~P1(f789(f789(f241(x75081),x75082),f789(x75085,x75086)))+~P1(f789(f789(f342(x75083),x75086),x75084))+P1(f789(f789(f241(x75081),x75082),f789(f789(f53(x75083,x75081),x75084),x75085)))
% 21.40/21.38 [9866]~P70(x98666)+~P1(f789(f70(x98661),x98665))+P1(f789(f789(f342(x98661),f640(x98662,x98663,x98664,x98665,x98661,x98666)),x98664))+P1(f789(f789(f287(x98666),f789(f789(f11(x98661,x98666),x98663),x98664)),f789(f789(f11(x98661,x98666),x98662),x98665)))+~P1(f789(f789(f240(f870(x98661,a856)),x98664),x98665))
% 21.40/21.38 [9991]~P70(x99911)+~P1(f789(f70(x99912),x99916))+~P1(f789(f789(f287(x99911),f789(x99913,f640(x99915,x99913,x99914,x99916,x99912,x99911))),f789(x99915,f640(x99915,x99913,x99914,x99916,x99912,x99911))))+P1(f789(f789(f287(x99911),f789(f789(f11(x99912,x99911),x99913),x99914)),f789(f789(f11(x99912,x99911),x99915),x99916)))+~P1(f789(f789(f240(f870(x99912,a856)),x99914),x99916))
% 21.40/21.38 [8185]~P101(x81851)+~P9(x81851)+~P1(f789(f789(f241(x81851),f789(x81854,x81856)),x81855))+~P1(f789(f789(f342(x81852),x81856),x81853))+P1(f789(f789(f241(x81851),f789(f789(f54(x81852,x81851),x81853),x81854)),x81855))
% 21.40/21.38 [8443]~P23(x84432,x84435,x84436,x84431)+~P1(f789(f70(x84432),x84434))+~P1(f789(f70(x84432),x84433))+~E(f789(f789(f111(f870(x84432,a856)),x84433),x84434),f184(f870(x84432,a856)))+E(f789(x84431,f789(f789(f110(f870(x84432,a856)),x84433),x84434)),f789(f82(x84435,x84435,x84435,f789(x84431,x84433)),f789(x84431,x84434)))
% 21.40/21.38 [9097]~P112(x90971)+~P109(x90971)+~P1(f789(f789(f287(x90971),x90972),x90975))+~P1(f789(f789(f287(x90971),x90972),f789(f789(f89(x90971),x90973),x90976)))+P1(f789(f789(f287(x90971),x90972),f789(f789(f89(x90971),f789(f789(f3(x90971),x90973),f789(f789(f90(x90971),x90974),x90975))),x90976)))
% 21.40/21.38 [9098]~P112(x90981)+~P109(x90981)+~P1(f789(f789(f287(x90981),x90982),x90985))+~P1(f789(f789(f287(x90981),x90982),f789(f789(f89(x90981),x90983),x90986)))+P1(f789(f789(f287(x90981),x90982),f789(f789(f89(x90981),f789(f789(f3(x90981),x90983),f789(f789(f90(x90981),x90984),x90985))),x90986)))
% 21.40/21.38 [9255]~P112(x92551)+~P109(x92551)+~P1(f789(f789(f287(x92551),x92552),x92555))+P1(f789(f789(f287(x92551),x92552),f789(f789(f89(x92551),x92553),x92554)))+~P1(f789(f789(f287(x92551),x92552),f789(f789(f89(x92551),f789(f789(f3(x92551),x92553),f789(f789(f90(x92551),x92556),x92555))),x92554)))
% 21.40/21.38 [9256]~P112(x92561)+~P109(x92561)+~P1(f789(f789(f287(x92561),x92562),x92565))+P1(f789(f789(f287(x92561),x92562),f789(f789(f89(x92561),x92563),x92564)))+~P1(f789(f789(f287(x92561),x92562),f789(f789(f89(x92561),f789(f789(f3(x92561),x92563),f789(f789(f90(x92561),x92566),x92565))),x92564)))
% 21.40/21.38 [8736]E(x87361,x87362)+~P55(x87364,x87365,x87366,x87363,x87367)+~E(f789(x87363,x87361),f789(x87363,x87362))+~P1(f789(f789(f342(x87365),x87362),x87367))+~P1(f789(f789(f342(x87365),x87361),x87367))
% 21.40/21.38 [10000]~P12(x100001,x100007,x100006)+~P16(x100001,f870(x100005,a856),x100006,x100004)+P1(f789(f789(f342(x100001),f438(x100002,x100003,x100004,x100005,x100006,x100007,x100001)),x100007))+~P1(f789(f789(f342(f870(x100001,a856)),x100003),f789(f789(f68(x100001),x100007),x100006)))+P1(f789(f789(f342(f870(x100005,a856)),f789(f789(f53(x100001,f870(x100005,a856)),x100003),x100004)),x100002))
% 21.40/21.38 [10048]~P12(x100482,x100486,x100487)+~P16(x100482,f870(x100481,a856),x100487,x100484)+~P1(f789(f789(f342(f870(x100482,a856)),x100483),f789(f789(f68(x100482),x100486),x100487)))+~P1(f789(f789(f342(f870(x100481,a856)),f789(x100484,f438(x100485,x100483,x100484,x100481,x100487,x100486,x100482))),x100485))+P1(f789(f789(f342(f870(x100481,a856)),f789(f789(f53(x100482,f870(x100481,a856)),x100483),x100484)),x100485))
% 21.40/21.38 [8353]~P69(x83532)+~P29(x83531,x83535,x83538,x83534)+~E(x83533,f789(f82(x83535,x83532,x83531,x83536),x83538))+~E(x83537,f789(f311(x83531,x83535,x83538),x83534))+E(f789(f789(f11(x83531,x83532),x83533),x83534),f789(f789(f11(x83535,x83532),x83536),x83537))
% 21.40/21.38 [10051]~P69(x100512)+~P29(x100515,x100511,x100518,x100517)+~E(f789(x100516,f542(x100513,x100516,x100514,x100517,x100518,x100511,x100515,x100512)),f789(f789(f82(x100511,x100512,x100515,x100513),x100518),f542(x100513,x100516,x100514,x100517,x100518,x100511,x100515,x100512)))+~E(x100514,f789(f311(x100515,x100511,x100518),x100517))+E(f789(f789(f11(x100511,x100512),x100513),x100514),f789(f789(f11(x100515,x100512),x100516),x100517))
% 21.40/21.38 [10054]~P69(x100542)+~P29(x100541,x100545,x100548,x100544)+~E(x100547,f789(f311(x100541,x100545,x100548),x100544))+E(f789(f789(f11(x100541,x100542),x100543),x100544),f789(f789(f11(x100545,x100542),x100546),x100547))+P1(f789(f789(f342(x100541),f542(x100546,x100543,x100547,x100544,x100548,x100545,x100541,x100542)),x100544))
% 21.40/21.38 [10055]~P4(x100552)+~P29(x100551,x100555,x100558,x100554)+~E(x100557,f789(f311(x100551,x100555,x100558),x100554))+E(f789(f789(f8(x100551,x100552),x100553),x100554),f789(f789(f8(x100555,x100552),x100556),x100557))+P1(f789(f789(f342(x100551),f642(x100556,x100553,x100557,x100554,x100558,x100555,x100551,x100552)),x100554))
% 21.40/21.38 [10060]~P4(x100602)+~P29(x100605,x100601,x100608,x100607)+~E(x100604,f789(f311(x100605,x100601,x100608),x100607))+~E(f789(x100606,f642(x100603,x100606,x100604,x100607,x100608,x100601,x100605,x100602)),f789(x100603,f789(x100608,f642(x100603,x100606,x100604,x100607,x100608,x100601,x100605,x100602))))+E(f789(f789(f8(x100601,x100602),x100603),x100604),f789(f789(f8(x100605,x100602),x100606),x100607))
% 21.40/21.38 [9445]~E(f789(f185(f864(x94452)),x94455),f789(f185(f864(x94451)),x94453))+~E(f789(f185(f864(x94452)),x94454),f789(f185(f864(x94451)),x94453))+~E(f789(f789(f789(f81(x94451,f867(x94452)),f170(x94451,x94452,f789(f789(f171(x94451,x94452),x94453),x94454))),x94456),f789(f234(x94452),x94457)),f789(f789(f789(f81(x94451,f867(x94452)),f170(x94451,x94452,f789(f789(f171(x94451,x94452),x94453),x94455))),x94456),f789(f234(x94452),x94458)))+E(f170(x94451,x94452,f789(f789(f171(x94451,x94452),x94453),x94454)),f170(x94451,x94452,f789(f789(f171(x94451,x94452),x94453),x94455)))+P1(f789(f789(f342(x94451),x94456),f789(f163(x94451),x94453)))
% 21.40/21.38 [9543]~P27(x95436,x95432,x95435,x95437,x95438,x95431)+~P1(f789(f70(x95432),x95434))+~P1(f789(f70(x95432),x95433))+~E(f789(f789(f111(f870(x95432,a856)),x95433),x95434),f184(f870(x95432,a856)))+E(f789(x95431,f789(f789(f110(f870(x95432,a856)),x95433),x95434)),f789(f789(x95435,f789(x95431,x95433)),f789(x95431,x95434)))
% 21.40/21.38 [9943]~P27(x99438,x99432,x99435,x99437,x99436,x99431)+~E(f789(x99436,f587(x99434,x99433,x99431,x99436,x99437,x99435,x99432)),x99437)+~P1(f789(f70(x99432),x99433))+~P1(f789(f70(x99432),x99434))+E(f789(x99431,f789(f789(f110(f870(x99432,a856)),x99433),x99434)),f789(f789(x99435,f789(x99431,x99433)),f789(x99431,x99434)))
% 21.40/21.38 [10006]~P27(x100068,x100062,x100065,x100067,x100066,x100061)+~P1(f789(f70(x100062),x100063))+~P1(f789(f70(x100062),x100064))+E(f789(x100061,f789(f789(f110(f870(x100062,a856)),x100063),x100064)),f789(f789(x100065,f789(x100061,x100063)),f789(x100061,x100064)))+P1(f789(f789(f342(x100062),f587(x100064,x100063,x100061,x100066,x100067,x100065,x100062)),f789(f789(f111(f870(x100062,a856)),x100063),x100064)))
% 21.40/21.38 [9693]~P12(x96934,x96938,x96935)+~P12(x96931,x96939,x96933)+~P17(x96931,x96934,f870(x96932,a856),x96933,x96935,x96937)+P16(x96931,f870(x96932,a856),x96933,f789(f789(f10(f870(x96934,f870(x96932,a856)),f870(x96932,a856),x96931),f789(f53(x96934,f870(x96932,a856)),f789(f285(x96934,x96934,x96935),f789(f789(f310(x96934),x96936),f184(f870(x96934,a856)))))),x96937))+~P1(f789(f789(f342(x96934),x96936),x96938))
% 21.40/21.38 [4979]~P122(x49792)+~P123(x49792)+~P138(x49792)+~P106(x49792)+E(x49791,f2(x49792))+~E(f789(f789(f250(x49792),x49791),x49793),f2(x49792))
% 21.40/21.38 [4980]~P122(x49802)+~P123(x49802)+~P138(x49802)+~P106(x49802)+~E(x49801,f2(a863))+~E(f789(f789(f250(x49802),x49803),x49801),f2(x49802))
% 21.40/21.38 [6416]~P82(x64161)+~E(x64163,f2(x64161))+~E(x64162,f2(x64161))+E(f789(f789(f89(x64161),x64162),x64163),f2(x64161))+~P1(f789(f789(f240(x64161),f2(x64161)),x64163))+~P1(f789(f789(f240(x64161),f2(x64161)),x64162))
% 21.40/21.38 [8782]E(x87821,f2(a863))+~E(x87822,f789(f789(f89(a863),f789(f789(f90(a863),f789(f248(a863,a863),x87823)),x87821)),f789(f258(a863,a863),x87823)))+P1(f789(f62(x87822,x87821),x87823))+~P1(f789(f789(f240(a863),f789(f258(a863,a863),x87823)),f2(a863)))+P1(f789(f789(f241(a863),f2(a863)),x87821))+~P1(f789(f789(f241(a863),x87821),f789(f258(a863,a863),x87823)))
% 21.40/21.38 [8794]~E(f789(f248(a863,a863),x87943),f2(a863))+~E(x87941,f789(f789(f89(a863),f789(f789(f90(a863),f789(f248(a863,a863),x87943)),x87942)),f789(f258(a863,a863),x87943)))+P1(f789(f62(x87941,x87942),x87943))+~P1(f789(f789(f240(a863),f789(f258(a863,a863),x87943)),f2(a863)))+P1(f789(f789(f241(a863),f2(a863)),x87942))+~P1(f789(f789(f241(a863),x87942),f789(f258(a863,a863),x87943)))
% 21.40/21.38 [8801]E(x88011,f2(a863))+~E(x88012,f789(f789(f89(a863),f789(f789(f90(a863),f789(f248(a863,a863),x88013)),x88011)),f789(f258(a863,a863),x88013)))+P1(f789(f62(x88012,x88011),x88013))+~P1(f789(f789(f241(a863),f2(a863)),x88011))+~P1(f789(f789(f240(a863),f2(a863)),f789(f258(a863,a863),x88013)))+~P1(f789(f789(f241(a863),f789(f258(a863,a863),x88013)),x88011))
% 21.40/21.38 [8815]~E(f789(f248(a863,a863),x88153),f2(a863))+~E(x88151,f789(f789(f89(a863),f789(f789(f90(a863),f789(f248(a863,a863),x88153)),x88152)),f789(f258(a863,a863),x88153)))+P1(f789(f62(x88151,x88152),x88153))+~P1(f789(f789(f241(a863),f2(a863)),x88152))+~P1(f789(f789(f240(a863),f2(a863)),f789(f258(a863,a863),x88153)))+~P1(f789(f789(f241(a863),f789(f258(a863,a863),x88153)),x88152))
% 21.40/21.38 [6814]~P95(x68142)+E(x68141,f184(f870(x68142,a856)))+E(x68143,f184(f870(x68142,a856)))+~P1(f789(f70(x68142),x68141))+~P1(f789(f70(x68142),x68143))+E(f12(x68142,f789(f789(f110(f870(x68142,a856)),x68143),x68141)),f789(f789(f111(x68142),f12(x68142,x68143)),f12(x68142,x68141)))
% 21.40/21.38 [6815]~P95(x68152)+E(x68151,f184(f870(x68152,a856)))+E(x68153,f184(f870(x68152,a856)))+~P1(f789(f70(x68152),x68151))+~P1(f789(f70(x68152),x68153))+E(f15(x68152,f789(f789(f110(f870(x68152,a856)),x68153),x68151)),f789(f789(f110(x68152),f15(x68152,x68153)),f15(x68152,x68151)))
% 21.40/21.38 [6816]~P101(x68162)+E(x68161,f184(f870(x68162,a856)))+E(x68163,f184(f870(x68162,a856)))+~P1(f789(f70(x68162),x68161))+~P1(f789(f70(x68162),x68163))+E(f16(x68162,f789(f789(f110(f870(x68162,a856)),x68163),x68161)),f789(f789(f239(x68162),f16(x68162,x68163)),f16(x68162,x68161)))
% 21.40/21.38 [6817]~P101(x68172)+E(x68171,f184(f870(x68172,a856)))+E(x68173,f184(f870(x68172,a856)))+~P1(f789(f70(x68172),x68171))+~P1(f789(f70(x68172),x68173))+E(f17(x68172,f789(f789(f110(f870(x68172,a856)),x68173),x68171)),f789(f789(f244(x68172),f17(x68172,x68173)),f17(x68172,x68171)))
% 21.40/21.38 [7480]~P91(x74802)+E(x74801,f184(f870(x74802,a856)))+E(x74803,f184(f870(x74802,a856)))+~P1(f789(f70(x74802),x74801))+~P1(f789(f70(x74802),x74803))+E(f789(f789(f90(x74802),f789(f72(x74802,f90(x74802)),x74803)),f789(f72(x74802,f90(x74802)),x74801)),f789(f72(x74802,f90(x74802)),f789(f789(f110(f870(x74802,a856)),x74803),x74801)))
% 21.40/21.38 [7645]~P101(x76452)+E(x76451,f184(f870(x76452,a856)))+E(x76453,f184(f870(x76452,a856)))+~P1(f789(f70(x76452),x76451))+~P1(f789(f70(x76452),x76453))+E(f789(f789(f239(x76452),f13(x76452,f239(x76452),x76453)),f13(x76452,f239(x76452),x76451)),f13(x76452,f239(x76452),f789(f789(f110(f870(x76452,a856)),x76453),x76451)))
% 21.40/21.38 [7646]~P101(x76462)+E(x76461,f184(f870(x76462,a856)))+E(x76463,f184(f870(x76462,a856)))+~P1(f789(f70(x76462),x76461))+~P1(f789(f70(x76462),x76463))+E(f789(f789(f244(x76462),f14(x76462,f244(x76462),x76463)),f14(x76462,f244(x76462),x76461)),f14(x76462,f244(x76462),f789(f789(f110(f870(x76462,a856)),x76463),x76461)))
% 21.40/21.38 [8651]~P1(f789(x86511,x86513))+P1(f789(x86511,f498(x86511,x86512)))+P1(f789(x86511,f484(x86511,x86512)))+~P1(f789(f789(f241(a1),f2(a1)),x86512))+~P1(f789(f789(f342(a1),x86513),f303(a1,f87(a1),x86512)))+P1(f789(x86511,f789(f789(f3(a1),f484(x86511,x86512)),f789(f789(f90(a1),f497(x86511,x86512)),x86512))))
% 21.40/21.38 [8915]~P1(f789(x89151,x89153))+~P1(f789(x89151,f484(x89151,x89152)))+P1(f789(x89151,f498(x89151,x89152)))+~P1(f789(f789(f241(a1),f2(a1)),x89152))+~P1(f789(f789(f342(a1),x89153),f303(a1,f87(a1),x89152)))+~P1(f789(x89151,f789(f789(f3(a1),f484(x89151,x89152)),f789(f789(f90(a1),f497(x89151,x89152)),x89152))))
% 21.40/21.38 [10081]~P96(x100812)+E(x100811,f184(f870(x100812,a856)))+E(x100813,f184(f870(x100812,a856)))+~P1(f789(f70(x100812),x100811))+~P1(f789(f70(x100812),x100813))+E(f12(x100812,f789(f264(x100812),f789(f789(f10(f870(x100812,a856),a856,x100812),f96(x100812)),f789(f789(f10(f870(x100812,f870(x100812,a856)),f870(x100812,a856),x100812),f789(f10(f870(x100812,a856),a856,x100812),f96(x100812))),f789(f789(f9(x100812,f870(x100812,f870(x100812,a856)),f870(x100812,f870(x100812,a856))),f789(f789(f10(f870(x100812,f870(f870(x100812,a856),f870(x100812,a856))),f870(f870(x100812,f870(x100812,a856)),f870(x100812,f870(x100812,a856))),x100812),f20(x100812,f870(x100812,a856),f870(x100812,a856))),f789(f789(f10(f870(x100812,f870(x100812,f870(a856,a856))),f870(x100812,f870(f870(x100812,a856),f870(x100812,a856))),x100812),f789(f10(f870(x100812,f870(a856,a856)),f870(f870(x100812,a856),f870(x100812,a856)),x100812),f20(x100812,a856,a856))),f789(f789(f10(f870(x100812,f870(x100812,a856)),f870(x100812,f870(x100812,f870(a856,a856))),x100812),f789(f10(f870(x100812,a856),f870(x100812,f870(a856,a856)),x100812),f789(f10(a856,f870(a856,a856),x100812),a339))),f789(f789(f9(x100812,f870(x100812,f870(x100812,x100812)),f870(x100812,f870(x100812,a856))),f789(f789(f10(f870(f870(x100812,x100812),f870(x100812,a856)),f870(f870(x100812,f870(x100812,x100812)),f870(x100812,f870(x100812,a856))),x100812),f10(f870(x100812,x100812),f870(x100812,a856),x100812)),f789(f789(f10(f870(x100812,a856),f870(f870(x100812,x100812),f870(x100812,a856)),x100812),f10(x100812,a856,x100812)),a338))),f110(x100812)))))),f789(f789(f9(x100812,f870(x100812,a856),f870(x100812,a856)),f789(f789(f10(f870(a856,a856),f870(f870(x100812,a856),f870(x100812,a856)),x100812),f10(a856,a856,x100812)),f789(f789(f10(a856,f870(a856,a856),x100812),a339),f789(f789(f9(x100812,f870(x100812,a856),a856),f342(x100812)),x100813)))),f789(f789(f9(x100812,f870(x100812,a856),a856),f342(x100812)),x100811))))))),f789(f789(f110(x100812),f12(x100812,x100813)),f12(x100812,x100811)))
% 21.40/21.38 [10082]~P96(x100822)+E(x100821,f184(f870(x100822,a856)))+E(x100823,f184(f870(x100822,a856)))+~P1(f789(f70(x100822),x100821))+~P1(f789(f70(x100822),x100823))+E(f15(x100822,f789(f264(x100822),f789(f789(f10(f870(x100822,a856),a856,x100822),f96(x100822)),f789(f789(f10(f870(x100822,f870(x100822,a856)),f870(x100822,a856),x100822),f789(f10(f870(x100822,a856),a856,x100822),f96(x100822))),f789(f789(f9(x100822,f870(x100822,f870(x100822,a856)),f870(x100822,f870(x100822,a856))),f789(f789(f10(f870(x100822,f870(f870(x100822,a856),f870(x100822,a856))),f870(f870(x100822,f870(x100822,a856)),f870(x100822,f870(x100822,a856))),x100822),f20(x100822,f870(x100822,a856),f870(x100822,a856))),f789(f789(f10(f870(x100822,f870(x100822,f870(a856,a856))),f870(x100822,f870(f870(x100822,a856),f870(x100822,a856))),x100822),f789(f10(f870(x100822,f870(a856,a856)),f870(f870(x100822,a856),f870(x100822,a856)),x100822),f20(x100822,a856,a856))),f789(f789(f10(f870(x100822,f870(x100822,a856)),f870(x100822,f870(x100822,f870(a856,a856))),x100822),f789(f10(f870(x100822,a856),f870(x100822,f870(a856,a856)),x100822),f789(f10(a856,f870(a856,a856),x100822),a339))),f789(f789(f9(x100822,f870(x100822,f870(x100822,x100822)),f870(x100822,f870(x100822,a856))),f789(f789(f10(f870(f870(x100822,x100822),f870(x100822,a856)),f870(f870(x100822,f870(x100822,x100822)),f870(x100822,f870(x100822,a856))),x100822),f10(f870(x100822,x100822),f870(x100822,a856),x100822)),f789(f789(f10(f870(x100822,a856),f870(f870(x100822,x100822),f870(x100822,a856)),x100822),f10(x100822,a856,x100822)),a338))),f111(x100822)))))),f789(f789(f9(x100822,f870(x100822,a856),f870(x100822,a856)),f789(f789(f10(f870(a856,a856),f870(f870(x100822,a856),f870(x100822,a856)),x100822),f10(a856,a856,x100822)),f789(f789(f10(a856,f870(a856,a856),x100822),a339),f789(f789(f9(x100822,f870(x100822,a856),a856),f342(x100822)),x100823)))),f789(f789(f9(x100822,f870(x100822,a856),a856),f342(x100822)),x100821))))))),f789(f789(f111(x100822),f15(x100822,x100823)),f15(x100822,x100821)))
% 21.40/21.38 [10083]~P101(x100832)+E(x100831,f184(f870(x100832,a856)))+E(x100833,f184(f870(x100832,a856)))+~P1(f789(f70(x100832),x100831))+~P1(f789(f70(x100832),x100833))+E(f13(x100832,f239(x100832),f789(f264(x100832),f789(f789(f10(f870(x100832,a856),a856,x100832),f96(x100832)),f789(f789(f10(f870(x100832,f870(x100832,a856)),f870(x100832,a856),x100832),f789(f10(f870(x100832,a856),a856,x100832),f96(x100832))),f789(f789(f9(x100832,f870(x100832,f870(x100832,a856)),f870(x100832,f870(x100832,a856))),f789(f789(f10(f870(x100832,f870(f870(x100832,a856),f870(x100832,a856))),f870(f870(x100832,f870(x100832,a856)),f870(x100832,f870(x100832,a856))),x100832),f20(x100832,f870(x100832,a856),f870(x100832,a856))),f789(f789(f10(f870(x100832,f870(x100832,f870(a856,a856))),f870(x100832,f870(f870(x100832,a856),f870(x100832,a856))),x100832),f789(f10(f870(x100832,f870(a856,a856)),f870(f870(x100832,a856),f870(x100832,a856)),x100832),f20(x100832,a856,a856))),f789(f789(f10(f870(x100832,f870(x100832,a856)),f870(x100832,f870(x100832,f870(a856,a856))),x100832),f789(f10(f870(x100832,a856),f870(x100832,f870(a856,a856)),x100832),f789(f10(a856,f870(a856,a856),x100832),a339))),f789(f789(f9(x100832,f870(x100832,f870(x100832,x100832)),f870(x100832,f870(x100832,a856))),f789(f789(f10(f870(f870(x100832,x100832),f870(x100832,a856)),f870(f870(x100832,f870(x100832,x100832)),f870(x100832,f870(x100832,a856))),x100832),f10(f870(x100832,x100832),f870(x100832,a856),x100832)),f789(f789(f10(f870(x100832,a856),f870(f870(x100832,x100832),f870(x100832,a856)),x100832),f10(x100832,a856,x100832)),a338))),f244(x100832)))))),f789(f789(f9(x100832,f870(x100832,a856),f870(x100832,a856)),f789(f789(f10(f870(a856,a856),f870(f870(x100832,a856),f870(x100832,a856)),x100832),f10(a856,a856,x100832)),f789(f789(f10(a856,f870(a856,a856),x100832),a339),f789(f789(f9(x100832,f870(x100832,a856),a856),f342(x100832)),x100833)))),f789(f789(f9(x100832,f870(x100832,a856),a856),f342(x100832)),x100831))))))),f789(f789(f244(x100832),f13(x100832,f239(x100832),x100833)),f13(x100832,f239(x100832),x100831)))
% 21.40/21.38 [10084]~P101(x100842)+E(x100841,f184(f870(x100842,a856)))+E(x100843,f184(f870(x100842,a856)))+~P1(f789(f70(x100842),x100841))+~P1(f789(f70(x100842),x100843))+E(f14(x100842,f244(x100842),f789(f264(x100842),f789(f789(f10(f870(x100842,a856),a856,x100842),f96(x100842)),f789(f789(f10(f870(x100842,f870(x100842,a856)),f870(x100842,a856),x100842),f789(f10(f870(x100842,a856),a856,x100842),f96(x100842))),f789(f789(f9(x100842,f870(x100842,f870(x100842,a856)),f870(x100842,f870(x100842,a856))),f789(f789(f10(f870(x100842,f870(f870(x100842,a856),f870(x100842,a856))),f870(f870(x100842,f870(x100842,a856)),f870(x100842,f870(x100842,a856))),x100842),f20(x100842,f870(x100842,a856),f870(x100842,a856))),f789(f789(f10(f870(x100842,f870(x100842,f870(a856,a856))),f870(x100842,f870(f870(x100842,a856),f870(x100842,a856))),x100842),f789(f10(f870(x100842,f870(a856,a856)),f870(f870(x100842,a856),f870(x100842,a856)),x100842),f20(x100842,a856,a856))),f789(f789(f10(f870(x100842,f870(x100842,a856)),f870(x100842,f870(x100842,f870(a856,a856))),x100842),f789(f10(f870(x100842,a856),f870(x100842,f870(a856,a856)),x100842),f789(f10(a856,f870(a856,a856),x100842),a339))),f789(f789(f9(x100842,f870(x100842,f870(x100842,x100842)),f870(x100842,f870(x100842,a856))),f789(f789(f10(f870(f870(x100842,x100842),f870(x100842,a856)),f870(f870(x100842,f870(x100842,x100842)),f870(x100842,f870(x100842,a856))),x100842),f10(f870(x100842,x100842),f870(x100842,a856),x100842)),f789(f789(f10(f870(x100842,a856),f870(f870(x100842,x100842),f870(x100842,a856)),x100842),f10(x100842,a856,x100842)),a338))),f239(x100842)))))),f789(f789(f9(x100842,f870(x100842,a856),f870(x100842,a856)),f789(f789(f10(f870(a856,a856),f870(f870(x100842,a856),f870(x100842,a856)),x100842),f10(a856,a856,x100842)),f789(f789(f10(a856,f870(a856,a856),x100842),a339),f789(f789(f9(x100842,f870(x100842,a856),a856),f342(x100842)),x100843)))),f789(f789(f9(x100842,f870(x100842,a856),a856),f342(x100842)),x100841))))))),f789(f789(f239(x100842),f14(x100842,f244(x100842),x100843)),f14(x100842,f244(x100842),x100841)))
% 21.40/21.38 [7145]~P117(x71453)+E(x71451,x71452)+~E(f789(f789(f250(x71453),x71451),x71454),f789(f789(f250(x71453),x71452),x71454))+~P1(f789(f789(f240(x71453),f2(x71453)),x71452))+~P1(f789(f789(f240(x71453),f2(x71453)),x71451))+~P1(f789(f789(f241(a863),f2(a863)),x71454))
% 21.40/21.38 [7997]~P62(x79971)+~P89(x79971)+P1(f789(f789(f241(x79971),x79972),f2(x79971)))+P1(f789(f789(f241(x79971),f2(x79971)),x79972))+P1(f789(f789(f241(x79971),f789(f789(f291(x79971),x79973),x79972)),f789(f113(x79971),x79974)))+~P1(f789(f789(f241(x79971),f2(x79971)),f789(f113(x79971),x79974)))
% 21.40/21.38 [7998]~P62(x79981)+~P89(x79981)+P1(f789(f789(f241(x79981),x79982),f2(x79981)))+P1(f789(f789(f241(x79981),f2(x79981)),x79982))+P1(f789(f789(f240(x79981),f789(f789(f291(x79981),x79983),x79982)),f789(f113(x79981),x79984)))+~P1(f789(f789(f240(x79981),f2(x79981)),f789(f113(x79981),x79984)))
% 21.40/21.38 [8231]~P62(x82311)+~P89(x82311)+P1(f789(f789(f241(x82311),x82312),f2(x82311)))+P1(f789(f789(f241(x82311),f2(x82311)),x82312))+~P1(f789(f789(f241(x82311),f789(f789(f291(x82311),x82314),x82312)),f789(f113(x82311),x82313)))+P1(f789(f789(f241(x82311),f2(x82311)),f789(f113(x82311),x82313)))
% 21.40/21.38 [8232]~P62(x82321)+~P89(x82321)+P1(f789(f789(f241(x82321),x82322),f2(x82321)))+P1(f789(f789(f241(x82321),f2(x82321)),x82322))+~P1(f789(f789(f240(x82321),f789(f789(f291(x82321),x82324),x82322)),f789(f113(x82321),x82323)))+P1(f789(f789(f240(x82321),f2(x82321)),f789(f113(x82321),x82323)))
% 21.40/21.38 [7440]~P101(x74402)+E(x74401,f184(f870(x74402,a856)))+~P1(f789(f70(x74402),x74401))+~P1(f789(f789(f342(x74402),x74404),x74401))+P1(f789(f789(f241(x74402),x74403),x74404))+~P1(f789(f789(f241(x74402),x74403),f789(f72(x74402,f244(x74402)),x74401)))
% 21.40/21.38 [7441]~P101(x74412)+E(x74411,f184(f870(x74412,a856)))+~P1(f789(f70(x74412),x74411))+~P1(f789(f789(f342(x74412),x74414),x74411))+P1(f789(f789(f240(x74412),x74413),x74414))+~P1(f789(f789(f240(x74412),x74413),f789(f72(x74412,f244(x74412)),x74411)))
% 21.40/21.38 [7442]~P98(x74422)+E(x74421,f184(f870(x74422,a856)))+~P1(f789(f70(x74422),x74421))+~P1(f789(f789(f342(x74422),x74424),x74421))+P1(f789(f789(f240(x74422),x74423),x74424))+~P1(f789(f789(f240(x74422),x74423),f789(f72(x74422,f111(x74422)),x74421)))
% 21.40/21.38 [7948]~P62(x79481)+~P89(x79481)+P1(f789(f789(f241(x79481),f789(f113(x79481),x79482)),f2(x79481)))+~P1(f789(f789(f241(x79481),x79483),f2(x79481)))+P1(f789(f789(f241(x79481),f2(x79481)),f789(f113(x79481),x79482)))+P1(f789(f789(f241(x79481),x79483),f789(f789(f291(x79481),x79484),f789(f113(x79481),x79482))))
% 21.40/21.38 [7949]~P62(x79491)+~P89(x79491)+P1(f789(f789(f241(x79491),f789(f113(x79491),x79492)),f2(x79491)))+~P1(f789(f789(f240(x79491),x79493),f2(x79491)))+P1(f789(f789(f241(x79491),f2(x79491)),f789(f113(x79491),x79492)))+P1(f789(f789(f240(x79491),x79493),f789(f789(f291(x79491),x79494),f789(f113(x79491),x79492))))
% 21.40/21.38 [7959]~P62(x79591)+~P89(x79591)+P1(f789(f789(f241(x79591),x79592),f2(x79591)))+~P1(f789(f789(f241(x79591),f789(f113(x79591),x79593)),f2(x79591)))+P1(f789(f789(f241(x79591),f2(x79591)),x79592))+P1(f789(f789(f241(x79591),f789(f113(x79591),x79593)),f789(f789(f291(x79591),x79594),x79592)))
% 21.40/21.38 [7960]~P62(x79601)+~P89(x79601)+P1(f789(f789(f241(x79601),x79602),f2(x79601)))+~P1(f789(f789(f240(x79601),f789(f113(x79601),x79603)),f2(x79601)))+P1(f789(f789(f241(x79601),f2(x79601)),x79602))+P1(f789(f789(f240(x79601),f789(f113(x79601),x79603)),f789(f789(f291(x79601),x79604),x79602)))
% 21.40/21.38 [8106]~P62(x81061)+~P89(x81061)+P1(f789(f789(f241(x81061),x81062),f2(x81061)))+P1(f789(f789(f241(x81061),f789(f113(x81061),x81063)),f2(x81061)))+P1(f789(f789(f241(x81061),f2(x81061)),x81062))+~P1(f789(f789(f241(x81061),f789(f113(x81061),x81063)),f789(f789(f291(x81061),x81064),x81062)))
% 21.40/21.38 [8107]~P62(x81071)+~P89(x81071)+P1(f789(f789(f241(x81071),x81072),f2(x81071)))+P1(f789(f789(f240(x81071),f789(f113(x81071),x81073)),f2(x81071)))+P1(f789(f789(f241(x81071),f2(x81071)),x81072))+~P1(f789(f789(f240(x81071),f789(f113(x81071),x81073)),f789(f789(f291(x81071),x81074),x81072)))
% 21.40/21.38 [8179]~P62(x81791)+~P89(x81791)+P1(f789(f789(f241(x81791),x81792),f2(x81791)))+P1(f789(f789(f241(x81791),f789(f113(x81791),x81793)),f2(x81791)))+P1(f789(f789(f241(x81791),f2(x81791)),f789(f113(x81791),x81793)))+~P1(f789(f789(f241(x81791),x81792),f789(f789(f291(x81791),x81794),f789(f113(x81791),x81793))))
% 21.40/21.38 [8180]~P62(x81801)+~P89(x81801)+P1(f789(f789(f240(x81801),x81802),f2(x81801)))+P1(f789(f789(f241(x81801),f789(f113(x81801),x81803)),f2(x81801)))+P1(f789(f789(f241(x81801),f2(x81801)),f789(f113(x81801),x81803)))+~P1(f789(f789(f240(x81801),x81802),f789(f789(f291(x81801),x81804),f789(f113(x81801),x81803))))
% 21.40/21.38 [8372]~P62(x83721)+~P89(x83721)+~P1(f789(f789(f241(x83721),x83723),f2(x83721)))+P1(f789(f789(f241(x83721),f2(x83721)),f789(f113(x83721),x83722)))+~P1(f789(f789(f241(x83721),x83724),f789(f789(f90(x83721),x83723),f789(f113(x83721),x83722))))+P1(f789(f789(f241(x83721),x83723),f789(f789(f291(x83721),x83724),f789(f113(x83721),x83722))))
% 21.40/21.38 [8373]~P62(x83731)+~P89(x83731)+~P1(f789(f789(f240(x83731),x83733),f2(x83731)))+P1(f789(f789(f241(x83731),f2(x83731)),f789(f113(x83731),x83732)))+~P1(f789(f789(f240(x83731),x83734),f789(f789(f90(x83731),x83733),f789(f113(x83731),x83732))))+P1(f789(f789(f240(x83731),x83733),f789(f789(f291(x83731),x83734),f789(f113(x83731),x83732))))
% 21.40/21.38 [8541]~P62(x85411)+~P89(x85411)+~P1(f789(f789(f241(x85411),f789(f113(x85411),x85412)),f2(x85411)))+P1(f789(f789(f241(x85411),f2(x85411)),f789(f113(x85411),x85412)))+~P1(f789(f789(f241(x85411),x85414),f789(f789(f90(x85411),x85413),f789(f113(x85411),x85412))))+P1(f789(f789(f241(x85411),x85413),f789(f789(f291(x85411),x85414),f789(f113(x85411),x85412))))
% 21.40/21.38 [8542]~P62(x85421)+~P89(x85421)+~P1(f789(f789(f241(x85421),f789(f113(x85421),x85422)),f2(x85421)))+P1(f789(f789(f241(x85421),f2(x85421)),f789(f113(x85421),x85422)))+~P1(f789(f789(f241(x85421),x85424),f789(f789(f291(x85421),x85423),f789(f113(x85421),x85422))))+P1(f789(f789(f241(x85421),x85423),f789(f789(f90(x85421),x85424),f789(f113(x85421),x85422))))
% 21.40/21.38 [8543]~P62(x85431)+~P89(x85431)+~P1(f789(f789(f241(x85431),f789(f113(x85431),x85432)),f2(x85431)))+P1(f789(f789(f241(x85431),f2(x85431)),f789(f113(x85431),x85432)))+~P1(f789(f789(f240(x85431),x85434),f789(f789(f90(x85431),x85433),f789(f113(x85431),x85432))))+P1(f789(f789(f240(x85431),x85433),f789(f789(f291(x85431),x85434),f789(f113(x85431),x85432))))
% 21.40/21.38 [8544]~P62(x85441)+~P89(x85441)+~P1(f789(f789(f241(x85441),f789(f113(x85441),x85442)),f2(x85441)))+P1(f789(f789(f241(x85441),f2(x85441)),f789(f113(x85441),x85442)))+~P1(f789(f789(f240(x85441),x85444),f789(f789(f291(x85441),x85443),f789(f113(x85441),x85442))))+P1(f789(f789(f240(x85441),x85443),f789(f789(f90(x85441),x85444),f789(f113(x85441),x85442))))
% 21.40/21.38 [7336]E(x73361,f2(a1))+E(f789(f789(f50(a1),x73362),x73361),x73363)+~P1(f789(f789(f240(a1),x73364),f2(a1)))+~E(x73362,f789(f789(f89(a1),f789(f789(f90(a1),x73361),x73363)),x73364))+P1(f789(f789(f241(a1),f2(a1)),x73361))+~P1(f789(f789(f241(a1),x73361),x73364))
% 21.40/21.38 [7352]E(f59(a1,x73522,x73521),x73523)+E(x73521,f2(a1))+~P1(f789(f789(f240(a1),x73523),f2(a1)))+~E(x73522,f789(f789(f89(a1),f789(f789(f90(a1),x73521),x73524)),x73523))+P1(f789(f789(f241(a1),f2(a1)),x73521))+~P1(f789(f789(f241(a1),x73521),x73523))
% 21.40/21.38 [7479]E(x74791,f2(a1))+E(f789(f789(f50(a1),x74792),x74791),x74793)+~E(x74792,f789(f789(f89(a1),f789(f789(f90(a1),x74791),x74793)),x74794))+~P1(f789(f789(f241(a1),f2(a1)),x74791))+~P1(f789(f789(f240(a1),f2(a1)),x74794))+~P1(f789(f789(f241(a1),x74794),x74791))
% 21.40/21.38 [7504]E(f59(a1,x75042,x75041),x75043)+E(x75041,f2(a1))+~E(x75042,f789(f789(f89(a1),f789(f789(f90(a1),x75041),x75044)),x75043))+~P1(f789(f789(f241(a1),f2(a1)),x75041))+~P1(f789(f789(f240(a1),f2(a1)),x75043))+~P1(f789(f789(f241(a1),x75043),x75041))
% 21.40/21.38 [7649]~P101(x76492)+E(x76491,f184(f870(x76492,a856)))+~P1(f789(f70(x76492),x76491))+~P1(f789(f789(f241(x76492),x76494),x76493))+~P1(f789(f789(f342(x76492),x76494),x76491))+P1(f789(f789(f241(x76492),f789(f72(x76492,f244(x76492)),x76491)),x76493))
% 21.40/21.38 [7650]~P101(x76502)+E(x76501,f184(f870(x76502,a856)))+~P1(f789(f70(x76502),x76501))+~P1(f789(f789(f240(x76502),x76504),x76503))+~P1(f789(f789(f342(x76502),x76504),x76501))+P1(f789(f789(f240(x76502),f789(f72(x76502,f244(x76502)),x76501)),x76503))
% 21.40/21.38 [8209]~P1(f789(f789(f240(a1),x82094),f2(a1)))+~E(x82091,f789(f789(f89(a1),f789(f789(f90(a1),x82092),x82093)),x82094))+~P1(f789(f789(f240(a1),f2(a1)),x82094))+~P1(f789(f789(f241(a1),x82094),x82092))+~P1(f789(f789(f241(a1),x82092),x82094))+P1(f789(f63(x82091,x82092),f789(f789(f249(a1,a1),x82093),x82094)))
% 21.40/21.38 [8329]~P62(x83291)+~P89(x83291)+P1(f789(f789(f241(x83291),f789(f113(x83291),x83292)),f2(x83291)))+~P1(f789(f789(f241(x83291),f2(x83291)),x83294))+P1(f789(f789(f241(x83291),f2(x83291)),f789(f113(x83291),x83292)))+P1(f789(f789(f241(x83291),f789(f789(f291(x83291),x83293),f789(f113(x83291),x83292))),x83294))
% 21.40/21.38 [8330]~P62(x83301)+~P89(x83301)+P1(f789(f789(f241(x83301),f789(f113(x83301),x83302)),f2(x83301)))+~P1(f789(f789(f240(x83301),f2(x83301)),x83304))+P1(f789(f789(f241(x83301),f2(x83301)),f789(f113(x83301),x83302)))+P1(f789(f789(f240(x83301),f789(f789(f291(x83301),x83303),f789(f113(x83301),x83302))),x83304))
% 21.40/21.38 [8446]~P62(x84461)+~P89(x84461)+~P1(f789(f789(f241(x84461),x84462),f2(x84461)))+P1(f789(f789(f241(x84461),f2(x84461)),x84462))+~P1(f789(f789(f241(x84461),f789(f113(x84461),x84464)),f789(f789(f291(x84461),x84463),x84462)))+P1(f789(f789(f241(x84461),x84463),f789(f789(f90(x84461),f789(f113(x84461),x84464)),x84462)))
% 21.40/21.38 [8447]~P62(x84471)+~P89(x84471)+~P1(f789(f789(f241(x84471),x84472),f2(x84471)))+P1(f789(f789(f241(x84471),f2(x84471)),x84472))+~P1(f789(f789(f240(x84471),f789(f113(x84471),x84474)),f789(f789(f291(x84471),x84473),x84472)))+P1(f789(f789(f240(x84471),x84473),f789(f789(f90(x84471),f789(f113(x84471),x84474)),x84472)))
% 21.40/21.38 [8486]~P62(x84861)+~P89(x84861)+~P1(f789(f789(f241(x84861),x84862),f2(x84861)))+P1(f789(f789(f241(x84861),f2(x84861)),x84862))+P1(f789(f789(f241(x84861),f789(f113(x84861),x84863)),f789(f789(f291(x84861),x84864),x84862)))+~P1(f789(f789(f241(x84861),x84864),f789(f789(f90(x84861),f789(f113(x84861),x84863)),x84862)))
% 21.40/21.38 [8487]~P62(x84871)+~P89(x84871)+~P1(f789(f789(f241(x84871),x84872),f2(x84871)))+P1(f789(f789(f241(x84871),f2(x84871)),x84872))+P1(f789(f789(f240(x84871),f789(f113(x84871),x84873)),f789(f789(f291(x84871),x84874),x84872)))+~P1(f789(f789(f240(x84871),x84874),f789(f789(f90(x84871),f789(f113(x84871),x84873)),x84872)))
% 21.40/21.38 [8572]~P62(x85721)+~P89(x85721)+P1(f789(f789(f241(x85721),f789(f113(x85721),x85723)),f2(x85721)))+P1(f789(f789(f241(x85721),f2(x85721)),x85722))+P1(f789(f789(f241(x85721),f2(x85721)),f789(f113(x85721),x85723)))+~P1(f789(f789(f241(x85721),f789(f789(f291(x85721),x85724),f789(f113(x85721),x85723))),x85722))
% 21.40/21.38 [8573]~P62(x85731)+~P89(x85731)+P1(f789(f789(f241(x85731),f789(f113(x85731),x85733)),f2(x85731)))+P1(f789(f789(f240(x85731),f2(x85731)),x85732))+P1(f789(f789(f241(x85731),f2(x85731)),f789(f113(x85731),x85733)))+~P1(f789(f789(f240(x85731),f789(f789(f291(x85731),x85734),f789(f113(x85731),x85733))),x85732))
% 21.40/21.38 [8613]~P62(x86131)+~P89(x86131)+~P1(f789(f789(f241(x86131),f789(f113(x86131),x86133)),f2(x86131)))+P1(f789(f789(f241(x86131),f2(x86131)),x86132))+P1(f789(f789(f241(x86131),f789(f113(x86131),x86133)),f789(f789(f291(x86131),x86134),x86132)))+~P1(f789(f789(f241(x86131),x86134),f789(f789(f90(x86131),f789(f113(x86131),x86133)),x86132)))
% 21.40/21.38 [8614]~P62(x86141)+~P89(x86141)+~P1(f789(f789(f240(x86141),f789(f113(x86141),x86143)),f2(x86141)))+P1(f789(f789(f241(x86141),f2(x86141)),x86142))+P1(f789(f789(f240(x86141),f789(f113(x86141),x86143)),f789(f789(f291(x86141),x86144),x86142)))+~P1(f789(f789(f240(x86141),x86144),f789(f789(f90(x86141),f789(f113(x86141),x86143)),x86142)))
% 21.40/21.38 [8621]~P62(x86211)+~P89(x86211)+P1(f789(f789(f241(x86211),x86212),f2(x86211)))+P1(f789(f789(f241(x86211),f789(f789(f291(x86211),x86213),x86212)),f789(f113(x86211),x86214)))+~P1(f789(f789(f241(x86211),f2(x86211)),f789(f113(x86211),x86214)))+~P1(f789(f789(f241(x86211),x86213),f789(f789(f90(x86211),f789(f113(x86211),x86214)),x86212)))
% 21.40/21.38 [8622]~P62(x86221)+~P89(x86221)+P1(f789(f789(f241(x86221),x86222),f2(x86221)))+P1(f789(f789(f240(x86221),f789(f789(f291(x86221),x86223),x86222)),f789(f113(x86221),x86224)))+~P1(f789(f789(f240(x86221),f2(x86221)),f789(f113(x86221),x86224)))+~P1(f789(f789(f240(x86221),x86223),f789(f789(f90(x86221),f789(f113(x86221),x86224)),x86222)))
% 21.40/21.38 [8639]~P62(x86391)+~P89(x86391)+P1(f789(f789(f241(x86391),f789(f113(x86391),x86392)),f2(x86391)))+~P1(f789(f789(f241(x86391),f2(x86391)),x86394))+~P1(f789(f789(f241(x86391),x86393),f789(f789(f90(x86391),x86394),f789(f113(x86391),x86392))))+P1(f789(f789(f241(x86391),f789(f789(f291(x86391),x86393),f789(f113(x86391),x86392))),x86394))
% 21.40/21.38 [8640]~P62(x86401)+~P89(x86401)+P1(f789(f789(f241(x86401),f789(f113(x86401),x86402)),f2(x86401)))+~P1(f789(f789(f240(x86401),f2(x86401)),x86404))+~P1(f789(f789(f240(x86401),x86403),f789(f789(f90(x86401),x86404),f789(f113(x86401),x86402))))+P1(f789(f789(f240(x86401),f789(f789(f291(x86401),x86403),f789(f113(x86401),x86402))),x86404))
% 21.40/21.38 [8721]~P62(x87211)+~P89(x87211)+P1(f789(f789(f241(x87211),f789(f113(x87211),x87212)),f2(x87211)))+~P1(f789(f789(f241(x87211),x87213),f2(x87211)))+P1(f789(f789(f241(x87211),x87213),f789(f789(f291(x87211),x87214),f789(f113(x87211),x87212))))+~P1(f789(f789(f241(x87211),f789(f789(f90(x87211),x87213),f789(f113(x87211),x87212))),x87214))
% 21.40/21.38 [8722]~P62(x87221)+~P89(x87221)+P1(f789(f789(f241(x87221),f789(f113(x87221),x87222)),f2(x87221)))+~P1(f789(f789(f240(x87221),x87223),f2(x87221)))+P1(f789(f789(f240(x87221),x87223),f789(f789(f291(x87221),x87224),f789(f113(x87221),x87222))))+~P1(f789(f789(f240(x87221),f789(f789(f90(x87221),x87223),f789(f113(x87221),x87222))),x87224))
% 21.40/21.38 [8819]~P62(x88191)+~P89(x88191)+~P1(f789(f789(f241(x88191),f2(x88191)),x88194))+P1(f789(f789(f241(x88191),f2(x88191)),f789(f113(x88191),x88192)))+~P1(f789(f789(f241(x88191),f789(f789(f90(x88191),x88194),f789(f113(x88191),x88192))),x88193))+P1(f789(f789(f241(x88191),f789(f789(f291(x88191),x88193),f789(f113(x88191),x88192))),x88194))
% 21.40/21.38 [8820]~P62(x88201)+~P89(x88201)+~P1(f789(f789(f240(x88201),f2(x88201)),x88204))+P1(f789(f789(f241(x88201),f2(x88201)),f789(f113(x88201),x88202)))+~P1(f789(f789(f240(x88201),f789(f789(f90(x88201),x88204),f789(f113(x88201),x88202))),x88203))+P1(f789(f789(f240(x88201),f789(f789(f291(x88201),x88203),f789(f113(x88201),x88202))),x88204))
% 21.40/21.38 [8871]~P62(x88711)+~P89(x88711)+~P1(f789(f789(f241(x88711),x88712),f2(x88711)))+P1(f789(f789(f241(x88711),x88712),f789(f789(f291(x88711),x88713),f789(f113(x88711),x88714))))+~P1(f789(f789(f241(x88711),x88713),f789(f789(f90(x88711),x88712),f789(f113(x88711),x88714))))+~P1(f789(f789(f241(x88711),f789(f789(f90(x88711),x88712),f789(f113(x88711),x88714))),x88713))
% 21.40/21.38 [8872]~P62(x88721)+~P89(x88721)+~P1(f789(f789(f240(x88721),x88722),f2(x88721)))+P1(f789(f789(f240(x88721),x88722),f789(f789(f291(x88721),x88723),f789(f113(x88721),x88724))))+~P1(f789(f789(f240(x88721),x88723),f789(f789(f90(x88721),x88722),f789(f113(x88721),x88724))))+~P1(f789(f789(f240(x88721),f789(f789(f90(x88721),x88722),f789(f113(x88721),x88724))),x88723))
% 21.40/21.38 [8895]~P62(x88951)+~P89(x88951)+~P1(f789(f789(f241(x88951),f789(f113(x88951),x88952)),f2(x88951)))+P1(f789(f789(f241(x88951),f2(x88951)),f789(f113(x88951),x88952)))+~P1(f789(f789(f241(x88951),f789(f789(f291(x88951),x88954),f789(f113(x88951),x88952))),x88953))+P1(f789(f789(f241(x88951),f789(f789(f90(x88951),x88953),f789(f113(x88951),x88952))),x88954))
% 21.40/21.38 [8896]~P62(x88961)+~P89(x88961)+~P1(f789(f789(f241(x88961),f789(f113(x88961),x88962)),f2(x88961)))+P1(f789(f789(f241(x88961),f2(x88961)),f789(f113(x88961),x88962)))+~P1(f789(f789(f241(x88961),f789(f789(f90(x88961),x88964),f789(f113(x88961),x88962))),x88963))+P1(f789(f789(f241(x88961),f789(f789(f291(x88961),x88963),f789(f113(x88961),x88962))),x88964))
% 21.40/21.38 [8897]~P62(x88971)+~P89(x88971)+~P1(f789(f789(f241(x88971),f789(f113(x88971),x88972)),f2(x88971)))+P1(f789(f789(f241(x88971),f2(x88971)),f789(f113(x88971),x88972)))+~P1(f789(f789(f240(x88971),f789(f789(f291(x88971),x88974),f789(f113(x88971),x88972))),x88973))+P1(f789(f789(f240(x88971),f789(f789(f90(x88971),x88973),f789(f113(x88971),x88972))),x88974))
% 21.40/21.38 [8898]~P62(x88981)+~P89(x88981)+~P1(f789(f789(f241(x88981),f789(f113(x88981),x88982)),f2(x88981)))+P1(f789(f789(f241(x88981),f2(x88981)),f789(f113(x88981),x88982)))+~P1(f789(f789(f240(x88981),f789(f789(f90(x88981),x88984),f789(f113(x88981),x88982))),x88983))+P1(f789(f789(f240(x88981),f789(f789(f291(x88981),x88983),f789(f113(x88981),x88982))),x88984))
% 21.40/21.38 [8974]~P62(x89741)+~P89(x89741)+~P1(f789(f789(f241(x89741),f789(f113(x89741),x89744)),f2(x89741)))+P1(f789(f789(f241(x89741),x89742),f789(f789(f291(x89741),x89743),f789(f113(x89741),x89744))))+~P1(f789(f789(f241(x89741),x89743),f789(f789(f90(x89741),x89742),f789(f113(x89741),x89744))))+~P1(f789(f789(f241(x89741),f789(f789(f90(x89741),x89742),f789(f113(x89741),x89744))),x89743))
% 21.40/21.38 [8975]~P62(x89751)+~P89(x89751)+~P1(f789(f789(f241(x89751),f789(f113(x89751),x89754)),f2(x89751)))+P1(f789(f789(f240(x89751),x89752),f789(f789(f291(x89751),x89753),f789(f113(x89751),x89754))))+~P1(f789(f789(f240(x89751),x89753),f789(f789(f90(x89751),x89752),f789(f113(x89751),x89754))))+~P1(f789(f789(f240(x89751),f789(f789(f90(x89751),x89752),f789(f113(x89751),x89754))),x89753))
% 21.40/21.38 [9013]~P62(x90131)+~P89(x90131)+~P1(f789(f789(f241(x90131),f2(x90131)),x90134))+~P1(f789(f789(f241(x90131),x90132),f789(f789(f90(x90131),x90134),f789(f113(x90131),x90133))))+~P1(f789(f789(f241(x90131),f789(f789(f90(x90131),x90134),f789(f113(x90131),x90133))),x90132))+P1(f789(f789(f241(x90131),f789(f789(f291(x90131),x90132),f789(f113(x90131),x90133))),x90134))
% 21.40/21.38 [9014]~P62(x90141)+~P89(x90141)+~P1(f789(f789(f240(x90141),f2(x90141)),x90144))+~P1(f789(f789(f240(x90141),x90142),f789(f789(f90(x90141),x90144),f789(f113(x90141),x90143))))+~P1(f789(f789(f240(x90141),f789(f789(f90(x90141),x90144),f789(f113(x90141),x90143))),x90142))+P1(f789(f789(f240(x90141),f789(f789(f291(x90141),x90142),f789(f113(x90141),x90143))),x90144))
% 21.40/21.38 [9051]~P62(x90511)+~P89(x90511)+~P1(f789(f789(f241(x90511),f789(f113(x90511),x90513)),f2(x90511)))+~P1(f789(f789(f241(x90511),x90512),f789(f789(f90(x90511),x90514),f789(f113(x90511),x90513))))+~P1(f789(f789(f241(x90511),f789(f789(f90(x90511),x90514),f789(f113(x90511),x90513))),x90512))+P1(f789(f789(f241(x90511),f789(f789(f291(x90511),x90512),f789(f113(x90511),x90513))),x90514))
% 21.40/21.38 [9052]~P62(x90521)+~P89(x90521)+~P1(f789(f789(f241(x90521),f789(f113(x90521),x90523)),f2(x90521)))+~P1(f789(f789(f240(x90521),x90522),f789(f789(f90(x90521),x90524),f789(f113(x90521),x90523))))+~P1(f789(f789(f240(x90521),f789(f789(f90(x90521),x90524),f789(f113(x90521),x90523))),x90522))+P1(f789(f789(f240(x90521),f789(f789(f291(x90521),x90522),f789(f113(x90521),x90523))),x90524))
% 21.40/21.38 [8778]~P62(x87781)+~P89(x87781)+~P1(f789(f789(f241(x87781),x87782),f2(x87781)))+~P1(f789(f789(f241(x87781),f789(f789(f291(x87781),x87784),x87782)),f789(f113(x87781),x87783)))+P1(f789(f789(f241(x87781),f2(x87781)),x87782))+P1(f789(f789(f241(x87781),f789(f789(f90(x87781),f789(f113(x87781),x87783)),x87782)),x87784))
% 21.40/21.38 [8779]~P62(x87791)+~P89(x87791)+~P1(f789(f789(f241(x87791),x87792),f2(x87791)))+~P1(f789(f789(f240(x87791),f789(f789(f291(x87791),x87794),x87792)),f789(f113(x87791),x87793)))+P1(f789(f789(f241(x87791),f2(x87791)),x87792))+P1(f789(f789(f240(x87791),f789(f789(f90(x87791),f789(f113(x87791),x87793)),x87792)),x87794))
% 21.40/21.38 [8873]~P62(x88731)+~P89(x88731)+~P1(f789(f789(f241(x88731),x88732),f2(x88731)))+P1(f789(f789(f241(x88731),f2(x88731)),x88732))+P1(f789(f789(f241(x88731),f789(f789(f291(x88731),x88733),x88732)),f789(f113(x88731),x88734)))+~P1(f789(f789(f241(x88731),f789(f789(f90(x88731),f789(f113(x88731),x88734)),x88732)),x88733))
% 21.40/21.38 [8874]~P62(x88741)+~P89(x88741)+~P1(f789(f789(f241(x88741),x88742),f2(x88741)))+P1(f789(f789(f241(x88741),f2(x88741)),x88742))+P1(f789(f789(f240(x88741),f789(f789(f291(x88741),x88743),x88742)),f789(f113(x88741),x88744)))+~P1(f789(f789(f240(x88741),f789(f789(f90(x88741),f789(f113(x88741),x88744)),x88742)),x88743))
% 21.40/21.38 [8912]~P62(x89121)+~P89(x89121)+P1(f789(f789(f241(x89121),x89122),f2(x89121)))+~P1(f789(f789(f241(x89121),f789(f113(x89121),x89123)),f2(x89121)))+P1(f789(f789(f241(x89121),f789(f113(x89121),x89123)),f789(f789(f291(x89121),x89124),x89122)))+~P1(f789(f789(f241(x89121),f789(f789(f90(x89121),f789(f113(x89121),x89123)),x89122)),x89124))
% 21.40/21.38 [8913]~P62(x89131)+~P89(x89131)+P1(f789(f789(f241(x89131),x89132),f2(x89131)))+~P1(f789(f789(f240(x89131),f789(f113(x89131),x89133)),f2(x89131)))+P1(f789(f789(f240(x89131),f789(f113(x89131),x89133)),f789(f789(f291(x89131),x89134),x89132)))+~P1(f789(f789(f240(x89131),f789(f789(f90(x89131),f789(f113(x89131),x89133)),x89132)),x89134))
% 21.40/21.38 [8928]~P62(x89281)+~P89(x89281)+P1(f789(f789(f241(x89281),f2(x89281)),x89282))+P1(f789(f789(f241(x89281),f789(f789(f291(x89281),x89283),x89282)),f789(f113(x89281),x89284)))+~P1(f789(f789(f241(x89281),f2(x89281)),f789(f113(x89281),x89284)))+~P1(f789(f789(f241(x89281),f789(f789(f90(x89281),f789(f113(x89281),x89284)),x89282)),x89283))
% 21.40/21.38 [8929]~P62(x89291)+~P89(x89291)+P1(f789(f789(f241(x89291),f2(x89291)),x89292))+P1(f789(f789(f240(x89291),f789(f789(f291(x89291),x89293),x89292)),f789(f113(x89291),x89294)))+~P1(f789(f789(f240(x89291),f2(x89291)),f789(f113(x89291),x89294)))+~P1(f789(f789(f240(x89291),f789(f789(f90(x89291),f789(f113(x89291),x89294)),x89292)),x89293))
% 21.40/21.38 [9083]~P62(x90831)+~P89(x90831)+~P1(f789(f789(f241(x90831),x90834),f2(x90831)))+P1(f789(f789(f241(x90831),f789(f113(x90831),x90832)),f789(f789(f291(x90831),x90833),x90834)))+~P1(f789(f789(f241(x90831),x90833),f789(f789(f90(x90831),f789(f113(x90831),x90832)),x90834)))+~P1(f789(f789(f241(x90831),f789(f789(f90(x90831),f789(f113(x90831),x90832)),x90834)),x90833))
% 21.40/21.38 [9084]~P62(x90841)+~P89(x90841)+~P1(f789(f789(f241(x90841),x90844),f2(x90841)))+P1(f789(f789(f240(x90841),f789(f113(x90841),x90842)),f789(f789(f291(x90841),x90843),x90844)))+~P1(f789(f789(f240(x90841),x90843),f789(f789(f90(x90841),f789(f113(x90841),x90842)),x90844)))+~P1(f789(f789(f240(x90841),f789(f789(f90(x90841),f789(f113(x90841),x90842)),x90844)),x90843))
% 21.40/21.38 [9114]~P62(x91141)+~P89(x91141)+~P1(f789(f789(f241(x91141),x91143),f2(x91141)))+P1(f789(f789(f241(x91141),f789(f789(f291(x91141),x91142),x91143)),f789(f113(x91141),x91144)))+~P1(f789(f789(f241(x91141),x91142),f789(f789(f90(x91141),f789(f113(x91141),x91144)),x91143)))+~P1(f789(f789(f241(x91141),f789(f789(f90(x91141),f789(f113(x91141),x91144)),x91143)),x91142))
% 21.40/21.38 [9115]~P62(x91151)+~P89(x91151)+~P1(f789(f789(f241(x91151),x91153),f2(x91151)))+P1(f789(f789(f240(x91151),f789(f789(f291(x91151),x91152),x91153)),f789(f113(x91151),x91154)))+~P1(f789(f789(f240(x91151),x91152),f789(f789(f90(x91151),f789(f113(x91151),x91154)),x91153)))+~P1(f789(f789(f240(x91151),f789(f789(f90(x91151),f789(f113(x91151),x91154)),x91153)),x91152))
% 21.40/21.38 [9133]~P62(x91331)+~P89(x91331)+~P1(f789(f789(f241(x91331),f789(f113(x91331),x91332)),f2(x91331)))+P1(f789(f789(f241(x91331),f789(f113(x91331),x91332)),f789(f789(f291(x91331),x91333),x91334)))+~P1(f789(f789(f241(x91331),x91333),f789(f789(f90(x91331),f789(f113(x91331),x91332)),x91334)))+~P1(f789(f789(f241(x91331),f789(f789(f90(x91331),f789(f113(x91331),x91332)),x91334)),x91333))
% 21.40/21.38 [9134]~P62(x91341)+~P89(x91341)+~P1(f789(f789(f240(x91341),f789(f113(x91341),x91342)),f2(x91341)))+P1(f789(f789(f240(x91341),f789(f113(x91341),x91342)),f789(f789(f291(x91341),x91343),x91344)))+~P1(f789(f789(f240(x91341),x91343),f789(f789(f90(x91341),f789(f113(x91341),x91342)),x91344)))+~P1(f789(f789(f240(x91341),f789(f789(f90(x91341),f789(f113(x91341),x91342)),x91344)),x91343))
% 21.40/21.38 [9138]~P62(x91381)+~P89(x91381)+P1(f789(f789(f241(x91381),f789(f789(f291(x91381),x91382),x91383)),f789(f113(x91381),x91384)))+~P1(f789(f789(f241(x91381),f2(x91381)),f789(f113(x91381),x91384)))+~P1(f789(f789(f241(x91381),x91382),f789(f789(f90(x91381),f789(f113(x91381),x91384)),x91383)))+~P1(f789(f789(f241(x91381),f789(f789(f90(x91381),f789(f113(x91381),x91384)),x91383)),x91382))
% 21.40/21.38 [9139]~P62(x91391)+~P89(x91391)+P1(f789(f789(f240(x91391),f789(f789(f291(x91391),x91392),x91393)),f789(f113(x91391),x91394)))+~P1(f789(f789(f240(x91391),f2(x91391)),f789(f113(x91391),x91394)))+~P1(f789(f789(f240(x91391),x91392),f789(f789(f90(x91391),f789(f113(x91391),x91394)),x91393)))+~P1(f789(f789(f240(x91391),f789(f789(f90(x91391),f789(f113(x91391),x91394)),x91393)),x91392))
% 21.40/21.38 [5982]~P70(x59822)+~P122(x59822)+~E(f789(x59823,x59825),f2(x59822))+E(f789(f789(f11(x59821,x59822),x59823),x59824),f2(x59822))+~P1(f789(f70(x59821),x59824))+~P1(f789(f789(f342(x59821),x59825),x59824))
% 21.40/21.38 [8376]~P99(x83761)+P1(f789(f789(f241(f870(x83761,a856)),f303(x83761,x83762,x83763)),f303(x83761,x83764,x83765)))+~P1(f789(f789(f241(x83761),x83763),x83765))+~P1(f789(f789(f240(x83761),x83764),x83762))+~P1(f789(f789(f240(x83761),x83764),x83765))+~P1(f789(f789(f240(x83761),x83763),x83765))
% 21.40/21.38 [8377]~P99(x83771)+P1(f789(f789(f241(f870(x83771,a856)),f303(x83771,x83772,x83773)),f303(x83771,x83774,x83775)))+~P1(f789(f789(f241(x83771),x83774),x83772))+~P1(f789(f789(f240(x83771),x83773),x83775))+~P1(f789(f789(f240(x83771),x83774),x83775))+~P1(f789(f789(f240(x83771),x83774),x83772))
% 21.40/21.38 [9161]P57(x91612,x91613,x91614,x91611)+E(x91611,f184(f870(x91612,a856)))+~P1(f789(f70(x91612),x91614))+~P1(f789(f70(x91612),x91611))+~P1(f789(f789(x91613,f552(x91611,x91614,x91613,x91612)),x91615))+~P1(f789(f789(f342(x91612),x91615),x91611))
% 21.40/21.38 [9284]~E(x92843,x92845)+~P4(x92841)+~P69(x92841)+~P38(x92843)+E(f789(f789(f11(a1,x92841),x92842),x92843),f789(f789(f11(a1,x92841),x92844),x92845))+P1(f789(f789(f240(a1),f2(a1)),f535(x92842,x92844,x92843,x92845,x92841)))
% 21.40/21.38 [9285]~E(x92853,x92855)+~P4(x92851)+~P69(x92851)+~P38(x92853)+E(f789(f789(f8(a1,x92851),x92852),x92853),f789(f789(f8(a1,x92851),x92854),x92855))+P1(f789(f789(f240(a1),f2(a1)),f538(x92852,x92854,x92853,x92855,x92851)))
% 21.40/21.38 [9452]~E(x94525,x94523)+~P4(x94521)+~P69(x94521)+~P38(x94525)+~E(f789(x94522,f535(x94524,x94522,x94525,x94523,x94521)),f789(x94524,f535(x94524,x94522,x94525,x94523,x94521)))+E(f789(f789(f11(a1,x94521),x94522),x94523),f789(f789(f11(a1,x94521),x94524),x94525))
% 21.40/21.38 [9453]~E(x94535,x94533)+~P4(x94531)+~P69(x94531)+~P38(x94535)+~E(f789(x94532,f538(x94534,x94532,x94535,x94533,x94531)),f789(x94534,f538(x94534,x94532,x94535,x94533,x94531)))+E(f789(f789(f8(a1,x94531),x94532),x94533),f789(f789(f8(a1,x94531),x94534),x94535))
% 21.40/21.38 [9540]~P76(x95403)+E(f789(x95401,x95402),f2(x95403))+~E(f789(f789(f8(x95404,x95403),x95401),x95405),f2(x95403))+~P1(f789(f70(x95404),x95405))+P1(f789(f789(f342(x95404),f530(x95402,x95401,x95405,x95404,x95403)),x95405))+~P1(f789(f789(f342(x95404),x95402),x95405))
% 21.40/21.38 [9669]~P76(x96693)+E(f789(x96691,x96692),f2(x96693))+~E(f789(f789(f8(x96694,x96693),x96691),x96695),f2(x96693))+~P1(f789(f70(x96694),x96695))+~P1(f789(f789(f342(x96694),x96692),x96695))+~P1(f789(f789(f240(x96693),f2(x96693)),f789(x96691,f530(x96692,x96691,x96695,x96694,x96693))))
% 21.40/21.38 [8289]~P124(x82891)+~P1(f789(f789(f240(x82891),f2(x82891)),x82893))+~P1(f789(f789(f241(x82891),x82893),x82895))+~P1(f789(f789(f241(x82891),x82892),x82894))+~P1(f789(f789(f241(x82891),f2(x82891)),x82894))+P1(f789(f789(f241(x82891),f789(f789(f90(x82891),x82892),x82893)),f789(f789(f90(x82891),x82894),x82895)))
% 21.40/21.38 [8290]~P124(x82901)+~P1(f789(f789(f240(x82901),f2(x82901)),x82903))+~P1(f789(f789(f240(x82901),f2(x82901)),x82902))+~P1(f789(f789(f241(x82901),x82903),x82905))+~P1(f789(f789(f241(x82901),x82902),x82904))+P1(f789(f789(f241(x82901),f789(f789(f90(x82901),x82902),x82903)),f789(f789(f90(x82901),x82904),x82905)))
% 21.40/21.38 [8291]~P124(x82911)+~P1(f789(f789(f240(x82911),x82912),x82914))+~P1(f789(f789(f240(x82911),f2(x82911)),x82913))+~P1(f789(f789(f241(x82911),x82913),x82915))+~P1(f789(f789(f241(x82911),f2(x82911)),x82912))+P1(f789(f789(f241(x82911),f789(f789(f90(x82911),x82912),x82913)),f789(f789(f90(x82911),x82914),x82915)))
% 21.40/21.38 [8292]~P124(x82921)+~P1(f789(f789(f240(x82921),x82923),x82925))+~P1(f789(f789(f240(x82921),f2(x82921)),x82922))+~P1(f789(f789(f241(x82921),x82922),x82924))+~P1(f789(f789(f241(x82921),f2(x82921)),x82923))+P1(f789(f789(f241(x82921),f789(f789(f90(x82921),x82922),x82923)),f789(f789(f90(x82921),x82924),x82925)))
% 21.40/21.38 [8293]~P63(x82931)+~P1(f789(f789(f240(x82931),x82932),x82934))+~P1(f789(f789(f241(x82931),x82935),x82933))+~P1(f789(f789(f241(x82931),f2(x82931)),x82935))+~P1(f789(f789(f241(x82931),f2(x82931)),x82932))+P1(f789(f789(f241(x82931),f789(f789(f291(x82931),x82932),x82933)),f789(f789(f291(x82931),x82934),x82935)))
% 21.40/21.38 [8294]~P63(x82941)+~P1(f789(f789(f240(x82941),x82945),x82943))+~P1(f789(f789(f240(x82941),f2(x82941)),x82942))+~P1(f789(f789(f241(x82941),x82942),x82944))+~P1(f789(f789(f241(x82941),f2(x82941)),x82945))+P1(f789(f789(f241(x82941),f789(f789(f291(x82941),x82942),x82943)),f789(f789(f291(x82941),x82944),x82945)))
% 21.40/21.38 [8295]~P131(x82951)+~P1(f789(f789(f240(x82951),x82953),x82955))+~P1(f789(f789(f240(x82951),x82952),x82954))+~P1(f789(f789(f240(x82951),f2(x82951)),x82953))+~P1(f789(f789(f240(x82951),f2(x82951)),x82954))+P1(f789(f789(f240(x82951),f789(f789(f90(x82951),x82952),x82953)),f789(f789(f90(x82951),x82954),x82955)))
% 21.40/21.38 [8296]~P131(x82961)+~P1(f789(f789(f240(x82961),x82963),x82965))+~P1(f789(f789(f240(x82961),x82962),x82964))+~P1(f789(f789(f240(x82961),f2(x82961)),x82963))+~P1(f789(f789(f240(x82961),f2(x82961)),x82962))+P1(f789(f789(f240(x82961),f789(f789(f90(x82961),x82962),x82963)),f789(f789(f90(x82961),x82964),x82965)))
% 21.40/21.38 [8297]~P63(x82971)+~P1(f789(f789(f241(x82971),f2(x82971)),x82975))+~P1(f789(f789(f240(x82971),x82975),x82973))+~P1(f789(f789(f240(x82971),x82972),x82974))+~P1(f789(f789(f240(x82971),f2(x82971)),x82972))+P1(f789(f789(f240(x82971),f789(f789(f291(x82971),x82972),x82973)),f789(f789(f291(x82971),x82974),x82975)))
% 21.40/21.38 [9578]~P4(x95785)+~P81(x95785)+E(x95781,f184(f870(x95782,a856)))+~P1(f789(f70(x95782),x95781))+P1(f789(f789(f342(x95782),f536(x95783,x95784,x95781,x95782,x95785)),x95781))+P1(f789(f789(f241(x95785),f789(f789(f8(x95782,x95785),x95784),x95781)),f789(f789(f8(x95782,x95785),x95783),x95781)))
% 21.40/21.38 [9689]~P4(x96891)+~P79(x96891)+~P1(f789(f70(x96892),x96895))+~P1(f789(f789(f240(x96891),f2(x96891)),f789(x96893,f531(x96893,x96894,x96895,x96892,x96891))))+P1(f789(f789(f240(x96891),f789(f789(f8(x96892,x96891),x96893),x96894)),f789(f789(f8(x96892,x96891),x96893),x96895)))+~P1(f789(f789(f240(f870(x96892,a856)),x96894),x96895))
% 21.40/21.38 [9854]~P4(x98543)+~P81(x98543)+E(x98541,f184(f870(x98542,a856)))+~P1(f789(f70(x98542),x98541))+~P1(f789(f789(f241(x98543),f789(x98544,f536(x98545,x98544,x98541,x98542,x98543))),f789(x98545,f536(x98545,x98544,x98541,x98542,x98543))))+P1(f789(f789(f241(x98543),f789(f789(f8(x98542,x98543),x98544),x98541)),f789(f789(f8(x98542,x98543),x98545),x98541)))
% 21.40/21.38 [7005]~P21(x70052,x70055,x70054)+E(x70051,f184(f870(x70052,a856)))+E(x70053,f184(f870(x70052,a856)))+~P1(f789(f70(x70052),x70051))+~P1(f789(f70(x70052),x70053))+E(f789(x70054,f789(f789(f110(f870(x70052,a856)),x70053),x70051)),f789(f789(x70055,f789(x70054,x70053)),f789(x70054,x70051)))
% 21.40/21.38 [7614]~P141(x76141,x76143,x76144)+P1(f789(x76141,x76142))+~P1(f789(f789(f241(a1),x76144),f2(a1)))+~P1(f789(f789(f240(a1),x76145),f2(a1)))+~E(x76143,f789(f789(f89(a1),f789(f789(f90(a1),x76144),x76142)),x76145))+~P1(f789(f789(f241(a1),x76144),x76145))
% 21.40/21.38 [7615]~P140(x76151,x76153,x76154)+P1(f789(x76151,x76152))+~P1(f789(f789(f241(a1),x76154),f2(a1)))+~P1(f789(f789(f240(a1),x76152),f2(a1)))+~E(x76153,f789(f789(f89(a1),f789(f789(f90(a1),x76154),x76155)),x76152))+~P1(f789(f789(f241(a1),x76154),x76152))
% 21.40/21.38 [7658]~P141(x76581,x76583,x76584)+P1(f789(x76581,x76582))+~E(x76583,f789(f789(f89(a1),f789(f789(f90(a1),x76584),x76582)),x76585))+~P1(f789(f789(f241(a1),f2(a1)),x76584))+~P1(f789(f789(f240(a1),f2(a1)),x76585))+~P1(f789(f789(f241(a1),x76585),x76584))
% 21.40/21.38 [7659]~P140(x76591,x76593,x76594)+P1(f789(x76591,x76592))+~E(x76593,f789(f789(f89(a1),f789(f789(f90(a1),x76594),x76595)),x76592))+~P1(f789(f789(f241(a1),f2(a1)),x76594))+~P1(f789(f789(f240(a1),f2(a1)),x76592))+~P1(f789(f789(f241(a1),x76592),x76594))
% 21.40/21.38 [8580]P1(f789(f789(x85801,x85802),x85803))+~P1(f789(f789(x85801,f789(f789(f50(a1),x85804),x85805)),f59(a1,x85804,x85805)))+~P1(f789(f789(f241(a1),x85805),f2(a1)))+~P1(f789(f789(f240(a1),x85803),f2(a1)))+~E(x85804,f789(f789(f89(a1),f789(f789(f90(a1),x85805),x85802)),x85803))+~P1(f789(f789(f241(a1),x85805),x85803))
% 21.40/21.38 [8587]P1(f789(f789(x85871,x85872),x85873))+~P1(f789(f789(x85871,f789(f789(f50(a1),x85874),x85875)),f59(a1,x85874,x85875)))+~E(x85874,f789(f789(f89(a1),f789(f789(f90(a1),x85875),x85872)),x85873))+~P1(f789(f789(f241(a1),f2(a1)),x85875))+~P1(f789(f789(f240(a1),f2(a1)),x85873))+~P1(f789(f789(f241(a1),x85873),x85875))
% 21.40/21.38 [8807]E(x88071,x88072)+~P54(x88073,x88075,x88074)+~P1(f789(f789(f342(x88073),x88072),x88075))+~P1(f789(f789(f342(x88073),x88071),x88075))+P1(f789(f789(f342(f869(x88073,x88073)),f789(f789(f249(x88073,x88073),x88071),x88072)),x88074))+P1(f789(f789(f342(f869(x88073,x88073)),f789(f789(f249(x88073,x88073),x88072),x88071)),x88074))
% 21.40/21.38 [9609]~P4(x96095)+~P79(x96095)+~P1(f789(f70(x96091),x96094))+P1(f789(f789(f240(x96095),f789(f789(f8(x96091,x96095),x96092),x96093)),f789(f789(f8(x96091,x96095),x96092),x96094)))+~P1(f789(f789(f240(f870(x96091,a856)),x96093),x96094))+P1(f789(f789(f342(x96091),f531(x96092,x96093,x96094,x96091,x96095)),f789(f789(f3(f870(x96091,a856)),x96094),x96093)))
% 21.40/21.38 [9696]E(x96961,f184(f870(x96962,a856)))+~P1(f789(f70(x96962),x96963))+~P1(f789(f70(x96962),x96961))+P1(f789(f789(f342(f869(f870(x96962,a856),f870(x96962,a856))),f789(f789(f249(f870(x96962,a856),f870(x96962,a856)),x96963),x96961)),f332(x96962,x96964)))+~P1(f789(f789(f342(x96962),x96965),x96961))+~P1(f789(f789(f342(f869(x96962,x96962)),f789(f789(f249(x96962,x96962),f555(x96964,x96961,x96963,x96962)),x96965)),x96964))
% 21.40/21.38 [9697]E(x96971,f184(f870(x96972,a856)))+~P1(f789(f70(x96972),x96973))+~P1(f789(f70(x96972),x96971))+P1(f789(f789(f342(f869(f870(x96972,a856),f870(x96972,a856))),f789(f789(f249(f870(x96972,a856),f870(x96972,a856)),x96973),x96971)),f332(x96972,x96974)))+~P1(f789(f789(f342(x96972),x96975),x96971))+~P1(f789(f789(f342(f869(x96972,x96972)),f789(f789(f249(x96972,x96972),f637(x96974,x96971,x96973,x96972)),x96975)),x96974))
% 21.40/21.38 [9857]~P76(x98571)+~E(f789(f789(f8(x98575,x98571),x98572),x98576),x98574)+~P1(f789(f70(x98575),x98576))+P1(f789(f789(f342(x98575),f532(x98573,x98574,x98572,x98576,x98575,x98571)),x98576))+P1(f789(f789(f240(x98571),f789(x98572,x98573)),x98574))+~P1(f789(f789(f342(x98575),x98573),x98576))
% 21.40/21.38 [9915]~P76(x99151)+~E(f789(f789(f8(x99155,x99151),x99152),x99156),x99154)+~P1(f789(f70(x99155),x99156))+~P1(f789(f789(f342(x99155),x99153),x99156))+~P1(f789(f789(f240(x99151),f2(x99151)),f789(x99152,f532(x99153,x99154,x99152,x99156,x99155,x99151))))+P1(f789(f789(f240(x99151),f789(x99152,x99153)),x99154))
% 21.40/21.38 [10034]~E(x100345,x100348)+~E(x100344,x100347)+~P4(x100342)+~P100(x100341)+E(f789(f789(f8(x100341,x100342),x100343),f789(f302(x100341,x100344),x100345)),f789(f789(f8(x100341,x100342),x100346),f789(f302(x100341,x100347),x100348)))+P1(f789(f789(f240(x100341),x100344),f645(x100343,x100346,x100345,x100348,x100344,x100347,x100341,x100342)))
% 21.40/21.38 [10050]~E(x100507,x100504)+~E(x100508,x100505)+~P4(x100502)+~P100(x100501)+~E(f789(x100503,f645(x100506,x100503,x100508,x100505,x100507,x100504,x100501,x100502)),f789(x100506,f645(x100506,x100503,x100508,x100505,x100507,x100504,x100501,x100502)))+E(f789(f789(f8(x100501,x100502),x100503),f789(f302(x100501,x100504),x100505)),f789(f789(f8(x100501,x100502),x100506),f789(f302(x100501,x100507),x100508)))
% 21.40/21.38 [10053]~E(x100534,x100537)+~E(x100535,x100538)+~P4(x100532)+~P100(x100531)+E(f789(f789(f8(x100531,x100532),x100533),f789(f302(x100531,x100534),x100535)),f789(f789(f8(x100531,x100532),x100536),f789(f302(x100531,x100537),x100538)))+P1(f789(f789(f241(x100531),f645(x100533,x100536,x100535,x100538,x100534,x100537,x100531,x100532)),x100535))
% 21.40/21.38 [9701]~P12(x97015,x97019,x97016)+~P12(x97011,x970110,x97013)+~P17(x97011,x97015,f870(x97012,a856),x97013,x97016,x97018)+~P1(f789(f789(f342(x97015),x97017),x97019))+~P1(f789(f789(f342(x97011),x97014),x970110))+E(f789(f789(f53(x97011,f870(x97012,a856)),f789(f285(x97011,x97011,x97013),f789(f789(f310(x97011),x97014),f184(f870(x97011,a856))))),f789(f789(f10(f870(x97015,f870(x97012,a856)),f870(x97012,a856),x97011),f789(f53(x97015,f870(x97012,a856)),f789(f285(x97015,x97015,x97016),f789(f789(f310(x97015),x97017),f184(f870(x97015,a856)))))),x97018)),f789(f789(x97018,x97014),x97017))
% 21.40/21.38 [5509]~P101(x55093)+~P18(x55093,x55092)+~P18(x55093,x55091)+E(x55091,x55092)+~E(f789(f163(x55093),x55091),f789(f163(x55093),x55092))+~P1(f789(f134(x55093),x55092))+~P1(f789(f134(x55093),x55091))
% 21.40/21.38 [4863]~P122(x48632)+~P123(x48632)+~P138(x48632)+~P106(x48632)+~E(x48633,f2(x48632))+E(x48631,f2(a863))+E(f789(f789(f250(x48632),x48633),x48631),f2(x48632))
% 21.40/21.38 [9045]E(x90451,f2(a863))+~E(x90452,f789(f789(f89(a863),f789(f789(f90(a863),f789(f248(a863,a863),x90453)),x90451)),f789(f258(a863,a863),x90453)))+P1(f789(f62(x90452,x90451),x90453))+~P1(f789(f789(f240(a863),f789(f258(a863,a863),x90453)),f2(a863)))+~P1(f789(f789(f240(a863),f2(a863)),f789(f258(a863,a863),x90453)))+~P1(f789(f789(f241(a863),x90451),f789(f258(a863,a863),x90453)))+~P1(f789(f789(f241(a863),f789(f258(a863,a863),x90453)),x90451))
% 21.40/21.38 [9054]~E(f789(f248(a863,a863),x90543),f2(a863))+~E(x90541,f789(f789(f89(a863),f789(f789(f90(a863),f789(f248(a863,a863),x90543)),x90542)),f789(f258(a863,a863),x90543)))+P1(f789(f62(x90541,x90542),x90543))+~P1(f789(f789(f240(a863),f789(f258(a863,a863),x90543)),f2(a863)))+~P1(f789(f789(f240(a863),f2(a863)),f789(f258(a863,a863),x90543)))+~P1(f789(f789(f241(a863),x90542),f789(f258(a863,a863),x90543)))+~P1(f789(f789(f241(a863),f789(f258(a863,a863),x90543)),x90542))
% 21.40/21.38 [7492]~P95(x74922)+E(x74921,f184(f870(x74922,a856)))+E(x74923,f184(f870(x74922,a856)))+~P1(f789(f70(x74922),x74921))+~P1(f789(f70(x74922),x74923))+~E(f789(f789(f111(f870(x74922,a856)),x74923),x74921),f184(f870(x74922,a856)))+E(f12(x74922,f789(f789(f110(f870(x74922,a856)),x74923),x74921)),f789(f789(f111(x74922),f12(x74922,x74923)),f12(x74922,x74921)))
% 21.40/21.38 [7493]~P95(x74932)+E(x74931,f184(f870(x74932,a856)))+E(x74933,f184(f870(x74932,a856)))+~P1(f789(f70(x74932),x74931))+~P1(f789(f70(x74932),x74933))+~E(f789(f789(f111(f870(x74932,a856)),x74933),x74931),f184(f870(x74932,a856)))+E(f15(x74932,f789(f789(f110(f870(x74932,a856)),x74933),x74931)),f789(f789(f110(x74932),f15(x74932,x74933)),f15(x74932,x74931)))
% 21.40/21.38 [7494]~P101(x74942)+E(x74941,f184(f870(x74942,a856)))+E(x74943,f184(f870(x74942,a856)))+~P1(f789(f70(x74942),x74941))+~P1(f789(f70(x74942),x74943))+~E(f789(f789(f111(f870(x74942,a856)),x74943),x74941),f184(f870(x74942,a856)))+E(f16(x74942,f789(f789(f110(f870(x74942,a856)),x74943),x74941)),f789(f789(f239(x74942),f16(x74942,x74943)),f16(x74942,x74941)))
% 21.40/21.38 [7495]~P101(x74952)+E(x74951,f184(f870(x74952,a856)))+E(x74953,f184(f870(x74952,a856)))+~P1(f789(f70(x74952),x74951))+~P1(f789(f70(x74952),x74953))+~E(f789(f789(f111(f870(x74952,a856)),x74953),x74951),f184(f870(x74952,a856)))+E(f17(x74952,f789(f789(f110(f870(x74952,a856)),x74953),x74951)),f789(f789(f244(x74952),f17(x74952,x74953)),f17(x74952,x74951)))
% 21.40/21.38 [7970]~P66(x79702)+E(x79701,f184(f870(x79702,a856)))+E(x79703,f184(f870(x79702,a856)))+~P1(f789(f70(x79702),x79701))+~P1(f789(f70(x79702),x79703))+~E(f789(f789(f111(f870(x79702,a856)),x79703),x79701),f184(f870(x79702,a856)))+E(f789(f789(f90(x79702),f789(f72(x79702,f90(x79702)),x79703)),f789(f72(x79702,f90(x79702)),x79701)),f789(f72(x79702,f90(x79702)),f789(f789(f110(f870(x79702,a856)),x79703),x79701)))
% 21.40/21.38 [8040]~P101(x80402)+E(x80401,f184(f870(x80402,a856)))+E(x80403,f184(f870(x80402,a856)))+~P1(f789(f70(x80402),x80401))+~P1(f789(f70(x80402),x80403))+~E(f789(f789(f111(f870(x80402,a856)),x80403),x80401),f184(f870(x80402,a856)))+E(f789(f789(f239(x80402),f13(x80402,f239(x80402),x80403)),f13(x80402,f239(x80402),x80401)),f13(x80402,f239(x80402),f789(f789(f110(f870(x80402,a856)),x80403),x80401)))
% 21.40/21.38 [8041]~P101(x80412)+E(x80411,f184(f870(x80412,a856)))+E(x80413,f184(f870(x80412,a856)))+~P1(f789(f70(x80412),x80411))+~P1(f789(f70(x80412),x80413))+~E(f789(f789(f111(f870(x80412,a856)),x80413),x80411),f184(f870(x80412,a856)))+E(f789(f789(f244(x80412),f14(x80412,f244(x80412),x80413)),f14(x80412,f244(x80412),x80411)),f14(x80412,f244(x80412),f789(f789(f110(f870(x80412,a856)),x80413),x80411)))
% 21.40/21.38 [7751]E(x77511,f2(a1))+E(f789(f789(f50(a1),x77512),x77511),x77513)+~P1(f789(f789(f240(a1),x77514),f2(a1)))+~E(x77512,f789(f789(f89(a1),f789(f789(f90(a1),x77511),x77513)),x77514))+~P1(f789(f789(f240(a1),f2(a1)),x77514))+~P1(f789(f789(f241(a1),x77514),x77511))+~P1(f789(f789(f241(a1),x77511),x77514))
% 21.40/21.38 [7757]E(f59(a1,x77572,x77571),x77573)+E(x77571,f2(a1))+~P1(f789(f789(f240(a1),x77573),f2(a1)))+~E(x77572,f789(f789(f89(a1),f789(f789(f90(a1),x77571),x77574)),x77573))+~P1(f789(f789(f240(a1),f2(a1)),x77573))+~P1(f789(f789(f241(a1),x77573),x77571))+~P1(f789(f789(f241(a1),x77571),x77573))
% 21.40/21.38 [6780]~P7(x67802)+E(x67801,f2(x67802))+E(x67803,f2(x67802))+~E(f789(f789(f50(x67802),x67804),x67803),f789(f789(f50(x67802),x67805),x67801))+E(f789(f789(f90(x67802),x67804),x67801),f789(f789(f90(x67802),x67803),x67805))+~P1(f789(f789(f287(x67802),x67801),x67805))+~P1(f789(f789(f287(x67802),x67803),x67804))
% 21.40/21.38 [6781]~P7(x67812)+E(x67811,f2(x67812))+E(x67813,f2(x67812))+~E(f789(f789(f90(x67812),x67814),x67813),f789(f789(f90(x67812),x67811),x67815))+E(f789(f789(f50(x67812),x67814),x67811),f789(f789(f50(x67812),x67815),x67813))+~P1(f789(f789(f287(x67812),x67811),x67814))+~P1(f789(f789(f287(x67812),x67813),x67815))
% 21.40/21.38 [7667]~P22(x76672,x76675,x76674)+E(x76671,f184(f870(x76672,a856)))+E(x76673,f184(f870(x76672,a856)))+~P1(f789(f70(x76672),x76671))+~P1(f789(f70(x76672),x76673))+~E(f789(f789(f111(f870(x76672,a856)),x76673),x76671),f184(f870(x76672,a856)))+E(f789(x76674,f789(f789(f110(f870(x76672,a856)),x76673),x76671)),f789(f789(x76675,f789(x76674,x76673)),f789(x76674,x76671)))
% 21.40/21.38 [9257]~P29(x92573,x92571,x92575,x92574)+~P29(x92571,x92573,x92576,x92572)+E(f789(f49(x92571),x92572),f789(f49(x92573),x92574))+~P1(f789(f70(x92573),x92574))+~P1(f789(f70(x92571),x92572))+~P1(f789(f789(f240(f870(x92573,a856)),f789(f311(x92571,x92573,x92576),x92572)),x92574))+~P1(f789(f789(f240(f870(x92571,a856)),f789(f311(x92573,x92571,x92575),x92574)),x92572))
% 21.40/21.38 [9207]~P1(f789(f789(f241(a1),f789(f789(f89(a1),f789(f789(f90(a1),x92075),x92071)),x92076)),f2(a1)))+~E(f789(f789(f89(a1),f789(f789(f90(a1),x92073),x92072)),x92074),f789(f789(f89(a1),f789(f789(f90(a1),x92075),x92071)),x92076))+~P1(f789(f789(f241(a1),f2(a1)),x92075))+~P1(f789(f789(f240(a1),f2(a1)),x92076))+~P1(f789(f789(f241(a1),x92074),x92073))+~P1(f789(f789(f240(a1),x92075),x92073))+P1(f789(f789(f240(a1),x92071),x92072))
% 21.40/21.38 [8996]~E(f789(f789(f89(a1),f789(f789(f90(a1),x89963),x89961)),x89964),f789(f789(f89(a1),f789(f789(f90(a1),x89965),x89962)),x89966))+~P1(f789(f789(f241(a1),f2(a1)),x89965))+~P1(f789(f789(f240(a1),f2(a1)),x89964))+~P1(f789(f789(f241(a1),x89966),x89965))+~P1(f789(f789(f240(a1),x89965),x89963))+P1(f789(f789(f240(a1),x89961),x89962))+~P1(f789(f789(f240(a1),f2(a1)),f789(f789(f89(a1),f789(f789(f90(a1),x89965),x89962)),x89966)))
% 21.40/21.38 [9163]~P127(x91631)+~E(f789(f789(f89(x91631),x91632),x91634),f87(x91631))+~P1(f789(f789(f240(x91631),f2(x91631)),x91634))+~P1(f789(f789(f240(x91631),f2(x91631)),x91632))+~P1(f789(f789(f241(x91631),x91635),x91636))+~P1(f789(f789(f241(x91631),x91633),x91636))+P1(f789(f789(f241(x91631),f789(f789(f89(x91631),f789(f789(f90(x91631),x91632),x91633)),f789(f789(f90(x91631),x91634),x91635))),x91636))
% 21.40/21.38 [9164]~P125(x91641)+~E(f789(f789(f89(x91641),x91642),x91644),f87(x91641))+~P1(f789(f789(f240(x91641),x91645),x91646))+~P1(f789(f789(f240(x91641),x91643),x91646))+~P1(f789(f789(f240(x91641),f2(x91641)),x91644))+~P1(f789(f789(f240(x91641),f2(x91641)),x91642))+P1(f789(f789(f240(x91641),f789(f789(f89(x91641),f789(f789(f90(x91641),x91642),x91643)),f789(f789(f90(x91641),x91644),x91645))),x91646))
% 21.40/21.38 [9957]~P12(x99577,x99576,x99575)+E(x99571,x99572)+~P16(x99577,f870(x99574,a856),x99575,x99573)+E(f789(x99573,f431(x99571,x99572,x99573,x99574,x99575,x99576,x99577)),f789(x99573,f432(x99571,x99572,x99573,x99574,x99575,x99576,x99577)))+~E(f789(f789(f53(x99577,f870(x99574,a856)),x99571),x99573),f789(f789(f53(x99577,f870(x99574,a856)),x99572),x99573))+~P1(f789(f789(f342(f870(x99577,a856)),x99572),f789(f789(f68(x99577),x99576),x99575)))+~P1(f789(f789(f342(f870(x99577,a856)),x99571),f789(f789(f68(x99577),x99576),x99575)))
% 21.40/21.38 [9998]~P12(x99983,x99987,x99986)+E(x99981,x99982)+~P16(x99983,f870(x99985,a856),x99986,x99984)+~E(f789(f789(f53(x99983,f870(x99985,a856)),x99981),x99984),f789(f789(f53(x99983,f870(x99985,a856)),x99982),x99984))+P1(f789(f789(f342(x99983),f432(x99981,x99982,x99984,x99985,x99986,x99987,x99983)),x99987))+~P1(f789(f789(f342(f870(x99983,a856)),x99982),f789(f789(f68(x99983),x99987),x99986)))+~P1(f789(f789(f342(f870(x99983,a856)),x99981),f789(f789(f68(x99983),x99987),x99986)))
% 21.40/21.38 [9999]~P12(x99993,x99997,x99996)+E(x99991,x99992)+~P16(x99993,f870(x99995,a856),x99996,x99994)+~E(f789(f789(f53(x99993,f870(x99995,a856)),x99991),x99994),f789(f789(f53(x99993,f870(x99995,a856)),x99992),x99994))+P1(f789(f789(f342(x99993),f431(x99991,x99992,x99994,x99995,x99996,x99997,x99993)),x99997))+~P1(f789(f789(f342(f870(x99993,a856)),x99992),f789(f789(f68(x99993),x99997),x99996)))+~P1(f789(f789(f342(f870(x99993,a856)),x99991),f789(f789(f68(x99993),x99997),x99996)))
% 21.40/21.38 [10068]E(x100681,x100682)+~P12(x100683,x100686,x100687)+~P16(x100683,f870(x100684,a856),x100687,x100685)+~E(f789(f789(f53(x100683,f870(x100684,a856)),x100681),x100685),f789(f789(f53(x100683,f870(x100684,a856)),x100682),x100685))+~P1(f789(f789(f342(f869(x100683,x100683)),f789(f789(f249(x100683,x100683),f432(x100681,x100682,x100685,x100684,x100687,x100686,x100683)),f431(x100681,x100682,x100685,x100684,x100687,x100686,x100683))),x100687))+~P1(f789(f789(f342(f870(x100683,a856)),x100682),f789(f789(f68(x100683),x100686),x100687)))+~P1(f789(f789(f342(f870(x100683,a856)),x100681),f789(f789(f68(x100683),x100686),x100687)))
% 21.40/21.38 [8995]~P12(x89951,x89957,x89954)+~E(x89955,x89956)+~P1(f789(f789(f342(x89951),x89953),x89956))+~P1(f789(f789(f342(x89951),x89952),x89955))+~P1(f789(f789(f342(f870(x89951,a856)),x89956),f789(f789(f68(x89951),x89957),x89954)))+~P1(f789(f789(f342(f870(x89951,a856)),x89955),f789(f789(f68(x89951),x89957),x89954)))+P1(f789(f789(f342(f869(x89951,x89951)),f789(f789(f249(x89951,x89951),x89952),x89953)),x89954))
% 21.40/21.38 [9128]E(x91281,x91282)+~P12(x91283,x91284,x91285)+~P1(f789(f789(f342(x91283),x91286),x91282))+~P1(f789(f789(f342(x91283),x91287),x91281))+~P1(f789(f789(f342(f870(x91283,a856)),x91282),f789(f789(f68(x91283),x91284),x91285)))+~P1(f789(f789(f342(f870(x91283,a856)),x91281),f789(f789(f68(x91283),x91284),x91285)))+~P1(f789(f789(f342(f869(x91283,x91283)),f789(f789(f249(x91283,x91283),x91287),x91286)),x91285))
% 21.40/21.38 [9129]E(x91291,x91292)+~P12(x91293,x91294,x91295)+~P1(f789(f789(f342(x91293),x91296),x91292))+~P1(f789(f789(f342(x91293),x91297),x91291))+~P1(f789(f789(f342(f870(x91293,a856)),x91292),f789(f789(f68(x91293),x91294),x91295)))+~P1(f789(f789(f342(f870(x91293,a856)),x91291),f789(f789(f68(x91293),x91294),x91295)))+~P1(f789(f789(f342(f869(x91293,x91293)),f789(f789(f249(x91293,x91293),x91297),x91296)),x91295))
% 21.40/21.38 [10086]~P12(x100869,x100868,x100867)+~P12(x100861,x1008611,x1008610)+~P17(x100861,x100869,f870(x100866,a856),x1008610,x100867,x100865)+P1(f789(f789(f342(x100861),f433(x100862,x100863,x100864,x100865,x100866,x100867,x100868,x100869,x1008610,x1008611,x100861)),x1008611))+~P1(f789(f789(f342(f870(x100869,a856)),x100863),f789(f789(f68(x100869),x100868),x100867)))+~P1(f789(f789(f342(f870(x100861,a856)),x100864),f789(f789(f68(x100861),x1008611),x1008610)))+P1(f789(f789(f342(f870(x100866,a856)),f789(f789(f53(x100861,f870(x100866,a856)),x100864),f789(f789(f10(f870(x100869,f870(x100866,a856)),f870(x100866,a856),x100861),f789(f53(x100869,f870(x100866,a856)),x100863)),x100865))),x100862))
% 21.40/21.38 [10087]~P12(x1008711,x1008710,x100879)+~P12(x100871,x100878,x100877)+~P17(x1008711,x100871,f870(x100876,a856),x100879,x100877,x100875)+P1(f789(f789(f342(x100871),f439(x100872,x100873,x100874,x100875,x100876,x100877,x100878,x100871,x100879,x1008710,x1008711)),x100878))+~P1(f789(f789(f342(f870(x1008711,a856)),x100874),f789(f789(f68(x1008711),x1008710),x100879)))+~P1(f789(f789(f342(f870(x100871,a856)),x100873),f789(f789(f68(x100871),x100878),x100877)))+P1(f789(f789(f342(f870(x100876,a856)),f789(f789(f53(x1008711,f870(x100876,a856)),x100874),f789(f789(f10(f870(x100871,f870(x100876,a856)),f870(x100876,a856),x1008711),f789(f53(x100871,f870(x100876,a856)),x100873)),x100875))),x100872))
% 21.40/21.38 [10090]~P12(x100902,x100908,x100909)+~P12(x100904,x1009010,x1009011)+~P17(x100902,x100904,f870(x100901,a856),x100909,x1009011,x100906)+~P1(f789(f789(f342(f870(x100902,a856)),x100903),f789(f789(f68(x100902),x100908),x100909)))+~P1(f789(f789(f342(f870(x100904,a856)),x100905),f789(f789(f68(x100904),x1009010),x1009011)))+~P1(f789(f789(f342(f870(x100901,a856)),f789(f789(x100906,f433(x100907,x100905,x100903,x100906,x100901,x1009011,x1009010,x100904,x100909,x100908,x100902)),f439(x100907,x100905,x100903,x100906,x100901,x1009011,x1009010,x100904,x100909,x100908,x100902))),x100907))+P1(f789(f789(f342(f870(x100901,a856)),f789(f789(f53(x100902,f870(x100901,a856)),x100903),f789(f789(f10(f870(x100904,f870(x100901,a856)),f870(x100901,a856),x100902),f789(f53(x100904,f870(x100901,a856)),x100905)),x100906))),x100907))
% 21.40/21.38 [9038]E(x90381,x90382)+~P101(x90384)+~P29(x90383,x90384,x90385,f789(f789(f110(f870(x90383,a856)),f789(f163(x90383),x90381)),f789(f163(x90383),x90382)))+~E(f789(f163(x90383),x90381),f789(f163(x90383),x90382))+~P18(x90384,f789(f789(f150(x90383,x90384),x90385),x90382))+~P18(x90384,f789(f789(f150(x90383,x90384),x90385),x90381))+~P1(f789(f134(x90384),f789(f789(f150(x90383,x90384),x90385),x90382)))+~P1(f789(f134(x90384),f789(f789(f150(x90383,x90384),x90385),x90381)))
% 21.40/21.38 %EqnAxiom
% 21.40/21.38 [1]E(x11,x11)
% 21.40/21.38 [2]E(x22,x21)+~E(x21,x22)
% 21.40/21.38 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 21.40/21.38 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 21.40/21.38 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 21.40/21.38 [6]~E(x61,x62)+E(f109(x61),f109(x62))
% 21.40/21.38 [7]~E(x71,x72)+E(f36(x71),f36(x72))
% 21.40/21.38 [8]~E(x81,x82)+E(f789(x81,x83),f789(x82,x83))
% 21.40/21.38 [9]~E(x91,x92)+E(f789(x93,x91),f789(x93,x92))
% 21.40/21.38 [10]~E(x101,x102)+E(f93(x101),f93(x102))
% 21.40/21.38 [11]~E(x111,x112)+E(f152(x111,x113,x114,x115),f152(x112,x113,x114,x115))
% 21.40/21.38 [12]~E(x121,x122)+E(f152(x123,x121,x124,x125),f152(x123,x122,x124,x125))
% 21.40/21.38 [13]~E(x131,x132)+E(f152(x133,x134,x131,x135),f152(x133,x134,x132,x135))
% 21.40/21.38 [14]~E(x141,x142)+E(f152(x143,x144,x145,x141),f152(x143,x144,x145,x142))
% 21.40/21.38 [15]~E(x151,x152)+E(f50(x151),f50(x152))
% 21.40/21.38 [16]~E(x161,x162)+E(f122(x161),f122(x162))
% 21.40/21.38 [17]~E(x171,x172)+E(f184(x171),f184(x172))
% 21.40/21.38 [18]~E(x181,x182)+E(f439(x181,x183,x184,x185,x186,x187,x188,x189,x1810,x1811,x1812),f439(x182,x183,x184,x185,x186,x187,x188,x189,x1810,x1811,x1812))
% 21.40/21.38 [19]~E(x191,x192)+E(f439(x193,x191,x194,x195,x196,x197,x198,x199,x1910,x1911,x1912),f439(x193,x192,x194,x195,x196,x197,x198,x199,x1910,x1911,x1912))
% 21.40/21.38 [20]~E(x201,x202)+E(f439(x203,x204,x201,x205,x206,x207,x208,x209,x2010,x2011,x2012),f439(x203,x204,x202,x205,x206,x207,x208,x209,x2010,x2011,x2012))
% 21.40/21.38 [21]~E(x211,x212)+E(f439(x213,x214,x215,x211,x216,x217,x218,x219,x2110,x2111,x2112),f439(x213,x214,x215,x212,x216,x217,x218,x219,x2110,x2111,x2112))
% 21.40/21.38 [22]~E(x221,x222)+E(f439(x223,x224,x225,x226,x221,x227,x228,x229,x2210,x2211,x2212),f439(x223,x224,x225,x226,x222,x227,x228,x229,x2210,x2211,x2212))
% 21.40/21.38 [23]~E(x231,x232)+E(f439(x233,x234,x235,x236,x237,x231,x238,x239,x2310,x2311,x2312),f439(x233,x234,x235,x236,x237,x232,x238,x239,x2310,x2311,x2312))
% 21.40/21.38 [24]~E(x241,x242)+E(f439(x243,x244,x245,x246,x247,x248,x241,x249,x2410,x2411,x2412),f439(x243,x244,x245,x246,x247,x248,x242,x249,x2410,x2411,x2412))
% 21.40/21.38 [25]~E(x251,x252)+E(f439(x253,x254,x255,x256,x257,x258,x259,x251,x2510,x2511,x2512),f439(x253,x254,x255,x256,x257,x258,x259,x252,x2510,x2511,x2512))
% 21.40/21.38 [26]~E(x261,x262)+E(f439(x263,x264,x265,x266,x267,x268,x269,x2610,x261,x2611,x2612),f439(x263,x264,x265,x266,x267,x268,x269,x2610,x262,x2611,x2612))
% 21.40/21.38 [27]~E(x271,x272)+E(f439(x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x271,x2712),f439(x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x272,x2712))
% 21.40/21.38 [28]~E(x281,x282)+E(f439(x283,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812,x281),f439(x283,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812,x282))
% 21.40/21.38 [29]~E(x291,x292)+E(f239(x291),f239(x292))
% 21.40/21.38 [30]~E(x301,x302)+E(f110(x301),f110(x302))
% 21.40/21.38 [31]~E(x311,x312)+E(f244(x311),f244(x312))
% 21.40/21.38 [32]~E(x321,x322)+E(f111(x321),f111(x322))
% 21.40/21.38 [33]~E(x331,x332)+E(f112(x331),f112(x332))
% 21.40/21.38 [34]~E(x341,x342)+E(f41(x341),f41(x342))
% 21.40/21.38 [35]~E(x351,x352)+E(f864(x351),f864(x352))
% 21.40/21.38 [36]~E(x361,x362)+E(f87(x361),f87(x362))
% 21.40/21.38 [37]~E(x371,x372)+E(f433(x371,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712),f433(x372,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712))
% 21.40/21.38 [38]~E(x381,x382)+E(f433(x383,x381,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f433(x383,x382,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812))
% 21.40/21.38 [39]~E(x391,x392)+E(f433(x393,x394,x391,x395,x396,x397,x398,x399,x3910,x3911,x3912),f433(x393,x394,x392,x395,x396,x397,x398,x399,x3910,x3911,x3912))
% 21.40/21.38 [40]~E(x401,x402)+E(f433(x403,x404,x405,x401,x406,x407,x408,x409,x4010,x4011,x4012),f433(x403,x404,x405,x402,x406,x407,x408,x409,x4010,x4011,x4012))
% 21.40/21.38 [41]~E(x411,x412)+E(f433(x413,x414,x415,x416,x411,x417,x418,x419,x4110,x4111,x4112),f433(x413,x414,x415,x416,x412,x417,x418,x419,x4110,x4111,x4112))
% 21.40/21.38 [42]~E(x421,x422)+E(f433(x423,x424,x425,x426,x427,x421,x428,x429,x4210,x4211,x4212),f433(x423,x424,x425,x426,x427,x422,x428,x429,x4210,x4211,x4212))
% 21.40/21.38 [43]~E(x431,x432)+E(f433(x433,x434,x435,x436,x437,x438,x431,x439,x4310,x4311,x4312),f433(x433,x434,x435,x436,x437,x438,x432,x439,x4310,x4311,x4312))
% 21.40/21.38 [44]~E(x441,x442)+E(f433(x443,x444,x445,x446,x447,x448,x449,x441,x4410,x4411,x4412),f433(x443,x444,x445,x446,x447,x448,x449,x442,x4410,x4411,x4412))
% 21.40/21.38 [45]~E(x451,x452)+E(f433(x453,x454,x455,x456,x457,x458,x459,x4510,x451,x4511,x4512),f433(x453,x454,x455,x456,x457,x458,x459,x4510,x452,x4511,x4512))
% 21.40/21.38 [46]~E(x461,x462)+E(f433(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x461,x4612),f433(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x462,x4612))
% 21.40/21.38 [47]~E(x471,x472)+E(f433(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x471),f433(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x472))
% 21.40/21.38 [48]~E(x481,x482)+E(f120(x481),f120(x482))
% 21.40/21.38 [49]~E(x491,x492)+E(f342(x491),f342(x492))
% 21.40/21.38 [50]~E(x501,x502)+E(f870(x501,x503),f870(x502,x503))
% 21.40/21.38 [51]~E(x511,x512)+E(f870(x513,x511),f870(x513,x512))
% 21.40/21.38 [52]~E(x521,x522)+E(f6(x521),f6(x522))
% 21.40/21.38 [53]~E(x531,x532)+E(f146(x531),f146(x532))
% 21.40/21.38 [54]~E(x541,x542)+E(f42(x541),f42(x542))
% 21.40/21.38 [55]~E(x551,x552)+E(f44(x551),f44(x552))
% 21.40/21.38 [56]~E(x561,x562)+E(f89(x561),f89(x562))
% 21.40/21.38 [57]~E(x571,x572)+E(f43(x571),f43(x572))
% 21.40/21.38 [58]~E(x581,x582)+E(f134(x581),f134(x582))
% 21.40/21.38 [59]~E(x591,x592)+E(f9(x591,x593,x594),f9(x592,x593,x594))
% 21.40/21.38 [60]~E(x601,x602)+E(f9(x603,x601,x604),f9(x603,x602,x604))
% 21.40/21.38 [61]~E(x611,x612)+E(f9(x613,x614,x611),f9(x613,x614,x612))
% 21.40/21.38 [62]~E(x621,x622)+E(f88(x621),f88(x622))
% 21.40/21.38 [63]~E(x631,x632)+E(f264(x631),f264(x632))
% 21.40/21.38 [64]~E(x641,x642)+E(f185(x641),f185(x642))
% 21.40/21.38 [65]~E(x651,x652)+E(f113(x651),f113(x652))
% 21.40/21.38 [66]~E(x661,x662)+E(f554(x661,x663,x664),f554(x662,x663,x664))
% 21.40/21.38 [67]~E(x671,x672)+E(f554(x673,x671,x674),f554(x673,x672,x674))
% 21.40/21.38 [68]~E(x681,x682)+E(f554(x683,x684,x681),f554(x683,x684,x682))
% 21.40/21.38 [69]~E(x691,x692)+E(f240(x691),f240(x692))
% 21.40/21.38 [70]~E(x701,x702)+E(f68(x701),f68(x702))
% 21.40/21.38 [71]~E(x711,x712)+E(f132(x711),f132(x712))
% 21.40/21.38 [72]~E(x721,x722)+E(f59(x721,x723,x724),f59(x722,x723,x724))
% 21.40/21.38 [73]~E(x731,x732)+E(f59(x733,x731,x734),f59(x733,x732,x734))
% 21.40/21.38 [74]~E(x741,x742)+E(f59(x743,x744,x741),f59(x743,x744,x742))
% 21.40/21.38 [75]~E(x751,x752)+E(f90(x751),f90(x752))
% 21.40/21.38 [76]~E(x761,x762)+E(f18(x761,x763),f18(x762,x763))
% 21.40/21.38 [77]~E(x771,x772)+E(f18(x773,x771),f18(x773,x772))
% 21.40/21.38 [78]~E(x781,x782)+E(f482(x781,x783,x784),f482(x782,x783,x784))
% 21.40/21.38 [79]~E(x791,x792)+E(f482(x793,x791,x794),f482(x793,x792,x794))
% 21.40/21.38 [80]~E(x801,x802)+E(f482(x803,x804,x801),f482(x803,x804,x802))
% 21.40/21.38 [81]~E(x811,x812)+E(f869(x811,x813),f869(x812,x813))
% 21.40/21.38 [82]~E(x821,x822)+E(f869(x823,x821),f869(x823,x822))
% 21.40/21.38 [83]~E(x831,x832)+E(f156(x831,x833),f156(x832,x833))
% 21.40/21.38 [84]~E(x841,x842)+E(f156(x843,x841),f156(x843,x842))
% 21.40/21.38 [85]~E(x851,x852)+E(f485(x851,x853,x854,x855),f485(x852,x853,x854,x855))
% 21.40/21.38 [86]~E(x861,x862)+E(f485(x863,x861,x864,x865),f485(x863,x862,x864,x865))
% 21.40/21.38 [87]~E(x871,x872)+E(f485(x873,x874,x871,x875),f485(x873,x874,x872,x875))
% 21.40/21.38 [88]~E(x881,x882)+E(f485(x883,x884,x885,x881),f485(x883,x884,x885,x882))
% 21.40/21.38 [89]~E(x891,x892)+E(f241(x891),f241(x892))
% 21.40/21.38 [90]~E(x901,x902)+E(f257(x901,x903,x904,x905),f257(x902,x903,x904,x905))
% 21.40/21.38 [91]~E(x911,x912)+E(f257(x913,x911,x914,x915),f257(x913,x912,x914,x915))
% 21.40/21.38 [92]~E(x921,x922)+E(f257(x923,x924,x921,x925),f257(x923,x924,x922,x925))
% 21.40/21.38 [93]~E(x931,x932)+E(f257(x933,x934,x935,x931),f257(x933,x934,x935,x932))
% 21.40/21.38 [94]~E(x941,x942)+E(f287(x941),f287(x942))
% 21.40/21.38 [95]~E(x951,x952)+E(f119(x951),f119(x952))
% 21.40/21.38 [96]~E(x961,x962)+E(f685(x961,x963,x964),f685(x962,x963,x964))
% 21.40/21.38 [97]~E(x971,x972)+E(f685(x973,x971,x974),f685(x973,x972,x974))
% 21.40/21.39 [98]~E(x981,x982)+E(f685(x983,x984,x981),f685(x983,x984,x982))
% 21.40/21.39 [99]~E(x991,x992)+E(f311(x991,x993,x994),f311(x992,x993,x994))
% 21.40/21.39 [100]~E(x1001,x1002)+E(f311(x1003,x1001,x1004),f311(x1003,x1002,x1004))
% 21.40/21.39 [101]~E(x1011,x1012)+E(f311(x1013,x1014,x1011),f311(x1013,x1014,x1012))
% 21.40/21.39 [102]~E(x1021,x1022)+E(f568(x1021,x1023,x1024,x1025),f568(x1022,x1023,x1024,x1025))
% 21.40/21.39 [103]~E(x1031,x1032)+E(f568(x1033,x1031,x1034,x1035),f568(x1033,x1032,x1034,x1035))
% 21.40/21.39 [104]~E(x1041,x1042)+E(f568(x1043,x1044,x1041,x1045),f568(x1043,x1044,x1042,x1045))
% 21.40/21.39 [105]~E(x1051,x1052)+E(f568(x1053,x1054,x1055,x1051),f568(x1053,x1054,x1055,x1052))
% 21.40/21.39 [106]~E(x1061,x1062)+E(f174(x1061,x1063,x1064,x1065),f174(x1062,x1063,x1064,x1065))
% 21.40/21.39 [107]~E(x1071,x1072)+E(f174(x1073,x1071,x1074,x1075),f174(x1073,x1072,x1074,x1075))
% 21.40/21.39 [108]~E(x1081,x1082)+E(f174(x1083,x1084,x1081,x1085),f174(x1083,x1084,x1082,x1085))
% 21.40/21.39 [109]~E(x1091,x1092)+E(f174(x1093,x1094,x1095,x1091),f174(x1093,x1094,x1095,x1092))
% 21.40/21.39 [110]~E(x1101,x1102)+E(f70(x1101),f70(x1102))
% 21.40/21.39 [111]~E(x1111,x1112)+E(f248(x1111,x1113),f248(x1112,x1113))
% 21.40/21.39 [112]~E(x1121,x1122)+E(f248(x1123,x1121),f248(x1123,x1122))
% 21.40/21.39 [113]~E(x1131,x1132)+E(f762(x1131,x1133,x1134),f762(x1132,x1133,x1134))
% 21.40/21.39 [114]~E(x1141,x1142)+E(f762(x1143,x1141,x1144),f762(x1143,x1142,x1144))
% 21.40/21.39 [115]~E(x1151,x1152)+E(f762(x1153,x1154,x1151),f762(x1153,x1154,x1152))
% 21.40/21.39 [116]~E(x1161,x1162)+E(f571(x1161,x1163,x1164,x1165),f571(x1162,x1163,x1164,x1165))
% 21.40/21.39 [117]~E(x1171,x1172)+E(f571(x1173,x1171,x1174,x1175),f571(x1173,x1172,x1174,x1175))
% 21.40/21.39 [118]~E(x1181,x1182)+E(f571(x1183,x1184,x1181,x1185),f571(x1183,x1184,x1182,x1185))
% 21.40/21.39 [119]~E(x1191,x1192)+E(f571(x1193,x1194,x1195,x1191),f571(x1193,x1194,x1195,x1192))
% 21.40/21.39 [120]~E(x1201,x1202)+E(f291(x1201),f291(x1202))
% 21.40/21.39 [121]~E(x1211,x1212)+E(f150(x1211,x1213),f150(x1212,x1213))
% 21.40/21.39 [122]~E(x1221,x1222)+E(f150(x1223,x1221),f150(x1223,x1222))
% 21.40/21.39 [123]~E(x1231,x1232)+E(f63(x1231,x1233),f63(x1232,x1233))
% 21.40/21.39 [124]~E(x1241,x1242)+E(f63(x1243,x1241),f63(x1243,x1242))
% 21.40/21.39 [125]~E(x1251,x1252)+E(f163(x1251),f163(x1252))
% 21.40/21.39 [126]~E(x1261,x1262)+E(f867(x1261),f867(x1262))
% 21.40/21.39 [127]~E(x1271,x1272)+E(f10(x1271,x1273,x1274),f10(x1272,x1273,x1274))
% 21.40/21.39 [128]~E(x1281,x1282)+E(f10(x1283,x1281,x1284),f10(x1283,x1282,x1284))
% 21.40/21.39 [129]~E(x1291,x1292)+E(f10(x1293,x1294,x1291),f10(x1293,x1294,x1292))
% 21.40/21.39 [130]~E(x1301,x1302)+E(f247(x1301),f247(x1302))
% 21.40/21.39 [131]~E(x1311,x1312)+E(f412(x1311,x1313,x1314),f412(x1312,x1313,x1314))
% 21.40/21.39 [132]~E(x1321,x1322)+E(f412(x1323,x1321,x1324),f412(x1323,x1322,x1324))
% 21.40/21.39 [133]~E(x1331,x1332)+E(f412(x1333,x1334,x1331),f412(x1333,x1334,x1332))
% 21.40/21.39 [134]~E(x1341,x1342)+E(f483(x1341,x1343,x1344),f483(x1342,x1343,x1344))
% 21.40/21.39 [135]~E(x1351,x1352)+E(f483(x1353,x1351,x1354),f483(x1353,x1352,x1354))
% 21.40/21.39 [136]~E(x1361,x1362)+E(f483(x1363,x1364,x1361),f483(x1363,x1364,x1362))
% 21.40/21.39 [137]~E(x1371,x1372)+E(f8(x1371,x1373),f8(x1372,x1373))
% 21.40/21.39 [138]~E(x1381,x1382)+E(f8(x1383,x1381),f8(x1383,x1382))
% 21.40/21.39 [139]~E(x1391,x1392)+E(f138(x1391,x1393,x1394,x1395),f138(x1392,x1393,x1394,x1395))
% 21.40/21.39 [140]~E(x1401,x1402)+E(f138(x1403,x1401,x1404,x1405),f138(x1403,x1402,x1404,x1405))
% 21.40/21.39 [141]~E(x1411,x1412)+E(f138(x1413,x1414,x1411,x1415),f138(x1413,x1414,x1412,x1415))
% 21.40/21.39 [142]~E(x1421,x1422)+E(f138(x1423,x1424,x1425,x1421),f138(x1423,x1424,x1425,x1422))
% 21.40/21.39 [143]~E(x1431,x1432)+E(f756(x1431,x1433,x1434,x1435),f756(x1432,x1433,x1434,x1435))
% 21.40/21.39 [144]~E(x1441,x1442)+E(f756(x1443,x1441,x1444,x1445),f756(x1443,x1442,x1444,x1445))
% 21.40/21.39 [145]~E(x1451,x1452)+E(f756(x1453,x1454,x1451,x1455),f756(x1453,x1454,x1452,x1455))
% 21.40/21.39 [146]~E(x1461,x1462)+E(f756(x1463,x1464,x1465,x1461),f756(x1463,x1464,x1465,x1462))
% 21.40/21.39 [147]~E(x1471,x1472)+E(f249(x1471,x1473),f249(x1472,x1473))
% 21.40/21.39 [148]~E(x1481,x1482)+E(f249(x1483,x1481),f249(x1483,x1482))
% 21.40/21.39 [149]~E(x1491,x1492)+E(f303(x1491,x1493,x1494),f303(x1492,x1493,x1494))
% 21.40/21.39 [150]~E(x1501,x1502)+E(f303(x1503,x1501,x1504),f303(x1503,x1502,x1504))
% 21.40/21.39 [151]~E(x1511,x1512)+E(f303(x1513,x1514,x1511),f303(x1513,x1514,x1512))
% 21.40/21.39 [152]~E(x1521,x1522)+E(f256(x1521,x1523),f256(x1522,x1523))
% 21.40/21.39 [153]~E(x1531,x1532)+E(f256(x1533,x1531),f256(x1533,x1532))
% 21.40/21.39 [154]~E(x1541,x1542)+E(f161(x1541),f161(x1542))
% 21.40/21.39 [155]~E(x1551,x1552)+E(f40(x1551,x1553,x1554,x1555,x1556,x1557,x1558,x1559,x15510,x15511),f40(x1552,x1553,x1554,x1555,x1556,x1557,x1558,x1559,x15510,x15511))
% 21.40/21.39 [156]~E(x1561,x1562)+E(f40(x1563,x1561,x1564,x1565,x1566,x1567,x1568,x1569,x15610,x15611),f40(x1563,x1562,x1564,x1565,x1566,x1567,x1568,x1569,x15610,x15611))
% 21.40/21.39 [157]~E(x1571,x1572)+E(f40(x1573,x1574,x1571,x1575,x1576,x1577,x1578,x1579,x15710,x15711),f40(x1573,x1574,x1572,x1575,x1576,x1577,x1578,x1579,x15710,x15711))
% 21.40/21.39 [158]~E(x1581,x1582)+E(f40(x1583,x1584,x1585,x1581,x1586,x1587,x1588,x1589,x15810,x15811),f40(x1583,x1584,x1585,x1582,x1586,x1587,x1588,x1589,x15810,x15811))
% 21.40/21.39 [159]~E(x1591,x1592)+E(f40(x1593,x1594,x1595,x1596,x1591,x1597,x1598,x1599,x15910,x15911),f40(x1593,x1594,x1595,x1596,x1592,x1597,x1598,x1599,x15910,x15911))
% 21.40/21.39 [160]~E(x1601,x1602)+E(f40(x1603,x1604,x1605,x1606,x1607,x1601,x1608,x1609,x16010,x16011),f40(x1603,x1604,x1605,x1606,x1607,x1602,x1608,x1609,x16010,x16011))
% 21.40/21.39 [161]~E(x1611,x1612)+E(f40(x1613,x1614,x1615,x1616,x1617,x1618,x1611,x1619,x16110,x16111),f40(x1613,x1614,x1615,x1616,x1617,x1618,x1612,x1619,x16110,x16111))
% 21.40/21.39 [162]~E(x1621,x1622)+E(f40(x1623,x1624,x1625,x1626,x1627,x1628,x1629,x1621,x16210,x16211),f40(x1623,x1624,x1625,x1626,x1627,x1628,x1629,x1622,x16210,x16211))
% 21.40/21.39 [163]~E(x1631,x1632)+E(f40(x1633,x1634,x1635,x1636,x1637,x1638,x1639,x16310,x1631,x16311),f40(x1633,x1634,x1635,x1636,x1637,x1638,x1639,x16310,x1632,x16311))
% 21.40/21.39 [164]~E(x1641,x1642)+E(f40(x1643,x1644,x1645,x1646,x1647,x1648,x1649,x16410,x16411,x1641),f40(x1643,x1644,x1645,x1646,x1647,x1648,x1649,x16410,x16411,x1642))
% 21.40/21.39 [165]~E(x1651,x1652)+E(f310(x1651),f310(x1652))
% 21.40/21.39 [166]~E(x1661,x1662)+E(f115(x1661),f115(x1662))
% 21.40/21.39 [167]~E(x1671,x1672)+E(f116(x1671),f116(x1672))
% 21.40/21.39 [168]~E(x1681,x1682)+E(f341(x1681),f341(x1682))
% 21.40/21.39 [169]~E(x1691,x1692)+E(f302(x1691,x1693),f302(x1692,x1693))
% 21.40/21.39 [170]~E(x1701,x1702)+E(f302(x1703,x1701),f302(x1703,x1702))
% 21.40/21.39 [171]~E(x1711,x1712)+E(f11(x1711,x1713),f11(x1712,x1713))
% 21.40/21.39 [172]~E(x1721,x1722)+E(f11(x1723,x1721),f11(x1723,x1722))
% 21.40/21.39 [173]~E(x1731,x1732)+E(f246(x1731,x1733),f246(x1732,x1733))
% 21.40/21.39 [174]~E(x1741,x1742)+E(f246(x1743,x1741),f246(x1743,x1742))
% 21.40/21.39 [175]~E(x1751,x1752)+E(f171(x1751,x1753),f171(x1752,x1753))
% 21.40/21.39 [176]~E(x1761,x1762)+E(f171(x1763,x1761),f171(x1763,x1762))
% 21.40/21.39 [177]~E(x1771,x1772)+E(f187(x1771),f187(x1772))
% 21.40/21.39 [178]~E(x1781,x1782)+E(f13(x1781,x1783,x1784),f13(x1782,x1783,x1784))
% 21.40/21.39 [179]~E(x1791,x1792)+E(f13(x1793,x1791,x1794),f13(x1793,x1792,x1794))
% 21.40/21.39 [180]~E(x1801,x1802)+E(f13(x1803,x1804,x1801),f13(x1803,x1804,x1802))
% 21.40/21.39 [181]~E(x1811,x1812)+E(f139(x1811,x1813),f139(x1812,x1813))
% 21.40/21.39 [182]~E(x1821,x1822)+E(f139(x1823,x1821),f139(x1823,x1822))
% 21.40/21.39 [183]~E(x1831,x1832)+E(f250(x1831),f250(x1832))
% 21.40/21.39 [184]~E(x1841,x1842)+E(f7(x1841),f7(x1842))
% 21.40/21.39 [185]~E(x1851,x1852)+E(f153(x1851,x1853),f153(x1852,x1853))
% 21.40/21.39 [186]~E(x1861,x1862)+E(f153(x1863,x1861),f153(x1863,x1862))
% 21.40/21.39 [187]~E(x1871,x1872)+E(f20(x1871,x1873,x1874),f20(x1872,x1873,x1874))
% 21.40/21.39 [188]~E(x1881,x1882)+E(f20(x1883,x1881,x1884),f20(x1883,x1882,x1884))
% 21.40/21.39 [189]~E(x1891,x1892)+E(f20(x1893,x1894,x1891),f20(x1893,x1894,x1892))
% 21.40/21.39 [190]~E(x1901,x1902)+E(f259(x1901,x1903,x1904),f259(x1902,x1903,x1904))
% 21.40/21.39 [191]~E(x1911,x1912)+E(f259(x1913,x1911,x1914),f259(x1913,x1912,x1914))
% 21.40/21.39 [192]~E(x1921,x1922)+E(f259(x1923,x1924,x1921),f259(x1923,x1924,x1922))
% 21.40/21.39 [193]~E(x1931,x1932)+E(f170(x1931,x1933,x1934),f170(x1932,x1933,x1934))
% 21.40/21.39 [194]~E(x1941,x1942)+E(f170(x1943,x1941,x1944),f170(x1943,x1942,x1944))
% 21.40/21.39 [195]~E(x1951,x1952)+E(f170(x1953,x1954,x1951),f170(x1953,x1954,x1952))
% 21.40/21.39 [196]~E(x1961,x1962)+E(f386(x1961),f386(x1962))
% 21.40/21.39 [197]~E(x1971,x1972)+E(f176(x1971,x1973,x1974,x1975,x1976),f176(x1972,x1973,x1974,x1975,x1976))
% 21.40/21.39 [198]~E(x1981,x1982)+E(f176(x1983,x1981,x1984,x1985,x1986),f176(x1983,x1982,x1984,x1985,x1986))
% 21.40/21.39 [199]~E(x1991,x1992)+E(f176(x1993,x1994,x1991,x1995,x1996),f176(x1993,x1994,x1992,x1995,x1996))
% 21.40/21.39 [200]~E(x2001,x2002)+E(f176(x2003,x2004,x2005,x2001,x2006),f176(x2003,x2004,x2005,x2002,x2006))
% 21.40/21.39 [201]~E(x2011,x2012)+E(f176(x2013,x2014,x2015,x2016,x2011),f176(x2013,x2014,x2015,x2016,x2012))
% 21.40/21.39 [202]~E(x2021,x2022)+E(f191(x2021),f191(x2022))
% 21.40/21.39 [203]~E(x2031,x2032)+E(f53(x2031,x2033),f53(x2032,x2033))
% 21.40/21.39 [204]~E(x2041,x2042)+E(f53(x2043,x2041),f53(x2043,x2042))
% 21.40/21.39 [205]~E(x2051,x2052)+E(f501(x2051,x2053,x2054,x2055),f501(x2052,x2053,x2054,x2055))
% 21.40/21.39 [206]~E(x2061,x2062)+E(f501(x2063,x2061,x2064,x2065),f501(x2063,x2062,x2064,x2065))
% 21.40/21.39 [207]~E(x2071,x2072)+E(f501(x2073,x2074,x2071,x2075),f501(x2073,x2074,x2072,x2075))
% 21.40/21.39 [208]~E(x2081,x2082)+E(f501(x2083,x2084,x2085,x2081),f501(x2083,x2084,x2085,x2082))
% 21.40/21.39 [209]~E(x2091,x2092)+E(f234(x2091),f234(x2092))
% 21.40/21.39 [210]~E(x2101,x2102)+E(f566(x2101,x2103,x2104),f566(x2102,x2103,x2104))
% 21.40/21.39 [211]~E(x2111,x2112)+E(f566(x2113,x2111,x2114),f566(x2113,x2112,x2114))
% 21.40/21.39 [212]~E(x2121,x2122)+E(f566(x2123,x2124,x2121),f566(x2123,x2124,x2122))
% 21.40/21.39 [213]~E(x2131,x2132)+E(f17(x2131,x2133),f17(x2132,x2133))
% 21.40/21.39 [214]~E(x2141,x2142)+E(f17(x2143,x2141),f17(x2143,x2142))
% 21.40/21.39 [215]~E(x2151,x2152)+E(f799(x2151,x2153,x2154),f799(x2152,x2153,x2154))
% 21.40/21.39 [216]~E(x2161,x2162)+E(f799(x2163,x2161,x2164),f799(x2163,x2162,x2164))
% 21.40/21.39 [217]~E(x2171,x2172)+E(f799(x2173,x2174,x2171),f799(x2173,x2174,x2172))
% 21.40/21.39 [218]~E(x2181,x2182)+E(f82(x2181,x2183,x2184,x2185),f82(x2182,x2183,x2184,x2185))
% 21.40/21.39 [219]~E(x2191,x2192)+E(f82(x2193,x2191,x2194,x2195),f82(x2193,x2192,x2194,x2195))
% 21.40/21.39 [220]~E(x2201,x2202)+E(f82(x2203,x2204,x2201,x2205),f82(x2203,x2204,x2202,x2205))
% 21.40/21.39 [221]~E(x2211,x2212)+E(f82(x2213,x2214,x2215,x2211),f82(x2213,x2214,x2215,x2212))
% 21.40/21.39 [222]~E(x2221,x2222)+E(f524(x2221,x2223,x2224,x2225),f524(x2222,x2223,x2224,x2225))
% 21.40/21.39 [223]~E(x2231,x2232)+E(f524(x2233,x2231,x2234,x2235),f524(x2233,x2232,x2234,x2235))
% 21.40/21.39 [224]~E(x2241,x2242)+E(f524(x2243,x2244,x2241,x2245),f524(x2243,x2244,x2242,x2245))
% 21.40/21.39 [225]~E(x2251,x2252)+E(f524(x2253,x2254,x2255,x2251),f524(x2253,x2254,x2255,x2252))
% 21.40/21.39 [226]~E(x2261,x2262)+E(f34(x2261,x2263,x2264),f34(x2262,x2263,x2264))
% 21.40/21.39 [227]~E(x2271,x2272)+E(f34(x2273,x2271,x2274),f34(x2273,x2272,x2274))
% 21.40/21.39 [228]~E(x2281,x2282)+E(f34(x2283,x2284,x2281),f34(x2283,x2284,x2282))
% 21.40/21.39 [229]~E(x2291,x2292)+E(f301(x2291),f301(x2292))
% 21.40/21.39 [230]~E(x2301,x2302)+E(f795(x2301,x2303,x2304),f795(x2302,x2303,x2304))
% 21.40/21.39 [231]~E(x2311,x2312)+E(f795(x2313,x2311,x2314),f795(x2313,x2312,x2314))
% 21.40/21.39 [232]~E(x2321,x2322)+E(f795(x2323,x2324,x2321),f795(x2323,x2324,x2322))
% 21.40/21.39 [233]~E(x2331,x2332)+E(f377(x2331),f377(x2332))
% 21.40/21.39 [234]~E(x2341,x2342)+E(f453(x2341,x2343,x2344),f453(x2342,x2343,x2344))
% 21.40/21.39 [235]~E(x2351,x2352)+E(f453(x2353,x2351,x2354),f453(x2353,x2352,x2354))
% 21.40/21.39 [236]~E(x2361,x2362)+E(f453(x2363,x2364,x2361),f453(x2363,x2364,x2362))
% 21.40/21.39 [237]~E(x2371,x2372)+E(f806(x2371),f806(x2372))
% 21.40/21.39 [238]~E(x2381,x2382)+E(f269(x2381,x2383),f269(x2382,x2383))
% 21.40/21.39 [239]~E(x2391,x2392)+E(f269(x2393,x2391),f269(x2393,x2392))
% 21.40/21.39 [240]~E(x2401,x2402)+E(f51(x2401,x2403),f51(x2402,x2403))
% 21.40/21.39 [241]~E(x2411,x2412)+E(f51(x2413,x2411),f51(x2413,x2412))
% 21.40/21.39 [242]~E(x2421,x2422)+E(f147(x2421,x2423),f147(x2422,x2423))
% 21.40/21.39 [243]~E(x2431,x2432)+E(f147(x2433,x2431),f147(x2433,x2432))
% 21.40/21.39 [244]~E(x2441,x2442)+E(f12(x2441,x2443),f12(x2442,x2443))
% 21.40/21.39 [245]~E(x2451,x2452)+E(f12(x2453,x2451),f12(x2453,x2452))
% 21.40/21.39 [246]~E(x2461,x2462)+E(f710(x2461,x2463),f710(x2462,x2463))
% 21.40/21.39 [247]~E(x2471,x2472)+E(f710(x2473,x2471),f710(x2473,x2472))
% 21.40/21.39 [248]~E(x2481,x2482)+E(f160(x2481,x2483,x2484,x2485),f160(x2482,x2483,x2484,x2485))
% 21.40/21.39 [249]~E(x2491,x2492)+E(f160(x2493,x2491,x2494,x2495),f160(x2493,x2492,x2494,x2495))
% 21.40/21.39 [250]~E(x2501,x2502)+E(f160(x2503,x2504,x2501,x2505),f160(x2503,x2504,x2502,x2505))
% 21.40/21.39 [251]~E(x2511,x2512)+E(f160(x2513,x2514,x2515,x2511),f160(x2513,x2514,x2515,x2512))
% 21.40/21.39 [252]~E(x2521,x2522)+E(f646(x2521,x2523,x2524,x2525,x2526),f646(x2522,x2523,x2524,x2525,x2526))
% 21.40/21.39 [253]~E(x2531,x2532)+E(f646(x2533,x2531,x2534,x2535,x2536),f646(x2533,x2532,x2534,x2535,x2536))
% 21.40/21.39 [254]~E(x2541,x2542)+E(f646(x2543,x2544,x2541,x2545,x2546),f646(x2543,x2544,x2542,x2545,x2546))
% 21.40/21.39 [255]~E(x2551,x2552)+E(f646(x2553,x2554,x2555,x2551,x2556),f646(x2553,x2554,x2555,x2552,x2556))
% 21.40/21.39 [256]~E(x2561,x2562)+E(f646(x2563,x2564,x2565,x2566,x2561),f646(x2563,x2564,x2565,x2566,x2562))
% 21.40/21.39 [257]~E(x2571,x2572)+E(f37(x2571,x2573),f37(x2572,x2573))
% 21.40/21.39 [258]~E(x2581,x2582)+E(f37(x2583,x2581),f37(x2583,x2582))
% 21.40/21.39 [259]~E(x2591,x2592)+E(f569(x2591,x2593,x2594),f569(x2592,x2593,x2594))
% 21.40/21.39 [260]~E(x2601,x2602)+E(f569(x2603,x2601,x2604),f569(x2603,x2602,x2604))
% 21.40/21.39 [261]~E(x2611,x2612)+E(f569(x2613,x2614,x2611),f569(x2613,x2614,x2612))
% 21.40/21.39 [262]~E(x2621,x2622)+E(f528(x2621,x2623,x2624,x2625,x2626),f528(x2622,x2623,x2624,x2625,x2626))
% 21.40/21.39 [263]~E(x2631,x2632)+E(f528(x2633,x2631,x2634,x2635,x2636),f528(x2633,x2632,x2634,x2635,x2636))
% 21.40/21.39 [264]~E(x2641,x2642)+E(f528(x2643,x2644,x2641,x2645,x2646),f528(x2643,x2644,x2642,x2645,x2646))
% 21.40/21.39 [265]~E(x2651,x2652)+E(f528(x2653,x2654,x2655,x2651,x2656),f528(x2653,x2654,x2655,x2652,x2656))
% 21.40/21.39 [266]~E(x2661,x2662)+E(f528(x2663,x2664,x2665,x2666,x2661),f528(x2663,x2664,x2665,x2666,x2662))
% 21.40/21.39 [267]~E(x2671,x2672)+E(f236(x2671,x2673,x2674,x2675),f236(x2672,x2673,x2674,x2675))
% 21.40/21.39 [268]~E(x2681,x2682)+E(f236(x2683,x2681,x2684,x2685),f236(x2683,x2682,x2684,x2685))
% 21.40/21.39 [269]~E(x2691,x2692)+E(f236(x2693,x2694,x2691,x2695),f236(x2693,x2694,x2692,x2695))
% 21.40/21.39 [270]~E(x2701,x2702)+E(f236(x2703,x2704,x2705,x2701),f236(x2703,x2704,x2705,x2702))
% 21.40/21.39 [271]~E(x2711,x2712)+E(f214(x2711),f214(x2712))
% 21.40/21.39 [272]~E(x2721,x2722)+E(f105(x2721),f105(x2722))
% 21.40/21.39 [273]~E(x2731,x2732)+E(f133(x2731,x2733),f133(x2732,x2733))
% 21.40/21.39 [274]~E(x2741,x2742)+E(f133(x2743,x2741),f133(x2743,x2742))
% 21.40/21.39 [275]~E(x2751,x2752)+E(f447(x2751,x2753,x2754),f447(x2752,x2753,x2754))
% 21.40/21.39 [276]~E(x2761,x2762)+E(f447(x2763,x2761,x2764),f447(x2763,x2762,x2764))
% 21.40/21.39 [277]~E(x2771,x2772)+E(f447(x2773,x2774,x2771),f447(x2773,x2774,x2772))
% 21.40/21.39 [278]~E(x2781,x2782)+E(f84(x2781),f84(x2782))
% 21.40/21.39 [279]~E(x2791,x2792)+E(f305(x2791,x2793,x2794),f305(x2792,x2793,x2794))
% 21.40/21.39 [280]~E(x2801,x2802)+E(f305(x2803,x2801,x2804),f305(x2803,x2802,x2804))
% 21.40/21.39 [281]~E(x2811,x2812)+E(f305(x2813,x2814,x2811),f305(x2813,x2814,x2812))
% 21.40/21.39 [282]~E(x2821,x2822)+E(f83(x2821,x2823),f83(x2822,x2823))
% 21.40/21.39 [283]~E(x2831,x2832)+E(f83(x2833,x2831),f83(x2833,x2832))
% 21.40/21.39 [284]~E(x2841,x2842)+E(f123(x2841,x2843),f123(x2842,x2843))
% 21.40/21.39 [285]~E(x2851,x2852)+E(f123(x2853,x2851),f123(x2853,x2852))
% 21.40/21.39 [286]~E(x2861,x2862)+E(f800(x2861,x2863,x2864),f800(x2862,x2863,x2864))
% 21.40/21.39 [287]~E(x2871,x2872)+E(f800(x2873,x2871,x2874),f800(x2873,x2872,x2874))
% 21.40/21.39 [288]~E(x2881,x2882)+E(f800(x2883,x2884,x2881),f800(x2883,x2884,x2882))
% 21.40/21.39 [289]~E(x2891,x2892)+E(f188(x2891),f188(x2892))
% 21.40/21.39 [290]~E(x2901,x2902)+E(f747(x2901,x2903,x2904),f747(x2902,x2903,x2904))
% 21.40/21.39 [291]~E(x2911,x2912)+E(f747(x2913,x2911,x2914),f747(x2913,x2912,x2914))
% 21.40/21.39 [292]~E(x2921,x2922)+E(f747(x2923,x2924,x2921),f747(x2923,x2924,x2922))
% 21.40/21.39 [293]~E(x2931,x2932)+E(f124(x2931),f124(x2932))
% 21.40/21.39 [294]~E(x2941,x2942)+E(f143(x2941,x2943),f143(x2942,x2943))
% 21.40/21.39 [295]~E(x2951,x2952)+E(f143(x2953,x2951),f143(x2953,x2952))
% 21.40/21.39 [296]~E(x2961,x2962)+E(f222(x2961,x2963,x2964,x2965),f222(x2962,x2963,x2964,x2965))
% 21.40/21.39 [297]~E(x2971,x2972)+E(f222(x2973,x2971,x2974,x2975),f222(x2973,x2972,x2974,x2975))
% 21.40/21.39 [298]~E(x2981,x2982)+E(f222(x2983,x2984,x2981,x2985),f222(x2983,x2984,x2982,x2985))
% 21.40/21.39 [299]~E(x2991,x2992)+E(f222(x2993,x2994,x2995,x2991),f222(x2993,x2994,x2995,x2992))
% 21.40/21.39 [300]~E(x3001,x3002)+E(f329(x3001,x3003),f329(x3002,x3003))
% 21.40/21.39 [301]~E(x3011,x3012)+E(f329(x3013,x3011),f329(x3013,x3012))
% 21.40/21.39 [302]~E(x3021,x3022)+E(f642(x3021,x3023,x3024,x3025,x3026,x3027,x3028,x3029),f642(x3022,x3023,x3024,x3025,x3026,x3027,x3028,x3029))
% 21.40/21.39 [303]~E(x3031,x3032)+E(f642(x3033,x3031,x3034,x3035,x3036,x3037,x3038,x3039),f642(x3033,x3032,x3034,x3035,x3036,x3037,x3038,x3039))
% 21.40/21.39 [304]~E(x3041,x3042)+E(f642(x3043,x3044,x3041,x3045,x3046,x3047,x3048,x3049),f642(x3043,x3044,x3042,x3045,x3046,x3047,x3048,x3049))
% 21.40/21.39 [305]~E(x3051,x3052)+E(f642(x3053,x3054,x3055,x3051,x3056,x3057,x3058,x3059),f642(x3053,x3054,x3055,x3052,x3056,x3057,x3058,x3059))
% 21.40/21.39 [306]~E(x3061,x3062)+E(f642(x3063,x3064,x3065,x3066,x3061,x3067,x3068,x3069),f642(x3063,x3064,x3065,x3066,x3062,x3067,x3068,x3069))
% 21.40/21.39 [307]~E(x3071,x3072)+E(f642(x3073,x3074,x3075,x3076,x3077,x3071,x3078,x3079),f642(x3073,x3074,x3075,x3076,x3077,x3072,x3078,x3079))
% 21.40/21.39 [308]~E(x3081,x3082)+E(f642(x3083,x3084,x3085,x3086,x3087,x3088,x3081,x3089),f642(x3083,x3084,x3085,x3086,x3087,x3088,x3082,x3089))
% 21.40/21.39 [309]~E(x3091,x3092)+E(f642(x3093,x3094,x3095,x3096,x3097,x3098,x3099,x3091),f642(x3093,x3094,x3095,x3096,x3097,x3098,x3099,x3092))
% 21.40/21.39 [310]~E(x3101,x3102)+E(f862(x3101),f862(x3102))
% 21.40/21.39 [311]~E(x3111,x3112)+E(f148(x3111),f148(x3112))
% 21.40/21.39 [312]~E(x3121,x3122)+E(f52(x3121,x3123),f52(x3122,x3123))
% 21.40/21.39 [313]~E(x3131,x3132)+E(f52(x3133,x3131),f52(x3133,x3132))
% 21.40/21.39 [314]~E(x3141,x3142)+E(f178(x3141,x3143),f178(x3142,x3143))
% 21.40/21.39 [315]~E(x3151,x3152)+E(f178(x3153,x3151),f178(x3153,x3152))
% 21.40/21.39 [316]~E(x3161,x3162)+E(f308(x3161,x3163),f308(x3162,x3163))
% 21.40/21.39 [317]~E(x3171,x3172)+E(f308(x3173,x3171),f308(x3173,x3172))
% 21.40/21.39 [318]~E(x3181,x3182)+E(f64(x3181,x3183),f64(x3182,x3183))
% 21.40/21.39 [319]~E(x3191,x3192)+E(f64(x3193,x3191),f64(x3193,x3192))
% 21.40/21.39 [320]~E(x3201,x3202)+E(f521(x3201,x3203,x3204,x3205),f521(x3202,x3203,x3204,x3205))
% 21.40/21.39 [321]~E(x3211,x3212)+E(f521(x3213,x3211,x3214,x3215),f521(x3213,x3212,x3214,x3215))
% 21.40/21.39 [322]~E(x3221,x3222)+E(f521(x3223,x3224,x3221,x3225),f521(x3223,x3224,x3222,x3225))
% 21.40/21.39 [323]~E(x3231,x3232)+E(f521(x3233,x3234,x3235,x3231),f521(x3233,x3234,x3235,x3232))
% 21.40/21.39 [324]~E(x3241,x3242)+E(f801(x3241,x3243,x3244),f801(x3242,x3243,x3244))
% 21.40/21.39 [325]~E(x3251,x3252)+E(f801(x3253,x3251,x3254),f801(x3253,x3252,x3254))
% 21.40/21.39 [326]~E(x3261,x3262)+E(f801(x3263,x3264,x3261),f801(x3263,x3264,x3262))
% 21.40/21.39 [327]~E(x3271,x3272)+E(f288(x3271,x3273),f288(x3272,x3273))
% 21.40/21.39 [328]~E(x3281,x3282)+E(f288(x3283,x3281),f288(x3283,x3282))
% 21.40/21.39 [329]~E(x3291,x3292)+E(f834(x3291,x3293,x3294),f834(x3292,x3293,x3294))
% 21.40/21.39 [330]~E(x3301,x3302)+E(f834(x3303,x3301,x3304),f834(x3303,x3302,x3304))
% 21.40/21.39 [331]~E(x3311,x3312)+E(f834(x3313,x3314,x3311),f834(x3313,x3314,x3312))
% 21.40/21.39 [332]~E(x3321,x3322)+E(f765(x3321,x3323,x3324,x3325),f765(x3322,x3323,x3324,x3325))
% 21.40/21.39 [333]~E(x3331,x3332)+E(f765(x3333,x3331,x3334,x3335),f765(x3333,x3332,x3334,x3335))
% 21.40/21.39 [334]~E(x3341,x3342)+E(f765(x3343,x3344,x3341,x3345),f765(x3343,x3344,x3342,x3345))
% 21.40/21.39 [335]~E(x3351,x3352)+E(f765(x3353,x3354,x3355,x3351),f765(x3353,x3354,x3355,x3352))
% 21.40/21.39 [336]~E(x3361,x3362)+E(f430(x3361,x3363,x3364,x3365,x3366),f430(x3362,x3363,x3364,x3365,x3366))
% 21.40/21.39 [337]~E(x3371,x3372)+E(f430(x3373,x3371,x3374,x3375,x3376),f430(x3373,x3372,x3374,x3375,x3376))
% 21.40/21.39 [338]~E(x3381,x3382)+E(f430(x3383,x3384,x3381,x3385,x3386),f430(x3383,x3384,x3382,x3385,x3386))
% 21.40/21.39 [339]~E(x3391,x3392)+E(f430(x3393,x3394,x3395,x3391,x3396),f430(x3393,x3394,x3395,x3392,x3396))
% 21.40/21.39 [340]~E(x3401,x3402)+E(f430(x3403,x3404,x3405,x3406,x3401),f430(x3403,x3404,x3405,x3406,x3402))
% 21.40/21.39 [341]~E(x3411,x3412)+E(f541(x3411,x3413,x3414,x3415,x3416,x3417),f541(x3412,x3413,x3414,x3415,x3416,x3417))
% 21.40/21.39 [342]~E(x3421,x3422)+E(f541(x3423,x3421,x3424,x3425,x3426,x3427),f541(x3423,x3422,x3424,x3425,x3426,x3427))
% 21.40/21.39 [343]~E(x3431,x3432)+E(f541(x3433,x3434,x3431,x3435,x3436,x3437),f541(x3433,x3434,x3432,x3435,x3436,x3437))
% 21.40/21.39 [344]~E(x3441,x3442)+E(f541(x3443,x3444,x3445,x3441,x3446,x3447),f541(x3443,x3444,x3445,x3442,x3446,x3447))
% 21.40/21.39 [345]~E(x3451,x3452)+E(f541(x3453,x3454,x3455,x3456,x3451,x3457),f541(x3453,x3454,x3455,x3456,x3452,x3457))
% 21.40/21.39 [346]~E(x3461,x3462)+E(f541(x3463,x3464,x3465,x3466,x3467,x3461),f541(x3463,x3464,x3465,x3466,x3467,x3462))
% 21.40/21.39 [347]~E(x3471,x3472)+E(f149(x3471),f149(x3472))
% 21.40/21.39 [348]~E(x3481,x3482)+E(f542(x3481,x3483,x3484,x3485,x3486,x3487,x3488,x3489),f542(x3482,x3483,x3484,x3485,x3486,x3487,x3488,x3489))
% 21.40/21.39 [349]~E(x3491,x3492)+E(f542(x3493,x3491,x3494,x3495,x3496,x3497,x3498,x3499),f542(x3493,x3492,x3494,x3495,x3496,x3497,x3498,x3499))
% 21.40/21.39 [350]~E(x3501,x3502)+E(f542(x3503,x3504,x3501,x3505,x3506,x3507,x3508,x3509),f542(x3503,x3504,x3502,x3505,x3506,x3507,x3508,x3509))
% 21.40/21.39 [351]~E(x3511,x3512)+E(f542(x3513,x3514,x3515,x3511,x3516,x3517,x3518,x3519),f542(x3513,x3514,x3515,x3512,x3516,x3517,x3518,x3519))
% 21.40/21.39 [352]~E(x3521,x3522)+E(f542(x3523,x3524,x3525,x3526,x3521,x3527,x3528,x3529),f542(x3523,x3524,x3525,x3526,x3522,x3527,x3528,x3529))
% 21.40/21.39 [353]~E(x3531,x3532)+E(f542(x3533,x3534,x3535,x3536,x3537,x3531,x3538,x3539),f542(x3533,x3534,x3535,x3536,x3537,x3532,x3538,x3539))
% 21.40/21.39 [354]~E(x3541,x3542)+E(f542(x3543,x3544,x3545,x3546,x3547,x3548,x3541,x3549),f542(x3543,x3544,x3545,x3546,x3547,x3548,x3542,x3549))
% 21.40/21.39 [355]~E(x3551,x3552)+E(f542(x3553,x3554,x3555,x3556,x3557,x3558,x3559,x3551),f542(x3553,x3554,x3555,x3556,x3557,x3558,x3559,x3552))
% 21.40/21.39 [356]~E(x3561,x3562)+E(f325(x3561,x3563,x3564,x3565),f325(x3562,x3563,x3564,x3565))
% 21.40/21.39 [357]~E(x3571,x3572)+E(f325(x3573,x3571,x3574,x3575),f325(x3573,x3572,x3574,x3575))
% 21.40/21.39 [358]~E(x3581,x3582)+E(f325(x3583,x3584,x3581,x3585),f325(x3583,x3584,x3582,x3585))
% 21.40/21.39 [359]~E(x3591,x3592)+E(f325(x3593,x3594,x3595,x3591),f325(x3593,x3594,x3595,x3592))
% 21.40/21.39 [360]~E(x3601,x3602)+E(f267(x3601,x3603),f267(x3602,x3603))
% 21.40/21.39 [361]~E(x3611,x3612)+E(f267(x3613,x3611),f267(x3613,x3612))
% 21.40/21.39 [362]~E(x3621,x3622)+E(f477(x3621,x3623,x3624,x3625),f477(x3622,x3623,x3624,x3625))
% 21.40/21.39 [363]~E(x3631,x3632)+E(f477(x3633,x3631,x3634,x3635),f477(x3633,x3632,x3634,x3635))
% 21.40/21.39 [364]~E(x3641,x3642)+E(f477(x3643,x3644,x3641,x3645),f477(x3643,x3644,x3642,x3645))
% 21.40/21.39 [365]~E(x3651,x3652)+E(f477(x3653,x3654,x3655,x3651),f477(x3653,x3654,x3655,x3652))
% 21.40/21.39 [366]~E(x3661,x3662)+E(f253(x3661,x3663),f253(x3662,x3663))
% 21.40/21.39 [367]~E(x3671,x3672)+E(f253(x3673,x3671),f253(x3673,x3672))
% 21.40/21.39 [368]~E(x3681,x3682)+E(f286(x3681,x3683),f286(x3682,x3683))
% 21.40/21.39 [369]~E(x3691,x3692)+E(f286(x3693,x3691),f286(x3693,x3692))
% 21.40/21.39 [370]~E(x3701,x3702)+E(f285(x3701,x3703,x3704),f285(x3702,x3703,x3704))
% 21.40/21.39 [371]~E(x3711,x3712)+E(f285(x3713,x3711,x3714),f285(x3713,x3712,x3714))
% 21.40/21.39 [372]~E(x3721,x3722)+E(f285(x3723,x3724,x3721),f285(x3723,x3724,x3722))
% 21.40/21.39 [373]~E(x3731,x3732)+E(f30(x3731,x3733),f30(x3732,x3733))
% 21.40/21.39 [374]~E(x3741,x3742)+E(f30(x3743,x3741),f30(x3743,x3742))
% 21.40/21.39 [375]~E(x3751,x3752)+E(f324(x3751,x3753,x3754,x3755),f324(x3752,x3753,x3754,x3755))
% 21.40/21.39 [376]~E(x3761,x3762)+E(f324(x3763,x3761,x3764,x3765),f324(x3763,x3762,x3764,x3765))
% 21.40/21.39 [377]~E(x3771,x3772)+E(f324(x3773,x3774,x3771,x3775),f324(x3773,x3774,x3772,x3775))
% 21.40/21.39 [378]~E(x3781,x3782)+E(f324(x3783,x3784,x3785,x3781),f324(x3783,x3784,x3785,x3782))
% 21.40/21.39 [379]~E(x3791,x3792)+E(f294(x3791,x3793,x3794),f294(x3792,x3793,x3794))
% 21.40/21.39 [380]~E(x3801,x3802)+E(f294(x3803,x3801,x3804),f294(x3803,x3802,x3804))
% 21.40/21.39 [381]~E(x3811,x3812)+E(f294(x3813,x3814,x3811),f294(x3813,x3814,x3812))
% 21.40/21.39 [382]~E(x3821,x3822)+E(f141(x3821,x3823),f141(x3822,x3823))
% 21.40/21.39 [383]~E(x3831,x3832)+E(f141(x3833,x3831),f141(x3833,x3832))
% 21.40/21.39 [384]~E(x3841,x3842)+E(f332(x3841,x3843),f332(x3842,x3843))
% 21.40/21.39 [385]~E(x3851,x3852)+E(f332(x3853,x3851),f332(x3853,x3852))
% 21.40/21.39 [386]~E(x3861,x3862)+E(f35(x3861,x3863,x3864),f35(x3862,x3863,x3864))
% 21.40/21.39 [387]~E(x3871,x3872)+E(f35(x3873,x3871,x3874),f35(x3873,x3872,x3874))
% 21.40/21.39 [388]~E(x3881,x3882)+E(f35(x3883,x3884,x3881),f35(x3883,x3884,x3882))
% 21.40/21.39 [389]~E(x3891,x3892)+E(f334(x3891,x3893),f334(x3892,x3893))
% 21.40/21.39 [390]~E(x3901,x3902)+E(f334(x3903,x3901),f334(x3903,x3902))
% 21.40/21.39 [391]~E(x3911,x3912)+E(f177(x3911,x3913,x3914,x3915),f177(x3912,x3913,x3914,x3915))
% 21.40/21.39 [392]~E(x3921,x3922)+E(f177(x3923,x3921,x3924,x3925),f177(x3923,x3922,x3924,x3925))
% 21.40/21.39 [393]~E(x3931,x3932)+E(f177(x3933,x3934,x3931,x3935),f177(x3933,x3934,x3932,x3935))
% 21.40/21.39 [394]~E(x3941,x3942)+E(f177(x3943,x3944,x3945,x3941),f177(x3943,x3944,x3945,x3942))
% 21.40/21.39 [395]~E(x3951,x3952)+E(f865(x3951),f865(x3952))
% 21.40/21.39 [396]~E(x3961,x3962)+E(f159(x3961),f159(x3962))
% 21.40/21.39 [397]~E(x3971,x3972)+E(f371(x3971,x3973,x3974,x3975,x3976),f371(x3972,x3973,x3974,x3975,x3976))
% 21.40/21.39 [398]~E(x3981,x3982)+E(f371(x3983,x3981,x3984,x3985,x3986),f371(x3983,x3982,x3984,x3985,x3986))
% 21.40/21.39 [399]~E(x3991,x3992)+E(f371(x3993,x3994,x3991,x3995,x3996),f371(x3993,x3994,x3992,x3995,x3996))
% 21.40/21.39 [400]~E(x4001,x4002)+E(f371(x4003,x4004,x4005,x4001,x4006),f371(x4003,x4004,x4005,x4002,x4006))
% 21.40/21.39 [401]~E(x4011,x4012)+E(f371(x4013,x4014,x4015,x4016,x4011),f371(x4013,x4014,x4015,x4016,x4012))
% 21.40/21.39 [402]~E(x4021,x4022)+E(f144(x4021,x4023,x4024),f144(x4022,x4023,x4024))
% 21.40/21.39 [403]~E(x4031,x4032)+E(f144(x4033,x4031,x4034),f144(x4033,x4032,x4034))
% 21.40/21.39 [404]~E(x4041,x4042)+E(f144(x4043,x4044,x4041),f144(x4043,x4044,x4042))
% 21.40/21.39 [405]~E(x4051,x4052)+E(f796(x4051,x4053,x4054),f796(x4052,x4053,x4054))
% 21.40/21.39 [406]~E(x4061,x4062)+E(f796(x4063,x4061,x4064),f796(x4063,x4062,x4064))
% 21.40/21.39 [407]~E(x4071,x4072)+E(f796(x4073,x4074,x4071),f796(x4073,x4074,x4072))
% 21.40/21.39 [408]~E(x4081,x4082)+E(f548(x4081),f548(x4082))
% 21.40/21.39 [409]~E(x4091,x4092)+E(f81(x4091,x4093),f81(x4092,x4093))
% 21.40/21.39 [410]~E(x4101,x4102)+E(f81(x4103,x4101),f81(x4103,x4102))
% 21.40/21.39 [411]~E(x4111,x4112)+E(f474(x4111,x4113,x4114),f474(x4112,x4113,x4114))
% 21.40/21.39 [412]~E(x4121,x4122)+E(f474(x4123,x4121,x4124),f474(x4123,x4122,x4124))
% 21.40/21.39 [413]~E(x4131,x4132)+E(f474(x4133,x4134,x4131),f474(x4133,x4134,x4132))
% 21.40/21.39 [414]~E(x4141,x4142)+E(f475(x4141,x4143,x4144),f475(x4142,x4143,x4144))
% 21.40/21.39 [415]~E(x4151,x4152)+E(f475(x4153,x4151,x4154),f475(x4153,x4152,x4154))
% 21.40/21.39 [416]~E(x4161,x4162)+E(f475(x4163,x4164,x4161),f475(x4163,x4164,x4162))
% 21.40/21.39 [417]~E(x4171,x4172)+E(f228(x4171,x4173),f228(x4172,x4173))
% 21.40/21.39 [418]~E(x4181,x4182)+E(f228(x4183,x4181),f228(x4183,x4182))
% 21.40/21.39 [419]~E(x4191,x4192)+E(f720(x4191,x4193,x4194,x4195),f720(x4192,x4193,x4194,x4195))
% 21.40/21.39 [420]~E(x4201,x4202)+E(f720(x4203,x4201,x4204,x4205),f720(x4203,x4202,x4204,x4205))
% 21.40/21.39 [421]~E(x4211,x4212)+E(f720(x4213,x4214,x4211,x4215),f720(x4213,x4214,x4212,x4215))
% 21.40/21.39 [422]~E(x4221,x4222)+E(f720(x4223,x4224,x4225,x4221),f720(x4223,x4224,x4225,x4222))
% 21.40/21.39 [423]~E(x4231,x4232)+E(f629(x4231,x4233),f629(x4232,x4233))
% 21.40/21.39 [424]~E(x4241,x4242)+E(f629(x4243,x4241),f629(x4243,x4242))
% 21.40/21.39 [425]~E(x4251,x4252)+E(f72(x4251,x4253),f72(x4252,x4253))
% 21.40/21.39 [426]~E(x4261,x4262)+E(f72(x4263,x4261),f72(x4263,x4262))
% 21.40/21.39 [427]~E(x4271,x4272)+E(f135(x4271),f135(x4272))
% 21.40/21.39 [428]~E(x4281,x4282)+E(f49(x4281),f49(x4282))
% 21.40/21.39 [429]~E(x4291,x4292)+E(f94(x4291,x4293),f94(x4292,x4293))
% 21.40/21.39 [430]~E(x4301,x4302)+E(f94(x4303,x4301),f94(x4303,x4302))
% 21.40/21.39 [431]~E(x4311,x4312)+E(f231(x4311,x4313,x4314),f231(x4312,x4313,x4314))
% 21.40/21.39 [432]~E(x4321,x4322)+E(f231(x4323,x4321,x4324),f231(x4323,x4322,x4324))
% 21.40/21.39 [433]~E(x4331,x4332)+E(f231(x4333,x4334,x4331),f231(x4333,x4334,x4332))
% 21.40/21.39 [434]~E(x4341,x4342)+E(f99(x4341,x4343),f99(x4342,x4343))
% 21.40/21.39 [435]~E(x4351,x4352)+E(f99(x4353,x4351),f99(x4353,x4352))
% 21.40/21.39 [436]~E(x4361,x4362)+E(f167(x4361,x4363),f167(x4362,x4363))
% 21.40/21.39 [437]~E(x4371,x4372)+E(f167(x4373,x4371),f167(x4373,x4372))
% 21.40/21.39 [438]~E(x4381,x4382)+E(f838(x4381,x4383,x4384,x4385),f838(x4382,x4383,x4384,x4385))
% 21.40/21.39 [439]~E(x4391,x4392)+E(f838(x4393,x4391,x4394,x4395),f838(x4393,x4392,x4394,x4395))
% 21.40/21.39 [440]~E(x4401,x4402)+E(f838(x4403,x4404,x4401,x4405),f838(x4403,x4404,x4402,x4405))
% 21.40/21.39 [441]~E(x4411,x4412)+E(f838(x4413,x4414,x4415,x4411),f838(x4413,x4414,x4415,x4412))
% 21.40/21.39 [442]~E(x4421,x4422)+E(f313(x4421,x4423,x4424),f313(x4422,x4423,x4424))
% 21.40/21.39 [443]~E(x4431,x4432)+E(f313(x4433,x4431,x4434),f313(x4433,x4432,x4434))
% 21.40/21.39 [444]~E(x4441,x4442)+E(f313(x4443,x4444,x4441),f313(x4443,x4444,x4442))
% 21.40/21.39 [445]~E(x4451,x4452)+E(f54(x4451,x4453),f54(x4452,x4453))
% 21.40/21.39 [446]~E(x4461,x4462)+E(f54(x4463,x4461),f54(x4463,x4462))
% 21.40/21.39 [447]~E(x4471,x4472)+E(f580(x4471,x4473,x4474,x4475,x4476),f580(x4472,x4473,x4474,x4475,x4476))
% 21.40/21.39 [448]~E(x4481,x4482)+E(f580(x4483,x4481,x4484,x4485,x4486),f580(x4483,x4482,x4484,x4485,x4486))
% 21.40/21.39 [449]~E(x4491,x4492)+E(f580(x4493,x4494,x4491,x4495,x4496),f580(x4493,x4494,x4492,x4495,x4496))
% 21.40/21.39 [450]~E(x4501,x4502)+E(f580(x4503,x4504,x4505,x4501,x4506),f580(x4503,x4504,x4505,x4502,x4506))
% 21.40/21.39 [451]~E(x4511,x4512)+E(f580(x4513,x4514,x4515,x4516,x4511),f580(x4513,x4514,x4515,x4516,x4512))
% 21.40/21.39 [452]~E(x4521,x4522)+E(f598(x4521,x4523,x4524),f598(x4522,x4523,x4524))
% 21.40/21.39 [453]~E(x4531,x4532)+E(f598(x4533,x4531,x4534),f598(x4533,x4532,x4534))
% 21.40/21.39 [454]~E(x4541,x4542)+E(f598(x4543,x4544,x4541),f598(x4543,x4544,x4542))
% 21.40/21.39 [455]~E(x4551,x4552)+E(f136(x4551,x4553),f136(x4552,x4553))
% 21.40/21.39 [456]~E(x4561,x4562)+E(f136(x4563,x4561),f136(x4563,x4562))
% 21.40/21.39 [457]~E(x4571,x4572)+E(f306(x4571,x4573,x4574),f306(x4572,x4573,x4574))
% 21.40/21.39 [458]~E(x4581,x4582)+E(f306(x4583,x4581,x4584),f306(x4583,x4582,x4584))
% 21.40/21.39 [459]~E(x4591,x4592)+E(f306(x4593,x4594,x4591),f306(x4593,x4594,x4592))
% 21.40/21.39 [460]~E(x4601,x4602)+E(f400(x4601,x4603),f400(x4602,x4603))
% 21.40/21.39 [461]~E(x4611,x4612)+E(f400(x4613,x4611),f400(x4613,x4612))
% 21.40/21.39 [462]~E(x4621,x4622)+E(f173(x4621,x4623,x4624),f173(x4622,x4623,x4624))
% 21.40/21.39 [463]~E(x4631,x4632)+E(f173(x4633,x4631,x4634),f173(x4633,x4632,x4634))
% 21.40/21.39 [464]~E(x4641,x4642)+E(f173(x4643,x4644,x4641),f173(x4643,x4644,x4642))
% 21.40/21.39 [465]~E(x4651,x4652)+E(f260(x4651,x4653,x4654,x4655,x4656,x4657),f260(x4652,x4653,x4654,x4655,x4656,x4657))
% 21.40/21.39 [466]~E(x4661,x4662)+E(f260(x4663,x4661,x4664,x4665,x4666,x4667),f260(x4663,x4662,x4664,x4665,x4666,x4667))
% 21.40/21.39 [467]~E(x4671,x4672)+E(f260(x4673,x4674,x4671,x4675,x4676,x4677),f260(x4673,x4674,x4672,x4675,x4676,x4677))
% 21.40/21.39 [468]~E(x4681,x4682)+E(f260(x4683,x4684,x4685,x4681,x4686,x4687),f260(x4683,x4684,x4685,x4682,x4686,x4687))
% 21.40/21.39 [469]~E(x4691,x4692)+E(f260(x4693,x4694,x4695,x4696,x4691,x4697),f260(x4693,x4694,x4695,x4696,x4692,x4697))
% 21.40/21.39 [470]~E(x4701,x4702)+E(f260(x4703,x4704,x4705,x4706,x4707,x4701),f260(x4703,x4704,x4705,x4706,x4707,x4702))
% 21.40/21.39 [471]~E(x4711,x4712)+E(f145(x4711,x4713,x4714,x4715,x4716),f145(x4712,x4713,x4714,x4715,x4716))
% 21.40/21.39 [472]~E(x4721,x4722)+E(f145(x4723,x4721,x4724,x4725,x4726),f145(x4723,x4722,x4724,x4725,x4726))
% 21.40/21.39 [473]~E(x4731,x4732)+E(f145(x4733,x4734,x4731,x4735,x4736),f145(x4733,x4734,x4732,x4735,x4736))
% 21.40/21.39 [474]~E(x4741,x4742)+E(f145(x4743,x4744,x4745,x4741,x4746),f145(x4743,x4744,x4745,x4742,x4746))
% 21.40/21.39 [475]~E(x4751,x4752)+E(f145(x4753,x4754,x4755,x4756,x4751),f145(x4753,x4754,x4755,x4756,x4752))
% 21.40/21.39 [476]~E(x4761,x4762)+E(f322(x4761,x4763,x4764,x4765),f322(x4762,x4763,x4764,x4765))
% 21.40/21.39 [477]~E(x4771,x4772)+E(f322(x4773,x4771,x4774,x4775),f322(x4773,x4772,x4774,x4775))
% 21.40/21.39 [478]~E(x4781,x4782)+E(f322(x4783,x4784,x4781,x4785),f322(x4783,x4784,x4782,x4785))
% 21.40/21.39 [479]~E(x4791,x4792)+E(f322(x4793,x4794,x4795,x4791),f322(x4793,x4794,x4795,x4792))
% 21.40/21.39 [480]~E(x4801,x4802)+E(f166(x4801,x4803,x4804),f166(x4802,x4803,x4804))
% 21.40/21.39 [481]~E(x4811,x4812)+E(f166(x4813,x4811,x4814),f166(x4813,x4812,x4814))
% 21.40/21.39 [482]~E(x4821,x4822)+E(f166(x4823,x4824,x4821),f166(x4823,x4824,x4822))
% 21.40/21.39 [483]~E(x4831,x4832)+E(f61(x4831,x4833),f61(x4832,x4833))
% 21.40/21.39 [484]~E(x4841,x4842)+E(f61(x4843,x4841),f61(x4843,x4842))
% 21.40/21.39 [485]~E(x4851,x4852)+E(f140(x4851,x4853),f140(x4852,x4853))
% 21.40/21.39 [486]~E(x4861,x4862)+E(f140(x4863,x4861),f140(x4863,x4862))
% 21.40/21.39 [487]~E(x4871,x4872)+E(f309(x4871),f309(x4872))
% 21.40/21.39 [488]~E(x4881,x4882)+E(f673(x4881,x4883,x4884,x4885,x4886),f673(x4882,x4883,x4884,x4885,x4886))
% 21.40/21.39 [489]~E(x4891,x4892)+E(f673(x4893,x4891,x4894,x4895,x4896),f673(x4893,x4892,x4894,x4895,x4896))
% 21.40/21.39 [490]~E(x4901,x4902)+E(f673(x4903,x4904,x4901,x4905,x4906),f673(x4903,x4904,x4902,x4905,x4906))
% 21.40/21.39 [491]~E(x4911,x4912)+E(f673(x4913,x4914,x4915,x4911,x4916),f673(x4913,x4914,x4915,x4912,x4916))
% 21.40/21.39 [492]~E(x4921,x4922)+E(f673(x4923,x4924,x4925,x4926,x4921),f673(x4923,x4924,x4925,x4926,x4922))
% 21.40/21.39 [493]~E(x4931,x4932)+E(f732(x4931,x4933,x4934,x4935,x4936),f732(x4932,x4933,x4934,x4935,x4936))
% 21.40/21.39 [494]~E(x4941,x4942)+E(f732(x4943,x4941,x4944,x4945,x4946),f732(x4943,x4942,x4944,x4945,x4946))
% 21.40/21.39 [495]~E(x4951,x4952)+E(f732(x4953,x4954,x4951,x4955,x4956),f732(x4953,x4954,x4952,x4955,x4956))
% 21.40/21.39 [496]~E(x4961,x4962)+E(f732(x4963,x4964,x4965,x4961,x4966),f732(x4963,x4964,x4965,x4962,x4966))
% 21.40/21.39 [497]~E(x4971,x4972)+E(f732(x4973,x4974,x4975,x4976,x4971),f732(x4973,x4974,x4975,x4976,x4972))
% 21.40/21.39 [498]~E(x4981,x4982)+E(f684(x4981,x4983,x4984),f684(x4982,x4983,x4984))
% 21.40/21.39 [499]~E(x4991,x4992)+E(f684(x4993,x4991,x4994),f684(x4993,x4992,x4994))
% 21.40/21.39 [500]~E(x5001,x5002)+E(f684(x5003,x5004,x5001),f684(x5003,x5004,x5002))
% 21.40/21.39 [501]~E(x5011,x5012)+E(f690(x5011,x5013,x5014,x5015),f690(x5012,x5013,x5014,x5015))
% 21.40/21.39 [502]~E(x5021,x5022)+E(f690(x5023,x5021,x5024,x5025),f690(x5023,x5022,x5024,x5025))
% 21.40/21.39 [503]~E(x5031,x5032)+E(f690(x5033,x5034,x5031,x5035),f690(x5033,x5034,x5032,x5035))
% 21.40/21.39 [504]~E(x5041,x5042)+E(f690(x5043,x5044,x5045,x5041),f690(x5043,x5044,x5045,x5042))
% 21.40/21.39 [505]~E(x5051,x5052)+E(f38(x5051,x5053),f38(x5052,x5053))
% 21.40/21.39 [506]~E(x5061,x5062)+E(f38(x5063,x5061),f38(x5063,x5062))
% 21.40/21.39 [507]~E(x5071,x5072)+E(f168(x5071,x5073),f168(x5072,x5073))
% 21.40/21.39 [508]~E(x5081,x5082)+E(f168(x5083,x5081),f168(x5083,x5082))
% 21.40/21.39 [509]~E(x5091,x5092)+E(f75(x5091,x5093,x5094,x5095,x5096),f75(x5092,x5093,x5094,x5095,x5096))
% 21.40/21.39 [510]~E(x5101,x5102)+E(f75(x5103,x5101,x5104,x5105,x5106),f75(x5103,x5102,x5104,x5105,x5106))
% 21.40/21.39 [511]~E(x5111,x5112)+E(f75(x5113,x5114,x5111,x5115,x5116),f75(x5113,x5114,x5112,x5115,x5116))
% 21.40/21.39 [512]~E(x5121,x5122)+E(f75(x5123,x5124,x5125,x5121,x5126),f75(x5123,x5124,x5125,x5122,x5126))
% 21.40/21.39 [513]~E(x5131,x5132)+E(f75(x5133,x5134,x5135,x5136,x5131),f75(x5133,x5134,x5135,x5136,x5132))
% 21.40/21.39 [514]~E(x5141,x5142)+E(f258(x5141,x5143),f258(x5142,x5143))
% 21.40/21.39 [515]~E(x5151,x5152)+E(f258(x5153,x5151),f258(x5153,x5152))
% 21.40/21.39 [516]~E(x5161,x5162)+E(f73(x5161,x5163,x5164),f73(x5162,x5163,x5164))
% 21.40/21.39 [517]~E(x5171,x5172)+E(f73(x5173,x5171,x5174),f73(x5173,x5172,x5174))
% 21.40/21.39 [518]~E(x5181,x5182)+E(f73(x5183,x5184,x5181),f73(x5183,x5184,x5182))
% 21.40/21.39 [519]~E(x5191,x5192)+E(f816(x5191,x5193,x5194),f816(x5192,x5193,x5194))
% 21.40/21.39 [520]~E(x5201,x5202)+E(f816(x5203,x5201,x5204),f816(x5203,x5202,x5204))
% 21.40/21.39 [521]~E(x5211,x5212)+E(f816(x5213,x5214,x5211),f816(x5213,x5214,x5212))
% 21.40/21.39 [522]~E(x5221,x5222)+E(f372(x5221,x5223,x5224,x5225),f372(x5222,x5223,x5224,x5225))
% 21.40/21.39 [523]~E(x5231,x5232)+E(f372(x5233,x5231,x5234,x5235),f372(x5233,x5232,x5234,x5235))
% 21.40/21.39 [524]~E(x5241,x5242)+E(f372(x5243,x5244,x5241,x5245),f372(x5243,x5244,x5242,x5245))
% 21.40/21.39 [525]~E(x5251,x5252)+E(f372(x5253,x5254,x5255,x5251),f372(x5253,x5254,x5255,x5252))
% 21.40/21.39 [526]~E(x5261,x5262)+E(f525(x5261,x5263,x5264),f525(x5262,x5263,x5264))
% 21.40/21.39 [527]~E(x5271,x5272)+E(f525(x5273,x5271,x5274),f525(x5273,x5272,x5274))
% 21.40/21.39 [528]~E(x5281,x5282)+E(f525(x5283,x5284,x5281),f525(x5283,x5284,x5282))
% 21.40/21.39 [529]~E(x5291,x5292)+E(f97(x5291),f97(x5292))
% 21.40/21.39 [530]~E(x5301,x5302)+E(f307(x5301),f307(x5302))
% 21.40/21.39 [531]~E(x5311,x5312)+E(f326(x5311,x5313,x5314,x5315,x5316),f326(x5312,x5313,x5314,x5315,x5316))
% 21.40/21.39 [532]~E(x5321,x5322)+E(f326(x5323,x5321,x5324,x5325,x5326),f326(x5323,x5322,x5324,x5325,x5326))
% 21.40/21.39 [533]~E(x5331,x5332)+E(f326(x5333,x5334,x5331,x5335,x5336),f326(x5333,x5334,x5332,x5335,x5336))
% 21.40/21.39 [534]~E(x5341,x5342)+E(f326(x5343,x5344,x5345,x5341,x5346),f326(x5343,x5344,x5345,x5342,x5346))
% 21.40/21.39 [535]~E(x5351,x5352)+E(f326(x5353,x5354,x5355,x5356,x5351),f326(x5353,x5354,x5355,x5356,x5352))
% 21.40/21.39 [536]~E(x5361,x5362)+E(f618(x5361,x5363,x5364),f618(x5362,x5363,x5364))
% 21.40/21.39 [537]~E(x5371,x5372)+E(f618(x5373,x5371,x5374),f618(x5373,x5372,x5374))
% 21.40/21.39 [538]~E(x5381,x5382)+E(f618(x5383,x5384,x5381),f618(x5383,x5384,x5382))
% 21.40/21.39 [539]~E(x5391,x5392)+E(f164(x5391),f164(x5392))
% 21.40/21.39 [540]~E(x5401,x5402)+E(f492(x5401,x5403,x5404,x5405),f492(x5402,x5403,x5404,x5405))
% 21.40/21.39 [541]~E(x5411,x5412)+E(f492(x5413,x5411,x5414,x5415),f492(x5413,x5412,x5414,x5415))
% 21.40/21.39 [542]~E(x5421,x5422)+E(f492(x5423,x5424,x5421,x5425),f492(x5423,x5424,x5422,x5425))
% 21.40/21.39 [543]~E(x5431,x5432)+E(f492(x5433,x5434,x5435,x5431),f492(x5433,x5434,x5435,x5432))
% 21.40/21.39 [544]~E(x5441,x5442)+E(f537(x5441,x5443,x5444,x5445),f537(x5442,x5443,x5444,x5445))
% 21.40/21.39 [545]~E(x5451,x5452)+E(f537(x5453,x5451,x5454,x5455),f537(x5453,x5452,x5454,x5455))
% 21.40/21.39 [546]~E(x5461,x5462)+E(f537(x5463,x5464,x5461,x5465),f537(x5463,x5464,x5462,x5465))
% 21.40/21.39 [547]~E(x5471,x5472)+E(f537(x5473,x5474,x5475,x5471),f537(x5473,x5474,x5475,x5472))
% 21.40/21.39 [548]~E(x5481,x5482)+E(f700(x5481,x5483),f700(x5482,x5483))
% 21.40/21.39 [549]~E(x5491,x5492)+E(f700(x5493,x5491),f700(x5493,x5492))
% 21.40/21.39 [550]~E(x5501,x5502)+E(f265(x5501),f265(x5502))
% 21.40/21.39 [551]~E(x5511,x5512)+E(f665(x5511),f665(x5512))
% 21.40/21.39 [552]~E(x5521,x5522)+E(f798(x5521,x5523,x5524),f798(x5522,x5523,x5524))
% 21.40/21.39 [553]~E(x5531,x5532)+E(f798(x5533,x5531,x5534),f798(x5533,x5532,x5534))
% 21.40/21.39 [554]~E(x5541,x5542)+E(f798(x5543,x5544,x5541),f798(x5543,x5544,x5542))
% 21.40/21.39 [555]~E(x5551,x5552)+E(f33(x5551,x5553,x5554),f33(x5552,x5553,x5554))
% 21.40/21.39 [556]~E(x5561,x5562)+E(f33(x5563,x5561,x5564),f33(x5563,x5562,x5564))
% 21.40/21.39 [557]~E(x5571,x5572)+E(f33(x5573,x5574,x5571),f33(x5573,x5574,x5572))
% 21.40/21.39 [558]~E(x5581,x5582)+E(f443(x5581,x5583,x5584),f443(x5582,x5583,x5584))
% 21.40/21.39 [559]~E(x5591,x5592)+E(f443(x5593,x5591,x5594),f443(x5593,x5592,x5594))
% 21.40/21.39 [560]~E(x5601,x5602)+E(f443(x5603,x5604,x5601),f443(x5603,x5604,x5602))
% 21.40/21.39 [561]~E(x5611,x5612)+E(f266(x5611),f266(x5612))
% 21.40/21.39 [562]~E(x5621,x5622)+E(f420(x5621,x5623,x5624,x5625,x5626),f420(x5622,x5623,x5624,x5625,x5626))
% 21.40/21.39 [563]~E(x5631,x5632)+E(f420(x5633,x5631,x5634,x5635,x5636),f420(x5633,x5632,x5634,x5635,x5636))
% 21.40/21.39 [564]~E(x5641,x5642)+E(f420(x5643,x5644,x5641,x5645,x5646),f420(x5643,x5644,x5642,x5645,x5646))
% 21.40/21.39 [565]~E(x5651,x5652)+E(f420(x5653,x5654,x5655,x5651,x5656),f420(x5653,x5654,x5655,x5652,x5656))
% 21.40/21.39 [566]~E(x5661,x5662)+E(f420(x5663,x5664,x5665,x5666,x5661),f420(x5663,x5664,x5665,x5666,x5662))
% 21.40/21.39 [567]~E(x5671,x5672)+E(f871(x5671,x5673),f871(x5672,x5673))
% 21.40/21.39 [568]~E(x5681,x5682)+E(f871(x5683,x5681),f871(x5683,x5682))
% 21.40/21.39 [569]~E(x5691,x5692)+E(f100(x5691),f100(x5692))
% 21.40/21.39 [570]~E(x5701,x5702)+E(f579(x5701,x5703,x5704,x5705,x5706),f579(x5702,x5703,x5704,x5705,x5706))
% 21.40/21.39 [571]~E(x5711,x5712)+E(f579(x5713,x5711,x5714,x5715,x5716),f579(x5713,x5712,x5714,x5715,x5716))
% 21.40/21.39 [572]~E(x5721,x5722)+E(f579(x5723,x5724,x5721,x5725,x5726),f579(x5723,x5724,x5722,x5725,x5726))
% 21.40/21.39 [573]~E(x5731,x5732)+E(f579(x5733,x5734,x5735,x5731,x5736),f579(x5733,x5734,x5735,x5732,x5736))
% 21.40/21.39 [574]~E(x5741,x5742)+E(f579(x5743,x5744,x5745,x5746,x5741),f579(x5743,x5744,x5745,x5746,x5742))
% 21.40/21.39 [575]~E(x5751,x5752)+E(f520(x5751,x5753,x5754,x5755),f520(x5752,x5753,x5754,x5755))
% 21.40/21.39 [576]~E(x5761,x5762)+E(f520(x5763,x5761,x5764,x5765),f520(x5763,x5762,x5764,x5765))
% 21.40/21.39 [577]~E(x5771,x5772)+E(f520(x5773,x5774,x5771,x5775),f520(x5773,x5774,x5772,x5775))
% 21.40/21.39 [578]~E(x5781,x5782)+E(f520(x5783,x5784,x5785,x5781),f520(x5783,x5784,x5785,x5782))
% 21.40/21.39 [579]~E(x5791,x5792)+E(f55(x5791),f55(x5792))
% 21.40/21.39 [580]~E(x5801,x5802)+E(f397(x5801,x5803),f397(x5802,x5803))
% 21.40/21.39 [581]~E(x5811,x5812)+E(f397(x5813,x5811),f397(x5813,x5812))
% 21.40/21.39 [582]~E(x5821,x5822)+E(f717(x5821,x5823,x5824,x5825,x5826,x5827),f717(x5822,x5823,x5824,x5825,x5826,x5827))
% 21.40/21.39 [583]~E(x5831,x5832)+E(f717(x5833,x5831,x5834,x5835,x5836,x5837),f717(x5833,x5832,x5834,x5835,x5836,x5837))
% 21.40/21.39 [584]~E(x5841,x5842)+E(f717(x5843,x5844,x5841,x5845,x5846,x5847),f717(x5843,x5844,x5842,x5845,x5846,x5847))
% 21.40/21.39 [585]~E(x5851,x5852)+E(f717(x5853,x5854,x5855,x5851,x5856,x5857),f717(x5853,x5854,x5855,x5852,x5856,x5857))
% 21.40/21.39 [586]~E(x5861,x5862)+E(f717(x5863,x5864,x5865,x5866,x5861,x5867),f717(x5863,x5864,x5865,x5866,x5862,x5867))
% 21.40/21.39 [587]~E(x5871,x5872)+E(f717(x5873,x5874,x5875,x5876,x5877,x5871),f717(x5873,x5874,x5875,x5876,x5877,x5872))
% 21.40/21.39 [588]~E(x5881,x5882)+E(f562(x5881,x5883,x5884),f562(x5882,x5883,x5884))
% 21.40/21.39 [589]~E(x5891,x5892)+E(f562(x5893,x5891,x5894),f562(x5893,x5892,x5894))
% 21.40/21.39 [590]~E(x5901,x5902)+E(f562(x5903,x5904,x5901),f562(x5903,x5904,x5902))
% 21.40/21.39 [591]~E(x5911,x5912)+E(f810(x5911,x5913),f810(x5912,x5913))
% 21.40/21.39 [592]~E(x5921,x5922)+E(f810(x5923,x5921),f810(x5923,x5922))
% 21.40/21.39 [593]~E(x5931,x5932)+E(f487(x5931,x5933,x5934,x5935),f487(x5932,x5933,x5934,x5935))
% 21.40/21.39 [594]~E(x5941,x5942)+E(f487(x5943,x5941,x5944,x5945),f487(x5943,x5942,x5944,x5945))
% 21.40/21.39 [595]~E(x5951,x5952)+E(f487(x5953,x5954,x5951,x5955),f487(x5953,x5954,x5952,x5955))
% 21.40/21.39 [596]~E(x5961,x5962)+E(f487(x5963,x5964,x5965,x5961),f487(x5963,x5964,x5965,x5962))
% 21.40/21.39 [597]~E(x5971,x5972)+E(f238(x5971),f238(x5972))
% 21.40/21.39 [598]~E(x5981,x5982)+E(f409(x5981,x5983,x5984,x5985),f409(x5982,x5983,x5984,x5985))
% 21.40/21.39 [599]~E(x5991,x5992)+E(f409(x5993,x5991,x5994,x5995),f409(x5993,x5992,x5994,x5995))
% 21.40/21.39 [600]~E(x6001,x6002)+E(f409(x6003,x6004,x6001,x6005),f409(x6003,x6004,x6002,x6005))
% 21.40/21.39 [601]~E(x6011,x6012)+E(f409(x6013,x6014,x6015,x6011),f409(x6013,x6014,x6015,x6012))
% 21.40/21.39 [602]~E(x6021,x6022)+E(f543(x6021,x6023,x6024,x6025,x6026),f543(x6022,x6023,x6024,x6025,x6026))
% 21.40/21.39 [603]~E(x6031,x6032)+E(f543(x6033,x6031,x6034,x6035,x6036),f543(x6033,x6032,x6034,x6035,x6036))
% 21.40/21.39 [604]~E(x6041,x6042)+E(f543(x6043,x6044,x6041,x6045,x6046),f543(x6043,x6044,x6042,x6045,x6046))
% 21.40/21.39 [605]~E(x6051,x6052)+E(f543(x6053,x6054,x6055,x6051,x6056),f543(x6053,x6054,x6055,x6052,x6056))
% 21.40/21.39 [606]~E(x6061,x6062)+E(f543(x6063,x6064,x6065,x6066,x6061),f543(x6063,x6064,x6065,x6066,x6062))
% 21.40/21.39 [607]~E(x6071,x6072)+E(f15(x6071,x6073),f15(x6072,x6073))
% 21.40/21.39 [608]~E(x6081,x6082)+E(f15(x6083,x6081),f15(x6083,x6082))
% 21.40/21.39 [609]~E(x6091,x6092)+E(f213(x6091,x6093,x6094,x6095,x6096,x6097,x6098),f213(x6092,x6093,x6094,x6095,x6096,x6097,x6098))
% 21.40/21.39 [610]~E(x6101,x6102)+E(f213(x6103,x6101,x6104,x6105,x6106,x6107,x6108),f213(x6103,x6102,x6104,x6105,x6106,x6107,x6108))
% 21.40/21.39 [611]~E(x6111,x6112)+E(f213(x6113,x6114,x6111,x6115,x6116,x6117,x6118),f213(x6113,x6114,x6112,x6115,x6116,x6117,x6118))
% 21.40/21.39 [612]~E(x6121,x6122)+E(f213(x6123,x6124,x6125,x6121,x6126,x6127,x6128),f213(x6123,x6124,x6125,x6122,x6126,x6127,x6128))
% 21.40/21.39 [613]~E(x6131,x6132)+E(f213(x6133,x6134,x6135,x6136,x6131,x6137,x6138),f213(x6133,x6134,x6135,x6136,x6132,x6137,x6138))
% 21.40/21.39 [614]~E(x6141,x6142)+E(f213(x6143,x6144,x6145,x6146,x6147,x6141,x6148),f213(x6143,x6144,x6145,x6146,x6147,x6142,x6148))
% 21.40/21.39 [615]~E(x6151,x6152)+E(f213(x6153,x6154,x6155,x6156,x6157,x6158,x6151),f213(x6153,x6154,x6155,x6156,x6157,x6158,x6152))
% 21.40/21.39 [616]~E(x6161,x6162)+E(f556(x6161,x6163,x6164,x6165,x6166),f556(x6162,x6163,x6164,x6165,x6166))
% 21.40/21.39 [617]~E(x6171,x6172)+E(f556(x6173,x6171,x6174,x6175,x6176),f556(x6173,x6172,x6174,x6175,x6176))
% 21.40/21.39 [618]~E(x6181,x6182)+E(f556(x6183,x6184,x6181,x6185,x6186),f556(x6183,x6184,x6182,x6185,x6186))
% 21.40/21.39 [619]~E(x6191,x6192)+E(f556(x6193,x6194,x6195,x6191,x6196),f556(x6193,x6194,x6195,x6192,x6196))
% 21.40/21.39 [620]~E(x6201,x6202)+E(f556(x6203,x6204,x6205,x6206,x6201),f556(x6203,x6204,x6205,x6206,x6202))
% 21.40/21.39 [621]~E(x6211,x6212)+E(f814(x6211,x6213,x6214,x6215),f814(x6212,x6213,x6214,x6215))
% 21.40/21.39 [622]~E(x6221,x6222)+E(f814(x6223,x6221,x6224,x6225),f814(x6223,x6222,x6224,x6225))
% 21.40/21.39 [623]~E(x6231,x6232)+E(f814(x6233,x6234,x6231,x6235),f814(x6233,x6234,x6232,x6235))
% 21.40/21.39 [624]~E(x6241,x6242)+E(f814(x6243,x6244,x6245,x6241),f814(x6243,x6244,x6245,x6242))
% 21.40/21.39 [625]~E(x6251,x6252)+E(f233(x6251,x6253),f233(x6252,x6253))
% 21.40/21.39 [626]~E(x6261,x6262)+E(f233(x6263,x6261),f233(x6263,x6262))
% 21.40/21.39 [627]~E(x6271,x6272)+E(f583(x6271,x6273,x6274,x6275,x6276,x6277,x6278,x6279),f583(x6272,x6273,x6274,x6275,x6276,x6277,x6278,x6279))
% 21.40/21.39 [628]~E(x6281,x6282)+E(f583(x6283,x6281,x6284,x6285,x6286,x6287,x6288,x6289),f583(x6283,x6282,x6284,x6285,x6286,x6287,x6288,x6289))
% 21.40/21.39 [629]~E(x6291,x6292)+E(f583(x6293,x6294,x6291,x6295,x6296,x6297,x6298,x6299),f583(x6293,x6294,x6292,x6295,x6296,x6297,x6298,x6299))
% 21.40/21.39 [630]~E(x6301,x6302)+E(f583(x6303,x6304,x6305,x6301,x6306,x6307,x6308,x6309),f583(x6303,x6304,x6305,x6302,x6306,x6307,x6308,x6309))
% 21.40/21.39 [631]~E(x6311,x6312)+E(f583(x6313,x6314,x6315,x6316,x6311,x6317,x6318,x6319),f583(x6313,x6314,x6315,x6316,x6312,x6317,x6318,x6319))
% 21.40/21.39 [632]~E(x6321,x6322)+E(f583(x6323,x6324,x6325,x6326,x6327,x6321,x6328,x6329),f583(x6323,x6324,x6325,x6326,x6327,x6322,x6328,x6329))
% 21.40/21.39 [633]~E(x6331,x6332)+E(f583(x6333,x6334,x6335,x6336,x6337,x6338,x6331,x6339),f583(x6333,x6334,x6335,x6336,x6337,x6338,x6332,x6339))
% 21.40/21.39 [634]~E(x6341,x6342)+E(f583(x6343,x6344,x6345,x6346,x6347,x6348,x6349,x6341),f583(x6343,x6344,x6345,x6346,x6347,x6348,x6349,x6342))
% 21.40/21.39 [635]~E(x6351,x6352)+E(f181(x6351),f181(x6352))
% 21.40/21.39 [636]~E(x6361,x6362)+E(f549(x6361,x6363,x6364),f549(x6362,x6363,x6364))
% 21.40/21.39 [637]~E(x6371,x6372)+E(f549(x6373,x6371,x6374),f549(x6373,x6372,x6374))
% 21.40/21.39 [638]~E(x6381,x6382)+E(f549(x6383,x6384,x6381),f549(x6383,x6384,x6382))
% 21.40/21.39 [639]~E(x6391,x6392)+E(f200(x6391,x6393,x6394,x6395),f200(x6392,x6393,x6394,x6395))
% 21.40/21.39 [640]~E(x6401,x6402)+E(f200(x6403,x6401,x6404,x6405),f200(x6403,x6402,x6404,x6405))
% 21.40/21.39 [641]~E(x6411,x6412)+E(f200(x6413,x6414,x6411,x6415),f200(x6413,x6414,x6412,x6415))
% 21.40/21.39 [642]~E(x6421,x6422)+E(f200(x6423,x6424,x6425,x6421),f200(x6423,x6424,x6425,x6422))
% 21.40/21.39 [643]~E(x6431,x6432)+E(f497(x6431,x6433),f497(x6432,x6433))
% 21.40/21.39 [644]~E(x6441,x6442)+E(f497(x6443,x6441),f497(x6443,x6442))
% 21.40/21.39 [645]~E(x6451,x6452)+E(f261(x6451,x6453,x6454,x6455),f261(x6452,x6453,x6454,x6455))
% 21.40/21.39 [646]~E(x6461,x6462)+E(f261(x6463,x6461,x6464,x6465),f261(x6463,x6462,x6464,x6465))
% 21.40/21.39 [647]~E(x6471,x6472)+E(f261(x6473,x6474,x6471,x6475),f261(x6473,x6474,x6472,x6475))
% 21.40/21.39 [648]~E(x6481,x6482)+E(f261(x6483,x6484,x6485,x6481),f261(x6483,x6484,x6485,x6482))
% 21.40/21.39 [649]~E(x6491,x6492)+E(f91(x6491,x6493),f91(x6492,x6493))
% 21.40/21.39 [650]~E(x6501,x6502)+E(f91(x6503,x6501),f91(x6503,x6502))
% 21.40/21.39 [651]~E(x6511,x6512)+E(f155(x6511,x6513),f155(x6512,x6513))
% 21.40/21.39 [652]~E(x6521,x6522)+E(f155(x6523,x6521),f155(x6523,x6522))
% 21.40/21.39 [653]~E(x6531,x6532)+E(f369(x6531,x6533,x6534,x6535),f369(x6532,x6533,x6534,x6535))
% 21.40/21.39 [654]~E(x6541,x6542)+E(f369(x6543,x6541,x6544,x6545),f369(x6543,x6542,x6544,x6545))
% 21.40/21.39 [655]~E(x6551,x6552)+E(f369(x6553,x6554,x6551,x6555),f369(x6553,x6554,x6552,x6555))
% 21.40/21.39 [656]~E(x6561,x6562)+E(f369(x6563,x6564,x6565,x6561),f369(x6563,x6564,x6565,x6562))
% 21.40/21.39 [657]~E(x6571,x6572)+E(f321(x6571,x6573),f321(x6572,x6573))
% 21.40/21.39 [658]~E(x6581,x6582)+E(f321(x6583,x6581),f321(x6583,x6582))
% 21.40/21.39 [659]~E(x6591,x6592)+E(f824(x6591,x6593,x6594),f824(x6592,x6593,x6594))
% 21.40/21.39 [660]~E(x6601,x6602)+E(f824(x6603,x6601,x6604),f824(x6603,x6602,x6604))
% 21.40/21.39 [661]~E(x6611,x6612)+E(f824(x6613,x6614,x6611),f824(x6613,x6614,x6612))
% 21.40/21.39 [662]~E(x6621,x6622)+E(f203(x6621,x6623),f203(x6622,x6623))
% 21.40/21.39 [663]~E(x6631,x6632)+E(f203(x6633,x6631),f203(x6633,x6632))
% 21.40/21.39 [664]~E(x6641,x6642)+E(f299(x6641,x6643,x6644,x6645),f299(x6642,x6643,x6644,x6645))
% 21.40/21.39 [665]~E(x6651,x6652)+E(f299(x6653,x6651,x6654,x6655),f299(x6653,x6652,x6654,x6655))
% 21.40/21.39 [666]~E(x6661,x6662)+E(f299(x6663,x6664,x6661,x6665),f299(x6663,x6664,x6662,x6665))
% 21.40/21.39 [667]~E(x6671,x6672)+E(f299(x6673,x6674,x6675,x6671),f299(x6673,x6674,x6675,x6672))
% 21.40/21.39 [668]~E(x6681,x6682)+E(f304(x6681),f304(x6682))
% 21.40/21.39 [669]~E(x6691,x6692)+E(f596(x6691,x6693,x6694,x6695),f596(x6692,x6693,x6694,x6695))
% 21.40/21.39 [670]~E(x6701,x6702)+E(f596(x6703,x6701,x6704,x6705),f596(x6703,x6702,x6704,x6705))
% 21.40/21.39 [671]~E(x6711,x6712)+E(f596(x6713,x6714,x6711,x6715),f596(x6713,x6714,x6712,x6715))
% 21.40/21.39 [672]~E(x6721,x6722)+E(f596(x6723,x6724,x6725,x6721),f596(x6723,x6724,x6725,x6722))
% 21.40/21.39 [673]~E(x6731,x6732)+E(f175(x6731,x6733,x6734),f175(x6732,x6733,x6734))
% 21.40/21.39 [674]~E(x6741,x6742)+E(f175(x6743,x6741,x6744),f175(x6743,x6742,x6744))
% 21.40/21.39 [675]~E(x6751,x6752)+E(f175(x6753,x6754,x6751),f175(x6753,x6754,x6752))
% 21.40/21.39 [676]~E(x6761,x6762)+E(f14(x6761,x6763,x6764),f14(x6762,x6763,x6764))
% 21.40/21.39 [677]~E(x6771,x6772)+E(f14(x6773,x6771,x6774),f14(x6773,x6772,x6774))
% 21.40/21.39 [678]~E(x6781,x6782)+E(f14(x6783,x6784,x6781),f14(x6783,x6784,x6782))
% 21.40/21.39 [679]~E(x6791,x6792)+E(f585(x6791,x6793,x6794,x6795,x6796),f585(x6792,x6793,x6794,x6795,x6796))
% 21.40/21.39 [680]~E(x6801,x6802)+E(f585(x6803,x6801,x6804,x6805,x6806),f585(x6803,x6802,x6804,x6805,x6806))
% 21.40/21.39 [681]~E(x6811,x6812)+E(f585(x6813,x6814,x6811,x6815,x6816),f585(x6813,x6814,x6812,x6815,x6816))
% 21.40/21.39 [682]~E(x6821,x6822)+E(f585(x6823,x6824,x6825,x6821,x6826),f585(x6823,x6824,x6825,x6822,x6826))
% 21.40/21.39 [683]~E(x6831,x6832)+E(f585(x6833,x6834,x6835,x6836,x6831),f585(x6833,x6834,x6835,x6836,x6832))
% 21.40/21.39 [684]~E(x6841,x6842)+E(f787(x6841,x6843,x6844),f787(x6842,x6843,x6844))
% 21.40/21.39 [685]~E(x6851,x6852)+E(f787(x6853,x6851,x6854),f787(x6853,x6852,x6854))
% 21.40/21.39 [686]~E(x6861,x6862)+E(f787(x6863,x6864,x6861),f787(x6863,x6864,x6862))
% 21.40/21.39 [687]~E(x6871,x6872)+E(f645(x6871,x6873,x6874,x6875,x6876,x6877,x6878,x6879),f645(x6872,x6873,x6874,x6875,x6876,x6877,x6878,x6879))
% 21.40/21.39 [688]~E(x6881,x6882)+E(f645(x6883,x6881,x6884,x6885,x6886,x6887,x6888,x6889),f645(x6883,x6882,x6884,x6885,x6886,x6887,x6888,x6889))
% 21.40/21.39 [689]~E(x6891,x6892)+E(f645(x6893,x6894,x6891,x6895,x6896,x6897,x6898,x6899),f645(x6893,x6894,x6892,x6895,x6896,x6897,x6898,x6899))
% 21.40/21.39 [690]~E(x6901,x6902)+E(f645(x6903,x6904,x6905,x6901,x6906,x6907,x6908,x6909),f645(x6903,x6904,x6905,x6902,x6906,x6907,x6908,x6909))
% 21.40/21.39 [691]~E(x6911,x6912)+E(f645(x6913,x6914,x6915,x6916,x6911,x6917,x6918,x6919),f645(x6913,x6914,x6915,x6916,x6912,x6917,x6918,x6919))
% 21.40/21.39 [692]~E(x6921,x6922)+E(f645(x6923,x6924,x6925,x6926,x6927,x6921,x6928,x6929),f645(x6923,x6924,x6925,x6926,x6927,x6922,x6928,x6929))
% 21.40/21.39 [693]~E(x6931,x6932)+E(f645(x6933,x6934,x6935,x6936,x6937,x6938,x6931,x6939),f645(x6933,x6934,x6935,x6936,x6937,x6938,x6932,x6939))
% 21.40/21.39 [694]~E(x6941,x6942)+E(f645(x6943,x6944,x6945,x6946,x6947,x6948,x6949,x6941),f645(x6943,x6944,x6945,x6946,x6947,x6948,x6949,x6942))
% 21.40/21.39 [695]~E(x6951,x6952)+E(f390(x6951,x6953,x6954),f390(x6952,x6953,x6954))
% 21.40/21.39 [696]~E(x6961,x6962)+E(f390(x6963,x6961,x6964),f390(x6963,x6962,x6964))
% 21.40/21.39 [697]~E(x6971,x6972)+E(f390(x6973,x6974,x6971),f390(x6973,x6974,x6972))
% 21.40/21.39 [698]~E(x6981,x6982)+E(f540(x6981,x6983,x6984,x6985,x6986,x6987),f540(x6982,x6983,x6984,x6985,x6986,x6987))
% 21.40/21.39 [699]~E(x6991,x6992)+E(f540(x6993,x6991,x6994,x6995,x6996,x6997),f540(x6993,x6992,x6994,x6995,x6996,x6997))
% 21.40/21.39 [700]~E(x7001,x7002)+E(f540(x7003,x7004,x7001,x7005,x7006,x7007),f540(x7003,x7004,x7002,x7005,x7006,x7007))
% 21.40/21.39 [701]~E(x7011,x7012)+E(f540(x7013,x7014,x7015,x7011,x7016,x7017),f540(x7013,x7014,x7015,x7012,x7016,x7017))
% 21.40/21.39 [702]~E(x7021,x7022)+E(f540(x7023,x7024,x7025,x7026,x7021,x7027),f540(x7023,x7024,x7025,x7026,x7022,x7027))
% 21.40/21.39 [703]~E(x7031,x7032)+E(f540(x7033,x7034,x7035,x7036,x7037,x7031),f540(x7033,x7034,x7035,x7036,x7037,x7032))
% 21.40/21.39 [704]~E(x7041,x7042)+E(f180(x7041,x7043,x7044,x7045),f180(x7042,x7043,x7044,x7045))
% 21.40/21.39 [705]~E(x7051,x7052)+E(f180(x7053,x7051,x7054,x7055),f180(x7053,x7052,x7054,x7055))
% 21.40/21.39 [706]~E(x7061,x7062)+E(f180(x7063,x7064,x7061,x7065),f180(x7063,x7064,x7062,x7065))
% 21.40/21.39 [707]~E(x7071,x7072)+E(f180(x7073,x7074,x7075,x7071),f180(x7073,x7074,x7075,x7072))
% 21.40/21.39 [708]~E(x7081,x7082)+E(f818(x7081,x7083,x7084),f818(x7082,x7083,x7084))
% 21.40/21.39 [709]~E(x7091,x7092)+E(f818(x7093,x7091,x7094),f818(x7093,x7092,x7094))
% 21.40/21.39 [710]~E(x7101,x7102)+E(f818(x7103,x7104,x7101),f818(x7103,x7104,x7102))
% 21.40/21.39 [711]~E(x7111,x7112)+E(f547(x7111,x7113,x7114,x7115),f547(x7112,x7113,x7114,x7115))
% 21.40/21.39 [712]~E(x7121,x7122)+E(f547(x7123,x7121,x7124,x7125),f547(x7123,x7122,x7124,x7125))
% 21.40/21.39 [713]~E(x7131,x7132)+E(f547(x7133,x7134,x7131,x7135),f547(x7133,x7134,x7132,x7135))
% 21.40/21.39 [714]~E(x7141,x7142)+E(f547(x7143,x7144,x7145,x7141),f547(x7143,x7144,x7145,x7142))
% 21.40/21.39 [715]~E(x7151,x7152)+E(f268(x7151,x7153),f268(x7152,x7153))
% 21.40/21.39 [716]~E(x7161,x7162)+E(f268(x7163,x7161),f268(x7163,x7162))
% 21.40/21.39 [717]~E(x7171,x7172)+E(f289(x7171,x7173,x7174),f289(x7172,x7173,x7174))
% 21.40/21.39 [718]~E(x7181,x7182)+E(f289(x7183,x7181,x7184),f289(x7183,x7182,x7184))
% 21.40/21.39 [719]~E(x7191,x7192)+E(f289(x7193,x7194,x7191),f289(x7193,x7194,x7192))
% 21.40/21.39 [720]~E(x7201,x7202)+E(f296(x7201,x7203,x7204),f296(x7202,x7203,x7204))
% 21.40/21.39 [721]~E(x7211,x7212)+E(f296(x7213,x7211,x7214),f296(x7213,x7212,x7214))
% 21.40/21.39 [722]~E(x7221,x7222)+E(f296(x7223,x7224,x7221),f296(x7223,x7224,x7222))
% 21.40/21.39 [723]~E(x7231,x7232)+E(f750(x7231,x7233,x7234,x7235),f750(x7232,x7233,x7234,x7235))
% 21.40/21.39 [724]~E(x7241,x7242)+E(f750(x7243,x7241,x7244,x7245),f750(x7243,x7242,x7244,x7245))
% 21.40/21.39 [725]~E(x7251,x7252)+E(f750(x7253,x7254,x7251,x7255),f750(x7253,x7254,x7252,x7255))
% 21.40/21.39 [726]~E(x7261,x7262)+E(f750(x7263,x7264,x7265,x7261),f750(x7263,x7264,x7265,x7262))
% 21.40/21.39 [727]~E(x7271,x7272)+E(f647(x7271,x7273,x7274,x7275,x7276),f647(x7272,x7273,x7274,x7275,x7276))
% 21.40/21.39 [728]~E(x7281,x7282)+E(f647(x7283,x7281,x7284,x7285,x7286),f647(x7283,x7282,x7284,x7285,x7286))
% 21.40/21.39 [729]~E(x7291,x7292)+E(f647(x7293,x7294,x7291,x7295,x7296),f647(x7293,x7294,x7292,x7295,x7296))
% 21.40/21.39 [730]~E(x7301,x7302)+E(f647(x7303,x7304,x7305,x7301,x7306),f647(x7303,x7304,x7305,x7302,x7306))
% 21.40/21.39 [731]~E(x7311,x7312)+E(f647(x7313,x7314,x7315,x7316,x7311),f647(x7313,x7314,x7315,x7316,x7312))
% 21.40/21.39 [732]~E(x7321,x7322)+E(f201(x7321,x7323),f201(x7322,x7323))
% 21.40/21.39 [733]~E(x7331,x7332)+E(f201(x7333,x7331),f201(x7333,x7332))
% 21.40/21.39 [734]~E(x7341,x7342)+E(f165(x7341,x7343,x7344),f165(x7342,x7343,x7344))
% 21.40/21.39 [735]~E(x7351,x7352)+E(f165(x7353,x7351,x7354),f165(x7353,x7352,x7354))
% 21.40/21.39 [736]~E(x7361,x7362)+E(f165(x7363,x7364,x7361),f165(x7363,x7364,x7362))
% 21.40/21.39 [737]~E(x7371,x7372)+E(f709(x7371,x7373),f709(x7372,x7373))
% 21.40/21.39 [738]~E(x7381,x7382)+E(f709(x7383,x7381),f709(x7383,x7382))
% 21.40/21.39 [739]~E(x7391,x7392)+E(f290(x7391,x7393,x7394,x7395),f290(x7392,x7393,x7394,x7395))
% 21.40/21.39 [740]~E(x7401,x7402)+E(f290(x7403,x7401,x7404,x7405),f290(x7403,x7402,x7404,x7405))
% 21.40/21.39 [741]~E(x7411,x7412)+E(f290(x7413,x7414,x7411,x7415),f290(x7413,x7414,x7412,x7415))
% 21.40/21.39 [742]~E(x7421,x7422)+E(f290(x7423,x7424,x7425,x7421),f290(x7423,x7424,x7425,x7422))
% 21.40/21.39 [743]~E(x7431,x7432)+E(f802(x7431,x7433,x7434),f802(x7432,x7433,x7434))
% 21.40/21.39 [744]~E(x7441,x7442)+E(f802(x7443,x7441,x7444),f802(x7443,x7442,x7444))
% 21.40/21.39 [745]~E(x7451,x7452)+E(f802(x7453,x7454,x7451),f802(x7453,x7454,x7452))
% 21.40/21.39 [746]~E(x7461,x7462)+E(f688(x7461,x7463,x7464,x7465,x7466,x7467,x7468),f688(x7462,x7463,x7464,x7465,x7466,x7467,x7468))
% 21.40/21.39 [747]~E(x7471,x7472)+E(f688(x7473,x7471,x7474,x7475,x7476,x7477,x7478),f688(x7473,x7472,x7474,x7475,x7476,x7477,x7478))
% 21.40/21.39 [748]~E(x7481,x7482)+E(f688(x7483,x7484,x7481,x7485,x7486,x7487,x7488),f688(x7483,x7484,x7482,x7485,x7486,x7487,x7488))
% 21.40/21.39 [749]~E(x7491,x7492)+E(f688(x7493,x7494,x7495,x7491,x7496,x7497,x7498),f688(x7493,x7494,x7495,x7492,x7496,x7497,x7498))
% 21.40/21.39 [750]~E(x7501,x7502)+E(f688(x7503,x7504,x7505,x7506,x7501,x7507,x7508),f688(x7503,x7504,x7505,x7506,x7502,x7507,x7508))
% 21.40/21.39 [751]~E(x7511,x7512)+E(f688(x7513,x7514,x7515,x7516,x7517,x7511,x7518),f688(x7513,x7514,x7515,x7516,x7517,x7512,x7518))
% 21.40/21.39 [752]~E(x7521,x7522)+E(f688(x7523,x7524,x7525,x7526,x7527,x7528,x7521),f688(x7523,x7524,x7525,x7526,x7527,x7528,x7522))
% 21.40/21.39 [753]~E(x7531,x7532)+E(f280(x7531,x7533,x7534,x7535),f280(x7532,x7533,x7534,x7535))
% 21.40/21.39 [754]~E(x7541,x7542)+E(f280(x7543,x7541,x7544,x7545),f280(x7543,x7542,x7544,x7545))
% 21.40/21.39 [755]~E(x7551,x7552)+E(f280(x7553,x7554,x7551,x7555),f280(x7553,x7554,x7552,x7555))
% 21.40/21.39 [756]~E(x7561,x7562)+E(f280(x7563,x7564,x7565,x7561),f280(x7563,x7564,x7565,x7562))
% 21.40/21.39 [757]~E(x7571,x7572)+E(f344(x7571,x7573,x7574,x7575),f344(x7572,x7573,x7574,x7575))
% 21.40/21.39 [758]~E(x7581,x7582)+E(f344(x7583,x7581,x7584,x7585),f344(x7583,x7582,x7584,x7585))
% 21.40/21.39 [759]~E(x7591,x7592)+E(f344(x7593,x7594,x7591,x7595),f344(x7593,x7594,x7592,x7595))
% 21.40/21.39 [760]~E(x7601,x7602)+E(f344(x7603,x7604,x7605,x7601),f344(x7603,x7604,x7605,x7602))
% 21.40/21.39 [761]~E(x7611,x7612)+E(f637(x7611,x7613,x7614,x7615),f637(x7612,x7613,x7614,x7615))
% 21.40/21.39 [762]~E(x7621,x7622)+E(f637(x7623,x7621,x7624,x7625),f637(x7623,x7622,x7624,x7625))
% 21.40/21.39 [763]~E(x7631,x7632)+E(f637(x7633,x7634,x7631,x7635),f637(x7633,x7634,x7632,x7635))
% 21.40/21.39 [764]~E(x7641,x7642)+E(f637(x7643,x7644,x7645,x7641),f637(x7643,x7644,x7645,x7642))
% 21.40/21.39 [765]~E(x7651,x7652)+E(f760(x7651,x7653,x7654,x7655),f760(x7652,x7653,x7654,x7655))
% 21.40/21.39 [766]~E(x7661,x7662)+E(f760(x7663,x7661,x7664,x7665),f760(x7663,x7662,x7664,x7665))
% 21.40/21.39 [767]~E(x7671,x7672)+E(f760(x7673,x7674,x7671,x7675),f760(x7673,x7674,x7672,x7675))
% 21.40/21.39 [768]~E(x7681,x7682)+E(f760(x7683,x7684,x7685,x7681),f760(x7683,x7684,x7685,x7682))
% 21.40/21.39 [769]~E(x7691,x7692)+E(f154(x7691,x7693),f154(x7692,x7693))
% 21.40/21.39 [770]~E(x7701,x7702)+E(f154(x7703,x7701),f154(x7703,x7702))
% 21.40/21.39 [771]~E(x7711,x7712)+E(f737(x7711,x7713,x7714),f737(x7712,x7713,x7714))
% 21.40/21.39 [772]~E(x7721,x7722)+E(f737(x7723,x7721,x7724),f737(x7723,x7722,x7724))
% 21.40/21.39 [773]~E(x7731,x7732)+E(f737(x7733,x7734,x7731),f737(x7733,x7734,x7732))
% 21.40/21.39 [774]~E(x7741,x7742)+E(f457(x7741,x7743),f457(x7742,x7743))
% 21.40/21.39 [775]~E(x7751,x7752)+E(f457(x7753,x7751),f457(x7753,x7752))
% 21.40/21.39 [776]~E(x7761,x7762)+E(f101(x7761,x7763,x7764),f101(x7762,x7763,x7764))
% 21.40/21.39 [777]~E(x7771,x7772)+E(f101(x7773,x7771,x7774),f101(x7773,x7772,x7774))
% 21.40/21.39 [778]~E(x7781,x7782)+E(f101(x7783,x7784,x7781),f101(x7783,x7784,x7782))
% 21.40/21.39 [779]~E(x7791,x7792)+E(f486(x7791,x7793,x7794,x7795),f486(x7792,x7793,x7794,x7795))
% 21.40/21.39 [780]~E(x7801,x7802)+E(f486(x7803,x7801,x7804,x7805),f486(x7803,x7802,x7804,x7805))
% 21.40/21.39 [781]~E(x7811,x7812)+E(f486(x7813,x7814,x7811,x7815),f486(x7813,x7814,x7812,x7815))
% 21.40/21.39 [782]~E(x7821,x7822)+E(f486(x7823,x7824,x7825,x7821),f486(x7823,x7824,x7825,x7822))
% 21.40/21.39 [783]~E(x7831,x7832)+E(f95(x7831,x7833),f95(x7832,x7833))
% 21.40/21.39 [784]~E(x7841,x7842)+E(f95(x7843,x7841),f95(x7843,x7842))
% 21.40/21.39 [785]~E(x7851,x7852)+E(f300(x7851,x7853,x7854,x7855,x7856),f300(x7852,x7853,x7854,x7855,x7856))
% 21.40/21.39 [786]~E(x7861,x7862)+E(f300(x7863,x7861,x7864,x7865,x7866),f300(x7863,x7862,x7864,x7865,x7866))
% 21.40/21.39 [787]~E(x7871,x7872)+E(f300(x7873,x7874,x7871,x7875,x7876),f300(x7873,x7874,x7872,x7875,x7876))
% 21.40/21.39 [788]~E(x7881,x7882)+E(f300(x7883,x7884,x7885,x7881,x7886),f300(x7883,x7884,x7885,x7882,x7886))
% 21.40/21.39 [789]~E(x7891,x7892)+E(f300(x7893,x7894,x7895,x7896,x7891),f300(x7893,x7894,x7895,x7896,x7892))
% 21.40/21.39 [790]~E(x7901,x7902)+E(f16(x7901,x7903),f16(x7902,x7903))
% 21.40/21.39 [791]~E(x7911,x7912)+E(f16(x7913,x7911),f16(x7913,x7912))
% 21.40/21.39 [792]~E(x7921,x7922)+E(f74(x7921,x7923,x7924),f74(x7922,x7923,x7924))
% 21.40/21.39 [793]~E(x7931,x7932)+E(f74(x7933,x7931,x7934),f74(x7933,x7932,x7934))
% 21.40/21.39 [794]~E(x7941,x7942)+E(f74(x7943,x7944,x7941),f74(x7943,x7944,x7942))
% 21.40/21.39 [795]~E(x7951,x7952)+E(f57(x7951),f57(x7952))
% 21.40/21.39 [796]~E(x7961,x7962)+E(f657(x7961,x7963,x7964),f657(x7962,x7963,x7964))
% 21.40/21.39 [797]~E(x7971,x7972)+E(f657(x7973,x7971,x7974),f657(x7973,x7972,x7974))
% 21.40/21.39 [798]~E(x7981,x7982)+E(f657(x7983,x7984,x7981),f657(x7983,x7984,x7982))
% 21.40/21.39 [799]~E(x7991,x7992)+E(f612(x7991,x7993),f612(x7992,x7993))
% 21.40/21.39 [800]~E(x8001,x8002)+E(f612(x8003,x8001),f612(x8003,x8002))
% 21.40/21.39 [801]~E(x8011,x8012)+E(f582(x8011,x8013,x8014,x8015,x8016,x8017,x8018,x8019),f582(x8012,x8013,x8014,x8015,x8016,x8017,x8018,x8019))
% 21.40/21.39 [802]~E(x8021,x8022)+E(f582(x8023,x8021,x8024,x8025,x8026,x8027,x8028,x8029),f582(x8023,x8022,x8024,x8025,x8026,x8027,x8028,x8029))
% 21.40/21.39 [803]~E(x8031,x8032)+E(f582(x8033,x8034,x8031,x8035,x8036,x8037,x8038,x8039),f582(x8033,x8034,x8032,x8035,x8036,x8037,x8038,x8039))
% 21.40/21.39 [804]~E(x8041,x8042)+E(f582(x8043,x8044,x8045,x8041,x8046,x8047,x8048,x8049),f582(x8043,x8044,x8045,x8042,x8046,x8047,x8048,x8049))
% 21.40/21.39 [805]~E(x8051,x8052)+E(f582(x8053,x8054,x8055,x8056,x8051,x8057,x8058,x8059),f582(x8053,x8054,x8055,x8056,x8052,x8057,x8058,x8059))
% 21.40/21.39 [806]~E(x8061,x8062)+E(f582(x8063,x8064,x8065,x8066,x8067,x8061,x8068,x8069),f582(x8063,x8064,x8065,x8066,x8067,x8062,x8068,x8069))
% 21.40/21.39 [807]~E(x8071,x8072)+E(f582(x8073,x8074,x8075,x8076,x8077,x8078,x8071,x8079),f582(x8073,x8074,x8075,x8076,x8077,x8078,x8072,x8079))
% 21.40/21.39 [808]~E(x8081,x8082)+E(f582(x8083,x8084,x8085,x8086,x8087,x8088,x8089,x8081),f582(x8083,x8084,x8085,x8086,x8087,x8088,x8089,x8082))
% 21.40/21.39 [809]~E(x8091,x8092)+E(f62(x8091,x8093),f62(x8092,x8093))
% 21.40/21.39 [810]~E(x8101,x8102)+E(f62(x8103,x8101),f62(x8103,x8102))
% 21.40/21.39 [811]~E(x8111,x8112)+E(f226(x8111,x8113,x8114,x8115,x8116),f226(x8112,x8113,x8114,x8115,x8116))
% 21.40/21.39 [812]~E(x8121,x8122)+E(f226(x8123,x8121,x8124,x8125,x8126),f226(x8123,x8122,x8124,x8125,x8126))
% 21.40/21.39 [813]~E(x8131,x8132)+E(f226(x8133,x8134,x8131,x8135,x8136),f226(x8133,x8134,x8132,x8135,x8136))
% 21.40/21.39 [814]~E(x8141,x8142)+E(f226(x8143,x8144,x8145,x8141,x8146),f226(x8143,x8144,x8145,x8142,x8146))
% 21.40/21.39 [815]~E(x8151,x8152)+E(f226(x8153,x8154,x8155,x8156,x8151),f226(x8153,x8154,x8155,x8156,x8152))
% 21.40/21.39 [816]~E(x8161,x8162)+E(f282(x8161,x8163,x8164,x8165),f282(x8162,x8163,x8164,x8165))
% 21.40/21.39 [817]~E(x8171,x8172)+E(f282(x8173,x8171,x8174,x8175),f282(x8173,x8172,x8174,x8175))
% 21.40/21.39 [818]~E(x8181,x8182)+E(f282(x8183,x8184,x8181,x8185),f282(x8183,x8184,x8182,x8185))
% 21.40/21.39 [819]~E(x8191,x8192)+E(f282(x8193,x8194,x8195,x8191),f282(x8193,x8194,x8195,x8192))
% 21.40/21.39 [820]~E(x8201,x8202)+E(f126(x8201,x8203,x8204,x8205),f126(x8202,x8203,x8204,x8205))
% 21.40/21.39 [821]~E(x8211,x8212)+E(f126(x8213,x8211,x8214,x8215),f126(x8213,x8212,x8214,x8215))
% 21.40/21.39 [822]~E(x8221,x8222)+E(f126(x8223,x8224,x8221,x8225),f126(x8223,x8224,x8222,x8225))
% 21.40/21.39 [823]~E(x8231,x8232)+E(f126(x8233,x8234,x8235,x8231),f126(x8233,x8234,x8235,x8232))
% 21.40/21.39 [824]~E(x8241,x8242)+E(f484(x8241,x8243),f484(x8242,x8243))
% 21.40/21.39 [825]~E(x8251,x8252)+E(f484(x8253,x8251),f484(x8253,x8252))
% 21.40/21.39 [826]~E(x8261,x8262)+E(f595(x8261,x8263,x8264,x8265,x8266,x8267),f595(x8262,x8263,x8264,x8265,x8266,x8267))
% 21.40/21.39 [827]~E(x8271,x8272)+E(f595(x8273,x8271,x8274,x8275,x8276,x8277),f595(x8273,x8272,x8274,x8275,x8276,x8277))
% 21.40/21.39 [828]~E(x8281,x8282)+E(f595(x8283,x8284,x8281,x8285,x8286,x8287),f595(x8283,x8284,x8282,x8285,x8286,x8287))
% 21.40/21.39 [829]~E(x8291,x8292)+E(f595(x8293,x8294,x8295,x8291,x8296,x8297),f595(x8293,x8294,x8295,x8292,x8296,x8297))
% 21.40/21.39 [830]~E(x8301,x8302)+E(f595(x8303,x8304,x8305,x8306,x8301,x8307),f595(x8303,x8304,x8305,x8306,x8302,x8307))
% 21.40/21.39 [831]~E(x8311,x8312)+E(f595(x8313,x8314,x8315,x8316,x8317,x8311),f595(x8313,x8314,x8315,x8316,x8317,x8312))
% 21.40/21.39 [832]~E(x8321,x8322)+E(f749(x8321,x8323,x8324,x8325,x8326),f749(x8322,x8323,x8324,x8325,x8326))
% 21.40/21.39 [833]~E(x8331,x8332)+E(f749(x8333,x8331,x8334,x8335,x8336),f749(x8333,x8332,x8334,x8335,x8336))
% 21.40/21.39 [834]~E(x8341,x8342)+E(f749(x8343,x8344,x8341,x8345,x8346),f749(x8343,x8344,x8342,x8345,x8346))
% 21.40/21.39 [835]~E(x8351,x8352)+E(f749(x8353,x8354,x8355,x8351,x8356),f749(x8353,x8354,x8355,x8352,x8356))
% 21.40/21.39 [836]~E(x8361,x8362)+E(f749(x8363,x8364,x8365,x8366,x8361),f749(x8363,x8364,x8365,x8366,x8362))
% 21.40/21.39 [837]~E(x8371,x8372)+E(f661(x8371,x8373,x8374),f661(x8372,x8373,x8374))
% 21.40/21.39 [838]~E(x8381,x8382)+E(f661(x8383,x8381,x8384),f661(x8383,x8382,x8384))
% 21.40/21.39 [839]~E(x8391,x8392)+E(f661(x8393,x8394,x8391),f661(x8393,x8394,x8392))
% 21.40/21.39 [840]~E(x8401,x8402)+E(f628(x8401,x8403,x8404,x8405,x8406,x8407),f628(x8402,x8403,x8404,x8405,x8406,x8407))
% 21.40/21.39 [841]~E(x8411,x8412)+E(f628(x8413,x8411,x8414,x8415,x8416,x8417),f628(x8413,x8412,x8414,x8415,x8416,x8417))
% 21.40/21.39 [842]~E(x8421,x8422)+E(f628(x8423,x8424,x8421,x8425,x8426,x8427),f628(x8423,x8424,x8422,x8425,x8426,x8427))
% 21.40/21.39 [843]~E(x8431,x8432)+E(f628(x8433,x8434,x8435,x8431,x8436,x8437),f628(x8433,x8434,x8435,x8432,x8436,x8437))
% 21.40/21.39 [844]~E(x8441,x8442)+E(f628(x8443,x8444,x8445,x8446,x8441,x8447),f628(x8443,x8444,x8445,x8446,x8442,x8447))
% 21.40/21.39 [845]~E(x8451,x8452)+E(f628(x8453,x8454,x8455,x8456,x8457,x8451),f628(x8453,x8454,x8455,x8456,x8457,x8452))
% 21.40/21.39 [846]~E(x8461,x8462)+E(f295(x8461,x8463,x8464),f295(x8462,x8463,x8464))
% 21.40/21.39 [847]~E(x8471,x8472)+E(f295(x8473,x8471,x8474),f295(x8473,x8472,x8474))
% 21.40/21.39 [848]~E(x8481,x8482)+E(f295(x8483,x8484,x8481),f295(x8483,x8484,x8482))
% 21.40/21.39 [849]~E(x8491,x8492)+E(f137(x8491),f137(x8492))
% 21.40/21.39 [850]~E(x8501,x8502)+E(f312(x8501,x8503),f312(x8502,x8503))
% 21.40/21.39 [851]~E(x8511,x8512)+E(f312(x8513,x8511),f312(x8513,x8512))
% 21.40/21.39 [852]~E(x8521,x8522)+E(f96(x8521),f96(x8522))
% 21.40/21.39 [853]~E(x8531,x8532)+E(f498(x8531,x8533),f498(x8532,x8533))
% 21.40/21.39 [854]~E(x8541,x8542)+E(f498(x8543,x8541),f498(x8543,x8542))
% 21.40/21.39 [855]~E(x8551,x8552)+E(f835(x8551,x8553,x8554),f835(x8552,x8553,x8554))
% 21.40/21.39 [856]~E(x8561,x8562)+E(f835(x8563,x8561,x8564),f835(x8563,x8562,x8564))
% 21.40/21.39 [857]~E(x8571,x8572)+E(f835(x8573,x8574,x8571),f835(x8573,x8574,x8572))
% 21.40/21.39 [858]~E(x8581,x8582)+E(f488(x8581,x8583,x8584,x8585),f488(x8582,x8583,x8584,x8585))
% 21.40/21.39 [859]~E(x8591,x8592)+E(f488(x8593,x8591,x8594,x8595),f488(x8593,x8592,x8594,x8595))
% 21.40/21.39 [860]~E(x8601,x8602)+E(f488(x8603,x8604,x8601,x8605),f488(x8603,x8604,x8602,x8605))
% 21.40/21.39 [861]~E(x8611,x8612)+E(f488(x8613,x8614,x8615,x8611),f488(x8613,x8614,x8615,x8612))
% 21.40/21.39 [862]~E(x8621,x8622)+E(f591(x8621,x8623),f591(x8622,x8623))
% 21.40/21.39 [863]~E(x8631,x8632)+E(f591(x8633,x8631),f591(x8633,x8632))
% 21.40/21.39 [864]~E(x8641,x8642)+E(f279(x8641,x8643,x8644,x8645),f279(x8642,x8643,x8644,x8645))
% 21.40/21.39 [865]~E(x8651,x8652)+E(f279(x8653,x8651,x8654,x8655),f279(x8653,x8652,x8654,x8655))
% 21.40/21.39 [866]~E(x8661,x8662)+E(f279(x8663,x8664,x8661,x8665),f279(x8663,x8664,x8662,x8665))
% 21.40/21.39 [867]~E(x8671,x8672)+E(f279(x8673,x8674,x8675,x8671),f279(x8673,x8674,x8675,x8672))
% 21.40/21.39 [868]~E(x8681,x8682)+E(f432(x8681,x8683,x8684,x8685,x8686,x8687,x8688),f432(x8682,x8683,x8684,x8685,x8686,x8687,x8688))
% 21.40/21.39 [869]~E(x8691,x8692)+E(f432(x8693,x8691,x8694,x8695,x8696,x8697,x8698),f432(x8693,x8692,x8694,x8695,x8696,x8697,x8698))
% 21.40/21.39 [870]~E(x8701,x8702)+E(f432(x8703,x8704,x8701,x8705,x8706,x8707,x8708),f432(x8703,x8704,x8702,x8705,x8706,x8707,x8708))
% 21.40/21.39 [871]~E(x8711,x8712)+E(f432(x8713,x8714,x8715,x8711,x8716,x8717,x8718),f432(x8713,x8714,x8715,x8712,x8716,x8717,x8718))
% 21.40/21.39 [872]~E(x8721,x8722)+E(f432(x8723,x8724,x8725,x8726,x8721,x8727,x8728),f432(x8723,x8724,x8725,x8726,x8722,x8727,x8728))
% 21.40/21.39 [873]~E(x8731,x8732)+E(f432(x8733,x8734,x8735,x8736,x8737,x8731,x8738),f432(x8733,x8734,x8735,x8736,x8737,x8732,x8738))
% 21.40/21.39 [874]~E(x8741,x8742)+E(f432(x8743,x8744,x8745,x8746,x8747,x8748,x8741),f432(x8743,x8744,x8745,x8746,x8747,x8748,x8742))
% 21.40/21.39 [875]~E(x8751,x8752)+E(f275(x8751,x8753),f275(x8752,x8753))
% 21.40/21.39 [876]~E(x8761,x8762)+E(f275(x8763,x8761),f275(x8763,x8762))
% 21.40/21.39 [877]~E(x8771,x8772)+E(f374(x8771,x8773),f374(x8772,x8773))
% 21.40/21.39 [878]~E(x8781,x8782)+E(f374(x8783,x8781),f374(x8783,x8782))
% 21.40/21.39 [879]~E(x8791,x8792)+E(f683(x8791,x8793,x8794),f683(x8792,x8793,x8794))
% 21.40/21.39 [880]~E(x8801,x8802)+E(f683(x8803,x8801,x8804),f683(x8803,x8802,x8804))
% 21.40/21.39 [881]~E(x8811,x8812)+E(f683(x8813,x8814,x8811),f683(x8813,x8814,x8812))
% 21.40/21.39 [882]~E(x8821,x8822)+E(f748(x8821,x8823,x8824,x8825,x8826),f748(x8822,x8823,x8824,x8825,x8826))
% 21.40/21.39 [883]~E(x8831,x8832)+E(f748(x8833,x8831,x8834,x8835,x8836),f748(x8833,x8832,x8834,x8835,x8836))
% 21.40/21.39 [884]~E(x8841,x8842)+E(f748(x8843,x8844,x8841,x8845,x8846),f748(x8843,x8844,x8842,x8845,x8846))
% 21.40/21.39 [885]~E(x8851,x8852)+E(f748(x8853,x8854,x8855,x8851,x8856),f748(x8853,x8854,x8855,x8852,x8856))
% 21.40/21.39 [886]~E(x8861,x8862)+E(f748(x8863,x8864,x8865,x8866,x8861),f748(x8863,x8864,x8865,x8866,x8862))
% 21.40/21.39 [887]~E(x8871,x8872)+E(f705(x8871,x8873,x8874,x8875),f705(x8872,x8873,x8874,x8875))
% 21.40/21.39 [888]~E(x8881,x8882)+E(f705(x8883,x8881,x8884,x8885),f705(x8883,x8882,x8884,x8885))
% 21.40/21.39 [889]~E(x8891,x8892)+E(f705(x8893,x8894,x8891,x8895),f705(x8893,x8894,x8892,x8895))
% 21.40/21.39 [890]~E(x8901,x8902)+E(f705(x8903,x8904,x8905,x8901),f705(x8903,x8904,x8905,x8902))
% 21.40/21.39 [891]~E(x8911,x8912)+E(f538(x8911,x8913,x8914,x8915,x8916),f538(x8912,x8913,x8914,x8915,x8916))
% 21.40/21.39 [892]~E(x8921,x8922)+E(f538(x8923,x8921,x8924,x8925,x8926),f538(x8923,x8922,x8924,x8925,x8926))
% 21.40/21.39 [893]~E(x8931,x8932)+E(f538(x8933,x8934,x8931,x8935,x8936),f538(x8933,x8934,x8932,x8935,x8936))
% 21.40/21.39 [894]~E(x8941,x8942)+E(f538(x8943,x8944,x8945,x8941,x8946),f538(x8943,x8944,x8945,x8942,x8946))
% 21.40/21.39 [895]~E(x8951,x8952)+E(f538(x8953,x8954,x8955,x8956,x8951),f538(x8953,x8954,x8955,x8956,x8952))
% 21.40/21.39 [896]~E(x8961,x8962)+E(f715(x8961,x8963,x8964,x8965),f715(x8962,x8963,x8964,x8965))
% 21.40/21.39 [897]~E(x8971,x8972)+E(f715(x8973,x8971,x8974,x8975),f715(x8973,x8972,x8974,x8975))
% 21.40/21.39 [898]~E(x8981,x8982)+E(f715(x8983,x8984,x8981,x8985),f715(x8983,x8984,x8982,x8985))
% 21.40/21.39 [899]~E(x8991,x8992)+E(f715(x8993,x8994,x8995,x8991),f715(x8993,x8994,x8995,x8992))
% 21.40/21.39 [900]~E(x9001,x9002)+E(f793(x9001),f793(x9002))
% 21.40/21.39 [901]~E(x9011,x9012)+E(f699(x9011,x9013),f699(x9012,x9013))
% 21.40/21.39 [902]~E(x9021,x9022)+E(f699(x9023,x9021),f699(x9023,x9022))
% 21.40/21.39 [903]~E(x9031,x9032)+E(f380(x9031,x9033,x9034),f380(x9032,x9033,x9034))
% 21.40/21.39 [904]~E(x9041,x9042)+E(f380(x9043,x9041,x9044),f380(x9043,x9042,x9044))
% 21.40/21.39 [905]~E(x9051,x9052)+E(f380(x9053,x9054,x9051),f380(x9053,x9054,x9052))
% 21.40/21.39 [906]~E(x9061,x9062)+E(f817(x9061,x9063,x9064),f817(x9062,x9063,x9064))
% 21.40/21.39 [907]~E(x9071,x9072)+E(f817(x9073,x9071,x9074),f817(x9073,x9072,x9074))
% 21.40/21.39 [908]~E(x9081,x9082)+E(f817(x9083,x9084,x9081),f817(x9083,x9084,x9082))
% 21.40/21.39 [909]~E(x9091,x9092)+E(f328(x9091,x9093,x9094,x9095,x9096,x9097),f328(x9092,x9093,x9094,x9095,x9096,x9097))
% 21.40/21.39 [910]~E(x9101,x9102)+E(f328(x9103,x9101,x9104,x9105,x9106,x9107),f328(x9103,x9102,x9104,x9105,x9106,x9107))
% 21.40/21.39 [911]~E(x9111,x9112)+E(f328(x9113,x9114,x9111,x9115,x9116,x9117),f328(x9113,x9114,x9112,x9115,x9116,x9117))
% 21.40/21.39 [912]~E(x9121,x9122)+E(f328(x9123,x9124,x9125,x9121,x9126,x9127),f328(x9123,x9124,x9125,x9122,x9126,x9127))
% 21.40/21.39 [913]~E(x9131,x9132)+E(f328(x9133,x9134,x9135,x9136,x9131,x9137),f328(x9133,x9134,x9135,x9136,x9132,x9137))
% 21.40/21.39 [914]~E(x9141,x9142)+E(f328(x9143,x9144,x9145,x9146,x9147,x9141),f328(x9143,x9144,x9145,x9146,x9147,x9142))
% 21.40/21.39 [915]~E(x9151,x9152)+E(f217(x9151,x9153),f217(x9152,x9153))
% 21.40/21.39 [916]~E(x9161,x9162)+E(f217(x9163,x9161),f217(x9163,x9162))
% 21.40/21.39 [917]~E(x9171,x9172)+E(f672(x9171,x9173,x9174,x9175,x9176),f672(x9172,x9173,x9174,x9175,x9176))
% 21.40/21.39 [918]~E(x9181,x9182)+E(f672(x9183,x9181,x9184,x9185,x9186),f672(x9183,x9182,x9184,x9185,x9186))
% 21.40/21.39 [919]~E(x9191,x9192)+E(f672(x9193,x9194,x9191,x9195,x9196),f672(x9193,x9194,x9192,x9195,x9196))
% 21.40/21.39 [920]~E(x9201,x9202)+E(f672(x9203,x9204,x9205,x9201,x9206),f672(x9203,x9204,x9205,x9202,x9206))
% 21.40/21.39 [921]~E(x9211,x9212)+E(f672(x9213,x9214,x9215,x9216,x9211),f672(x9213,x9214,x9215,x9216,x9212))
% 21.40/21.39 [922]~E(x9221,x9222)+E(f192(x9221,x9223),f192(x9222,x9223))
% 21.40/21.39 [923]~E(x9231,x9232)+E(f192(x9233,x9231),f192(x9233,x9232))
% 21.40/21.39 [924]~E(x9241,x9242)+E(f67(x9241,x9243),f67(x9242,x9243))
% 21.40/21.39 [925]~E(x9251,x9252)+E(f67(x9253,x9251),f67(x9253,x9252))
% 21.40/21.39 [926]~E(x9261,x9262)+E(f638(x9261,x9263,x9264,x9265,x9266),f638(x9262,x9263,x9264,x9265,x9266))
% 21.40/21.39 [927]~E(x9271,x9272)+E(f638(x9273,x9271,x9274,x9275,x9276),f638(x9273,x9272,x9274,x9275,x9276))
% 21.40/21.39 [928]~E(x9281,x9282)+E(f638(x9283,x9284,x9281,x9285,x9286),f638(x9283,x9284,x9282,x9285,x9286))
% 21.40/21.39 [929]~E(x9291,x9292)+E(f638(x9293,x9294,x9295,x9291,x9296),f638(x9293,x9294,x9295,x9292,x9296))
% 21.40/21.39 [930]~E(x9301,x9302)+E(f638(x9303,x9304,x9305,x9306,x9301),f638(x9303,x9304,x9305,x9306,x9302))
% 21.40/21.39 [931]~E(x9311,x9312)+E(f273(x9311,x9313),f273(x9312,x9313))
% 21.40/21.39 [932]~E(x9321,x9322)+E(f273(x9323,x9321),f273(x9323,x9322))
% 21.40/21.39 [933]~E(x9331,x9332)+E(f770(x9331,x9333,x9334),f770(x9332,x9333,x9334))
% 21.40/21.39 [934]~E(x9341,x9342)+E(f770(x9343,x9341,x9344),f770(x9343,x9342,x9344))
% 21.40/21.39 [935]~E(x9351,x9352)+E(f770(x9353,x9354,x9351),f770(x9353,x9354,x9352))
% 21.40/21.39 [936]~E(x9361,x9362)+E(f86(x9361,x9363,x9364,x9365),f86(x9362,x9363,x9364,x9365))
% 21.40/21.39 [937]~E(x9371,x9372)+E(f86(x9373,x9371,x9374,x9375),f86(x9373,x9372,x9374,x9375))
% 21.40/21.39 [938]~E(x9381,x9382)+E(f86(x9383,x9384,x9381,x9385),f86(x9383,x9384,x9382,x9385))
% 21.40/21.39 [939]~E(x9391,x9392)+E(f86(x9393,x9394,x9395,x9391),f86(x9393,x9394,x9395,x9392))
% 21.40/21.39 [940]~E(x9401,x9402)+E(f271(x9401,x9403),f271(x9402,x9403))
% 21.40/21.39 [941]~E(x9411,x9412)+E(f271(x9413,x9411),f271(x9413,x9412))
% 21.40/21.39 [942]~E(x9421,x9422)+E(f436(x9421,x9423,x9424),f436(x9422,x9423,x9424))
% 21.40/21.39 [943]~E(x9431,x9432)+E(f436(x9433,x9431,x9434),f436(x9433,x9432,x9434))
% 21.40/21.39 [944]~E(x9441,x9442)+E(f436(x9443,x9444,x9441),f436(x9443,x9444,x9442))
% 21.40/21.39 [945]~E(x9451,x9452)+E(f631(x9451,x9453,x9454),f631(x9452,x9453,x9454))
% 21.40/21.39 [946]~E(x9461,x9462)+E(f631(x9463,x9461,x9464),f631(x9463,x9462,x9464))
% 21.40/21.39 [947]~E(x9471,x9472)+E(f631(x9473,x9474,x9471),f631(x9473,x9474,x9472))
% 21.40/21.39 [948]~E(x9481,x9482)+E(f127(x9481,x9483),f127(x9482,x9483))
% 21.40/21.39 [949]~E(x9491,x9492)+E(f127(x9493,x9491),f127(x9493,x9492))
% 21.40/21.39 [950]~E(x9501,x9502)+E(f189(x9501,x9503),f189(x9502,x9503))
% 21.40/21.39 [951]~E(x9511,x9512)+E(f189(x9513,x9511),f189(x9513,x9512))
% 21.40/21.39 [952]~E(x9521,x9522)+E(f255(x9521,x9523,x9524),f255(x9522,x9523,x9524))
% 21.40/21.39 [953]~E(x9531,x9532)+E(f255(x9533,x9531,x9534),f255(x9533,x9532,x9534))
% 21.40/21.39 [954]~E(x9541,x9542)+E(f255(x9543,x9544,x9541),f255(x9543,x9544,x9542))
% 21.40/21.39 [955]~E(x9551,x9552)+E(f128(x9551,x9553),f128(x9552,x9553))
% 21.40/21.39 [956]~E(x9561,x9562)+E(f128(x9563,x9561),f128(x9563,x9562))
% 21.40/21.39 [957]~E(x9571,x9572)+E(f526(x9571,x9573,x9574,x9575),f526(x9572,x9573,x9574,x9575))
% 21.40/21.39 [958]~E(x9581,x9582)+E(f526(x9583,x9581,x9584,x9585),f526(x9583,x9582,x9584,x9585))
% 21.40/21.39 [959]~E(x9591,x9592)+E(f526(x9593,x9594,x9591,x9595),f526(x9593,x9594,x9592,x9595))
% 21.40/21.39 [960]~E(x9601,x9602)+E(f526(x9603,x9604,x9605,x9601),f526(x9603,x9604,x9605,x9602))
% 21.40/21.39 [961]~E(x9611,x9612)+E(f237(x9611,x9613,x9614,x9615,x9616),f237(x9612,x9613,x9614,x9615,x9616))
% 21.40/21.39 [962]~E(x9621,x9622)+E(f237(x9623,x9621,x9624,x9625,x9626),f237(x9623,x9622,x9624,x9625,x9626))
% 21.40/21.39 [963]~E(x9631,x9632)+E(f237(x9633,x9634,x9631,x9635,x9636),f237(x9633,x9634,x9632,x9635,x9636))
% 21.40/21.39 [964]~E(x9641,x9642)+E(f237(x9643,x9644,x9645,x9641,x9646),f237(x9643,x9644,x9645,x9642,x9646))
% 21.40/21.39 [965]~E(x9651,x9652)+E(f237(x9653,x9654,x9655,x9656,x9651),f237(x9653,x9654,x9655,x9656,x9652))
% 21.40/21.39 [966]~E(x9661,x9662)+E(f426(x9661,x9663,x9664,x9665,x9666),f426(x9662,x9663,x9664,x9665,x9666))
% 21.40/21.39 [967]~E(x9671,x9672)+E(f426(x9673,x9671,x9674,x9675,x9676),f426(x9673,x9672,x9674,x9675,x9676))
% 21.40/21.39 [968]~E(x9681,x9682)+E(f426(x9683,x9684,x9681,x9685,x9686),f426(x9683,x9684,x9682,x9685,x9686))
% 21.40/21.39 [969]~E(x9691,x9692)+E(f426(x9693,x9694,x9695,x9691,x9696),f426(x9693,x9694,x9695,x9692,x9696))
% 21.40/21.39 [970]~E(x9701,x9702)+E(f426(x9703,x9704,x9705,x9706,x9701),f426(x9703,x9704,x9705,x9706,x9702))
% 21.40/21.39 [971]~E(x9711,x9712)+E(f437(x9711,x9713,x9714),f437(x9712,x9713,x9714))
% 21.40/21.39 [972]~E(x9721,x9722)+E(f437(x9723,x9721,x9724),f437(x9723,x9722,x9724))
% 21.40/21.39 [973]~E(x9731,x9732)+E(f437(x9733,x9734,x9731),f437(x9733,x9734,x9732))
% 21.40/21.39 [974]~E(x9741,x9742)+E(f348(x9741,x9743,x9744),f348(x9742,x9743,x9744))
% 21.40/21.39 [975]~E(x9751,x9752)+E(f348(x9753,x9751,x9754),f348(x9753,x9752,x9754))
% 21.40/21.39 [976]~E(x9761,x9762)+E(f348(x9763,x9764,x9761),f348(x9763,x9764,x9762))
% 21.40/21.39 [977]~E(x9771,x9772)+E(f441(x9771,x9773,x9774,x9775,x9776),f441(x9772,x9773,x9774,x9775,x9776))
% 21.40/21.39 [978]~E(x9781,x9782)+E(f441(x9783,x9781,x9784,x9785,x9786),f441(x9783,x9782,x9784,x9785,x9786))
% 21.40/21.39 [979]~E(x9791,x9792)+E(f441(x9793,x9794,x9791,x9795,x9796),f441(x9793,x9794,x9792,x9795,x9796))
% 21.40/21.39 [980]~E(x9801,x9802)+E(f441(x9803,x9804,x9805,x9801,x9806),f441(x9803,x9804,x9805,x9802,x9806))
% 21.40/21.39 [981]~E(x9811,x9812)+E(f441(x9813,x9814,x9815,x9816,x9811),f441(x9813,x9814,x9815,x9816,x9812))
% 21.40/21.39 [982]~E(x9821,x9822)+E(f327(x9821,x9823,x9824,x9825,x9826),f327(x9822,x9823,x9824,x9825,x9826))
% 21.40/21.39 [983]~E(x9831,x9832)+E(f327(x9833,x9831,x9834,x9835,x9836),f327(x9833,x9832,x9834,x9835,x9836))
% 21.40/21.39 [984]~E(x9841,x9842)+E(f327(x9843,x9844,x9841,x9845,x9846),f327(x9843,x9844,x9842,x9845,x9846))
% 21.40/21.39 [985]~E(x9851,x9852)+E(f327(x9853,x9854,x9855,x9851,x9856),f327(x9853,x9854,x9855,x9852,x9856))
% 21.40/21.39 [986]~E(x9861,x9862)+E(f327(x9863,x9864,x9865,x9866,x9861),f327(x9863,x9864,x9865,x9866,x9862))
% 21.40/21.39 [987]~E(x9871,x9872)+E(f85(x9871,x9873,x9874,x9875,x9876),f85(x9872,x9873,x9874,x9875,x9876))
% 21.40/21.39 [988]~E(x9881,x9882)+E(f85(x9883,x9881,x9884,x9885,x9886),f85(x9883,x9882,x9884,x9885,x9886))
% 21.40/21.39 [989]~E(x9891,x9892)+E(f85(x9893,x9894,x9891,x9895,x9896),f85(x9893,x9894,x9892,x9895,x9896))
% 21.40/21.39 [990]~E(x9901,x9902)+E(f85(x9903,x9904,x9905,x9901,x9906),f85(x9903,x9904,x9905,x9902,x9906))
% 21.40/21.39 [991]~E(x9911,x9912)+E(f85(x9913,x9914,x9915,x9916,x9911),f85(x9913,x9914,x9915,x9916,x9912))
% 21.40/21.39 [992]~E(x9921,x9922)+E(f625(x9921,x9923,x9924,x9925,x9926,x9927),f625(x9922,x9923,x9924,x9925,x9926,x9927))
% 21.40/21.39 [993]~E(x9931,x9932)+E(f625(x9933,x9931,x9934,x9935,x9936,x9937),f625(x9933,x9932,x9934,x9935,x9936,x9937))
% 21.40/21.39 [994]~E(x9941,x9942)+E(f625(x9943,x9944,x9941,x9945,x9946,x9947),f625(x9943,x9944,x9942,x9945,x9946,x9947))
% 21.40/21.39 [995]~E(x9951,x9952)+E(f625(x9953,x9954,x9955,x9951,x9956,x9957),f625(x9953,x9954,x9955,x9952,x9956,x9957))
% 21.40/21.39 [996]~E(x9961,x9962)+E(f625(x9963,x9964,x9965,x9966,x9961,x9967),f625(x9963,x9964,x9965,x9966,x9962,x9967))
% 21.40/21.39 [997]~E(x9971,x9972)+E(f625(x9973,x9974,x9975,x9976,x9977,x9971),f625(x9973,x9974,x9975,x9976,x9977,x9972))
% 21.40/21.39 [998]~E(x9981,x9982)+E(f330(x9981,x9983),f330(x9982,x9983))
% 21.40/21.39 [999]~E(x9991,x9992)+E(f330(x9993,x9991),f330(x9993,x9992))
% 21.40/21.39 [1000]~E(x10001,x10002)+E(f570(x10001,x10003,x10004,x10005,x10006),f570(x10002,x10003,x10004,x10005,x10006))
% 21.40/21.39 [1001]~E(x10011,x10012)+E(f570(x10013,x10011,x10014,x10015,x10016),f570(x10013,x10012,x10014,x10015,x10016))
% 21.40/21.39 [1002]~E(x10021,x10022)+E(f570(x10023,x10024,x10021,x10025,x10026),f570(x10023,x10024,x10022,x10025,x10026))
% 21.40/21.39 [1003]~E(x10031,x10032)+E(f570(x10033,x10034,x10035,x10031,x10036),f570(x10033,x10034,x10035,x10032,x10036))
% 21.40/21.39 [1004]~E(x10041,x10042)+E(f570(x10043,x10044,x10045,x10046,x10041),f570(x10043,x10044,x10045,x10046,x10042))
% 21.40/21.39 [1005]~E(x10051,x10052)+E(f468(x10051,x10053),f468(x10052,x10053))
% 21.40/21.39 [1006]~E(x10061,x10062)+E(f468(x10063,x10061),f468(x10063,x10062))
% 21.40/21.39 [1007]~E(x10071,x10072)+E(f779(x10071,x10073,x10074),f779(x10072,x10073,x10074))
% 21.40/21.39 [1008]~E(x10081,x10082)+E(f779(x10083,x10081,x10084),f779(x10083,x10082,x10084))
% 21.40/21.39 [1009]~E(x10091,x10092)+E(f779(x10093,x10094,x10091),f779(x10093,x10094,x10092))
% 21.40/21.39 [1010]~E(x10101,x10102)+E(f761(x10101,x10103,x10104),f761(x10102,x10103,x10104))
% 21.40/21.39 [1011]~E(x10111,x10112)+E(f761(x10113,x10111,x10114),f761(x10113,x10112,x10114))
% 21.40/21.39 [1012]~E(x10121,x10122)+E(f761(x10123,x10124,x10121),f761(x10123,x10124,x10122))
% 21.40/21.39 [1013]~E(x10131,x10132)+E(f353(x10131,x10133,x10134,x10135,x10136),f353(x10132,x10133,x10134,x10135,x10136))
% 21.40/21.39 [1014]~E(x10141,x10142)+E(f353(x10143,x10141,x10144,x10145,x10146),f353(x10143,x10142,x10144,x10145,x10146))
% 21.40/21.39 [1015]~E(x10151,x10152)+E(f353(x10153,x10154,x10151,x10155,x10156),f353(x10153,x10154,x10152,x10155,x10156))
% 21.40/21.39 [1016]~E(x10161,x10162)+E(f353(x10163,x10164,x10165,x10161,x10166),f353(x10163,x10164,x10165,x10162,x10166))
% 21.40/21.39 [1017]~E(x10171,x10172)+E(f353(x10173,x10174,x10175,x10176,x10171),f353(x10173,x10174,x10175,x10176,x10172))
% 21.40/21.39 [1018]~E(x10181,x10182)+E(f179(x10181,x10183,x10184),f179(x10182,x10183,x10184))
% 21.40/21.39 [1019]~E(x10191,x10192)+E(f179(x10193,x10191,x10194),f179(x10193,x10192,x10194))
% 21.40/21.39 [1020]~E(x10201,x10202)+E(f179(x10203,x10204,x10201),f179(x10203,x10204,x10202))
% 21.40/21.39 [1021]~E(x10211,x10212)+E(f851(x10211,x10213,x10214),f851(x10212,x10213,x10214))
% 21.40/21.39 [1022]~E(x10221,x10222)+E(f851(x10223,x10221,x10224),f851(x10223,x10222,x10224))
% 21.40/21.39 [1023]~E(x10231,x10232)+E(f851(x10233,x10234,x10231),f851(x10233,x10234,x10232))
% 21.40/21.39 [1024]~E(x10241,x10242)+E(f314(x10241,x10243),f314(x10242,x10243))
% 21.40/21.39 [1025]~E(x10251,x10252)+E(f314(x10253,x10251),f314(x10253,x10252))
% 21.40/21.39 [1026]~E(x10261,x10262)+E(f703(x10261,x10263,x10264,x10265),f703(x10262,x10263,x10264,x10265))
% 21.40/21.39 [1027]~E(x10271,x10272)+E(f703(x10273,x10271,x10274,x10275),f703(x10273,x10272,x10274,x10275))
% 21.40/21.39 [1028]~E(x10281,x10282)+E(f703(x10283,x10284,x10281,x10285),f703(x10283,x10284,x10282,x10285))
% 21.40/21.39 [1029]~E(x10291,x10292)+E(f703(x10293,x10294,x10295,x10291),f703(x10293,x10294,x10295,x10292))
% 21.40/21.39 [1030]~E(x10301,x10302)+E(f634(x10301,x10303,x10304,x10305),f634(x10302,x10303,x10304,x10305))
% 21.40/21.39 [1031]~E(x10311,x10312)+E(f634(x10313,x10311,x10314,x10315),f634(x10313,x10312,x10314,x10315))
% 21.40/21.39 [1032]~E(x10321,x10322)+E(f634(x10323,x10324,x10321,x10325),f634(x10323,x10324,x10322,x10325))
% 21.40/21.39 [1033]~E(x10331,x10332)+E(f634(x10333,x10334,x10335,x10331),f634(x10333,x10334,x10335,x10332))
% 21.40/21.39 [1034]~E(x10341,x10342)+E(f832(x10341,x10343,x10344),f832(x10342,x10343,x10344))
% 21.40/21.39 [1035]~E(x10351,x10352)+E(f832(x10353,x10351,x10354),f832(x10353,x10352,x10354))
% 21.40/21.39 [1036]~E(x10361,x10362)+E(f832(x10363,x10364,x10361),f832(x10363,x10364,x10362))
% 21.40/21.39 [1037]~E(x10371,x10372)+E(f385(x10371,x10373),f385(x10372,x10373))
% 21.40/21.39 [1038]~E(x10381,x10382)+E(f385(x10383,x10381),f385(x10383,x10382))
% 21.40/21.39 [1039]~E(x10391,x10392)+E(f370(x10391,x10393,x10394,x10395,x10396),f370(x10392,x10393,x10394,x10395,x10396))
% 21.40/21.39 [1040]~E(x10401,x10402)+E(f370(x10403,x10401,x10404,x10405,x10406),f370(x10403,x10402,x10404,x10405,x10406))
% 21.40/21.39 [1041]~E(x10411,x10412)+E(f370(x10413,x10414,x10411,x10415,x10416),f370(x10413,x10414,x10412,x10415,x10416))
% 21.40/21.39 [1042]~E(x10421,x10422)+E(f370(x10423,x10424,x10425,x10421,x10426),f370(x10423,x10424,x10425,x10422,x10426))
% 21.40/21.39 [1043]~E(x10431,x10432)+E(f370(x10433,x10434,x10435,x10436,x10431),f370(x10433,x10434,x10435,x10436,x10432))
% 21.40/21.39 [1044]~E(x10441,x10442)+E(f364(x10441,x10443,x10444,x10445),f364(x10442,x10443,x10444,x10445))
% 21.40/21.39 [1045]~E(x10451,x10452)+E(f364(x10453,x10451,x10454,x10455),f364(x10453,x10452,x10454,x10455))
% 21.40/21.39 [1046]~E(x10461,x10462)+E(f364(x10463,x10464,x10461,x10465),f364(x10463,x10464,x10462,x10465))
% 21.40/21.39 [1047]~E(x10471,x10472)+E(f364(x10473,x10474,x10475,x10471),f364(x10473,x10474,x10475,x10472))
% 21.40/21.39 [1048]~E(x10481,x10482)+E(f754(x10481,x10483,x10484),f754(x10482,x10483,x10484))
% 21.40/21.39 [1049]~E(x10491,x10492)+E(f754(x10493,x10491,x10494),f754(x10493,x10492,x10494))
% 21.40/21.39 [1050]~E(x10501,x10502)+E(f754(x10503,x10504,x10501),f754(x10503,x10504,x10502))
% 21.40/21.39 [1051]~E(x10511,x10512)+E(f603(x10511,x10513,x10514,x10515),f603(x10512,x10513,x10514,x10515))
% 21.40/21.39 [1052]~E(x10521,x10522)+E(f603(x10523,x10521,x10524,x10525),f603(x10523,x10522,x10524,x10525))
% 21.40/21.39 [1053]~E(x10531,x10532)+E(f603(x10533,x10534,x10531,x10535),f603(x10533,x10534,x10532,x10535))
% 21.40/21.39 [1054]~E(x10541,x10542)+E(f603(x10543,x10544,x10545,x10541),f603(x10543,x10544,x10545,x10542))
% 21.40/21.39 [1055]~E(x10551,x10552)+E(f251(x10551,x10553,x10554),f251(x10552,x10553,x10554))
% 21.40/21.39 [1056]~E(x10561,x10562)+E(f251(x10563,x10561,x10564),f251(x10563,x10562,x10564))
% 21.40/21.39 [1057]~E(x10571,x10572)+E(f251(x10573,x10574,x10571),f251(x10573,x10574,x10572))
% 21.40/21.39 [1058]~E(x10581,x10582)+E(f297(x10581,x10583,x10584,x10585,x10586),f297(x10582,x10583,x10584,x10585,x10586))
% 21.40/21.39 [1059]~E(x10591,x10592)+E(f297(x10593,x10591,x10594,x10595,x10596),f297(x10593,x10592,x10594,x10595,x10596))
% 21.40/21.39 [1060]~E(x10601,x10602)+E(f297(x10603,x10604,x10601,x10605,x10606),f297(x10603,x10604,x10602,x10605,x10606))
% 21.40/21.39 [1061]~E(x10611,x10612)+E(f297(x10613,x10614,x10615,x10611,x10616),f297(x10613,x10614,x10615,x10612,x10616))
% 21.40/21.39 [1062]~E(x10621,x10622)+E(f297(x10623,x10624,x10625,x10626,x10621),f297(x10623,x10624,x10625,x10626,x10622))
% 21.40/21.39 [1063]~E(x10631,x10632)+E(f607(x10631,x10633,x10634,x10635),f607(x10632,x10633,x10634,x10635))
% 21.40/21.39 [1064]~E(x10641,x10642)+E(f607(x10643,x10641,x10644,x10645),f607(x10643,x10642,x10644,x10645))
% 21.40/21.39 [1065]~E(x10651,x10652)+E(f607(x10653,x10654,x10651,x10655),f607(x10653,x10654,x10652,x10655))
% 21.40/21.39 [1066]~E(x10661,x10662)+E(f607(x10663,x10664,x10665,x10661),f607(x10663,x10664,x10665,x10662))
% 21.40/21.39 [1067]~E(x10671,x10672)+E(f284(x10671),f284(x10672))
% 21.40/21.39 [1068]~E(x10681,x10682)+E(f462(x10681,x10683,x10684,x10685),f462(x10682,x10683,x10684,x10685))
% 21.40/21.39 [1069]~E(x10691,x10692)+E(f462(x10693,x10691,x10694,x10695),f462(x10693,x10692,x10694,x10695))
% 21.40/21.39 [1070]~E(x10701,x10702)+E(f462(x10703,x10704,x10701,x10705),f462(x10703,x10704,x10702,x10705))
% 21.40/21.39 [1071]~E(x10711,x10712)+E(f462(x10713,x10714,x10715,x10711),f462(x10713,x10714,x10715,x10712))
% 21.40/21.39 [1072]~E(x10721,x10722)+E(f766(x10721,x10723,x10724),f766(x10722,x10723,x10724))
% 21.40/21.39 [1073]~E(x10731,x10732)+E(f766(x10733,x10731,x10734),f766(x10733,x10732,x10734))
% 21.40/21.39 [1074]~E(x10741,x10742)+E(f766(x10743,x10744,x10741),f766(x10743,x10744,x10742))
% 21.40/21.39 [1075]~E(x10751,x10752)+E(f671(x10751,x10753,x10754,x10755,x10756),f671(x10752,x10753,x10754,x10755,x10756))
% 21.40/21.39 [1076]~E(x10761,x10762)+E(f671(x10763,x10761,x10764,x10765,x10766),f671(x10763,x10762,x10764,x10765,x10766))
% 21.40/21.39 [1077]~E(x10771,x10772)+E(f671(x10773,x10774,x10771,x10775,x10776),f671(x10773,x10774,x10772,x10775,x10776))
% 21.40/21.39 [1078]~E(x10781,x10782)+E(f671(x10783,x10784,x10785,x10781,x10786),f671(x10783,x10784,x10785,x10782,x10786))
% 21.40/21.39 [1079]~E(x10791,x10792)+E(f671(x10793,x10794,x10795,x10796,x10791),f671(x10793,x10794,x10795,x10796,x10792))
% 21.40/21.39 [1080]~E(x10801,x10802)+E(f781(x10801,x10803,x10804),f781(x10802,x10803,x10804))
% 21.40/21.39 [1081]~E(x10811,x10812)+E(f781(x10813,x10811,x10814),f781(x10813,x10812,x10814))
% 21.40/21.39 [1082]~E(x10821,x10822)+E(f781(x10823,x10824,x10821),f781(x10823,x10824,x10822))
% 21.40/21.39 [1083]~E(x10831,x10832)+E(f393(x10831,x10833),f393(x10832,x10833))
% 21.40/21.39 [1084]~E(x10841,x10842)+E(f393(x10843,x10841),f393(x10843,x10842))
% 21.40/21.39 [1085]~E(x10851,x10852)+E(f103(x10851,x10853,x10854,x10855),f103(x10852,x10853,x10854,x10855))
% 21.40/21.39 [1086]~E(x10861,x10862)+E(f103(x10863,x10861,x10864,x10865),f103(x10863,x10862,x10864,x10865))
% 21.40/21.39 [1087]~E(x10871,x10872)+E(f103(x10873,x10874,x10871,x10875),f103(x10873,x10874,x10872,x10875))
% 21.40/21.39 [1088]~E(x10881,x10882)+E(f103(x10883,x10884,x10885,x10881),f103(x10883,x10884,x10885,x10882))
% 21.40/21.39 [1089]~E(x10891,x10892)+E(f232(x10891,x10893,x10894,x10895),f232(x10892,x10893,x10894,x10895))
% 21.40/21.39 [1090]~E(x10901,x10902)+E(f232(x10903,x10901,x10904,x10905),f232(x10903,x10902,x10904,x10905))
% 21.40/21.39 [1091]~E(x10911,x10912)+E(f232(x10913,x10914,x10911,x10915),f232(x10913,x10914,x10912,x10915))
% 21.40/21.39 [1092]~E(x10921,x10922)+E(f232(x10923,x10924,x10925,x10921),f232(x10923,x10924,x10925,x10922))
% 21.40/21.39 [1093]~E(x10931,x10932)+E(f513(x10931,x10933,x10934,x10935,x10936),f513(x10932,x10933,x10934,x10935,x10936))
% 21.40/21.39 [1094]~E(x10941,x10942)+E(f513(x10943,x10941,x10944,x10945,x10946),f513(x10943,x10942,x10944,x10945,x10946))
% 21.40/21.39 [1095]~E(x10951,x10952)+E(f513(x10953,x10954,x10951,x10955,x10956),f513(x10953,x10954,x10952,x10955,x10956))
% 21.40/21.39 [1096]~E(x10961,x10962)+E(f513(x10963,x10964,x10965,x10961,x10966),f513(x10963,x10964,x10965,x10962,x10966))
% 21.40/21.39 [1097]~E(x10971,x10972)+E(f513(x10973,x10974,x10975,x10976,x10971),f513(x10973,x10974,x10975,x10976,x10972))
% 21.40/21.39 [1098]~E(x10981,x10982)+E(f452(x10981,x10983,x10984),f452(x10982,x10983,x10984))
% 21.40/21.39 [1099]~E(x10991,x10992)+E(f452(x10993,x10991,x10994),f452(x10993,x10992,x10994))
% 21.40/21.39 [1100]~E(x11001,x11002)+E(f452(x11003,x11004,x11001),f452(x11003,x11004,x11002))
% 21.40/21.39 [1101]~E(x11011,x11012)+E(f158(x11011,x11013,x11014),f158(x11012,x11013,x11014))
% 21.40/21.39 [1102]~E(x11021,x11022)+E(f158(x11023,x11021,x11024),f158(x11023,x11022,x11024))
% 21.40/21.39 [1103]~E(x11031,x11032)+E(f158(x11033,x11034,x11031),f158(x11033,x11034,x11032))
% 21.40/21.39 [1104]~E(x11041,x11042)+E(f555(x11041,x11043,x11044,x11045),f555(x11042,x11043,x11044,x11045))
% 21.40/21.39 [1105]~E(x11051,x11052)+E(f555(x11053,x11051,x11054,x11055),f555(x11053,x11052,x11054,x11055))
% 21.40/21.39 [1106]~E(x11061,x11062)+E(f555(x11063,x11064,x11061,x11065),f555(x11063,x11064,x11062,x11065))
% 21.40/21.39 [1107]~E(x11071,x11072)+E(f555(x11073,x11074,x11075,x11071),f555(x11073,x11074,x11075,x11072))
% 21.40/21.39 [1108]~E(x11081,x11082)+E(f785(x11081,x11083,x11084),f785(x11082,x11083,x11084))
% 21.40/21.39 [1109]~E(x11091,x11092)+E(f785(x11093,x11091,x11094),f785(x11093,x11092,x11094))
% 21.40/21.39 [1110]~E(x11101,x11102)+E(f785(x11103,x11104,x11101),f785(x11103,x11104,x11102))
% 21.40/21.39 [1111]~E(x11111,x11112)+E(f670(x11111,x11113,x11114,x11115,x11116),f670(x11112,x11113,x11114,x11115,x11116))
% 21.40/21.39 [1112]~E(x11121,x11122)+E(f670(x11123,x11121,x11124,x11125,x11126),f670(x11123,x11122,x11124,x11125,x11126))
% 21.40/21.39 [1113]~E(x11131,x11132)+E(f670(x11133,x11134,x11131,x11135,x11136),f670(x11133,x11134,x11132,x11135,x11136))
% 21.40/21.39 [1114]~E(x11141,x11142)+E(f670(x11143,x11144,x11145,x11141,x11146),f670(x11143,x11144,x11145,x11142,x11146))
% 21.40/21.39 [1115]~E(x11151,x11152)+E(f670(x11153,x11154,x11155,x11156,x11151),f670(x11153,x11154,x11155,x11156,x11152))
% 21.40/21.39 [1116]~E(x11161,x11162)+E(f224(x11161,x11163,x11164),f224(x11162,x11163,x11164))
% 21.40/21.39 [1117]~E(x11171,x11172)+E(f224(x11173,x11171,x11174),f224(x11173,x11172,x11174))
% 21.40/21.39 [1118]~E(x11181,x11182)+E(f224(x11183,x11184,x11181),f224(x11183,x11184,x11182))
% 21.40/21.39 [1119]~E(x11191,x11192)+E(f493(x11191,x11193,x11194,x11195),f493(x11192,x11193,x11194,x11195))
% 21.40/21.39 [1120]~E(x11201,x11202)+E(f493(x11203,x11201,x11204,x11205),f493(x11203,x11202,x11204,x11205))
% 21.40/21.39 [1121]~E(x11211,x11212)+E(f493(x11213,x11214,x11211,x11215),f493(x11213,x11214,x11212,x11215))
% 21.40/21.39 [1122]~E(x11221,x11222)+E(f493(x11223,x11224,x11225,x11221),f493(x11223,x11224,x11225,x11222))
% 21.40/21.39 [1123]~E(x11231,x11232)+E(f697(x11231,x11233,x11234,x11235,x11236),f697(x11232,x11233,x11234,x11235,x11236))
% 21.40/21.39 [1124]~E(x11241,x11242)+E(f697(x11243,x11241,x11244,x11245,x11246),f697(x11243,x11242,x11244,x11245,x11246))
% 21.40/21.39 [1125]~E(x11251,x11252)+E(f697(x11253,x11254,x11251,x11255,x11256),f697(x11253,x11254,x11252,x11255,x11256))
% 21.40/21.39 [1126]~E(x11261,x11262)+E(f697(x11263,x11264,x11265,x11261,x11266),f697(x11263,x11264,x11265,x11262,x11266))
% 21.40/21.39 [1127]~E(x11271,x11272)+E(f697(x11273,x11274,x11275,x11276,x11271),f697(x11273,x11274,x11275,x11276,x11272))
% 21.40/21.39 [1128]~E(x11281,x11282)+E(f151(x11281,x11283,x11284),f151(x11282,x11283,x11284))
% 21.40/21.39 [1129]~E(x11291,x11292)+E(f151(x11293,x11291,x11294),f151(x11293,x11292,x11294))
% 21.40/21.39 [1130]~E(x11301,x11302)+E(f151(x11303,x11304,x11301),f151(x11303,x11304,x11302))
% 21.40/21.39 [1131]~E(x11311,x11312)+E(f529(x11311,x11313,x11314),f529(x11312,x11313,x11314))
% 21.40/21.39 [1132]~E(x11321,x11322)+E(f529(x11323,x11321,x11324),f529(x11323,x11322,x11324))
% 21.40/21.39 [1133]~E(x11331,x11332)+E(f529(x11333,x11334,x11331),f529(x11333,x11334,x11332))
% 21.40/21.39 [1134]~E(x11341,x11342)+E(f587(x11341,x11343,x11344,x11345,x11346,x11347,x11348),f587(x11342,x11343,x11344,x11345,x11346,x11347,x11348))
% 21.40/21.39 [1135]~E(x11351,x11352)+E(f587(x11353,x11351,x11354,x11355,x11356,x11357,x11358),f587(x11353,x11352,x11354,x11355,x11356,x11357,x11358))
% 21.40/21.39 [1136]~E(x11361,x11362)+E(f587(x11363,x11364,x11361,x11365,x11366,x11367,x11368),f587(x11363,x11364,x11362,x11365,x11366,x11367,x11368))
% 21.40/21.39 [1137]~E(x11371,x11372)+E(f587(x11373,x11374,x11375,x11371,x11376,x11377,x11378),f587(x11373,x11374,x11375,x11372,x11376,x11377,x11378))
% 21.40/21.39 [1138]~E(x11381,x11382)+E(f587(x11383,x11384,x11385,x11386,x11381,x11387,x11388),f587(x11383,x11384,x11385,x11386,x11382,x11387,x11388))
% 21.40/21.39 [1139]~E(x11391,x11392)+E(f587(x11393,x11394,x11395,x11396,x11397,x11391,x11398),f587(x11393,x11394,x11395,x11396,x11397,x11392,x11398))
% 21.40/21.39 [1140]~E(x11401,x11402)+E(f587(x11403,x11404,x11405,x11406,x11407,x11408,x11401),f587(x11403,x11404,x11405,x11406,x11407,x11408,x11402))
% 21.40/21.39 [1141]~E(x11411,x11412)+E(f365(x11411,x11413,x11414,x11415,x11416,x11417,x11418),f365(x11412,x11413,x11414,x11415,x11416,x11417,x11418))
% 21.40/21.39 [1142]~E(x11421,x11422)+E(f365(x11423,x11421,x11424,x11425,x11426,x11427,x11428),f365(x11423,x11422,x11424,x11425,x11426,x11427,x11428))
% 21.40/21.39 [1143]~E(x11431,x11432)+E(f365(x11433,x11434,x11431,x11435,x11436,x11437,x11438),f365(x11433,x11434,x11432,x11435,x11436,x11437,x11438))
% 21.40/21.39 [1144]~E(x11441,x11442)+E(f365(x11443,x11444,x11445,x11441,x11446,x11447,x11448),f365(x11443,x11444,x11445,x11442,x11446,x11447,x11448))
% 21.40/21.39 [1145]~E(x11451,x11452)+E(f365(x11453,x11454,x11455,x11456,x11451,x11457,x11458),f365(x11453,x11454,x11455,x11456,x11452,x11457,x11458))
% 21.40/21.39 [1146]~E(x11461,x11462)+E(f365(x11463,x11464,x11465,x11466,x11467,x11461,x11468),f365(x11463,x11464,x11465,x11466,x11467,x11462,x11468))
% 21.40/21.39 [1147]~E(x11471,x11472)+E(f365(x11473,x11474,x11475,x11476,x11477,x11478,x11471),f365(x11473,x11474,x11475,x11476,x11477,x11478,x11472))
% 21.40/21.39 [1148]~E(x11481,x11482)+E(f39(x11481,x11483,x11484,x11485,x11486,x11487,x11488,x11489,x114810,x114811),f39(x11482,x11483,x11484,x11485,x11486,x11487,x11488,x11489,x114810,x114811))
% 21.40/21.39 [1149]~E(x11491,x11492)+E(f39(x11493,x11491,x11494,x11495,x11496,x11497,x11498,x11499,x114910,x114911),f39(x11493,x11492,x11494,x11495,x11496,x11497,x11498,x11499,x114910,x114911))
% 21.40/21.39 [1150]~E(x11501,x11502)+E(f39(x11503,x11504,x11501,x11505,x11506,x11507,x11508,x11509,x115010,x115011),f39(x11503,x11504,x11502,x11505,x11506,x11507,x11508,x11509,x115010,x115011))
% 21.40/21.39 [1151]~E(x11511,x11512)+E(f39(x11513,x11514,x11515,x11511,x11516,x11517,x11518,x11519,x115110,x115111),f39(x11513,x11514,x11515,x11512,x11516,x11517,x11518,x11519,x115110,x115111))
% 21.40/21.39 [1152]~E(x11521,x11522)+E(f39(x11523,x11524,x11525,x11526,x11521,x11527,x11528,x11529,x115210,x115211),f39(x11523,x11524,x11525,x11526,x11522,x11527,x11528,x11529,x115210,x115211))
% 21.40/21.39 [1153]~E(x11531,x11532)+E(f39(x11533,x11534,x11535,x11536,x11537,x11531,x11538,x11539,x115310,x115311),f39(x11533,x11534,x11535,x11536,x11537,x11532,x11538,x11539,x115310,x115311))
% 21.40/21.39 [1154]~E(x11541,x11542)+E(f39(x11543,x11544,x11545,x11546,x11547,x11548,x11541,x11549,x115410,x115411),f39(x11543,x11544,x11545,x11546,x11547,x11548,x11542,x11549,x115410,x115411))
% 21.40/21.39 [1155]~E(x11551,x11552)+E(f39(x11553,x11554,x11555,x11556,x11557,x11558,x11559,x11551,x115510,x115511),f39(x11553,x11554,x11555,x11556,x11557,x11558,x11559,x11552,x115510,x115511))
% 21.40/21.39 [1156]~E(x11561,x11562)+E(f39(x11563,x11564,x11565,x11566,x11567,x11568,x11569,x115610,x11561,x115611),f39(x11563,x11564,x11565,x11566,x11567,x11568,x11569,x115610,x11562,x115611))
% 21.40/21.39 [1157]~E(x11571,x11572)+E(f39(x11573,x11574,x11575,x11576,x11577,x11578,x11579,x115710,x115711,x11571),f39(x11573,x11574,x11575,x11576,x11577,x11578,x11579,x115710,x115711,x11572))
% 21.40/21.39 [1158]~E(x11581,x11582)+E(f609(x11581,x11583,x11584,x11585),f609(x11582,x11583,x11584,x11585))
% 21.40/21.39 [1159]~E(x11591,x11592)+E(f609(x11593,x11591,x11594,x11595),f609(x11593,x11592,x11594,x11595))
% 21.40/21.39 [1160]~E(x11601,x11602)+E(f609(x11603,x11604,x11601,x11605),f609(x11603,x11604,x11602,x11605))
% 21.40/21.39 [1161]~E(x11611,x11612)+E(f609(x11613,x11614,x11615,x11611),f609(x11613,x11614,x11615,x11612))
% 21.40/21.39 [1162]~E(x11621,x11622)+E(f254(x11621,x11623,x11624),f254(x11622,x11623,x11624))
% 21.40/21.39 [1163]~E(x11631,x11632)+E(f254(x11633,x11631,x11634),f254(x11633,x11632,x11634))
% 21.40/21.39 [1164]~E(x11641,x11642)+E(f254(x11643,x11644,x11641),f254(x11643,x11644,x11642))
% 21.40/21.39 [1165]~E(x11651,x11652)+E(f812(x11651,x11653,x11654,x11655),f812(x11652,x11653,x11654,x11655))
% 21.40/21.39 [1166]~E(x11661,x11662)+E(f812(x11663,x11661,x11664,x11665),f812(x11663,x11662,x11664,x11665))
% 21.40/21.39 [1167]~E(x11671,x11672)+E(f812(x11673,x11674,x11671,x11675),f812(x11673,x11674,x11672,x11675))
% 21.40/21.39 [1168]~E(x11681,x11682)+E(f812(x11683,x11684,x11685,x11681),f812(x11683,x11684,x11685,x11682))
% 21.40/21.39 [1169]~E(x11691,x11692)+E(f708(x11691,x11693,x11694),f708(x11692,x11693,x11694))
% 21.40/21.39 [1170]~E(x11701,x11702)+E(f708(x11703,x11701,x11704),f708(x11703,x11702,x11704))
% 21.40/21.39 [1171]~E(x11711,x11712)+E(f708(x11713,x11714,x11711),f708(x11713,x11714,x11712))
% 21.40/21.39 [1172]~E(x11721,x11722)+E(f356(x11721,x11723,x11724,x11725,x11726,x11727),f356(x11722,x11723,x11724,x11725,x11726,x11727))
% 21.40/21.39 [1173]~E(x11731,x11732)+E(f356(x11733,x11731,x11734,x11735,x11736,x11737),f356(x11733,x11732,x11734,x11735,x11736,x11737))
% 21.40/21.39 [1174]~E(x11741,x11742)+E(f356(x11743,x11744,x11741,x11745,x11746,x11747),f356(x11743,x11744,x11742,x11745,x11746,x11747))
% 21.40/21.39 [1175]~E(x11751,x11752)+E(f356(x11753,x11754,x11755,x11751,x11756,x11757),f356(x11753,x11754,x11755,x11752,x11756,x11757))
% 21.40/21.39 [1176]~E(x11761,x11762)+E(f356(x11763,x11764,x11765,x11766,x11761,x11767),f356(x11763,x11764,x11765,x11766,x11762,x11767))
% 21.40/21.39 [1177]~E(x11771,x11772)+E(f356(x11773,x11774,x11775,x11776,x11777,x11771),f356(x11773,x11774,x11775,x11776,x11777,x11772))
% 21.40/21.39 [1178]~E(x11781,x11782)+E(f662(x11781,x11783,x11784),f662(x11782,x11783,x11784))
% 21.40/21.39 [1179]~E(x11791,x11792)+E(f662(x11793,x11791,x11794),f662(x11793,x11792,x11794))
% 21.40/21.39 [1180]~E(x11801,x11802)+E(f662(x11803,x11804,x11801),f662(x11803,x11804,x11802))
% 21.40/21.39 [1181]~E(x11811,x11812)+E(f775(x11811),f775(x11812))
% 21.40/21.39 [1182]~E(x11821,x11822)+E(f512(x11821,x11823,x11824,x11825,x11826),f512(x11822,x11823,x11824,x11825,x11826))
% 21.40/21.39 [1183]~E(x11831,x11832)+E(f512(x11833,x11831,x11834,x11835,x11836),f512(x11833,x11832,x11834,x11835,x11836))
% 21.40/21.39 [1184]~E(x11841,x11842)+E(f512(x11843,x11844,x11841,x11845,x11846),f512(x11843,x11844,x11842,x11845,x11846))
% 21.40/21.39 [1185]~E(x11851,x11852)+E(f512(x11853,x11854,x11855,x11851,x11856),f512(x11853,x11854,x11855,x11852,x11856))
% 21.40/21.39 [1186]~E(x11861,x11862)+E(f512(x11863,x11864,x11865,x11866,x11861),f512(x11863,x11864,x11865,x11866,x11862))
% 21.40/21.39 [1187]~E(x11871,x11872)+E(f594(x11871,x11873,x11874,x11875,x11876,x11877),f594(x11872,x11873,x11874,x11875,x11876,x11877))
% 21.40/21.39 [1188]~E(x11881,x11882)+E(f594(x11883,x11881,x11884,x11885,x11886,x11887),f594(x11883,x11882,x11884,x11885,x11886,x11887))
% 21.40/21.39 [1189]~E(x11891,x11892)+E(f594(x11893,x11894,x11891,x11895,x11896,x11897),f594(x11893,x11894,x11892,x11895,x11896,x11897))
% 21.40/21.39 [1190]~E(x11901,x11902)+E(f594(x11903,x11904,x11905,x11901,x11906,x11907),f594(x11903,x11904,x11905,x11902,x11906,x11907))
% 21.40/21.39 [1191]~E(x11911,x11912)+E(f594(x11913,x11914,x11915,x11916,x11911,x11917),f594(x11913,x11914,x11915,x11916,x11912,x11917))
% 21.40/21.39 [1192]~E(x11921,x11922)+E(f594(x11923,x11924,x11925,x11926,x11927,x11921),f594(x11923,x11924,x11925,x11926,x11927,x11922))
% 21.40/21.39 [1193]~E(x11931,x11932)+E(f553(x11931,x11933,x11934,x11935,x11936),f553(x11932,x11933,x11934,x11935,x11936))
% 21.40/21.39 [1194]~E(x11941,x11942)+E(f553(x11943,x11941,x11944,x11945,x11946),f553(x11943,x11942,x11944,x11945,x11946))
% 21.40/21.39 [1195]~E(x11951,x11952)+E(f553(x11953,x11954,x11951,x11955,x11956),f553(x11953,x11954,x11952,x11955,x11956))
% 21.40/21.39 [1196]~E(x11961,x11962)+E(f553(x11963,x11964,x11965,x11961,x11966),f553(x11963,x11964,x11965,x11962,x11966))
% 21.40/21.39 [1197]~E(x11971,x11972)+E(f553(x11973,x11974,x11975,x11976,x11971),f553(x11973,x11974,x11975,x11976,x11972))
% 21.40/21.39 [1198]~E(x11981,x11982)+E(f701(x11981,x11983,x11984),f701(x11982,x11983,x11984))
% 21.40/21.39 [1199]~E(x11991,x11992)+E(f701(x11993,x11991,x11994),f701(x11993,x11992,x11994))
% 21.40/21.39 [1200]~E(x12001,x12002)+E(f701(x12003,x12004,x12001),f701(x12003,x12004,x12002))
% 21.40/21.39 [1201]~E(x12011,x12012)+E(f357(x12011,x12013,x12014,x12015,x12016,x12017),f357(x12012,x12013,x12014,x12015,x12016,x12017))
% 21.40/21.39 [1202]~E(x12021,x12022)+E(f357(x12023,x12021,x12024,x12025,x12026,x12027),f357(x12023,x12022,x12024,x12025,x12026,x12027))
% 21.40/21.39 [1203]~E(x12031,x12032)+E(f357(x12033,x12034,x12031,x12035,x12036,x12037),f357(x12033,x12034,x12032,x12035,x12036,x12037))
% 21.40/21.39 [1204]~E(x12041,x12042)+E(f357(x12043,x12044,x12045,x12041,x12046,x12047),f357(x12043,x12044,x12045,x12042,x12046,x12047))
% 21.40/21.39 [1205]~E(x12051,x12052)+E(f357(x12053,x12054,x12055,x12056,x12051,x12057),f357(x12053,x12054,x12055,x12056,x12052,x12057))
% 21.40/21.39 [1206]~E(x12061,x12062)+E(f357(x12063,x12064,x12065,x12066,x12067,x12061),f357(x12063,x12064,x12065,x12066,x12067,x12062))
% 21.40/21.39 [1207]~E(x12071,x12072)+E(f845(x12071,x12073,x12074),f845(x12072,x12073,x12074))
% 21.40/21.39 [1208]~E(x12081,x12082)+E(f845(x12083,x12081,x12084),f845(x12083,x12082,x12084))
% 21.40/21.39 [1209]~E(x12091,x12092)+E(f845(x12093,x12094,x12091),f845(x12093,x12094,x12092))
% 21.40/21.39 [1210]~E(x12101,x12102)+E(f71(x12101,x12103,x12104),f71(x12102,x12103,x12104))
% 21.40/21.39 [1211]~E(x12111,x12112)+E(f71(x12113,x12111,x12114),f71(x12113,x12112,x12114))
% 21.40/21.39 [1212]~E(x12121,x12122)+E(f71(x12123,x12124,x12121),f71(x12123,x12124,x12122))
% 21.40/21.39 [1213]~E(x12131,x12132)+E(f545(x12131,x12133,x12134,x12135,x12136),f545(x12132,x12133,x12134,x12135,x12136))
% 21.40/21.39 [1214]~E(x12141,x12142)+E(f545(x12143,x12141,x12144,x12145,x12146),f545(x12143,x12142,x12144,x12145,x12146))
% 21.40/21.39 [1215]~E(x12151,x12152)+E(f545(x12153,x12154,x12151,x12155,x12156),f545(x12153,x12154,x12152,x12155,x12156))
% 21.40/21.39 [1216]~E(x12161,x12162)+E(f545(x12163,x12164,x12165,x12161,x12166),f545(x12163,x12164,x12165,x12162,x12166))
% 21.40/21.39 [1217]~E(x12171,x12172)+E(f545(x12173,x12174,x12175,x12176,x12171),f545(x12173,x12174,x12175,x12176,x12172))
% 21.40/21.39 [1218]~E(x12181,x12182)+E(f406(x12181,x12183,x12184,x12185),f406(x12182,x12183,x12184,x12185))
% 21.40/21.39 [1219]~E(x12191,x12192)+E(f406(x12193,x12191,x12194,x12195),f406(x12193,x12192,x12194,x12195))
% 21.40/21.39 [1220]~E(x12201,x12202)+E(f406(x12203,x12204,x12201,x12205),f406(x12203,x12204,x12202,x12205))
% 21.40/21.39 [1221]~E(x12211,x12212)+E(f406(x12213,x12214,x12215,x12211),f406(x12213,x12214,x12215,x12212))
% 21.40/21.39 [1222]~E(x12221,x12222)+E(f384(x12221,x12223,x12224,x12225,x12226,x12227,x12228,x12229,x122210),f384(x12222,x12223,x12224,x12225,x12226,x12227,x12228,x12229,x122210))
% 21.40/21.39 [1223]~E(x12231,x12232)+E(f384(x12233,x12231,x12234,x12235,x12236,x12237,x12238,x12239,x122310),f384(x12233,x12232,x12234,x12235,x12236,x12237,x12238,x12239,x122310))
% 21.40/21.39 [1224]~E(x12241,x12242)+E(f384(x12243,x12244,x12241,x12245,x12246,x12247,x12248,x12249,x122410),f384(x12243,x12244,x12242,x12245,x12246,x12247,x12248,x12249,x122410))
% 21.40/21.39 [1225]~E(x12251,x12252)+E(f384(x12253,x12254,x12255,x12251,x12256,x12257,x12258,x12259,x122510),f384(x12253,x12254,x12255,x12252,x12256,x12257,x12258,x12259,x122510))
% 21.40/21.39 [1226]~E(x12261,x12262)+E(f384(x12263,x12264,x12265,x12266,x12261,x12267,x12268,x12269,x122610),f384(x12263,x12264,x12265,x12266,x12262,x12267,x12268,x12269,x122610))
% 21.40/21.39 [1227]~E(x12271,x12272)+E(f384(x12273,x12274,x12275,x12276,x12277,x12271,x12278,x12279,x122710),f384(x12273,x12274,x12275,x12276,x12277,x12272,x12278,x12279,x122710))
% 21.40/21.39 [1228]~E(x12281,x12282)+E(f384(x12283,x12284,x12285,x12286,x12287,x12288,x12281,x12289,x122810),f384(x12283,x12284,x12285,x12286,x12287,x12288,x12282,x12289,x122810))
% 21.40/21.39 [1229]~E(x12291,x12292)+E(f384(x12293,x12294,x12295,x12296,x12297,x12298,x12299,x12291,x122910),f384(x12293,x12294,x12295,x12296,x12297,x12298,x12299,x12292,x122910))
% 21.40/21.39 [1230]~E(x12301,x12302)+E(f384(x12303,x12304,x12305,x12306,x12307,x12308,x12309,x123010,x12301),f384(x12303,x12304,x12305,x12306,x12307,x12308,x12309,x123010,x12302))
% 21.40/21.39 [1231]~E(x12311,x12312)+E(f507(x12311,x12313,x12314),f507(x12312,x12313,x12314))
% 21.40/21.39 [1232]~E(x12321,x12322)+E(f507(x12323,x12321,x12324),f507(x12323,x12322,x12324))
% 21.40/21.39 [1233]~E(x12331,x12332)+E(f507(x12333,x12334,x12331),f507(x12333,x12334,x12332))
% 21.40/21.39 [1234]~E(x12341,x12342)+E(f21(x12341,x12343,x12344,x12345),f21(x12342,x12343,x12344,x12345))
% 21.40/21.39 [1235]~E(x12351,x12352)+E(f21(x12353,x12351,x12354,x12355),f21(x12353,x12352,x12354,x12355))
% 21.40/21.39 [1236]~E(x12361,x12362)+E(f21(x12363,x12364,x12361,x12365),f21(x12363,x12364,x12362,x12365))
% 21.40/21.39 [1237]~E(x12371,x12372)+E(f21(x12373,x12374,x12375,x12371),f21(x12373,x12374,x12375,x12372))
% 21.40/21.39 [1238]~E(x12381,x12382)+E(f653(x12381),f653(x12382))
% 21.40/21.39 [1239]~E(x12391,x12392)+E(f517(x12391,x12393,x12394,x12395,x12396),f517(x12392,x12393,x12394,x12395,x12396))
% 21.40/21.39 [1240]~E(x12401,x12402)+E(f517(x12403,x12401,x12404,x12405,x12406),f517(x12403,x12402,x12404,x12405,x12406))
% 21.40/21.39 [1241]~E(x12411,x12412)+E(f517(x12413,x12414,x12411,x12415,x12416),f517(x12413,x12414,x12412,x12415,x12416))
% 21.40/21.39 [1242]~E(x12421,x12422)+E(f517(x12423,x12424,x12425,x12421,x12426),f517(x12423,x12424,x12425,x12422,x12426))
% 21.40/21.39 [1243]~E(x12431,x12432)+E(f517(x12433,x12434,x12435,x12436,x12431),f517(x12433,x12434,x12435,x12436,x12432))
% 21.40/21.39 [1244]~E(x12441,x12442)+E(f417(x12441,x12443,x12444),f417(x12442,x12443,x12444))
% 21.40/21.39 [1245]~E(x12451,x12452)+E(f417(x12453,x12451,x12454),f417(x12453,x12452,x12454))
% 21.40/21.39 [1246]~E(x12461,x12462)+E(f417(x12463,x12464,x12461),f417(x12463,x12464,x12462))
% 21.40/21.39 [1247]~E(x12471,x12472)+E(f367(x12471,x12473,x12474,x12475),f367(x12472,x12473,x12474,x12475))
% 21.40/21.39 [1248]~E(x12481,x12482)+E(f367(x12483,x12481,x12484,x12485),f367(x12483,x12482,x12484,x12485))
% 21.40/21.39 [1249]~E(x12491,x12492)+E(f367(x12493,x12494,x12491,x12495),f367(x12493,x12494,x12492,x12495))
% 21.40/21.39 [1250]~E(x12501,x12502)+E(f367(x12503,x12504,x12505,x12501),f367(x12503,x12504,x12505,x12502))
% 21.40/21.39 [1251]~E(x12511,x12512)+E(f791(x12511),f791(x12512))
% 21.40/21.39 [1252]~E(x12521,x12522)+E(f450(x12521,x12523,x12524),f450(x12522,x12523,x12524))
% 21.40/21.39 [1253]~E(x12531,x12532)+E(f450(x12533,x12531,x12534),f450(x12533,x12532,x12534))
% 21.40/21.39 [1254]~E(x12541,x12542)+E(f450(x12543,x12544,x12541),f450(x12543,x12544,x12542))
% 21.40/21.39 [1255]~E(x12551,x12552)+E(f102(x12551,x12553,x12554),f102(x12552,x12553,x12554))
% 21.40/21.39 [1256]~E(x12561,x12562)+E(f102(x12563,x12561,x12564),f102(x12563,x12562,x12564))
% 21.40/21.39 [1257]~E(x12571,x12572)+E(f102(x12573,x12574,x12571),f102(x12573,x12574,x12572))
% 21.40/21.39 [1258]~E(x12581,x12582)+E(f807(x12581,x12583),f807(x12582,x12583))
% 21.40/21.39 [1259]~E(x12591,x12592)+E(f807(x12593,x12591),f807(x12593,x12592))
% 21.40/21.39 [1260]~E(x12601,x12602)+E(f772(x12601,x12603,x12604,x12605),f772(x12602,x12603,x12604,x12605))
% 21.40/21.39 [1261]~E(x12611,x12612)+E(f772(x12613,x12611,x12614,x12615),f772(x12613,x12612,x12614,x12615))
% 21.40/21.39 [1262]~E(x12621,x12622)+E(f772(x12623,x12624,x12621,x12625),f772(x12623,x12624,x12622,x12625))
% 21.40/21.39 [1263]~E(x12631,x12632)+E(f772(x12633,x12634,x12635,x12631),f772(x12633,x12634,x12635,x12632))
% 21.40/21.39 [1264]~E(x12641,x12642)+E(f751(x12641,x12643,x12644,x12645,x12646),f751(x12642,x12643,x12644,x12645,x12646))
% 21.40/21.39 [1265]~E(x12651,x12652)+E(f751(x12653,x12651,x12654,x12655,x12656),f751(x12653,x12652,x12654,x12655,x12656))
% 21.40/21.39 [1266]~E(x12661,x12662)+E(f751(x12663,x12664,x12661,x12665,x12666),f751(x12663,x12664,x12662,x12665,x12666))
% 21.40/21.39 [1267]~E(x12671,x12672)+E(f751(x12673,x12674,x12675,x12671,x12676),f751(x12673,x12674,x12675,x12672,x12676))
% 21.40/21.39 [1268]~E(x12681,x12682)+E(f751(x12683,x12684,x12685,x12686,x12681),f751(x12683,x12684,x12685,x12686,x12682))
% 21.40/21.39 [1269]~E(x12691,x12692)+E(f162(x12691,x12693,x12694),f162(x12692,x12693,x12694))
% 21.40/21.39 [1270]~E(x12701,x12702)+E(f162(x12703,x12701,x12704),f162(x12703,x12702,x12704))
% 21.40/21.39 [1271]~E(x12711,x12712)+E(f162(x12713,x12714,x12711),f162(x12713,x12714,x12712))
% 21.40/21.39 [1272]~E(x12721,x12722)+E(f186(x12721,x12723,x12724,x12725),f186(x12722,x12723,x12724,x12725))
% 21.40/21.39 [1273]~E(x12731,x12732)+E(f186(x12733,x12731,x12734,x12735),f186(x12733,x12732,x12734,x12735))
% 21.40/21.39 [1274]~E(x12741,x12742)+E(f186(x12743,x12744,x12741,x12745),f186(x12743,x12744,x12742,x12745))
% 21.40/21.39 [1275]~E(x12751,x12752)+E(f186(x12753,x12754,x12755,x12751),f186(x12753,x12754,x12755,x12752))
% 21.40/21.39 [1276]~E(x12761,x12762)+E(f206(x12761),f206(x12762))
% 21.40/21.39 [1277]~E(x12771,x12772)+E(f391(x12771,x12773,x12774,x12775),f391(x12772,x12773,x12774,x12775))
% 21.40/21.39 [1278]~E(x12781,x12782)+E(f391(x12783,x12781,x12784,x12785),f391(x12783,x12782,x12784,x12785))
% 21.40/21.39 [1279]~E(x12791,x12792)+E(f391(x12793,x12794,x12791,x12795),f391(x12793,x12794,x12792,x12795))
% 21.40/21.39 [1280]~E(x12801,x12802)+E(f391(x12803,x12804,x12805,x12801),f391(x12803,x12804,x12805,x12802))
% 21.40/21.39 [1281]~E(x12811,x12812)+E(f530(x12811,x12813,x12814,x12815,x12816),f530(x12812,x12813,x12814,x12815,x12816))
% 21.40/21.39 [1282]~E(x12821,x12822)+E(f530(x12823,x12821,x12824,x12825,x12826),f530(x12823,x12822,x12824,x12825,x12826))
% 21.40/21.39 [1283]~E(x12831,x12832)+E(f530(x12833,x12834,x12831,x12835,x12836),f530(x12833,x12834,x12832,x12835,x12836))
% 21.40/21.39 [1284]~E(x12841,x12842)+E(f530(x12843,x12844,x12845,x12841,x12846),f530(x12843,x12844,x12845,x12842,x12846))
% 21.40/21.39 [1285]~E(x12851,x12852)+E(f530(x12853,x12854,x12855,x12856,x12851),f530(x12853,x12854,x12855,x12856,x12852))
% 21.40/21.39 [1286]~E(x12861,x12862)+E(f678(x12861,x12863),f678(x12862,x12863))
% 21.40/21.39 [1287]~E(x12871,x12872)+E(f678(x12873,x12871),f678(x12873,x12872))
% 21.40/21.39 [1288]~E(x12881,x12882)+E(f602(x12881,x12883,x12884,x12885),f602(x12882,x12883,x12884,x12885))
% 21.40/21.39 [1289]~E(x12891,x12892)+E(f602(x12893,x12891,x12894,x12895),f602(x12893,x12892,x12894,x12895))
% 21.40/21.39 [1290]~E(x12901,x12902)+E(f602(x12903,x12904,x12901,x12905),f602(x12903,x12904,x12902,x12905))
% 21.40/21.39 [1291]~E(x12911,x12912)+E(f602(x12913,x12914,x12915,x12911),f602(x12913,x12914,x12915,x12912))
% 21.40/21.39 [1292]~E(x12921,x12922)+E(f767(x12921,x12923,x12924,x12925,x12926),f767(x12922,x12923,x12924,x12925,x12926))
% 21.40/21.39 [1293]~E(x12931,x12932)+E(f767(x12933,x12931,x12934,x12935,x12936),f767(x12933,x12932,x12934,x12935,x12936))
% 21.40/21.39 [1294]~E(x12941,x12942)+E(f767(x12943,x12944,x12941,x12945,x12946),f767(x12943,x12944,x12942,x12945,x12946))
% 21.40/21.39 [1295]~E(x12951,x12952)+E(f767(x12953,x12954,x12955,x12951,x12956),f767(x12953,x12954,x12955,x12952,x12956))
% 21.40/21.39 [1296]~E(x12961,x12962)+E(f767(x12963,x12964,x12965,x12966,x12961),f767(x12963,x12964,x12965,x12966,x12962))
% 21.40/21.39 [1297]~E(x12971,x12972)+E(f682(x12971,x12973,x12974),f682(x12972,x12973,x12974))
% 21.40/21.39 [1298]~E(x12981,x12982)+E(f682(x12983,x12981,x12984),f682(x12983,x12982,x12984))
% 21.40/21.39 [1299]~E(x12991,x12992)+E(f682(x12993,x12994,x12991),f682(x12993,x12994,x12992))
% 21.40/21.39 [1300]~E(x13001,x13002)+E(f495(x13001,x13003,x13004,x13005,x13006),f495(x13002,x13003,x13004,x13005,x13006))
% 21.40/21.39 [1301]~E(x13011,x13012)+E(f495(x13013,x13011,x13014,x13015,x13016),f495(x13013,x13012,x13014,x13015,x13016))
% 21.40/21.39 [1302]~E(x13021,x13022)+E(f495(x13023,x13024,x13021,x13025,x13026),f495(x13023,x13024,x13022,x13025,x13026))
% 21.40/21.39 [1303]~E(x13031,x13032)+E(f495(x13033,x13034,x13035,x13031,x13036),f495(x13033,x13034,x13035,x13032,x13036))
% 21.40/21.39 [1304]~E(x13041,x13042)+E(f495(x13043,x13044,x13045,x13046,x13041),f495(x13043,x13044,x13045,x13046,x13042))
% 21.40/21.39 [1305]~E(x13051,x13052)+E(f60(x13051,x13053),f60(x13052,x13053))
% 21.40/21.39 [1306]~E(x13061,x13062)+E(f60(x13063,x13061),f60(x13063,x13062))
% 21.40/21.39 [1307]~E(x13071,x13072)+E(f368(x13071,x13073,x13074,x13075),f368(x13072,x13073,x13074,x13075))
% 21.40/21.39 [1308]~E(x13081,x13082)+E(f368(x13083,x13081,x13084,x13085),f368(x13083,x13082,x13084,x13085))
% 21.40/21.39 [1309]~E(x13091,x13092)+E(f368(x13093,x13094,x13091,x13095),f368(x13093,x13094,x13092,x13095))
% 21.40/21.39 [1310]~E(x13101,x13102)+E(f368(x13103,x13104,x13105,x13101),f368(x13103,x13104,x13105,x13102))
% 21.40/21.39 [1311]~E(x13111,x13112)+E(f608(x13111,x13113,x13114,x13115),f608(x13112,x13113,x13114,x13115))
% 21.40/21.39 [1312]~E(x13121,x13122)+E(f608(x13123,x13121,x13124,x13125),f608(x13123,x13122,x13124,x13125))
% 21.40/21.39 [1313]~E(x13131,x13132)+E(f608(x13133,x13134,x13131,x13135),f608(x13133,x13134,x13132,x13135))
% 21.40/21.39 [1314]~E(x13141,x13142)+E(f608(x13143,x13144,x13145,x13141),f608(x13143,x13144,x13145,x13142))
% 21.40/21.39 [1315]~E(x13151,x13152)+E(f208(x13151,x13153,x13154,x13155),f208(x13152,x13153,x13154,x13155))
% 21.40/21.39 [1316]~E(x13161,x13162)+E(f208(x13163,x13161,x13164,x13165),f208(x13163,x13162,x13164,x13165))
% 21.40/21.39 [1317]~E(x13171,x13172)+E(f208(x13173,x13174,x13171,x13175),f208(x13173,x13174,x13172,x13175))
% 21.40/21.39 [1318]~E(x13181,x13182)+E(f208(x13183,x13184,x13185,x13181),f208(x13183,x13184,x13185,x13182))
% 21.40/21.39 [1319]~E(x13191,x13192)+E(f531(x13191,x13193,x13194,x13195,x13196),f531(x13192,x13193,x13194,x13195,x13196))
% 21.40/21.39 [1320]~E(x13201,x13202)+E(f531(x13203,x13201,x13204,x13205,x13206),f531(x13203,x13202,x13204,x13205,x13206))
% 21.40/21.39 [1321]~E(x13211,x13212)+E(f531(x13213,x13214,x13211,x13215,x13216),f531(x13213,x13214,x13212,x13215,x13216))
% 21.40/21.39 [1322]~E(x13221,x13222)+E(f531(x13223,x13224,x13225,x13221,x13226),f531(x13223,x13224,x13225,x13222,x13226))
% 21.40/21.39 [1323]~E(x13231,x13232)+E(f531(x13233,x13234,x13235,x13236,x13231),f531(x13233,x13234,x13235,x13236,x13232))
% 21.40/21.39 [1324]~E(x13241,x13242)+E(f734(x13241,x13243,x13244,x13245,x13246),f734(x13242,x13243,x13244,x13245,x13246))
% 21.40/21.39 [1325]~E(x13251,x13252)+E(f734(x13253,x13251,x13254,x13255,x13256),f734(x13253,x13252,x13254,x13255,x13256))
% 21.40/21.39 [1326]~E(x13261,x13262)+E(f734(x13263,x13264,x13261,x13265,x13266),f734(x13263,x13264,x13262,x13265,x13266))
% 21.40/21.39 [1327]~E(x13271,x13272)+E(f734(x13273,x13274,x13275,x13271,x13276),f734(x13273,x13274,x13275,x13272,x13276))
% 21.40/21.39 [1328]~E(x13281,x13282)+E(f734(x13283,x13284,x13285,x13286,x13281),f734(x13283,x13284,x13285,x13286,x13282))
% 21.40/21.39 [1329]~E(x13291,x13292)+E(f402(x13291,x13293),f402(x13292,x13293))
% 21.40/21.39 [1330]~E(x13301,x13302)+E(f402(x13303,x13301),f402(x13303,x13302))
% 21.40/21.39 [1331]~E(x13311,x13312)+E(f852(x13311,x13313,x13314),f852(x13312,x13313,x13314))
% 21.40/21.39 [1332]~E(x13321,x13322)+E(f852(x13323,x13321,x13324),f852(x13323,x13322,x13324))
% 21.40/21.39 [1333]~E(x13331,x13332)+E(f852(x13333,x13334,x13331),f852(x13333,x13334,x13332))
% 21.40/21.39 [1334]~E(x13341,x13342)+E(f757(x13341,x13343,x13344,x13345),f757(x13342,x13343,x13344,x13345))
% 21.40/21.39 [1335]~E(x13351,x13352)+E(f757(x13353,x13351,x13354,x13355),f757(x13353,x13352,x13354,x13355))
% 21.40/21.39 [1336]~E(x13361,x13362)+E(f757(x13363,x13364,x13361,x13365),f757(x13363,x13364,x13362,x13365))
% 21.40/21.39 [1337]~E(x13371,x13372)+E(f757(x13373,x13374,x13375,x13371),f757(x13373,x13374,x13375,x13372))
% 21.40/21.39 [1338]~E(x13381,x13382)+E(f56(x13381),f56(x13382))
% 21.40/21.39 [1339]~E(x13391,x13392)+E(f46(x13391,x13393,x13394,x13395),f46(x13392,x13393,x13394,x13395))
% 21.40/21.39 [1340]~E(x13401,x13402)+E(f46(x13403,x13401,x13404,x13405),f46(x13403,x13402,x13404,x13405))
% 21.40/21.39 [1341]~E(x13411,x13412)+E(f46(x13413,x13414,x13411,x13415),f46(x13413,x13414,x13412,x13415))
% 21.40/21.39 [1342]~E(x13421,x13422)+E(f46(x13423,x13424,x13425,x13421),f46(x13423,x13424,x13425,x13422))
% 21.40/21.39 [1343]~E(x13431,x13432)+E(f769(x13431,x13433,x13434,x13435),f769(x13432,x13433,x13434,x13435))
% 21.40/21.39 [1344]~E(x13441,x13442)+E(f769(x13443,x13441,x13444,x13445),f769(x13443,x13442,x13444,x13445))
% 21.40/21.39 [1345]~E(x13451,x13452)+E(f769(x13453,x13454,x13451,x13455),f769(x13453,x13454,x13452,x13455))
% 21.40/21.39 [1346]~E(x13461,x13462)+E(f769(x13463,x13464,x13465,x13461),f769(x13463,x13464,x13465,x13462))
% 21.40/21.39 [1347]~E(x13471,x13472)+E(f515(x13471,x13473,x13474,x13475,x13476),f515(x13472,x13473,x13474,x13475,x13476))
% 21.40/21.39 [1348]~E(x13481,x13482)+E(f515(x13483,x13481,x13484,x13485,x13486),f515(x13483,x13482,x13484,x13485,x13486))
% 21.40/21.39 [1349]~E(x13491,x13492)+E(f515(x13493,x13494,x13491,x13495,x13496),f515(x13493,x13494,x13492,x13495,x13496))
% 21.40/21.39 [1350]~E(x13501,x13502)+E(f515(x13503,x13504,x13505,x13501,x13506),f515(x13503,x13504,x13505,x13502,x13506))
% 21.40/21.39 [1351]~E(x13511,x13512)+E(f515(x13513,x13514,x13515,x13516,x13511),f515(x13513,x13514,x13515,x13516,x13512))
% 21.40/21.39 [1352]~E(x13521,x13522)+E(f808(x13521,x13523),f808(x13522,x13523))
% 21.40/21.39 [1353]~E(x13531,x13532)+E(f808(x13533,x13531),f808(x13533,x13532))
% 21.40/21.39 [1354]~E(x13541,x13542)+E(f643(x13541,x13543,x13544,x13545),f643(x13542,x13543,x13544,x13545))
% 21.40/21.39 [1355]~E(x13551,x13552)+E(f643(x13553,x13551,x13554,x13555),f643(x13553,x13552,x13554,x13555))
% 21.40/21.39 [1356]~E(x13561,x13562)+E(f643(x13563,x13564,x13561,x13565),f643(x13563,x13564,x13562,x13565))
% 21.40/21.39 [1357]~E(x13571,x13572)+E(f643(x13573,x13574,x13575,x13571),f643(x13573,x13574,x13575,x13572))
% 21.40/21.39 [1358]~E(x13581,x13582)+E(f550(x13581,x13583,x13584),f550(x13582,x13583,x13584))
% 21.40/21.39 [1359]~E(x13591,x13592)+E(f550(x13593,x13591,x13594),f550(x13593,x13592,x13594))
% 21.40/21.39 [1360]~E(x13601,x13602)+E(f550(x13603,x13604,x13601),f550(x13603,x13604,x13602))
% 21.40/21.39 [1361]~E(x13611,x13612)+E(f745(x13611,x13613,x13614,x13615),f745(x13612,x13613,x13614,x13615))
% 21.40/21.39 [1362]~E(x13621,x13622)+E(f745(x13623,x13621,x13624,x13625),f745(x13623,x13622,x13624,x13625))
% 21.40/21.39 [1363]~E(x13631,x13632)+E(f745(x13633,x13634,x13631,x13635),f745(x13633,x13634,x13632,x13635))
% 21.40/21.39 [1364]~E(x13641,x13642)+E(f745(x13643,x13644,x13645,x13641),f745(x13643,x13644,x13645,x13642))
% 21.40/21.39 [1365]~E(x13651,x13652)+E(f615(x13651,x13653,x13654),f615(x13652,x13653,x13654))
% 21.40/21.39 [1366]~E(x13661,x13662)+E(f615(x13663,x13661,x13664),f615(x13663,x13662,x13664))
% 21.40/21.39 [1367]~E(x13671,x13672)+E(f615(x13673,x13674,x13671),f615(x13673,x13674,x13672))
% 21.40/21.39 [1368]~E(x13681,x13682)+E(f847(x13681,x13683,x13684),f847(x13682,x13683,x13684))
% 21.40/21.39 [1369]~E(x13691,x13692)+E(f847(x13693,x13691,x13694),f847(x13693,x13692,x13694))
% 21.40/21.39 [1370]~E(x13701,x13702)+E(f847(x13703,x13704,x13701),f847(x13703,x13704,x13702))
% 21.40/21.39 [1371]~E(x13711,x13712)+E(f692(x13711,x13713,x13714,x13715,x13716),f692(x13712,x13713,x13714,x13715,x13716))
% 21.40/21.39 [1372]~E(x13721,x13722)+E(f692(x13723,x13721,x13724,x13725,x13726),f692(x13723,x13722,x13724,x13725,x13726))
% 21.40/21.39 [1373]~E(x13731,x13732)+E(f692(x13733,x13734,x13731,x13735,x13736),f692(x13733,x13734,x13732,x13735,x13736))
% 21.40/21.39 [1374]~E(x13741,x13742)+E(f692(x13743,x13744,x13745,x13741,x13746),f692(x13743,x13744,x13745,x13742,x13746))
% 21.40/21.39 [1375]~E(x13751,x13752)+E(f692(x13753,x13754,x13755,x13756,x13751),f692(x13753,x13754,x13755,x13756,x13752))
% 21.40/21.39 [1376]~E(x13761,x13762)+E(f827(x13761,x13763,x13764),f827(x13762,x13763,x13764))
% 21.40/21.39 [1377]~E(x13771,x13772)+E(f827(x13773,x13771,x13774),f827(x13773,x13772,x13774))
% 21.40/21.39 [1378]~E(x13781,x13782)+E(f827(x13783,x13784,x13781),f827(x13783,x13784,x13782))
% 21.40/21.39 [1379]~E(x13791,x13792)+E(f768(x13791,x13793,x13794,x13795),f768(x13792,x13793,x13794,x13795))
% 21.40/21.39 [1380]~E(x13801,x13802)+E(f768(x13803,x13801,x13804,x13805),f768(x13803,x13802,x13804,x13805))
% 21.40/21.39 [1381]~E(x13811,x13812)+E(f768(x13813,x13814,x13811,x13815),f768(x13813,x13814,x13812,x13815))
% 21.40/21.39 [1382]~E(x13821,x13822)+E(f768(x13823,x13824,x13825,x13821),f768(x13823,x13824,x13825,x13822))
% 21.40/21.39 [1383]~E(x13831,x13832)+E(f792(x13831),f792(x13832))
% 21.40/21.39 [1384]~E(x13841,x13842)+E(f202(x13841),f202(x13842))
% 21.40/21.39 [1385]~E(x13851,x13852)+E(f503(x13851,x13853,x13854,x13855,x13856),f503(x13852,x13853,x13854,x13855,x13856))
% 21.40/21.39 [1386]~E(x13861,x13862)+E(f503(x13863,x13861,x13864,x13865,x13866),f503(x13863,x13862,x13864,x13865,x13866))
% 21.40/21.39 [1387]~E(x13871,x13872)+E(f503(x13873,x13874,x13871,x13875,x13876),f503(x13873,x13874,x13872,x13875,x13876))
% 21.40/21.39 [1388]~E(x13881,x13882)+E(f503(x13883,x13884,x13885,x13881,x13886),f503(x13883,x13884,x13885,x13882,x13886))
% 21.40/21.39 [1389]~E(x13891,x13892)+E(f503(x13893,x13894,x13895,x13896,x13891),f503(x13893,x13894,x13895,x13896,x13892))
% 21.40/21.39 [1390]~E(x13901,x13902)+E(f597(x13901,x13903),f597(x13902,x13903))
% 21.40/21.39 [1391]~E(x13911,x13912)+E(f597(x13913,x13911),f597(x13913,x13912))
% 21.40/21.39 [1392]~E(x13921,x13922)+E(f378(x13921,x13923,x13924,x13925),f378(x13922,x13923,x13924,x13925))
% 21.40/21.39 [1393]~E(x13931,x13932)+E(f378(x13933,x13931,x13934,x13935),f378(x13933,x13932,x13934,x13935))
% 21.40/21.39 [1394]~E(x13941,x13942)+E(f378(x13943,x13944,x13941,x13945),f378(x13943,x13944,x13942,x13945))
% 21.40/21.39 [1395]~E(x13951,x13952)+E(f378(x13953,x13954,x13955,x13951),f378(x13953,x13954,x13955,x13952))
% 21.40/21.39 [1396]~E(x13961,x13962)+E(f616(x13961,x13963),f616(x13962,x13963))
% 21.40/21.39 [1397]~E(x13971,x13972)+E(f616(x13973,x13971),f616(x13973,x13972))
% 21.40/21.39 [1398]~E(x13981,x13982)+E(f736(x13981,x13983),f736(x13982,x13983))
% 21.40/21.39 [1399]~E(x13991,x13992)+E(f736(x13993,x13991),f736(x13993,x13992))
% 21.40/21.39 [1400]~E(x14001,x14002)+E(f839(x14001,x14003,x14004,x14005),f839(x14002,x14003,x14004,x14005))
% 21.40/21.39 [1401]~E(x14011,x14012)+E(f839(x14013,x14011,x14014,x14015),f839(x14013,x14012,x14014,x14015))
% 21.40/21.39 [1402]~E(x14021,x14022)+E(f839(x14023,x14024,x14021,x14025),f839(x14023,x14024,x14022,x14025))
% 21.40/21.39 [1403]~E(x14031,x14032)+E(f839(x14033,x14034,x14035,x14031),f839(x14033,x14034,x14035,x14032))
% 21.40/21.39 [1404]~E(x14041,x14042)+E(f649(x14041,x14043,x14044,x14045,x14046),f649(x14042,x14043,x14044,x14045,x14046))
% 21.40/21.39 [1405]~E(x14051,x14052)+E(f649(x14053,x14051,x14054,x14055,x14056),f649(x14053,x14052,x14054,x14055,x14056))
% 21.40/21.39 [1406]~E(x14061,x14062)+E(f649(x14063,x14064,x14061,x14065,x14066),f649(x14063,x14064,x14062,x14065,x14066))
% 21.40/21.39 [1407]~E(x14071,x14072)+E(f649(x14073,x14074,x14075,x14071,x14076),f649(x14073,x14074,x14075,x14072,x14076))
% 21.40/21.39 [1408]~E(x14081,x14082)+E(f649(x14083,x14084,x14085,x14086,x14081),f649(x14083,x14084,x14085,x14086,x14082))
% 21.40/21.39 [1409]~E(x14091,x14092)+E(f836(x14091,x14093,x14094),f836(x14092,x14093,x14094))
% 21.40/21.39 [1410]~E(x14101,x14102)+E(f836(x14103,x14101,x14104),f836(x14103,x14102,x14104))
% 21.40/21.39 [1411]~E(x14111,x14112)+E(f836(x14113,x14114,x14111),f836(x14113,x14114,x14112))
% 21.40/21.39 [1412]~E(x14121,x14122)+E(f379(x14121,x14123),f379(x14122,x14123))
% 21.40/21.39 [1413]~E(x14131,x14132)+E(f379(x14133,x14131),f379(x14133,x14132))
% 21.40/21.39 [1414]~E(x14141,x14142)+E(f691(x14141,x14143,x14144,x14145,x14146),f691(x14142,x14143,x14144,x14145,x14146))
% 21.40/21.39 [1415]~E(x14151,x14152)+E(f691(x14153,x14151,x14154,x14155,x14156),f691(x14153,x14152,x14154,x14155,x14156))
% 21.40/21.39 [1416]~E(x14161,x14162)+E(f691(x14163,x14164,x14161,x14165,x14166),f691(x14163,x14164,x14162,x14165,x14166))
% 21.40/21.39 [1417]~E(x14171,x14172)+E(f691(x14173,x14174,x14175,x14171,x14176),f691(x14173,x14174,x14175,x14172,x14176))
% 21.40/21.39 [1418]~E(x14181,x14182)+E(f691(x14183,x14184,x14185,x14186,x14181),f691(x14183,x14184,x14185,x14186,x14182))
% 21.40/21.39 [1419]~E(x14191,x14192)+E(f281(x14191),f281(x14192))
% 21.40/21.39 [1420]~E(x14201,x14202)+E(f828(x14201,x14203,x14204),f828(x14202,x14203,x14204))
% 21.40/21.39 [1421]~E(x14211,x14212)+E(f828(x14213,x14211,x14214),f828(x14213,x14212,x14214))
% 21.40/21.39 [1422]~E(x14221,x14222)+E(f828(x14223,x14224,x14221),f828(x14223,x14224,x14222))
% 21.40/21.39 [1423]~E(x14231,x14232)+E(f797(x14231,x14233,x14234),f797(x14232,x14233,x14234))
% 21.40/21.39 [1424]~E(x14241,x14242)+E(f797(x14243,x14241,x14244),f797(x14243,x14242,x14244))
% 21.40/21.39 [1425]~E(x14251,x14252)+E(f797(x14253,x14254,x14251),f797(x14253,x14254,x14252))
% 21.40/21.39 [1426]~E(x14261,x14262)+E(f544(x14261,x14263,x14264),f544(x14262,x14263,x14264))
% 21.40/21.39 [1427]~E(x14271,x14272)+E(f544(x14273,x14271,x14274),f544(x14273,x14272,x14274))
% 21.40/21.39 [1428]~E(x14281,x14282)+E(f544(x14283,x14284,x14281),f544(x14283,x14284,x14282))
% 21.40/21.39 [1429]~E(x14291,x14292)+E(f283(x14291,x14293,x14294,x14295),f283(x14292,x14293,x14294,x14295))
% 21.40/21.39 [1430]~E(x14301,x14302)+E(f283(x14303,x14301,x14304,x14305),f283(x14303,x14302,x14304,x14305))
% 21.40/21.39 [1431]~E(x14311,x14312)+E(f283(x14313,x14314,x14311,x14315),f283(x14313,x14314,x14312,x14315))
% 21.40/21.39 [1432]~E(x14321,x14322)+E(f283(x14323,x14324,x14325,x14321),f283(x14323,x14324,x14325,x14322))
% 21.40/21.39 [1433]~E(x14331,x14332)+E(f740(x14331,x14333),f740(x14332,x14333))
% 21.40/21.39 [1434]~E(x14341,x14342)+E(f740(x14343,x14341),f740(x14343,x14342))
% 21.40/21.39 [1435]~E(x14351,x14352)+E(f726(x14351,x14353,x14354,x14355,x14356,x14357,x14358),f726(x14352,x14353,x14354,x14355,x14356,x14357,x14358))
% 21.40/21.39 [1436]~E(x14361,x14362)+E(f726(x14363,x14361,x14364,x14365,x14366,x14367,x14368),f726(x14363,x14362,x14364,x14365,x14366,x14367,x14368))
% 21.40/21.39 [1437]~E(x14371,x14372)+E(f726(x14373,x14374,x14371,x14375,x14376,x14377,x14378),f726(x14373,x14374,x14372,x14375,x14376,x14377,x14378))
% 21.40/21.39 [1438]~E(x14381,x14382)+E(f726(x14383,x14384,x14385,x14381,x14386,x14387,x14388),f726(x14383,x14384,x14385,x14382,x14386,x14387,x14388))
% 21.40/21.39 [1439]~E(x14391,x14392)+E(f726(x14393,x14394,x14395,x14396,x14391,x14397,x14398),f726(x14393,x14394,x14395,x14396,x14392,x14397,x14398))
% 21.40/21.39 [1440]~E(x14401,x14402)+E(f726(x14403,x14404,x14405,x14406,x14407,x14401,x14408),f726(x14403,x14404,x14405,x14406,x14407,x14402,x14408))
% 21.40/21.39 [1441]~E(x14411,x14412)+E(f726(x14413,x14414,x14415,x14416,x14417,x14418,x14411),f726(x14413,x14414,x14415,x14416,x14417,x14418,x14412))
% 21.40/21.39 [1442]~E(x14421,x14422)+E(f771(x14421,x14423,x14424,x14425),f771(x14422,x14423,x14424,x14425))
% 21.40/21.39 [1443]~E(x14431,x14432)+E(f771(x14433,x14431,x14434,x14435),f771(x14433,x14432,x14434,x14435))
% 21.40/21.39 [1444]~E(x14441,x14442)+E(f771(x14443,x14444,x14441,x14445),f771(x14443,x14444,x14442,x14445))
% 21.40/21.39 [1445]~E(x14451,x14452)+E(f771(x14453,x14454,x14455,x14451),f771(x14453,x14454,x14455,x14452))
% 21.40/21.39 [1446]~E(x14461,x14462)+E(f461(x14461,x14463,x14464,x14465),f461(x14462,x14463,x14464,x14465))
% 21.40/21.39 [1447]~E(x14471,x14472)+E(f461(x14473,x14471,x14474,x14475),f461(x14473,x14472,x14474,x14475))
% 21.40/21.39 [1448]~E(x14481,x14482)+E(f461(x14483,x14484,x14481,x14485),f461(x14483,x14484,x14482,x14485))
% 21.40/21.39 [1449]~E(x14491,x14492)+E(f461(x14493,x14494,x14495,x14491),f461(x14493,x14494,x14495,x14492))
% 21.40/21.39 [1450]~E(x14501,x14502)+E(f142(x14501,x14503),f142(x14502,x14503))
% 21.40/21.39 [1451]~E(x14511,x14512)+E(f142(x14513,x14511),f142(x14513,x14512))
% 21.40/21.39 [1452]~E(x14521,x14522)+E(f846(x14521,x14523,x14524),f846(x14522,x14523,x14524))
% 21.40/21.39 [1453]~E(x14531,x14532)+E(f846(x14533,x14531,x14534),f846(x14533,x14532,x14534))
% 21.40/21.39 [1454]~E(x14541,x14542)+E(f846(x14543,x14544,x14541),f846(x14543,x14544,x14542))
% 21.40/21.39 [1455]~E(x14551,x14552)+E(f346(x14551,x14553),f346(x14552,x14553))
% 21.40/21.39 [1456]~E(x14561,x14562)+E(f346(x14563,x14561),f346(x14563,x14562))
% 21.40/21.39 [1457]~E(x14571,x14572)+E(f125(x14571,x14573,x14574,x14575),f125(x14572,x14573,x14574,x14575))
% 21.40/21.39 [1458]~E(x14581,x14582)+E(f125(x14583,x14581,x14584,x14585),f125(x14583,x14582,x14584,x14585))
% 21.40/21.39 [1459]~E(x14591,x14592)+E(f125(x14593,x14594,x14591,x14595),f125(x14593,x14594,x14592,x14595))
% 21.40/21.39 [1460]~E(x14601,x14602)+E(f125(x14603,x14604,x14605,x14601),f125(x14603,x14604,x14605,x14602))
% 21.40/21.39 [1461]~E(x14611,x14612)+E(f527(x14611,x14613,x14614,x14615,x14616),f527(x14612,x14613,x14614,x14615,x14616))
% 21.40/21.39 [1462]~E(x14621,x14622)+E(f527(x14623,x14621,x14624,x14625,x14626),f527(x14623,x14622,x14624,x14625,x14626))
% 21.40/21.39 [1463]~E(x14631,x14632)+E(f527(x14633,x14634,x14631,x14635,x14636),f527(x14633,x14634,x14632,x14635,x14636))
% 21.40/21.39 [1464]~E(x14641,x14642)+E(f527(x14643,x14644,x14645,x14641,x14646),f527(x14643,x14644,x14645,x14642,x14646))
% 21.40/21.39 [1465]~E(x14651,x14652)+E(f527(x14653,x14654,x14655,x14656,x14651),f527(x14653,x14654,x14655,x14656,x14652))
% 21.40/21.39 [1466]~E(x14661,x14662)+E(f235(x14661,x14663,x14664),f235(x14662,x14663,x14664))
% 21.40/21.39 [1467]~E(x14671,x14672)+E(f235(x14673,x14671,x14674),f235(x14673,x14672,x14674))
% 21.40/21.39 [1468]~E(x14681,x14682)+E(f235(x14683,x14684,x14681),f235(x14683,x14684,x14682))
% 21.40/21.39 [1469]~E(x14691,x14692)+E(f848(x14691,x14693,x14694),f848(x14692,x14693,x14694))
% 21.40/21.39 [1470]~E(x14701,x14702)+E(f848(x14703,x14701,x14704),f848(x14703,x14702,x14704))
% 21.40/21.39 [1471]~E(x14711,x14712)+E(f848(x14713,x14714,x14711),f848(x14713,x14714,x14712))
% 21.40/21.39 [1472]~E(x14721,x14722)+E(f358(x14721,x14723,x14724,x14725,x14726,x14727),f358(x14722,x14723,x14724,x14725,x14726,x14727))
% 21.40/21.39 [1473]~E(x14731,x14732)+E(f358(x14733,x14731,x14734,x14735,x14736,x14737),f358(x14733,x14732,x14734,x14735,x14736,x14737))
% 21.40/21.39 [1474]~E(x14741,x14742)+E(f358(x14743,x14744,x14741,x14745,x14746,x14747),f358(x14743,x14744,x14742,x14745,x14746,x14747))
% 21.40/21.39 [1475]~E(x14751,x14752)+E(f358(x14753,x14754,x14755,x14751,x14756,x14757),f358(x14753,x14754,x14755,x14752,x14756,x14757))
% 21.40/21.39 [1476]~E(x14761,x14762)+E(f358(x14763,x14764,x14765,x14766,x14761,x14767),f358(x14763,x14764,x14765,x14766,x14762,x14767))
% 21.40/21.39 [1477]~E(x14771,x14772)+E(f358(x14773,x14774,x14775,x14776,x14777,x14771),f358(x14773,x14774,x14775,x14776,x14777,x14772))
% 21.40/21.39 [1478]~E(x14781,x14782)+E(f476(x14781,x14783,x14784,x14785),f476(x14782,x14783,x14784,x14785))
% 21.40/21.39 [1479]~E(x14791,x14792)+E(f476(x14793,x14791,x14794,x14795),f476(x14793,x14792,x14794,x14795))
% 21.40/21.39 [1480]~E(x14801,x14802)+E(f476(x14803,x14804,x14801,x14805),f476(x14803,x14804,x14802,x14805))
% 21.40/21.39 [1481]~E(x14811,x14812)+E(f476(x14813,x14814,x14815,x14811),f476(x14813,x14814,x14815,x14812))
% 21.40/21.39 [1482]~E(x14821,x14822)+E(f533(x14821,x14823,x14824,x14825,x14826),f533(x14822,x14823,x14824,x14825,x14826))
% 21.40/21.39 [1483]~E(x14831,x14832)+E(f533(x14833,x14831,x14834,x14835,x14836),f533(x14833,x14832,x14834,x14835,x14836))
% 21.40/21.39 [1484]~E(x14841,x14842)+E(f533(x14843,x14844,x14841,x14845,x14846),f533(x14843,x14844,x14842,x14845,x14846))
% 21.40/21.39 [1485]~E(x14851,x14852)+E(f533(x14853,x14854,x14855,x14851,x14856),f533(x14853,x14854,x14855,x14852,x14856))
% 21.40/21.39 [1486]~E(x14861,x14862)+E(f533(x14863,x14864,x14865,x14866,x14861),f533(x14863,x14864,x14865,x14866,x14862))
% 21.40/21.39 [1487]~E(x14871,x14872)+E(f698(x14871,x14873,x14874,x14875),f698(x14872,x14873,x14874,x14875))
% 21.40/21.39 [1488]~E(x14881,x14882)+E(f698(x14883,x14881,x14884,x14885),f698(x14883,x14882,x14884,x14885))
% 21.40/21.39 [1489]~E(x14891,x14892)+E(f698(x14893,x14894,x14891,x14895),f698(x14893,x14894,x14892,x14895))
% 21.40/21.39 [1490]~E(x14901,x14902)+E(f698(x14903,x14904,x14905,x14901),f698(x14903,x14904,x14905,x14902))
% 21.40/21.39 [1491]~E(x14911,x14912)+E(f491(x14911,x14913,x14914,x14915),f491(x14912,x14913,x14914,x14915))
% 21.40/21.39 [1492]~E(x14921,x14922)+E(f491(x14923,x14921,x14924,x14925),f491(x14923,x14922,x14924,x14925))
% 21.40/21.39 [1493]~E(x14931,x14932)+E(f491(x14933,x14934,x14931,x14935),f491(x14933,x14934,x14932,x14935))
% 21.40/21.39 [1494]~E(x14941,x14942)+E(f491(x14943,x14944,x14945,x14941),f491(x14943,x14944,x14945,x14942))
% 21.40/21.39 [1495]~E(x14951,x14952)+E(f464(x14951,x14953,x14954,x14955),f464(x14952,x14953,x14954,x14955))
% 21.40/21.39 [1496]~E(x14961,x14962)+E(f464(x14963,x14961,x14964,x14965),f464(x14963,x14962,x14964,x14965))
% 21.40/21.39 [1497]~E(x14971,x14972)+E(f464(x14973,x14974,x14971,x14975),f464(x14973,x14974,x14972,x14975))
% 21.40/21.39 [1498]~E(x14981,x14982)+E(f464(x14983,x14984,x14985,x14981),f464(x14983,x14984,x14985,x14982))
% 21.40/21.39 [1499]~E(x14991,x14992)+E(f535(x14991,x14993,x14994,x14995,x14996),f535(x14992,x14993,x14994,x14995,x14996))
% 21.40/21.39 [1500]~E(x15001,x15002)+E(f535(x15003,x15001,x15004,x15005,x15006),f535(x15003,x15002,x15004,x15005,x15006))
% 21.40/21.39 [1501]~E(x15011,x15012)+E(f535(x15013,x15014,x15011,x15015,x15016),f535(x15013,x15014,x15012,x15015,x15016))
% 21.40/21.39 [1502]~E(x15021,x15022)+E(f535(x15023,x15024,x15025,x15021,x15026),f535(x15023,x15024,x15025,x15022,x15026))
% 21.40/21.39 [1503]~E(x15031,x15032)+E(f535(x15033,x15034,x15035,x15036,x15031),f535(x15033,x15034,x15035,x15036,x15032))
% 21.40/21.39 [1504]~E(x15041,x15042)+E(f449(x15041,x15043,x15044),f449(x15042,x15043,x15044))
% 21.40/21.39 [1505]~E(x15051,x15052)+E(f449(x15053,x15051,x15054),f449(x15053,x15052,x15054))
% 21.40/21.39 [1506]~E(x15061,x15062)+E(f449(x15063,x15064,x15061),f449(x15063,x15064,x15062))
% 21.40/21.39 [1507]~E(x15071,x15072)+E(f702(x15071,x15073,x15074),f702(x15072,x15073,x15074))
% 21.40/21.39 [1508]~E(x15081,x15082)+E(f702(x15083,x15081,x15084),f702(x15083,x15082,x15084))
% 21.40/21.39 [1509]~E(x15091,x15092)+E(f702(x15093,x15094,x15091),f702(x15093,x15094,x15092))
% 21.40/21.39 [1510]~E(x15101,x15102)+E(f815(x15101,x15103,x15104),f815(x15102,x15103,x15104))
% 21.40/21.39 [1511]~E(x15111,x15112)+E(f815(x15113,x15111,x15114),f815(x15113,x15112,x15114))
% 21.40/21.39 [1512]~E(x15121,x15122)+E(f815(x15123,x15124,x15121),f815(x15123,x15124,x15122))
% 21.40/21.39 [1513]~E(x15131,x15132)+E(f359(x15131,x15133,x15134,x15135,x15136,x15137),f359(x15132,x15133,x15134,x15135,x15136,x15137))
% 21.40/21.39 [1514]~E(x15141,x15142)+E(f359(x15143,x15141,x15144,x15145,x15146,x15147),f359(x15143,x15142,x15144,x15145,x15146,x15147))
% 21.40/21.39 [1515]~E(x15151,x15152)+E(f359(x15153,x15154,x15151,x15155,x15156,x15157),f359(x15153,x15154,x15152,x15155,x15156,x15157))
% 21.40/21.39 [1516]~E(x15161,x15162)+E(f359(x15163,x15164,x15165,x15161,x15166,x15167),f359(x15163,x15164,x15165,x15162,x15166,x15167))
% 21.40/21.39 [1517]~E(x15171,x15172)+E(f359(x15173,x15174,x15175,x15176,x15171,x15177),f359(x15173,x15174,x15175,x15176,x15172,x15177))
% 21.40/21.39 [1518]~E(x15181,x15182)+E(f359(x15183,x15184,x15185,x15186,x15187,x15181),f359(x15183,x15184,x15185,x15186,x15187,x15182))
% 21.40/21.39 [1519]~E(x15191,x15192)+E(f640(x15191,x15193,x15194,x15195,x15196,x15197),f640(x15192,x15193,x15194,x15195,x15196,x15197))
% 21.40/21.39 [1520]~E(x15201,x15202)+E(f640(x15203,x15201,x15204,x15205,x15206,x15207),f640(x15203,x15202,x15204,x15205,x15206,x15207))
% 21.40/21.39 [1521]~E(x15211,x15212)+E(f640(x15213,x15214,x15211,x15215,x15216,x15217),f640(x15213,x15214,x15212,x15215,x15216,x15217))
% 21.40/21.39 [1522]~E(x15221,x15222)+E(f640(x15223,x15224,x15225,x15221,x15226,x15227),f640(x15223,x15224,x15225,x15222,x15226,x15227))
% 21.40/21.39 [1523]~E(x15231,x15232)+E(f640(x15233,x15234,x15235,x15236,x15231,x15237),f640(x15233,x15234,x15235,x15236,x15232,x15237))
% 21.40/21.39 [1524]~E(x15241,x15242)+E(f640(x15243,x15244,x15245,x15246,x15247,x15241),f640(x15243,x15244,x15245,x15246,x15247,x15242))
% 21.40/21.39 [1525]~E(x15251,x15252)+E(f592(x15251,x15253),f592(x15252,x15253))
% 21.40/21.39 [1526]~E(x15261,x15262)+E(f592(x15263,x15261),f592(x15263,x15262))
% 21.40/21.39 [1527]~E(x15271,x15272)+E(f480(x15271,x15273,x15274,x15275),f480(x15272,x15273,x15274,x15275))
% 21.40/21.39 [1528]~E(x15281,x15282)+E(f480(x15283,x15281,x15284,x15285),f480(x15283,x15282,x15284,x15285))
% 21.40/21.39 [1529]~E(x15291,x15292)+E(f480(x15293,x15294,x15291,x15295),f480(x15293,x15294,x15292,x15295))
% 21.40/21.39 [1530]~E(x15301,x15302)+E(f480(x15303,x15304,x15305,x15301),f480(x15303,x15304,x15305,x15302))
% 21.40/21.39 [1531]~E(x15311,x15312)+E(f218(x15311,x15313),f218(x15312,x15313))
% 21.40/21.39 [1532]~E(x15321,x15322)+E(f218(x15323,x15321),f218(x15323,x15322))
% 21.40/21.39 [1533]~E(x15331,x15332)+E(f648(x15331,x15333,x15334,x15335,x15336,x15337,x15338),f648(x15332,x15333,x15334,x15335,x15336,x15337,x15338))
% 21.40/21.39 [1534]~E(x15341,x15342)+E(f648(x15343,x15341,x15344,x15345,x15346,x15347,x15348),f648(x15343,x15342,x15344,x15345,x15346,x15347,x15348))
% 21.40/21.39 [1535]~E(x15351,x15352)+E(f648(x15353,x15354,x15351,x15355,x15356,x15357,x15358),f648(x15353,x15354,x15352,x15355,x15356,x15357,x15358))
% 21.40/21.39 [1536]~E(x15361,x15362)+E(f648(x15363,x15364,x15365,x15361,x15366,x15367,x15368),f648(x15363,x15364,x15365,x15362,x15366,x15367,x15368))
% 21.40/21.39 [1537]~E(x15371,x15372)+E(f648(x15373,x15374,x15375,x15376,x15371,x15377,x15378),f648(x15373,x15374,x15375,x15376,x15372,x15377,x15378))
% 21.40/21.39 [1538]~E(x15381,x15382)+E(f648(x15383,x15384,x15385,x15386,x15387,x15381,x15388),f648(x15383,x15384,x15385,x15386,x15387,x15382,x15388))
% 21.40/21.39 [1539]~E(x15391,x15392)+E(f648(x15393,x15394,x15395,x15396,x15397,x15398,x15391),f648(x15393,x15394,x15395,x15396,x15397,x15398,x15392))
% 21.40/21.39 [1540]~E(x15401,x15402)+E(f605(x15401,x15403,x15404,x15405),f605(x15402,x15403,x15404,x15405))
% 21.40/21.39 [1541]~E(x15411,x15412)+E(f605(x15413,x15411,x15414,x15415),f605(x15413,x15412,x15414,x15415))
% 21.40/21.39 [1542]~E(x15421,x15422)+E(f605(x15423,x15424,x15421,x15425),f605(x15423,x15424,x15422,x15425))
% 21.40/21.39 [1543]~E(x15431,x15432)+E(f605(x15433,x15434,x15435,x15431),f605(x15433,x15434,x15435,x15432))
% 21.40/21.39 [1544]~E(x15441,x15442)+E(f776(x15441,x15443),f776(x15442,x15443))
% 21.40/21.39 [1545]~E(x15451,x15452)+E(f776(x15453,x15451),f776(x15453,x15452))
% 21.40/21.39 [1546]~E(x15461,x15462)+E(f803(x15461),f803(x15462))
% 21.40/21.39 [1547]~E(x15471,x15472)+E(f843(x15471,x15473,x15474),f843(x15472,x15473,x15474))
% 21.40/21.39 [1548]~E(x15481,x15482)+E(f843(x15483,x15481,x15484),f843(x15483,x15482,x15484))
% 21.40/21.39 [1549]~E(x15491,x15492)+E(f843(x15493,x15494,x15491),f843(x15493,x15494,x15492))
% 21.40/21.39 [1550]~E(x15501,x15502)+E(f557(x15501,x15503,x15504,x15505,x15506),f557(x15502,x15503,x15504,x15505,x15506))
% 21.40/21.39 [1551]~E(x15511,x15512)+E(f557(x15513,x15511,x15514,x15515,x15516),f557(x15513,x15512,x15514,x15515,x15516))
% 21.40/21.39 [1552]~E(x15521,x15522)+E(f557(x15523,x15524,x15521,x15525,x15526),f557(x15523,x15524,x15522,x15525,x15526))
% 21.40/21.39 [1553]~E(x15531,x15532)+E(f557(x15533,x15534,x15535,x15531,x15536),f557(x15533,x15534,x15535,x15532,x15536))
% 21.40/21.39 [1554]~E(x15541,x15542)+E(f557(x15543,x15544,x15545,x15546,x15541),f557(x15543,x15544,x15545,x15546,x15542))
% 21.40/21.39 [1555]~E(x15551,x15552)+E(f434(x15551,x15553,x15554),f434(x15552,x15553,x15554))
% 21.40/21.39 [1556]~E(x15561,x15562)+E(f434(x15563,x15561,x15564),f434(x15563,x15562,x15564))
% 21.40/21.39 [1557]~E(x15571,x15572)+E(f434(x15573,x15574,x15571),f434(x15573,x15574,x15572))
% 21.40/21.39 [1558]~E(x15581,x15582)+E(f825(x15581,x15583,x15584),f825(x15582,x15583,x15584))
% 21.40/21.39 [1559]~E(x15591,x15592)+E(f825(x15593,x15591,x15594),f825(x15593,x15592,x15594))
% 21.40/21.39 [1560]~E(x15601,x15602)+E(f825(x15603,x15604,x15601),f825(x15603,x15604,x15602))
% 21.40/21.39 [1561]~E(x15611,x15612)+E(f454(x15611,x15613,x15614),f454(x15612,x15613,x15614))
% 21.40/21.39 [1562]~E(x15621,x15622)+E(f454(x15623,x15621,x15624),f454(x15623,x15622,x15624))
% 21.40/21.39 [1563]~E(x15631,x15632)+E(f454(x15633,x15634,x15631),f454(x15633,x15634,x15632))
% 21.40/21.39 [1564]~E(x15641,x15642)+E(f383(x15641,x15643,x15644,x15645,x15646),f383(x15642,x15643,x15644,x15645,x15646))
% 21.40/21.39 [1565]~E(x15651,x15652)+E(f383(x15653,x15651,x15654,x15655,x15656),f383(x15653,x15652,x15654,x15655,x15656))
% 21.40/21.39 [1566]~E(x15661,x15662)+E(f383(x15663,x15664,x15661,x15665,x15666),f383(x15663,x15664,x15662,x15665,x15666))
% 21.40/21.39 [1567]~E(x15671,x15672)+E(f383(x15673,x15674,x15675,x15671,x15676),f383(x15673,x15674,x15675,x15672,x15676))
% 21.40/21.39 [1568]~E(x15681,x15682)+E(f383(x15683,x15684,x15685,x15686,x15681),f383(x15683,x15684,x15685,x15686,x15682))
% 21.40/21.39 [1569]~E(x15691,x15692)+E(f435(x15691,x15693,x15694),f435(x15692,x15693,x15694))
% 21.40/21.39 [1570]~E(x15701,x15702)+E(f435(x15703,x15701,x15704),f435(x15703,x15702,x15704))
% 21.40/21.39 [1571]~E(x15711,x15712)+E(f435(x15713,x15714,x15711),f435(x15713,x15714,x15712))
% 21.40/21.39 [1572]~E(x15721,x15722)+E(f577(x15721,x15723,x15724),f577(x15722,x15723,x15724))
% 21.40/21.39 [1573]~E(x15731,x15732)+E(f577(x15733,x15731,x15734),f577(x15733,x15732,x15734))
% 21.40/21.39 [1574]~E(x15741,x15742)+E(f577(x15743,x15744,x15741),f577(x15743,x15744,x15742))
% 21.40/21.39 [1575]~E(x15751,x15752)+E(f614(x15751,x15753),f614(x15752,x15753))
% 21.40/21.39 [1576]~E(x15761,x15762)+E(f614(x15763,x15761),f614(x15763,x15762))
% 21.40/21.39 [1577]~E(x15771,x15772)+E(f739(x15771,x15773,x15774),f739(x15772,x15773,x15774))
% 21.40/21.39 [1578]~E(x15781,x15782)+E(f739(x15783,x15781,x15784),f739(x15783,x15782,x15784))
% 21.40/21.39 [1579]~E(x15791,x15792)+E(f739(x15793,x15794,x15791),f739(x15793,x15794,x15792))
% 21.40/21.39 [1580]~E(x15801,x15802)+E(f459(x15801,x15803,x15804),f459(x15802,x15803,x15804))
% 21.40/21.39 [1581]~E(x15811,x15812)+E(f459(x15813,x15811,x15814),f459(x15813,x15812,x15814))
% 21.40/21.39 [1582]~E(x15821,x15822)+E(f459(x15823,x15824,x15821),f459(x15823,x15824,x15822))
% 21.40/21.39 [1583]~E(x15831,x15832)+E(f243(x15831,x15833),f243(x15832,x15833))
% 21.40/21.39 [1584]~E(x15841,x15842)+E(f243(x15843,x15841),f243(x15843,x15842))
% 21.40/21.39 [1585]~E(x15851,x15852)+E(f444(x15851,x15853,x15854),f444(x15852,x15853,x15854))
% 21.40/21.39 [1586]~E(x15861,x15862)+E(f444(x15863,x15861,x15864),f444(x15863,x15862,x15864))
% 21.40/21.39 [1587]~E(x15871,x15872)+E(f444(x15873,x15874,x15871),f444(x15873,x15874,x15872))
% 21.40/21.39 [1588]~E(x15881,x15882)+E(f621(x15881,x15883),f621(x15882,x15883))
% 21.40/21.39 [1589]~E(x15891,x15892)+E(f621(x15893,x15891),f621(x15893,x15892))
% 21.40/21.39 [1590]~E(x15901,x15902)+E(f496(x15901,x15903),f496(x15902,x15903))
% 21.40/21.39 [1591]~E(x15911,x15912)+E(f496(x15913,x15911),f496(x15913,x15912))
% 21.40/21.39 [1592]~E(x15921,x15922)+E(f361(x15921,x15923,x15924),f361(x15922,x15923,x15924))
% 21.40/21.39 [1593]~E(x15931,x15932)+E(f361(x15933,x15931,x15934),f361(x15933,x15932,x15934))
% 21.40/21.39 [1594]~E(x15941,x15942)+E(f361(x15943,x15944,x15941),f361(x15943,x15944,x15942))
% 21.40/21.39 [1595]~E(x15951,x15952)+E(f782(x15951,x15953),f782(x15952,x15953))
% 21.40/21.39 [1596]~E(x15961,x15962)+E(f782(x15963,x15961),f782(x15963,x15962))
% 21.40/21.39 [1597]~E(x15971,x15972)+E(f394(x15971,x15973),f394(x15972,x15973))
% 21.40/21.39 [1598]~E(x15981,x15982)+E(f394(x15983,x15981),f394(x15983,x15982))
% 21.40/21.39 [1599]~E(x15991,x15992)+E(f773(x15991,x15993,x15994),f773(x15992,x15993,x15994))
% 21.40/21.39 [1600]~E(x16001,x16002)+E(f773(x16003,x16001,x16004),f773(x16003,x16002,x16004))
% 21.40/21.39 [1601]~E(x16011,x16012)+E(f773(x16013,x16014,x16011),f773(x16013,x16014,x16012))
% 21.40/21.39 [1602]~E(x16021,x16022)+E(f626(x16021,x16023,x16024,x16025,x16026,x16027),f626(x16022,x16023,x16024,x16025,x16026,x16027))
% 21.40/21.39 [1603]~E(x16031,x16032)+E(f626(x16033,x16031,x16034,x16035,x16036,x16037),f626(x16033,x16032,x16034,x16035,x16036,x16037))
% 21.40/21.39 [1604]~E(x16041,x16042)+E(f626(x16043,x16044,x16041,x16045,x16046,x16047),f626(x16043,x16044,x16042,x16045,x16046,x16047))
% 21.40/21.39 [1605]~E(x16051,x16052)+E(f626(x16053,x16054,x16055,x16051,x16056,x16057),f626(x16053,x16054,x16055,x16052,x16056,x16057))
% 21.40/21.39 [1606]~E(x16061,x16062)+E(f626(x16063,x16064,x16065,x16066,x16061,x16067),f626(x16063,x16064,x16065,x16066,x16062,x16067))
% 21.40/21.39 [1607]~E(x16071,x16072)+E(f626(x16073,x16074,x16075,x16076,x16077,x16071),f626(x16073,x16074,x16075,x16076,x16077,x16072))
% 21.40/21.39 [1608]~E(x16081,x16082)+E(f731(x16081,x16083,x16084,x16085,x16086),f731(x16082,x16083,x16084,x16085,x16086))
% 21.40/21.39 [1609]~E(x16091,x16092)+E(f731(x16093,x16091,x16094,x16095,x16096),f731(x16093,x16092,x16094,x16095,x16096))
% 21.40/21.39 [1610]~E(x16101,x16102)+E(f731(x16103,x16104,x16101,x16105,x16106),f731(x16103,x16104,x16102,x16105,x16106))
% 21.40/21.39 [1611]~E(x16111,x16112)+E(f731(x16113,x16114,x16115,x16111,x16116),f731(x16113,x16114,x16115,x16112,x16116))
% 21.40/21.39 [1612]~E(x16121,x16122)+E(f731(x16123,x16124,x16125,x16126,x16121),f731(x16123,x16124,x16125,x16126,x16122))
% 21.40/21.39 [1613]~E(x16131,x16132)+E(f837(x16131,x16133,x16134),f837(x16132,x16133,x16134))
% 21.40/21.39 [1614]~E(x16141,x16142)+E(f837(x16143,x16141,x16144),f837(x16143,x16142,x16144))
% 21.40/21.39 [1615]~E(x16151,x16152)+E(f837(x16153,x16154,x16151),f837(x16153,x16154,x16152))
% 21.40/21.39 [1616]~E(x16161,x16162)+E(f451(x16161,x16163,x16164),f451(x16162,x16163,x16164))
% 21.40/21.39 [1617]~E(x16171,x16172)+E(f451(x16173,x16171,x16174),f451(x16173,x16172,x16174))
% 21.40/21.39 [1618]~E(x16181,x16182)+E(f451(x16183,x16184,x16181),f451(x16183,x16184,x16182))
% 21.40/21.39 [1619]~E(x16191,x16192)+E(f581(x16191,x16193,x16194,x16195,x16196,x16197),f581(x16192,x16193,x16194,x16195,x16196,x16197))
% 21.40/21.39 [1620]~E(x16201,x16202)+E(f581(x16203,x16201,x16204,x16205,x16206,x16207),f581(x16203,x16202,x16204,x16205,x16206,x16207))
% 21.40/21.39 [1621]~E(x16211,x16212)+E(f581(x16213,x16214,x16211,x16215,x16216,x16217),f581(x16213,x16214,x16212,x16215,x16216,x16217))
% 21.40/21.39 [1622]~E(x16221,x16222)+E(f581(x16223,x16224,x16225,x16221,x16226,x16227),f581(x16223,x16224,x16225,x16222,x16226,x16227))
% 21.40/21.39 [1623]~E(x16231,x16232)+E(f581(x16233,x16234,x16235,x16236,x16231,x16237),f581(x16233,x16234,x16235,x16236,x16232,x16237))
% 21.40/21.39 [1624]~E(x16241,x16242)+E(f581(x16243,x16244,x16245,x16246,x16247,x16241),f581(x16243,x16244,x16245,x16246,x16247,x16242))
% 21.40/21.39 [1625]~E(x16251,x16252)+E(f473(x16251,x16253,x16254,x16255),f473(x16252,x16253,x16254,x16255))
% 21.40/21.39 [1626]~E(x16261,x16262)+E(f473(x16263,x16261,x16264,x16265),f473(x16263,x16262,x16264,x16265))
% 21.40/21.39 [1627]~E(x16271,x16272)+E(f473(x16273,x16274,x16271,x16275),f473(x16273,x16274,x16272,x16275))
% 21.40/21.39 [1628]~E(x16281,x16282)+E(f473(x16283,x16284,x16285,x16281),f473(x16283,x16284,x16285,x16282))
% 21.40/21.39 [1629]~E(x16291,x16292)+E(f693(x16291,x16293,x16294,x16295,x16296),f693(x16292,x16293,x16294,x16295,x16296))
% 21.40/21.39 [1630]~E(x16301,x16302)+E(f693(x16303,x16301,x16304,x16305,x16306),f693(x16303,x16302,x16304,x16305,x16306))
% 21.40/21.39 [1631]~E(x16311,x16312)+E(f693(x16313,x16314,x16311,x16315,x16316),f693(x16313,x16314,x16312,x16315,x16316))
% 21.40/21.39 [1632]~E(x16321,x16322)+E(f693(x16323,x16324,x16325,x16321,x16326),f693(x16323,x16324,x16325,x16322,x16326))
% 21.40/21.39 [1633]~E(x16331,x16332)+E(f693(x16333,x16334,x16335,x16336,x16331),f693(x16333,x16334,x16335,x16336,x16332))
% 21.40/21.39 [1634]~E(x16341,x16342)+E(f711(x16341,x16343),f711(x16342,x16343))
% 21.40/21.39 [1635]~E(x16351,x16352)+E(f711(x16353,x16351),f711(x16353,x16352))
% 21.40/21.39 [1636]~E(x16361,x16362)+E(f724(x16361,x16363,x16364,x16365,x16366),f724(x16362,x16363,x16364,x16365,x16366))
% 21.40/21.39 [1637]~E(x16371,x16372)+E(f724(x16373,x16371,x16374,x16375,x16376),f724(x16373,x16372,x16374,x16375,x16376))
% 21.40/21.39 [1638]~E(x16381,x16382)+E(f724(x16383,x16384,x16381,x16385,x16386),f724(x16383,x16384,x16382,x16385,x16386))
% 21.40/21.39 [1639]~E(x16391,x16392)+E(f724(x16393,x16394,x16395,x16391,x16396),f724(x16393,x16394,x16395,x16392,x16396))
% 21.40/21.39 [1640]~E(x16401,x16402)+E(f724(x16403,x16404,x16405,x16406,x16401),f724(x16403,x16404,x16405,x16406,x16402))
% 21.40/21.39 [1641]~E(x16411,x16412)+E(f315(x16411,x16413,x16414),f315(x16412,x16413,x16414))
% 21.40/21.39 [1642]~E(x16421,x16422)+E(f315(x16423,x16421,x16424),f315(x16423,x16422,x16424))
% 21.40/21.39 [1643]~E(x16431,x16432)+E(f315(x16433,x16434,x16431),f315(x16433,x16434,x16432))
% 21.40/21.39 [1644]~E(x16441,x16442)+E(f721(x16441,x16443,x16444,x16445),f721(x16442,x16443,x16444,x16445))
% 21.40/21.39 [1645]~E(x16451,x16452)+E(f721(x16453,x16451,x16454,x16455),f721(x16453,x16452,x16454,x16455))
% 21.40/21.39 [1646]~E(x16461,x16462)+E(f721(x16463,x16464,x16461,x16465),f721(x16463,x16464,x16462,x16465))
% 21.40/21.39 [1647]~E(x16471,x16472)+E(f721(x16473,x16474,x16475,x16471),f721(x16473,x16474,x16475,x16472))
% 21.40/21.39 [1648]~E(x16481,x16482)+E(f624(x16481,x16483,x16484,x16485),f624(x16482,x16483,x16484,x16485))
% 21.40/21.39 [1649]~E(x16491,x16492)+E(f624(x16493,x16491,x16494,x16495),f624(x16493,x16492,x16494,x16495))
% 21.40/21.39 [1650]~E(x16501,x16502)+E(f624(x16503,x16504,x16501,x16505),f624(x16503,x16504,x16502,x16505))
% 21.40/21.39 [1651]~E(x16511,x16512)+E(f624(x16513,x16514,x16515,x16511),f624(x16513,x16514,x16515,x16512))
% 21.40/21.39 [1652]~E(x16521,x16522)+E(f664(x16521,x16523,x16524),f664(x16522,x16523,x16524))
% 21.40/21.39 [1653]~E(x16531,x16532)+E(f664(x16533,x16531,x16534),f664(x16533,x16532,x16534))
% 21.40/21.39 [1654]~E(x16541,x16542)+E(f664(x16543,x16544,x16541),f664(x16543,x16544,x16542))
% 21.40/21.39 [1655]~E(x16551,x16552)+E(f333(x16551,x16553,x16554,x16555),f333(x16552,x16553,x16554,x16555))
% 21.40/21.39 [1656]~E(x16561,x16562)+E(f333(x16563,x16561,x16564,x16565),f333(x16563,x16562,x16564,x16565))
% 21.40/21.39 [1657]~E(x16571,x16572)+E(f333(x16573,x16574,x16571,x16575),f333(x16573,x16574,x16572,x16575))
% 21.40/21.39 [1658]~E(x16581,x16582)+E(f333(x16583,x16584,x16585,x16581),f333(x16583,x16584,x16585,x16582))
% 21.40/21.39 [1659]~E(x16591,x16592)+E(f416(x16591,x16593,x16594,x16595),f416(x16592,x16593,x16594,x16595))
% 21.40/21.39 [1660]~E(x16601,x16602)+E(f416(x16603,x16601,x16604,x16605),f416(x16603,x16602,x16604,x16605))
% 21.40/21.39 [1661]~E(x16611,x16612)+E(f416(x16613,x16614,x16611,x16615),f416(x16613,x16614,x16612,x16615))
% 21.40/21.39 [1662]~E(x16621,x16622)+E(f416(x16623,x16624,x16625,x16621),f416(x16623,x16624,x16625,x16622))
% 21.40/21.39 [1663]~E(x16631,x16632)+E(f446(x16631,x16633,x16634),f446(x16632,x16633,x16634))
% 21.40/21.39 [1664]~E(x16641,x16642)+E(f446(x16643,x16641,x16644),f446(x16643,x16642,x16644))
% 21.40/21.39 [1665]~E(x16651,x16652)+E(f446(x16653,x16654,x16651),f446(x16653,x16654,x16652))
% 21.40/21.39 [1666]~E(x16661,x16662)+E(f58(x16661),f58(x16662))
% 21.40/21.39 [1667]~E(x16671,x16672)+E(f617(x16671,x16673,x16674,x16675),f617(x16672,x16673,x16674,x16675))
% 21.40/21.39 [1668]~E(x16681,x16682)+E(f617(x16683,x16681,x16684,x16685),f617(x16683,x16682,x16684,x16685))
% 21.40/21.39 [1669]~E(x16691,x16692)+E(f617(x16693,x16694,x16691,x16695),f617(x16693,x16694,x16692,x16695))
% 21.40/21.39 [1670]~E(x16701,x16702)+E(f617(x16703,x16704,x16705,x16701),f617(x16703,x16704,x16705,x16702))
% 21.40/21.39 [1671]~E(x16711,x16712)+E(f438(x16711,x16713,x16714,x16715,x16716,x16717,x16718),f438(x16712,x16713,x16714,x16715,x16716,x16717,x16718))
% 21.40/21.39 [1672]~E(x16721,x16722)+E(f438(x16723,x16721,x16724,x16725,x16726,x16727,x16728),f438(x16723,x16722,x16724,x16725,x16726,x16727,x16728))
% 21.40/21.39 [1673]~E(x16731,x16732)+E(f438(x16733,x16734,x16731,x16735,x16736,x16737,x16738),f438(x16733,x16734,x16732,x16735,x16736,x16737,x16738))
% 21.40/21.39 [1674]~E(x16741,x16742)+E(f438(x16743,x16744,x16745,x16741,x16746,x16747,x16748),f438(x16743,x16744,x16745,x16742,x16746,x16747,x16748))
% 21.40/21.39 [1675]~E(x16751,x16752)+E(f438(x16753,x16754,x16755,x16756,x16751,x16757,x16758),f438(x16753,x16754,x16755,x16756,x16752,x16757,x16758))
% 21.40/21.39 [1676]~E(x16761,x16762)+E(f438(x16763,x16764,x16765,x16766,x16767,x16761,x16768),f438(x16763,x16764,x16765,x16766,x16767,x16762,x16768))
% 21.40/21.39 [1677]~E(x16771,x16772)+E(f438(x16773,x16774,x16775,x16776,x16777,x16778,x16771),f438(x16773,x16774,x16775,x16776,x16777,x16778,x16772))
% 21.40/21.39 [1678]~E(x16781,x16782)+E(f197(x16781,x16783,x16784,x16785),f197(x16782,x16783,x16784,x16785))
% 21.40/21.39 [1679]~E(x16791,x16792)+E(f197(x16793,x16791,x16794,x16795),f197(x16793,x16792,x16794,x16795))
% 21.40/21.39 [1680]~E(x16801,x16802)+E(f197(x16803,x16804,x16801,x16805),f197(x16803,x16804,x16802,x16805))
% 21.40/21.39 [1681]~E(x16811,x16812)+E(f197(x16813,x16814,x16815,x16811),f197(x16813,x16814,x16815,x16812))
% 21.40/21.39 [1682]~E(x16821,x16822)+E(f650(x16821,x16823,x16824,x16825),f650(x16822,x16823,x16824,x16825))
% 21.40/21.39 [1683]~E(x16831,x16832)+E(f650(x16833,x16831,x16834,x16835),f650(x16833,x16832,x16834,x16835))
% 21.40/21.39 [1684]~E(x16841,x16842)+E(f650(x16843,x16844,x16841,x16845),f650(x16843,x16844,x16842,x16845))
% 21.40/21.39 [1685]~E(x16851,x16852)+E(f650(x16853,x16854,x16855,x16851),f650(x16853,x16854,x16855,x16852))
% 21.40/21.39 [1686]~E(x16861,x16862)+E(f733(x16861,x16863,x16864,x16865,x16866),f733(x16862,x16863,x16864,x16865,x16866))
% 21.40/21.39 [1687]~E(x16871,x16872)+E(f733(x16873,x16871,x16874,x16875,x16876),f733(x16873,x16872,x16874,x16875,x16876))
% 21.40/21.39 [1688]~E(x16881,x16882)+E(f733(x16883,x16884,x16881,x16885,x16886),f733(x16883,x16884,x16882,x16885,x16886))
% 21.40/21.39 [1689]~E(x16891,x16892)+E(f733(x16893,x16894,x16895,x16891,x16896),f733(x16893,x16894,x16895,x16892,x16896))
% 21.40/21.39 [1690]~E(x16901,x16902)+E(f733(x16903,x16904,x16905,x16906,x16901),f733(x16903,x16904,x16905,x16906,x16902))
% 21.40/21.39 [1691]~E(x16911,x16912)+E(f778(x16911,x16913,x16914),f778(x16912,x16913,x16914))
% 21.40/21.39 [1692]~E(x16921,x16922)+E(f778(x16923,x16921,x16924),f778(x16923,x16922,x16924))
% 21.40/21.39 [1693]~E(x16931,x16932)+E(f778(x16933,x16934,x16931),f778(x16933,x16934,x16932))
% 21.40/21.39 [1694]~E(x16941,x16942)+E(f576(x16941,x16943),f576(x16942,x16943))
% 21.40/21.39 [1695]~E(x16951,x16952)+E(f576(x16953,x16951),f576(x16953,x16952))
% 21.40/21.39 [1696]~E(x16961,x16962)+E(f753(x16961,x16963,x16964,x16965,x16966),f753(x16962,x16963,x16964,x16965,x16966))
% 21.40/21.39 [1697]~E(x16971,x16972)+E(f753(x16973,x16971,x16974,x16975,x16976),f753(x16973,x16972,x16974,x16975,x16976))
% 21.40/21.39 [1698]~E(x16981,x16982)+E(f753(x16983,x16984,x16981,x16985,x16986),f753(x16983,x16984,x16982,x16985,x16986))
% 21.40/21.39 [1699]~E(x16991,x16992)+E(f753(x16993,x16994,x16995,x16991,x16996),f753(x16993,x16994,x16995,x16992,x16996))
% 21.40/21.39 [1700]~E(x17001,x17002)+E(f753(x17003,x17004,x17005,x17006,x17001),f753(x17003,x17004,x17005,x17006,x17002))
% 21.40/21.39 [1701]~E(x17011,x17012)+E(f639(x17011,x17013,x17014,x17015,x17016,x17017),f639(x17012,x17013,x17014,x17015,x17016,x17017))
% 21.40/21.39 [1702]~E(x17021,x17022)+E(f639(x17023,x17021,x17024,x17025,x17026,x17027),f639(x17023,x17022,x17024,x17025,x17026,x17027))
% 21.40/21.39 [1703]~E(x17031,x17032)+E(f639(x17033,x17034,x17031,x17035,x17036,x17037),f639(x17033,x17034,x17032,x17035,x17036,x17037))
% 21.40/21.39 [1704]~E(x17041,x17042)+E(f639(x17043,x17044,x17045,x17041,x17046,x17047),f639(x17043,x17044,x17045,x17042,x17046,x17047))
% 21.40/21.39 [1705]~E(x17051,x17052)+E(f639(x17053,x17054,x17055,x17056,x17051,x17057),f639(x17053,x17054,x17055,x17056,x17052,x17057))
% 21.40/21.39 [1706]~E(x17061,x17062)+E(f639(x17063,x17064,x17065,x17066,x17067,x17061),f639(x17063,x17064,x17065,x17066,x17067,x17062))
% 21.40/21.39 [1707]~E(x17071,x17072)+E(f725(x17071,x17073,x17074,x17075,x17076,x17077),f725(x17072,x17073,x17074,x17075,x17076,x17077))
% 21.40/21.39 [1708]~E(x17081,x17082)+E(f725(x17083,x17081,x17084,x17085,x17086,x17087),f725(x17083,x17082,x17084,x17085,x17086,x17087))
% 21.40/21.39 [1709]~E(x17091,x17092)+E(f725(x17093,x17094,x17091,x17095,x17096,x17097),f725(x17093,x17094,x17092,x17095,x17096,x17097))
% 21.40/21.39 [1710]~E(x17101,x17102)+E(f725(x17103,x17104,x17105,x17101,x17106,x17107),f725(x17103,x17104,x17105,x17102,x17106,x17107))
% 21.40/21.39 [1711]~E(x17111,x17112)+E(f725(x17113,x17114,x17115,x17116,x17111,x17117),f725(x17113,x17114,x17115,x17116,x17112,x17117))
% 21.40/21.39 [1712]~E(x17121,x17122)+E(f725(x17123,x17124,x17125,x17126,x17127,x17121),f725(x17123,x17124,x17125,x17126,x17127,x17122))
% 21.40/21.39 [1713]~E(x17131,x17132)+E(f210(x17131,x17133,x17134,x17135,x17136,x17137,x17138),f210(x17132,x17133,x17134,x17135,x17136,x17137,x17138))
% 21.40/21.39 [1714]~E(x17141,x17142)+E(f210(x17143,x17141,x17144,x17145,x17146,x17147,x17148),f210(x17143,x17142,x17144,x17145,x17146,x17147,x17148))
% 21.40/21.39 [1715]~E(x17151,x17152)+E(f210(x17153,x17154,x17151,x17155,x17156,x17157,x17158),f210(x17153,x17154,x17152,x17155,x17156,x17157,x17158))
% 21.40/21.39 [1716]~E(x17161,x17162)+E(f210(x17163,x17164,x17165,x17161,x17166,x17167,x17168),f210(x17163,x17164,x17165,x17162,x17166,x17167,x17168))
% 21.40/21.39 [1717]~E(x17171,x17172)+E(f210(x17173,x17174,x17175,x17176,x17171,x17177,x17178),f210(x17173,x17174,x17175,x17176,x17172,x17177,x17178))
% 21.40/21.39 [1718]~E(x17181,x17182)+E(f210(x17183,x17184,x17185,x17186,x17187,x17181,x17188),f210(x17183,x17184,x17185,x17186,x17187,x17182,x17188))
% 21.40/21.39 [1719]~E(x17191,x17192)+E(f210(x17193,x17194,x17195,x17196,x17197,x17198,x17191),f210(x17193,x17194,x17195,x17196,x17197,x17198,x17192))
% 21.40/21.39 [1720]~E(x17201,x17202)+E(f198(x17201,x17203,x17204,x17205),f198(x17202,x17203,x17204,x17205))
% 21.40/21.39 [1721]~E(x17211,x17212)+E(f198(x17213,x17211,x17214,x17215),f198(x17213,x17212,x17214,x17215))
% 21.40/21.39 [1722]~E(x17221,x17222)+E(f198(x17223,x17224,x17221,x17225),f198(x17223,x17224,x17222,x17225))
% 21.40/21.39 [1723]~E(x17231,x17232)+E(f198(x17233,x17234,x17235,x17231),f198(x17233,x17234,x17235,x17232))
% 21.40/21.39 [1724]~E(x17241,x17242)+E(f758(x17241,x17243,x17244,x17245),f758(x17242,x17243,x17244,x17245))
% 21.40/21.39 [1725]~E(x17251,x17252)+E(f758(x17253,x17251,x17254,x17255),f758(x17253,x17252,x17254,x17255))
% 21.40/21.39 [1726]~E(x17261,x17262)+E(f758(x17263,x17264,x17261,x17265),f758(x17263,x17264,x17262,x17265))
% 21.40/21.39 [1727]~E(x17271,x17272)+E(f758(x17273,x17274,x17275,x17271),f758(x17273,x17274,x17275,x17272))
% 21.40/21.39 [1728]~E(x17281,x17282)+E(f676(x17281,x17283,x17284,x17285),f676(x17282,x17283,x17284,x17285))
% 21.40/21.39 [1729]~E(x17291,x17292)+E(f676(x17293,x17291,x17294,x17295),f676(x17293,x17292,x17294,x17295))
% 21.40/21.39 [1730]~E(x17301,x17302)+E(f676(x17303,x17304,x17301,x17305),f676(x17303,x17304,x17302,x17305))
% 21.40/21.39 [1731]~E(x17311,x17312)+E(f676(x17313,x17314,x17315,x17311),f676(x17313,x17314,x17315,x17312))
% 21.40/21.39 [1732]~E(x17321,x17322)+E(f534(x17321,x17323,x17324,x17325),f534(x17322,x17323,x17324,x17325))
% 21.40/21.39 [1733]~E(x17331,x17332)+E(f534(x17333,x17331,x17334,x17335),f534(x17333,x17332,x17334,x17335))
% 21.40/21.39 [1734]~E(x17341,x17342)+E(f534(x17343,x17344,x17341,x17345),f534(x17343,x17344,x17342,x17345))
% 21.40/21.39 [1735]~E(x17351,x17352)+E(f534(x17353,x17354,x17355,x17351),f534(x17353,x17354,x17355,x17352))
% 21.40/21.39 [1736]~E(x17361,x17362)+E(f681(x17361,x17363,x17364),f681(x17362,x17363,x17364))
% 21.40/21.39 [1737]~E(x17371,x17372)+E(f681(x17373,x17371,x17374),f681(x17373,x17372,x17374))
% 21.40/21.39 [1738]~E(x17381,x17382)+E(f681(x17383,x17384,x17381),f681(x17383,x17384,x17382))
% 21.40/21.39 [1739]~E(x17391,x17392)+E(f735(x17391,x17393),f735(x17392,x17393))
% 21.40/21.39 [1740]~E(x17401,x17402)+E(f735(x17403,x17401),f735(x17403,x17402))
% 21.40/21.39 [1741]~E(x17411,x17412)+E(f759(x17411,x17413,x17414,x17415),f759(x17412,x17413,x17414,x17415))
% 21.40/21.39 [1742]~E(x17421,x17422)+E(f759(x17423,x17421,x17424,x17425),f759(x17423,x17422,x17424,x17425))
% 21.40/21.39 [1743]~E(x17431,x17432)+E(f759(x17433,x17434,x17431,x17435),f759(x17433,x17434,x17432,x17435))
% 21.40/21.39 [1744]~E(x17441,x17442)+E(f759(x17443,x17444,x17445,x17441),f759(x17443,x17444,x17445,x17442))
% 21.40/21.39 [1745]~E(x17451,x17452)+E(f211(x17451,x17453,x17454,x17455),f211(x17452,x17453,x17454,x17455))
% 21.40/21.39 [1746]~E(x17461,x17462)+E(f211(x17463,x17461,x17464,x17465),f211(x17463,x17462,x17464,x17465))
% 21.40/21.39 [1747]~E(x17471,x17472)+E(f211(x17473,x17474,x17471,x17475),f211(x17473,x17474,x17472,x17475))
% 21.40/21.39 [1748]~E(x17481,x17482)+E(f211(x17483,x17484,x17485,x17481),f211(x17483,x17484,x17485,x17482))
% 21.40/21.39 [1749]~E(x17491,x17492)+E(f363(x17491,x17493),f363(x17492,x17493))
% 21.40/21.39 [1750]~E(x17501,x17502)+E(f363(x17503,x17501),f363(x17503,x17502))
% 21.40/21.39 [1751]~E(x17511,x17512)+E(f651(x17511,x17513,x17514,x17515,x17516),f651(x17512,x17513,x17514,x17515,x17516))
% 21.40/21.39 [1752]~E(x17521,x17522)+E(f651(x17523,x17521,x17524,x17525,x17526),f651(x17523,x17522,x17524,x17525,x17526))
% 21.40/21.39 [1753]~E(x17531,x17532)+E(f651(x17533,x17534,x17531,x17535,x17536),f651(x17533,x17534,x17532,x17535,x17536))
% 21.40/21.39 [1754]~E(x17541,x17542)+E(f651(x17543,x17544,x17545,x17541,x17546),f651(x17543,x17544,x17545,x17542,x17546))
% 21.40/21.39 [1755]~E(x17551,x17552)+E(f651(x17553,x17554,x17555,x17556,x17551),f651(x17553,x17554,x17555,x17556,x17552))
% 21.40/21.39 [1756]~E(x17561,x17562)+E(f252(x17561,x17563,x17564),f252(x17562,x17563,x17564))
% 21.40/21.39 [1757]~E(x17571,x17572)+E(f252(x17573,x17571,x17574),f252(x17573,x17572,x17574))
% 21.40/21.39 [1758]~E(x17581,x17582)+E(f252(x17583,x17584,x17581),f252(x17583,x17584,x17582))
% 21.40/21.39 [1759]~E(x17591,x17592)+E(f76(x17591,x17593,x17594),f76(x17592,x17593,x17594))
% 21.40/21.39 [1760]~E(x17601,x17602)+E(f76(x17603,x17601,x17604),f76(x17603,x17602,x17604))
% 21.40/21.39 [1761]~E(x17611,x17612)+E(f76(x17613,x17614,x17611),f76(x17613,x17614,x17612))
% 21.40/21.39 [1762]~E(x17621,x17622)+E(f752(x17621,x17623,x17624,x17625,x17626),f752(x17622,x17623,x17624,x17625,x17626))
% 21.40/21.39 [1763]~E(x17631,x17632)+E(f752(x17633,x17631,x17634,x17635,x17636),f752(x17633,x17632,x17634,x17635,x17636))
% 21.40/21.39 [1764]~E(x17641,x17642)+E(f752(x17643,x17644,x17641,x17645,x17646),f752(x17643,x17644,x17642,x17645,x17646))
% 21.40/21.39 [1765]~E(x17651,x17652)+E(f752(x17653,x17654,x17655,x17651,x17656),f752(x17653,x17654,x17655,x17652,x17656))
% 21.40/21.39 [1766]~E(x17661,x17662)+E(f752(x17663,x17664,x17665,x17666,x17661),f752(x17663,x17664,x17665,x17666,x17662))
% 21.40/21.39 [1767]~E(x17671,x17672)+E(f727(x17671,x17673,x17674),f727(x17672,x17673,x17674))
% 21.40/21.39 [1768]~E(x17681,x17682)+E(f727(x17683,x17681,x17684),f727(x17683,x17682,x17684))
% 21.40/21.39 [1769]~E(x17691,x17692)+E(f727(x17693,x17694,x17691),f727(x17693,x17694,x17692))
% 21.40/21.39 [1770]~E(x17701,x17702)+E(f511(x17701,x17703,x17704,x17705,x17706),f511(x17702,x17703,x17704,x17705,x17706))
% 21.40/21.39 [1771]~E(x17711,x17712)+E(f511(x17713,x17711,x17714,x17715,x17716),f511(x17713,x17712,x17714,x17715,x17716))
% 21.40/21.39 [1772]~E(x17721,x17722)+E(f511(x17723,x17724,x17721,x17725,x17726),f511(x17723,x17724,x17722,x17725,x17726))
% 21.40/21.39 [1773]~E(x17731,x17732)+E(f511(x17733,x17734,x17735,x17731,x17736),f511(x17733,x17734,x17735,x17732,x17736))
% 21.40/21.39 [1774]~E(x17741,x17742)+E(f511(x17743,x17744,x17745,x17746,x17741),f511(x17743,x17744,x17745,x17746,x17742))
% 21.40/21.39 [1775]~E(x17751,x17752)+E(f652(x17751,x17753,x17754,x17755,x17756),f652(x17752,x17753,x17754,x17755,x17756))
% 21.40/21.39 [1776]~E(x17761,x17762)+E(f652(x17763,x17761,x17764,x17765,x17766),f652(x17763,x17762,x17764,x17765,x17766))
% 21.40/21.39 [1777]~E(x17771,x17772)+E(f652(x17773,x17774,x17771,x17775,x17776),f652(x17773,x17774,x17772,x17775,x17776))
% 21.40/21.39 [1778]~E(x17781,x17782)+E(f652(x17783,x17784,x17785,x17781,x17786),f652(x17783,x17784,x17785,x17782,x17786))
% 21.40/21.39 [1779]~E(x17791,x17792)+E(f652(x17793,x17794,x17795,x17796,x17791),f652(x17793,x17794,x17795,x17796,x17792))
% 21.40/21.39 [1780]~E(x17801,x17802)+E(f853(x17801,x17803,x17804,x17805,x17806),f853(x17802,x17803,x17804,x17805,x17806))
% 21.40/21.39 [1781]~E(x17811,x17812)+E(f853(x17813,x17811,x17814,x17815,x17816),f853(x17813,x17812,x17814,x17815,x17816))
% 21.40/21.39 [1782]~E(x17821,x17822)+E(f853(x17823,x17824,x17821,x17825,x17826),f853(x17823,x17824,x17822,x17825,x17826))
% 21.40/21.39 [1783]~E(x17831,x17832)+E(f853(x17833,x17834,x17835,x17831,x17836),f853(x17833,x17834,x17835,x17832,x17836))
% 21.40/21.39 [1784]~E(x17841,x17842)+E(f853(x17843,x17844,x17845,x17846,x17841),f853(x17843,x17844,x17845,x17846,x17842))
% 21.40/21.39 [1785]~E(x17851,x17852)+E(f408(x17851,x17853,x17854),f408(x17852,x17853,x17854))
% 21.40/21.39 [1786]~E(x17861,x17862)+E(f408(x17863,x17861,x17864),f408(x17863,x17862,x17864))
% 21.40/21.39 [1787]~E(x17871,x17872)+E(f408(x17873,x17874,x17871),f408(x17873,x17874,x17872))
% 21.40/21.39 [1788]~E(x17881,x17882)+E(f622(x17881,x17883),f622(x17882,x17883))
% 21.40/21.39 [1789]~E(x17891,x17892)+E(f622(x17893,x17891),f622(x17893,x17892))
% 21.40/21.39 [1790]~E(x17901,x17902)+E(f317(x17901,x17903,x17904),f317(x17902,x17903,x17904))
% 21.40/21.39 [1791]~E(x17911,x17912)+E(f317(x17913,x17911,x17914),f317(x17913,x17912,x17914))
% 21.40/21.39 [1792]~E(x17921,x17922)+E(f317(x17923,x17924,x17921),f317(x17923,x17924,x17922))
% 21.40/21.39 [1793]~E(x17931,x17932)+E(f674(x17931,x17933,x17934),f674(x17932,x17933,x17934))
% 21.40/21.39 [1794]~E(x17941,x17942)+E(f674(x17943,x17941,x17944),f674(x17943,x17942,x17944))
% 21.40/21.39 [1795]~E(x17951,x17952)+E(f674(x17953,x17954,x17951),f674(x17953,x17954,x17952))
% 21.40/21.39 [1796]~E(x17961,x17962)+E(f351(x17961,x17963,x17964),f351(x17962,x17963,x17964))
% 21.40/21.39 [1797]~E(x17971,x17972)+E(f351(x17973,x17971,x17974),f351(x17973,x17972,x17974))
% 21.40/21.39 [1798]~E(x17981,x17982)+E(f351(x17983,x17984,x17981),f351(x17983,x17984,x17982))
% 21.40/21.39 [1799]~E(x17991,x17992)+E(f404(x17991,x17993),f404(x17992,x17993))
% 21.40/21.39 [1800]~E(x18001,x18002)+E(f404(x18003,x18001),f404(x18003,x18002))
% 21.40/21.39 [1801]~E(x18011,x18012)+E(f463(x18011,x18013,x18014,x18015),f463(x18012,x18013,x18014,x18015))
% 21.40/21.39 [1802]~E(x18021,x18022)+E(f463(x18023,x18021,x18024,x18025),f463(x18023,x18022,x18024,x18025))
% 21.40/21.39 [1803]~E(x18031,x18032)+E(f463(x18033,x18034,x18031,x18035),f463(x18033,x18034,x18032,x18035))
% 21.40/21.39 [1804]~E(x18041,x18042)+E(f463(x18043,x18044,x18045,x18041),f463(x18043,x18044,x18045,x18042))
% 21.40/21.39 [1805]~E(x18051,x18052)+E(f422(x18051,x18053,x18054,x18055,x18056),f422(x18052,x18053,x18054,x18055,x18056))
% 21.40/21.39 [1806]~E(x18061,x18062)+E(f422(x18063,x18061,x18064,x18065,x18066),f422(x18063,x18062,x18064,x18065,x18066))
% 21.40/21.39 [1807]~E(x18071,x18072)+E(f422(x18073,x18074,x18071,x18075,x18076),f422(x18073,x18074,x18072,x18075,x18076))
% 21.40/21.39 [1808]~E(x18081,x18082)+E(f422(x18083,x18084,x18085,x18081,x18086),f422(x18083,x18084,x18085,x18082,x18086))
% 21.40/21.39 [1809]~E(x18091,x18092)+E(f422(x18093,x18094,x18095,x18096,x18091),f422(x18093,x18094,x18095,x18096,x18092))
% 21.40/21.39 [1810]~E(x18101,x18102)+E(f719(x18101,x18103,x18104,x18105),f719(x18102,x18103,x18104,x18105))
% 21.40/21.39 [1811]~E(x18111,x18112)+E(f719(x18113,x18111,x18114,x18115),f719(x18113,x18112,x18114,x18115))
% 21.40/21.39 [1812]~E(x18121,x18122)+E(f719(x18123,x18124,x18121,x18125),f719(x18123,x18124,x18122,x18125))
% 21.40/21.39 [1813]~E(x18131,x18132)+E(f719(x18133,x18134,x18135,x18131),f719(x18133,x18134,x18135,x18132))
% 21.40/21.39 [1814]~E(x18141,x18142)+E(f399(x18141,x18143),f399(x18142,x18143))
% 21.40/21.39 [1815]~E(x18151,x18152)+E(f399(x18153,x18151),f399(x18153,x18152))
% 21.40/21.39 [1816]~E(x18161,x18162)+E(f567(x18161,x18163,x18164,x18165),f567(x18162,x18163,x18164,x18165))
% 21.40/21.39 [1817]~E(x18171,x18172)+E(f567(x18173,x18171,x18174,x18175),f567(x18173,x18172,x18174,x18175))
% 21.40/21.39 [1818]~E(x18181,x18182)+E(f567(x18183,x18184,x18181,x18185),f567(x18183,x18184,x18182,x18185))
% 21.40/21.39 [1819]~E(x18191,x18192)+E(f567(x18193,x18194,x18195,x18191),f567(x18193,x18194,x18195,x18192))
% 21.40/21.39 [1820]~E(x18201,x18202)+E(f387(x18201,x18203,x18204),f387(x18202,x18203,x18204))
% 21.40/21.39 [1821]~E(x18211,x18212)+E(f387(x18213,x18211,x18214),f387(x18213,x18212,x18214))
% 21.40/21.39 [1822]~E(x18221,x18222)+E(f387(x18223,x18224,x18221),f387(x18223,x18224,x18222))
% 21.40/21.39 [1823]~E(x18231,x18232)+E(f509(x18231,x18233,x18234,x18235),f509(x18232,x18233,x18234,x18235))
% 21.40/21.39 [1824]~E(x18241,x18242)+E(f509(x18243,x18241,x18244,x18245),f509(x18243,x18242,x18244,x18245))
% 21.40/21.39 [1825]~E(x18251,x18252)+E(f509(x18253,x18254,x18251,x18255),f509(x18253,x18254,x18252,x18255))
% 21.40/21.39 [1826]~E(x18261,x18262)+E(f509(x18263,x18264,x18265,x18261),f509(x18263,x18264,x18265,x18262))
% 21.40/21.39 [1827]~E(x18271,x18272)+E(f494(x18271,x18273,x18274,x18275),f494(x18272,x18273,x18274,x18275))
% 21.40/21.39 [1828]~E(x18281,x18282)+E(f494(x18283,x18281,x18284,x18285),f494(x18283,x18282,x18284,x18285))
% 21.40/21.39 [1829]~E(x18291,x18292)+E(f494(x18293,x18294,x18291,x18295),f494(x18293,x18294,x18292,x18295))
% 21.40/21.39 [1830]~E(x18301,x18302)+E(f494(x18303,x18304,x18305,x18301),f494(x18303,x18304,x18305,x18302))
% 21.40/21.39 [1831]~E(x18311,x18312)+E(f539(x18311,x18313,x18314,x18315,x18316),f539(x18312,x18313,x18314,x18315,x18316))
% 21.40/21.39 [1832]~E(x18321,x18322)+E(f539(x18323,x18321,x18324,x18325,x18326),f539(x18323,x18322,x18324,x18325,x18326))
% 21.40/21.39 [1833]~E(x18331,x18332)+E(f539(x18333,x18334,x18331,x18335,x18336),f539(x18333,x18334,x18332,x18335,x18336))
% 21.40/21.39 [1834]~E(x18341,x18342)+E(f539(x18343,x18344,x18345,x18341,x18346),f539(x18343,x18344,x18345,x18342,x18346))
% 21.40/21.39 [1835]~E(x18351,x18352)+E(f539(x18353,x18354,x18355,x18356,x18351),f539(x18353,x18354,x18355,x18356,x18352))
% 21.40/21.39 [1836]~E(x18361,x18362)+E(f478(x18361,x18363,x18364,x18365),f478(x18362,x18363,x18364,x18365))
% 21.40/21.39 [1837]~E(x18371,x18372)+E(f478(x18373,x18371,x18374,x18375),f478(x18373,x18372,x18374,x18375))
% 21.40/21.39 [1838]~E(x18381,x18382)+E(f478(x18383,x18384,x18381,x18385),f478(x18383,x18384,x18382,x18385))
% 21.40/21.39 [1839]~E(x18391,x18392)+E(f478(x18393,x18394,x18395,x18391),f478(x18393,x18394,x18395,x18392))
% 21.40/21.39 [1840]~E(x18401,x18402)+E(f714(x18401,x18403,x18404,x18405),f714(x18402,x18403,x18404,x18405))
% 21.40/21.39 [1841]~E(x18411,x18412)+E(f714(x18413,x18411,x18414,x18415),f714(x18413,x18412,x18414,x18415))
% 21.40/21.39 [1842]~E(x18421,x18422)+E(f714(x18423,x18424,x18421,x18425),f714(x18423,x18424,x18422,x18425))
% 21.40/21.39 [1843]~E(x18431,x18432)+E(f714(x18433,x18434,x18435,x18431),f714(x18433,x18434,x18435,x18432))
% 21.40/21.39 [1844]~E(x18441,x18442)+E(f352(x18441,x18443,x18444),f352(x18442,x18443,x18444))
% 21.40/21.39 [1845]~E(x18451,x18452)+E(f352(x18453,x18451,x18454),f352(x18453,x18452,x18454))
% 21.40/21.39 [1846]~E(x18461,x18462)+E(f352(x18463,x18464,x18461),f352(x18463,x18464,x18462))
% 21.40/21.39 [1847]~E(x18471,x18472)+E(f471(x18471,x18473),f471(x18472,x18473))
% 21.40/21.39 [1848]~E(x18481,x18482)+E(f471(x18483,x18481),f471(x18483,x18482))
% 21.40/21.39 [1849]~E(x18491,x18492)+E(f427(x18491,x18493,x18494,x18495,x18496),f427(x18492,x18493,x18494,x18495,x18496))
% 21.40/21.39 [1850]~E(x18501,x18502)+E(f427(x18503,x18501,x18504,x18505,x18506),f427(x18503,x18502,x18504,x18505,x18506))
% 21.40/21.39 [1851]~E(x18511,x18512)+E(f427(x18513,x18514,x18511,x18515,x18516),f427(x18513,x18514,x18512,x18515,x18516))
% 21.40/21.39 [1852]~E(x18521,x18522)+E(f427(x18523,x18524,x18525,x18521,x18526),f427(x18523,x18524,x18525,x18522,x18526))
% 21.40/21.39 [1853]~E(x18531,x18532)+E(f427(x18533,x18534,x18535,x18536,x18531),f427(x18533,x18534,x18535,x18536,x18532))
% 21.40/21.39 [1854]~E(x18541,x18542)+E(f405(x18541,x18543),f405(x18542,x18543))
% 21.40/21.39 [1855]~E(x18551,x18552)+E(f405(x18553,x18551),f405(x18553,x18552))
% 21.40/21.39 [1856]~E(x18561,x18562)+E(f784(x18561,x18563),f784(x18562,x18563))
% 21.40/21.39 [1857]~E(x18571,x18572)+E(f784(x18573,x18571),f784(x18573,x18572))
% 21.40/21.39 [1858]~E(x18581,x18582)+E(f573(x18581,x18583,x18584,x18585,x18586,x18587),f573(x18582,x18583,x18584,x18585,x18586,x18587))
% 21.40/21.39 [1859]~E(x18591,x18592)+E(f573(x18593,x18591,x18594,x18595,x18596,x18597),f573(x18593,x18592,x18594,x18595,x18596,x18597))
% 21.40/21.39 [1860]~E(x18601,x18602)+E(f573(x18603,x18604,x18601,x18605,x18606,x18607),f573(x18603,x18604,x18602,x18605,x18606,x18607))
% 21.40/21.39 [1861]~E(x18611,x18612)+E(f573(x18613,x18614,x18615,x18611,x18616,x18617),f573(x18613,x18614,x18615,x18612,x18616,x18617))
% 21.40/21.39 [1862]~E(x18621,x18622)+E(f573(x18623,x18624,x18625,x18626,x18621,x18627),f573(x18623,x18624,x18625,x18626,x18622,x18627))
% 21.40/21.39 [1863]~E(x18631,x18632)+E(f573(x18633,x18634,x18635,x18636,x18637,x18631),f573(x18633,x18634,x18635,x18636,x18637,x18632))
% 21.40/21.39 [1864]~E(x18641,x18642)+E(f220(x18641,x18643),f220(x18642,x18643))
% 21.40/21.39 [1865]~E(x18651,x18652)+E(f220(x18653,x18651),f220(x18653,x18652))
% 21.40/21.39 [1866]~E(x18661,x18662)+E(f373(x18661,x18663,x18664,x18665),f373(x18662,x18663,x18664,x18665))
% 21.40/21.39 [1867]~E(x18671,x18672)+E(f373(x18673,x18671,x18674,x18675),f373(x18673,x18672,x18674,x18675))
% 21.40/21.39 [1868]~E(x18681,x18682)+E(f373(x18683,x18684,x18681,x18685),f373(x18683,x18684,x18682,x18685))
% 21.40/21.39 [1869]~E(x18691,x18692)+E(f373(x18693,x18694,x18695,x18691),f373(x18693,x18694,x18695,x18692))
% 21.40/21.39 [1870]~E(x18701,x18702)+E(f546(x18701,x18703,x18704,x18705),f546(x18702,x18703,x18704,x18705))
% 21.40/21.39 [1871]~E(x18711,x18712)+E(f546(x18713,x18711,x18714,x18715),f546(x18713,x18712,x18714,x18715))
% 21.40/21.39 [1872]~E(x18721,x18722)+E(f546(x18723,x18724,x18721,x18725),f546(x18723,x18724,x18722,x18725))
% 21.40/21.39 [1873]~E(x18731,x18732)+E(f546(x18733,x18734,x18735,x18731),f546(x18733,x18734,x18735,x18732))
% 21.40/21.39 [1874]~E(x18741,x18742)+E(f274(x18741,x18743),f274(x18742,x18743))
% 21.40/21.39 [1875]~E(x18751,x18752)+E(f274(x18753,x18751),f274(x18753,x18752))
% 21.40/21.39 [1876]~E(x18761,x18762)+E(f277(x18761,x18763,x18764),f277(x18762,x18763,x18764))
% 21.40/21.39 [1877]~E(x18771,x18772)+E(f277(x18773,x18771,x18774),f277(x18773,x18772,x18774))
% 21.40/21.39 [1878]~E(x18781,x18782)+E(f277(x18783,x18784,x18781),f277(x18783,x18784,x18782))
% 21.40/21.39 [1879]~E(x18791,x18792)+E(f718(x18791,x18793,x18794,x18795,x18796,x18797),f718(x18792,x18793,x18794,x18795,x18796,x18797))
% 21.40/21.39 [1880]~E(x18801,x18802)+E(f718(x18803,x18801,x18804,x18805,x18806,x18807),f718(x18803,x18802,x18804,x18805,x18806,x18807))
% 21.40/21.39 [1881]~E(x18811,x18812)+E(f718(x18813,x18814,x18811,x18815,x18816,x18817),f718(x18813,x18814,x18812,x18815,x18816,x18817))
% 21.40/21.39 [1882]~E(x18821,x18822)+E(f718(x18823,x18824,x18825,x18821,x18826,x18827),f718(x18823,x18824,x18825,x18822,x18826,x18827))
% 21.40/21.39 [1883]~E(x18831,x18832)+E(f718(x18833,x18834,x18835,x18836,x18831,x18837),f718(x18833,x18834,x18835,x18836,x18832,x18837))
% 21.40/21.39 [1884]~E(x18841,x18842)+E(f718(x18843,x18844,x18845,x18846,x18847,x18841),f718(x18843,x18844,x18845,x18846,x18847,x18842))
% 21.40/21.39 [1885]~E(x18851,x18852)+E(f536(x18851,x18853,x18854,x18855,x18856),f536(x18852,x18853,x18854,x18855,x18856))
% 21.40/21.39 [1886]~E(x18861,x18862)+E(f536(x18863,x18861,x18864,x18865,x18866),f536(x18863,x18862,x18864,x18865,x18866))
% 21.40/21.39 [1887]~E(x18871,x18872)+E(f536(x18873,x18874,x18871,x18875,x18876),f536(x18873,x18874,x18872,x18875,x18876))
% 21.40/21.39 [1888]~E(x18881,x18882)+E(f536(x18883,x18884,x18885,x18881,x18886),f536(x18883,x18884,x18885,x18882,x18886))
% 21.40/21.39 [1889]~E(x18891,x18892)+E(f536(x18893,x18894,x18895,x18896,x18891),f536(x18893,x18894,x18895,x18896,x18892))
% 21.40/21.39 [1890]~E(x18901,x18902)+E(f335(x18901,x18903,x18904),f335(x18902,x18903,x18904))
% 21.40/21.39 [1891]~E(x18911,x18912)+E(f335(x18913,x18911,x18914),f335(x18913,x18912,x18914))
% 21.40/21.39 [1892]~E(x18921,x18922)+E(f335(x18923,x18924,x18921),f335(x18923,x18924,x18922))
% 21.40/21.39 [1893]~E(x18931,x18932)+E(f783(x18931,x18933,x18934),f783(x18932,x18933,x18934))
% 21.40/21.39 [1894]~E(x18941,x18942)+E(f783(x18943,x18941,x18944),f783(x18943,x18942,x18944))
% 21.40/21.39 [1895]~E(x18951,x18952)+E(f783(x18953,x18954,x18951),f783(x18953,x18954,x18952))
% 21.40/21.39 [1896]~E(x18961,x18962)+E(f403(x18961,x18963),f403(x18962,x18963))
% 21.40/21.39 [1897]~E(x18971,x18972)+E(f403(x18973,x18971),f403(x18973,x18972))
% 21.40/21.39 [1898]~E(x18981,x18982)+E(f278(x18981,x18983),f278(x18982,x18983))
% 21.40/21.39 [1899]~E(x18991,x18992)+E(f278(x18993,x18991),f278(x18993,x18992))
% 21.40/21.39 [1900]~E(x19001,x19002)+E(f830(x19001,x19003,x19004),f830(x19002,x19003,x19004))
% 21.40/21.39 [1901]~E(x19011,x19012)+E(f830(x19013,x19011,x19014),f830(x19013,x19012,x19014))
% 21.40/21.39 [1902]~E(x19021,x19022)+E(f830(x19023,x19024,x19021),f830(x19023,x19024,x19022))
% 21.40/21.39 [1903]~E(x19031,x19032)+E(f500(x19031,x19033,x19034,x19035),f500(x19032,x19033,x19034,x19035))
% 21.40/21.39 [1904]~E(x19041,x19042)+E(f500(x19043,x19041,x19044,x19045),f500(x19043,x19042,x19044,x19045))
% 21.40/21.39 [1905]~E(x19051,x19052)+E(f500(x19053,x19054,x19051,x19055),f500(x19053,x19054,x19052,x19055))
% 21.40/21.39 [1906]~E(x19061,x19062)+E(f500(x19063,x19064,x19065,x19061),f500(x19063,x19064,x19065,x19062))
% 21.40/21.39 [1907]~E(x19071,x19072)+E(f272(x19071),f272(x19072))
% 21.40/21.39 [1908]~E(x19081,x19082)+E(f600(x19081,x19083),f600(x19082,x19083))
% 21.40/21.39 [1909]~E(x19091,x19092)+E(f600(x19093,x19091),f600(x19093,x19092))
% 21.40/21.39 [1910]~E(x19101,x19102)+E(f844(x19101,x19103,x19104),f844(x19102,x19103,x19104))
% 21.40/21.39 [1911]~E(x19111,x19112)+E(f844(x19113,x19111,x19114),f844(x19113,x19112,x19114))
% 21.40/21.39 [1912]~E(x19121,x19122)+E(f844(x19123,x19124,x19121),f844(x19123,x19124,x19122))
% 21.40/21.39 [1913]~E(x19131,x19132)+E(f826(x19131,x19133,x19134),f826(x19132,x19133,x19134))
% 21.40/21.39 [1914]~E(x19141,x19142)+E(f826(x19143,x19141,x19144),f826(x19143,x19142,x19144))
% 21.40/21.39 [1915]~E(x19151,x19152)+E(f826(x19153,x19154,x19151),f826(x19153,x19154,x19152))
% 21.40/21.39 [1916]~E(x19161,x19162)+E(f489(x19161,x19163,x19164,x19165),f489(x19162,x19163,x19164,x19165))
% 21.40/21.39 [1917]~E(x19171,x19172)+E(f489(x19173,x19171,x19174,x19175),f489(x19173,x19172,x19174,x19175))
% 21.40/21.39 [1918]~E(x19181,x19182)+E(f489(x19183,x19184,x19181,x19185),f489(x19183,x19184,x19182,x19185))
% 21.40/21.39 [1919]~E(x19191,x19192)+E(f489(x19193,x19194,x19195,x19191),f489(x19193,x19194,x19195,x19192))
% 21.40/21.39 [1920]~E(x19201,x19202)+E(f429(x19201,x19203,x19204,x19205,x19206),f429(x19202,x19203,x19204,x19205,x19206))
% 21.40/21.39 [1921]~E(x19211,x19212)+E(f429(x19213,x19211,x19214,x19215,x19216),f429(x19213,x19212,x19214,x19215,x19216))
% 21.40/21.39 [1922]~E(x19221,x19222)+E(f429(x19223,x19224,x19221,x19225,x19226),f429(x19223,x19224,x19222,x19225,x19226))
% 21.40/21.39 [1923]~E(x19231,x19232)+E(f429(x19233,x19234,x19235,x19231,x19236),f429(x19233,x19234,x19235,x19232,x19236))
% 21.40/21.39 [1924]~E(x19241,x19242)+E(f429(x19243,x19244,x19245,x19246,x19241),f429(x19243,x19244,x19245,x19246,x19242))
% 21.40/21.39 [1925]~E(x19251,x19252)+E(f679(x19251,x19253,x19254),f679(x19252,x19253,x19254))
% 21.40/21.39 [1926]~E(x19261,x19262)+E(f679(x19263,x19261,x19264),f679(x19263,x19262,x19264))
% 21.40/21.39 [1927]~E(x19271,x19272)+E(f679(x19273,x19274,x19271),f679(x19273,x19274,x19272))
% 21.40/21.39 [1928]~E(x19281,x19282)+E(f490(x19281,x19283,x19284,x19285),f490(x19282,x19283,x19284,x19285))
% 21.40/21.39 [1929]~E(x19291,x19292)+E(f490(x19293,x19291,x19294,x19295),f490(x19293,x19292,x19294,x19295))
% 21.40/21.39 [1930]~E(x19301,x19302)+E(f490(x19303,x19304,x19301,x19305),f490(x19303,x19304,x19302,x19305))
% 21.40/21.39 [1931]~E(x19311,x19312)+E(f490(x19313,x19314,x19315,x19311),f490(x19313,x19314,x19315,x19312))
% 21.40/21.39 [1932]~E(x19321,x19322)+E(f298(x19321,x19323,x19324),f298(x19322,x19323,x19324))
% 21.40/21.39 [1933]~E(x19331,x19332)+E(f298(x19333,x19331,x19334),f298(x19333,x19332,x19334))
% 21.40/21.39 [1934]~E(x19341,x19342)+E(f298(x19343,x19344,x19341),f298(x19343,x19344,x19342))
% 21.40/21.39 [1935]~E(x19351,x19352)+E(f716(x19351,x19353,x19354,x19355,x19356,x19357),f716(x19352,x19353,x19354,x19355,x19356,x19357))
% 21.40/21.39 [1936]~E(x19361,x19362)+E(f716(x19363,x19361,x19364,x19365,x19366,x19367),f716(x19363,x19362,x19364,x19365,x19366,x19367))
% 21.40/21.39 [1937]~E(x19371,x19372)+E(f716(x19373,x19374,x19371,x19375,x19376,x19377),f716(x19373,x19374,x19372,x19375,x19376,x19377))
% 21.40/21.39 [1938]~E(x19381,x19382)+E(f716(x19383,x19384,x19385,x19381,x19386,x19387),f716(x19383,x19384,x19385,x19382,x19386,x19387))
% 21.40/21.39 [1939]~E(x19391,x19392)+E(f716(x19393,x19394,x19395,x19396,x19391,x19397),f716(x19393,x19394,x19395,x19396,x19392,x19397))
% 21.40/21.39 [1940]~E(x19401,x19402)+E(f716(x19403,x19404,x19405,x19406,x19407,x19401),f716(x19403,x19404,x19405,x19406,x19407,x19402))
% 21.40/21.39 [1941]~E(x19411,x19412)+E(f129(x19411,x19413,x19414,x19415),f129(x19412,x19413,x19414,x19415))
% 21.40/21.39 [1942]~E(x19421,x19422)+E(f129(x19423,x19421,x19424,x19425),f129(x19423,x19422,x19424,x19425))
% 21.40/21.39 [1943]~E(x19431,x19432)+E(f129(x19433,x19434,x19431,x19435),f129(x19433,x19434,x19432,x19435))
% 21.40/21.39 [1944]~E(x19441,x19442)+E(f129(x19443,x19444,x19445,x19441),f129(x19443,x19444,x19445,x19442))
% 21.40/21.39 [1945]~E(x19451,x19452)+E(f169(x19451),f169(x19452))
% 21.40/21.39 [1946]~E(x19461,x19462)+E(f738(x19461,x19463,x19464),f738(x19462,x19463,x19464))
% 21.40/21.39 [1947]~E(x19471,x19472)+E(f738(x19473,x19471,x19474),f738(x19473,x19472,x19474))
% 21.40/21.39 [1948]~E(x19481,x19482)+E(f738(x19483,x19484,x19481),f738(x19483,x19484,x19482))
% 21.40/21.39 [1949]~E(x19491,x19492)+E(f519(x19491,x19493,x19494),f519(x19492,x19493,x19494))
% 21.40/21.39 [1950]~E(x19501,x19502)+E(f519(x19503,x19501,x19504),f519(x19503,x19502,x19504))
% 21.40/21.39 [1951]~E(x19511,x19512)+E(f519(x19513,x19514,x19511),f519(x19513,x19514,x19512))
% 21.40/21.39 [1952]~E(x19521,x19522)+E(f469(x19521,x19523),f469(x19522,x19523))
% 21.40/21.39 [1953]~E(x19531,x19532)+E(f469(x19533,x19531),f469(x19533,x19532))
% 21.40/21.39 [1954]~E(x19541,x19542)+E(f216(x19541,x19543),f216(x19542,x19543))
% 21.40/21.39 [1955]~E(x19551,x19552)+E(f216(x19553,x19551),f216(x19553,x19552))
% 21.40/21.39 [1956]~E(x19561,x19562)+E(f448(x19561,x19563,x19564),f448(x19562,x19563,x19564))
% 21.40/21.39 [1957]~E(x19571,x19572)+E(f448(x19573,x19571,x19574),f448(x19573,x19572,x19574))
% 21.40/21.39 [1958]~E(x19581,x19582)+E(f448(x19583,x19584,x19581),f448(x19583,x19584,x19582))
% 21.40/21.39 [1959]~E(x19591,x19592)+E(f204(x19591),f204(x19592))
% 21.40/21.39 [1960]~E(x19601,x19602)+E(f829(x19601,x19603,x19604),f829(x19602,x19603,x19604))
% 21.40/21.39 [1961]~E(x19611,x19612)+E(f829(x19613,x19611,x19614),f829(x19613,x19612,x19614))
% 21.40/21.39 [1962]~E(x19621,x19622)+E(f829(x19623,x19624,x19621),f829(x19623,x19624,x19622))
% 21.40/21.39 [1963]~E(x19631,x19632)+E(f660(x19631,x19633,x19634,x19635,x19636,x19637,x19638,x19639),f660(x19632,x19633,x19634,x19635,x19636,x19637,x19638,x19639))
% 21.40/21.39 [1964]~E(x19641,x19642)+E(f660(x19643,x19641,x19644,x19645,x19646,x19647,x19648,x19649),f660(x19643,x19642,x19644,x19645,x19646,x19647,x19648,x19649))
% 21.40/21.39 [1965]~E(x19651,x19652)+E(f660(x19653,x19654,x19651,x19655,x19656,x19657,x19658,x19659),f660(x19653,x19654,x19652,x19655,x19656,x19657,x19658,x19659))
% 21.40/21.39 [1966]~E(x19661,x19662)+E(f660(x19663,x19664,x19665,x19661,x19666,x19667,x19668,x19669),f660(x19663,x19664,x19665,x19662,x19666,x19667,x19668,x19669))
% 21.40/21.39 [1967]~E(x19671,x19672)+E(f660(x19673,x19674,x19675,x19676,x19671,x19677,x19678,x19679),f660(x19673,x19674,x19675,x19676,x19672,x19677,x19678,x19679))
% 21.40/21.39 [1968]~E(x19681,x19682)+E(f660(x19683,x19684,x19685,x19686,x19687,x19681,x19688,x19689),f660(x19683,x19684,x19685,x19686,x19687,x19682,x19688,x19689))
% 21.40/21.39 [1969]~E(x19691,x19692)+E(f660(x19693,x19694,x19695,x19696,x19697,x19698,x19691,x19699),f660(x19693,x19694,x19695,x19696,x19697,x19698,x19692,x19699))
% 21.40/21.39 [1970]~E(x19701,x19702)+E(f660(x19703,x19704,x19705,x19706,x19707,x19708,x19709,x19701),f660(x19703,x19704,x19705,x19706,x19707,x19708,x19709,x19702))
% 21.40/21.39 [1971]~E(x19711,x19712)+E(f707(x19711,x19713),f707(x19712,x19713))
% 21.40/21.39 [1972]~E(x19721,x19722)+E(f707(x19723,x19721),f707(x19723,x19722))
% 21.40/21.39 [1973]~E(x19731,x19732)+E(f205(x19731,x19733),f205(x19732,x19733))
% 21.40/21.39 [1974]~E(x19741,x19742)+E(f205(x19743,x19741),f205(x19743,x19742))
% 21.40/21.39 [1975]~E(x19751,x19752)+E(f157(x19751,x19753),f157(x19752,x19753))
% 21.40/21.39 [1976]~E(x19761,x19762)+E(f157(x19763,x19761),f157(x19763,x19762))
% 21.40/21.39 [1977]~E(x19771,x19772)+E(f842(x19771,x19773,x19774),f842(x19772,x19773,x19774))
% 21.40/21.39 [1978]~E(x19781,x19782)+E(f842(x19783,x19781,x19784),f842(x19783,x19782,x19784))
% 21.40/21.39 [1979]~E(x19791,x19792)+E(f842(x19793,x19794,x19791),f842(x19793,x19794,x19792))
% 21.40/21.39 [1980]~E(x19801,x19802)+E(f578(x19801,x19803,x19804),f578(x19802,x19803,x19804))
% 21.40/21.39 [1981]~E(x19811,x19812)+E(f578(x19813,x19811,x19814),f578(x19813,x19812,x19814))
% 21.40/21.39 [1982]~E(x19821,x19822)+E(f578(x19823,x19824,x19821),f578(x19823,x19824,x19822))
% 21.40/21.39 [1983]~E(x19831,x19832)+E(f375(x19831,x19833,x19834,x19835,x19836),f375(x19832,x19833,x19834,x19835,x19836))
% 21.40/21.39 [1984]~E(x19841,x19842)+E(f375(x19843,x19841,x19844,x19845,x19846),f375(x19843,x19842,x19844,x19845,x19846))
% 21.40/21.39 [1985]~E(x19851,x19852)+E(f375(x19853,x19854,x19851,x19855,x19856),f375(x19853,x19854,x19852,x19855,x19856))
% 21.40/21.39 [1986]~E(x19861,x19862)+E(f375(x19863,x19864,x19865,x19861,x19866),f375(x19863,x19864,x19865,x19862,x19866))
% 21.40/21.39 [1987]~E(x19871,x19872)+E(f375(x19873,x19874,x19875,x19876,x19871),f375(x19873,x19874,x19875,x19876,x19872))
% 21.40/21.39 [1988]~E(x19881,x19882)+E(f396(x19881,x19883),f396(x19882,x19883))
% 21.40/21.39 [1989]~E(x19891,x19892)+E(f396(x19893,x19891),f396(x19893,x19892))
% 21.40/21.39 [1990]~E(x19901,x19902)+E(f263(x19901,x19903,x19904,x19905,x19906),f263(x19902,x19903,x19904,x19905,x19906))
% 21.40/21.39 [1991]~E(x19911,x19912)+E(f263(x19913,x19911,x19914,x19915,x19916),f263(x19913,x19912,x19914,x19915,x19916))
% 21.40/21.39 [1992]~E(x19921,x19922)+E(f263(x19923,x19924,x19921,x19925,x19926),f263(x19923,x19924,x19922,x19925,x19926))
% 21.40/21.39 [1993]~E(x19931,x19932)+E(f263(x19933,x19934,x19935,x19931,x19936),f263(x19933,x19934,x19935,x19932,x19936))
% 21.40/21.39 [1994]~E(x19941,x19942)+E(f263(x19943,x19944,x19945,x19946,x19941),f263(x19943,x19944,x19945,x19946,x19942))
% 21.40/21.39 [1995]~E(x19951,x19952)+E(f623(x19951,x19953,x19954,x19955),f623(x19952,x19953,x19954,x19955))
% 21.40/21.39 [1996]~E(x19961,x19962)+E(f623(x19963,x19961,x19964,x19965),f623(x19963,x19962,x19964,x19965))
% 21.40/21.39 [1997]~E(x19971,x19972)+E(f623(x19973,x19974,x19971,x19975),f623(x19973,x19974,x19972,x19975))
% 21.40/21.39 [1998]~E(x19981,x19982)+E(f623(x19983,x19984,x19985,x19981),f623(x19983,x19984,x19985,x19982))
% 21.40/21.39 [1999]~E(x19991,x19992)+E(f654(x19991,x19993),f654(x19992,x19993))
% 21.40/21.39 [2000]~E(x20001,x20002)+E(f654(x20003,x20001),f654(x20003,x20002))
% 21.40/21.39 [2001]~E(x20011,x20012)+E(f841(x20011,x20013,x20014),f841(x20012,x20013,x20014))
% 21.40/21.39 [2002]~E(x20021,x20022)+E(f841(x20023,x20021,x20024),f841(x20023,x20022,x20024))
% 21.40/21.39 [2003]~E(x20031,x20032)+E(f841(x20033,x20034,x20031),f841(x20033,x20034,x20032))
% 21.40/21.39 [2004]~E(x20041,x20042)+E(f663(x20041,x20043,x20044),f663(x20042,x20043,x20044))
% 21.40/21.39 [2005]~E(x20051,x20052)+E(f663(x20053,x20051,x20054),f663(x20053,x20052,x20054))
% 21.40/21.39 [2006]~E(x20061,x20062)+E(f663(x20063,x20064,x20061),f663(x20063,x20064,x20062))
% 21.40/21.39 [2007]~E(x20071,x20072)+E(f696(x20071,x20073,x20074,x20075,x20076),f696(x20072,x20073,x20074,x20075,x20076))
% 21.40/21.39 [2008]~E(x20081,x20082)+E(f696(x20083,x20081,x20084,x20085,x20086),f696(x20083,x20082,x20084,x20085,x20086))
% 21.40/21.39 [2009]~E(x20091,x20092)+E(f696(x20093,x20094,x20091,x20095,x20096),f696(x20093,x20094,x20092,x20095,x20096))
% 21.40/21.39 [2010]~E(x20101,x20102)+E(f696(x20103,x20104,x20105,x20101,x20106),f696(x20103,x20104,x20105,x20102,x20106))
% 21.40/21.39 [2011]~E(x20111,x20112)+E(f696(x20113,x20114,x20115,x20116,x20111),f696(x20113,x20114,x20115,x20116,x20112))
% 21.40/21.39 [2012]~E(x20121,x20122)+E(f572(x20121,x20123,x20124,x20125,x20126,x20127),f572(x20122,x20123,x20124,x20125,x20126,x20127))
% 21.40/21.39 [2013]~E(x20131,x20132)+E(f572(x20133,x20131,x20134,x20135,x20136,x20137),f572(x20133,x20132,x20134,x20135,x20136,x20137))
% 21.40/21.39 [2014]~E(x20141,x20142)+E(f572(x20143,x20144,x20141,x20145,x20146,x20147),f572(x20143,x20144,x20142,x20145,x20146,x20147))
% 21.40/21.39 [2015]~E(x20151,x20152)+E(f572(x20153,x20154,x20155,x20151,x20156,x20157),f572(x20153,x20154,x20155,x20152,x20156,x20157))
% 21.40/21.39 [2016]~E(x20161,x20162)+E(f572(x20163,x20164,x20165,x20166,x20161,x20167),f572(x20163,x20164,x20165,x20166,x20162,x20167))
% 21.40/21.39 [2017]~E(x20171,x20172)+E(f572(x20173,x20174,x20175,x20176,x20177,x20171),f572(x20173,x20174,x20175,x20176,x20177,x20172))
% 21.40/21.39 [2018]~E(x20181,x20182)+E(f805(x20181),f805(x20182))
% 21.40/21.39 [2019]~E(x20191,x20192)+E(f398(x20191,x20193),f398(x20192,x20193))
% 21.40/21.39 [2020]~E(x20201,x20202)+E(f398(x20203,x20201),f398(x20203,x20202))
% 21.40/21.39 [2021]~E(x20211,x20212)+E(f481(x20211,x20213,x20214,x20215),f481(x20212,x20213,x20214,x20215))
% 21.40/21.39 [2022]~E(x20221,x20222)+E(f481(x20223,x20221,x20224,x20225),f481(x20223,x20222,x20224,x20225))
% 21.40/21.39 [2023]~E(x20231,x20232)+E(f481(x20233,x20234,x20231,x20235),f481(x20233,x20234,x20232,x20235))
% 21.40/21.39 [2024]~E(x20241,x20242)+E(f481(x20243,x20244,x20245,x20241),f481(x20243,x20244,x20245,x20242))
% 21.40/21.39 [2025]~E(x20251,x20252)+E(f523(x20251,x20253,x20254,x20255),f523(x20252,x20253,x20254,x20255))
% 21.40/21.39 [2026]~E(x20261,x20262)+E(f523(x20263,x20261,x20264,x20265),f523(x20263,x20262,x20264,x20265))
% 21.40/21.39 [2027]~E(x20271,x20272)+E(f523(x20273,x20274,x20271,x20275),f523(x20273,x20274,x20272,x20275))
% 21.40/21.39 [2028]~E(x20281,x20282)+E(f523(x20283,x20284,x20285,x20281),f523(x20283,x20284,x20285,x20282))
% 21.40/21.39 [2029]~E(x20291,x20292)+E(f561(x20291,x20293,x20294),f561(x20292,x20293,x20294))
% 21.40/21.39 [2030]~E(x20301,x20302)+E(f561(x20303,x20301,x20304),f561(x20303,x20302,x20304))
% 21.40/21.39 [2031]~E(x20311,x20312)+E(f561(x20313,x20314,x20311),f561(x20313,x20314,x20312))
% 21.40/21.39 [2032]~E(x20321,x20322)+E(f809(x20321,x20323),f809(x20322,x20323))
% 21.40/21.39 [2033]~E(x20331,x20332)+E(f809(x20333,x20331),f809(x20333,x20332))
% 21.40/21.39 [2034]~E(x20341,x20342)+E(f694(x20341,x20343,x20344,x20345,x20346),f694(x20342,x20343,x20344,x20345,x20346))
% 21.40/21.39 [2035]~E(x20351,x20352)+E(f694(x20353,x20351,x20354,x20355,x20356),f694(x20353,x20352,x20354,x20355,x20356))
% 21.40/21.39 [2036]~E(x20361,x20362)+E(f694(x20363,x20364,x20361,x20365,x20366),f694(x20363,x20364,x20362,x20365,x20366))
% 21.40/21.39 [2037]~E(x20371,x20372)+E(f694(x20373,x20374,x20375,x20371,x20376),f694(x20373,x20374,x20375,x20372,x20376))
% 21.40/21.39 [2038]~E(x20381,x20382)+E(f694(x20383,x20384,x20385,x20386,x20381),f694(x20383,x20384,x20385,x20386,x20382))
% 21.40/21.39 [2039]~E(x20391,x20392)+E(f425(x20391,x20393,x20394,x20395,x20396),f425(x20392,x20393,x20394,x20395,x20396))
% 21.40/21.39 [2040]~E(x20401,x20402)+E(f425(x20403,x20401,x20404,x20405,x20406),f425(x20403,x20402,x20404,x20405,x20406))
% 21.40/21.39 [2041]~E(x20411,x20412)+E(f425(x20413,x20414,x20411,x20415,x20416),f425(x20413,x20414,x20412,x20415,x20416))
% 21.40/21.39 [2042]~E(x20421,x20422)+E(f425(x20423,x20424,x20425,x20421,x20426),f425(x20423,x20424,x20425,x20422,x20426))
% 21.40/21.39 [2043]~E(x20431,x20432)+E(f425(x20433,x20434,x20435,x20436,x20431),f425(x20433,x20434,x20435,x20436,x20432))
% 21.40/21.39 [2044]~E(x20441,x20442)+E(f428(x20441,x20443,x20444,x20445,x20446),f428(x20442,x20443,x20444,x20445,x20446))
% 21.40/21.39 [2045]~E(x20451,x20452)+E(f428(x20453,x20451,x20454,x20455,x20456),f428(x20453,x20452,x20454,x20455,x20456))
% 21.40/21.39 [2046]~E(x20461,x20462)+E(f428(x20463,x20464,x20461,x20465,x20466),f428(x20463,x20464,x20462,x20465,x20466))
% 21.40/21.39 [2047]~E(x20471,x20472)+E(f428(x20473,x20474,x20475,x20471,x20476),f428(x20473,x20474,x20475,x20472,x20476))
% 21.40/21.39 [2048]~E(x20481,x20482)+E(f428(x20483,x20484,x20485,x20486,x20481),f428(x20483,x20484,x20485,x20486,x20482))
% 21.40/21.39 [2049]~E(x20491,x20492)+E(f522(x20491),f522(x20492))
% 21.40/21.39 [2050]~E(x20501,x20502)+E(f323(x20501,x20503,x20504),f323(x20502,x20503,x20504))
% 21.40/21.39 [2051]~E(x20511,x20512)+E(f323(x20513,x20511,x20514),f323(x20513,x20512,x20514))
% 21.40/21.39 [2052]~E(x20521,x20522)+E(f323(x20523,x20524,x20521),f323(x20523,x20524,x20522))
% 21.40/21.39 [2053]~E(x20531,x20532)+E(f445(x20531,x20533,x20534,x20535),f445(x20532,x20533,x20534,x20535))
% 21.40/21.39 [2054]~E(x20541,x20542)+E(f445(x20543,x20541,x20544,x20545),f445(x20543,x20542,x20544,x20545))
% 21.40/21.39 [2055]~E(x20551,x20552)+E(f445(x20553,x20554,x20551,x20555),f445(x20553,x20554,x20552,x20555))
% 21.40/21.39 [2056]~E(x20561,x20562)+E(f445(x20563,x20564,x20565,x20561),f445(x20563,x20564,x20565,x20562))
% 21.40/21.39 [2057]~E(x20571,x20572)+E(f811(x20571),f811(x20572))
% 21.40/21.39 [2058]~E(x20581,x20582)+E(f401(x20581,x20583),f401(x20582,x20583))
% 21.40/21.39 [2059]~E(x20591,x20592)+E(f401(x20593,x20591),f401(x20593,x20592))
% 21.40/21.39 [2060]~E(x20601,x20602)+E(f777(x20601,x20603),f777(x20602,x20603))
% 21.40/21.39 [2061]~E(x20611,x20612)+E(f777(x20613,x20611),f777(x20613,x20612))
% 21.40/21.39 [2062]~E(x20621,x20622)+E(f421(x20621,x20623,x20624,x20625),f421(x20622,x20623,x20624,x20625))
% 21.40/21.39 [2063]~E(x20631,x20632)+E(f421(x20633,x20631,x20634,x20635),f421(x20633,x20632,x20634,x20635))
% 21.40/21.39 [2064]~E(x20641,x20642)+E(f421(x20643,x20644,x20641,x20645),f421(x20643,x20644,x20642,x20645))
% 21.40/21.39 [2065]~E(x20651,x20652)+E(f421(x20653,x20654,x20655,x20651),f421(x20653,x20654,x20655,x20652))
% 21.40/21.39 [2066]~E(x20661,x20662)+E(f559(x20661,x20663,x20664,x20665,x20666,x20667),f559(x20662,x20663,x20664,x20665,x20666,x20667))
% 21.40/21.39 [2067]~E(x20671,x20672)+E(f559(x20673,x20671,x20674,x20675,x20676,x20677),f559(x20673,x20672,x20674,x20675,x20676,x20677))
% 21.40/21.39 [2068]~E(x20681,x20682)+E(f559(x20683,x20684,x20681,x20685,x20686,x20687),f559(x20683,x20684,x20682,x20685,x20686,x20687))
% 21.40/21.39 [2069]~E(x20691,x20692)+E(f559(x20693,x20694,x20695,x20691,x20696,x20697),f559(x20693,x20694,x20695,x20692,x20696,x20697))
% 21.40/21.39 [2070]~E(x20701,x20702)+E(f559(x20703,x20704,x20705,x20706,x20701,x20707),f559(x20703,x20704,x20705,x20706,x20702,x20707))
% 21.40/21.39 [2071]~E(x20711,x20712)+E(f559(x20713,x20714,x20715,x20716,x20717,x20711),f559(x20713,x20714,x20715,x20716,x20717,x20712))
% 21.40/21.39 [2072]~E(x20721,x20722)+E(f620(x20721,x20723,x20724),f620(x20722,x20723,x20724))
% 21.40/21.39 [2073]~E(x20731,x20732)+E(f620(x20733,x20731,x20734),f620(x20733,x20732,x20734))
% 21.40/21.39 [2074]~E(x20741,x20742)+E(f620(x20743,x20744,x20741),f620(x20743,x20744,x20742))
% 21.40/21.39 [2075]~E(x20751,x20752)+E(f635(x20751,x20753,x20754),f635(x20752,x20753,x20754))
% 21.40/21.39 [2076]~E(x20761,x20762)+E(f635(x20763,x20761,x20764),f635(x20763,x20762,x20764))
% 21.40/21.39 [2077]~E(x20771,x20772)+E(f635(x20773,x20774,x20771),f635(x20773,x20774,x20772))
% 21.40/21.39 [2078]~E(x20781,x20782)+E(f822(x20781,x20783,x20784),f822(x20782,x20783,x20784))
% 21.40/21.39 [2079]~E(x20791,x20792)+E(f822(x20793,x20791,x20794),f822(x20793,x20792,x20794))
% 21.40/21.39 [2080]~E(x20801,x20802)+E(f822(x20803,x20804,x20801),f822(x20803,x20804,x20802))
% 21.40/21.39 [2081]~E(x20811,x20812)+E(f574(x20811,x20813,x20814,x20815,x20816,x20817),f574(x20812,x20813,x20814,x20815,x20816,x20817))
% 21.40/21.39 [2082]~E(x20821,x20822)+E(f574(x20823,x20821,x20824,x20825,x20826,x20827),f574(x20823,x20822,x20824,x20825,x20826,x20827))
% 21.40/21.39 [2083]~E(x20831,x20832)+E(f574(x20833,x20834,x20831,x20835,x20836,x20837),f574(x20833,x20834,x20832,x20835,x20836,x20837))
% 21.40/21.39 [2084]~E(x20841,x20842)+E(f574(x20843,x20844,x20845,x20841,x20846,x20847),f574(x20843,x20844,x20845,x20842,x20846,x20847))
% 21.40/21.39 [2085]~E(x20851,x20852)+E(f574(x20853,x20854,x20855,x20856,x20851,x20857),f574(x20853,x20854,x20855,x20856,x20852,x20857))
% 21.40/21.39 [2086]~E(x20861,x20862)+E(f574(x20863,x20864,x20865,x20866,x20867,x20861),f574(x20863,x20864,x20865,x20866,x20867,x20862))
% 21.40/21.39 [2087]~E(x20871,x20872)+E(f746(x20871,x20873,x20874,x20875),f746(x20872,x20873,x20874,x20875))
% 21.40/21.39 [2088]~E(x20881,x20882)+E(f746(x20883,x20881,x20884,x20885),f746(x20883,x20882,x20884,x20885))
% 21.40/21.39 [2089]~E(x20891,x20892)+E(f746(x20893,x20894,x20891,x20895),f746(x20893,x20894,x20892,x20895))
% 21.40/21.39 [2090]~E(x20901,x20902)+E(f746(x20903,x20904,x20905,x20901),f746(x20903,x20904,x20905,x20902))
% 21.40/21.39 [2091]~E(x20911,x20912)+E(f242(x20911,x20913),f242(x20912,x20913))
% 21.40/21.39 [2092]~E(x20921,x20922)+E(f242(x20923,x20921),f242(x20923,x20922))
% 21.40/21.39 [2093]~E(x20931,x20932)+E(f764(x20931,x20933,x20934),f764(x20932,x20933,x20934))
% 21.40/21.39 [2094]~E(x20941,x20942)+E(f764(x20943,x20941,x20944),f764(x20943,x20942,x20944))
% 21.40/21.39 [2095]~E(x20951,x20952)+E(f764(x20953,x20954,x20951),f764(x20953,x20954,x20952))
% 21.40/21.39 [2096]~E(x20961,x20962)+E(f611(x20961,x20963),f611(x20962,x20963))
% 21.40/21.39 [2097]~E(x20971,x20972)+E(f611(x20973,x20971),f611(x20973,x20972))
% 21.40/21.39 [2098]~E(x20981,x20982)+E(f458(x20981,x20983,x20984),f458(x20982,x20983,x20984))
% 21.40/21.39 [2099]~E(x20991,x20992)+E(f458(x20993,x20991,x20994),f458(x20993,x20992,x20994))
% 21.40/21.39 [2100]~E(x21001,x21002)+E(f458(x21003,x21004,x21001),f458(x21003,x21004,x21002))
% 21.40/21.39 [2101]~E(x21011,x21012)+E(f669(x21011,x21013,x21014),f669(x21012,x21013,x21014))
% 21.40/21.39 [2102]~E(x21021,x21022)+E(f669(x21023,x21021,x21024),f669(x21023,x21022,x21024))
% 21.40/21.39 [2103]~E(x21031,x21032)+E(f669(x21033,x21034,x21031),f669(x21033,x21034,x21032))
% 21.40/21.39 [2104]~E(x21041,x21042)+E(f632(x21041,x21043,x21044,x21045,x21046,x21047),f632(x21042,x21043,x21044,x21045,x21046,x21047))
% 21.40/21.39 [2105]~E(x21051,x21052)+E(f632(x21053,x21051,x21054,x21055,x21056,x21057),f632(x21053,x21052,x21054,x21055,x21056,x21057))
% 21.40/21.39 [2106]~E(x21061,x21062)+E(f632(x21063,x21064,x21061,x21065,x21066,x21067),f632(x21063,x21064,x21062,x21065,x21066,x21067))
% 21.40/21.39 [2107]~E(x21071,x21072)+E(f632(x21073,x21074,x21075,x21071,x21076,x21077),f632(x21073,x21074,x21075,x21072,x21076,x21077))
% 21.40/21.39 [2108]~E(x21081,x21082)+E(f632(x21083,x21084,x21085,x21086,x21081,x21087),f632(x21083,x21084,x21085,x21086,x21082,x21087))
% 21.40/21.39 [2109]~E(x21091,x21092)+E(f632(x21093,x21094,x21095,x21096,x21097,x21091),f632(x21093,x21094,x21095,x21096,x21097,x21092))
% 21.40/21.39 [2110]~E(x21101,x21102)+E(f532(x21101,x21103,x21104,x21105,x21106,x21107),f532(x21102,x21103,x21104,x21105,x21106,x21107))
% 21.40/21.39 [2111]~E(x21111,x21112)+E(f532(x21113,x21111,x21114,x21115,x21116,x21117),f532(x21113,x21112,x21114,x21115,x21116,x21117))
% 21.40/21.39 [2112]~E(x21121,x21122)+E(f532(x21123,x21124,x21121,x21125,x21126,x21127),f532(x21123,x21124,x21122,x21125,x21126,x21127))
% 21.40/21.39 [2113]~E(x21131,x21132)+E(f532(x21133,x21134,x21135,x21131,x21136,x21137),f532(x21133,x21134,x21135,x21132,x21136,x21137))
% 21.40/21.39 [2114]~E(x21141,x21142)+E(f532(x21143,x21144,x21145,x21146,x21141,x21147),f532(x21143,x21144,x21145,x21146,x21142,x21147))
% 21.40/21.39 [2115]~E(x21151,x21152)+E(f532(x21153,x21154,x21155,x21156,x21157,x21151),f532(x21153,x21154,x21155,x21156,x21157,x21152))
% 21.40/21.39 [2116]~E(x21161,x21162)+E(f225(x21161,x21163,x21164,x21165,x21166),f225(x21162,x21163,x21164,x21165,x21166))
% 21.40/21.39 [2117]~E(x21171,x21172)+E(f225(x21173,x21171,x21174,x21175,x21176),f225(x21173,x21172,x21174,x21175,x21176))
% 21.40/21.39 [2118]~E(x21181,x21182)+E(f225(x21183,x21184,x21181,x21185,x21186),f225(x21183,x21184,x21182,x21185,x21186))
% 21.40/21.39 [2119]~E(x21191,x21192)+E(f225(x21193,x21194,x21195,x21191,x21196),f225(x21193,x21194,x21195,x21192,x21196))
% 21.40/21.39 [2120]~E(x21201,x21202)+E(f225(x21203,x21204,x21205,x21206,x21201),f225(x21203,x21204,x21205,x21206,x21202))
% 21.40/21.39 [2121]~E(x21211,x21212)+E(f410(x21211,x21213,x21214,x21215),f410(x21212,x21213,x21214,x21215))
% 21.40/21.39 [2122]~E(x21221,x21222)+E(f410(x21223,x21221,x21224,x21225),f410(x21223,x21222,x21224,x21225))
% 21.40/21.39 [2123]~E(x21231,x21232)+E(f410(x21233,x21234,x21231,x21235),f410(x21233,x21234,x21232,x21235))
% 21.40/21.39 [2124]~E(x21241,x21242)+E(f410(x21243,x21244,x21245,x21241),f410(x21243,x21244,x21245,x21242))
% 21.40/21.39 [2125]~E(x21251,x21252)+E(f823(x21251,x21253,x21254),f823(x21252,x21253,x21254))
% 21.40/21.39 [2126]~E(x21261,x21262)+E(f823(x21263,x21261,x21264),f823(x21263,x21262,x21264))
% 21.40/21.39 [2127]~E(x21271,x21272)+E(f823(x21273,x21274,x21271),f823(x21273,x21274,x21272))
% 21.40/21.39 [2128]~E(x21281,x21282)+E(f636(x21281,x21283,x21284),f636(x21282,x21283,x21284))
% 21.40/21.39 [2129]~E(x21291,x21292)+E(f636(x21293,x21291,x21294),f636(x21293,x21292,x21294))
% 21.40/21.39 [2130]~E(x21301,x21302)+E(f636(x21303,x21304,x21301),f636(x21303,x21304,x21302))
% 21.40/21.39 [2131]~E(x21311,x21312)+E(f389(x21311,x21313,x21314),f389(x21312,x21313,x21314))
% 21.40/21.39 [2132]~E(x21321,x21322)+E(f389(x21323,x21321,x21324),f389(x21323,x21322,x21324))
% 21.40/21.39 [2133]~E(x21331,x21332)+E(f389(x21333,x21334,x21331),f389(x21333,x21334,x21332))
% 21.40/21.39 [2134]~E(x21341,x21342)+E(f502(x21341,x21343,x21344,x21345),f502(x21342,x21343,x21344,x21345))
% 21.40/21.39 [2135]~E(x21351,x21352)+E(f502(x21353,x21351,x21354,x21355),f502(x21353,x21352,x21354,x21355))
% 21.40/21.39 [2136]~E(x21361,x21362)+E(f502(x21363,x21364,x21361,x21365),f502(x21363,x21364,x21362,x21365))
% 21.40/21.39 [2137]~E(x21371,x21372)+E(f502(x21373,x21374,x21375,x21371),f502(x21373,x21374,x21375,x21372))
% 21.40/21.39 [2138]~E(x21381,x21382)+E(f641(x21381,x21383,x21384),f641(x21382,x21383,x21384))
% 21.40/21.39 [2139]~E(x21391,x21392)+E(f641(x21393,x21391,x21394),f641(x21393,x21392,x21394))
% 21.40/21.39 [2140]~E(x21401,x21402)+E(f641(x21403,x21404,x21401),f641(x21403,x21404,x21402))
% 21.40/21.39 [2141]~E(x21411,x21412)+E(f821(x21411,x21413,x21414),f821(x21412,x21413,x21414))
% 21.40/21.39 [2142]~E(x21421,x21422)+E(f821(x21423,x21421,x21424),f821(x21423,x21422,x21424))
% 21.40/21.39 [2143]~E(x21431,x21432)+E(f821(x21433,x21434,x21431),f821(x21433,x21434,x21432))
% 21.40/21.39 [2144]~E(x21441,x21442)+E(f349(x21441,x21443,x21444,x21445,x21446,x21447,x21448),f349(x21442,x21443,x21444,x21445,x21446,x21447,x21448))
% 21.40/21.39 [2145]~E(x21451,x21452)+E(f349(x21453,x21451,x21454,x21455,x21456,x21457,x21458),f349(x21453,x21452,x21454,x21455,x21456,x21457,x21458))
% 21.40/21.39 [2146]~E(x21461,x21462)+E(f349(x21463,x21464,x21461,x21465,x21466,x21467,x21468),f349(x21463,x21464,x21462,x21465,x21466,x21467,x21468))
% 21.40/21.39 [2147]~E(x21471,x21472)+E(f349(x21473,x21474,x21475,x21471,x21476,x21477,x21478),f349(x21473,x21474,x21475,x21472,x21476,x21477,x21478))
% 21.40/21.39 [2148]~E(x21481,x21482)+E(f349(x21483,x21484,x21485,x21486,x21481,x21487,x21488),f349(x21483,x21484,x21485,x21486,x21482,x21487,x21488))
% 21.40/21.39 [2149]~E(x21491,x21492)+E(f349(x21493,x21494,x21495,x21496,x21497,x21491,x21498),f349(x21493,x21494,x21495,x21496,x21497,x21492,x21498))
% 21.40/21.39 [2150]~E(x21501,x21502)+E(f349(x21503,x21504,x21505,x21506,x21507,x21508,x21501),f349(x21503,x21504,x21505,x21506,x21507,x21508,x21502))
% 21.40/21.39 [2151]~E(x21511,x21512)+E(f729(x21511,x21513,x21514,x21515,x21516),f729(x21512,x21513,x21514,x21515,x21516))
% 21.40/21.39 [2152]~E(x21521,x21522)+E(f729(x21523,x21521,x21524,x21525,x21526),f729(x21523,x21522,x21524,x21525,x21526))
% 21.40/21.39 [2153]~E(x21531,x21532)+E(f729(x21533,x21534,x21531,x21535,x21536),f729(x21533,x21534,x21532,x21535,x21536))
% 21.40/21.39 [2154]~E(x21541,x21542)+E(f729(x21543,x21544,x21545,x21541,x21546),f729(x21543,x21544,x21545,x21542,x21546))
% 21.40/21.39 [2155]~E(x21551,x21552)+E(f729(x21553,x21554,x21555,x21556,x21551),f729(x21553,x21554,x21555,x21556,x21552))
% 21.40/21.39 [2156]~E(x21561,x21562)+E(f466(x21561,x21563),f466(x21562,x21563))
% 21.40/21.39 [2157]~E(x21571,x21572)+E(f466(x21573,x21571),f466(x21573,x21572))
% 21.40/21.39 [2158]~E(x21581,x21582)+E(f419(x21581,x21583,x21584,x21585,x21586),f419(x21582,x21583,x21584,x21585,x21586))
% 21.40/21.39 [2159]~E(x21591,x21592)+E(f419(x21593,x21591,x21594,x21595,x21596),f419(x21593,x21592,x21594,x21595,x21596))
% 21.40/21.39 [2160]~E(x21601,x21602)+E(f419(x21603,x21604,x21601,x21605,x21606),f419(x21603,x21604,x21602,x21605,x21606))
% 21.40/21.39 [2161]~E(x21611,x21612)+E(f419(x21613,x21614,x21615,x21611,x21616),f419(x21613,x21614,x21615,x21612,x21616))
% 21.40/21.39 [2162]~E(x21621,x21622)+E(f419(x21623,x21624,x21625,x21626,x21621),f419(x21623,x21624,x21625,x21626,x21622))
% 21.40/21.39 [2163]~E(x21631,x21632)+E(f627(x21631,x21633,x21634,x21635,x21636,x21637),f627(x21632,x21633,x21634,x21635,x21636,x21637))
% 21.40/21.39 [2164]~E(x21641,x21642)+E(f627(x21643,x21641,x21644,x21645,x21646,x21647),f627(x21643,x21642,x21644,x21645,x21646,x21647))
% 21.40/21.39 [2165]~E(x21651,x21652)+E(f627(x21653,x21654,x21651,x21655,x21656,x21657),f627(x21653,x21654,x21652,x21655,x21656,x21657))
% 21.40/21.39 [2166]~E(x21661,x21662)+E(f627(x21663,x21664,x21665,x21661,x21666,x21667),f627(x21663,x21664,x21665,x21662,x21666,x21667))
% 21.40/21.39 [2167]~E(x21671,x21672)+E(f627(x21673,x21674,x21675,x21676,x21671,x21677),f627(x21673,x21674,x21675,x21676,x21672,x21677))
% 21.40/21.39 [2168]~E(x21681,x21682)+E(f627(x21683,x21684,x21685,x21686,x21687,x21681),f627(x21683,x21684,x21685,x21686,x21687,x21682))
% 21.40/21.39 [2169]~E(x21691,x21692)+E(f588(x21691),f588(x21692))
% 21.40/21.39 [2170]~E(x21701,x21702)+E(f593(x21701,x21703,x21704,x21705),f593(x21702,x21703,x21704,x21705))
% 21.40/21.39 [2171]~E(x21711,x21712)+E(f593(x21713,x21711,x21714,x21715),f593(x21713,x21712,x21714,x21715))
% 21.40/21.39 [2172]~E(x21721,x21722)+E(f593(x21723,x21724,x21721,x21725),f593(x21723,x21724,x21722,x21725))
% 21.40/21.39 [2173]~E(x21731,x21732)+E(f593(x21733,x21734,x21735,x21731),f593(x21733,x21734,x21735,x21732))
% 21.40/21.39 [2174]~E(x21741,x21742)+E(f479(x21741,x21743,x21744,x21745),f479(x21742,x21743,x21744,x21745))
% 21.40/21.39 [2175]~E(x21751,x21752)+E(f479(x21753,x21751,x21754,x21755),f479(x21753,x21752,x21754,x21755))
% 21.40/21.39 [2176]~E(x21761,x21762)+E(f479(x21763,x21764,x21761,x21765),f479(x21763,x21764,x21762,x21765))
% 21.40/21.39 [2177]~E(x21771,x21772)+E(f479(x21773,x21774,x21775,x21771),f479(x21773,x21774,x21775,x21772))
% 21.40/21.39 [2178]~E(x21781,x21782)+E(f504(x21781,x21783,x21784,x21785,x21786),f504(x21782,x21783,x21784,x21785,x21786))
% 21.40/21.39 [2179]~E(x21791,x21792)+E(f504(x21793,x21791,x21794,x21795,x21796),f504(x21793,x21792,x21794,x21795,x21796))
% 21.40/21.39 [2180]~E(x21801,x21802)+E(f504(x21803,x21804,x21801,x21805,x21806),f504(x21803,x21804,x21802,x21805,x21806))
% 21.40/21.39 [2181]~E(x21811,x21812)+E(f504(x21813,x21814,x21815,x21811,x21816),f504(x21813,x21814,x21815,x21812,x21816))
% 21.40/21.39 [2182]~E(x21821,x21822)+E(f504(x21823,x21824,x21825,x21826,x21821),f504(x21823,x21824,x21825,x21826,x21822))
% 21.40/21.39 [2183]~E(x21831,x21832)+E(f499(x21831,x21833,x21834,x21835),f499(x21832,x21833,x21834,x21835))
% 21.40/21.39 [2184]~E(x21841,x21842)+E(f499(x21843,x21841,x21844,x21845),f499(x21843,x21842,x21844,x21845))
% 21.40/21.39 [2185]~E(x21851,x21852)+E(f499(x21853,x21854,x21851,x21855),f499(x21853,x21854,x21852,x21855))
% 21.40/21.39 [2186]~E(x21861,x21862)+E(f499(x21863,x21864,x21865,x21861),f499(x21863,x21864,x21865,x21862))
% 21.40/21.39 [2187]~E(x21871,x21872)+E(f706(x21871,x21873,x21874,x21875),f706(x21872,x21873,x21874,x21875))
% 21.40/21.39 [2188]~E(x21881,x21882)+E(f706(x21883,x21881,x21884,x21885),f706(x21883,x21882,x21884,x21885))
% 21.40/21.39 [2189]~E(x21891,x21892)+E(f706(x21893,x21894,x21891,x21895),f706(x21893,x21894,x21892,x21895))
% 21.40/21.39 [2190]~E(x21901,x21902)+E(f706(x21903,x21904,x21905,x21901),f706(x21903,x21904,x21905,x21902))
% 21.40/21.39 [2191]~E(x21911,x21912)+E(f350(x21911,x21913,x21914,x21915,x21916,x21917,x21918),f350(x21912,x21913,x21914,x21915,x21916,x21917,x21918))
% 21.40/21.39 [2192]~E(x21921,x21922)+E(f350(x21923,x21921,x21924,x21925,x21926,x21927,x21928),f350(x21923,x21922,x21924,x21925,x21926,x21927,x21928))
% 21.40/21.39 [2193]~E(x21931,x21932)+E(f350(x21933,x21934,x21931,x21935,x21936,x21937,x21938),f350(x21933,x21934,x21932,x21935,x21936,x21937,x21938))
% 21.40/21.39 [2194]~E(x21941,x21942)+E(f350(x21943,x21944,x21945,x21941,x21946,x21947,x21948),f350(x21943,x21944,x21945,x21942,x21946,x21947,x21948))
% 21.40/21.39 [2195]~E(x21951,x21952)+E(f350(x21953,x21954,x21955,x21956,x21951,x21957,x21958),f350(x21953,x21954,x21955,x21956,x21952,x21957,x21958))
% 21.40/21.39 [2196]~E(x21961,x21962)+E(f350(x21963,x21964,x21965,x21966,x21967,x21961,x21968),f350(x21963,x21964,x21965,x21966,x21967,x21962,x21968))
% 21.40/21.39 [2197]~E(x21971,x21972)+E(f350(x21973,x21974,x21975,x21976,x21977,x21978,x21971),f350(x21973,x21974,x21975,x21976,x21977,x21978,x21972))
% 21.40/21.39 [2198]~E(x21981,x21982)+E(f418(x21981,x21983,x21984,x21985,x21986),f418(x21982,x21983,x21984,x21985,x21986))
% 21.40/21.39 [2199]~E(x21991,x21992)+E(f418(x21993,x21991,x21994,x21995,x21996),f418(x21993,x21992,x21994,x21995,x21996))
% 21.40/21.39 [2200]~E(x22001,x22002)+E(f418(x22003,x22004,x22001,x22005,x22006),f418(x22003,x22004,x22002,x22005,x22006))
% 21.40/21.39 [2201]~E(x22011,x22012)+E(f418(x22013,x22014,x22015,x22011,x22016),f418(x22013,x22014,x22015,x22012,x22016))
% 21.40/21.39 [2202]~E(x22021,x22022)+E(f418(x22023,x22024,x22025,x22026,x22021),f418(x22023,x22024,x22025,x22026,x22022))
% 21.40/21.39 [2203]~E(x22031,x22032)+E(f415(x22031,x22033,x22034,x22035),f415(x22032,x22033,x22034,x22035))
% 21.40/21.39 [2204]~E(x22041,x22042)+E(f415(x22043,x22041,x22044,x22045),f415(x22043,x22042,x22044,x22045))
% 21.40/21.39 [2205]~E(x22051,x22052)+E(f415(x22053,x22054,x22051,x22055),f415(x22053,x22054,x22052,x22055))
% 21.40/21.39 [2206]~E(x22061,x22062)+E(f415(x22063,x22064,x22065,x22061),f415(x22063,x22064,x22065,x22062))
% 21.40/21.39 [2207]~E(x22071,x22072)+E(f813(x22071,x22073),f813(x22072,x22073))
% 21.40/21.39 [2208]~E(x22081,x22082)+E(f813(x22083,x22081),f813(x22083,x22082))
% 21.40/21.39 [2209]~E(x22091,x22092)+E(f712(x22091,x22093,x22094),f712(x22092,x22093,x22094))
% 21.40/21.39 [2210]~E(x22101,x22102)+E(f712(x22103,x22101,x22104),f712(x22103,x22102,x22104))
% 21.40/21.39 [2211]~E(x22111,x22112)+E(f712(x22113,x22114,x22111),f712(x22113,x22114,x22112))
% 21.40/21.39 [2212]~E(x22121,x22122)+E(f366(x22121,x22123,x22124,x22125,x22126,x22127,x22128),f366(x22122,x22123,x22124,x22125,x22126,x22127,x22128))
% 21.40/21.39 [2213]~E(x22131,x22132)+E(f366(x22133,x22131,x22134,x22135,x22136,x22137,x22138),f366(x22133,x22132,x22134,x22135,x22136,x22137,x22138))
% 21.40/21.39 [2214]~E(x22141,x22142)+E(f366(x22143,x22144,x22141,x22145,x22146,x22147,x22148),f366(x22143,x22144,x22142,x22145,x22146,x22147,x22148))
% 21.40/21.39 [2215]~E(x22151,x22152)+E(f366(x22153,x22154,x22155,x22151,x22156,x22157,x22158),f366(x22153,x22154,x22155,x22152,x22156,x22157,x22158))
% 21.40/21.39 [2216]~E(x22161,x22162)+E(f366(x22163,x22164,x22165,x22166,x22161,x22167,x22168),f366(x22163,x22164,x22165,x22166,x22162,x22167,x22168))
% 21.40/21.39 [2217]~E(x22171,x22172)+E(f366(x22173,x22174,x22175,x22176,x22177,x22171,x22178),f366(x22173,x22174,x22175,x22176,x22177,x22172,x22178))
% 21.40/21.39 [2218]~E(x22181,x22182)+E(f366(x22183,x22184,x22185,x22186,x22187,x22188,x22181),f366(x22183,x22184,x22185,x22186,x22187,x22188,x22182))
% 21.40/21.39 [2219]~E(x22191,x22192)+E(f472(x22191,x22193),f472(x22192,x22193))
% 21.40/21.39 [2220]~E(x22201,x22202)+E(f472(x22203,x22201),f472(x22203,x22202))
% 21.40/21.39 [2221]~E(x22211,x22212)+E(f565(x22211),f565(x22212))
% 21.40/21.39 [2222]~E(x22221,x22222)+E(f730(x22221,x22223,x22224,x22225),f730(x22222,x22223,x22224,x22225))
% 21.40/21.39 [2223]~E(x22231,x22232)+E(f730(x22233,x22231,x22234,x22235),f730(x22233,x22232,x22234,x22235))
% 21.40/21.39 [2224]~E(x22241,x22242)+E(f730(x22243,x22244,x22241,x22245),f730(x22243,x22244,x22242,x22245))
% 21.40/21.39 [2225]~E(x22251,x22252)+E(f730(x22253,x22254,x22255,x22251),f730(x22253,x22254,x22255,x22252))
% 21.40/21.39 [2226]~E(x22261,x22262)+E(f292(x22261,x22263),f292(x22262,x22263))
% 21.40/21.39 [2227]~E(x22271,x22272)+E(f292(x22273,x22271),f292(x22273,x22272))
% 21.40/21.39 [2228]~E(x22281,x22282)+E(f395(x22281,x22283,x22284,x22285,x22286),f395(x22282,x22283,x22284,x22285,x22286))
% 21.40/21.39 [2229]~E(x22291,x22292)+E(f395(x22293,x22291,x22294,x22295,x22296),f395(x22293,x22292,x22294,x22295,x22296))
% 21.40/21.39 [2230]~E(x22301,x22302)+E(f395(x22303,x22304,x22301,x22305,x22306),f395(x22303,x22304,x22302,x22305,x22306))
% 21.40/21.39 [2231]~E(x22311,x22312)+E(f395(x22313,x22314,x22315,x22311,x22316),f395(x22313,x22314,x22315,x22312,x22316))
% 21.40/21.39 [2232]~E(x22321,x22322)+E(f395(x22323,x22324,x22325,x22326,x22321),f395(x22323,x22324,x22325,x22326,x22322))
% 21.40/21.39 [2233]~E(x22331,x22332)+E(f45(x22331,x22333,x22334,x22335),f45(x22332,x22333,x22334,x22335))
% 21.40/21.39 [2234]~E(x22341,x22342)+E(f45(x22343,x22341,x22344,x22345),f45(x22343,x22342,x22344,x22345))
% 21.40/21.39 [2235]~E(x22351,x22352)+E(f45(x22353,x22354,x22351,x22355),f45(x22353,x22354,x22352,x22355))
% 21.40/21.39 [2236]~E(x22361,x22362)+E(f45(x22363,x22364,x22365,x22361),f45(x22363,x22364,x22365,x22362))
% 21.40/21.39 [2237]~E(x22371,x22372)+E(f744(x22371,x22373,x22374),f744(x22372,x22373,x22374))
% 21.40/21.39 [2238]~E(x22381,x22382)+E(f744(x22383,x22381,x22384),f744(x22383,x22382,x22384))
% 21.40/21.39 [2239]~E(x22391,x22392)+E(f744(x22393,x22394,x22391),f744(x22393,x22394,x22392))
% 21.40/21.39 [2240]~E(x22401,x22402)+E(f606(x22401,x22403),f606(x22402,x22403))
% 21.40/21.39 [2241]~E(x22411,x22412)+E(f606(x22413,x22411),f606(x22413,x22412))
% 21.40/21.39 [2242]~E(x22421,x22422)+E(f318(x22421),f318(x22422))
% 21.40/21.39 [2243]~E(x22431,x22432)+E(f456(x22431),f456(x22432))
% 21.40/21.39 [2244]~E(x22441,x22442)+E(f207(x22441),f207(x22442))
% 21.40/21.39 [2245]~E(x22451,x22452)+E(f774(x22451,x22453),f774(x22452,x22453))
% 21.40/21.39 [2246]~E(x22461,x22462)+E(f774(x22463,x22461),f774(x22463,x22462))
% 21.40/21.39 [2247]~E(x22471,x22472)+E(f763(x22471,x22473,x22474),f763(x22472,x22473,x22474))
% 21.40/21.39 [2248]~E(x22481,x22482)+E(f763(x22483,x22481,x22484),f763(x22483,x22482,x22484))
% 21.40/21.39 [2249]~E(x22491,x22492)+E(f763(x22493,x22494,x22491),f763(x22493,x22494,x22492))
% 21.40/21.39 [2250]~E(x22501,x22502)+E(f590(x22501,x22503),f590(x22502,x22503))
% 21.40/21.39 [2251]~E(x22511,x22512)+E(f590(x22513,x22511),f590(x22513,x22512))
% 21.40/21.39 [2252]~E(x22521,x22522)+E(f516(x22521,x22523,x22524,x22525,x22526),f516(x22522,x22523,x22524,x22525,x22526))
% 21.40/21.39 [2253]~E(x22531,x22532)+E(f516(x22533,x22531,x22534,x22535,x22536),f516(x22533,x22532,x22534,x22535,x22536))
% 21.40/21.39 [2254]~E(x22541,x22542)+E(f516(x22543,x22544,x22541,x22545,x22546),f516(x22543,x22544,x22542,x22545,x22546))
% 21.40/21.39 [2255]~E(x22551,x22552)+E(f516(x22553,x22554,x22555,x22551,x22556),f516(x22553,x22554,x22555,x22552,x22556))
% 21.40/21.39 [2256]~E(x22561,x22562)+E(f516(x22563,x22564,x22565,x22566,x22561),f516(x22563,x22564,x22565,x22566,x22562))
% 21.40/21.39 [2257]~E(x22571,x22572)+E(f658(x22571,x22573,x22574,x22575,x22576),f658(x22572,x22573,x22574,x22575,x22576))
% 21.40/21.39 [2258]~E(x22581,x22582)+E(f658(x22583,x22581,x22584,x22585,x22586),f658(x22583,x22582,x22584,x22585,x22586))
% 21.40/21.39 [2259]~E(x22591,x22592)+E(f658(x22593,x22594,x22591,x22595,x22596),f658(x22593,x22594,x22592,x22595,x22596))
% 21.40/21.39 [2260]~E(x22601,x22602)+E(f658(x22603,x22604,x22605,x22601,x22606),f658(x22603,x22604,x22605,x22602,x22606))
% 21.40/21.39 [2261]~E(x22611,x22612)+E(f658(x22613,x22614,x22615,x22616,x22611),f658(x22613,x22614,x22615,x22616,x22612))
% 21.40/21.39 [2262]~E(x22621,x22622)+E(f467(x22621,x22623),f467(x22622,x22623))
% 21.40/21.39 [2263]~E(x22631,x22632)+E(f467(x22633,x22631),f467(x22633,x22632))
% 21.40/21.39 [2264]~E(x22641,x22642)+E(f209(x22641,x22643,x22644,x22645),f209(x22642,x22643,x22644,x22645))
% 21.40/21.39 [2265]~E(x22651,x22652)+E(f209(x22653,x22651,x22654,x22655),f209(x22653,x22652,x22654,x22655))
% 21.40/21.39 [2266]~E(x22661,x22662)+E(f209(x22663,x22664,x22661,x22665),f209(x22663,x22664,x22662,x22665))
% 21.40/21.39 [2267]~E(x22671,x22672)+E(f209(x22673,x22674,x22675,x22671),f209(x22673,x22674,x22675,x22672))
% 21.40/21.39 [2268]~E(x22681,x22682)+E(f868(x22681,x22683),f868(x22682,x22683))
% 21.40/21.39 [2269]~E(x22691,x22692)+E(f868(x22693,x22691),f868(x22693,x22692))
% 21.40/21.39 [2270]~E(x22701,x22702)+E(f360(x22701,x22703),f360(x22702,x22703))
% 21.40/21.39 [2271]~E(x22711,x22712)+E(f360(x22713,x22711),f360(x22713,x22712))
% 21.40/21.39 [2272]~E(x22721,x22722)+E(f276(x22721,x22723,x22724,x22725),f276(x22722,x22723,x22724,x22725))
% 21.40/21.39 [2273]~E(x22731,x22732)+E(f276(x22733,x22731,x22734,x22735),f276(x22733,x22732,x22734,x22735))
% 21.40/21.39 [2274]~E(x22741,x22742)+E(f276(x22743,x22744,x22741,x22745),f276(x22743,x22744,x22742,x22745))
% 21.40/21.39 [2275]~E(x22751,x22752)+E(f276(x22753,x22754,x22755,x22751),f276(x22753,x22754,x22755,x22752))
% 21.40/21.39 [2276]~E(x22761,x22762)+E(f633(x22761,x22763,x22764),f633(x22762,x22763,x22764))
% 21.40/21.39 [2277]~E(x22771,x22772)+E(f633(x22773,x22771,x22774),f633(x22773,x22772,x22774))
% 21.40/21.39 [2278]~E(x22781,x22782)+E(f633(x22783,x22784,x22781),f633(x22783,x22784,x22782))
% 21.40/21.39 [2279]~E(x22791,x22792)+E(f675(x22791,x22793,x22794),f675(x22792,x22793,x22794))
% 21.40/21.39 [2280]~E(x22801,x22802)+E(f675(x22803,x22801,x22804),f675(x22803,x22802,x22804))
% 21.40/21.39 [2281]~E(x22811,x22812)+E(f675(x22813,x22814,x22811),f675(x22813,x22814,x22812))
% 21.40/21.39 [2282]~E(x22821,x22822)+E(f586(x22821,x22823,x22824,x22825,x22826),f586(x22822,x22823,x22824,x22825,x22826))
% 21.40/21.39 [2283]~E(x22831,x22832)+E(f586(x22833,x22831,x22834,x22835,x22836),f586(x22833,x22832,x22834,x22835,x22836))
% 21.40/21.39 [2284]~E(x22841,x22842)+E(f586(x22843,x22844,x22841,x22845,x22846),f586(x22843,x22844,x22842,x22845,x22846))
% 21.40/21.39 [2285]~E(x22851,x22852)+E(f586(x22853,x22854,x22855,x22851,x22856),f586(x22853,x22854,x22855,x22852,x22856))
% 21.40/21.39 [2286]~E(x22861,x22862)+E(f586(x22863,x22864,x22865,x22866,x22861),f586(x22863,x22864,x22865,x22866,x22862))
% 21.40/21.39 [2287]~E(x22871,x22872)+E(f613(x22871,x22873),f613(x22872,x22873))
% 21.40/21.39 [2288]~E(x22881,x22882)+E(f613(x22883,x22881),f613(x22883,x22882))
% 21.40/21.39 [2289]~E(x22891,x22892)+E(f440(x22891,x22893,x22894,x22895,x22896,x22897,x22898),f440(x22892,x22893,x22894,x22895,x22896,x22897,x22898))
% 21.40/21.39 [2290]~E(x22901,x22902)+E(f440(x22903,x22901,x22904,x22905,x22906,x22907,x22908),f440(x22903,x22902,x22904,x22905,x22906,x22907,x22908))
% 21.40/21.39 [2291]~E(x22911,x22912)+E(f440(x22913,x22914,x22911,x22915,x22916,x22917,x22918),f440(x22913,x22914,x22912,x22915,x22916,x22917,x22918))
% 21.40/21.39 [2292]~E(x22921,x22922)+E(f440(x22923,x22924,x22925,x22921,x22926,x22927,x22928),f440(x22923,x22924,x22925,x22922,x22926,x22927,x22928))
% 21.40/21.39 [2293]~E(x22931,x22932)+E(f440(x22933,x22934,x22935,x22936,x22931,x22937,x22938),f440(x22933,x22934,x22935,x22936,x22932,x22937,x22938))
% 21.40/21.39 [2294]~E(x22941,x22942)+E(f440(x22943,x22944,x22945,x22946,x22947,x22941,x22948),f440(x22943,x22944,x22945,x22946,x22947,x22942,x22948))
% 21.40/21.39 [2295]~E(x22951,x22952)+E(f440(x22953,x22954,x22955,x22956,x22957,x22958,x22951),f440(x22953,x22954,x22955,x22956,x22957,x22958,x22952))
% 21.40/21.39 [2296]~E(x22961,x22962)+E(f355(x22961,x22963,x22964,x22965,x22966),f355(x22962,x22963,x22964,x22965,x22966))
% 21.40/21.39 [2297]~E(x22971,x22972)+E(f355(x22973,x22971,x22974,x22975,x22976),f355(x22973,x22972,x22974,x22975,x22976))
% 21.40/21.39 [2298]~E(x22981,x22982)+E(f355(x22983,x22984,x22981,x22985,x22986),f355(x22983,x22984,x22982,x22985,x22986))
% 21.40/21.39 [2299]~E(x22991,x22992)+E(f355(x22993,x22994,x22995,x22991,x22996),f355(x22993,x22994,x22995,x22992,x22996))
% 21.40/21.39 [2300]~E(x23001,x23002)+E(f355(x23003,x23004,x23005,x23006,x23001),f355(x23003,x23004,x23005,x23006,x23002))
% 21.40/21.39 [2301]~E(x23011,x23012)+E(f514(x23011,x23013,x23014,x23015,x23016),f514(x23012,x23013,x23014,x23015,x23016))
% 21.40/21.39 [2302]~E(x23021,x23022)+E(f514(x23023,x23021,x23024,x23025,x23026),f514(x23023,x23022,x23024,x23025,x23026))
% 21.40/21.39 [2303]~E(x23031,x23032)+E(f514(x23033,x23034,x23031,x23035,x23036),f514(x23033,x23034,x23032,x23035,x23036))
% 21.40/21.39 [2304]~E(x23041,x23042)+E(f514(x23043,x23044,x23045,x23041,x23046),f514(x23043,x23044,x23045,x23042,x23046))
% 21.40/21.39 [2305]~E(x23051,x23052)+E(f514(x23053,x23054,x23055,x23056,x23051),f514(x23053,x23054,x23055,x23056,x23052))
% 21.40/21.39 [2306]~E(x23061,x23062)+E(f388(x23061,x23063,x23064),f388(x23062,x23063,x23064))
% 21.40/21.39 [2307]~E(x23071,x23072)+E(f388(x23073,x23071,x23074),f388(x23073,x23072,x23074))
% 21.40/21.39 [2308]~E(x23081,x23082)+E(f388(x23083,x23084,x23081),f388(x23083,x23084,x23082))
% 21.40/21.39 [2309]~E(x23091,x23092)+E(f820(x23091,x23093,x23094),f820(x23092,x23093,x23094))
% 21.40/21.39 [2310]~E(x23101,x23102)+E(f820(x23103,x23101,x23104),f820(x23103,x23102,x23104))
% 21.40/21.39 [2311]~E(x23111,x23112)+E(f820(x23113,x23114,x23111),f820(x23113,x23114,x23112))
% 21.40/21.39 [2312]~E(x23121,x23122)+E(f470(x23121,x23123,x23124,x23125),f470(x23122,x23123,x23124,x23125))
% 21.40/21.39 [2313]~E(x23131,x23132)+E(f470(x23133,x23131,x23134,x23135),f470(x23133,x23132,x23134,x23135))
% 21.40/21.39 [2314]~E(x23141,x23142)+E(f470(x23143,x23144,x23141,x23145),f470(x23143,x23144,x23142,x23145))
% 21.40/21.39 [2315]~E(x23151,x23152)+E(f470(x23153,x23154,x23155,x23151),f470(x23153,x23154,x23155,x23152))
% 21.40/21.39 [2316]~E(x23161,x23162)+E(f411(x23161,x23163,x23164),f411(x23162,x23163,x23164))
% 21.40/21.39 [2317]~E(x23171,x23172)+E(f411(x23173,x23171,x23174),f411(x23173,x23172,x23174))
% 21.40/21.39 [2318]~E(x23181,x23182)+E(f411(x23183,x23184,x23181),f411(x23183,x23184,x23182))
% 21.40/21.39 [2319]~E(x23191,x23192)+E(f382(x23191),f382(x23192))
% 21.40/21.39 [2320]~E(x23201,x23202)+E(f833(x23201,x23203,x23204),f833(x23202,x23203,x23204))
% 21.40/21.39 [2321]~E(x23211,x23212)+E(f833(x23213,x23211,x23214),f833(x23213,x23212,x23214))
% 21.40/21.39 [2322]~E(x23221,x23222)+E(f833(x23223,x23224,x23221),f833(x23223,x23224,x23222))
% 21.40/21.39 [2323]~E(x23231,x23232)+E(f695(x23231,x23233,x23234,x23235,x23236),f695(x23232,x23233,x23234,x23235,x23236))
% 21.40/21.39 [2324]~E(x23241,x23242)+E(f695(x23243,x23241,x23244,x23245,x23246),f695(x23243,x23242,x23244,x23245,x23246))
% 21.40/21.39 [2325]~E(x23251,x23252)+E(f695(x23253,x23254,x23251,x23255,x23256),f695(x23253,x23254,x23252,x23255,x23256))
% 21.40/21.39 [2326]~E(x23261,x23262)+E(f695(x23263,x23264,x23265,x23261,x23266),f695(x23263,x23264,x23265,x23262,x23266))
% 21.40/21.39 [2327]~E(x23271,x23272)+E(f695(x23273,x23274,x23275,x23276,x23271),f695(x23273,x23274,x23275,x23276,x23272))
% 21.40/21.39 [2328]~E(x23281,x23282)+E(f293(x23281,x23283),f293(x23282,x23283))
% 21.40/21.39 [2329]~E(x23291,x23292)+E(f293(x23293,x23291),f293(x23293,x23292))
% 21.40/21.39 [2330]~E(x23301,x23302)+E(f655(x23301,x23303,x23304),f655(x23302,x23303,x23304))
% 21.40/21.39 [2331]~E(x23311,x23312)+E(f655(x23313,x23311,x23314),f655(x23313,x23312,x23314))
% 21.40/21.39 [2332]~E(x23321,x23322)+E(f655(x23323,x23324,x23321),f655(x23323,x23324,x23322))
% 21.40/21.39 [2333]~E(x23331,x23332)+E(f414(x23331,x23333,x23334,x23335),f414(x23332,x23333,x23334,x23335))
% 21.40/21.39 [2334]~E(x23341,x23342)+E(f414(x23343,x23341,x23344,x23345),f414(x23343,x23342,x23344,x23345))
% 21.40/21.39 [2335]~E(x23351,x23352)+E(f414(x23353,x23354,x23351,x23355),f414(x23353,x23354,x23352,x23355))
% 21.40/21.39 [2336]~E(x23361,x23362)+E(f414(x23363,x23364,x23365,x23361),f414(x23363,x23364,x23365,x23362))
% 21.40/21.39 [2337]~E(x23371,x23372)+E(f563(x23371,x23373),f563(x23372,x23373))
% 21.40/21.39 [2338]~E(x23381,x23382)+E(f563(x23383,x23381),f563(x23383,x23382))
% 21.40/21.39 [2339]~E(x23391,x23392)+E(f506(x23391,x23393,x23394),f506(x23392,x23393,x23394))
% 21.40/21.39 [2340]~E(x23401,x23402)+E(f506(x23403,x23401,x23404),f506(x23403,x23402,x23404))
% 21.40/21.39 [2341]~E(x23411,x23412)+E(f506(x23413,x23414,x23411),f506(x23413,x23414,x23412))
% 21.40/21.39 [2342]~E(x23421,x23422)+E(f362(x23421,x23423,x23424,x23425),f362(x23422,x23423,x23424,x23425))
% 21.40/21.39 [2343]~E(x23431,x23432)+E(f362(x23433,x23431,x23434,x23435),f362(x23433,x23432,x23434,x23435))
% 21.40/21.39 [2344]~E(x23441,x23442)+E(f362(x23443,x23444,x23441,x23445),f362(x23443,x23444,x23442,x23445))
% 21.40/21.39 [2345]~E(x23451,x23452)+E(f362(x23453,x23454,x23455,x23451),f362(x23453,x23454,x23455,x23452))
% 21.40/21.39 [2346]~E(x23461,x23462)+E(f686(x23461,x23463),f686(x23462,x23463))
% 21.40/21.39 [2347]~E(x23471,x23472)+E(f686(x23473,x23471),f686(x23473,x23472))
% 21.40/21.39 [2348]~E(x23481,x23482)+E(f668(x23481,x23483,x23484),f668(x23482,x23483,x23484))
% 21.40/21.39 [2349]~E(x23491,x23492)+E(f668(x23493,x23491,x23494),f668(x23493,x23492,x23494))
% 21.40/21.39 [2350]~E(x23501,x23502)+E(f668(x23503,x23504,x23501),f668(x23503,x23504,x23502))
% 21.40/21.39 [2351]~E(x23511,x23512)+E(f442(x23511,x23513,x23514),f442(x23512,x23513,x23514))
% 21.40/21.39 [2352]~E(x23521,x23522)+E(f442(x23523,x23521,x23524),f442(x23523,x23522,x23524))
% 21.40/21.39 [2353]~E(x23531,x23532)+E(f442(x23533,x23534,x23531),f442(x23533,x23534,x23532))
% 21.40/21.39 [2354]~E(x23541,x23542)+E(f689(x23541,x23543,x23544,x23545),f689(x23542,x23543,x23544,x23545))
% 21.40/21.39 [2355]~E(x23551,x23552)+E(f689(x23553,x23551,x23554,x23555),f689(x23553,x23552,x23554,x23555))
% 21.40/21.39 [2356]~E(x23561,x23562)+E(f689(x23563,x23564,x23561,x23565),f689(x23563,x23564,x23562,x23565))
% 21.40/21.39 [2357]~E(x23571,x23572)+E(f689(x23573,x23574,x23575,x23571),f689(x23573,x23574,x23575,x23572))
% 21.40/21.39 [2358]~E(x23581,x23582)+E(f713(x23581,x23583,x23584,x23585,x23586),f713(x23582,x23583,x23584,x23585,x23586))
% 21.40/21.39 [2359]~E(x23591,x23592)+E(f713(x23593,x23591,x23594,x23595,x23596),f713(x23593,x23592,x23594,x23595,x23596))
% 21.40/21.39 [2360]~E(x23601,x23602)+E(f713(x23603,x23604,x23601,x23605,x23606),f713(x23603,x23604,x23602,x23605,x23606))
% 21.40/21.39 [2361]~E(x23611,x23612)+E(f713(x23613,x23614,x23615,x23611,x23616),f713(x23613,x23614,x23615,x23612,x23616))
% 21.40/21.39 [2362]~E(x23621,x23622)+E(f713(x23623,x23624,x23625,x23626,x23621),f713(x23623,x23624,x23625,x23626,x23622))
% 21.40/21.39 [2363]~E(x23631,x23632)+E(f381(x23631,x23633),f381(x23632,x23633))
% 21.40/21.39 [2364]~E(x23641,x23642)+E(f381(x23643,x23641),f381(x23643,x23642))
% 21.40/21.39 [2365]~E(x23651,x23652)+E(f680(x23651,x23653,x23654,x23655),f680(x23652,x23653,x23654,x23655))
% 21.40/21.39 [2366]~E(x23661,x23662)+E(f680(x23663,x23661,x23664,x23665),f680(x23663,x23662,x23664,x23665))
% 21.40/21.39 [2367]~E(x23671,x23672)+E(f680(x23673,x23674,x23671,x23675),f680(x23673,x23674,x23672,x23675))
% 21.40/21.39 [2368]~E(x23681,x23682)+E(f680(x23683,x23684,x23685,x23681),f680(x23683,x23684,x23685,x23682))
% 21.40/21.39 [2369]~E(x23691,x23692)+E(f347(x23691,x23693,x23694),f347(x23692,x23693,x23694))
% 21.40/21.39 [2370]~E(x23701,x23702)+E(f347(x23703,x23701,x23704),f347(x23703,x23702,x23704))
% 21.40/21.39 [2371]~E(x23711,x23712)+E(f347(x23713,x23714,x23711),f347(x23713,x23714,x23712))
% 21.40/21.39 [2372]~E(x23721,x23722)+E(f199(x23721,x23723,x23724,x23725),f199(x23722,x23723,x23724,x23725))
% 21.40/21.39 [2373]~E(x23731,x23732)+E(f199(x23733,x23731,x23734,x23735),f199(x23733,x23732,x23734,x23735))
% 21.40/21.39 [2374]~E(x23741,x23742)+E(f199(x23743,x23744,x23741,x23745),f199(x23743,x23744,x23742,x23745))
% 21.40/21.39 [2375]~E(x23751,x23752)+E(f199(x23753,x23754,x23755,x23751),f199(x23753,x23754,x23755,x23752))
% 21.40/21.39 [2376]~E(x23761,x23762)+E(f354(x23761,x23763,x23764,x23765,x23766),f354(x23762,x23763,x23764,x23765,x23766))
% 21.40/21.39 [2377]~E(x23771,x23772)+E(f354(x23773,x23771,x23774,x23775,x23776),f354(x23773,x23772,x23774,x23775,x23776))
% 21.40/21.39 [2378]~E(x23781,x23782)+E(f354(x23783,x23784,x23781,x23785,x23786),f354(x23783,x23784,x23782,x23785,x23786))
% 21.40/21.39 [2379]~E(x23791,x23792)+E(f354(x23793,x23794,x23795,x23791,x23796),f354(x23793,x23794,x23795,x23792,x23796))
% 21.40/21.39 [2380]~E(x23801,x23802)+E(f354(x23803,x23804,x23805,x23806,x23801),f354(x23803,x23804,x23805,x23806,x23802))
% 21.40/21.39 [2381]~E(x23811,x23812)+E(f755(x23811,x23813),f755(x23812,x23813))
% 21.40/21.39 [2382]~E(x23821,x23822)+E(f755(x23823,x23821),f755(x23823,x23822))
% 21.40/21.39 [2383]~E(x23831,x23832)+E(f558(x23831,x23833,x23834,x23835,x23836),f558(x23832,x23833,x23834,x23835,x23836))
% 21.40/21.39 [2384]~E(x23841,x23842)+E(f558(x23843,x23841,x23844,x23845,x23846),f558(x23843,x23842,x23844,x23845,x23846))
% 21.40/21.39 [2385]~E(x23851,x23852)+E(f558(x23853,x23854,x23851,x23855,x23856),f558(x23853,x23854,x23852,x23855,x23856))
% 21.40/21.39 [2386]~E(x23861,x23862)+E(f558(x23863,x23864,x23865,x23861,x23866),f558(x23863,x23864,x23865,x23862,x23866))
% 21.40/21.39 [2387]~E(x23871,x23872)+E(f558(x23873,x23874,x23875,x23876,x23871),f558(x23873,x23874,x23875,x23876,x23872))
% 21.40/21.39 [2388]~E(x23881,x23882)+E(f560(x23881,x23883,x23884,x23885,x23886),f560(x23882,x23883,x23884,x23885,x23886))
% 21.40/21.39 [2389]~E(x23891,x23892)+E(f560(x23893,x23891,x23894,x23895,x23896),f560(x23893,x23892,x23894,x23895,x23896))
% 21.40/21.39 [2390]~E(x23901,x23902)+E(f560(x23903,x23904,x23901,x23905,x23906),f560(x23903,x23904,x23902,x23905,x23906))
% 21.40/21.39 [2391]~E(x23911,x23912)+E(f560(x23913,x23914,x23915,x23911,x23916),f560(x23913,x23914,x23915,x23912,x23916))
% 21.40/21.39 [2392]~E(x23921,x23922)+E(f560(x23923,x23924,x23925,x23926,x23921),f560(x23923,x23924,x23925,x23926,x23922))
% 21.40/21.39 [2393]~E(x23931,x23932)+E(f589(x23931),f589(x23932))
% 21.40/21.39 [2394]~E(x23941,x23942)+E(f575(x23941,x23943),f575(x23942,x23943))
% 21.40/21.39 [2395]~E(x23951,x23952)+E(f575(x23953,x23951),f575(x23953,x23952))
% 21.40/21.39 [2396]~E(x23961,x23962)+E(f794(x23961),f794(x23962))
% 21.40/21.39 [2397]~E(x23971,x23972)+E(f659(x23971,x23973,x23974,x23975,x23976,x23977,x23978),f659(x23972,x23973,x23974,x23975,x23976,x23977,x23978))
% 21.40/21.39 [2398]~E(x23981,x23982)+E(f659(x23983,x23981,x23984,x23985,x23986,x23987,x23988),f659(x23983,x23982,x23984,x23985,x23986,x23987,x23988))
% 21.40/21.39 [2399]~E(x23991,x23992)+E(f659(x23993,x23994,x23991,x23995,x23996,x23997,x23998),f659(x23993,x23994,x23992,x23995,x23996,x23997,x23998))
% 21.40/21.39 [2400]~E(x24001,x24002)+E(f659(x24003,x24004,x24005,x24001,x24006,x24007,x24008),f659(x24003,x24004,x24005,x24002,x24006,x24007,x24008))
% 21.40/21.39 [2401]~E(x24011,x24012)+E(f659(x24013,x24014,x24015,x24016,x24011,x24017,x24018),f659(x24013,x24014,x24015,x24016,x24012,x24017,x24018))
% 21.40/21.39 [2402]~E(x24021,x24022)+E(f659(x24023,x24024,x24025,x24026,x24027,x24021,x24028),f659(x24023,x24024,x24025,x24026,x24027,x24022,x24028))
% 21.40/21.39 [2403]~E(x24031,x24032)+E(f659(x24033,x24034,x24035,x24036,x24037,x24038,x24031),f659(x24033,x24034,x24035,x24036,x24037,x24038,x24032))
% 21.40/21.39 [2404]~E(x24041,x24042)+E(f413(x24041,x24043,x24044,x24045,x24046,x24047),f413(x24042,x24043,x24044,x24045,x24046,x24047))
% 21.40/21.39 [2405]~E(x24051,x24052)+E(f413(x24053,x24051,x24054,x24055,x24056,x24057),f413(x24053,x24052,x24054,x24055,x24056,x24057))
% 21.40/21.39 [2406]~E(x24061,x24062)+E(f413(x24063,x24064,x24061,x24065,x24066,x24067),f413(x24063,x24064,x24062,x24065,x24066,x24067))
% 21.40/21.39 [2407]~E(x24071,x24072)+E(f413(x24073,x24074,x24075,x24071,x24076,x24077),f413(x24073,x24074,x24075,x24072,x24076,x24077))
% 21.40/21.39 [2408]~E(x24081,x24082)+E(f413(x24083,x24084,x24085,x24086,x24081,x24087),f413(x24083,x24084,x24085,x24086,x24082,x24087))
% 21.40/21.39 [2409]~E(x24091,x24092)+E(f413(x24093,x24094,x24095,x24096,x24097,x24091),f413(x24093,x24094,x24095,x24096,x24097,x24092))
% 21.40/21.39 [2410]~E(x24101,x24102)+E(f518(x24101,x24103,x24104,x24105,x24106),f518(x24102,x24103,x24104,x24105,x24106))
% 21.40/21.39 [2411]~E(x24111,x24112)+E(f518(x24113,x24111,x24114,x24115,x24116),f518(x24113,x24112,x24114,x24115,x24116))
% 21.40/21.39 [2412]~E(x24121,x24122)+E(f518(x24123,x24124,x24121,x24125,x24126),f518(x24123,x24124,x24122,x24125,x24126))
% 21.40/21.39 [2413]~E(x24131,x24132)+E(f518(x24133,x24134,x24135,x24131,x24136),f518(x24133,x24134,x24135,x24132,x24136))
% 21.40/21.39 [2414]~E(x24141,x24142)+E(f518(x24143,x24144,x24145,x24146,x24141),f518(x24143,x24144,x24145,x24146,x24142))
% 21.40/21.39 [2415]~E(x24151,x24152)+E(f505(x24151,x24153,x24154,x24155,x24156,x24157),f505(x24152,x24153,x24154,x24155,x24156,x24157))
% 21.40/21.39 [2416]~E(x24161,x24162)+E(f505(x24163,x24161,x24164,x24165,x24166,x24167),f505(x24163,x24162,x24164,x24165,x24166,x24167))
% 21.40/21.39 [2417]~E(x24171,x24172)+E(f505(x24173,x24174,x24171,x24175,x24176,x24177),f505(x24173,x24174,x24172,x24175,x24176,x24177))
% 21.40/21.39 [2418]~E(x24181,x24182)+E(f505(x24183,x24184,x24185,x24181,x24186,x24187),f505(x24183,x24184,x24185,x24182,x24186,x24187))
% 21.40/21.39 [2419]~E(x24191,x24192)+E(f505(x24193,x24194,x24195,x24196,x24191,x24197),f505(x24193,x24194,x24195,x24196,x24192,x24197))
% 21.40/21.39 [2420]~E(x24201,x24202)+E(f505(x24203,x24204,x24205,x24206,x24207,x24201),f505(x24203,x24204,x24205,x24206,x24207,x24202))
% 21.40/21.39 [2421]~E(x24211,x24212)+E(f742(x24211,x24213),f742(x24212,x24213))
% 21.40/21.39 [2422]~E(x24221,x24222)+E(f742(x24223,x24221),f742(x24223,x24222))
% 21.40/21.39 [2423]~E(x24231,x24232)+E(f667(x24231,x24233,x24234),f667(x24232,x24233,x24234))
% 21.40/21.39 [2424]~E(x24241,x24242)+E(f667(x24243,x24241,x24244),f667(x24243,x24242,x24244))
% 21.40/21.39 [2425]~E(x24251,x24252)+E(f667(x24253,x24254,x24251),f667(x24253,x24254,x24252))
% 21.40/21.39 [2426]~E(x24261,x24262)+E(f780(x24261,x24263,x24264),f780(x24262,x24263,x24264))
% 21.40/21.39 [2427]~E(x24271,x24272)+E(f780(x24273,x24271,x24274),f780(x24273,x24272,x24274))
% 21.40/21.39 [2428]~E(x24281,x24282)+E(f780(x24283,x24284,x24281),f780(x24283,x24284,x24282))
% 21.40/21.39 [2429]~E(x24291,x24292)+E(f423(x24291,x24293,x24294,x24295,x24296),f423(x24292,x24293,x24294,x24295,x24296))
% 21.40/21.39 [2430]~E(x24301,x24302)+E(f423(x24303,x24301,x24304,x24305,x24306),f423(x24303,x24302,x24304,x24305,x24306))
% 21.40/21.39 [2431]~E(x24311,x24312)+E(f423(x24313,x24314,x24311,x24315,x24316),f423(x24313,x24314,x24312,x24315,x24316))
% 21.40/21.39 [2432]~E(x24321,x24322)+E(f423(x24323,x24324,x24325,x24321,x24326),f423(x24323,x24324,x24325,x24322,x24326))
% 21.40/21.39 [2433]~E(x24331,x24332)+E(f423(x24333,x24334,x24335,x24336,x24331),f423(x24333,x24334,x24335,x24336,x24332))
% 21.40/21.39 [2434]~E(x24341,x24342)+E(f508(x24341,x24343),f508(x24342,x24343))
% 21.40/21.39 [2435]~E(x24351,x24352)+E(f508(x24353,x24351),f508(x24353,x24352))
% 21.40/21.39 [2436]~E(x24361,x24362)+E(f831(x24361,x24363,x24364),f831(x24362,x24363,x24364))
% 21.40/21.39 [2437]~E(x24371,x24372)+E(f831(x24373,x24371,x24374),f831(x24373,x24372,x24374))
% 21.40/21.39 [2438]~E(x24381,x24382)+E(f831(x24383,x24384,x24381),f831(x24383,x24384,x24382))
% 21.40/21.39 [2439]~E(x24391,x24392)+E(f666(x24391,x24393),f666(x24392,x24393))
% 21.40/21.39 [2440]~E(x24401,x24402)+E(f666(x24403,x24401),f666(x24403,x24402))
% 21.40/21.39 [2441]~E(x24411,x24412)+E(f431(x24411,x24413,x24414,x24415,x24416,x24417,x24418),f431(x24412,x24413,x24414,x24415,x24416,x24417,x24418))
% 21.40/21.39 [2442]~E(x24421,x24422)+E(f431(x24423,x24421,x24424,x24425,x24426,x24427,x24428),f431(x24423,x24422,x24424,x24425,x24426,x24427,x24428))
% 21.40/21.39 [2443]~E(x24431,x24432)+E(f431(x24433,x24434,x24431,x24435,x24436,x24437,x24438),f431(x24433,x24434,x24432,x24435,x24436,x24437,x24438))
% 21.40/21.39 [2444]~E(x24441,x24442)+E(f431(x24443,x24444,x24445,x24441,x24446,x24447,x24448),f431(x24443,x24444,x24445,x24442,x24446,x24447,x24448))
% 21.40/21.39 [2445]~E(x24451,x24452)+E(f431(x24453,x24454,x24455,x24456,x24451,x24457,x24458),f431(x24453,x24454,x24455,x24456,x24452,x24457,x24458))
% 21.40/21.39 [2446]~E(x24461,x24462)+E(f431(x24463,x24464,x24465,x24466,x24467,x24461,x24468),f431(x24463,x24464,x24465,x24466,x24467,x24462,x24468))
% 21.40/21.39 [2447]~E(x24471,x24472)+E(f431(x24473,x24474,x24475,x24476,x24477,x24478,x24471),f431(x24473,x24474,x24475,x24476,x24477,x24478,x24472))
% 21.40/21.39 [2448]~E(x24481,x24482)+E(f687(x24481,x24483,x24484,x24485,x24486,x24487),f687(x24482,x24483,x24484,x24485,x24486,x24487))
% 21.40/21.39 [2449]~E(x24491,x24492)+E(f687(x24493,x24491,x24494,x24495,x24496,x24497),f687(x24493,x24492,x24494,x24495,x24496,x24497))
% 21.40/21.39 [2450]~E(x24501,x24502)+E(f687(x24503,x24504,x24501,x24505,x24506,x24507),f687(x24503,x24504,x24502,x24505,x24506,x24507))
% 21.40/21.39 [2451]~E(x24511,x24512)+E(f687(x24513,x24514,x24515,x24511,x24516,x24517),f687(x24513,x24514,x24515,x24512,x24516,x24517))
% 21.40/21.39 [2452]~E(x24521,x24522)+E(f687(x24523,x24524,x24525,x24526,x24521,x24527),f687(x24523,x24524,x24525,x24526,x24522,x24527))
% 21.40/21.39 [2453]~E(x24531,x24532)+E(f687(x24533,x24534,x24535,x24536,x24537,x24531),f687(x24533,x24534,x24535,x24536,x24537,x24532))
% 21.40/21.39 [2454]~E(x24541,x24542)+E(f656(x24541,x24543,x24544),f656(x24542,x24543,x24544))
% 21.40/21.39 [2455]~E(x24551,x24552)+E(f656(x24553,x24551,x24554),f656(x24553,x24552,x24554))
% 21.40/21.39 [2456]~E(x24561,x24562)+E(f656(x24563,x24564,x24561),f656(x24563,x24564,x24562))
% 21.40/21.39 [2457]~E(x24571,x24572)+E(f819(x24571,x24573,x24574),f819(x24572,x24573,x24574))
% 21.40/21.39 [2458]~E(x24581,x24582)+E(f819(x24583,x24581,x24584),f819(x24583,x24582,x24584))
% 21.40/21.39 [2459]~E(x24591,x24592)+E(f819(x24593,x24594,x24591),f819(x24593,x24594,x24592))
% 21.40/21.39 [2460]~E(x24601,x24602)+E(f804(x24601),f804(x24602))
% 21.40/21.39 [2461]~E(x24611,x24612)+E(f212(x24611,x24613,x24614,x24615),f212(x24612,x24613,x24614,x24615))
% 21.40/21.39 [2462]~E(x24621,x24622)+E(f212(x24623,x24621,x24624,x24625),f212(x24623,x24622,x24624,x24625))
% 21.40/21.39 [2463]~E(x24631,x24632)+E(f212(x24633,x24634,x24631,x24635),f212(x24633,x24634,x24632,x24635))
% 21.40/21.39 [2464]~E(x24641,x24642)+E(f212(x24643,x24644,x24645,x24641),f212(x24643,x24644,x24645,x24642))
% 21.40/21.39 [2465]~E(x24651,x24652)+E(f564(x24651),f564(x24652))
% 21.40/21.39 [2466]~E(x24661,x24662)+E(f604(x24661,x24663,x24664,x24665),f604(x24662,x24663,x24664,x24665))
% 21.40/21.39 [2467]~E(x24671,x24672)+E(f604(x24673,x24671,x24674,x24675),f604(x24673,x24672,x24674,x24675))
% 21.40/21.39 [2468]~E(x24681,x24682)+E(f604(x24683,x24684,x24681,x24685),f604(x24683,x24684,x24682,x24685))
% 21.40/21.39 [2469]~E(x24691,x24692)+E(f604(x24693,x24694,x24695,x24691),f604(x24693,x24694,x24695,x24692))
% 21.40/21.39 [2470]~E(x24701,x24702)+E(f316(x24701,x24703,x24704),f316(x24702,x24703,x24704))
% 21.40/21.39 [2471]~E(x24711,x24712)+E(f316(x24713,x24711,x24714),f316(x24713,x24712,x24714))
% 21.40/21.39 [2472]~E(x24721,x24722)+E(f316(x24723,x24724,x24721),f316(x24723,x24724,x24722))
% 21.40/21.39 [2473]~E(x24731,x24732)+E(f270(x24731,x24733,x24734),f270(x24732,x24733,x24734))
% 21.40/21.39 [2474]~E(x24741,x24742)+E(f270(x24743,x24741,x24744),f270(x24743,x24742,x24744))
% 21.40/21.39 [2475]~E(x24751,x24752)+E(f270(x24753,x24754,x24751),f270(x24753,x24754,x24752))
% 21.40/21.39 [2476]~E(x24761,x24762)+E(f840(x24761,x24763,x24764),f840(x24762,x24763,x24764))
% 21.40/21.39 [2477]~E(x24771,x24772)+E(f840(x24773,x24771,x24774),f840(x24773,x24772,x24774))
% 21.40/21.39 [2478]~E(x24781,x24782)+E(f840(x24783,x24784,x24781),f840(x24783,x24784,x24782))
% 21.40/21.39 [2479]~E(x24791,x24792)+E(f24(x24791,x24793),f24(x24792,x24793))
% 21.40/21.39 [2480]~E(x24801,x24802)+E(f24(x24803,x24801),f24(x24803,x24802))
% 21.40/21.39 [2481]~E(x24811,x24812)+E(f551(x24811,x24813,x24814),f551(x24812,x24813,x24814))
% 21.40/21.39 [2482]~E(x24821,x24822)+E(f551(x24823,x24821,x24824),f551(x24823,x24822,x24824))
% 21.40/21.39 [2483]~E(x24831,x24832)+E(f551(x24833,x24834,x24831),f551(x24833,x24834,x24832))
% 21.40/21.39 [2484]~E(x24841,x24842)+E(f19(x24841,x24843,x24844,x24845),f19(x24842,x24843,x24844,x24845))
% 21.40/21.39 [2485]~E(x24851,x24852)+E(f19(x24853,x24851,x24854,x24855),f19(x24853,x24852,x24854,x24855))
% 21.40/21.39 [2486]~E(x24861,x24862)+E(f19(x24863,x24864,x24861,x24865),f19(x24863,x24864,x24862,x24865))
% 21.40/21.39 [2487]~E(x24871,x24872)+E(f19(x24873,x24874,x24875,x24871),f19(x24873,x24874,x24875,x24872))
% 21.40/21.39 [2488]~E(x24881,x24882)+E(f599(x24881,x24883),f599(x24882,x24883))
% 21.40/21.39 [2489]~E(x24891,x24892)+E(f599(x24893,x24891),f599(x24893,x24892))
% 21.40/21.39 [2490]~E(x24901,x24902)+E(f552(x24901,x24903,x24904,x24905),f552(x24902,x24903,x24904,x24905))
% 21.40/21.39 [2491]~E(x24911,x24912)+E(f552(x24913,x24911,x24914,x24915),f552(x24913,x24912,x24914,x24915))
% 21.40/21.39 [2492]~E(x24921,x24922)+E(f552(x24923,x24924,x24921,x24925),f552(x24923,x24924,x24922,x24925))
% 21.40/21.39 [2493]~E(x24931,x24932)+E(f552(x24933,x24934,x24935,x24931),f552(x24933,x24934,x24935,x24932))
% 21.40/21.39 [2494]~E(x24941,x24942)+E(f644(x24941,x24943),f644(x24942,x24943))
% 21.40/21.39 [2495]~E(x24951,x24952)+E(f644(x24953,x24951),f644(x24953,x24952))
% 21.40/21.39 [2496]~E(x24961,x24962)+E(f786(x24961,x24963,x24964,x24965),f786(x24962,x24963,x24964,x24965))
% 21.40/21.39 [2497]~E(x24971,x24972)+E(f786(x24973,x24971,x24974,x24975),f786(x24973,x24972,x24974,x24975))
% 21.40/21.39 [2498]~E(x24981,x24982)+E(f786(x24983,x24984,x24981,x24985),f786(x24983,x24984,x24982,x24985))
% 21.40/21.39 [2499]~E(x24991,x24992)+E(f786(x24993,x24994,x24995,x24991),f786(x24993,x24994,x24995,x24992))
% 21.40/21.39 [2500]~E(x25001,x25002)+E(f677(x25001,x25003),f677(x25002,x25003))
% 21.40/21.39 [2501]~E(x25011,x25012)+E(f677(x25013,x25011),f677(x25013,x25012))
% 21.40/21.39 [2502]~E(x25021,x25022)+E(f392(x25021,x25023,x25024,x25025,x25026),f392(x25022,x25023,x25024,x25025,x25026))
% 21.40/21.39 [2503]~E(x25031,x25032)+E(f392(x25033,x25031,x25034,x25035,x25036),f392(x25033,x25032,x25034,x25035,x25036))
% 21.40/21.39 [2504]~E(x25041,x25042)+E(f392(x25043,x25044,x25041,x25045,x25046),f392(x25043,x25044,x25042,x25045,x25046))
% 21.40/21.39 [2505]~E(x25051,x25052)+E(f392(x25053,x25054,x25055,x25051,x25056),f392(x25053,x25054,x25055,x25052,x25056))
% 21.40/21.39 [2506]~E(x25061,x25062)+E(f392(x25063,x25064,x25065,x25066,x25061),f392(x25063,x25064,x25065,x25066,x25062))
% 21.40/21.39 [2507]~E(x25071,x25072)+E(f376(x25071),f376(x25072))
% 21.40/21.39 [2508]~E(x25081,x25082)+E(f630(x25081,x25083,x25084),f630(x25082,x25083,x25084))
% 21.40/21.39 [2509]~E(x25091,x25092)+E(f630(x25093,x25091,x25094),f630(x25093,x25092,x25094))
% 21.40/21.39 [2510]~E(x25101,x25102)+E(f630(x25103,x25104,x25101),f630(x25103,x25104,x25102))
% 21.40/21.39 [2511]~E(x25111,x25112)+E(f723(x25111,x25113,x25114,x25115,x25116),f723(x25112,x25113,x25114,x25115,x25116))
% 21.40/21.39 [2512]~E(x25121,x25122)+E(f723(x25123,x25121,x25124,x25125,x25126),f723(x25123,x25122,x25124,x25125,x25126))
% 21.40/21.39 [2513]~E(x25131,x25132)+E(f723(x25133,x25134,x25131,x25135,x25136),f723(x25133,x25134,x25132,x25135,x25136))
% 21.40/21.39 [2514]~E(x25141,x25142)+E(f723(x25143,x25144,x25145,x25141,x25146),f723(x25143,x25144,x25145,x25142,x25146))
% 21.40/21.39 [2515]~E(x25151,x25152)+E(f723(x25153,x25154,x25155,x25156,x25151),f723(x25153,x25154,x25155,x25156,x25152))
% 21.40/21.39 [2516]~E(x25161,x25162)+E(f104(x25161,x25163,x25164,x25165),f104(x25162,x25163,x25164,x25165))
% 21.40/21.39 [2517]~E(x25171,x25172)+E(f104(x25173,x25171,x25174,x25175),f104(x25173,x25172,x25174,x25175))
% 21.40/21.39 [2518]~E(x25181,x25182)+E(f104(x25183,x25184,x25181,x25185),f104(x25183,x25184,x25182,x25185))
% 21.40/21.39 [2519]~E(x25191,x25192)+E(f104(x25193,x25194,x25195,x25191),f104(x25193,x25194,x25195,x25192))
% 21.40/21.39 [2520]~E(x25201,x25202)+E(f262(x25201,x25203,x25204,x25205,x25206),f262(x25202,x25203,x25204,x25205,x25206))
% 21.40/21.39 [2521]~E(x25211,x25212)+E(f262(x25213,x25211,x25214,x25215,x25216),f262(x25213,x25212,x25214,x25215,x25216))
% 21.40/21.39 [2522]~E(x25221,x25222)+E(f262(x25223,x25224,x25221,x25225,x25226),f262(x25223,x25224,x25222,x25225,x25226))
% 21.40/21.39 [2523]~E(x25231,x25232)+E(f262(x25233,x25234,x25235,x25231,x25236),f262(x25233,x25234,x25235,x25232,x25236))
% 21.40/21.39 [2524]~E(x25241,x25242)+E(f262(x25243,x25244,x25245,x25246,x25241),f262(x25243,x25244,x25245,x25246,x25242))
% 21.40/21.39 [2525]~E(x25251,x25252)+E(f849(x25251,x25253,x25254),f849(x25252,x25253,x25254))
% 21.40/21.39 [2526]~E(x25261,x25262)+E(f849(x25263,x25261,x25264),f849(x25263,x25262,x25264))
% 21.40/21.39 [2527]~E(x25271,x25272)+E(f849(x25273,x25274,x25271),f849(x25273,x25274,x25272))
% 21.40/21.39 [2528]~E(x25281,x25282)+E(f465(x25281,x25283,x25284,x25285),f465(x25282,x25283,x25284,x25285))
% 21.40/21.39 [2529]~E(x25291,x25292)+E(f465(x25293,x25291,x25294,x25295),f465(x25293,x25292,x25294,x25295))
% 21.40/21.39 [2530]~E(x25301,x25302)+E(f465(x25303,x25304,x25301,x25305),f465(x25303,x25304,x25302,x25305))
% 21.40/21.39 [2531]~E(x25311,x25312)+E(f465(x25313,x25314,x25315,x25311),f465(x25313,x25314,x25315,x25312))
% 21.40/21.39 [2532]~E(x25321,x25322)+E(f584(x25321,x25323),f584(x25322,x25323))
% 21.40/21.39 [2533]~E(x25331,x25332)+E(f584(x25333,x25331),f584(x25333,x25332))
% 21.40/21.39 [2534]~E(x25341,x25342)+E(f850(x25341,x25343,x25344),f850(x25342,x25343,x25344))
% 21.40/21.39 [2535]~E(x25351,x25352)+E(f850(x25353,x25351,x25354),f850(x25353,x25352,x25354))
% 21.40/21.39 [2536]~E(x25361,x25362)+E(f850(x25363,x25364,x25361),f850(x25363,x25364,x25362))
% 21.40/21.39 [2537]~E(x25371,x25372)+E(f610(x25371),f610(x25372))
% 21.40/21.39 [2538]~E(x25381,x25382)+E(f619(x25381,x25383,x25384),f619(x25382,x25383,x25384))
% 21.40/21.39 [2539]~E(x25391,x25392)+E(f619(x25393,x25391,x25394),f619(x25393,x25392,x25394))
% 21.40/21.39 [2540]~E(x25401,x25402)+E(f619(x25403,x25404,x25401),f619(x25403,x25404,x25402))
% 21.40/21.39 [2541]~E(x25411,x25412)+E(f130(x25411),f130(x25412))
% 21.40/21.39 [2542]~E(x25421,x25422)+E(f345(x25421),f345(x25422))
% 21.40/21.39 [2543]~E(x25431,x25432)+E(f227(x25431,x25433,x25434,x25435,x25436),f227(x25432,x25433,x25434,x25435,x25436))
% 21.40/21.39 [2544]~E(x25441,x25442)+E(f227(x25443,x25441,x25444,x25445,x25446),f227(x25443,x25442,x25444,x25445,x25446))
% 21.40/21.39 [2545]~E(x25451,x25452)+E(f227(x25453,x25454,x25451,x25455,x25456),f227(x25453,x25454,x25452,x25455,x25456))
% 21.40/21.39 [2546]~E(x25461,x25462)+E(f227(x25463,x25464,x25465,x25461,x25466),f227(x25463,x25464,x25465,x25462,x25466))
% 21.40/21.39 [2547]~E(x25471,x25472)+E(f227(x25473,x25474,x25475,x25476,x25471),f227(x25473,x25474,x25475,x25476,x25472))
% 21.40/21.39 [2548]~E(x25481,x25482)+E(f704(x25481,x25483),f704(x25482,x25483))
% 21.40/21.39 [2549]~E(x25491,x25492)+E(f704(x25493,x25491),f704(x25493,x25492))
% 21.40/21.39 [2550]~E(x25501,x25502)+E(f424(x25501,x25503,x25504,x25505,x25506),f424(x25502,x25503,x25504,x25505,x25506))
% 21.40/21.39 [2551]~E(x25511,x25512)+E(f424(x25513,x25511,x25514,x25515,x25516),f424(x25513,x25512,x25514,x25515,x25516))
% 21.40/21.39 [2552]~E(x25521,x25522)+E(f424(x25523,x25524,x25521,x25525,x25526),f424(x25523,x25524,x25522,x25525,x25526))
% 21.40/21.39 [2553]~E(x25531,x25532)+E(f424(x25533,x25534,x25535,x25531,x25536),f424(x25533,x25534,x25535,x25532,x25536))
% 21.40/21.39 [2554]~E(x25541,x25542)+E(f424(x25543,x25544,x25545,x25546,x25541),f424(x25543,x25544,x25545,x25546,x25542))
% 21.40/21.39 [2555]~E(x25551,x25552)+E(f460(x25551,x25553,x25554,x25555,x25556),f460(x25552,x25553,x25554,x25555,x25556))
% 21.40/21.39 [2556]~E(x25561,x25562)+E(f460(x25563,x25561,x25564,x25565,x25566),f460(x25563,x25562,x25564,x25565,x25566))
% 21.40/21.39 [2557]~E(x25571,x25572)+E(f460(x25573,x25574,x25571,x25575,x25576),f460(x25573,x25574,x25572,x25575,x25576))
% 21.40/21.39 [2558]~E(x25581,x25582)+E(f460(x25583,x25584,x25585,x25581,x25586),f460(x25583,x25584,x25585,x25582,x25586))
% 21.40/21.39 [2559]~E(x25591,x25592)+E(f460(x25593,x25594,x25595,x25596,x25591),f460(x25593,x25594,x25595,x25596,x25592))
% 21.40/21.39 [2560]~E(x25601,x25602)+E(f741(x25601),f741(x25602))
% 21.40/21.39 [2561]~E(x25611,x25612)+E(f455(x25611,x25613,x25614,x25615,x25616),f455(x25612,x25613,x25614,x25615,x25616))
% 21.40/21.39 [2562]~E(x25621,x25622)+E(f455(x25623,x25621,x25624,x25625,x25626),f455(x25623,x25622,x25624,x25625,x25626))
% 21.40/21.39 [2563]~E(x25631,x25632)+E(f455(x25633,x25634,x25631,x25635,x25636),f455(x25633,x25634,x25632,x25635,x25636))
% 21.40/21.39 [2564]~E(x25641,x25642)+E(f455(x25643,x25644,x25645,x25641,x25646),f455(x25643,x25644,x25645,x25642,x25646))
% 21.40/21.39 [2565]~E(x25651,x25652)+E(f455(x25653,x25654,x25655,x25656,x25651),f455(x25653,x25654,x25655,x25656,x25652))
% 21.40/21.39 [2566]~E(x25661,x25662)+E(f131(x25661),f131(x25662))
% 21.40/21.39 [2567]~E(x25671,x25672)+E(f320(x25671,x25673,x25674),f320(x25672,x25673,x25674))
% 21.40/21.39 [2568]~E(x25681,x25682)+E(f320(x25683,x25681,x25684),f320(x25683,x25682,x25684))
% 21.40/21.39 [2569]~E(x25691,x25692)+E(f320(x25693,x25694,x25691),f320(x25693,x25694,x25692))
% 21.40/21.39 [2570]~E(x25701,x25702)+E(f601(x25701,x25703),f601(x25702,x25703))
% 21.40/21.39 [2571]~E(x25711,x25712)+E(f601(x25713,x25711),f601(x25713,x25712))
% 21.40/21.39 [2572]~E(x25721,x25722)+E(f407(x25721,x25723,x25724,x25725),f407(x25722,x25723,x25724,x25725))
% 21.40/21.39 [2573]~E(x25731,x25732)+E(f407(x25733,x25731,x25734,x25735),f407(x25733,x25732,x25734,x25735))
% 21.40/21.39 [2574]~E(x25741,x25742)+E(f407(x25743,x25744,x25741,x25745),f407(x25743,x25744,x25742,x25745))
% 21.40/21.39 [2575]~E(x25751,x25752)+E(f407(x25753,x25754,x25755,x25751),f407(x25753,x25754,x25755,x25752))
% 21.40/21.39 [2576]~E(x25761,x25762)+E(f743(x25761,x25763,x25764),f743(x25762,x25763,x25764))
% 21.40/21.39 [2577]~E(x25771,x25772)+E(f743(x25773,x25771,x25774),f743(x25773,x25772,x25774))
% 21.40/21.39 [2578]~E(x25781,x25782)+E(f743(x25783,x25784,x25781),f743(x25783,x25784,x25782))
% 21.40/21.39 [2579]~E(x25791,x25792)+E(f230(x25791,x25793,x25794,x25795),f230(x25792,x25793,x25794,x25795))
% 21.40/21.39 [2580]~E(x25801,x25802)+E(f230(x25803,x25801,x25804,x25805),f230(x25803,x25802,x25804,x25805))
% 21.40/21.39 [2581]~E(x25811,x25812)+E(f230(x25813,x25814,x25811,x25815),f230(x25813,x25814,x25812,x25815))
% 21.40/21.39 [2582]~E(x25821,x25822)+E(f230(x25823,x25824,x25825,x25821),f230(x25823,x25824,x25825,x25822))
% 21.40/21.39 [2583]~E(x25831,x25832)+E(f510(x25831,x25833,x25834,x25835,x25836),f510(x25832,x25833,x25834,x25835,x25836))
% 21.40/21.39 [2584]~E(x25841,x25842)+E(f510(x25843,x25841,x25844,x25845,x25846),f510(x25843,x25842,x25844,x25845,x25846))
% 21.40/21.39 [2585]~E(x25851,x25852)+E(f510(x25853,x25854,x25851,x25855,x25856),f510(x25853,x25854,x25852,x25855,x25856))
% 21.40/21.39 [2586]~E(x25861,x25862)+E(f510(x25863,x25864,x25865,x25861,x25866),f510(x25863,x25864,x25865,x25862,x25866))
% 21.40/21.39 [2587]~E(x25871,x25872)+E(f510(x25873,x25874,x25875,x25876,x25871),f510(x25873,x25874,x25875,x25876,x25872))
% 21.40/21.40 [2588]~E(x25881,x25882)+E(f728(x25881,x25883,x25884,x25885,x25886),f728(x25882,x25883,x25884,x25885,x25886))
% 21.40/21.40 [2589]~E(x25891,x25892)+E(f728(x25893,x25891,x25894,x25895,x25896),f728(x25893,x25892,x25894,x25895,x25896))
% 21.40/21.40 [2590]~E(x25901,x25902)+E(f728(x25903,x25904,x25901,x25905,x25906),f728(x25903,x25904,x25902,x25905,x25906))
% 21.40/21.40 [2591]~E(x25911,x25912)+E(f728(x25913,x25914,x25915,x25911,x25916),f728(x25913,x25914,x25915,x25912,x25916))
% 21.40/21.40 [2592]~E(x25921,x25922)+E(f728(x25923,x25924,x25925,x25926,x25921),f728(x25923,x25924,x25925,x25926,x25922))
% 21.40/21.40 [2593]~E(x25931,x25932)+E(f229(x25931,x25933,x25934),f229(x25932,x25933,x25934))
% 21.40/21.40 [2594]~E(x25941,x25942)+E(f229(x25943,x25941,x25944),f229(x25943,x25942,x25944))
% 21.40/21.40 [2595]~E(x25951,x25952)+E(f229(x25953,x25954,x25951),f229(x25953,x25954,x25952))
% 21.40/21.40 [2596]~P1(x25961)+P1(x25962)+~E(x25961,x25962)
% 21.40/21.40 [2597]~P2(x25971)+P2(x25972)+~E(x25971,x25972)
% 21.40/21.40 [2598]~P88(x25981)+P88(x25982)+~E(x25981,x25982)
% 21.40/21.40 [2599]P36(x25992,x25993)+~E(x25991,x25992)+~P36(x25991,x25993)
% 21.40/21.40 [2600]P36(x26003,x26002)+~E(x26001,x26002)+~P36(x26003,x26001)
% 21.40/21.40 [2601]~P3(x26011)+P3(x26012)+~E(x26011,x26012)
% 21.40/21.40 [2602]~P137(x26021)+P137(x26022)+~E(x26021,x26022)
% 21.40/21.40 [2603]P21(x26032,x26033,x26034)+~E(x26031,x26032)+~P21(x26031,x26033,x26034)
% 21.40/21.40 [2604]P21(x26043,x26042,x26044)+~E(x26041,x26042)+~P21(x26043,x26041,x26044)
% 21.40/21.40 [2605]P21(x26053,x26054,x26052)+~E(x26051,x26052)+~P21(x26053,x26054,x26051)
% 21.40/21.40 [2606]~P4(x26061)+P4(x26062)+~E(x26061,x26062)
% 21.40/21.40 [2607]~P99(x26071)+P99(x26072)+~E(x26071,x26072)
% 21.40/21.40 [2608]~P132(x26081)+P132(x26082)+~E(x26081,x26082)
% 21.40/21.40 [2609]~P70(x26091)+P70(x26092)+~E(x26091,x26092)
% 21.40/21.40 [2610]~P117(x26101)+P117(x26102)+~E(x26101,x26102)
% 21.40/21.40 [2611]~P101(x26111)+P101(x26112)+~E(x26111,x26112)
% 21.40/21.40 [2612]~P71(x26121)+P71(x26122)+~E(x26121,x26122)
% 21.40/21.40 [2613]P29(x26132,x26133,x26134,x26135)+~E(x26131,x26132)+~P29(x26131,x26133,x26134,x26135)
% 21.40/21.40 [2614]P29(x26143,x26142,x26144,x26145)+~E(x26141,x26142)+~P29(x26143,x26141,x26144,x26145)
% 21.40/21.40 [2615]P29(x26153,x26154,x26152,x26155)+~E(x26151,x26152)+~P29(x26153,x26154,x26151,x26155)
% 21.40/21.40 [2616]P29(x26163,x26164,x26165,x26162)+~E(x26161,x26162)+~P29(x26163,x26164,x26165,x26161)
% 21.40/21.40 [2617]~P110(x26171)+P110(x26172)+~E(x26171,x26172)
% 21.40/21.40 [2618]~P74(x26181)+P74(x26182)+~E(x26181,x26182)
% 21.40/21.40 [2619]~P10(x26191)+P10(x26192)+~E(x26191,x26192)
% 21.40/21.40 [2620]~P75(x26201)+P75(x26202)+~E(x26201,x26202)
% 21.40/21.40 [2621]~P5(x26211)+P5(x26212)+~E(x26211,x26212)
% 21.40/21.40 [2622]~P111(x26221)+P111(x26222)+~E(x26221,x26222)
% 21.40/21.40 [2623]~P120(x26231)+P120(x26232)+~E(x26231,x26232)
% 21.40/21.40 [2624]~P64(x26241)+P64(x26242)+~E(x26241,x26242)
% 21.40/21.40 [2625]~P38(x26251)+P38(x26252)+~E(x26251,x26252)
% 21.40/21.40 [2626]~P9(x26261)+P9(x26262)+~E(x26261,x26262)
% 21.40/21.40 [2627]~P65(x26271)+P65(x26272)+~E(x26271,x26272)
% 21.40/21.40 [2628]~P61(x26281)+P61(x26282)+~E(x26281,x26282)
% 21.40/21.40 [2629]P56(x26292,x26293)+~E(x26291,x26292)+~P56(x26291,x26293)
% 21.40/21.40 [2630]P56(x26303,x26302)+~E(x26301,x26302)+~P56(x26303,x26301)
% 21.40/21.40 [2631]~P118(x26311)+P118(x26312)+~E(x26311,x26312)
% 21.40/21.40 [2632]P18(x26322,x26323)+~E(x26321,x26322)+~P18(x26321,x26323)
% 21.40/21.40 [2633]P18(x26333,x26332)+~E(x26331,x26332)+~P18(x26333,x26331)
% 21.40/21.40 [2634]~P63(x26341)+P63(x26342)+~E(x26341,x26342)
% 21.40/21.40 [2635]~P81(x26351)+P81(x26352)+~E(x26351,x26352)
% 21.40/21.40 [2636]~P7(x26361)+P7(x26362)+~E(x26361,x26362)
% 21.40/21.40 [2637]~P68(x26371)+P68(x26372)+~E(x26371,x26372)
% 21.40/21.40 [2638]~P82(x26381)+P82(x26382)+~E(x26381,x26382)
% 21.40/21.40 [2639]P55(x26392,x26393,x26394,x26395,x26396)+~E(x26391,x26392)+~P55(x26391,x26393,x26394,x26395,x26396)
% 21.40/21.40 [2640]P55(x26403,x26402,x26404,x26405,x26406)+~E(x26401,x26402)+~P55(x26403,x26401,x26404,x26405,x26406)
% 21.40/21.40 [2641]P55(x26413,x26414,x26412,x26415,x26416)+~E(x26411,x26412)+~P55(x26413,x26414,x26411,x26415,x26416)
% 21.40/21.40 [2642]P55(x26423,x26424,x26425,x26422,x26426)+~E(x26421,x26422)+~P55(x26423,x26424,x26425,x26421,x26426)
% 21.40/21.40 [2643]P55(x26433,x26434,x26435,x26436,x26432)+~E(x26431,x26432)+~P55(x26433,x26434,x26435,x26436,x26431)
% 21.40/21.40 [2644]~P62(x26441)+P62(x26442)+~E(x26441,x26442)
% 21.40/21.40 [2645]~P76(x26451)+P76(x26452)+~E(x26451,x26452)
% 21.40/21.40 [2646]P47(x26462,x26463,x26464)+~E(x26461,x26462)+~P47(x26461,x26463,x26464)
% 21.40/21.40 [2647]P47(x26473,x26472,x26474)+~E(x26471,x26472)+~P47(x26473,x26471,x26474)
% 21.40/21.40 [2648]P47(x26483,x26484,x26482)+~E(x26481,x26482)+~P47(x26483,x26484,x26481)
% 21.40/21.40 [2649]P140(x26492,x26493,x26494)+~E(x26491,x26492)+~P140(x26491,x26493,x26494)
% 21.40/21.40 [2650]P140(x26503,x26502,x26504)+~E(x26501,x26502)+~P140(x26503,x26501,x26504)
% 21.40/21.40 [2651]P140(x26513,x26514,x26512)+~E(x26511,x26512)+~P140(x26513,x26514,x26511)
% 21.40/21.40 [2652]P39(x26522,x26523,x26524,x26525)+~E(x26521,x26522)+~P39(x26521,x26523,x26524,x26525)
% 21.40/21.40 [2653]P39(x26533,x26532,x26534,x26535)+~E(x26531,x26532)+~P39(x26533,x26531,x26534,x26535)
% 21.40/21.40 [2654]P39(x26543,x26544,x26542,x26545)+~E(x26541,x26542)+~P39(x26543,x26544,x26541,x26545)
% 21.40/21.40 [2655]P39(x26553,x26554,x26555,x26552)+~E(x26551,x26552)+~P39(x26553,x26554,x26555,x26551)
% 21.40/21.40 [2656]~P86(x26561)+P86(x26562)+~E(x26561,x26562)
% 21.40/21.40 [2657]~P69(x26571)+P69(x26572)+~E(x26571,x26572)
% 21.40/21.40 [2658]~P80(x26581)+P80(x26582)+~E(x26581,x26582)
% 21.40/21.40 [2659]~P105(x26591)+P105(x26592)+~E(x26591,x26592)
% 21.40/21.40 [2660]~P126(x26601)+P126(x26602)+~E(x26601,x26602)
% 21.40/21.40 [2661]P141(x26612,x26613,x26614)+~E(x26611,x26612)+~P141(x26611,x26613,x26614)
% 21.40/21.40 [2662]P141(x26623,x26622,x26624)+~E(x26621,x26622)+~P141(x26623,x26621,x26624)
% 21.40/21.40 [2663]P141(x26633,x26634,x26632)+~E(x26631,x26632)+~P141(x26633,x26634,x26631)
% 21.40/21.40 [2664]~P89(x26641)+P89(x26642)+~E(x26641,x26642)
% 21.40/21.40 [2665]~P124(x26651)+P124(x26652)+~E(x26651,x26652)
% 21.40/21.40 [2666]P57(x26662,x26663,x26664,x26665)+~E(x26661,x26662)+~P57(x26661,x26663,x26664,x26665)
% 21.40/21.40 [2667]P57(x26673,x26672,x26674,x26675)+~E(x26671,x26672)+~P57(x26673,x26671,x26674,x26675)
% 21.40/21.40 [2668]P57(x26683,x26684,x26682,x26685)+~E(x26681,x26682)+~P57(x26683,x26684,x26681,x26685)
% 21.40/21.40 [2669]P57(x26693,x26694,x26695,x26692)+~E(x26691,x26692)+~P57(x26693,x26694,x26695,x26691)
% 21.40/21.40 [2670]~P87(x26701)+P87(x26702)+~E(x26701,x26702)
% 21.40/21.40 [2671]~P66(x26711)+P66(x26712)+~E(x26711,x26712)
% 21.40/21.40 [2672]P27(x26722,x26723,x26724,x26725,x26726,x26727)+~E(x26721,x26722)+~P27(x26721,x26723,x26724,x26725,x26726,x26727)
% 21.40/21.40 [2673]P27(x26733,x26732,x26734,x26735,x26736,x26737)+~E(x26731,x26732)+~P27(x26733,x26731,x26734,x26735,x26736,x26737)
% 21.40/21.40 [2674]P27(x26743,x26744,x26742,x26745,x26746,x26747)+~E(x26741,x26742)+~P27(x26743,x26744,x26741,x26745,x26746,x26747)
% 21.40/21.40 [2675]P27(x26753,x26754,x26755,x26752,x26756,x26757)+~E(x26751,x26752)+~P27(x26753,x26754,x26755,x26751,x26756,x26757)
% 21.40/21.40 [2676]P27(x26763,x26764,x26765,x26766,x26762,x26767)+~E(x26761,x26762)+~P27(x26763,x26764,x26765,x26766,x26761,x26767)
% 21.40/21.40 [2677]P27(x26773,x26774,x26775,x26776,x26777,x26772)+~E(x26771,x26772)+~P27(x26773,x26774,x26775,x26776,x26777,x26771)
% 21.40/21.40 [2678]P16(x26782,x26783,x26784,x26785)+~E(x26781,x26782)+~P16(x26781,x26783,x26784,x26785)
% 21.40/21.40 [2679]P16(x26793,x26792,x26794,x26795)+~E(x26791,x26792)+~P16(x26793,x26791,x26794,x26795)
% 21.40/21.40 [2680]P16(x26803,x26804,x26802,x26805)+~E(x26801,x26802)+~P16(x26803,x26804,x26801,x26805)
% 21.40/21.40 [2681]P16(x26813,x26814,x26815,x26812)+~E(x26811,x26812)+~P16(x26813,x26814,x26815,x26811)
% 21.40/21.40 [2682]~P121(x26821)+P121(x26822)+~E(x26821,x26822)
% 21.40/21.40 [2683]~P90(x26831)+P90(x26832)+~E(x26831,x26832)
% 21.40/21.40 [2684]~P128(x26841)+P128(x26842)+~E(x26841,x26842)
% 21.40/21.40 [2685]~P6(x26851)+P6(x26852)+~E(x26851,x26852)
% 21.40/21.40 [2686]~P122(x26861)+P122(x26862)+~E(x26861,x26862)
% 21.40/21.40 [2687]~P94(x26871)+P94(x26872)+~E(x26871,x26872)
% 21.40/21.40 [2688]P53(x26882,x26883,x26884)+~E(x26881,x26882)+~P53(x26881,x26883,x26884)
% 21.40/21.40 [2689]P53(x26893,x26892,x26894)+~E(x26891,x26892)+~P53(x26893,x26891,x26894)
% 21.40/21.40 [2690]P53(x26903,x26904,x26902)+~E(x26901,x26902)+~P53(x26903,x26904,x26901)
% 21.40/21.40 [2691]~P133(x26911)+P133(x26912)+~E(x26911,x26912)
% 21.40/21.40 [2692]~P123(x26921)+P123(x26922)+~E(x26921,x26922)
% 21.40/21.40 [2693]P48(x26932,x26933)+~E(x26931,x26932)+~P48(x26931,x26933)
% 21.40/21.40 [2694]P48(x26943,x26942)+~E(x26941,x26942)+~P48(x26943,x26941)
% 21.40/21.40 [2695]P11(x26952,x26953)+~E(x26951,x26952)+~P11(x26951,x26953)
% 21.40/21.40 [2696]P11(x26963,x26962)+~E(x26961,x26962)+~P11(x26963,x26961)
% 21.40/21.40 [2697]~P135(x26971)+P135(x26972)+~E(x26971,x26972)
% 21.40/21.40 [2698]P41(x26982,x26983,x26984,x26985,x26986,x26987)+~E(x26981,x26982)+~P41(x26981,x26983,x26984,x26985,x26986,x26987)
% 21.40/21.40 [2699]P41(x26993,x26992,x26994,x26995,x26996,x26997)+~E(x26991,x26992)+~P41(x26993,x26991,x26994,x26995,x26996,x26997)
% 21.40/21.40 [2700]P41(x27003,x27004,x27002,x27005,x27006,x27007)+~E(x27001,x27002)+~P41(x27003,x27004,x27001,x27005,x27006,x27007)
% 21.40/21.40 [2701]P41(x27013,x27014,x27015,x27012,x27016,x27017)+~E(x27011,x27012)+~P41(x27013,x27014,x27015,x27011,x27016,x27017)
% 21.40/21.40 [2702]P41(x27023,x27024,x27025,x27026,x27022,x27027)+~E(x27021,x27022)+~P41(x27023,x27024,x27025,x27026,x27021,x27027)
% 21.40/21.40 [2703]P41(x27033,x27034,x27035,x27036,x27037,x27032)+~E(x27031,x27032)+~P41(x27033,x27034,x27035,x27036,x27037,x27031)
% 21.40/21.40 [2704]P31(x27042,x27043,x27044)+~E(x27041,x27042)+~P31(x27041,x27043,x27044)
% 21.40/21.40 [2705]P31(x27053,x27052,x27054)+~E(x27051,x27052)+~P31(x27053,x27051,x27054)
% 21.40/21.40 [2706]P31(x27063,x27064,x27062)+~E(x27061,x27062)+~P31(x27063,x27064,x27061)
% 21.40/21.40 [2707]~P103(x27071)+P103(x27072)+~E(x27071,x27072)
% 21.40/21.40 [2708]~P95(x27081)+P95(x27082)+~E(x27081,x27082)
% 21.40/21.40 [2709]~P78(x27091)+P78(x27092)+~E(x27091,x27092)
% 21.40/21.40 [2710]~P98(x27101)+P98(x27102)+~E(x27101,x27102)
% 21.40/21.40 [2711]~P115(x27111)+P115(x27112)+~E(x27111,x27112)
% 21.40/21.40 [2712]~P8(x27121)+P8(x27122)+~E(x27121,x27122)
% 21.40/21.40 [2713]P26(x27132,x27133,x27134,x27135,x27136,x27137)+~E(x27131,x27132)+~P26(x27131,x27133,x27134,x27135,x27136,x27137)
% 21.40/21.40 [2714]P26(x27143,x27142,x27144,x27145,x27146,x27147)+~E(x27141,x27142)+~P26(x27143,x27141,x27144,x27145,x27146,x27147)
% 21.40/21.40 [2715]P26(x27153,x27154,x27152,x27155,x27156,x27157)+~E(x27151,x27152)+~P26(x27153,x27154,x27151,x27155,x27156,x27157)
% 21.40/21.40 [2716]P26(x27163,x27164,x27165,x27162,x27166,x27167)+~E(x27161,x27162)+~P26(x27163,x27164,x27165,x27161,x27166,x27167)
% 21.40/21.40 [2717]P26(x27173,x27174,x27175,x27176,x27172,x27177)+~E(x27171,x27172)+~P26(x27173,x27174,x27175,x27176,x27171,x27177)
% 21.40/21.40 [2718]P26(x27183,x27184,x27185,x27186,x27187,x27182)+~E(x27181,x27182)+~P26(x27183,x27184,x27185,x27186,x27187,x27181)
% 21.40/21.40 [2719]P33(x27192,x27193)+~E(x27191,x27192)+~P33(x27191,x27193)
% 21.40/21.40 [2720]P33(x27203,x27202)+~E(x27201,x27202)+~P33(x27203,x27201)
% 21.40/21.40 [2721]~P91(x27211)+P91(x27212)+~E(x27211,x27212)
% 21.40/21.40 [2722]P54(x27222,x27223,x27224)+~E(x27221,x27222)+~P54(x27221,x27223,x27224)
% 21.40/21.40 [2723]P54(x27233,x27232,x27234)+~E(x27231,x27232)+~P54(x27233,x27231,x27234)
% 21.40/21.40 [2724]P54(x27243,x27244,x27242)+~E(x27241,x27242)+~P54(x27243,x27244,x27241)
% 21.40/21.40 [2725]~P119(x27251)+P119(x27252)+~E(x27251,x27252)
% 21.40/21.40 [2726]~P77(x27261)+P77(x27262)+~E(x27261,x27262)
% 21.40/21.40 [2727]~P60(x27271)+P60(x27272)+~E(x27271,x27272)
% 21.40/21.40 [2728]P17(x27282,x27283,x27284,x27285,x27286,x27287)+~E(x27281,x27282)+~P17(x27281,x27283,x27284,x27285,x27286,x27287)
% 21.40/21.40 [2729]P17(x27293,x27292,x27294,x27295,x27296,x27297)+~E(x27291,x27292)+~P17(x27293,x27291,x27294,x27295,x27296,x27297)
% 21.40/21.40 [2730]P17(x27303,x27304,x27302,x27305,x27306,x27307)+~E(x27301,x27302)+~P17(x27303,x27304,x27301,x27305,x27306,x27307)
% 21.40/21.40 [2731]P17(x27313,x27314,x27315,x27312,x27316,x27317)+~E(x27311,x27312)+~P17(x27313,x27314,x27315,x27311,x27316,x27317)
% 21.40/21.40 [2732]P17(x27323,x27324,x27325,x27326,x27322,x27327)+~E(x27321,x27322)+~P17(x27323,x27324,x27325,x27326,x27321,x27327)
% 21.40/21.40 [2733]P17(x27333,x27334,x27335,x27336,x27337,x27332)+~E(x27331,x27332)+~P17(x27333,x27334,x27335,x27336,x27337,x27331)
% 21.40/21.40 [2734]~P138(x27341)+P138(x27342)+~E(x27341,x27342)
% 21.40/21.40 [2735]P23(x27352,x27353,x27354,x27355)+~E(x27351,x27352)+~P23(x27351,x27353,x27354,x27355)
% 21.40/21.40 [2736]P23(x27363,x27362,x27364,x27365)+~E(x27361,x27362)+~P23(x27363,x27361,x27364,x27365)
% 21.40/21.40 [2737]P23(x27373,x27374,x27372,x27375)+~E(x27371,x27372)+~P23(x27373,x27374,x27371,x27375)
% 21.40/21.40 [2738]P23(x27383,x27384,x27385,x27382)+~E(x27381,x27382)+~P23(x27383,x27384,x27385,x27381)
% 21.40/21.40 [2739]P42(x27392,x27393)+~E(x27391,x27392)+~P42(x27391,x27393)
% 21.40/21.40 [2740]P42(x27403,x27402)+~E(x27401,x27402)+~P42(x27403,x27401)
% 21.40/21.40 [2741]P19(x27412,x27413,x27414)+~E(x27411,x27412)+~P19(x27411,x27413,x27414)
% 21.40/21.40 [2742]P19(x27423,x27422,x27424)+~E(x27421,x27422)+~P19(x27423,x27421,x27424)
% 21.40/21.40 [2743]P19(x27433,x27434,x27432)+~E(x27431,x27432)+~P19(x27433,x27434,x27431)
% 21.40/21.40 [2744]P12(x27442,x27443,x27444)+~E(x27441,x27442)+~P12(x27441,x27443,x27444)
% 21.40/21.40 [2745]P12(x27453,x27452,x27454)+~E(x27451,x27452)+~P12(x27453,x27451,x27454)
% 21.40/21.40 [2746]P12(x27463,x27464,x27462)+~E(x27461,x27462)+~P12(x27463,x27464,x27461)
% 21.40/21.40 [2747]P58(x27472,x27473)+~E(x27471,x27472)+~P58(x27471,x27473)
% 21.40/21.40 [2748]P58(x27483,x27482)+~E(x27481,x27482)+~P58(x27483,x27481)
% 21.40/21.40 [2749]~P112(x27491)+P112(x27492)+~E(x27491,x27492)
% 21.40/21.40 [2750]~P113(x27501)+P113(x27502)+~E(x27501,x27502)
% 21.40/21.40 [2751]~P131(x27511)+P131(x27512)+~E(x27511,x27512)
% 21.40/21.40 [2752]~P79(x27521)+P79(x27522)+~E(x27521,x27522)
% 21.40/21.40 [2753]P34(x27532,x27533,x27534,x27535)+~E(x27531,x27532)+~P34(x27531,x27533,x27534,x27535)
% 21.40/21.40 [2754]P34(x27543,x27542,x27544,x27545)+~E(x27541,x27542)+~P34(x27543,x27541,x27544,x27545)
% 21.40/21.40 [2755]P34(x27553,x27554,x27552,x27555)+~E(x27551,x27552)+~P34(x27553,x27554,x27551,x27555)
% 21.40/21.40 [2756]P34(x27563,x27564,x27565,x27562)+~E(x27561,x27562)+~P34(x27563,x27564,x27565,x27561)
% 21.40/21.40 [2757]P20(x27572,x27573,x27574)+~E(x27571,x27572)+~P20(x27571,x27573,x27574)
% 21.40/21.40 [2758]P20(x27583,x27582,x27584)+~E(x27581,x27582)+~P20(x27583,x27581,x27584)
% 21.40/21.40 [2759]P20(x27593,x27594,x27592)+~E(x27591,x27592)+~P20(x27593,x27594,x27591)
% 21.40/21.40 [2760]~P125(x27601)+P125(x27602)+~E(x27601,x27602)
% 21.40/21.40 [2761]~P127(x27611)+P127(x27612)+~E(x27611,x27612)
% 21.40/21.40 [2762]P22(x27622,x27623,x27624)+~E(x27621,x27622)+~P22(x27621,x27623,x27624)
% 21.40/21.40 [2763]P22(x27633,x27632,x27634)+~E(x27631,x27632)+~P22(x27633,x27631,x27634)
% 21.40/21.40 [2764]P22(x27643,x27644,x27642)+~E(x27641,x27642)+~P22(x27643,x27644,x27641)
% 21.40/21.40 [2765]P30(x27652,x27653)+~E(x27651,x27652)+~P30(x27651,x27653)
% 21.40/21.40 [2766]P30(x27663,x27662)+~E(x27661,x27662)+~P30(x27663,x27661)
% 21.40/21.40 [2767]~P114(x27671)+P114(x27672)+~E(x27671,x27672)
% 21.40/21.40 [2768]~P129(x27681)+P129(x27682)+~E(x27681,x27682)
% 21.40/21.40 [2769]~P97(x27691)+P97(x27692)+~E(x27691,x27692)
% 21.40/21.40 [2770]~P100(x27701)+P100(x27702)+~E(x27701,x27702)
% 21.40/21.40 [2771]P28(x27712,x27713,x27714)+~E(x27711,x27712)+~P28(x27711,x27713,x27714)
% 21.40/21.40 [2772]P28(x27723,x27722,x27724)+~E(x27721,x27722)+~P28(x27723,x27721,x27724)
% 21.40/21.40 [2773]P28(x27733,x27734,x27732)+~E(x27731,x27732)+~P28(x27733,x27734,x27731)
% 21.40/21.40 [2774]~P130(x27741)+P130(x27742)+~E(x27741,x27742)
% 21.40/21.40 [2775]~P93(x27751)+P93(x27752)+~E(x27751,x27752)
% 21.40/21.40 [2776]~P136(x27761)+P136(x27762)+~E(x27761,x27762)
% 21.40/21.40 [2777]~P134(x27771)+P134(x27772)+~E(x27771,x27772)
% 21.40/21.40 [2778]~P104(x27781)+P104(x27782)+~E(x27781,x27782)
% 21.40/21.40 [2779]P24(x27792,x27793,x27794,x27795)+~E(x27791,x27792)+~P24(x27791,x27793,x27794,x27795)
% 21.40/21.40 [2780]P24(x27803,x27802,x27804,x27805)+~E(x27801,x27802)+~P24(x27803,x27801,x27804,x27805)
% 21.40/21.40 [2781]P24(x27813,x27814,x27812,x27815)+~E(x27811,x27812)+~P24(x27813,x27814,x27811,x27815)
% 21.40/21.40 [2782]P24(x27823,x27824,x27825,x27822)+~E(x27821,x27822)+~P24(x27823,x27824,x27825,x27821)
% 21.40/21.40 [2783]~P59(x27831)+P59(x27832)+~E(x27831,x27832)
% 21.40/21.40 [2784]P37(x27842,x27843)+~E(x27841,x27842)+~P37(x27841,x27843)
% 21.40/21.40 [2785]P37(x27853,x27852)+~E(x27851,x27852)+~P37(x27853,x27851)
% 21.40/21.40 [2786]~P109(x27861)+P109(x27862)+~E(x27861,x27862)
% 21.40/21.40 [2787]~P83(x27871)+P83(x27872)+~E(x27871,x27872)
% 21.40/21.40 [2788]~P96(x27881)+P96(x27882)+~E(x27881,x27882)
% 21.40/21.40 [2789]~P84(x27891)+P84(x27892)+~E(x27891,x27892)
% 21.40/21.40 [2790]~P106(x27901)+P106(x27902)+~E(x27901,x27902)
% 21.40/21.40 [2791]P25(x27912,x27913,x27914,x27915,x27916)+~E(x27911,x27912)+~P25(x27911,x27913,x27914,x27915,x27916)
% 21.40/21.40 [2792]P25(x27923,x27922,x27924,x27925,x27926)+~E(x27921,x27922)+~P25(x27923,x27921,x27924,x27925,x27926)
% 21.40/21.40 [2793]P25(x27933,x27934,x27932,x27935,x27936)+~E(x27931,x27932)+~P25(x27933,x27934,x27931,x27935,x27936)
% 21.40/21.40 [2794]P25(x27943,x27944,x27945,x27942,x27946)+~E(x27941,x27942)+~P25(x27943,x27944,x27945,x27941,x27946)
% 21.40/21.40 [2795]P25(x27953,x27954,x27955,x27956,x27952)+~E(x27951,x27952)+~P25(x27953,x27954,x27955,x27956,x27951)
% 21.40/21.40 [2796]~P139(x27961)+P139(x27962)+~E(x27961,x27962)
% 21.40/21.40 [2797]P51(x27972,x27973,x27974,x27975,x27976,x27977,x27978)+~E(x27971,x27972)+~P51(x27971,x27973,x27974,x27975,x27976,x27977,x27978)
% 21.40/21.40 [2798]P51(x27983,x27982,x27984,x27985,x27986,x27987,x27988)+~E(x27981,x27982)+~P51(x27983,x27981,x27984,x27985,x27986,x27987,x27988)
% 21.40/21.40 [2799]P51(x27993,x27994,x27992,x27995,x27996,x27997,x27998)+~E(x27991,x27992)+~P51(x27993,x27994,x27991,x27995,x27996,x27997,x27998)
% 21.40/21.40 [2800]P51(x28003,x28004,x28005,x28002,x28006,x28007,x28008)+~E(x28001,x28002)+~P51(x28003,x28004,x28005,x28001,x28006,x28007,x28008)
% 21.40/21.40 [2801]P51(x28013,x28014,x28015,x28016,x28012,x28017,x28018)+~E(x28011,x28012)+~P51(x28013,x28014,x28015,x28016,x28011,x28017,x28018)
% 21.40/21.40 [2802]P51(x28023,x28024,x28025,x28026,x28027,x28022,x28028)+~E(x28021,x28022)+~P51(x28023,x28024,x28025,x28026,x28027,x28021,x28028)
% 21.40/21.40 [2803]P51(x28033,x28034,x28035,x28036,x28037,x28038,x28032)+~E(x28031,x28032)+~P51(x28033,x28034,x28035,x28036,x28037,x28038,x28031)
% 21.40/21.40 [2804]~P92(x28041)+P92(x28042)+~E(x28041,x28042)
% 21.40/21.40 [2805]~P35(x28051)+P35(x28052)+~E(x28051,x28052)
% 21.40/21.40 [2806]P15(x28062,x28063,x28064,x28065,x28066)+~E(x28061,x28062)+~P15(x28061,x28063,x28064,x28065,x28066)
% 21.40/21.40 [2807]P15(x28073,x28072,x28074,x28075,x28076)+~E(x28071,x28072)+~P15(x28073,x28071,x28074,x28075,x28076)
% 21.40/21.40 [2808]P15(x28083,x28084,x28082,x28085,x28086)+~E(x28081,x28082)+~P15(x28083,x28084,x28081,x28085,x28086)
% 21.40/21.40 [2809]P15(x28093,x28094,x28095,x28092,x28096)+~E(x28091,x28092)+~P15(x28093,x28094,x28095,x28091,x28096)
% 21.40/21.40 [2810]P15(x28103,x28104,x28105,x28106,x28102)+~E(x28101,x28102)+~P15(x28103,x28104,x28105,x28106,x28101)
% 21.40/21.40 [2811]P32(x28112,x28113,x28114)+~E(x28111,x28112)+~P32(x28111,x28113,x28114)
% 21.40/21.40 [2812]P32(x28123,x28122,x28124)+~E(x28121,x28122)+~P32(x28123,x28121,x28124)
% 21.40/21.40 [2813]P32(x28133,x28134,x28132)+~E(x28131,x28132)+~P32(x28133,x28134,x28131)
% 21.40/21.40 [2814]~P85(x28141)+P85(x28142)+~E(x28141,x28142)
% 21.40/21.40 [2815]P142(x28152,x28153)+~E(x28151,x28152)+~P142(x28151,x28153)
% 21.40/21.40 [2816]P142(x28163,x28162)+~E(x28161,x28162)+~P142(x28163,x28161)
% 21.40/21.40 [2817]P52(x28172,x28173,x28174,x28175)+~E(x28171,x28172)+~P52(x28171,x28173,x28174,x28175)
% 21.40/21.40 [2818]P52(x28183,x28182,x28184,x28185)+~E(x28181,x28182)+~P52(x28183,x28181,x28184,x28185)
% 21.40/21.40 [2819]P52(x28193,x28194,x28192,x28195)+~E(x28191,x28192)+~P52(x28193,x28194,x28191,x28195)
% 21.40/21.40 [2820]P52(x28203,x28204,x28205,x28202)+~E(x28201,x28202)+~P52(x28203,x28204,x28205,x28201)
% 21.40/21.40 [2821]P40(x28212,x28213,x28214,x28215)+~E(x28211,x28212)+~P40(x28211,x28213,x28214,x28215)
% 21.40/21.40 [2822]P40(x28223,x28222,x28224,x28225)+~E(x28221,x28222)+~P40(x28223,x28221,x28224,x28225)
% 21.40/21.40 [2823]P40(x28233,x28234,x28232,x28235)+~E(x28231,x28232)+~P40(x28233,x28234,x28231,x28235)
% 21.40/21.40 [2824]P40(x28243,x28244,x28245,x28242)+~E(x28241,x28242)+~P40(x28243,x28244,x28245,x28241)
% 21.40/21.40 [2825]~P72(x28251)+P72(x28252)+~E(x28251,x28252)
% 21.40/21.40 [2826]~P43(x28261)+P43(x28262)+~E(x28261,x28262)
% 21.40/21.40 [2827]~P13(x28271)+P13(x28272)+~E(x28271,x28272)
% 21.40/21.40 [2828]~P108(x28281)+P108(x28282)+~E(x28281,x28282)
% 21.40/21.40 [2829]~P73(x28291)+P73(x28292)+~E(x28291,x28292)
% 21.40/21.40 [2830]~P102(x28301)+P102(x28302)+~E(x28301,x28302)
% 21.40/21.40 [2831]P45(x28312,x28313,x28314)+~E(x28311,x28312)+~P45(x28311,x28313,x28314)
% 21.40/21.40 [2832]P45(x28323,x28322,x28324)+~E(x28321,x28322)+~P45(x28323,x28321,x28324)
% 21.40/21.40 [2833]P45(x28333,x28334,x28332)+~E(x28331,x28332)+~P45(x28333,x28334,x28331)
% 21.40/21.40 [2834]P14(x28342,x28343,x28344)+~E(x28341,x28342)+~P14(x28341,x28343,x28344)
% 21.40/21.40 [2835]P14(x28353,x28352,x28354)+~E(x28351,x28352)+~P14(x28353,x28351,x28354)
% 21.40/21.40 [2836]P14(x28363,x28364,x28362)+~E(x28361,x28362)+~P14(x28363,x28364,x28361)
% 21.40/21.40 [2837]P44(x28372,x28373)+~E(x28371,x28372)+~P44(x28371,x28373)
% 21.40/21.40 [2838]P44(x28383,x28382)+~E(x28381,x28382)+~P44(x28383,x28381)
% 21.40/21.40 [2839]~P107(x28391)+P107(x28392)+~E(x28391,x28392)
% 21.40/21.40 [2840]~P67(x28401)+P67(x28402)+~E(x28401,x28402)
% 21.40/21.40 [2841]P49(x28412,x28413)+~E(x28411,x28412)+~P49(x28411,x28413)
% 21.40/21.40 [2842]P49(x28423,x28422)+~E(x28421,x28422)+~P49(x28423,x28421)
% 21.40/21.40 [2843]P46(x28432,x28433,x28434)+~E(x28431,x28432)+~P46(x28431,x28433,x28434)
% 21.40/21.40 [2844]P46(x28443,x28442,x28444)+~E(x28441,x28442)+~P46(x28443,x28441,x28444)
% 21.40/21.40 [2845]P46(x28453,x28454,x28452)+~E(x28451,x28452)+~P46(x28453,x28454,x28451)
% 21.40/21.40 [2846]P50(x28462,x28463,x28464,x28465)+~E(x28461,x28462)+~P50(x28461,x28463,x28464,x28465)
% 21.40/21.40 [2847]P50(x28473,x28472,x28474,x28475)+~E(x28471,x28472)+~P50(x28473,x28471,x28474,x28475)
% 21.40/21.40 [2848]P50(x28483,x28484,x28482,x28485)+~E(x28481,x28482)+~P50(x28483,x28484,x28481,x28485)
% 21.40/21.40 [2849]P50(x28493,x28494,x28495,x28492)+~E(x28491,x28492)+~P50(x28493,x28494,x28495,x28491)
% 21.40/21.40 [2850]~P116(x28501)+P116(x28502)+~E(x28501,x28502)
% 21.40/21.40
% 21.40/21.40 %-------------------------------------------
% 21.40/21.40 cnf(10095,plain,
% 21.40/21.40 (~E(f789(f789(f146(x100951),x100952),x100953),x100953)),
% 21.40/21.40 inference(rename_variables,[],[4443])).
% 21.40/21.40 cnf(10102,plain,
% 21.40/21.40 (~E(f789(f789(f146(x101021),x101022),x101023),x101023)),
% 21.40/21.40 inference(rename_variables,[],[4443])).
% 21.40/21.40 cnf(10111,plain,
% 21.40/21.40 (~E(f789(a121,x101111),x101111)),
% 21.40/21.40 inference(rename_variables,[],[4409])).
% 21.40/21.40 cnf(10118,plain,
% 21.40/21.40 (~E(f789(a121,x101181),x101181)),
% 21.40/21.40 inference(rename_variables,[],[4409])).
% 21.40/21.40 cnf(10121,plain,
% 21.40/21.40 (E(f39(x101211,x101212,x101213,x101214,x101215,x101216,x101217,x101218,x101219,a25),x101212)),
% 21.40/21.40 inference(rename_variables,[],[4381])).
% 21.40/21.40 cnf(10124,plain,
% 21.40/21.40 (P1(f789(f789(f240(a863),f59(a863,x101241,x101242)),x101241))),
% 21.40/21.40 inference(rename_variables,[],[3687])).
% 21.40/21.40 cnf(10127,plain,
% 21.40/21.40 (~P1(f789(f789(f241(a863),f789(f789(f89(a863),x101271),x101272)),x101272))),
% 21.40/21.40 inference(rename_variables,[],[4522])).
% 21.40/21.40 cnf(10130,plain,
% 21.40/21.40 (~P1(f789(f789(f241(a863),f789(f789(f89(a863),x101301),x101302)),x101302))),
% 21.40/21.40 inference(rename_variables,[],[4522])).
% 21.40/21.40 cnf(10133,plain,
% 21.40/21.40 (~P1(f789(f789(f241(a863),x101331),x101331))),
% 21.40/21.40 inference(rename_variables,[],[4493])).
% 21.40/21.40 cnf(10144,plain,
% 21.40/21.40 (~E(f789(f321(x101441,x101442),x101443),f789(f312(x101442,x101441),x101444))),
% 21.40/21.40 inference(rename_variables,[],[4480])).
% 21.40/21.40 cnf(10146,plain,
% 21.40/21.40 (P1(f789(f789(f342(x101461),x101462),f247(f870(x101461,a856))))),
% 21.40/21.40 inference(rename_variables,[],[3388])).
% 21.40/21.40 cnf(10149,plain,
% 21.40/21.40 (~E(f789(a121,x101491),x101491)),
% 21.40/21.40 inference(rename_variables,[],[4409])).
% 21.40/21.41 cnf(10152,plain,
% 21.40/21.41 (E(f327(x101521,x101522,x101523,f789(f789(f10(f871(x101521,x101523),x101522,x101521),x101524),f312(x101521,x101523)),f789(f789(f10(f871(x101521,x101523),x101522,x101523),x101524),f321(x101523,x101521))),x101524)),
% 21.40/21.41 inference(rename_variables,[],[4091])).
% 21.40/21.41 cnf(10158,plain,
% 21.40/21.41 (~E(f789(a29,x101581),a25)),
% 21.40/21.41 inference(rename_variables,[],[4407])).
% 21.40/21.41 cnf(10163,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x101631),x101631))),
% 21.40/21.41 inference(rename_variables,[],[3231])).
% 21.40/21.41 cnf(10180,plain,
% 21.40/21.41 (P1(f789(f789(f342(x101801),x101802),f247(f870(x101801,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(10185,plain,
% 21.40/21.41 (P1(f789(f789(f241(a863),x101851),f789(a121,x101851)))),
% 21.40/21.41 inference(rename_variables,[],[3300])).
% 21.40/21.41 cnf(10209,plain,
% 21.40/21.41 (P1(f789(f789(f241(a863),x102091),f789(a121,x102091)))),
% 21.40/21.41 inference(rename_variables,[],[3300])).
% 21.40/21.41 cnf(10218,plain,
% 21.40/21.41 (P1(f789(f789(f191(a25),x102181),x102181))),
% 21.40/21.41 inference(rename_variables,[],[3229])).
% 21.40/21.41 cnf(10233,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),x102331),x102331))),
% 21.40/21.41 inference(rename_variables,[],[4493])).
% 21.40/21.41 cnf(10248,plain,
% 21.40/21.41 (P1(f789(f789(f241(a863),x102481),f789(a121,x102481)))),
% 21.40/21.41 inference(rename_variables,[],[3300])).
% 21.40/21.41 cnf(10251,plain,
% 21.40/21.41 (P1(f789(f789(f241(a863),x102511),f789(a121,x102511)))),
% 21.40/21.41 inference(rename_variables,[],[3300])).
% 21.40/21.41 cnf(10278,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),f789(f789(f89(a863),x102781),x102782)),x102782))),
% 21.40/21.41 inference(rename_variables,[],[4522])).
% 21.40/21.41 cnf(10283,plain,
% 21.40/21.41 (~P1(f789(f789(f240(a863),f789(a121,x102831)),x102831))),
% 21.40/21.41 inference(rename_variables,[],[4507])).
% 21.40/21.41 cnf(10297,plain,
% 21.40/21.41 (E(f39(x102971,x102972,x102973,x102974,x102975,x102976,x102977,x102978,x102979,a25),x102972)),
% 21.40/21.41 inference(rename_variables,[],[4381])).
% 21.40/21.41 cnf(10300,plain,
% 21.40/21.41 (E(f40(x103001,x103002,x103003,x103004,x103005,x103006,x103007,x103008,x103009,a25),x103002)),
% 21.40/21.41 inference(rename_variables,[],[4382])).
% 21.40/21.41 cnf(10309,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x103091),x103092),f184(f870(x103091,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(10312,plain,
% 21.40/21.41 (E(f39(x103121,x103122,x103123,x103124,x103125,x103126,x103127,x103128,x103129,a25),x103122)),
% 21.40/21.41 inference(rename_variables,[],[4381])).
% 21.40/21.41 cnf(10324,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x103241,a856)),x103242),x103242))),
% 21.40/21.41 inference(rename_variables,[],[3534])).
% 21.40/21.41 cnf(10329,plain,
% 21.40/21.41 (P1(f789(f789(f241(a863),x103291),f789(a121,x103291)))),
% 21.40/21.41 inference(rename_variables,[],[3300])).
% 21.40/21.41 cnf(10348,plain,
% 21.40/21.41 (P1(f789(f789(f191(a25),x103481),x103481))),
% 21.40/21.41 inference(rename_variables,[],[3229])).
% 21.40/21.41 cnf(10351,plain,
% 21.40/21.41 (P1(f789(f789(f241(a863),x103511),f789(a121,x103511)))),
% 21.40/21.41 inference(rename_variables,[],[3300])).
% 21.40/21.41 cnf(10358,plain,
% 21.40/21.41 (P1(f789(f789(f241(a863),x103581),f789(a121,x103581)))),
% 21.40/21.41 inference(rename_variables,[],[3300])).
% 21.40/21.41 cnf(10361,plain,
% 21.40/21.41 (P1(f789(f789(f241(a863),x103611),f789(a121,x103611)))),
% 21.40/21.41 inference(rename_variables,[],[3300])).
% 21.40/21.41 cnf(10366,plain,
% 21.40/21.41 (P1(f789(f789(f191(a25),x103661),x103661))),
% 21.40/21.41 inference(rename_variables,[],[3229])).
% 21.40/21.41 cnf(10379,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),x103791),x103791))),
% 21.40/21.41 inference(rename_variables,[],[4493])).
% 21.40/21.41 cnf(10386,plain,
% 21.40/21.41 (~E(f789(a29,x103861),a25)),
% 21.40/21.41 inference(rename_variables,[],[4407])).
% 21.40/21.41 cnf(10395,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),x103951),x103951))),
% 21.40/21.41 inference(rename_variables,[],[4493])).
% 21.40/21.41 cnf(10404,plain,
% 21.40/21.41 (~E(f789(a121,x104041),x104041)),
% 21.40/21.41 inference(rename_variables,[],[4409])).
% 21.40/21.41 cnf(10407,plain,
% 21.40/21.41 (~E(f789(f789(f146(x104071),x104072),x104073),x104073)),
% 21.40/21.41 inference(rename_variables,[],[4443])).
% 21.40/21.41 cnf(10435,plain,
% 21.40/21.41 (P1(f789(f789(f191(a25),x104351),x104351))),
% 21.40/21.41 inference(rename_variables,[],[3229])).
% 21.40/21.41 cnf(10440,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),x104401),x104401))),
% 21.40/21.41 inference(rename_variables,[],[4493])).
% 21.40/21.41 cnf(10450,plain,
% 21.40/21.41 (E(f39(x104501,x104502,x104503,x104504,x104505,x104506,x104507,x104508,x104509,a25),x104502)),
% 21.40/21.41 inference(rename_variables,[],[4381])).
% 21.40/21.41 cnf(10453,plain,
% 21.40/21.41 (E(f39(x104531,x104532,x104533,x104534,x104535,x104536,x104537,x104538,x104539,a25),x104532)),
% 21.40/21.41 inference(rename_variables,[],[4381])).
% 21.40/21.41 cnf(10456,plain,
% 21.40/21.41 (~E(f789(a121,x104561),x104561)),
% 21.40/21.41 inference(rename_variables,[],[4409])).
% 21.40/21.41 cnf(10459,plain,
% 21.40/21.41 (~P1(f789(f71(x104591,x104592,f184(f870(x104591,a856))),x104593))),
% 21.40/21.41 inference(rename_variables,[],[4521])).
% 21.40/21.41 cnf(10464,plain,
% 21.40/21.41 (~P1(f789(f71(x104641,x104642,f184(f870(x104641,a856))),x104643))),
% 21.40/21.41 inference(rename_variables,[],[4521])).
% 21.40/21.41 cnf(10483,plain,
% 21.40/21.41 (~P1(f789(f789(f241(f870(x104831,a856)),x104832),f184(f870(x104831,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4519])).
% 21.40/21.41 cnf(10488,plain,
% 21.40/21.41 (~P1(f789(f789(f240(a863),f789(a121,x104881)),x104881))),
% 21.40/21.41 inference(rename_variables,[],[4507])).
% 21.40/21.41 cnf(10491,plain,
% 21.40/21.41 (~P1(f789(f789(f240(a863),f789(a121,x104911)),x104911))),
% 21.40/21.41 inference(rename_variables,[],[4507])).
% 21.40/21.41 cnf(10496,plain,
% 21.40/21.41 (~E(f789(f311(x104961,f870(x104961,a856),x104962),x104963),f789(f309(x104961),x104963))),
% 21.40/21.41 inference(rename_variables,[],[4508])).
% 21.40/21.41 cnf(10505,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),f2(a863)),x105051))),
% 21.40/21.41 inference(rename_variables,[],[3253])).
% 21.40/21.41 cnf(10508,plain,
% 21.40/21.41 (P1(f789(f789(f287(a863),x105081),x105081))),
% 21.40/21.41 inference(rename_variables,[],[3233])).
% 21.40/21.41 cnf(10511,plain,
% 21.40/21.41 (P1(f789(f789(f240(a1),x105111),x105111))),
% 21.40/21.41 inference(rename_variables,[],[3232])).
% 21.40/21.41 cnf(10516,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x105161),f789(f789(f90(a863),x105161),x105161)))),
% 21.40/21.41 inference(rename_variables,[],[3504])).
% 21.40/21.41 cnf(10519,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x105191),f789(f789(f90(a863),x105191),x105191)))),
% 21.40/21.41 inference(rename_variables,[],[3504])).
% 21.40/21.41 cnf(10522,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x105221),f789(f789(f89(a863),x105222),x105221)))),
% 21.40/21.41 inference(rename_variables,[],[3502])).
% 21.40/21.41 cnf(10525,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x105251),f789(f789(f89(a863),x105252),x105251)))),
% 21.40/21.41 inference(rename_variables,[],[3502])).
% 21.40/21.41 cnf(10528,plain,
% 21.40/21.41 (P1(f789(f789(f241(a863),x105281),f789(a121,f789(f789(f89(a863),x105282),x105281))))),
% 21.40/21.41 inference(rename_variables,[],[3680])).
% 21.40/21.41 cnf(10533,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x105331,a856)),f789(f311(x105332,x105331,x105333),f789(f313(x105332,x105331,x105333),x105334))),x105334))),
% 21.40/21.41 inference(rename_variables,[],[4110])).
% 21.40/21.41 cnf(10536,plain,
% 21.40/21.41 (P1(f789(f789(f287(a863),x105361),x105361))),
% 21.40/21.41 inference(rename_variables,[],[3233])).
% 21.40/21.41 cnf(10541,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),x105411),x105411))),
% 21.40/21.41 inference(rename_variables,[],[4493])).
% 21.40/21.41 cnf(10548,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),x105481),x105481))),
% 21.40/21.41 inference(rename_variables,[],[4493])).
% 21.40/21.41 cnf(10555,plain,
% 21.40/21.41 (P1(f789(f789(f240(a1),x105551),x105551))),
% 21.40/21.41 inference(rename_variables,[],[3232])).
% 21.40/21.41 cnf(10572,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x105721),f789(f789(f90(a863),x105721),x105721)))),
% 21.40/21.41 inference(rename_variables,[],[3504])).
% 21.40/21.41 cnf(10575,plain,
% 21.40/21.41 (~P1(f789(f789(f240(a863),f789(a121,x105751)),x105751))),
% 21.40/21.41 inference(rename_variables,[],[4507])).
% 21.40/21.41 cnf(10580,plain,
% 21.40/21.41 (~P1(f789(f789(f240(a863),f789(a121,x105801)),x105801))),
% 21.40/21.41 inference(rename_variables,[],[4507])).
% 21.40/21.41 cnf(10585,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),f789(f789(f89(a863),x105851),x105852)),x105852))),
% 21.40/21.41 inference(rename_variables,[],[4522])).
% 21.40/21.41 cnf(10588,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),f789(f789(f89(a863),x105881),x105882)),x105881))),
% 21.40/21.41 inference(rename_variables,[],[4523])).
% 21.40/21.41 cnf(10591,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),f789(f789(f89(a863),x105911),x105912)),x105912))),
% 21.40/21.41 inference(rename_variables,[],[4522])).
% 21.40/21.41 cnf(10597,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x105971),x105971))),
% 21.40/21.41 inference(rename_variables,[],[3231])).
% 21.40/21.41 cnf(10600,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x106001),f789(f789(f90(a863),x106001),x106001)))),
% 21.40/21.41 inference(rename_variables,[],[3504])).
% 21.40/21.41 cnf(10609,plain,
% 21.40/21.41 (P1(f789(f789(f241(a863),x106091),f789(a121,x106091)))),
% 21.40/21.41 inference(rename_variables,[],[3300])).
% 21.40/21.41 cnf(10730,plain,
% 21.40/21.41 (~E(f789(a121,x107301),x107301)),
% 21.40/21.41 inference(rename_variables,[],[4409])).
% 21.40/21.41 cnf(10743,plain,
% 21.40/21.41 (P1(f789(f789(f342(x107431),x107432),f247(f870(x107431,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(10746,plain,
% 21.40/21.41 (P1(f789(f789(f342(x107461),x107462),f789(f789(f310(x107461),x107462),x107463)))),
% 21.40/21.41 inference(rename_variables,[],[3548])).
% 21.40/21.41 cnf(10749,plain,
% 21.40/21.41 (P1(f789(f789(f342(x107491),x107492),f247(f870(x107491,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(10752,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x107521),x107522),f184(f870(x107521,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(10760,plain,
% 21.40/21.41 (~E(f789(a121,x107601),x107601)),
% 21.40/21.41 inference(rename_variables,[],[4409])).
% 21.40/21.41 cnf(10767,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x107671),x107672),f184(f870(x107671,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(10813,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),x108131),f2(a863)))),
% 21.40/21.41 inference(rename_variables,[],[4496])).
% 21.40/21.41 cnf(10816,plain,
% 21.40/21.41 (~P1(f789(f789(f184(f870(x108161,f870(x108162,a856))),x108163),x108164))),
% 21.40/21.41 inference(rename_variables,[],[4525])).
% 21.40/21.41 cnf(10840,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x108401),x108401))),
% 21.40/21.41 inference(rename_variables,[],[3231])).
% 21.40/21.41 cnf(10843,plain,
% 21.40/21.41 (P1(f789(f789(f241(a863),x108431),f789(a121,x108431)))),
% 21.40/21.41 inference(rename_variables,[],[3300])).
% 21.40/21.41 cnf(10848,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),x108481),x108481))),
% 21.40/21.41 inference(rename_variables,[],[4493])).
% 21.40/21.41 cnf(10851,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x108511),x108511))),
% 21.40/21.41 inference(rename_variables,[],[3231])).
% 21.40/21.41 cnf(10858,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x108581),x108581))),
% 21.40/21.41 inference(rename_variables,[],[3231])).
% 21.40/21.41 cnf(10879,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x108791),x108791))),
% 21.40/21.41 inference(rename_variables,[],[3231])).
% 21.40/21.41 cnf(10890,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),x108901),f2(a863)))),
% 21.40/21.41 inference(rename_variables,[],[4496])).
% 21.40/21.41 cnf(10893,plain,
% 21.40/21.41 (~E(f789(a121,x108931),x108931)),
% 21.40/21.41 inference(rename_variables,[],[4409])).
% 21.40/21.41 cnf(10900,plain,
% 21.40/21.41 (~P1(f789(f789(f184(f870(x109001,f870(x109002,a856))),x109003),x109004))),
% 21.40/21.41 inference(rename_variables,[],[4525])).
% 21.40/21.41 cnf(10917,plain,
% 21.40/21.41 (E(f789(f789(f132(x109171),f122(x109171)),x109172),x109172)),
% 21.40/21.41 inference(rename_variables,[],[3187])).
% 21.40/21.41 cnf(10931,plain,
% 21.40/21.41 (E(f39(x109311,x109312,x109313,x109314,x109315,x109316,x109317,x109318,x109319,a25),x109312)),
% 21.40/21.41 inference(rename_variables,[],[4381])).
% 21.40/21.41 cnf(10934,plain,
% 21.40/21.41 (E(f39(x109341,x109342,x109343,x109344,x109345,x109346,x109347,x109348,x109349,a25),x109342)),
% 21.40/21.41 inference(rename_variables,[],[4381])).
% 21.40/21.41 cnf(10937,plain,
% 21.40/21.41 (~E(f789(a121,x109371),x109371)),
% 21.40/21.41 inference(rename_variables,[],[4409])).
% 21.40/21.41 cnf(10940,plain,
% 21.40/21.41 (~E(f789(a121,x109401),x109401)),
% 21.40/21.41 inference(rename_variables,[],[4409])).
% 21.40/21.41 cnf(10962,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x109621),x109622),f184(f870(x109621,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(10969,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x109691,a856)),f184(f870(x109691,a856))),x109692))),
% 21.40/21.41 inference(rename_variables,[],[3679])).
% 21.40/21.41 cnf(10974,plain,
% 21.40/21.41 (~E(f789(a121,x109741),x109741)),
% 21.40/21.41 inference(rename_variables,[],[4409])).
% 21.40/21.41 cnf(10977,plain,
% 21.40/21.41 (P1(f789(f789(f241(a863),x109771),f789(a121,x109771)))),
% 21.40/21.41 inference(rename_variables,[],[3300])).
% 21.40/21.41 cnf(10982,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x109821,a856)),x109822),f789(f789(f310(x109821),x109823),x109822)))),
% 21.40/21.41 inference(rename_variables,[],[3675])).
% 21.40/21.41 cnf(10987,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x109871,a856)),x109872),f789(f789(f310(x109871),x109873),x109872)))),
% 21.40/21.41 inference(rename_variables,[],[3675])).
% 21.40/21.41 cnf(10993,plain,
% 21.40/21.41 (P1(f789(f789(f342(x109931),x109932),f247(f870(x109931,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11002,plain,
% 21.40/21.41 (P1(f789(f789(f342(x110021),x110022),f247(f870(x110021,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11009,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),x110091),x110091))),
% 21.40/21.41 inference(rename_variables,[],[4493])).
% 21.40/21.41 cnf(11024,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x110241),x110241))),
% 21.40/21.41 inference(rename_variables,[],[3231])).
% 21.40/21.41 cnf(11030,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x110301),x110301))),
% 21.40/21.41 inference(rename_variables,[],[3231])).
% 21.40/21.41 cnf(11056,plain,
% 21.40/21.41 (~E(f789(a121,x110561),x110561)),
% 21.40/21.41 inference(rename_variables,[],[4409])).
% 21.40/21.41 cnf(11061,plain,
% 21.40/21.41 (E(f789(f49(a863),f789(f265(a863),x110611)),x110611)),
% 21.40/21.41 inference(rename_variables,[],[3132])).
% 21.40/21.41 cnf(11068,plain,
% 21.40/21.41 (~P1(f789(f789(f342(f869(f864(x110681),f864(x110681))),f789(f789(f249(f864(x110681),f864(x110681)),x110682),f122(x110681))),f143(x110681,x110683)))),
% 21.40/21.41 inference(rename_variables,[],[4527])).
% 21.40/21.41 cnf(11075,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x110751,a856)),f184(f870(x110751,a856))),x110752))),
% 21.40/21.41 inference(rename_variables,[],[3679])).
% 21.40/21.41 cnf(11081,plain,
% 21.40/21.41 (~E(f789(f321(x110811,x110812),x110813),f789(f312(x110812,x110811),x110814))),
% 21.40/21.41 inference(rename_variables,[],[4480])).
% 21.40/21.41 cnf(11093,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x110931,a856)),x110932),x110932))),
% 21.40/21.41 inference(rename_variables,[],[3534])).
% 21.40/21.41 cnf(11099,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x110991),x110992),f184(f870(x110991,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11123,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x111231),x111232),f184(f870(x111231,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11129,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x111291),x111292),f184(f870(x111291,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11134,plain,
% 21.40/21.41 (~P1(f789(f71(x111341,x111342,f184(f870(x111341,a856))),x111343))),
% 21.40/21.41 inference(rename_variables,[],[4521])).
% 21.40/21.41 cnf(11139,plain,
% 21.40/21.41 (~E(f789(a121,x111391),x111391)),
% 21.40/21.41 inference(rename_variables,[],[4409])).
% 21.40/21.41 cnf(11147,plain,
% 21.40/21.41 (P1(f789(f789(f342(x111471),x111472),f247(f870(x111471,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11154,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x111541),x111542),f184(f870(x111541,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11157,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x111571,a856)),x111572),f247(f870(x111571,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3612])).
% 21.40/21.41 cnf(11160,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x111601,a856)),x111602),f247(f870(x111601,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3612])).
% 21.40/21.41 cnf(11167,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x111671),x111671))),
% 21.40/21.41 inference(rename_variables,[],[3231])).
% 21.40/21.41 cnf(11176,plain,
% 21.40/21.41 (P1(f789(f789(f342(x111761),x111762),f247(f870(x111761,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11179,plain,
% 21.40/21.41 (P1(f789(f789(f342(x111791),x111792),f247(f870(x111791,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11202,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),x112021),x112021))),
% 21.40/21.41 inference(rename_variables,[],[4493])).
% 21.40/21.41 cnf(11208,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x112081,a856)),x112082),x112082))),
% 21.40/21.41 inference(rename_variables,[],[3534])).
% 21.40/21.41 cnf(11211,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x112111),x112112),f184(f870(x112111,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11217,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x112171,a856)),x112172),f247(f870(x112171,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3612])).
% 21.40/21.41 cnf(11220,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x112201,a856)),x112202),f247(f870(x112201,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3612])).
% 21.40/21.41 cnf(11223,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x112231),x112232),f184(f870(x112231,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11228,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x112281,a856)),x112282),f247(f870(x112281,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3612])).
% 21.40/21.41 cnf(11233,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x112331),x112332),f184(f870(x112331,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11236,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x112361),x112362),f184(f870(x112361,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11241,plain,
% 21.40/21.41 (P1(f789(f789(f240(a863),x112411),x112411))),
% 21.40/21.41 inference(rename_variables,[],[3231])).
% 21.40/21.41 cnf(11251,plain,
% 21.40/21.41 (P1(f789(f789(f342(x112511),x112512),f247(f870(x112511,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11256,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x112561),x112562),f184(f870(x112561,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11263,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x112631),x112632),f184(f870(x112631,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11268,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x112681,a856)),x112682),f247(f870(x112681,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3612])).
% 21.40/21.41 cnf(11271,plain,
% 21.40/21.41 (P1(f789(f789(f342(x112711),x112712),f247(f870(x112711,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11274,plain,
% 21.40/21.41 (P1(f789(f789(f342(x112741),x112742),f789(f789(f310(x112741),x112742),x112743)))),
% 21.40/21.41 inference(rename_variables,[],[3548])).
% 21.40/21.41 cnf(11277,plain,
% 21.40/21.41 (P1(f789(f789(f342(x112771),x112772),f247(f870(x112771,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11280,plain,
% 21.40/21.41 (P1(f789(f789(f342(x112801),x112802),f789(f789(f310(x112801),x112802),x112803)))),
% 21.40/21.41 inference(rename_variables,[],[3548])).
% 21.40/21.41 cnf(11283,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x112831,a856)),x112832),f247(f870(x112831,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3612])).
% 21.40/21.41 cnf(11307,plain,
% 21.40/21.41 (~P1(f789(f789(f241(a863),x113071),x113071))),
% 21.40/21.41 inference(rename_variables,[],[4493])).
% 21.40/21.41 cnf(11313,plain,
% 21.40/21.41 (E(f39(x113131,x113132,x113133,x113134,x113135,x113136,x113137,x113138,x113139,a25),x113132)),
% 21.40/21.41 inference(rename_variables,[],[4381])).
% 21.40/21.41 cnf(11321,plain,
% 21.40/21.41 (~P1(f789(f789(f184(f870(x113211,f870(x113212,a856))),x113213),x113214))),
% 21.40/21.41 inference(rename_variables,[],[4525])).
% 21.40/21.41 cnf(11330,plain,
% 21.40/21.41 (P1(f789(f789(f342(x113301),x113302),f247(f870(x113301,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11333,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x113331),x113332),f184(f870(x113331,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11345,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x113451),x113452),f184(f870(x113451,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11350,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x113501,a856)),x113502),x113502))),
% 21.40/21.41 inference(rename_variables,[],[3534])).
% 21.40/21.41 cnf(11355,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x113551),x113552),f184(f870(x113551,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11358,plain,
% 21.40/21.41 (~P1(f789(f789(f342(f869(f864(x113581),f864(x113581))),f789(f789(f249(f864(x113581),f864(x113581)),x113582),f122(x113581))),f141(x113581,x113583)))),
% 21.40/21.41 inference(rename_variables,[],[4526])).
% 21.40/21.41 cnf(11364,plain,
% 21.40/21.41 (P1(f789(f789(f342(x113641),x113642),f247(f870(x113641,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11370,plain,
% 21.40/21.41 (P1(f789(f789(f342(x113701),x113702),f247(f870(x113701,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11375,plain,
% 21.40/21.41 (P1(f789(f789(f342(x113751),x113752),f247(f870(x113751,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11378,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x113781),x113782),f184(f870(x113781,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11381,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x113811,a856)),x113812),x113812))),
% 21.40/21.41 inference(rename_variables,[],[3534])).
% 21.40/21.41 cnf(11384,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x113841),x113842),f184(f870(x113841,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11390,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x113901),x113902),f184(f870(x113901,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11393,plain,
% 21.40/21.41 (~P1(f789(f789(f342(f869(f864(x113931),f864(x113931))),f789(f789(f249(f864(x113931),f864(x113931)),x113932),f122(x113931))),f141(x113931,x113933)))),
% 21.40/21.41 inference(rename_variables,[],[4526])).
% 21.40/21.41 cnf(11396,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x113961),x113962),f184(f870(x113961,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11399,plain,
% 21.40/21.41 (~P1(f789(f789(f342(f869(f864(x113991),f864(x113991))),f789(f789(f249(f864(x113991),f864(x113991)),f122(x113991)),x113992)),f141(x113991,x113993)))),
% 21.40/21.41 inference(rename_variables,[],[4529])).
% 21.40/21.41 cnf(11402,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x114021,a856)),x114022),x114022))),
% 21.40/21.41 inference(rename_variables,[],[3534])).
% 21.40/21.41 cnf(11405,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x114051,a856)),x114052),x114052))),
% 21.40/21.41 inference(rename_variables,[],[3534])).
% 21.40/21.41 cnf(11408,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x114081),x114082),f184(f870(x114081,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11413,plain,
% 21.40/21.41 (P1(f789(f789(f342(x114131),x114132),f247(f870(x114131,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11416,plain,
% 21.40/21.41 (P1(f789(f789(f342(x114161),x114162),f789(f789(f310(x114161),x114162),x114163)))),
% 21.40/21.41 inference(rename_variables,[],[3548])).
% 21.40/21.41 cnf(11421,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x114211),x114212),f184(f870(x114211,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11430,plain,
% 21.40/21.41 (P1(f789(f789(f342(x114301),x114302),f247(f870(x114301,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11433,plain,
% 21.40/21.41 (P1(f789(f789(f342(x114331),x114332),f247(f870(x114331,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11436,plain,
% 21.40/21.41 (P1(f789(f789(f342(x114361),x114362),f247(f870(x114361,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3388])).
% 21.40/21.41 cnf(11441,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x114411),x114412),f184(f870(x114411,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11447,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x114471),x114472),f184(f870(x114471,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11455,plain,
% 21.40/21.41 (~E(f789(f321(x114551,x114552),x114553),f789(f312(x114552,x114551),x114554))),
% 21.40/21.41 inference(rename_variables,[],[4480])).
% 21.40/21.41 cnf(11466,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x114661),x114662),f184(f870(x114661,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11469,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x114691),x114692),f184(f870(x114691,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11472,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x114721),x114722),f184(f870(x114721,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11475,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x114751),x114752),f184(f870(x114751,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11478,plain,
% 21.40/21.41 (P1(f789(f789(f342(f869(f864(x114781),f864(x114781))),f789(f789(f249(f864(x114781),f864(x114781)),x114782),x114782)),f154(x114781,f308(x114781,x114783))))),
% 21.40/21.41 inference(rename_variables,[],[4001])).
% 21.40/21.41 cnf(11481,plain,
% 21.40/21.41 (P1(f789(f789(f342(f869(f864(x114811),f864(x114811))),f789(f789(f249(f864(x114811),f864(x114811)),x114812),x114812)),f154(x114811,f308(x114811,x114813))))),
% 21.40/21.41 inference(rename_variables,[],[4001])).
% 21.40/21.41 cnf(11484,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x114841,a856)),x114842),x114842))),
% 21.40/21.41 inference(rename_variables,[],[3534])).
% 21.40/21.41 cnf(11489,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x114891),x114892),f184(f870(x114891,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11508,plain,
% 21.40/21.41 (~P1(f789(f789(f342(x115081),x115082),f184(f870(x115081,a856))))),
% 21.40/21.41 inference(rename_variables,[],[4509])).
% 21.40/21.41 cnf(11514,plain,
% 21.40/21.41 (P1(f789(f789(f240(f870(x115141,a856)),x115142),f247(f870(x115141,a856))))),
% 21.40/21.41 inference(rename_variables,[],[3612])).
% 21.40/21.41 cnf(11540,plain,
% 21.40/21.41 ($false),
% 21.40/21.41 inference(scs_inference,[],[3048,3440,3439,4406,2986,2994,3026,2851,3035,4438,4439,3547,3512,3428,4486,4487,4489,3209,3210,3212,4488,4490,3211,3078,3234,4495,4506,4505,3119,3261,3259,3260,3745,3326,4235,4381,10121,10297,10312,10450,10453,10931,10934,11313,4382,10300,4409,10111,10118,10149,10404,10456,10730,10760,10893,10937,10940,10974,11056,11139,4407,10158,10386,4417,3075,3690,3290,4443,10095,10102,10407,3337,3151,3441,3229,10218,10348,10366,10435,3231,10163,10597,10840,10851,10858,10879,11024,11030,11167,11241,3232,10511,10555,3233,10508,10536,4493,10133,10233,10379,10395,10440,10541,10548,10848,11009,11202,11307,3294,4480,10144,11081,11455,3100,3168,3187,10917,3144,3132,11061,3300,10185,10209,10248,10251,10329,10351,10358,10361,10609,10843,10977,4496,10813,10890,3253,10505,3687,10124,4507,10283,10488,10491,10575,10580,4521,10459,10464,11134,3534,10324,11093,11208,11350,11381,11402,11405,11484,4508,10496,3314,3559,3388,10146,10180,10743,10749,10993,11002,11147,11176,11179,11251,11271,11277,11330,11364,11370,11375,11413,11430,11433,11436,4509,10309,10752,10767,10962,11099,11123,11129,11154,11211,11223,11233,11236,11256,11263,11333,11345,11355,11378,11384,11390,11396,11408,11421,11441,11447,11466,11469,11472,11475,11489,11508,3390,4525,10816,10900,11321,3429,4514,3612,11157,11160,11217,11220,11228,11268,11283,11514,4519,10483,3759,3548,10746,11274,11280,11416,3679,10969,11075,4511,3504,10516,10519,10572,10600,3502,10522,10525,3503,4522,10127,10130,10278,10585,10591,4523,10588,3682,3675,10982,10987,3680,10528,3681,3335,3864,3835,4110,10533,3540,3818,3959,4524,4091,10152,4518,3531,3751,4526,11358,11393,4527,11068,4528,4529,11399,4001,11478,11481,4052,4214,2,6040,9522,6214,5189,4992,4945,4903,4902,4737,4640,4639,4548,4542,5149,5138,5061,4998,4537,5026,4942,9,8,9764,9523,9157,9156,8581,7675,7055,6658,6373,6353,6207,6206,6199,6182,6056,5969,5840,5817,5750,5739,5738,5683,5668,5667,5663,5661,5609,5603,5602,5597,5584,5566,5555,5551,5534,5533,5524,5438,5344,5337,5328,5327,5284,5270,5263,5255,5254,5247,5181,5157,5123,5117,5116,5115,5114,5113,5112,5072,5064,5051,5050,4988,4971,4965,4731,4665,4612,4610,4609,4603,4602,9707,8668,8502,8501,8491,7475,7213,6914,6700,6514,6513,6512,6511,6399,6374,6306,6305,6208,6188,6176,6103,6062,6055,6054,6048,6027,6024,6023,5940,5939,5867,5824,5803,5759,5754,5747,5746,5718,5712,5687,5684,5619,5536,5535,5520,5507,5496,5485,5463,5416,5370,5341,5340,5339,5313,5274,5264,5174,5147,5136,5134,5042,5004,5003,4879,4841,4721,4842,9835,9792,9791,9790,9789,9777,9444,9018,8985,8813,8780,8735,8690,8650,8646,8350,7841,7653,7409,7390,7329,7311,7310,7309,7308,7307,7267,6861,6858,6750,6737,6649,6648,6628,6579,6578,6568,6298,6297,6295,6294,6293,6292,6253,6246,6161,6160,6159,6158,6157,6156,6155,6154,6034,6033,6032,6031,6030,6010,6008,6007,6006,6005,6004,5966,5858,5857,5856,5850,5780,5753,5719,5674,5673,5672,5671,5670,5669,5622,5577,5497,5494,5493,5492,5491,5490,5489,5466,5465,5462,5412,5403,5336,5306,5305,5295,5289,5288,5287,5258,5239,5222,5184,5161,5160,5158,5125,5066,4928,4927,4926,4702,4701,4700,4666,4659,4658,4559,8531,8530,8529,8528,8422,8421,8420,7806,7713,7603,7400,7282,6939,6844,6753,6752,6593,6289,5991,5988,5987,5745,5744,5698,5697,5658,5657,5656,5614,5506,5444,5388,5387,5376,5262,9861,9855,9457,9456,9455,9454,8603,8511,8510,8509,8508,8434,7705,7704,7623,7470,7337,6997,6862,6838,6767,6766,6723,6722,6721,6720,6719,6718,6717,6699,6670,6669,6668,6667,6633,6560,6492,6491,6469,6454,6453,6452,6191,6060,6059,5885,5611,5610,5386,5326,5325,5279,5276,5275,5246,5245,4993,9022,9021,9020,9019,8844,8843,8822,8821,8816,8704,8703,8512,8503,8496,8409,8374,8220,8158,8023,7995,7752,7629,7610,7609,7474,7335,7334,7201,7143,7142,6974,6973,6823,6822,6711,6710,6414,6403,6344,6184,6171,6121,6112,6104,5888,5828,5677,5676,5541,5480,5232,5137,8848,8552,8495,8494,8483,8482,8440,8439,8369,8177,8111,7963,7936,7931,7930,7816,7754,7721,7522,7521,7467,7297,6836,6807,6764,6693,6692,6415,5666,5362,5242,5241,9135,8855,8839,8742,8444,8388,8344,8313,8242,8008,7945,7944,7943,7762,7422,6899,6898,6837,6714,6713,6656,6655,6423,6422,9323,9126,9125,9025,8991,8864,8769,8768,8726,8633,8602,8532,7899,7750,7540,7024,6907,6173,5917,9351,9350,9137,9136,8746,8745,8693,8689,8570,8569,8568,8567,8554,8370,8347,8346,8342,7689,7406,7405,7280,7140,7139,7112,6941,6288,5925,9603,9063,8845,8842,8826,8692,8540,8467,8201,6435,9628,9561,9560,9182,9066,8958,8957,8956,8576,8521,9935,9458,9184,9171,9146,9634,9518,9516,9515,9322,9321,9425,9391,8972,8971,8927,8926,8753,9809,9808,9668,9552,9358,9357,9196,9640,9562,9385,9202,9158,9797,9796,9282,9223,9834,9829,9746,9664,9616,9587,9368,9799,9613,9473,9404,9403,9739,9615,9478,9402,10014,10013,9954,9953,10067,10080,9970,9934,10020,9989,2840,2839,2837,2829,2825,2822,2821,2816]),
% 21.40/21.41 ['proof']).
% 21.40/21.41 % SZS output end Proof
% 21.40/21.41 % Total time :17.650000s
%------------------------------------------------------------------------------